diff --git a/.gitignore b/.gitignore index 73394cb6..98224199 100644 --- a/.gitignore +++ b/.gitignore @@ -1,5 +1,6 @@ bin/ +debug/ depend/ include/ lib/ diff --git a/COPYRIGHT b/COPYRIGHT index ba203874..dcbb70bf 100644 --- a/COPYRIGHT +++ b/COPYRIGHT @@ -6,7 +6,12 @@ Please contact the author at gilbert@gilbertbernstein.com if you would like to discuss licensing under other terms. -Triangle (used by Franky) is Copyright Jonathan Shewchuk according to the terms spelled out in the comments of triangle.c +The CDT constrained Delaunay triangulation library (src/isct/cdt) is +Copyright Artem Amirkhanov and is licensed under the Mozilla Public +License 2.0, see src/isct/cdt/LICENSE_CDT_MPL2.txt. Its bundled robust +geometric predicates (src/isct/cdt/predicates.h) are Copyright +William C. Lenthe under the BSD 3-Clause license, see the comments of +that file. GNU LESSER GENERAL PUBLIC LICENSE diff --git a/Makefile b/Makefile index a9fbb62c..4224fed8 100644 --- a/Makefile +++ b/Makefile @@ -35,8 +35,8 @@ PLATFORM := $(shell uname) # | Programs | # +----------+ CPP11_FLAGS := -std=c++11 -CC := clang -CXX := clang++ +CC := gcc +CXX := g++ ifeq ($(PLATFORM),Darwin) # on mac CPP11_FLAGS := $(CPP11_FLAGS) -stdlib=libc++ -Wno-c++11-extensions endif @@ -79,6 +79,12 @@ ifeq ($(PLATFORM),Darwin) LINKD := $(LINK) -Wl,-no_pie endif +ARCH = $(shell uname -m) + +ifeq ($(findstring x86_64,$(ARCH)), x86_64) + CCFLAGS += -m64 + CXXFLAGS+= -m64 +endif # *********************** # * SOURCE DECLARATIONS * @@ -112,8 +118,7 @@ UTIL_HEADERS := prelude.h memPool.h iterPool.h shortVec.h \ ISCT_HEADERS := unsafeRayTriIsct.h \ ext4.h fixext4.h gmpext4.h absext4.h \ quantization.h fixint.h \ - empty3d.h \ - triangle.h + empty3d.h RAWMESH_HEADERS := rawMesh.h rawMesh.tpp MESH_HEADERS := mesh.h mesh.decl.h \ mesh.tpp mesh.topoCache.tpp \ @@ -150,15 +155,11 @@ DEPENDS := $(addprefix depend/,$(addsuffix .d,$(ALL_SRCS))) # | Object Aggregation for Targets | # +--------------------------------+ -OBJ := $(addprefix obj/,$(addsuffix .o,$(SRCS))) \ - obj/isct/triangle.o -DEBUG := $(addprefix debug/,$(addsuffix .o,$(SRCS))) \ - obj/isct/triangle.o +OBJ := $(addprefix obj/,$(addsuffix .o,$(SRCS))) +DEBUG := $(addprefix debug/,$(addsuffix .o,$(SRCS))) -MAIN_OBJ := $(addprefix obj/,$(addsuffix .o,$(MAIN_SRC))) \ - obj/isct/triangle.o -MAIN_DEBUG := $(addprefix debug/,$(addsuffix .o,$(MAIN_SRC))) \ - obj/isct/triangle.o +MAIN_OBJ := $(addprefix obj/,$(addsuffix .o,$(MAIN_SRC))) +MAIN_DEBUG := $(addprefix debug/,$(addsuffix .o,$(MAIN_SRC))) LIB_TARGET_NAME := cork @@ -181,24 +182,12 @@ lib/lib$(LIB_TARGET_NAME)debug.a: $(DEBUG) bin/cork: $(MAIN_OBJ) @echo "Linking cork command line tool" - @$(CXX) -o bin/cork $(MAIN_OBJ) $(LINK) + $(CXX) -o bin/cork $(MAIN_OBJ) $(LINK) bin/off2obj: obj/off2obj.o @echo "Linking off2obj" @$(CXX) -o bin/off2obj obj/off2obj.o $(LINK) -# +------------------------------+ -# | Specialized File Build Rules | -# +------------------------------+ - -obj/isct/triangle.o: src/isct/triangle.c - @echo "Compiling the Triangle library" - @$(CC) -O2 -DNO_TIMER \ - -DREDUCED \ - -DCDT_ONLY -DTRILIBRARY \ - -Wall -DANSI_DECLARATORS \ - -o obj/isct/triangle.o -c src/isct/triangle.c - # +------------------------------------+ # | Generic Source->Object Build Rules | # +------------------------------------+ diff --git a/README.md b/README.md index f9098395..32bd3b54 100644 --- a/README.md +++ b/README.md @@ -63,4 +63,16 @@ Cork is licensed under the LGPL with an exception (from QT) to more easily allow Of course, none of the above supercedes the actual COPYRIGHT. +Third-Party Code +================ + +Cork bundles the [CDT](https://github.com/artem-ogre/CDT) constrained +Delaunay triangulation library (`src/isct/cdt`), Copyright Artem +Amirkhanov, licensed under the Mozilla Public License 2.0 (see +`src/isct/cdt/LICENSE_CDT_MPL2.txt`). CDT's bundled robust geometric +predicates (`src/isct/cdt/predicates.h`) are Copyright William C. +Lenthe, licensed under the BSD 3-Clause license. CDT replaces the +Triangle library used by earlier versions of Cork, whose license did +not permit free redistribution. + diff --git a/src/cork.cpp b/src/cork.cpp index 75302b32..2438e750 100644 --- a/src/cork.cpp +++ b/src/cork.cpp @@ -206,6 +206,9 @@ void computeUnion( cmIn0.boolUnion(cmIn1); + if(out->remesh) + cmIn0.remesh(); + corkMesh2CorkTriMesh(&cmIn0, out); } @@ -218,6 +221,9 @@ void computeDifference( cmIn0.boolDiff(cmIn1); + if(out->remesh) + cmIn0.remesh(); + corkMesh2CorkTriMesh(&cmIn0, out); } @@ -230,6 +236,9 @@ void computeIntersection( cmIn0.boolIsct(cmIn1); + if(out->remesh) + cmIn0.remesh(); + corkMesh2CorkTriMesh(&cmIn0, out); } @@ -242,6 +251,9 @@ void computeSymmetricDifference( cmIn0.boolXor(cmIn1); + if(out->remesh) + cmIn0.remesh(); + corkMesh2CorkTriMesh(&cmIn0, out); } @@ -255,6 +267,50 @@ void resolveIntersections( cmIn0.disjointUnion(cmIn1); cmIn0.resolveIntersections(); + if(out->remesh){ + cmIn0.remesh(); + } + corkMesh2CorkTriMesh(&cmIn0, out); +} + +void computeFirst( + CorkTriMesh in0, CorkTriMesh in1, CorkTriMesh *out +) { + CorkMesh cmIn0, cmIn1; + corkTriMesh2CorkMesh(in0, &cmIn0); + corkTriMesh2CorkMesh(in1, &cmIn1); + + cmIn0.boolFirst(cmIn1); + + if(out->remesh) + cmIn0.remesh(); + corkMesh2CorkTriMesh(&cmIn0, out); } +void computeSecond( + CorkTriMesh in0, CorkTriMesh in1, CorkTriMesh *out +) { + CorkMesh cmIn0, cmIn1; + corkTriMesh2CorkMesh(in0, &cmIn0); + corkTriMesh2CorkMesh(in1, &cmIn1); + + cmIn1.boolFirst(cmIn0); + + if(out->remesh) + cmIn1.remesh(); + + corkMesh2CorkTriMesh(&cmIn1, out); +} + + +void remeshTriangles( + CorkTriMesh in, CorkTriMesh *out +) { + CorkMesh cmIn; + corkTriMesh2CorkMesh(in, &cmIn); + + cmIn.remesh(); + + corkMesh2CorkTriMesh(&cmIn, out); +} diff --git a/src/cork.h b/src/cork.h index 78bcb8a8..bbb6e65a 100644 --- a/src/cork.h +++ b/src/cork.h @@ -38,6 +38,7 @@ struct CorkTriMesh uint n_vertices; uint *triangles; float *vertices; + uint remesh; }; void freeCorkTriMesh(CorkTriMesh *mesh); @@ -72,3 +73,9 @@ void computeSymmetricDifference( // such that the two surfaces are now connected. void resolveIntersections(CorkTriMesh in0, CorkTriMesh in1, CorkTriMesh *out); +// result = A cut by B +void computeFirst(CorkTriMesh in0, CorkTriMesh in1, CorkTriMesh *out); +// result = B cut by A +void computeSecond(CorkTriMesh in0, CorkTriMesh in1, CorkTriMesh *out); +// result = remesh(A) +void remeshTriangles(CorkTriMesh in, CorkTriMesh *out); diff --git a/src/file_formats/off.cpp b/src/file_formats/off.cpp index 3b125716..f5e032d6 100644 --- a/src/file_formats/off.cpp +++ b/src/file_formats/off.cpp @@ -93,6 +93,7 @@ int writeOFF(string filename, FileMesh *data) int numfaces = data->triangles.size(); out << numvertices << ' ' << numfaces << ' ' << 0 << endl; + out.precision(18); // vertex data for(const auto &v : data->vertices) { const Vec3d &p = v.pos; diff --git a/src/isct/cdt/CDT.h b/src/isct/cdt/CDT.h new file mode 100644 index 00000000..bccb4711 --- /dev/null +++ b/src/isct/cdt/CDT.h @@ -0,0 +1,448 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at https://mozilla.org/MPL/2.0/. */ + +/** + * @file + * Public API + */ + +#ifndef CDT_lNrmUayWQaIR5fxnsg9B +#define CDT_lNrmUayWQaIR5fxnsg9B + +#include "CDTUtils.h" +#include "Triangulation.h" + +#include "remove_at.hpp" + +#include +#include +#include +#include +#include +#include +#include + +/// Namespace containing triangulation functionality +namespace CDT +{ + +/** @defgroup API Public API + * Contains API for constrained and conforming Delaunay triangulations + */ +/// @{ + +/** + * Type used for storing layer depths for triangles + * @note LayerDepth should support 60K+ layers, which could be to much or + * too little for some use cases. Feel free to re-define this typedef. + */ +typedef unsigned short LayerDepth; +typedef LayerDepth BoundaryOverlapCount; + +/// Triangles by vertex index +typedef std::vector VerticesTriangles; + +/** @defgroup helpers Helpers + * Helpers for working with CDT::Triangulation. + */ +/// @{ + +/** + * Calculate triangles adjacent to vertices (triangles by vertex index) + * @param triangles triangulation + * @param verticesSize total number of vertices to pre-allocate the output + * @return triangles by vertex index + */ +CDT_EXPORT VerticesTriangles +calculateTrianglesByVertex(const TriangleVec& triangles, VertInd verticesSize); + +/** + * Information about removed duplicated vertices. + * + * Contains mapping information and removed duplicates indices. + * @note vertices {0,1,2,3,4} where 0 and 3 are the same will produce mapping + * {0,1,2,0,3} (to new vertices {0,1,2,3}) and duplicates {3} + */ +struct CDT_EXPORT DuplicatesInfo +{ + std::vector mapping; ///< vertex index mapping + std::vector duplicates; ///< duplicates' indices +}; + +/** + * Find duplicates in given custom point-type range + * @note duplicates are points with exactly same X and Y coordinates + * @tparam TVertexIter iterator that dereferences to custom point type + * @tparam TGetVertexCoordX function object getting x coordinate from vertex. + * Getter signature: const TVertexIter::value_type& -> T + * @tparam TGetVertexCoordY function object getting y coordinate from vertex. + * Getter signature: const TVertexIter::value_type& -> T + * @param first beginning of the range of vertices + * @param last end of the range of vertices + * @param getX getter of X-coordinate + * @param getY getter of Y-coordinate + * @returns information about vertex duplicates + */ +template < + typename T, + typename TVertexIter, + typename TGetVertexCoordX, + typename TGetVertexCoordY> +DuplicatesInfo FindDuplicates( + TVertexIter first, + TVertexIter last, + TGetVertexCoordX getX, + TGetVertexCoordY getY); + +/** + * Remove duplicates in-place from vector of custom points + * @tparam TVertex vertex type + * @tparam TAllocator allocator used by input vector of vertices + * @param vertices vertices to remove duplicates from + * @param duplicates information about duplicates + */ +template +void RemoveDuplicates( + std::vector& vertices, + const std::vector& duplicates); + +/** + * Remove duplicated points in-place + * + * @tparam T type of vertex coordinates (e.g., float, double) + * @param[in, out] vertices collection of vertices to remove duplicates from + * @returns information about duplicated vertices that were removed. + */ +template +CDT_EXPORT DuplicatesInfo RemoveDuplicates(std::vector >& vertices); + +/** + * Remap vertex indices in edges (in-place) using given vertex-index mapping. + * @tparam TEdgeIter iterator that dereferences to custom edge type + * @tparam TGetEdgeVertexStart function object getting start vertex index + * from an edge. + * Getter signature: const TEdgeIter::value_type& -> CDT::VertInd + * @tparam TGetEdgeVertexEnd function object getting end vertex index from + * an edge. Getter signature: const TEdgeIter::value_type& -> CDT::VertInd + * @tparam TMakeEdgeFromStartAndEnd function object that makes new edge from + * start and end vertices + * @param first beginning of the range of edges + * @param last end of the range of edges + * @param mapping vertex-index mapping + * @param getStart getter of edge start vertex index + * @param getEnd getter of edge end vertex index + * @param makeEdge factory for making edge from vetices + */ +template < + typename TEdgeIter, + typename TGetEdgeVertexStart, + typename TGetEdgeVertexEnd, + typename TMakeEdgeFromStartAndEnd> +void RemapEdges( + TEdgeIter first, + TEdgeIter last, + const std::vector& mapping, + TGetEdgeVertexStart getStart, + TGetEdgeVertexEnd getEnd, + TMakeEdgeFromStartAndEnd makeEdge); + +/** + * Remap vertex indices in edges (in-place) using given vertex-index mapping. + * + * @note Mapping can be a result of RemoveDuplicates function + * @param[in,out] edges collection of edges to remap + * @param mapping vertex-index mapping + */ +CDT_EXPORT void +RemapEdges(std::vector& edges, const std::vector& mapping); + +/** + * Find point duplicates, remove them from vector (in-place) and remap edges + * (in-place) + * @note Same as a chained call of CDT::FindDuplicates, CDT::RemoveDuplicates, + * and CDT::RemapEdges + * @tparam T type of vertex coordinates (e.g., float, double) + * @tparam TVertex type of vertex + * @tparam TGetVertexCoordX function object getting x coordinate from vertex. + * Getter signature: const TVertexIter::value_type& -> T + * @tparam TGetVertexCoordY function object getting y coordinate from vertex. + * Getter signature: const TVertexIter::value_type& -> T + * @tparam TEdgeIter iterator that dereferences to custom edge type + * @tparam TGetEdgeVertexStart function object getting start vertex index + * from an edge. + * Getter signature: const TEdgeIter::value_type& -> CDT::VertInd + * @tparam TGetEdgeVertexEnd function object getting end vertex index from + * an edge. Getter signature: const TEdgeIter::value_type& -> CDT::VertInd + * @tparam TMakeEdgeFromStartAndEnd function object that makes new edge from + * start and end vertices + * @param[in, out] vertices vertices to remove duplicates from + * @param[in, out] edges collection of edges connecting vertices + * @param getX getter of X-coordinate + * @param getY getter of Y-coordinate + * @param edgesFirst beginning of the range of edges + * @param edgesLast end of the range of edges + * @param getStart getter of edge start vertex index + * @param getEnd getter of edge end vertex index + * @param makeEdge factory for making edge from vetices + * @returns information about vertex duplicates + */ +template < + typename T, + typename TVertex, + typename TGetVertexCoordX, + typename TGetVertexCoordY, + typename TVertexAllocator, + typename TEdgeIter, + typename TGetEdgeVertexStart, + typename TGetEdgeVertexEnd, + typename TMakeEdgeFromStartAndEnd> +DuplicatesInfo RemoveDuplicatesAndRemapEdges( + std::vector& vertices, + TGetVertexCoordX getX, + TGetVertexCoordY getY, + TEdgeIter edgesFirst, + TEdgeIter edgesLast, + TGetEdgeVertexStart getStart, + TGetEdgeVertexEnd getEnd, + TMakeEdgeFromStartAndEnd makeEdge); + +/** + * Same as a chained call of CDT::RemoveDuplicates + CDT::RemapEdges + * + * @tparam T type of vertex coordinates (e.g., float, double) + * @param[in, out] vertices collection of vertices to remove duplicates from + * @param[in,out] edges collection of edges to remap + */ +template +CDT_EXPORT DuplicatesInfo RemoveDuplicatesAndRemapEdges( + std::vector >& vertices, + std::vector& edges); + +/** + * Extract all edges of triangles + * + * @param triangles triangles used to extract edges + * @return an unordered set of all edges of triangulation + */ +CDT_EXPORT EdgeUSet extractEdgesFromTriangles(const TriangleVec& triangles); + +/*! + * Converts piece->original_edges mapping to original_edge->pieces + * @param pieceToOriginals maps pieces to original edges + * @return mapping of original edges to pieces + */ +CDT_EXPORT unordered_map +EdgeToPiecesMapping(const unordered_map& pieceToOriginals); + +/*! + * Convert edge-to-pieces mapping into edge-to-split-vertices mapping + * @tparam T type of vertex coordinates (e.g., float, double) + * @param edgeToPieces edge-to-pieces mapping + * @param vertices vertex buffer + * @return mapping of edge-to-split-points. + * Split points are sorted from edge's start (v1) to end (v2) + */ +template +unordered_map > EdgeToSplitVertices( + const unordered_map& edgeToPieces, + const std::vector >& vertices); + +/// @} + +/// @} + +} // namespace CDT + +//***************************************************************************** +// Implementations of template functionlity +//***************************************************************************** +// hash for CDT::V2d +#ifdef CDT_CXX11_IS_SUPPORTED +namespace std +#else +namespace boost +#endif +{ +template +struct hash > +{ + size_t operator()(const CDT::V2d& xy) const + { +#ifdef CDT_CXX11_IS_SUPPORTED + typedef std::hash Hasher; +#else + typedef boost::hash Hasher; +#endif + return Hasher()(xy.x) ^ Hasher()(xy.y); + } +}; +} // namespace std + +namespace CDT +{ + +//----- +// API +//----- +template < + typename T, + typename TVertexIter, + typename TGetVertexCoordX, + typename TGetVertexCoordY> +DuplicatesInfo FindDuplicates( + TVertexIter first, + TVertexIter last, + TGetVertexCoordX getX, + TGetVertexCoordY getY) +{ + typedef unordered_map, std::size_t> PosToIndex; + PosToIndex uniqueVerts; + const std::size_t verticesSize = std::distance(first, last); + DuplicatesInfo di = { + std::vector(verticesSize), std::vector()}; + for(std::size_t iIn = 0, iOut = iIn; iIn < verticesSize; ++iIn, ++first) + { + typename PosToIndex::const_iterator it; + bool isUnique; + tie(it, isUnique) = uniqueVerts.insert( + std::make_pair(V2d(getX(*first), getY(*first)), iOut)); + if(isUnique) + { + di.mapping[iIn] = iOut++; + continue; + } + di.mapping[iIn] = it->second; // found a duplicate + di.duplicates.push_back(iIn); + } + return di; +} + +template +void RemoveDuplicates( + std::vector& vertices, + const std::vector& duplicates) +{ + vertices.erase( + remove_at( + vertices.begin(), + vertices.end(), + duplicates.begin(), + duplicates.end()), + vertices.end()); +} + +template < + typename TEdgeIter, + typename TGetEdgeVertexStart, + typename TGetEdgeVertexEnd, + typename TMakeEdgeFromStartAndEnd> +void RemapEdges( + TEdgeIter first, + const TEdgeIter last, + const std::vector& mapping, + TGetEdgeVertexStart getStart, + TGetEdgeVertexEnd getEnd, + TMakeEdgeFromStartAndEnd makeEdge) +{ + for(; first != last; ++first) + { + *first = makeEdge( + static_cast(mapping[getStart(*first)]), + static_cast(mapping[getEnd(*first)])); + } +} + +template < + typename T, + typename TVertex, + typename TGetVertexCoordX, + typename TGetVertexCoordY, + typename TVertexAllocator, + typename TEdgeIter, + typename TGetEdgeVertexStart, + typename TGetEdgeVertexEnd, + typename TMakeEdgeFromStartAndEnd> +DuplicatesInfo RemoveDuplicatesAndRemapEdges( + std::vector& vertices, + TGetVertexCoordX getX, + TGetVertexCoordY getY, + const TEdgeIter edgesFirst, + const TEdgeIter edgesLast, + TGetEdgeVertexStart getStart, + TGetEdgeVertexEnd getEnd, + TMakeEdgeFromStartAndEnd makeEdge) +{ + const DuplicatesInfo di = + FindDuplicates(vertices.begin(), vertices.end(), getX, getY); + RemoveDuplicates(vertices, di.duplicates); + RemapEdges(edgesFirst, edgesLast, di.mapping, getStart, getEnd, makeEdge); + return di; +} + +template +unordered_map > EdgeToSplitVertices( + const unordered_map& edgeToPieces, + const std::vector >& vertices) +{ + typedef std::pair VertCoordPair; + struct ComparePred + { + bool operator()(const VertCoordPair& a, const VertCoordPair& b) const + { + return a.second < b.second; + } + } comparePred; + + unordered_map > edgeToSplitVerts; + typedef unordered_map::const_iterator It; + for(It e2pIt = edgeToPieces.begin(); e2pIt != edgeToPieces.end(); ++e2pIt) + { + const Edge& e = e2pIt->first; + const T dX = vertices[e.v2()].x - vertices[e.v1()].x; + const T dY = vertices[e.v2()].y - vertices[e.v1()].y; + const bool isX = std::abs(dX) >= std::abs(dY); // X-coord longer + const bool isAscending = + isX ? dX >= 0 : dY >= 0; // Longer coordinate ascends + const EdgeVec& pieces = e2pIt->second; + std::vector splitVerts; + // size is: 2[ends] + (pieces - 1)[split vertices] = pieces + 1 + splitVerts.reserve(pieces.size() + 1); + typedef EdgeVec::const_iterator EIt; + for(EIt pieceIt = pieces.begin(); pieceIt != pieces.end(); ++pieceIt) + { + const array vv = {pieceIt->v1(), pieceIt->v2()}; + typedef array::const_iterator VIt; + for(VIt v = vv.begin(); v != vv.end(); ++v) + { + const T c = isX ? vertices[*v].x : vertices[*v].y; + splitVerts.push_back(std::make_pair(*v, isAscending ? c : -c)); + } + } + // sort by longest coordinate + std::sort(splitVerts.begin(), splitVerts.end(), comparePred); + // remove duplicates + splitVerts.erase( + std::unique(splitVerts.begin(), splitVerts.end()), + splitVerts.end()); + assert(splitVerts.size() > 2); // 2 end points with split vertices + std::pair > val = + std::make_pair(e, std::vector()); + val.second.reserve(splitVerts.size()); + typedef typename std::vector::const_iterator SEIt; + for(SEIt it = splitVerts.begin() + 1; it != splitVerts.end() - 1; ++it) + { + val.second.push_back(it->first); + } + edgeToSplitVerts.insert(val); + } + return edgeToSplitVerts; +} + +} // namespace CDT + +#ifndef CDT_USE_AS_COMPILED_LIBRARY +#include "CDT.hpp" +#endif + +#endif // header-guard diff --git a/src/isct/cdt/CDT.hpp b/src/isct/cdt/CDT.hpp new file mode 100644 index 00000000..66f9f26c --- /dev/null +++ b/src/isct/cdt/CDT.hpp @@ -0,0 +1,107 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at https://mozilla.org/MPL/2.0/. */ + +/** + * @file + * Public API - implementation + */ + +#include "CDT.h" + +#include +#include +#include +#include + +namespace CDT +{ + +CDT_INLINE_IF_HEADER_ONLY VerticesTriangles calculateTrianglesByVertex( + const TriangleVec& triangles, + const VertInd verticesSize) +{ + VerticesTriangles vertTris(verticesSize); + for(TriInd iT(0); iT < triangles.size(); ++iT) + { + const VerticesArr3& vv = triangles[iT].vertices; + for(VerticesArr3::const_iterator v = vv.begin(); v != vv.end(); ++v) + { + vertTris[*v].push_back(iT); + } + } + return vertTris; +} + +template +DuplicatesInfo RemoveDuplicates(std::vector >& vertices) +{ + const DuplicatesInfo di = FindDuplicates( + vertices.begin(), vertices.end(), getX_V2d, getY_V2d); + RemoveDuplicates(vertices, di.duplicates); + return di; +} + +CDT_INLINE_IF_HEADER_ONLY void +RemapEdges(std::vector& edges, const std::vector& mapping) +{ + RemapEdges( + edges.begin(), + edges.end(), + mapping, + edge_get_v1, + edge_get_v2, + edge_make); +} + +template +DuplicatesInfo RemoveDuplicatesAndRemapEdges( + std::vector >& vertices, + std::vector& edges) +{ + return RemoveDuplicatesAndRemapEdges( + vertices, + getX_V2d, + getY_V2d, + edges.begin(), + edges.end(), + edge_get_v1, + edge_get_v2, + edge_make); +} + +CDT_INLINE_IF_HEADER_ONLY EdgeUSet +extractEdgesFromTriangles(const TriangleVec& triangles) +{ + EdgeUSet edges; + typedef TriangleVec::const_iterator CIt; + for(CIt t = triangles.begin(); t != triangles.end(); ++t) + { + edges.insert(Edge(VertInd(t->vertices[0]), VertInd(t->vertices[1]))); + edges.insert(Edge(VertInd(t->vertices[1]), VertInd(t->vertices[2]))); + edges.insert(Edge(VertInd(t->vertices[2]), VertInd(t->vertices[0]))); + } + return edges; +} + +CDT_INLINE_IF_HEADER_ONLY unordered_map +EdgeToPiecesMapping(const unordered_map& pieceToOriginals) +{ + unordered_map originalToPieces; + typedef unordered_map::const_iterator Cit; + for(Cit ptoIt = pieceToOriginals.begin(); ptoIt != pieceToOriginals.end(); + ++ptoIt) + { + const Edge piece = ptoIt->first; + const EdgeVec& originals = ptoIt->second; + for(EdgeVec::const_iterator origIt = originals.begin(); + origIt != originals.end(); + ++origIt) + { + originalToPieces[*origIt].push_back(piece); + } + } + return originalToPieces; +} + +} // namespace CDT diff --git a/src/isct/cdt/CDTUtils.h b/src/isct/cdt/CDTUtils.h new file mode 100644 index 00000000..8941eeb7 --- /dev/null +++ b/src/isct/cdt/CDTUtils.h @@ -0,0 +1,592 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at https://mozilla.org/MPL/2.0/. */ + +/** + * @file + * Utilities and helpers + */ + +#ifndef CDT_obwOaxOTdAWcLNTlNnaq +#define CDT_obwOaxOTdAWcLNTlNnaq + +#ifdef CDT_DONT_USE_BOOST_RTREE +// CDT_DONT_USE_BOOST_RTREE was replaced with CDT_USE_BOOST +typedef char CDT_DONT_USE_BOOST_RTREE__was__replaced__with__CDT_USE_BOOST[-1]; +#endif + +// #define CDT_USE_STRONG_TYPING // strong type checks on indices + +// check if c++11 is supported +#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900) +#define CDT_CXX11_IS_SUPPORTED +#elif !defined(__cplusplus) && !defined(_MSC_VER) +typedef char couldnt_parse_cxx_standard[-1]; ///< Error: couldn't parse standard +#endif + +// Functions defined outside the class need to be 'inline' +// if CDT is configured to be used as header-only library: +// single-definition rule is violated otherwise +#ifdef CDT_USE_AS_COMPILED_LIBRARY +#define CDT_INLINE_IF_HEADER_ONLY +#include "cdt_export.h" // automatically generated by CMake +#else +/** + * Macro for inlining non-template functions when in header-only mode to + * avoid multiple declaration errors. + */ +#define CDT_INLINE_IF_HEADER_ONLY inline +/// Export not needed in header-only mode +#define CDT_EXPORT +#endif + +#include +#include +#include +#include +#include + +#ifdef CDT_USE_STRONG_TYPING +#include +#endif + +// use fall-backs for c++11 features +#ifdef CDT_CXX11_IS_SUPPORTED + +#include +#include +#include +#include +#include +#include + +#ifdef CDT_DISABLE_EXCEPTIONS +#include +#endif + +namespace CDT +{ +using std::array; +using std::get; +using std::make_tuple; +using std::tie; +using std::to_string; +using std::tuple; +using std::unordered_map; +using std::unordered_set; +} // namespace CDT + +#else +#include +#include +#include +#include +#include +#include +namespace CDT +{ +using boost::array; +using boost::get; +using boost::make_tuple; +using boost::tie; +using boost::tuple; +using boost::unordered_map; +using boost::unordered_set; + +template +std::string to_string(const T& value) +{ + return boost::lexical_cast(value); +} +} // namespace CDT +#endif + +namespace CDT +{ + +template +void handleException(const T& error) +{ +#ifdef CDT_DISABLE_EXCEPTIONS + std::terminate(); +#else + throw error; +#endif +} + +/// Needed for c++03 compatibility (no uniform initialization available) +template +array arr3(const T& v0, const T& v1, const T& v2) +{ + const array out = {v0, v1, v2}; + return out; +} + +/// Needed for c++03 compatibility (no uniform initialization available) +template +array arr3(const T& v) +{ + const array out = {v, v, v}; + return out; +} + +/// 2D vector +template +struct CDT_EXPORT V2d +{ + T x; ///< X-coordinate + T y; ///< Y-coordinate + + /// Vertex with zero coordinates + V2d() + : x(T(0)) + , y(T(0)) + {} + + /// Vertex with given coordinates + V2d(const T x, const T y) + : x(x) + , y(y) + {} +}; + +/// X- coordinate getter for V2d +template +const T& getX_V2d(const V2d& v) +{ + return v.x; +} + +/// Y-coordinate getter for V2d +template +const T& getY_V2d(const V2d& v) +{ + return v.y; +} + +/// If two 2D vectors are exactly equal +template +bool operator==(const CDT::V2d& lhs, const CDT::V2d& rhs) +{ + return lhs.x == rhs.x && lhs.y == rhs.y; +} + +#ifdef CDT_USE_64_BIT_INDEX_TYPE +typedef unsigned long long IndexSizeType; +#else +typedef unsigned int IndexSizeType; +#endif + +#ifdef CDT_USE_STRONG_TYPING +/// Index in triangle +BOOST_STRONG_TYPEDEF(unsigned char, Index); +/// Vertex index +BOOST_STRONG_TYPEDEF(IndexSizeType, VertInd); +/// Triangle index +BOOST_STRONG_TYPEDEF(IndexSizeType, TriInd); +#else +/// Index in triangle +typedef unsigned char Index; +/// Vertex index +typedef IndexSizeType VertInd; +/// Triangle index +typedef IndexSizeType TriInd; +#endif + +/// Constant representing no valid value for index +const static Index invalidIndex(std::numeric_limits::max()); +/// Constant representing no valid value for index size +const static IndexSizeType + invalidIndexSizeType(std::numeric_limits::max()); +/// Number of super triangle vertices +/// @note placed in a constant so that it's easier to find usages in code +const static IndexSizeType nSuperTriangleVertices(3); +/// Constant representing no valid neighbor for a triangle +const static TriInd noNeighbor(invalidIndexSizeType); +/// Constant representing no valid vertex for a triangle +const static VertInd noVertex(invalidIndexSizeType); + +typedef std::vector TriIndVec; ///< Vector of triangle indices +typedef array VerticesArr3; ///< array of three vertex indices +typedef array NeighborsArr3; ///< array of three neighbors + +/// 2D bounding box +template +struct CDT_EXPORT Box2d +{ + V2d min; ///< min box corner + V2d max; ///< max box corner + + /// Box that doesn't contain any point + Box2d() + : min(std::numeric_limits::max(), std::numeric_limits::max()) + , max(-std::numeric_limits::max(), -std::numeric_limits::max()) + {} + + /// Envelop box around a point + Box2d& envelopPoint(const V2d& p) + { + return envelopPoint(p.x, p.y); + } + + /// Envelop box around a point with given coordinates + Box2d& envelopPoint(const T x, const T y) + { + min.x = std::min(x, min.x); + max.x = std::max(x, max.x); + min.y = std::min(y, min.y); + max.y = std::max(y, max.y); + return *this; + } + + /// Envelop box around a collection of custom points + template < + typename TVertexIter, + typename TGetVertexCoordX, + typename TGetVertexCoordY> + Box2d& envelopPoints( + TVertexIter first, + TVertexIter last, + TGetVertexCoordX getX, + TGetVertexCoordY getY) + { + for(; first != last; ++first) + { + envelopPoint(getX(*first), getY(*first)); + } + return *this; + } + + /// Envelop box around a collection of points + Box2d& envelopPoints(const std::vector >& vertices) + { + return envelopPoints( + vertices.begin(), vertices.end(), getX_V2d, getY_V2d); + } +}; + +/// Edge connecting two vertices: vertex with smaller index is always first +/// @note: hash Edge is specialized at the bottom +struct CDT_EXPORT Edge +{ + /// Constructor + Edge(const VertInd iV1, const VertInd iV2) + : m_vertices( + iV1 < iV2 ? std::make_pair(iV1, iV2) : std::make_pair(iV2, iV1)) + {} + + /// Equals operator + bool operator==(const Edge& other) const + { + return m_vertices == other.m_vertices; + } + + /// Not-equals operator + bool operator!=(const Edge& other) const + { + return !(this->operator==(other)); + } + + /// V1 getter + VertInd v1() const + { + return m_vertices.first; + } + + /// V2 getter + VertInd v2() const + { + return m_vertices.second; + } + + /// Edges' vertices + const std::pair& verts() const + { + return m_vertices; + } + +private: + std::pair m_vertices; +}; + +/// Get edge first vertex +inline VertInd edge_get_v1(const Edge& e) +{ + return e.v1(); +} + +/// Get edge second vertex +inline VertInd edge_get_v2(const Edge& e) +{ + return e.v2(); +} + +/// Get edge second vertex +inline Edge edge_make(VertInd iV1, VertInd iV2) +{ + return Edge(iV1, iV2); +} + +typedef std::vector EdgeVec; ///< Vector of edges +typedef unordered_set EdgeUSet; ///< Hash table of edges +typedef unordered_set TriIndUSet; ///< Hash table of triangles +typedef unordered_map TriIndUMap; ///< Triangle hash map + +/// Triangulation triangle (counter-clockwise winding) +/* + * v3 + * /\ + * n3/ \n2 + * /____\ + * v1 n1 v2 + */ +struct CDT_EXPORT Triangle +{ + VerticesArr3 vertices; ///< triangle's three vertices + NeighborsArr3 neighbors; ///< triangle's three neighbors + + /// Triangle with no vertices and no neighbors + Triangle() + : vertices(arr3(noVertex)) + , neighbors(arr3(noNeighbor)) + {} + + /// Triangle with given vertices and neighbors + Triangle(const VerticesArr3& vertices, const NeighborsArr3& neighbors) + : vertices(vertices) + , neighbors(neighbors) + {} + + /// Next triangle adjacent to a vertex (clockwise) + /// @returns pair of next triangle and the other vertex of a common edge + std::pair next(const VertInd i) const + { + assert(vertices[0] == i || vertices[1] == i || vertices[2] == i); + if(vertices[0] == i) + { + return std::make_pair(neighbors[0], vertices[1]); + } + if(vertices[1] == i) + { + return std::make_pair(neighbors[1], vertices[2]); + } + return std::make_pair(neighbors[2], vertices[0]); + } + + /// Previous triangle adjacent to a vertex (counter-clockwise) + /// @returns pair of previous triangle and the other vertex of a common edge + std::pair prev(const VertInd i) const + { + assert(vertices[0] == i || vertices[1] == i || vertices[2] == i); + if(vertices[0] == i) + return std::make_pair(neighbors[2], vertices[2]); + if(vertices[1] == i) + return std::make_pair(neighbors[0], vertices[0]); + return std::make_pair(neighbors[1], vertices[1]); + } + + /// Check if triangle contains a vertex + bool containsVertex(const VertInd i) const + { + return std::find(vertices.begin(), vertices.end(), i) != vertices.end(); + } +}; + +typedef std::vector TriangleVec; ///< Vector of triangles + +/// Advance vertex or neighbor index counter-clockwise +CDT_EXPORT Index ccw(Index i); + +/// Advance vertex or neighbor index clockwise +CDT_EXPORT Index cw(Index i); + +/// Location of point on a triangle +struct CDT_EXPORT PtTriLocation +{ + /// Enum + enum Enum + { + Inside, + Outside, + OnEdge1, + OnEdge2, + OnEdge3, + OnVertex, + }; +}; + +/// Check if location is classified as on any of three edges +CDT_EXPORT bool isOnEdge(PtTriLocation::Enum location); + +/// Neighbor index from a on-edge location +/// @note Call only if located on the edge! +CDT_EXPORT Index edgeNeighbor(PtTriLocation::Enum location); + +/// Relative location of point to a line +struct CDT_EXPORT PtLineLocation +{ + /// Enum + enum Enum + { + Left, + Right, + OnLine, + }; +}; + +/// Orient p against line v1-v2 2D: robust geometric predicate +template +CDT_EXPORT T orient2D(const V2d& p, const V2d& v1, const V2d& v2); + +/// Check if point lies to the left of, to the right of, or on a line +template +CDT_EXPORT PtLineLocation::Enum locatePointLine( + const V2d& p, + const V2d& v1, + const V2d& v2, + T orientationTolerance = T(0)); + +/// Classify value of orient2d predicate +template +CDT_EXPORT PtLineLocation::Enum +classifyOrientation(T orientation, T orientationTolerance = T(0)); + +/// Check if point a lies inside of, outside of, or on an edge of a triangle +template +CDT_EXPORT PtTriLocation::Enum locatePointTriangle( + const V2d& p, + const V2d& v1, + const V2d& v2, + const V2d& v3); + +/// Opposed neighbor index from vertex index +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY Index opoNbr(Index vertIndex); + +/// Opposed vertex index from neighbor index +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY Index opoVrt(Index neighborIndex); + +/// Index of triangle's neighbor opposed to a vertex +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY Index +opposedTriangleInd(const VerticesArr3& vv, VertInd iVert); + +/// Index of triangle's neighbor opposed to an edge +CDT_INLINE_IF_HEADER_ONLY Index +edgeNeighborInd(const VerticesArr3& vv, VertInd iVedge1, VertInd iVedge2); + +/// Index of triangle's vertex opposed to a triangle +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY Index +opposedVertexInd(const NeighborsArr3& nn, TriInd iTopo); + +/// If triangle has a given vertex return vertex-index +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY Index +vertexInd(const VerticesArr3& vv, VertInd iV); + +/// Given triangle and a vertex find opposed triangle +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY TriInd +opposedTriangle(const Triangle& tri, VertInd iVert); + +/// Given triangle and an edge find neighbor sharing the edge +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY TriInd +edgeNeighbor(const Triangle& tri, VertInd iVedge1, VertInd iVedge2); + +/// Given two triangles, return vertex of first triangle opposed to the second +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY VertInd +opposedVertex(const Triangle& tri, TriInd iTopo); + +/// Test if point lies in a circumscribed circle of a triangle +template +CDT_EXPORT bool isInCircumcircle( + const V2d& p, + const V2d& v1, + const V2d& v2, + const V2d& v3); + +/// Test if two vertices share at least one common triangle +CDT_EXPORT CDT_INLINE_IF_HEADER_ONLY bool +verticesShareEdge(const TriIndVec& aTris, const TriIndVec& bTris); + +/// Distance between two 2D points +template +CDT_EXPORT T distance(const V2d& a, const V2d& b); + +/// Squared distance between two 2D points +template +CDT_EXPORT T distanceSquared(const V2d& a, const V2d& b); + +/// Check if any of triangle's vertices belongs to a super-triangle +CDT_INLINE_IF_HEADER_ONLY bool touchesSuperTriangle(const Triangle& t); +} // namespace CDT + +#ifndef CDT_USE_AS_COMPILED_LIBRARY +#include "CDTUtils.hpp" +#endif + +//***************************************************************************** +// Specialize hash functions +//***************************************************************************** +#ifdef CDT_CXX11_IS_SUPPORTED +namespace std +#else +namespace boost +#endif +{ + +#ifdef CDT_USE_STRONG_TYPING + +/// Vertex index hasher +template <> +struct hash +{ + /// Hash operator + std::size_t operator()(const CDT::VertInd& vi) const + { + return std::hash()(vi.t); + } +}; + +/// Triangle index hasher +template <> +struct hash +{ + /// Hash operator + std::size_t operator()(const CDT::TriInd& vi) const + { + return std::hash()(vi.t); + } +}; + +#endif // CDT_USE_STRONG_TYPING + +/// Edge hasher +template <> +struct hash +{ + /// Hash operator + std::size_t operator()(const CDT::Edge& e) const + { + return hashEdge(e); + } + +private: + static void hashCombine(std::size_t& seed, const CDT::VertInd& key) + { +#ifdef CDT_CXX11_IS_SUPPORTED + typedef std::hash Hasher; +#else + typedef boost::hash Hasher; +#endif + seed ^= Hasher()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2); + } + + static std::size_t hashEdge(const CDT::Edge& e) + { + std::size_t seed(0); + hashCombine(seed, e.v1()); + hashCombine(seed, e.v2()); + return seed; + } +}; + +} // namespace std/boost + +#endif // header guard diff --git a/src/isct/cdt/CDTUtils.hpp b/src/isct/cdt/CDTUtils.hpp new file mode 100644 index 00000000..2976a0e9 --- /dev/null +++ b/src/isct/cdt/CDTUtils.hpp @@ -0,0 +1,264 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at https://mozilla.org/MPL/2.0/. */ + +/** + * @file + * Utilities and helpers - implementation + */ + +#include "CDTUtils.h" + +#include "predicates.h" // robust predicates: orient, in-circle + +#include + +namespace CDT +{ + +CDT_INLINE_IF_HEADER_ONLY Index ccw(Index i) +{ + return Index((i + 1) % 3); +} + +CDT_INLINE_IF_HEADER_ONLY Index cw(Index i) +{ + return Index((i + 2) % 3); +} + +CDT_INLINE_IF_HEADER_ONLY bool isOnEdge(const PtTriLocation::Enum location) +{ + return location == PtTriLocation::OnEdge1 || + location == PtTriLocation::OnEdge2 || + location == PtTriLocation::OnEdge3; +} + +CDT_INLINE_IF_HEADER_ONLY Index edgeNeighbor(const PtTriLocation::Enum location) +{ + assert(isOnEdge(location)); + return static_cast(location - PtTriLocation::OnEdge1); +} + +template +T orient2D(const V2d& p, const V2d& v1, const V2d& v2) +{ + return predicates::adaptive::orient2d(v1.x, v1.y, v2.x, v2.y, p.x, p.y); +} + +template +PtLineLocation::Enum locatePointLine( + const V2d& p, + const V2d& v1, + const V2d& v2, + const T orientationTolerance) +{ + return classifyOrientation(orient2D(p, v1, v2), orientationTolerance); +} + +template +PtLineLocation::Enum +classifyOrientation(const T orientation, const T orientationTolerance) +{ + if(orientation < -orientationTolerance) + return PtLineLocation::Right; + if(orientation > orientationTolerance) + return PtLineLocation::Left; + return PtLineLocation::OnLine; +} + +template +PtTriLocation::Enum locatePointTriangle( + const V2d& p, + const V2d& v1, + const V2d& v2, + const V2d& v3) +{ + using namespace predicates::adaptive; + PtTriLocation::Enum result = PtTriLocation::Inside; + PtLineLocation::Enum edgeCheck = locatePointLine(p, v1, v2); + if(edgeCheck == PtLineLocation::Right) + return PtTriLocation::Outside; + if(edgeCheck == PtLineLocation::OnLine) + result = PtTriLocation::OnEdge1; + edgeCheck = locatePointLine(p, v2, v3); + if(edgeCheck == PtLineLocation::Right) + return PtTriLocation::Outside; + if(edgeCheck == PtLineLocation::OnLine) + { + result = (result == PtTriLocation::Inside) ? PtTriLocation::OnEdge2 + : PtTriLocation::OnVertex; + } + edgeCheck = locatePointLine(p, v3, v1); + if(edgeCheck == PtLineLocation::Right) + return PtTriLocation::Outside; + if(edgeCheck == PtLineLocation::OnLine) + { + result = (result == PtTriLocation::Inside) ? PtTriLocation::OnEdge3 + : PtTriLocation::OnVertex; + } + return result; +} + +CDT_INLINE_IF_HEADER_ONLY Index opoNbr(const Index vertIndex) +{ + if(vertIndex == Index(0)) + return Index(1); + if(vertIndex == Index(1)) + return Index(2); + if(vertIndex == Index(2)) + return Index(0); + assert(false && "Invalid vertex index"); + handleException(std::runtime_error("Invalid vertex index")); + return invalidIndex; +} + +CDT_INLINE_IF_HEADER_ONLY Index opoVrt(const Index neighborIndex) +{ + if(neighborIndex == Index(0)) + return Index(2); + if(neighborIndex == Index(1)) + return Index(0); + if(neighborIndex == Index(2)) + return Index(1); + assert(false && "Invalid neighbor index"); + handleException(std::runtime_error("Invalid neighbor index")); + return invalidIndex; +} + +CDT_INLINE_IF_HEADER_ONLY Index +opposedTriangleInd(const VerticesArr3& vv, const VertInd iVert) +{ + assert(vv[0] == iVert || vv[1] == iVert || vv[2] == iVert); + if(vv[0] == iVert) + return Index(1); + if(vv[1] == iVert) + return Index(2); + return Index(0); +} + +CDT_INLINE_IF_HEADER_ONLY Index edgeNeighborInd( + const VerticesArr3& vv, + const VertInd iVedge1, + const VertInd iVedge2) +{ + assert(vv[0] == iVedge1 || vv[1] == iVedge1 || vv[2] == iVedge1); + assert(vv[0] == iVedge2 || vv[1] == iVedge2 || vv[2] == iVedge2); + assert( + (vv[0] != iVedge1 && vv[0] != iVedge2) || + (vv[1] != iVedge1 && vv[1] != iVedge2) || + (vv[2] != iVedge1 && vv[2] != iVedge2)); + /* + * vv[2] + * /\ + * n[2]/ \n[1] + * /____\ + * vv[0] n[0] vv[1] + */ + if(vv[0] == iVedge1) + { + if(vv[1] == iVedge2) + return Index(0); + return Index(2); + } + if(vv[0] == iVedge2) + { + if(vv[1] == iVedge1) + return Index(0); + return Index(2); + } + return Index(1); +} + +CDT_INLINE_IF_HEADER_ONLY Index +opposedVertexInd(const NeighborsArr3& nn, const TriInd iTopo) +{ + assert(nn[0] == iTopo || nn[1] == iTopo || nn[2] == iTopo); + if(nn[0] == iTopo) + return Index(2); + if(nn[1] == iTopo) + return Index(0); + return Index(1); +} + +CDT_INLINE_IF_HEADER_ONLY Index +vertexInd(const VerticesArr3& vv, const VertInd iV) +{ + assert(vv[0] == iV || vv[1] == iV || vv[2] == iV); + if(vv[0] == iV) + return Index(0); + if(vv[1] == iV) + return Index(1); + return Index(2); +} + +CDT_INLINE_IF_HEADER_ONLY TriInd +opposedTriangle(const Triangle& tri, const VertInd iVert) +{ + return tri.neighbors[opposedTriangleInd(tri.vertices, iVert)]; +} + +CDT_INLINE_IF_HEADER_ONLY VertInd +opposedVertex(const Triangle& tri, const TriInd iTopo) +{ + return tri.vertices[opposedVertexInd(tri.neighbors, iTopo)]; +} + +/// Given triangle and an edge find neighbor sharing the edge +CDT_INLINE_IF_HEADER_ONLY TriInd +edgeNeighbor(const Triangle& tri, VertInd iVedge1, VertInd iVedge2) +{ + return tri.neighbors[edgeNeighborInd(tri.vertices, iVedge1, iVedge2)]; +} + +template +bool isInCircumcircle( + const V2d& p, + const V2d& v1, + const V2d& v2, + const V2d& v3) +{ + using namespace predicates::adaptive; + return incircle(v1.x, v1.y, v2.x, v2.y, v3.x, v3.y, p.x, p.y) > T(0); +} + +CDT_INLINE_IF_HEADER_ONLY +bool verticesShareEdge(const TriIndVec& aTris, const TriIndVec& bTris) +{ + for(TriIndVec::const_iterator it = aTris.begin(); it != aTris.end(); ++it) + if(std::find(bTris.begin(), bTris.end(), *it) != bTris.end()) + return true; + return false; +} + +template +T distanceSquared(const T ax, const T ay, const T bx, const T by) +{ + const T dx = bx - ax; + const T dy = by - ay; + return dx * dx + dy * dy; +} + +template +T distance(const T ax, const T ay, const T bx, const T by) +{ + return std::sqrt(distanceSquared(ax, ay, bx, by)); +} + +template +T distance(const V2d& a, const V2d& b) +{ + return distance(a.x, a.y, b.x, b.y); +} + +template +T distanceSquared(const V2d& a, const V2d& b) +{ + return distanceSquared(a.x, a.y, b.x, b.y); +} + +bool touchesSuperTriangle(const Triangle& t) +{ + return t.vertices[0] < 3 || t.vertices[1] < 3 || t.vertices[2] < 3; +} + +} // namespace CDT diff --git a/src/isct/cdt/KDTree.h b/src/isct/cdt/KDTree.h new file mode 100644 index 00000000..bc408e61 --- /dev/null +++ b/src/isct/cdt/KDTree.h @@ -0,0 +1,471 @@ +/// This Source Code Form is subject to the terms of the Mozilla Public +/// License, v. 2.0. If a copy of the MPL was not distributed with this +/// file, You can obtain one at https://mozilla.org/MPL/2.0/. +/// Contribution of original implementation: +/// Andre Fecteau + +#ifndef KDTREE_KDTREE_H +#define KDTREE_KDTREE_H + +#include "CDTUtils.h" + +#include + +namespace CDT +{ +namespace KDTree +{ + +struct NodeSplitDirection +{ + enum Enum + { + X, + Y, + }; +}; + +/// Simple tree structure with alternating half splitting nodes +/// @details Simple tree structure +/// - Tree to incrementally add points to the structure. +/// - Get the nearest point to a given input. +/// - Does not check for duplicates, expect unique points. +/// @tparam TCoordType type used for storing point coordinate. +/// @tparam NumVerticesInLeaf The number of points per leaf. +/// @tparam InitialStackDepth initial size of stack depth for nearest query. +/// Should be at least 1. +/// @tparam StackDepthIncrement increment of stack depth for nearest query when +/// stack depth is reached. +template < + typename TCoordType, + size_t NumVerticesInLeaf, + size_t InitialStackDepth, + size_t StackDepthIncrement> +class KDTree +{ +public: + typedef TCoordType coord_type; + typedef CDT::V2d point_type; + typedef CDT::VertInd point_index; + typedef std::pair value_type; + typedef std::vector point_data_vec; + typedef point_data_vec::const_iterator pd_cit; + typedef CDT::VertInd node_index; + typedef CDT::array children_type; + + /// Stores kd-tree node data + struct Node + { + children_type children; ///< two children if not leaf; {0,0} if leaf + point_data_vec data; ///< points' data if leaf + /// Create empty leaf + Node() + { + setChildren(node_index(0), node_index(0)); + data.reserve(NumVerticesInLeaf); + } + /// Children setter for convenience + void setChildren(const node_index c1, const node_index c2) + { + children[0] = c1; + children[1] = c2; + } + /// Check if node is a leaf (has no valid children) + bool isLeaf() const + { + return children[0] == children[1]; + } + }; + + /// Default constructor + KDTree() + : m_rootDir(NodeSplitDirection::X) + , m_min(point_type( + -std::numeric_limits::max(), + -std::numeric_limits::max())) + , m_max(point_type( + std::numeric_limits::max(), + std::numeric_limits::max())) + , m_size(0) + , m_isRootBoxInitialized(false) + , m_tasksStack(InitialStackDepth, NearestTask()) + { + m_root = addNewNode(); + } + + /// Constructor with bounding box known in advance + KDTree(const point_type& min, const point_type& max) + : m_rootDir(NodeSplitDirection::X) + , m_min(min) + , m_max(max) + , m_size(0) + , m_isRootBoxInitialized(true) + , m_tasksStack(InitialStackDepth, NearestTask()) + { + m_root = addNewNode(); + } + + CDT::VertInd size() const + { + return m_size; + } + + /// Insert a point into kd-tree + /// @note external point-buffer is used to reduce kd-tree's memory footprint + /// @param iPoint index of point in external point-buffer + /// @param points external point-buffer + void + insert(const point_index& iPoint, const std::vector& points) + { + ++m_size; + // if point is outside root, extend tree by adding new roots + const point_type& pos = points[iPoint]; + while(!isInsideBox(pos, m_min, m_max)) + { + extendTree(pos); + } + // now insert the point into the tree + node_index node = m_root; + point_type min = m_min; + point_type max = m_max; + NodeSplitDirection::Enum dir = m_rootDir; + + // below: initialized only to suppress warnings + NodeSplitDirection::Enum newDir(NodeSplitDirection::X); + coord_type mid(0); + point_type newMin, newMax; + while(true) + { + if(m_nodes[node].isLeaf()) + { + // add point if capacity is not reached + point_data_vec& pd = m_nodes[node].data; + if(pd.size() < NumVerticesInLeaf) + { + pd.push_back(iPoint); + return; + } + // initialize bbox first time the root capacity is reached + if(!m_isRootBoxInitialized) + { + initializeRootBox(points); + min = m_min; + max = m_max; + } + // split a full leaf node + calcSplitInfo(min, max, dir, mid, newDir, newMin, newMax); + const node_index c1 = addNewNode(), c2 = addNewNode(); + Node& n = m_nodes[node]; + n.setChildren(c1, c2); + point_data_vec& c1data = m_nodes[c1].data; + point_data_vec& c2data = m_nodes[c2].data; + // move node's points to children + for(pd_cit it = n.data.begin(); it != n.data.end(); ++it) + { + whichChild(points[*it], mid, dir) == 0 + ? c1data.push_back(*it) + : c2data.push_back(*it); + } + n.data = point_data_vec(); + } + else + { + calcSplitInfo(min, max, dir, mid, newDir, newMin, newMax); + } + // add the point to a child + const std::size_t iChild = whichChild(points[iPoint], mid, dir); + iChild == 0 ? max = newMax : min = newMin; + node = m_nodes[node].children[iChild]; + dir = newDir; + } + } + + /// Query kd-tree for a nearest neighbor point + /// @note external point-buffer is used to reduce kd-tree's memory footprint + /// @param point query point position + /// @param points external point-buffer + value_type nearest( + const point_type& point, + const std::vector& points) const + { + value_type out; + int iTask = -1; + coord_type minDistSq = std::numeric_limits::max(); + m_tasksStack[++iTask] = NearestTask( + m_root, + m_min, + m_max, + m_rootDir, + distanceSquaredToBox(point, m_min, m_max)); + while(iTask != -1) + { + const NearestTask t = m_tasksStack[iTask--]; + if(t.distSq > minDistSq) + continue; + const Node& n = m_nodes[t.node]; + if(n.isLeaf()) + { + for(pd_cit it = n.data.begin(); it != n.data.end(); ++it) + { + const point_type& p = points[*it]; + const coord_type distSq = CDT::distanceSquared(point, p); + if(distSq < minDistSq) + { + minDistSq = distSq; + out.first = p; + out.second = *it; + } + } + } + else + { + coord_type mid(0); + NodeSplitDirection::Enum newDir(NodeSplitDirection::X); + point_type newMin = t.min, newMax = t.max; + coord_type dSqFarther = std::numeric_limits::max(); + switch(t.dir) + { + case NodeSplitDirection::X: + { + mid = (t.min.x + t.max.x) / coord_type(2); + newDir = NodeSplitDirection::Y; + newMin.x = mid; + newMax.x = mid; + const coord_type dx = point.x - mid; + const coord_type dy = std::max( + std::max(t.min.y - point.y, coord_type(0)), + point.y - t.max.y); + dSqFarther = dx * dx + dy * dy; + break; + } + case NodeSplitDirection::Y: + { + mid = (t.min.y + t.max.y) / coord_type(2); + newDir = NodeSplitDirection::X; + newMin.y = mid; + newMax.y = mid; + const coord_type dx = std::max( + std::max(t.min.x - point.x, coord_type(0)), + point.x - t.max.x); + const coord_type dy = point.y - mid; + dSqFarther = dx * dx + dy * dy; + break; + } + } + + if(iTask + 2 >= static_cast(m_tasksStack.size())) + { + m_tasksStack.resize( + m_tasksStack.size() + StackDepthIncrement); + } + + // put the closest node on top of the stack + if(isAfterSplit(point, mid, t.dir)) + { + if(dSqFarther <= minDistSq) + { + m_tasksStack[++iTask] = NearestTask( + n.children[0], t.min, newMax, newDir, dSqFarther); + } + m_tasksStack[++iTask] = NearestTask( + n.children[1], newMin, t.max, newDir, t.distSq); + } + else + { + if(dSqFarther <= minDistSq) + { + m_tasksStack[++iTask] = NearestTask( + n.children[1], newMin, t.max, newDir, dSqFarther); + } + m_tasksStack[++iTask] = NearestTask( + n.children[0], t.min, newMax, newDir, t.distSq); + } + } + } + return out; + } + +private: + /// Add a new node and return it's index in nodes buffer + node_index addNewNode() + { + const node_index newNodeIndex = static_cast(m_nodes.size()); + m_nodes.push_back(Node()); + return newNodeIndex; + } + + static bool isAfterSplit( + const point_type& point, + const coord_type& split, + const NodeSplitDirection::Enum dir) + { + return dir == NodeSplitDirection::X ? point.x > split : point.y > split; + } + + /// Test which child point belongs to after the split + /// @returns 0 if first child, 1 if second child + static std::size_t whichChild( + const point_type& point, + const coord_type& split, + const NodeSplitDirection::Enum dir) + { + return isAfterSplit(point, split, dir); + } + + /// Calculate split location, direction, and children boxes + static void calcSplitInfo( + const point_type& min, + const point_type& max, + const NodeSplitDirection::Enum dir, + coord_type& midOut, + NodeSplitDirection::Enum& newDirOut, + point_type& newMinOut, + point_type& newMaxOut) + { + newMaxOut = max; + newMinOut = min; + switch(dir) + { + case NodeSplitDirection::X: + midOut = (min.x + max.x) / coord_type(2); + newDirOut = NodeSplitDirection::Y; + newMinOut.x = midOut; + newMaxOut.x = midOut; + return; + case NodeSplitDirection::Y: + midOut = (min.y + max.y) / coord_type(2); + newDirOut = NodeSplitDirection::X; + newMinOut.y = midOut; + newMaxOut.y = midOut; + return; + } + } + + /// Test if point is inside a box + static bool isInsideBox( + const point_type& p, + const point_type& min, + const point_type& max) + { + return p.x >= min.x && p.x <= max.x && p.y >= min.y && p.y <= max.y; + } + + /// Extend a tree by creating new root with old root and a new node as + /// children + void extendTree(const point_type& point) + { + const node_index newRoot = addNewNode(); + const node_index newLeaf = addNewNode(); + switch(m_rootDir) + { + case NodeSplitDirection::X: + m_rootDir = NodeSplitDirection::Y; + if(point.y < m_min.y) + { + m_min.y -= m_max.y - m_min.y; + m_nodes[newRoot].setChildren(newLeaf, m_root); + } + else + { + m_max.y += m_max.y - m_min.y; + m_nodes[newRoot].setChildren(m_root, newLeaf); + } + break; + case NodeSplitDirection::Y: + m_rootDir = NodeSplitDirection::X; + if(point.x < m_min.x) + { + m_min.x -= m_max.x - m_min.x; + m_nodes[newRoot].setChildren(newLeaf, m_root); + } + else + { + m_max.x += m_max.x - m_min.x; + m_nodes[newRoot].setChildren(m_root, newLeaf); + } + break; + } + m_root = newRoot; + } + + /// Calculate root's box enclosing all root points + void initializeRootBox(const std::vector& points) + { + const point_data_vec& data = m_nodes[m_root].data; + m_min = points[data.front()]; + m_max = m_min; + for(pd_cit it = data.begin(); it != data.end(); ++it) + { + const point_type& p = points[*it]; + m_min = point_type(std::min(m_min.x, p.x), std::min(m_min.y, p.y)); + m_max = point_type(std::max(m_max.x, p.x), std::max(m_max.y, p.y)); + } + // Make sure bounding box does not have a zero size by adding padding: + // zero-size bounding box cannot be extended properly + const TCoordType padding(1); + if(m_min.x == m_max.x) + { + m_min.x -= padding; + m_max.x += padding; + } + if(m_min.y == m_max.y) + { + m_min.y -= padding; + m_max.y += padding; + } + m_isRootBoxInitialized = true; + } + + static coord_type distanceSquaredToBox( + const point_type& p, + const point_type& min, + const point_type& max) + { + const coord_type dx = + std::max(std::max(min.x - p.x, coord_type(0)), p.x - max.x); + const coord_type dy = + std::max(std::max(min.y - p.y, coord_type(0)), p.y - max.y); + return dx * dx + dy * dy; + } + +private: + node_index m_root; + std::vector m_nodes; + NodeSplitDirection::Enum m_rootDir; + point_type m_min; + point_type m_max; + CDT::VertInd m_size; + + bool m_isRootBoxInitialized; + + // used for nearest query + struct NearestTask + { + node_index node; + point_type min, max; + NodeSplitDirection::Enum dir; + coord_type distSq; + NearestTask() + : dir(NodeSplitDirection::X) + {} + NearestTask( + const node_index node, + const point_type& min, + const point_type& max, + const NodeSplitDirection::Enum dir, + const coord_type distSq = std::numeric_limits::max()) + : node(node) + , min(min) + , max(max) + , dir(dir) + , distSq(distSq) + {} + }; + // allocated in class (not in the 'nearest' method) for better performance + mutable std::vector m_tasksStack; +}; + +} // namespace KDTree +} // namespace CDT + +#endif // header guard diff --git a/src/isct/cdt/LICENSE_CDT_MPL2.txt b/src/isct/cdt/LICENSE_CDT_MPL2.txt new file mode 100644 index 00000000..14e2f777 --- /dev/null +++ b/src/isct/cdt/LICENSE_CDT_MPL2.txt @@ -0,0 +1,373 @@ +Mozilla Public License Version 2.0 +================================== + +1. Definitions +-------------- + +1.1. "Contributor" + means each individual or legal entity that creates, contributes to + the creation of, or owns Covered Software. + +1.2. "Contributor Version" + means the combination of the Contributions of others (if any) used + by a Contributor and that particular Contributor's Contribution. + +1.3. "Contribution" + means Covered Software of a particular Contributor. + +1.4. "Covered Software" + means Source Code Form to which the initial Contributor has attached + the notice in Exhibit A, the Executable Form of such Source Code + Form, and Modifications of such Source Code Form, in each case + including portions thereof. + +1.5. "Incompatible With Secondary Licenses" + means + + (a) that the initial Contributor has attached the notice described + in Exhibit B to the Covered Software; or + + (b) that the Covered Software was made available under the terms of + version 1.1 or earlier of the License, but not also under the + terms of a Secondary License. + +1.6. "Executable Form" + means any form of the work other than Source Code Form. + +1.7. "Larger Work" + means a work that combines Covered Software with other material, in + a separate file or files, that is not Covered Software. + +1.8. "License" + means this document. + +1.9. "Licensable" + means having the right to grant, to the maximum extent possible, + whether at the time of the initial grant or subsequently, any and + all of the rights conveyed by this License. + +1.10. "Modifications" + means any of the following: + + (a) any file in Source Code Form that results from an addition to, + deletion from, or modification of the contents of Covered + Software; or + + (b) any new file in Source Code Form that contains any Covered + Software. + +1.11. "Patent Claims" of a Contributor + means any patent claim(s), including without limitation, method, + process, and apparatus claims, in any patent Licensable by such + Contributor that would be infringed, but for the grant of the + License, by the making, using, selling, offering for sale, having + made, import, or transfer of either its Contributions or its + Contributor Version. + +1.12. "Secondary License" + means either the GNU General Public License, Version 2.0, the GNU + Lesser General Public License, Version 2.1, the GNU Affero General + Public License, Version 3.0, or any later versions of those + licenses. + +1.13. "Source Code Form" + means the form of the work preferred for making modifications. + +1.14. "You" (or "Your") + means an individual or a legal entity exercising rights under this + License. For legal entities, "You" includes any entity that + controls, is controlled by, or is under common control with You. For + purposes of this definition, "control" means (a) the power, direct + or indirect, to cause the direction or management of such entity, + whether by contract or otherwise, or (b) ownership of more than + fifty percent (50%) of the outstanding shares or beneficial + ownership of such entity. + +2. License Grants and Conditions +-------------------------------- + +2.1. Grants + +Each Contributor hereby grants You a world-wide, royalty-free, +non-exclusive license: + +(a) under intellectual property rights (other than patent or trademark) + Licensable by such Contributor to use, reproduce, make available, + modify, display, perform, distribute, and otherwise exploit its + Contributions, either on an unmodified basis, with Modifications, or + as part of a Larger Work; and + +(b) under Patent Claims of such Contributor to make, use, sell, offer + for sale, have made, import, and otherwise transfer either its + Contributions or its Contributor Version. + +2.2. Effective Date + +The licenses granted in Section 2.1 with respect to any Contribution +become effective for each Contribution on the date the Contributor first +distributes such Contribution. + +2.3. Limitations on Grant Scope + +The licenses granted in this Section 2 are the only rights granted under +this License. No additional rights or licenses will be implied from the +distribution or licensing of Covered Software under this License. +Notwithstanding Section 2.1(b) above, no patent license is granted by a +Contributor: + +(a) for any code that a Contributor has removed from Covered Software; + or + +(b) for infringements caused by: (i) Your and any other third party's + modifications of Covered Software, or (ii) the combination of its + Contributions with other software (except as part of its Contributor + Version); or + +(c) under Patent Claims infringed by Covered Software in the absence of + its Contributions. + +This License does not grant any rights in the trademarks, service marks, +or logos of any Contributor (except as may be necessary to comply with +the notice requirements in Section 3.4). + +2.4. Subsequent Licenses + +No Contributor makes additional grants as a result of Your choice to +distribute the Covered Software under a subsequent version of this +License (see Section 10.2) or under the terms of a Secondary License (if +permitted under the terms of Section 3.3). + +2.5. Representation + +Each Contributor represents that the Contributor believes its +Contributions are its original creation(s) or it has sufficient rights +to grant the rights to its Contributions conveyed by this License. + +2.6. Fair Use + +This License is not intended to limit any rights You have under +applicable copyright doctrines of fair use, fair dealing, or other +equivalents. + +2.7. Conditions + +Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted +in Section 2.1. + +3. Responsibilities +------------------- + +3.1. Distribution of Source Form + +All distribution of Covered Software in Source Code Form, including any +Modifications that You create or to which You contribute, must be under +the terms of this License. You must inform recipients that the Source +Code Form of the Covered Software is governed by the terms of this +License, and how they can obtain a copy of this License. You may not +attempt to alter or restrict the recipients' rights in the Source Code +Form. + +3.2. Distribution of Executable Form + +If You distribute Covered Software in Executable Form then: + +(a) such Covered Software must also be made available in Source Code + Form, as described in Section 3.1, and You must inform recipients of + the Executable Form how they can obtain a copy of such Source Code + Form by reasonable means in a timely manner, at a charge no more + than the cost of distribution to the recipient; and + +(b) You may distribute such Executable Form under the terms of this + License, or sublicense it under different terms, provided that the + license for the Executable Form does not attempt to limit or alter + the recipients' rights in the Source Code Form under this License. + +3.3. Distribution of a Larger Work + +You may create and distribute a Larger Work under terms of Your choice, +provided that You also comply with the requirements of this License for +the Covered Software. If the Larger Work is a combination of Covered +Software with a work governed by one or more Secondary Licenses, and the +Covered Software is not Incompatible With Secondary Licenses, this +License permits You to additionally distribute such Covered Software +under the terms of such Secondary License(s), so that the recipient of +the Larger Work may, at their option, further distribute the Covered +Software under the terms of either this License or such Secondary +License(s). + +3.4. Notices + +You may not remove or alter the substance of any license notices +(including copyright notices, patent notices, disclaimers of warranty, +or limitations of liability) contained within the Source Code Form of +the Covered Software, except that You may alter any license notices to +the extent required to remedy known factual inaccuracies. + +3.5. Application of Additional Terms + +You may choose to offer, and to charge a fee for, warranty, support, +indemnity or liability obligations to one or more recipients of Covered +Software. However, You may do so only on Your own behalf, and not on +behalf of any Contributor. You must make it absolutely clear that any +such warranty, support, indemnity, or liability obligation is offered by +You alone, and You hereby agree to indemnify every Contributor for any +liability incurred by such Contributor as a result of warranty, support, +indemnity or liability terms You offer. You may include additional +disclaimers of warranty and limitations of liability specific to any +jurisdiction. + +4. Inability to Comply Due to Statute or Regulation +--------------------------------------------------- + +If it is impossible for You to comply with any of the terms of this +License with respect to some or all of the Covered Software due to +statute, judicial order, or regulation then You must: (a) comply with +the terms of this License to the maximum extent possible; and (b) +describe the limitations and the code they affect. Such description must +be placed in a text file included with all distributions of the Covered +Software under this License. Except to the extent prohibited by statute +or regulation, such description must be sufficiently detailed for a +recipient of ordinary skill to be able to understand it. + +5. Termination +-------------- + +5.1. The rights granted under this License will terminate automatically +if You fail to comply with any of its terms. However, if You become +compliant, then the rights granted under this License from a particular +Contributor are reinstated (a) provisionally, unless and until such +Contributor explicitly and finally terminates Your grants, and (b) on an +ongoing basis, if such Contributor fails to notify You of the +non-compliance by some reasonable means prior to 60 days after You have +come back into compliance. Moreover, Your grants from a particular +Contributor are reinstated on an ongoing basis if such Contributor +notifies You of the non-compliance by some reasonable means, this is the +first time You have received notice of non-compliance with this License +from such Contributor, and You become compliant prior to 30 days after +Your receipt of the notice. + +5.2. If You initiate litigation against any entity by asserting a patent +infringement claim (excluding declaratory judgment actions, +counter-claims, and cross-claims) alleging that a Contributor Version +directly or indirectly infringes any patent, then the rights granted to +You by any and all Contributors for the Covered Software under Section +2.1 of this License shall terminate. + +5.3. In the event of termination under Sections 5.1 or 5.2 above, all +end user license agreements (excluding distributors and resellers) which +have been validly granted by You or Your distributors under this License +prior to termination shall survive termination. + +************************************************************************ +* * +* 6. Disclaimer of Warranty * +* ------------------------- * +* * +* Covered Software is provided under this License on an "as is" * +* basis, without warranty of any kind, either expressed, implied, or * +* statutory, including, without limitation, warranties that the * +* Covered Software is free of defects, merchantable, fit for a * +* particular purpose or non-infringing. The entire risk as to the * +* quality and performance of the Covered Software is with You. * +* Should any Covered Software prove defective in any respect, You * +* (not any Contributor) assume the cost of any necessary servicing, * +* repair, or correction. This disclaimer of warranty constitutes an * +* essential part of this License. No use of any Covered Software is * +* authorized under this License except under this disclaimer. * +* * +************************************************************************ + +************************************************************************ +* * +* 7. Limitation of Liability * +* -------------------------- * +* * +* Under no circumstances and under no legal theory, whether tort * +* (including negligence), contract, or otherwise, shall any * +* Contributor, or anyone who distributes Covered Software as * +* permitted above, be liable to You for any direct, indirect, * +* special, incidental, or consequential damages of any character * +* including, without limitation, damages for lost profits, loss of * +* goodwill, work stoppage, computer failure or malfunction, or any * +* and all other commercial damages or losses, even if such party * +* shall have been informed of the possibility of such damages. This * +* limitation of liability shall not apply to liability for death or * +* personal injury resulting from such party's negligence to the * +* extent applicable law prohibits such limitation. Some * +* jurisdictions do not allow the exclusion or limitation of * +* incidental or consequential damages, so this exclusion and * +* limitation may not apply to You. * +* * +************************************************************************ + +8. Litigation +------------- + +Any litigation relating to this License may be brought only in the +courts of a jurisdiction where the defendant maintains its principal +place of business and such litigation shall be governed by laws of that +jurisdiction, without reference to its conflict-of-law provisions. +Nothing in this Section shall prevent a party's ability to bring +cross-claims or counter-claims. + +9. Miscellaneous +---------------- + +This License represents the complete agreement concerning the subject +matter hereof. If any provision of this License is held to be +unenforceable, such provision shall be reformed only to the extent +necessary to make it enforceable. Any law or regulation which provides +that the language of a contract shall be construed against the drafter +shall not be used to construe this License against a Contributor. + +10. Versions of the License +--------------------------- + +10.1. New Versions + +Mozilla Foundation is the license steward. Except as provided in Section +10.3, no one other than the license steward has the right to modify or +publish new versions of this License. Each version will be given a +distinguishing version number. + +10.2. Effect of New Versions + +You may distribute the Covered Software under the terms of the version +of the License under which You originally received the Covered Software, +or under the terms of any subsequent version published by the license +steward. + +10.3. Modified Versions + +If you create software not governed by this License, and you want to +create a new license for such software, you may create and use a +modified version of this License if you rename the license and remove +any references to the name of the license steward (except to note that +such modified license differs from this License). + +10.4. Distributing Source Code Form that is Incompatible With Secondary +Licenses + +If You choose to distribute Source Code Form that is Incompatible With +Secondary Licenses under the terms of this version of the License, the +notice described in Exhibit B of this License must be attached. + +Exhibit A - Source Code Form License Notice +------------------------------------------- + + This Source Code Form is subject to the terms of the Mozilla Public + License, v. 2.0. If a copy of the MPL was not distributed with this + file, You can obtain one at http://mozilla.org/MPL/2.0/. + +If it is not possible or desirable to put the notice in a particular +file, then You may include the notice in a location (such as a LICENSE +file in a relevant directory) where a recipient would be likely to look +for such a notice. + +You may add additional accurate notices of copyright ownership. + +Exhibit B - "Incompatible With Secondary Licenses" Notice +--------------------------------------------------------- + + This Source Code Form is "Incompatible With Secondary Licenses", as + defined by the Mozilla Public License, v. 2.0. diff --git a/src/isct/cdt/LocatorKDTree.h b/src/isct/cdt/LocatorKDTree.h new file mode 100644 index 00000000..06aa8062 --- /dev/null +++ b/src/isct/cdt/LocatorKDTree.h @@ -0,0 +1,81 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at https://mozilla.org/MPL/2.0/. */ + +/** + * @file + * Adapter between for KDTree and CDT + */ + +#ifndef CDT_POINTKDTREE_H +#define CDT_POINTKDTREE_H + +#include "CDTUtils.h" +#include "KDTree.h" + +namespace CDT +{ + +/// KD-tree holding points +template < + typename TCoordType, + size_t NumVerticesInLeaf = 32, + size_t InitialStackDepth = 32, + size_t StackDepthIncrement = 32> +class LocatorKDTree +{ +public: + /// Initialize KD-tree with points + void initialize(const std::vector >& points) + { + typedef V2d V2d_t; + V2d_t min = points.front(); + V2d_t max = min; + typedef typename std::vector::const_iterator Cit; + for(Cit it = points.begin(); it != points.end(); ++it) + { + min = V2d_t(std::min(min.x, it->x), std::min(min.y, it->y)); + max = V2d_t(std::max(max.x, it->x), std::max(max.y, it->y)); + } + m_kdTree = KDTree_t(min, max); + for(VertInd i(0); i < points.size(); ++i) + { + m_kdTree.insert(i, points); + } + } + /// Add point to KD-tree + void addPoint(const VertInd i, const std::vector >& points) + { + m_kdTree.insert(i, points); + } + /// Find nearest point using R-tree + VertInd nearPoint( + const V2d& pos, + const std::vector >& points) const + { + return m_kdTree.nearest(pos, points).second; + } + + CDT::VertInd size() const + { + return m_kdTree.size(); + } + + bool empty() const + { + return !size(); + } + +private: + typedef KDTree::KDTree< + TCoordType, + NumVerticesInLeaf, + InitialStackDepth, + StackDepthIncrement> + KDTree_t; + KDTree_t m_kdTree; +}; + +} // namespace CDT + +#endif diff --git a/src/isct/cdt/Triangulation.h b/src/isct/cdt/Triangulation.h new file mode 100644 index 00000000..91949352 --- /dev/null +++ b/src/isct/cdt/Triangulation.h @@ -0,0 +1,1160 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at https://mozilla.org/MPL/2.0/. */ + +/** + * @file + * Triangulation class + */ + +#ifndef CDT_vW1vZ0lO8rS4gY4uI4fB +#define CDT_vW1vZ0lO8rS4gY4uI4fB + +#include "CDTUtils.h" +#include "LocatorKDTree.h" + +#include +#include +#include +#include +#include +#include +#include +#include + +/// Namespace containing triangulation functionality +namespace CDT +{ + +/// @addtogroup API +/// @{ + +/** + * Enum of strategies specifying order in which a range of vertices is inserted + * @note VertexInsertionOrder::Randomized will only randomize order of + * inserting in triangulation, vertex indices will be preserved as they were + * specified in the final triangulation + */ +struct CDT_EXPORT VertexInsertionOrder +{ + /** + * The Enum itself + * @note needed to pre c++11 compilers that don't support 'class enum' + */ + enum Enum + { + /** + * Automatic insertion order optimized for better performance + * @details breadth-first traversal of a Kd-tree for initial bulk-load, + * randomized for subsequent insertions + */ + Auto, + /// insert vertices in same order they are provided + AsProvided, + }; +}; + +/// Enum of what type of geometry used to embed triangulation into +struct CDT_EXPORT SuperGeometryType +{ + /** + * The Enum itself + * @note needed to pre c++11 compilers that don't support 'class enum' + */ + enum Enum + { + SuperTriangle, ///< conventional super-triangle + Custom, ///< user-specified custom geometry (e.g., grid) + }; +}; + +/** + * Enum of strategies for treating intersecting constraint edges + */ +struct CDT_EXPORT IntersectingConstraintEdges +{ + /** + * The Enum itself + * @note needed to pre c++11 compilers that don't support 'class enum' + */ + enum Enum + { + NotAllowed, ///< constraint edge intersections are not allowed + TryResolve, ///< attempt to resolve constraint edge intersections + /** + * No checks: slightly faster but less safe. + * User must provide a valid input without intersecting constraints. + */ + DontCheck, + }; +}; + +/** + * Type used for storing layer depths for triangles + * @note LayerDepth should support 60K+ layers, which could be to much or + * too little for some use cases. Feel free to re-define this typedef. + */ +typedef unsigned short LayerDepth; +typedef LayerDepth BoundaryOverlapCount; + +/** + * Contains source location info: file, function, line + */ +class SourceLocation +{ +public: + /// Constructor + SourceLocation(const std::string& file, const std::string& func, int line) + : m_file(file) + , m_func(func) + , m_line(line) + {} + /// source file + const std::string& file() const + { + return m_file; + } + /// source function + const std::string& func() const + { + return m_func; + } + /// source line + int line() const + { + return m_line; + } + +private: + std::string m_file; + std::string m_func; + int m_line; +}; + +/// Macro for getting source location +#define CDT_SOURCE_LOCATION \ + SourceLocation(std::string(__FILE__), std::string(__func__), __LINE__) + +/** + * Base class for errors. Contains error description and source location: file, + * function, line + */ +class Error : public std::runtime_error +{ +public: + /// Constructor + Error(const std::string& description, const SourceLocation& srcLoc) + : std::runtime_error( + description + "\nin '" + srcLoc.func() + "' at " + srcLoc.file() + + ":" + CDT::to_string(srcLoc.line())) + , m_description(description) + , m_srcLoc(srcLoc) + {} + /// Get error description + const std::string& description() const + { + return m_description; + } + /// Get source location from where the error was thrown + const SourceLocation& sourceLocation() const + { + return m_srcLoc; + } + +private: + std::string m_description; + SourceLocation m_srcLoc; +}; + +/** + * Error thrown when triangulation modification is attempted after it was + * finalized + */ +class FinalizedError : public Error +{ +public: + /// Constructor + FinalizedError(const SourceLocation& srcLoc) + : Error( + "Triangulation was finalized with 'erase...' method. Further " + "modification is not possible.", + srcLoc) + {} +}; + +/** + * Error thrown when duplicate vertex is detected during vertex insertion + */ +class DuplicateVertexError : public Error +{ +public: + /// Constructor + DuplicateVertexError( + const VertInd v1, + const VertInd v2, + const SourceLocation& srcLoc) + : Error( + "Duplicate vertex detected: #" + CDT::to_string(v1) + + " is a duplicate of #" + CDT::to_string(v2), + srcLoc) + , m_v1(v1) + , m_v2(v2) + {} + /// first duplicate + VertInd v1() const + { + return m_v1; + } + /// second duplicate + VertInd v2() const + { + return m_v2; + } + +private: + VertInd m_v1, m_v2; +}; + +/** + * Error thrown when intersecting constraint edges are detected, but + * triangulation is not configured to attempt to resolve them + */ +class IntersectingConstraintsError : public Error +{ +public: + /// Constructor + IntersectingConstraintsError( + const Edge& e1, + const Edge& e2, + const SourceLocation& srcLoc) + : Error( + "Intersecting constraint edges detected: (" + + CDT::to_string(e1.v1()) + ", " + CDT::to_string(e1.v2()) + + ") intersects (" + CDT::to_string(e2.v1()) + ", " + + CDT::to_string(e2.v2()) + ")", + srcLoc) + , m_e1(e1) + , m_e2(e2) + {} + /// first intersecting constraint + const Edge& e1() const + { + return m_e1; + } + /// second intersecting constraint + const Edge& e2() const + { + return m_e2; + } + +private: + Edge m_e1, m_e2; +}; + +#ifdef CDT_ENABLE_CALLBACK_HANDLER + +/** + * What type of vertex is added to the triangulation + */ +struct CDT_EXPORT AddVertexType +{ + /** + * The Enum itself + * @note needed to pre c++11 compilers that don't support 'class enum' + */ + enum Enum + { + /// Original vertex from user input + UserInput, + /// During conforming triangulation edge mid-point is added + FixedEdgeMidpoint, + /// Resolving fixed/constraint edges' intersection + FixedEdgesIntersection, + }; +}; + +/** + * What type of triangle change happened + */ +struct CDT_EXPORT TriangleChangeType +{ + /** + * The Enum itself + * @note needed to pre c++11 compilers that don't support 'class enum' + */ + enum Enum + { + AddedNew, ///< new triangle added to the triangulation + ModifiedExisting, ///< existing triangle was modified + }; +}; + +// parameter names are used for documentation purposes, even if they are un-used +// in the interface's default implementation +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wunused-parameter" + +/** + * Interface for the callback handler that user can derive from and inject into + * the triangulation to monitor certain events or order aborting the calculation + */ +class CDT_EXPORT ICallbackHandler +{ +public: + /// Virtual destructor + virtual ~ICallbackHandler() + {} + + /** + * Called when super-triangle is added. + * 1.Added three new vertices with indices 0, 1, 2 + * 2. Added one a new triangle with an index 0 + */ + virtual void onAddSuperTriangle() + {} + + /** + * Called when inserted vertex is inside a triangle. + * The triangle is split in three: original trianlge is re-purposed and two + * new triangles are added + * @param iRepurposedTri index of original triangle containing the point + * that will be modified (re-purposed) + * @param iNewTri1 index of first added new triangle + * @param iNewTri2 index of second added new triangle + */ + virtual void onInsertVertexInsideTriangle( + const TriInd iRepurposedTri, + const TriInd iNewTri1, + const TriInd iNewTri2) + {} + + /** + * Called when inserted vertex is on an edge. + * Two triangles sharing an edge are split in four:original triangles are + * re-purposed and two new triangles are added. + * @param iRepurposedTri1 index of first original triangle sharing an edge + * that will be modified (re-purposed) + * @param iRepurposedTri2 index of second original triangle sharing + * an edge that will be modified (re-purposed) + * @param iNewTri1 index of first added new triangle + * @param iNewTri2 index of second added new triangle + */ + virtual void onInsertVertexOnEdge( + const TriInd iRepurposedTri1, + const TriInd iRepurposedTri2, + const TriInd iNewTri1, + const TriInd iNewTri2) + {} + + /** + * Called just before an edge between tro triangles is flipped + * @param iT index of the first triangle sharing an edge + * @param iTopo index of the second triangle sharing an edge + */ + virtual void onFlipEdge(const TriInd iT, const TriInd iTopo) + {} + + /** + * Called at the start of adding new vertex to the triangulation + * @param iV index of the vertex + * @param vertexType what type of vertex is being added + */ + virtual void + onAddVertexStart(const VertInd iV, const AddVertexType::Enum vertexType) + {} + + /** + * Called at the start of adding a constraint edge to the triangulation + * @param edge constraint that is added/enforced + */ + virtual void onAddEdgeStart(const Edge& edge) + {} + + /** + * Called when inserting a constraint edge causes polygon containing + * triangles to be re-triangulated + * @tris triangles in the polygon that will be re-triangulated and triangles + * re-purposed + */ + virtual void onReTriangulatePolygon(const std::vector& tris) + {} + + /** + * Tells whether the user wants to abort the triangulation at the earliest + * opportunity + */ + virtual bool isAbortCalculation() const + { + return false; + }; +}; + +// parameter names are used for documentation purposes, even if they are +// un-used in the interface's default implementation +#pragma GCC diagnostic pop + +#endif + +/** + * @defgroup Triangulation Triangulation Class + * Class performing triangulations. + */ +/// @{ + +/** + * Data structure representing a 2D constrained Delaunay triangulation + * + * @tparam T type of vertex coordinates (e.g., float, double) + * @tparam TNearPointLocator class providing locating near point for efficiently + * inserting new points. Provides methods: 'addPoint(vPos, iV)' and + * 'nearPoint(vPos) -> iV' + */ +template > +class CDT_EXPORT Triangulation +{ +public: + typedef std::vector > V2dVec; ///< Vertices vector + V2dVec vertices; ///< triangulation's vertices + TriangleVec triangles; ///< triangulation's triangles + EdgeUSet fixedEdges; ///< triangulation's constraints (fixed edges) + + /** Stores count of overlapping boundaries for a fixed edge. If no entry is + * present for an edge: no boundaries overlap. + * @note map only has entries for fixed for edges that represent overlapping + * boundaries + * @note needed for handling depth calculations and hole-removel in case of + * overlapping boundaries + */ + unordered_map overlapCount; + + /** Stores list of original edges represented by a given fixed edge + * @note map only has entries for edges where multiple original fixed edges + * overlap or where a fixed edge is a part of original edge created by + * conforming Delaunay triangulation vertex insertion + */ + unordered_map pieceToOriginals; + + /*____ API _____*/ + /// Default constructor + Triangulation(); + /** + * Constructor + * @param vertexInsertionOrder strategy used for ordering vertex insertions + */ + explicit Triangulation(VertexInsertionOrder::Enum vertexInsertionOrder); + /** + * Constructor + * @param vertexInsertionOrder strategy used for ordering vertex insertions + * @param intersectingEdgesStrategy strategy for treating intersecting + * constraint edges + * @param minDistToConstraintEdge distance within which point is considered + * to be lying on a constraint edge. Used when adding constraints to the + * triangulation. + */ + Triangulation( + VertexInsertionOrder::Enum vertexInsertionOrder, + IntersectingConstraintEdges::Enum intersectingEdgesStrategy, + T minDistToConstraintEdge); + /** + * Constructor + * @param vertexInsertionOrder strategy used for ordering vertex insertions + * @param nearPtLocator class providing locating near point for efficiently + * inserting new points + * @param intersectingEdgesStrategy strategy for treating intersecting + * constraint edges + * @param minDistToConstraintEdge distance within which point is considered + * to be lying on a constraint edge. Used when adding constraints to the + * triangulation. + */ + Triangulation( + VertexInsertionOrder::Enum vertexInsertionOrder, + const TNearPointLocator& nearPtLocator, + IntersectingConstraintEdges::Enum intersectingEdgesStrategy, + T minDistToConstraintEdge); + /** + * Insert custom point-types specified by iterator range and X/Y-getters + * @tparam TVertexIter iterator that dereferences to custom point type + * @tparam TGetVertexCoordX function object getting x coordinate from + * vertex. Getter signature: const TVertexIter::value_type& -> T + * @tparam TGetVertexCoordY function object getting y coordinate from + * vertex. Getter signature: const TVertexIter::value_type& -> T + * @param first beginning of the range of vertices to add + * @param last end of the range of vertices to add + * @param getX getter of X-coordinate + * @param getY getter of Y-coordinate + */ + template < + typename TVertexIter, + typename TGetVertexCoordX, + typename TGetVertexCoordY> + void insertVertices( + TVertexIter first, + TVertexIter last, + TGetVertexCoordX getX, + TGetVertexCoordY getY); + /** + * Insert vertices into triangulation + * @param vertices vector of vertices to insert + */ + void insertVertices(const std::vector >& vertices); + /** + * Insert constraint edges into triangulation for Constrained Delaunay + * Triangulation (for example see figure below). + * + * Uses only original vertices: no new verties are added + * + * CDT show-case: constrained and + * conforming triangulations, convex hulls, automatically removing holes + * + * @note Each fixed edge is inserted by deleting the triangles it crosses, + * followed by the triangulation of the polygons on each side of the edge. + * No new vertices are inserted. + * @note If some edge appears more than once in the input this means that + * multiple boundaries overlap at the edge and impacts how hole detection + * algorithm of Triangulation::eraseOuterTrianglesAndHoles works. + * Make sure there are no erroneous duplicates. + * @tparam TEdgeIter iterator that dereferences to custom edge type + * @tparam TGetEdgeVertexStart function object getting start vertex index + * from an edge. + * Getter signature: const TEdgeIter::value_type& -> CDT::VertInd + * @tparam TGetEdgeVertexEnd function object getting end vertex index from + * an edge. Getter signature: const TEdgeIter::value_type& -> CDT::VertInd + * @param first beginning of the range of edges to add + * @param last end of the range of edges to add + * @param getStart getter of edge start vertex index + * @param getEnd getter of edge end vertex index + */ + template < + typename TEdgeIter, + typename TGetEdgeVertexStart, + typename TGetEdgeVertexEnd> + void insertEdges( + TEdgeIter first, + TEdgeIter last, + TGetEdgeVertexStart getStart, + TGetEdgeVertexEnd getEnd); + /** + * Insert constraint edges into triangulation for Constrained Delaunay + * Triangulation (for example see figure below). + * + * Uses only original vertices: no new verties are added + * + * CDT show-case: constrained and + * conforming triangulations, convex hulls, automatically removing holes + * + * @note Each fixed edge is inserted by deleting the triangles it crosses, + * followed by the triangulation of the polygons on each side of the edge. + * No new vertices are inserted. + * @note If some edge appears more than once in the input this means that + * multiple boundaries overlap at the edge and impacts how hole detection + * algorithm of Triangulation::eraseOuterTrianglesAndHoles works. + * Make sure there are no erroneous duplicates. + * @tparam edges constraint edges + */ + void insertEdges(const std::vector& edges); + /** + * Insert constraint edges into triangulation for Conforming Delaunay + * Triangulation (for example see figure below). + * + * May add new vertices. + * + * CDT show-case: constrained and + * conforming triangulations, convex hulls, automatically removing holes + * + * @note For each fixed edge that is not present in the triangulation its + * midpoint is recursively added until the original edge is represented by a + * sequence of its pieces. New vertices are inserted. + * @note If some edge appears more than once the input this + * means that multiple boundaries overlap at the edge and impacts how hole + * detection algorithm of Triangulation::eraseOuterTrianglesAndHoles works. + * Make sure there are no erroneous duplicates. + * @tparam TEdgeIter iterator that dereferences to custom edge type + * @tparam TGetEdgeVertexStart function object getting start vertex index + * from an edge. + * Getter signature: const TEdgeIter::value_type& -> CDT::VertInd + * @tparam TGetEdgeVertexEnd function object getting end vertex index from + * an edge. Getter signature: const TEdgeIter::value_type& -> CDT::VertInd + * @param first beginning of the range of edges to add + * @param last end of the range of edges to add + * @param getStart getter of edge start vertex index + * @param getEnd getter of edge end vertex index + */ + template < + typename TEdgeIter, + typename TGetEdgeVertexStart, + typename TGetEdgeVertexEnd> + void conformToEdges( + TEdgeIter first, + TEdgeIter last, + TGetEdgeVertexStart getStart, + TGetEdgeVertexEnd getEnd); + /** + * Insert constraint edges into triangulation for Conforming Delaunay + * Triangulation (for example see figure below). + * + * May add new vertices. + * + * CDT show-case: constrained and + * conforming triangulations, convex hulls, automatically removing holes + * + * @note For each fixed edge that is not present in the triangulation its + * midpoint is recursively added until the original edge is represented by a + * sequence of its pieces. New vertices are inserted. + * @note If some edge appears more than once the input this + * means that multiple boundaries overlap at the edge and impacts how hole + * detection algorithm of Triangulation::eraseOuterTrianglesAndHoles works. + * Make sure there are no erroneous duplicates. + * @tparam edges edges to conform to + */ + void conformToEdges(const std::vector& edges); + /** + * Erase triangles adjacent to super triangle + * + * @note does nothing if custom geometry is used + */ + void eraseSuperTriangle(); + /// Erase triangles outside of constrained boundary using growing + void eraseOuterTriangles(); + /** + * Erase triangles outside of constrained boundary and auto-detected holes + * + * @note detecting holes relies on layer peeling based on layer depth + * @note supports overlapping or touching boundaries + */ + void eraseOuterTrianglesAndHoles(); + /** + * Call this method after directly setting custom super-geometry via + * vertices and triangles members + */ + void initializedWithCustomSuperGeometry(); + + /** + * Check if the triangulation was finalized with `erase...` method and + * super-triangle was removed. + * @return true if triangulation is finalized, false otherwise + */ + bool isFinalized() const; + + /** + * Calculate depth of each triangle in constraint triangulation. Supports + * overlapping boundaries. + * + * Perform depth peeling from super triangle to outermost boundary, + * then to next boundary and so on until all triangles are traversed.@n + * For example depth is: + * - 0 for triangles outside outermost boundary + * - 1 for triangles inside boundary but outside hole + * - 2 for triangles in hole + * - 3 for triangles in island and so on... + * @return vector where element at index i stores depth of i-th triangle + */ + std::vector calculateTriangleDepths() const; + +#ifdef CDT_ENABLE_CALLBACK_HANDLER + /** + * Set user-provided callback handler + * @warning callback handler must outlive the triangulation class + * @warning triangulatio does not own the callback and does not try to free + * it + * @param callbackHandler pointer to the callback handler + */ + void setCallbackHandler(ICallbackHandler* callbackHandler); +#endif + /** + * @defgroup Advanced Advanced Triangulation Methods + * Advanced methods for manually modifying the triangulation from + * outside. Please only use them when you know what you are doing. + */ + /// @{ + + /** + * Flip an edge between two triangle. + * @note Advanced method for manually modifying the triangulation from + * outside. Please call it when you know what you are doing. + * @param iT first triangle + * @param iTopo second triangle + */ + void flipEdge(TriInd iT, TriInd iTopo); + + /** + * Flip edge between two triangles given all the information such as + * triangle vertices and neighbors + */ + void flipEdge( + TriInd iT, + TriInd iTopo, + VertInd v1, + VertInd v2, + VertInd v3, + VertInd v4, + TriInd n1, + TriInd n2, + TriInd n3, + TriInd n4); + + /** + * Remove triangles with specified indices. + * Adjust internal triangulation state accordingly. + * @param removedTriangles indices of triangles to remove + */ + void removeTriangles(const TriIndUSet& removedTriangles); + + /// Access internal vertex adjacent triangles + TriIndVec& VertTrisInternal(); + /// Access internal vertex adjacent triangles + const TriIndVec& VertTrisInternal() const; + /// @} + +private: + /*____ Detail __*/ + void addSuperTriangle(const Box2d& box); + void addNewVertex(const V2d& pos, TriInd iT); + void insertVertex(VertInd iVert); + void insertVertex(VertInd iVert, VertInd walkStart); + void ensureDelaunayByEdgeFlips(VertInd iV1, std::stack& triStack); + /// Flip fixed edges and return a list of flipped fixed edges + std::vector insertVertex_FlipFixedEdges(VertInd iV1); + + /// State for an iteration of triangulate pseudo-polygon + typedef tuple + TriangulatePseudoPolygonTask; + + /** + * Insert an edge into constraint Delaunay triangulation + * @param edge edge to insert + * @param originalEdge original edge inserted edge is part of + * @param[in,out] remaining parts of the edge that still need to + * be inserted + * @param[in,out] tppIterations stack to be used for storing iterations of + * triangulating pseudo-polygon + * @note in-out state (@param remaining @param tppIterations) is shared + * between different runs for performance gains (reducing memory + * allocations) + */ + void insertEdge( + Edge edge, + Edge originalEdge, + EdgeVec& remaining, + std::vector& tppIterations); + + /** + * Insert an edge or its part into constraint Delaunay triangulation + * @param edge edge to insert + * @param originalEdge original edge inserted edge is part of + * @param[in,out] remainingStack parts of the edge that still need to + * be inserted + * @param[in,out] tppIterations stack to be used for storing iterations of + * triangulating pseudo-polygon + * @note in-out state (@param remaining @param tppIterations) is shared + * between different runs for performance gains (reducing memory + * allocations) + */ + void insertEdgeIteration( + Edge edge, + Edge originalEdge, + EdgeVec& remaining, + std::vector& tppIterations); + + /// State for iteration of conforming to edge + typedef tuple ConformToEdgeTask; + + /** + * Conform Delaunay triangulation to a fixed edge by recursively inserting + * mid point of the edge and then conforming to its halves + * @param edge fixed edge to conform to + * @param originals original edges that new edge is piece of + * @param overlaps count of overlapping boundaries at the edge. Only used + * when re-introducing edge with overlaps > 0 + * @param[in,out] remaining remaining edge parts to be conformed to + * @note in-out state (@param remaining @param reintroduce) is shared + * between different runs for performance gains (reducing memory + * allocations) + */ + void conformToEdge( + Edge edge, + EdgeVec originals, + BoundaryOverlapCount overlaps, + std::vector& remaining); + + /** + * Iteration of conform to fixed edge. + * @param edge fixed edge to conform to + * @param originals original edges that new edge is piece of + * @param overlaps count of overlapping boundaries at the edge. Only used + * when re-introducing edge with overlaps > 0 + * @param[in,out] remaining remaining edge parts + * @note in-out state (@param remaining @param reintroduce) is shared + * between different runs for performance gains (reducing memory + * allocations) + */ + void conformToEdgeIteration( + Edge edge, + const EdgeVec& originals, + BoundaryOverlapCount overlaps, + std::vector& remaining); + + tuple intersectedTriangle( + VertInd iA, + const V2d& a, + const V2d& b, + T orientationTolerance = T(0)) const; + /// Returns indices of three resulting triangles + std::stack insertVertexInsideTriangle(VertInd v, TriInd iT); + /// Returns indices of four resulting triangles + std::stack insertVertexOnEdge( + VertInd v, + TriInd iT1, + TriInd iT2, + const bool doHandleFixedSplitEdge = false); + array trianglesAt(const V2d& pos) const; + array + walkingSearchTrianglesAt(VertInd iV, VertInd startVertex) const; + TriInd walkTriangles(VertInd startVertex, const V2d& pos) const; + /// Given triangle and its vertex find opposite triangle and the other three + /// vertices and surrounding neighbors + void edgeFlipInfo( + TriInd iT, + VertInd iV1, + TriInd& iTopo, + VertInd& iV2, + VertInd& iV3, + VertInd& iV4, + TriInd& n1, + TriInd& n2, + TriInd& n3, + TriInd& n4); + bool isFlipNeeded(VertInd iV1, VertInd iV2, VertInd iV3, VertInd iV4) const; + void changeNeighbor(TriInd iT, TriInd oldNeighbor, TriInd newNeighbor); + void changeNeighbor( + TriInd iT, + VertInd iVedge1, + VertInd iVedge2, + TriInd newNeighbor); + void triangulatePseudoPolygon( + const std::vector& poly, + unordered_map& outerTris, + TriInd iT, + TriInd iN, + std::vector& trianglesToReuse, + std::vector& iterations); + void triangulatePseudoPolygonIteration( + const std::vector& poly, + unordered_map& outerTris, + std::vector& trianglesToReuse, + std::vector& iterations); + IndexSizeType findDelaunayPoint( + const std::vector& poly, + IndexSizeType iA, + IndexSizeType iB) const; + TriInd addTriangle(const Triangle& t); + TriInd addTriangle(); + /** + * Remove super-triangle (if used) and triangles with specified indices. + * Adjust internal triangulation state accordingly. + * @removedTriangles indices of triangles to remove + */ + void finalizeTriangulation(const TriIndUSet& removedTriangles); + TriIndUSet growToBoundary(std::stack seeds) const; + void fixEdge(const Edge& edge); + void fixEdge(const Edge& edge, const Edge& originalEdge); + /** + * Split existing constraint (fixed) edge + * @param edge fixed edge to split + * @param iSplitVert index of the vertex to be used as a split vertex + */ + void splitFixedEdge(const Edge& edge, const VertInd iSplitVert); + /** + * Add a vertex that splits an edge into the triangulation + * @param splitVert position of split vertex + * @param iT index of a first triangle adjacent to the split edge + * @param iTopo index of a second triangle adjacent to the split edge + * (opposed to the first triangle) + * @return index of a newly added split vertex + */ + VertInd addSplitEdgeVertex( + const V2d& splitVert, + const TriInd iT, + const TriInd iTopo); + /** + * Split fixed edge and add a split vertex into the triangulation + * @param edge fixed edge to split + * @param splitVert position of split vertex + * @param iT index of a first triangle adjacent to the split edge + * @param iTopo index of a second triangle adjacent to the split edge + * (opposed to the first triangle) + * @return index of a newly added split vertex + */ + VertInd splitFixedEdgeAt( + const Edge& edge, + const V2d& splitVert, + const TriInd iT, + const TriInd iTopo); + /** + * Depth-peel a layer in triangulation, used when calculating triangle + * depths + * + * It takes starting seed triangles, traverses neighboring triangles, and + * assigns given layer depth to the traversed triangles. Traversal is + * blocked by constraint edges. Triangles behind constraint edges are + * recorded as seeds of next layer and returned from the function. + * + * @param seeds indices of seed triangles + * @param layerDepth current layer's depth to mark triangles with + * @param[in, out] triDepths depths of triangles + * @return triangles of the deeper layers that are adjacent to the peeled + * layer. To be used as seeds when peeling deeper layers. + */ + unordered_map peelLayer( + std::stack seeds, + LayerDepth layerDepth, + std::vector& triDepths) const; + + void insertVertices_AsProvided(VertInd superGeomVertCount); + void insertVertices_Randomized(VertInd superGeomVertCount); + void insertVertices_KDTreeBFS(VertInd superGeomVertCount, Box2d box); + std::pair edgeTriangles(VertInd a, VertInd b) const; + bool hasEdge(VertInd a, VertInd b) const; + void setAdjacentTriangle(const VertInd v, const TriInd t); + void pivotVertexTriangleCW(VertInd v); + /// Add vertex to nearest-point locator if locator is initialized + void tryAddVertexToLocator(const VertInd v); + /// Perform lazy initialization of nearest-point locator after the Kd-tree + /// BFS bulk load if necessary + void tryInitNearestPointLocator(); + + TNearPointLocator m_nearPtLocator; + VertInd m_nTargetVerts; + SuperGeometryType::Enum m_superGeomType; + VertexInsertionOrder::Enum m_vertexInsertionOrder; + IntersectingConstraintEdges::Enum m_intersectingEdgesStrategy; + T m_minDistToConstraintEdge; + TriIndVec m_vertTris; /// one triangle adjacent to each vertex +#ifdef CDT_ENABLE_CALLBACK_HANDLER + ICallbackHandler* m_callbackHandler; /// user-provided callback handler +#endif +}; + +/// @} +/// @} + +namespace detail +{ + +/// SplitMix64 pseudo-random number generator +struct SplitMix64RandGen +{ + typedef unsigned long long uint64; ///< uint64 type + uint64 m_state; ///< PRNG's state + /// constructor + explicit SplitMix64RandGen(uint64 state) + : m_state(state) + {} + /// default constructor + explicit SplitMix64RandGen() + : m_state(0) + {} + /// functor's operator + uint64 operator()() + { + uint64 z = (m_state += 0x9e3779b97f4a7c15); + z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9; + z = (z ^ (z >> 27)) * 0x94d049bb133111eb; + return z ^ (z >> 31); + } +}; + +/// backport from c++11 +template +void random_shuffle(RandomIt first, RandomIt last) +{ + detail::SplitMix64RandGen prng; + typename std::iterator_traits::difference_type i, n; + n = last - first; + for(i = n - 1; i > 0; --i) + { + std::swap(first[i], first[prng() % (i + 1)]); + } +} + +/// backport from c++11 +template +void iota(ForwardIt first, ForwardIt last, T value) +{ + while(first != last) + { + *first++ = value; + ++value; + } +} + +} // namespace detail + +//----------------------- +// Triangulation methods +//----------------------- +template +template < + typename TVertexIter, + typename TGetVertexCoordX, + typename TGetVertexCoordY> +void Triangulation::insertVertices( + const TVertexIter first, + const TVertexIter last, + TGetVertexCoordX getX, + TGetVertexCoordY getY) +{ + if(isFinalized()) + handleException(FinalizedError(CDT_SOURCE_LOCATION)); + + const bool isFirstTime = vertices.empty(); + + // + // performance optimization: pre-allocate triangles and vertices + // + const std::size_t nNewVertices = std::distance(first, last); + std::size_t exactCapacityTriangles = triangles.size() + 2 * nNewVertices; + std::size_t exactCapacityVertices = vertices.size() + nNewVertices; + if(isFirstTime) // account for adding super-triangle on the first run + { + exactCapacityTriangles += 1; + exactCapacityVertices += nSuperTriangleVertices; + } + std::size_t capacityTriangles = exactCapacityTriangles; + std::size_t capacityVertices = exactCapacityVertices; + // to avoid re-allocation and unused memory + // over-allocate by a fixed factor + // when constraint edge intersections are resolved and vertices are many + // because vertex is added for each intersection + // and total number of intersections is unknown + const VertInd overAllocationVerticesThreshold(1000); + const T overAllocationFactor(1.1); + const bool isOverPreAllocated = + m_intersectingEdgesStrategy == + IntersectingConstraintEdges::TryResolve && + VertInd(nNewVertices) >= overAllocationVerticesThreshold; + if(isOverPreAllocated) + { + capacityTriangles *= overAllocationFactor; + capacityVertices *= overAllocationFactor; + } + triangles.reserve(capacityTriangles); + vertices.reserve(capacityVertices); + m_vertTris.reserve(capacityVertices); + + Box2d box; + if(isFirstTime) + { + box.envelopPoints(first, last, getX, getY); + addSuperTriangle(box); + } + tryInitNearestPointLocator(); + const VertInd nExistingVerts = static_cast(vertices.size()); + + for(TVertexIter it = first; it != last; ++it) + addNewVertex(V2d(getX(*it), getY(*it)), noNeighbor); + + switch(m_vertexInsertionOrder) + { + case VertexInsertionOrder::AsProvided: + insertVertices_AsProvided(nExistingVerts); + break; + case VertexInsertionOrder::Auto: + isFirstTime ? insertVertices_KDTreeBFS(nExistingVerts, box) + : insertVertices_Randomized(nExistingVerts); + break; + } + +// make sure pre-allocation was correct +#ifdef CDT_ENABLE_CALLBACK_HANDLER + assert( + !m_callbackHandler || m_callbackHandler->isAbortCalculation() || + (vertices.size() == exactCapacityVertices)); + assert( + !m_callbackHandler || m_callbackHandler->isAbortCalculation() || + (triangles.size() == exactCapacityTriangles)); +#else + assert(vertices.size() == exactCapacityVertices); + assert(triangles.size() == exactCapacityTriangles); +#endif +} + +template +template < + typename TEdgeIter, + typename TGetEdgeVertexStart, + typename TGetEdgeVertexEnd> +void Triangulation::insertEdges( + TEdgeIter first, + const TEdgeIter last, + TGetEdgeVertexStart getStart, + TGetEdgeVertexEnd getEnd) +{ + if(isFinalized()) + handleException(FinalizedError(CDT_SOURCE_LOCATION)); + + std::vector tppIterations; + EdgeVec remaining; + for(; first != last; ++first) + { +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler && m_callbackHandler->isAbortCalculation()) + { + return; + } +#endif + // +3 to account for super-triangle vertices + const Edge edge( + VertInd(getStart(*first) + m_nTargetVerts), + VertInd(getEnd(*first) + m_nTargetVerts)); + insertEdge(edge, edge, remaining, tppIterations); + } +} + +template +template < + typename TEdgeIter, + typename TGetEdgeVertexStart, + typename TGetEdgeVertexEnd> +void Triangulation::conformToEdges( + TEdgeIter first, + const TEdgeIter last, + TGetEdgeVertexStart getStart, + TGetEdgeVertexEnd getEnd) +{ + if(isFinalized()) + handleException(FinalizedError(CDT_SOURCE_LOCATION)); + + tryInitNearestPointLocator(); + // state shared between different runs for performance gains + std::vector remaining; + for(; first != last; ++first) + { +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler && m_callbackHandler->isAbortCalculation()) + { + return; + } +#endif + // +3 to account for super-triangle vertices + const Edge e( + VertInd(getStart(*first) + m_nTargetVerts), + VertInd(getEnd(*first) + m_nTargetVerts)); + conformToEdge(e, EdgeVec(1, e), 0, remaining); + } +} + +} // namespace CDT + +#ifndef CDT_USE_AS_COMPILED_LIBRARY +#include "Triangulation.hpp" +#endif + +#endif // header-guard diff --git a/src/isct/cdt/Triangulation.hpp b/src/isct/cdt/Triangulation.hpp new file mode 100644 index 00000000..fde546e5 --- /dev/null +++ b/src/isct/cdt/Triangulation.hpp @@ -0,0 +1,2178 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at https://mozilla.org/MPL/2.0/. */ + +/** + * @file + * Triangulation class - implementation + */ + +#include "Triangulation.h" +#include "portable_nth_element.hpp" + +#include +#include +#include +#include +#include + +namespace CDT +{ + +typedef std::deque TriDeque; + +namespace detail +{ + +namespace defaults +{ + +const std::size_t nTargetVerts = 0; +const SuperGeometryType::Enum superGeomType = SuperGeometryType::SuperTriangle; +const VertexInsertionOrder::Enum vertexInsertionOrder = + VertexInsertionOrder::Auto; +const IntersectingConstraintEdges::Enum intersectingEdgesStrategy = + IntersectingConstraintEdges::NotAllowed; +const float minDistToConstraintEdge(0); + +} // namespace defaults + +} // namespace detail + +template +Triangulation::Triangulation() + : m_nTargetVerts(detail::defaults::nTargetVerts) + , m_superGeomType(detail::defaults::superGeomType) + , m_vertexInsertionOrder(detail::defaults::vertexInsertionOrder) + , m_intersectingEdgesStrategy(detail::defaults::intersectingEdgesStrategy) + , m_minDistToConstraintEdge(detail::defaults::minDistToConstraintEdge) +#ifdef CDT_ENABLE_CALLBACK_HANDLER + , m_callbackHandler(NULL) +#endif +{} + +template +Triangulation::Triangulation( + const VertexInsertionOrder::Enum vertexInsertionOrder) + : m_nTargetVerts(detail::defaults::nTargetVerts) + , m_superGeomType(detail::defaults::superGeomType) + , m_vertexInsertionOrder(vertexInsertionOrder) + , m_intersectingEdgesStrategy(detail::defaults::intersectingEdgesStrategy) + , m_minDistToConstraintEdge(detail::defaults::minDistToConstraintEdge) +#ifdef CDT_ENABLE_CALLBACK_HANDLER + , m_callbackHandler(NULL) +#endif +{} + +template +Triangulation::Triangulation( + const VertexInsertionOrder::Enum vertexInsertionOrder, + const IntersectingConstraintEdges::Enum intersectingEdgesStrategy, + const T minDistToConstraintEdge) + : m_nTargetVerts(detail::defaults::nTargetVerts) + , m_superGeomType(detail::defaults::superGeomType) + , m_vertexInsertionOrder(vertexInsertionOrder) + , m_intersectingEdgesStrategy(intersectingEdgesStrategy) + , m_minDistToConstraintEdge(minDistToConstraintEdge) +#ifdef CDT_ENABLE_CALLBACK_HANDLER + , m_callbackHandler(NULL) +#endif +{} + +template +Triangulation::Triangulation( + const VertexInsertionOrder::Enum vertexInsertionOrder, + const TNearPointLocator& nearPtLocator, + const IntersectingConstraintEdges::Enum intersectingEdgesStrategy, + const T minDistToConstraintEdge) + : m_nearPtLocator(nearPtLocator) + , m_nTargetVerts(detail::defaults::nTargetVerts) + , m_superGeomType(detail::defaults::superGeomType) + , m_vertexInsertionOrder(vertexInsertionOrder) + , m_intersectingEdgesStrategy(intersectingEdgesStrategy) + , m_minDistToConstraintEdge(minDistToConstraintEdge) +#ifdef CDT_ENABLE_CALLBACK_HANDLER + , m_callbackHandler(NULL) +#endif +{} + +template +void Triangulation::eraseSuperTriangle() +{ + if(m_superGeomType != SuperGeometryType::SuperTriangle) + return; + // find triangles adjacent to super-triangle's vertices + TriIndUSet toErase; + for(TriInd iT(0); iT < TriInd(triangles.size()); ++iT) + { + if(touchesSuperTriangle(triangles[iT])) + toErase.insert(iT); + } + finalizeTriangulation(toErase); +} + +template +void Triangulation::eraseOuterTriangles() +{ + assert(m_vertTris[0] != noNeighbor); + const std::stack seed(std::deque(1, m_vertTris[0])); + const TriIndUSet toErase = growToBoundary(seed); + finalizeTriangulation(toErase); +} + +template +void Triangulation::eraseOuterTrianglesAndHoles() +{ + const std::vector triDepths = calculateTriangleDepths(); + TriIndUSet toErase; + toErase.reserve(triangles.size()); + for(std::size_t iT = 0; iT != triangles.size(); ++iT) + { + if(triDepths[iT] % 2 == 0) + toErase.insert(static_cast(iT)); + } + finalizeTriangulation(toErase); +} + +/// Remap removing super-triangle: subtract 3 from vertices +inline Edge RemapNoSuperTriangle(const Edge& e) +{ + return Edge(VertInd(e.v1() - 3), VertInd(e.v2() - 3)); +} + +template +void Triangulation::removeTriangles( + const TriIndUSet& removedTriangles) +{ + if(removedTriangles.empty()) + return; + // remove triangles and calculate triangle index mapping + TriIndUMap triIndMap; + for(TriInd iT(0), iTnew(0); iT < TriInd(triangles.size()); ++iT) + { + if(removedTriangles.count(iT)) + continue; + triIndMap[iT] = iTnew; + triangles[iTnew] = triangles[iT]; + iTnew++; + } + triangles.erase(triangles.end() - removedTriangles.size(), triangles.end()); + // adjust triangles' neighbors + for(TriInd iT(0); iT < triangles.size(); ++iT) + { + Triangle& t = triangles[iT]; + // update neighbors to account for removed triangles + NeighborsArr3& nn = t.neighbors; + for(NeighborsArr3::iterator n = nn.begin(); n != nn.end(); ++n) + { + if(removedTriangles.count(*n)) + { + *n = noNeighbor; + } + else if(*n != noNeighbor) + { + *n = triIndMap[*n]; + } + } + } +} + +template +TriIndVec& Triangulation::VertTrisInternal() +{ + return m_vertTris; +} + +template +const TriIndVec& Triangulation::VertTrisInternal() const +{ + return m_vertTris; +} + +template +void Triangulation::finalizeTriangulation( + const TriIndUSet& removedTriangles) +{ + m_vertTris = TriIndVec(); + // remove super-triangle + if(m_superGeomType == SuperGeometryType::SuperTriangle) + { + vertices.erase( + vertices.begin(), vertices.begin() + nSuperTriangleVertices); + // Edge re-mapping + { // fixed edges + EdgeUSet updatedFixedEdges; + typedef CDT::EdgeUSet::const_iterator It; + for(It e = fixedEdges.begin(); e != fixedEdges.end(); ++e) + { + updatedFixedEdges.insert(RemapNoSuperTriangle(*e)); + } + fixedEdges = updatedFixedEdges; + } + { // overlap count + unordered_map updatedOverlapCount; + typedef unordered_map::const_iterator + It; + for(It it = overlapCount.begin(); it != overlapCount.end(); ++it) + { + updatedOverlapCount.insert( + std::make_pair( + RemapNoSuperTriangle(it->first), it->second)); + } + overlapCount = updatedOverlapCount; + } + { // split edges mapping + unordered_map updatedPieceToOriginals; + typedef unordered_map::const_iterator It; + for(It it = pieceToOriginals.begin(); it != pieceToOriginals.end(); + ++it) + { + EdgeVec ee = it->second; + for(EdgeVec::iterator eeIt = ee.begin(); eeIt != ee.end(); + ++eeIt) + { + *eeIt = RemapNoSuperTriangle(*eeIt); + } + updatedPieceToOriginals.insert( + std::make_pair(RemapNoSuperTriangle(it->first), ee)); + } + pieceToOriginals = updatedPieceToOriginals; + } + } + // remove other triangles + removeTriangles(removedTriangles); + // adjust triangle vertices: account for removed super-triangle + if(m_superGeomType == SuperGeometryType::SuperTriangle) + { + for(TriangleVec::iterator t = triangles.begin(); t != triangles.end(); + ++t) + { + VerticesArr3& vv = t->vertices; + for(VerticesArr3::iterator v = vv.begin(); v != vv.end(); ++v) + { + *v -= nSuperTriangleVertices; + } + } + } +} + +template +void Triangulation::initializedWithCustomSuperGeometry() +{ + m_nearPtLocator.initialize(vertices); + m_nTargetVerts = static_cast(vertices.size()); + m_superGeomType = SuperGeometryType::Custom; +} + +template +TriIndUSet Triangulation::growToBoundary( + std::stack seeds) const +{ + TriIndUSet traversed; + while(!seeds.empty()) + { + const TriInd iT = seeds.top(); + seeds.pop(); + traversed.insert(iT); + const Triangle& t = triangles[iT]; + for(Index i(0); i < Index(3); ++i) + { + const Edge opEdge(t.vertices[ccw(i)], t.vertices[cw(i)]); + if(fixedEdges.count(opEdge)) + continue; + const TriInd iN = t.neighbors[opoNbr(i)]; + if(iN != noNeighbor && traversed.count(iN) == 0) + seeds.push(iN); + } + } + return traversed; +} + +template +TriInd Triangulation::addTriangle(const Triangle& t) +{ + const TriInd iT(triangles.size()); + triangles.push_back(t); + return iT; +} + +template +TriInd Triangulation::addTriangle() +{ + return addTriangle(Triangle()); +} + +template +void Triangulation::insertEdges( + const std::vector& edges) +{ + insertEdges(edges.begin(), edges.end(), edge_get_v1, edge_get_v2); +} + +template +void Triangulation::conformToEdges( + const std::vector& edges) +{ + conformToEdges(edges.begin(), edges.end(), edge_get_v1, edge_get_v2); +} + +template +void Triangulation::fixEdge(const Edge& edge) +{ + if(!fixedEdges.insert(edge).second) + { + ++overlapCount[edge]; // if edge is already fixed increment the counter + } +} + +namespace detail +{ + +// add element to 'to' if not already in 'to' +template +void insert_unique(std::vector& to, const T& elem) +{ + if(std::find(to.begin(), to.end(), elem) == to.end()) + { + to.push_back(elem); + } +} + +// add elements of 'from' that are not present in 'to' to 'to' +template +void insert_unique( + std::vector& to, + const std::vector& from) +{ + typedef typename std::vector::const_iterator Cit; + to.reserve(to.size() + from.size()); + for(Cit cit = from.begin(); cit != from.end(); ++cit) + { + insert_unique(to, *cit); + } +} + +} // namespace detail + +template +void Triangulation::splitFixedEdge( + const Edge& edge, + const VertInd iSplitVert) +{ + // split constraint (fixed) edge that already exists in triangulation + const Edge half1(edge.v1(), iSplitVert); + const Edge half2(iSplitVert, edge.v2()); + // remove the edge that and add its halves + fixedEdges.erase(edge); + fixEdge(half1); + fixEdge(half2); + // maintain overlaps + typedef unordered_map::const_iterator It; + const It overlapIt = overlapCount.find(edge); + if(overlapIt != overlapCount.end()) + { + overlapCount[half1] += overlapIt->second; + overlapCount[half2] += overlapIt->second; + overlapCount.erase(overlapIt); + } + // maintain piece-to-original mapping + EdgeVec newOriginals(1, edge); + const unordered_map::const_iterator originalsIt = + pieceToOriginals.find(edge); + if(originalsIt != pieceToOriginals.end()) + { // edge being split was split before: pass-through originals + newOriginals = originalsIt->second; + pieceToOriginals.erase(originalsIt); + } + detail::insert_unique(pieceToOriginals[half1], newOriginals); + detail::insert_unique(pieceToOriginals[half2], newOriginals); +} + +template +VertInd Triangulation::addSplitEdgeVertex( + const V2d& splitVert, + const TriInd iT, + const TriInd iTopo) +{ + // add a new point on the edge that splits an edge in two + const VertInd iSplitVert = static_cast(vertices.size()); + addNewVertex(splitVert, noNeighbor); + +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onAddVertexStart( + iSplitVert, AddVertexType::FixedEdgesIntersection); + } +#endif + + std::stack triStack = insertVertexOnEdge(iSplitVert, iT, iTopo); + tryAddVertexToLocator(iSplitVert); + ensureDelaunayByEdgeFlips(iSplitVert, triStack); + return iSplitVert; +} + +template +VertInd Triangulation::splitFixedEdgeAt( + const Edge& edge, + const V2d& splitVert, + const TriInd iT, + const TriInd iTopo) +{ + const VertInd iSplitVert = addSplitEdgeVertex(splitVert, iT, iTopo); + splitFixedEdge(edge, iSplitVert); + return iSplitVert; +} + +template +void Triangulation::fixEdge( + const Edge& edge, + const Edge& originalEdge) +{ + fixEdge(edge); + if(edge != originalEdge) + detail::insert_unique(pieceToOriginals[edge], originalEdge); +} + +namespace detail +{ + +template +T lerp(const T& a, const T& b, const T t) +{ + return (T(1) - t) * a + t * b; +} + +// Precondition: ab and cd intersect normally +template +V2d intersectionPosition( + const V2d& a, + const V2d& b, + const V2d& c, + const V2d& d) +{ + using namespace predicates::adaptive; + + // note: for better accuracy we interpolate x and y separately + // on a segment with the shortest x/y-projection correspondingly + const T a_cd = orient2d(c.x, c.y, d.x, d.y, a.x, a.y); + const T b_cd = orient2d(c.x, c.y, d.x, d.y, b.x, b.y); + const T t_ab = a_cd / (a_cd - b_cd); + + const T c_ab = orient2d(a.x, a.y, b.x, b.y, c.x, c.y); + const T d_ab = orient2d(a.x, a.y, b.x, b.y, d.x, d.y); + const T t_cd = c_ab / (c_ab - d_ab); + + return V2d( + std::fabs(a.x - b.x) < std::fabs(c.x - d.x) ? lerp(a.x, b.x, t_ab) + : lerp(c.x, d.x, t_cd), + std::fabs(a.y - b.y) < std::fabs(c.y - d.y) ? lerp(a.y, b.y, t_ab) + : lerp(c.y, d.y, t_cd)); +} + +} // namespace detail + +template +void Triangulation::insertEdgeIteration( + const Edge edge, + const Edge originalEdge, + EdgeVec& remaining, + std::vector& tppIterations) +{ + const VertInd iA = edge.v1(); + VertInd iB = edge.v2(); + if(iA == iB) // edge connects a vertex to itself + return; + + if(hasEdge(iA, iB)) + { + fixEdge(edge, originalEdge); + return; + } + + const V2d& a = vertices[iA]; + const V2d& b = vertices[iB]; + const T distanceTolerance = + m_minDistToConstraintEdge == T(0) + ? T(0) + : m_minDistToConstraintEdge * distance(a, b); + + TriInd iT; + // Note: 'L' is left and 'R' is right of the inserted constraint edge + VertInd iVL, iVR; + tie(iT, iVL, iVR) = intersectedTriangle(iA, a, b, distanceTolerance); + // if one of the triangle vertices is on the edge, move edge start + if(iT == noNeighbor) + { + const Edge edgePart(iA, iVL); + fixEdge(edgePart, originalEdge); + remaining.push_back(Edge(iVL, iB)); + return; + } + Triangle t = triangles[iT]; + std::vector intersected(1, iT); + std::vector polyL, polyR; + polyL.reserve(2); + polyL.push_back(iA); + polyL.push_back(iVL); + polyR.reserve(2); + polyR.push_back(iA); + polyR.push_back(iVR); + unordered_map outerTris; + outerTris[Edge(iA, iVL)] = edgeNeighbor(t, iA, iVL); + outerTris[Edge(iA, iVR)] = edgeNeighbor(t, iA, iVR); + VertInd iV = iA; + + while(!t.containsVertex(iB)) + { + const TriInd iTopo = opposedTriangle(t, iV); + const Triangle& tOpo = triangles[iTopo]; + const VertInd iVopo = opposedVertex(tOpo, iT); + + switch(m_intersectingEdgesStrategy) + { + case IntersectingConstraintEdges::NotAllowed: + if(fixedEdges.count(Edge(iVL, iVR))) + { + // make sure to report original input edges in the exception + Edge e1 = originalEdge; + Edge e2 = Edge(iVL, iVR); + e2 = pieceToOriginals.count(e2) + ? pieceToOriginals.at(e2).front() + : e2; + // don't count super-triangle vertices + e1 = Edge( + VertInd(e1.v1() - m_nTargetVerts), + VertInd(e1.v2() - m_nTargetVerts)); + e2 = Edge( + VertInd(e2.v1() - m_nTargetVerts), + VertInd(e2.v2() - m_nTargetVerts)); + handleException(IntersectingConstraintsError( + e1, + pieceToOriginals.count(e2) ? pieceToOriginals.at(e2).front() + : e2, + CDT_SOURCE_LOCATION)); + } + break; + case IntersectingConstraintEdges::TryResolve: + { + if(!fixedEdges.count(Edge(iVL, iVR))) + break; + // split edge at the intersection of two constraint edges + const V2d newV = detail::intersectionPosition( + vertices[iA], vertices[iB], vertices[iVL], vertices[iVR]); + const VertInd iNewVert = + splitFixedEdgeAt(Edge(iVL, iVR), newV, iT, iTopo); + // TODO: is it's possible to re-use pseudo-polygons + // for inserting [iA, iNewVert] edge half? + remaining.push_back(Edge(iA, iNewVert)); + remaining.push_back(Edge(iNewVert, iB)); + return; + } + case IntersectingConstraintEdges::DontCheck: + assert(!fixedEdges.count(Edge(iVL, iVR))); + break; + } + + const PtLineLocation::Enum loc = + locatePointLine(vertices[iVopo], a, b, distanceTolerance); + if(loc == PtLineLocation::Left) + { + const Edge e(polyL.back(), iVopo); + const TriInd outer = edgeNeighbor(tOpo, e.v1(), e.v2()); + if(!outerTris.insert(std::make_pair(e, outer)).second) + outerTris.at(e) = noNeighbor; // hanging edge detected + polyL.push_back(iVopo); + iV = iVL; + iVL = iVopo; + } + else if(loc == PtLineLocation::Right) + { + const Edge e(polyR.back(), iVopo); + const TriInd outer = edgeNeighbor(tOpo, e.v1(), e.v2()); + if(!outerTris.insert(std::make_pair(e, outer)).second) + outerTris.at(e) = noNeighbor; // hanging edge detected + polyR.push_back(iVopo); + iV = iVR; + iVR = iVopo; + } + else // encountered point on the edge + iB = iVopo; + + intersected.push_back(iTopo); + iT = iTopo; + t = triangles[iT]; + } + outerTris[Edge(polyL.back(), iB)] = edgeNeighbor(t, polyL.back(), iB); + outerTris[Edge(polyR.back(), iB)] = edgeNeighbor(t, polyR.back(), iB); + polyL.push_back(iB); + polyR.push_back(iB); + + assert(!intersected.empty()); + // make sure start/end vertices have a valid adjacent triangle + // that is not intersected by an edge + if(m_vertTris[iA] == intersected.front()) + pivotVertexTriangleCW(iA); + if(m_vertTris[iB] == intersected.back()) + pivotVertexTriangleCW(iB); + + { +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onReTriangulatePolygon(intersected); + } +#endif + + // Triangulate pseudo-polygons on both sides + std::reverse(polyR.begin(), polyR.end()); + + // note: intersected triangles are re-used for new triangles + // every triangulation of an n-gon has n − 2 triangles + // even if outer polygon has hanging edges it holds + assert(intersected.size() >= 2); + const TriInd iTL = intersected.back(); + intersected.pop_back(); + const TriInd iTR = intersected.back(); + intersected.pop_back(); + + triangulatePseudoPolygon( + polyL, outerTris, iTL, iTR, intersected, tppIterations); + triangulatePseudoPolygon( + polyR, outerTris, iTR, iTL, intersected, tppIterations); + assert(intersected.empty()); + } + + if(iB != edge.v2()) // encountered point on the edge + { + // fix edge part + const Edge edgePart(iA, iB); + fixEdge(edgePart, originalEdge); + remaining.push_back(Edge(iB, edge.v2())); + return; + } + else + { + fixEdge(edge, originalEdge); + } +} + +template +void Triangulation::insertEdge( + Edge edge, + const Edge originalEdge, + EdgeVec& remaining, + std::vector& tppIterations) +{ +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onAddEdgeStart(edge); + } +#endif + + // use iteration over recursion to avoid stack overflows + remaining.clear(); + remaining.push_back(edge); + while(!remaining.empty()) + { + edge = remaining.back(); + remaining.pop_back(); + insertEdgeIteration(edge, originalEdge, remaining, tppIterations); + } +} + +template +void Triangulation::conformToEdgeIteration( + Edge edge, + const EdgeVec& originals, + BoundaryOverlapCount overlaps, + std::vector& remaining) +{ + const VertInd iA = edge.v1(); + VertInd iB = edge.v2(); + if(iA == iB) // edge connects a vertex to itself + return; + + if(hasEdge(iA, iB)) + { + fixEdge(edge); + if(overlaps > 0) + overlapCount[edge] = overlaps; + // avoid marking edge as a part of itself + if(!originals.empty() && edge != originals.front()) + { + detail::insert_unique(pieceToOriginals[edge], originals); + } + return; + } + + const V2d& a = vertices[iA]; + const V2d& b = vertices[iB]; + const T distanceTolerance = + m_minDistToConstraintEdge == T(0) + ? T(0) + : m_minDistToConstraintEdge * distance(a, b); + TriInd iT; + VertInd iVleft, iVright; + tie(iT, iVleft, iVright) = intersectedTriangle(iA, a, b, distanceTolerance); + // if one of the triangle vertices is on the edge, move edge start + if(iT == noNeighbor) + { + const Edge edgePart(iA, iVleft); + fixEdge(edgePart); + if(overlaps > 0) + overlapCount[edgePart] = overlaps; + detail::insert_unique(pieceToOriginals[edgePart], originals); +#ifdef CDT_CXX11_IS_SUPPORTED + remaining.emplace_back(Edge(iVleft, iB), originals, overlaps); +#else + remaining.push_back(make_tuple(Edge(iVleft, iB), originals, overlaps)); +#endif + return; + } + + VertInd iV = iA; + Triangle t = triangles[iT]; + while(std::find(t.vertices.begin(), t.vertices.end(), iB) == + t.vertices.end()) + { + const TriInd iTopo = opposedTriangle(t, iV); + const Triangle& tOpo = triangles[iTopo]; + const VertInd iVopo = opposedVertex(tOpo, iT); + const V2d vOpo = vertices[iVopo]; + + switch(m_intersectingEdgesStrategy) + { + case IntersectingConstraintEdges::NotAllowed: + if(fixedEdges.count(Edge(iVleft, iVright))) + { + // make sure to report original input edges in the exception + Edge e1 = pieceToOriginals.count(edge) + ? pieceToOriginals.at(edge).front() + : edge; + Edge e2(iVleft, iVright); + e2 = pieceToOriginals.count(e2) + ? pieceToOriginals.at(e2).front() + : e2; + // don't count super-triangle vertices + e1 = Edge( + VertInd(e1.v1() - m_nTargetVerts), + VertInd(e1.v2() - m_nTargetVerts)); + e2 = Edge( + VertInd(e2.v1() - m_nTargetVerts), + VertInd(e2.v2() - m_nTargetVerts)); + handleException( + IntersectingConstraintsError(e1, e2, CDT_SOURCE_LOCATION)); + } + break; + case IntersectingConstraintEdges::TryResolve: + { + if(!fixedEdges.count(Edge(iVleft, iVright))) + break; + // split edge at the intersection of two constraint edges + const V2d newV = detail::intersectionPosition( + vertices[iA], + vertices[iB], + vertices[iVleft], + vertices[iVright]); + const VertInd iNewVert = + splitFixedEdgeAt(Edge(iVleft, iVright), newV, iT, iTopo); +#ifdef CDT_CXX11_IS_SUPPORTED + remaining.emplace_back(Edge(iNewVert, iB), originals, overlaps); + remaining.emplace_back(Edge(iA, iNewVert), originals, overlaps); +#else + remaining.push_back( + make_tuple(Edge(iNewVert, iB), originals, overlaps)); + remaining.push_back( + make_tuple(Edge(iA, iNewVert), originals, overlaps)); +#endif + return; + } + case IntersectingConstraintEdges::DontCheck: + assert(!fixedEdges.count(Edge(iVleft, iVright))); + break; + } + + iT = iTopo; + t = triangles[iT]; + + const PtLineLocation::Enum loc = + locatePointLine(vOpo, a, b, distanceTolerance); + if(loc == PtLineLocation::Left) + { + iV = iVleft; + iVleft = iVopo; + } + else if(loc == PtLineLocation::Right) + { + iV = iVright; + iVright = iVopo; + } + else // encountered point on the edge + iB = iVopo; + } + + // encountered one or more points on the edge: add remaining edge part + if(iB != edge.v2()) + { +#ifdef CDT_CXX11_IS_SUPPORTED + remaining.emplace_back(Edge(iB, edge.v2()), originals, overlaps); +#else + remaining.push_back( + make_tuple(Edge(iB, edge.v2()), originals, overlaps)); +#endif + } + + // add mid-point to triangulation + const VertInd iMid = static_cast(vertices.size()); + const V2d& start = vertices[iA]; + const V2d& end = vertices[iB]; + addNewVertex( + V2d((start.x + end.x) / T(2), (start.y + end.y) / T(2)), noNeighbor); + +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onAddVertexStart( + iMid, AddVertexType::FixedEdgeMidpoint); + } +#endif + + const std::vector flippedFixedEdges = + insertVertex_FlipFixedEdges(iMid); + +#ifdef CDT_CXX11_IS_SUPPORTED + remaining.emplace_back(Edge(iMid, iB), originals, overlaps); + remaining.emplace_back(Edge(iA, iMid), originals, overlaps); +#else + remaining.push_back(make_tuple(Edge(iMid, iB), originals, overlaps)); + remaining.push_back(make_tuple(Edge(iA, iMid), originals, overlaps)); +#endif + + // re-introduce fixed edges that were flipped + // and make sure overlap count is preserved + for(std::vector::const_iterator it = flippedFixedEdges.begin(); + it != flippedFixedEdges.end(); + ++it) + { + const Edge& flippedFixedEdge = *it; + fixedEdges.erase(flippedFixedEdge); + + BoundaryOverlapCount prevOverlaps = 0; + const unordered_map::const_iterator + overlapsIt = overlapCount.find(flippedFixedEdge); + if(overlapsIt != overlapCount.end()) + { + prevOverlaps = overlapsIt->second; + overlapCount.erase(overlapsIt); + } + // override overlapping boundaries count when re-inserting an edge + EdgeVec prevOriginals(1, flippedFixedEdge); + const unordered_map::const_iterator originalsIt = + pieceToOriginals.find(flippedFixedEdge); + if(originalsIt != pieceToOriginals.end()) + { + prevOriginals = originalsIt->second; + } +#ifdef CDT_CXX11_IS_SUPPORTED + remaining.emplace_back(flippedFixedEdge, prevOriginals, prevOverlaps); +#else + remaining.push_back( + make_tuple(flippedFixedEdge, prevOriginals, prevOverlaps)); +#endif + } +} + +template +void Triangulation::conformToEdge( + Edge edge, + EdgeVec originals, + BoundaryOverlapCount overlaps, + std::vector& remaining) +{ +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onAddEdgeStart(edge); + } +#endif + + // use iteration over recursion to avoid stack overflows + remaining.clear(); +#ifdef CDT_CXX11_IS_SUPPORTED + remaining.emplace_back(edge, originals, overlaps); +#else + remaining.push_back(make_tuple(edge, originals, overlaps)); +#endif + while(!remaining.empty()) + { + tie(edge, originals, overlaps) = remaining.back(); + remaining.pop_back(); + conformToEdgeIteration(edge, originals, overlaps, remaining); + } +} + +/*! + * Returns: + * - intersected triangle index + * - index of point on the left of the line + * - index of point on the right of the line + * If left point is right on the line: no triangle is intersected: + * - triangle index is no-neighbor (invalid) + * - index of point on the line + * - index of point on the right of the line + */ +template +tuple +Triangulation::intersectedTriangle( + const VertInd iA, + const V2d& a, + const V2d& b, + const T orientationTolerance) const +{ + const TriInd startTri = m_vertTris[iA]; + TriInd iT = startTri; + do + { + const Triangle t = triangles[iT]; + const Index i = vertexInd(t.vertices, iA); + const VertInd iP2 = t.vertices[ccw(i)]; + const T orientP2 = orient2D(vertices[iP2], a, b); + const PtLineLocation::Enum locP2 = classifyOrientation(orientP2); + if(locP2 == PtLineLocation::Right) + { + const VertInd iP1 = t.vertices[cw(i)]; + const T orientP1 = orient2D(vertices[iP1], a, b); + const PtLineLocation::Enum locP1 = classifyOrientation(orientP1); + if(locP1 == PtLineLocation::OnLine) + { + return make_tuple(noNeighbor, iP1, iP1); + } + if(locP1 == PtLineLocation::Left) + { + if(orientationTolerance) + { + T closestOrient; + VertInd iClosestP; + if(std::abs(orientP1) <= std::abs(orientP2)) + { + closestOrient = orientP1; + iClosestP = iP1; + } + else + { + closestOrient = orientP2; + iClosestP = iP2; + } + if(classifyOrientation( + closestOrient, orientationTolerance) == + PtLineLocation::OnLine) + { + return make_tuple(noNeighbor, iClosestP, iClosestP); + } + } + return make_tuple(iT, iP1, iP2); + } + } + iT = t.next(iA).first; + } while(iT != startTri); + + handleException(Error( + "Could not find vertex triangle intersected by an edge.", + CDT_SOURCE_LOCATION)); + return make_tuple(noNeighbor, noVertex, noVertex); +} + +template +void Triangulation::addSuperTriangle(const Box2d& box) +{ + m_nTargetVerts = nSuperTriangleVertices; + m_superGeomType = SuperGeometryType::SuperTriangle; + + const V2d center = { + (box.min.x + box.max.x) / T(2), (box.min.y + box.max.y) / T(2)}; + const T w = box.max.x - box.min.x; + const T h = box.max.y - box.min.y; + T r = std::max(w, h); // incircle radius upper bound + + // Note: make sure radius is big enough. Constants chosen experimentally. + // - for tiny bounding boxes: use 1.0 as the smallest radius + // - multiply radius by 2.0 for extra safety margin + r = std::max(T(2) * r, T(1)); + + // Note: for very large floating point numbers rounding can lead to wrong + // super-triangle coordinates. This is a very rare corner-case so the + // handling is very primitive. + { // note: '<=' means '==' but avoids the warning + while(center.y <= center.y - r) + r *= T(2); + } + + const T R = T(2) * r; // excircle radius + const T cos_30_deg = T(0.8660254037844386); // note: (std::sqrt(3.0) / 2.0) + const T shiftX = R * cos_30_deg; + const V2d posV1 = {center.x - shiftX, center.y - r}; + const V2d posV2 = {center.x + shiftX, center.y - r}; + const V2d posV3 = {center.x, center.y + R}; + addNewVertex(posV1, TriInd(0)); + addNewVertex(posV2, TriInd(0)); + addNewVertex(posV3, TriInd(0)); + +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onAddSuperTriangle(); + } +#endif + + addTriangle( + Triangle(arr3(VertInd(0), VertInd(1), VertInd(2)), arr3(noNeighbor))); + + if(m_vertexInsertionOrder != VertexInsertionOrder::Auto) + { + m_nearPtLocator.initialize(vertices); + } +} + +template +void Triangulation::addNewVertex( + const V2d& pos, + const TriInd iT) +{ + vertices.push_back(pos); + m_vertTris.push_back(iT); +} + +template +std::vector +Triangulation::insertVertex_FlipFixedEdges( + const VertInd iV1) +{ + std::vector flippedFixedEdges; + + const V2d& v1 = vertices[iV1]; + const VertInd startVertex = m_nearPtLocator.nearPoint(v1, vertices); + array trisAt = walkingSearchTrianglesAt(iV1, startVertex); + std::stack triStack = + trisAt[1] == noNeighbor ? insertVertexInsideTriangle(iV1, trisAt[0]) + : insertVertexOnEdge(iV1, trisAt[0], trisAt[1]); + + TriInd iTopo, n1, n2, n3, n4; + VertInd iV2, iV3, iV4; + while(!triStack.empty()) + { + const TriInd iT = triStack.top(); + triStack.pop(); + + edgeFlipInfo(iT, iV1, iTopo, iV2, iV3, iV4, n1, n2, n3, n4); + if(iTopo != noNeighbor && isFlipNeeded(iV1, iV2, iV3, iV4)) + { + // if flipped edge is fixed, remember it + const Edge flippedEdge(iV2, iV4); + if(!fixedEdges.empty() && + fixedEdges.find(flippedEdge) != fixedEdges.end()) + { + flippedFixedEdges.push_back(flippedEdge); + } + + flipEdge(iT, iTopo, iV1, iV2, iV3, iV4, n1, n2, n3, n4); + triStack.push(iT); + triStack.push(iTopo); + } + } + + tryAddVertexToLocator(iV1); + return flippedFixedEdges; +} + +template +void Triangulation::insertVertex( + const VertInd iVert, + const VertInd walkStart) +{ +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onAddVertexStart(iVert, AddVertexType::UserInput); + } +#endif + + const array trisAt = walkingSearchTrianglesAt(iVert, walkStart); + std::stack triStack = + trisAt[1] == noNeighbor + ? insertVertexInsideTriangle(iVert, trisAt[0]) + : insertVertexOnEdge(iVert, trisAt[0], trisAt[1], true); + ensureDelaunayByEdgeFlips(iVert, triStack); +} + +template +void Triangulation::insertVertex(const VertInd iVert) +{ + const V2d& v = vertices[iVert]; + const VertInd walkStart = m_nearPtLocator.nearPoint(v, vertices); + insertVertex(iVert, walkStart); + tryAddVertexToLocator(iVert); +} + +template +void Triangulation::ensureDelaunayByEdgeFlips( + const VertInd iV1, + std::stack& triStack) +{ + TriInd iTopo, n1, n2, n3, n4; + VertInd iV2, iV3, iV4; + while(!triStack.empty()) + { + const TriInd iT = triStack.top(); + triStack.pop(); + + edgeFlipInfo(iT, iV1, iTopo, iV2, iV3, iV4, n1, n2, n3, n4); + if(iTopo != noNeighbor && isFlipNeeded(iV1, iV2, iV3, iV4)) + { + flipEdge(iT, iTopo, iV1, iV2, iV3, iV4, n1, n2, n3, n4); + triStack.push(iT); + triStack.push(iTopo); + } + } +} + +/* + * v4 original edge: (v1, v3) + * /|\ flip-candidate edge: (v, v2) + * / | \ + * n3 / | \ n4 + * / | \ + * new vertex--> v1 T | Topo v3 + * \ | / + * n1 \ | / n2 + * \ | / + * \|/ + * v2 + */ +template +void Triangulation::edgeFlipInfo( + const TriInd iT, + const VertInd iV1, + TriInd& iTopo, + VertInd& iV2, + VertInd& iV3, + VertInd& iV4, + TriInd& n1, + TriInd& n2, + TriInd& n3, + TriInd& n4) +{ + /* v[2] + / \ + n[2]/ \n[1] + /_____\ + v[0] n[0] v[1] */ + const Triangle& t = triangles[iT]; + if(t.vertices[0] == iV1) + { + iV2 = t.vertices[1]; + iV4 = t.vertices[2]; + n1 = t.neighbors[0]; + n3 = t.neighbors[2]; + iTopo = t.neighbors[1]; + } + else if(t.vertices[1] == iV1) + { + iV2 = t.vertices[2]; + iV4 = t.vertices[0]; + n1 = t.neighbors[1]; + n3 = t.neighbors[0]; + iTopo = t.neighbors[2]; + } + else + { + iV2 = t.vertices[0]; + iV4 = t.vertices[1]; + n1 = t.neighbors[2]; + n3 = t.neighbors[1]; + iTopo = t.neighbors[0]; + } + if(iTopo == noNeighbor) + return; + const Triangle& tOpo = triangles[iTopo]; + if(tOpo.neighbors[0] == iT) + { + iV3 = tOpo.vertices[2]; + n2 = tOpo.neighbors[1]; + n4 = tOpo.neighbors[2]; + } + else if(tOpo.neighbors[1] == iT) + { + iV3 = tOpo.vertices[0]; + n2 = tOpo.neighbors[2]; + n4 = tOpo.neighbors[0]; + } + else + { + iV3 = tOpo.vertices[1]; + n2 = tOpo.neighbors[0]; + n4 = tOpo.neighbors[1]; + } +} + +/*! + * Handles super-triangle vertices. + * Super-tri points are not infinitely far and influence the input points + * Three cases are possible: + * 1. If one of the opposed vertices is super-tri: no flip needed + * 2. One of the shared vertices is super-tri: + * check if on point is same side of line formed by non-super-tri + * vertices as the non-super-tri shared vertex + * 3. None of the vertices are super-tri: normal circumcircle test + */ +/* + * v4 original edge: (v2, v4) + * /|\ flip-candidate edge: (v1, v3) + * / | \ + * / | \ + * / | \ + * new vertex--> v1 | v3 + * \ | / + * \ | / + * \ | / + * \|/ + * v2 + */ +template +bool Triangulation::isFlipNeeded( + const VertInd iV1, + const VertInd iV2, + const VertInd iV3, + const VertInd iV4) const +{ + if(fixedEdges.count(Edge(iV2, iV4))) + return false; // flip not needed if the original edge is fixed + const V2d& v1 = vertices[iV1]; + const V2d& v2 = vertices[iV2]; + const V2d& v3 = vertices[iV3]; + const V2d& v4 = vertices[iV4]; + if(m_superGeomType == SuperGeometryType::SuperTriangle) + { + // If flip-candidate edge touches super-triangle in-circumference + // test has to be replaced with orient2d test against the line + // formed by two non-artificial vertices (that don't belong to + // super-triangle) + if(iV1 < 3) // flip-candidate edge touches super-triangle + { + // does original edge also touch super-triangle? + if(iV2 < 3) + return locatePointLine(v2, v3, v4) == + locatePointLine(v1, v3, v4); + if(iV4 < 3) + return locatePointLine(v4, v2, v3) == + locatePointLine(v1, v2, v3); + return false; // original edge does not touch super-triangle + } + if(iV3 < 3) // flip-candidate edge touches super-triangle + { + // does original edge also touch super-triangle? + if(iV2 < 3) + { + return locatePointLine(v2, v1, v4) == + locatePointLine(v3, v1, v4); + } + if(iV4 < 3) + { + return locatePointLine(v4, v2, v1) == + locatePointLine(v3, v2, v1); + } + return false; // original edge does not touch super-triangle + } + // flip-candidate edge does not touch super-triangle + if(iV2 < 3) + return locatePointLine(v2, v3, v4) == locatePointLine(v1, v3, v4); + if(iV4 < 3) + return locatePointLine(v4, v2, v3) == locatePointLine(v1, v2, v3); + } + return isInCircumcircle(v1, v2, v3, v4); +} + +/* Flip edge between T and Topo: + * + * v4 | - old edge + * /|\ ~ - new edge + * / | \ + * n3 / T' \ n4 + * / | \ + * / | \ + * T -> v1~~~~~~~~~v3 <- Topo + * \ | / + * \ | / + * n1 \Topo'/ n2 + * \ | / + * \|/ + * v2 + */ +template +void Triangulation::flipEdge( + const TriInd iT, + const TriInd iTopo) +{ +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onFlipEdge(iT, iTopo); + } +#endif + + Triangle& t = triangles[iT]; + Triangle& tOpo = triangles[iTopo]; + const array& triNs = t.neighbors; + const array& triOpoNs = tOpo.neighbors; + const array& triVs = t.vertices; + const array& triOpoVs = tOpo.vertices; + // find vertices and neighbors + Index i = opposedVertexInd(t.neighbors, iTopo); + const VertInd v1 = triVs[i]; + const VertInd v2 = triVs[ccw(i)]; + const TriInd n1 = triNs[i]; + const TriInd n3 = triNs[cw(i)]; + i = opposedVertexInd(tOpo.neighbors, iT); + const VertInd v3 = triOpoVs[i]; + const VertInd v4 = triOpoVs[ccw(i)]; + const TriInd n4 = triOpoNs[i]; + const TriInd n2 = triOpoNs[cw(i)]; + // change vertices and neighbors + t = Triangle(arr3(v4, v1, v3), arr3(n3, iTopo, n4)); + tOpo = Triangle(arr3(v2, v3, v1), arr3(n2, iT, n1)); + // adjust neighboring triangles and vertices + changeNeighbor(n1, iT, iTopo); + changeNeighbor(n4, iTopo, iT); + // only adjust adjacent triangles if triangulation is not finalized: + // can happen when called from outside on an already finalized + // triangulation + if(!isFinalized()) + { + setAdjacentTriangle(v4, iT); + setAdjacentTriangle(v2, iTopo); + } +} + +/* Flip edge between T and Topo: + * + * v4 | - old edge + * /|\ ~ - new edge + * / | \ + * n3 / T' \ n4 + * / | \ + * / | \ + * T -> v1 ~~~~~~~~ v3 <- Topo + * \ | / + * \ | / + * n1 \Topo'/ n2 + * \ | / + * \|/ + * v2 + */ +template +void Triangulation::flipEdge( + const TriInd iT, + const TriInd iTopo, + const VertInd v1, + const VertInd v2, + const VertInd v3, + const VertInd v4, + const TriInd n1, + const TriInd n2, + const TriInd n3, + const TriInd n4) +{ +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onFlipEdge(iT, iTopo); + } +#endif + + // change vertices and neighbors + triangles[iT] = Triangle(arr3(v4, v1, v3), arr3(n3, iTopo, n4)); + triangles[iTopo] = Triangle(arr3(v2, v3, v1), arr3(n2, iT, n1)); + // adjust neighboring triangles and vertices + changeNeighbor(n1, iT, iTopo); + changeNeighbor(n4, iTopo, iT); + // only adjust adjacent triangles if triangulation is not finalized: + // can happen when called from outside on an already finalized + // triangulation + if(!isFinalized()) + { + setAdjacentTriangle(v4, iT); + setAdjacentTriangle(v2, iTopo); + } +} + +/* Insert point into triangle: split into 3 triangles: + * - create 2 new triangles + * - re-use old triangle for the 3rd + * v3 + * / | \ + * / | \ <-- original triangle (t) + * / | \ + * n3 / | \ n2 + * /newT2|newT1\ + * / v \ + * / __/ \__ \ + * / __/ \__ \ + * / _/ t' \_ \ + * v1 ___________________ v2 + * n1 + */ +template +std::stack +Triangulation::insertVertexInsideTriangle( + VertInd v, + TriInd iT) +{ + const TriInd iNewT1 = addTriangle(); + const TriInd iNewT2 = addTriangle(); + +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onInsertVertexInsideTriangle(iT, iNewT1, iNewT2); + } +#endif + + Triangle& t = triangles[iT]; + const array vv = t.vertices; + const array nn = t.neighbors; + const VertInd v1 = vv[0], v2 = vv[1], v3 = vv[2]; + const TriInd n1 = nn[0], n2 = nn[1], n3 = nn[2]; + // make two new triangles and convert current triangle to 3rd new + // triangle + triangles[iNewT1] = Triangle(arr3(v2, v3, v), arr3(n2, iNewT2, iT)); + triangles[iNewT2] = Triangle(arr3(v3, v1, v), arr3(n3, iT, iNewT1)); + t = Triangle(arr3(v1, v2, v), arr3(n1, iNewT1, iNewT2)); + // adjust adjacent triangles + setAdjacentTriangle(v, iT); + setAdjacentTriangle(v3, iNewT1); + // change triangle neighbor's neighbors to new triangles + changeNeighbor(n2, iT, iNewT1); + changeNeighbor(n3, iT, iNewT2); + // return newly added triangles + std::stack newTriangles; + newTriangles.push(iT); + newTriangles.push(iNewT1); + newTriangles.push(iNewT2); + return newTriangles; +} + +/* Inserting a point on the edge between two triangles + * T1 (top) v1 + * /|\ + * n1 / | \ n4 + * / | \ + * / T1' | Tnew1\ + * v2-------v-------v4 + * \ T2' | Tnew2/ + * \ | / + * n2 \ | / n3 + * \|/ + * T2 (bottom) v3 + */ +template +std::stack Triangulation::insertVertexOnEdge( + VertInd v, + TriInd iT1, + TriInd iT2, + const bool doHandleFixedSplitEdge) +{ + const TriInd iTnew1 = addTriangle(); + const TriInd iTnew2 = addTriangle(); + +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler) + { + m_callbackHandler->onInsertVertexOnEdge(iT1, iT2, iTnew1, iTnew2); + } +#endif + + Triangle& t1 = triangles[iT1]; + Triangle& t2 = triangles[iT2]; + Index i = opposedVertexInd(t1.neighbors, iT2); + const VertInd v1 = t1.vertices[i]; + const VertInd v2 = t1.vertices[ccw(i)]; + const TriInd n1 = t1.neighbors[i]; + const TriInd n4 = t1.neighbors[cw(i)]; + i = opposedVertexInd(t2.neighbors, iT1); + const VertInd v3 = t2.vertices[i]; + const VertInd v4 = t2.vertices[ccw(i)]; + const TriInd n3 = t2.neighbors[i]; + const TriInd n2 = t2.neighbors[cw(i)]; + // add new triangles and change existing ones + t1 = Triangle(arr3(v, v1, v2), arr3(iTnew1, n1, iT2)); + t2 = Triangle(arr3(v, v2, v3), arr3(iT1, n2, iTnew2)); + triangles[iTnew1] = Triangle(arr3(v, v4, v1), arr3(iTnew2, n4, iT1)); + triangles[iTnew2] = Triangle(arr3(v, v3, v4), arr3(iT2, n3, iTnew1)); + // adjust adjacent triangles + setAdjacentTriangle(v, iT1); + setAdjacentTriangle(v4, iTnew1); + // adjust neighboring triangles and vertices + changeNeighbor(n4, iT1, iTnew1); + changeNeighbor(n3, iT2, iTnew2); + // properly handle the case when the split edge is a fixed edge + if(doHandleFixedSplitEdge) + { + const Edge sharedEdge(v2, v4); + if(fixedEdges.count(sharedEdge)) + splitFixedEdge(sharedEdge, v); + } + // return newly added triangles + std::stack newTriangles; + newTriangles.push(iT1); + newTriangles.push(iTnew2); + newTriangles.push(iT2); + newTriangles.push(iTnew1); + return newTriangles; +} + +template +array +Triangulation::trianglesAt(const V2d& pos) const +{ + array out = {noNeighbor, noNeighbor}; + for(TriInd i = TriInd(0); i < TriInd(triangles.size()); ++i) + { + const Triangle& t = triangles[i]; + const V2d& v1 = vertices[t.vertices[0]]; + const V2d& v2 = vertices[t.vertices[1]]; + const V2d& v3 = vertices[t.vertices[2]]; + const PtTriLocation::Enum loc = locatePointTriangle(pos, v1, v2, v3); + if(loc == PtTriLocation::Outside) + continue; + out[0] = i; + if(isOnEdge(loc)) + out[1] = t.neighbors[edgeNeighbor(loc)]; + return out; + } + handleException( + Error("No triangle was found at position", CDT_SOURCE_LOCATION)); + return out; +} + +template +TriInd Triangulation::walkTriangles( + const VertInd startVertex, + const V2d& pos) const +{ + // begin walk in search of triangle at pos + TriInd currTri = m_vertTris[startVertex]; + bool found = false; + detail::SplitMix64RandGen prng; + while(!found) + { + const Triangle& t = triangles[currTri]; + found = true; + // stochastic offset to randomize which edge we check first + const Index offset(prng() % 3); + for(Index i_(0); i_ < Index(3); ++i_) + { + const Index i((i_ + offset) % 3); + const V2d& vStart = vertices[t.vertices[i]]; + const V2d& vEnd = vertices[t.vertices[ccw(i)]]; + const PtLineLocation::Enum edgeCheck = + locatePointLine(pos, vStart, vEnd); + const TriInd iN = t.neighbors[i]; + if(edgeCheck == PtLineLocation::Right && iN != noNeighbor) + { + found = false; + currTri = iN; + break; + } + } + } + return currTri; +} + +template +array Triangulation::walkingSearchTrianglesAt( + const VertInd iV, + const VertInd startVertex) const +{ + const V2d v = vertices[iV]; + array out = {noNeighbor, noNeighbor}; + const TriInd iT = walkTriangles(startVertex, v); + // Finished walk, locate point in current triangle + const Triangle& t = triangles[iT]; + const V2d& v1 = vertices[t.vertices[0]]; + const V2d& v2 = vertices[t.vertices[1]]; + const V2d& v3 = vertices[t.vertices[2]]; + const PtTriLocation::Enum loc = locatePointTriangle(v, v1, v2, v3); + + if(loc == PtTriLocation::Outside) + { + handleException( + Error("No triangle was found at position", CDT_SOURCE_LOCATION)); + } + if(loc == PtTriLocation::OnVertex) + { + const VertInd iDupe = v1 == v ? t.vertices[0] + : v2 == v ? t.vertices[1] + : t.vertices[2]; + handleException(DuplicateVertexError( + VertInd(iV - m_nTargetVerts), + VertInd(iDupe - m_nTargetVerts), + CDT_SOURCE_LOCATION)); + } + + out[0] = iT; + if(isOnEdge(loc)) + out[1] = t.neighbors[edgeNeighbor(loc)]; + return out; +} + +template +void Triangulation::changeNeighbor( + const TriInd iT, + const TriInd oldNeighbor, + const TriInd newNeighbor) +{ + if(iT == noNeighbor) + return; + NeighborsArr3& nn = triangles[iT].neighbors; + assert( + nn[0] == oldNeighbor || nn[1] == oldNeighbor || nn[2] == oldNeighbor); + if(nn[0] == oldNeighbor) + nn[0] = newNeighbor; + else if(nn[1] == oldNeighbor) + nn[1] = newNeighbor; + else + nn[2] = newNeighbor; +} + +template +void Triangulation::changeNeighbor( + const TriInd iT, + const VertInd iVedge1, + const VertInd iVedge2, + const TriInd newNeighbor) +{ + assert(iT != noNeighbor); + Triangle& t = triangles[iT]; + t.neighbors[edgeNeighborInd(t.vertices, iVedge1, iVedge2)] = newNeighbor; +} + +template +void Triangulation::triangulatePseudoPolygon( + const std::vector& poly, + unordered_map& outerTris, + TriInd iT, + TriInd iN, + std::vector& trianglesToReuse, + std::vector& iterations) +{ + assert(poly.size() > 2); + // note: uses iteration instead of recursion to avoid stack overflows + iterations.clear(); + iterations.push_back(make_tuple( + IndexSizeType(0), + static_cast(poly.size() - 1), + iT, + iN, + Index(0))); + while(!iterations.empty()) + { + triangulatePseudoPolygonIteration( + poly, outerTris, trianglesToReuse, iterations); + } +} + +template +void Triangulation::triangulatePseudoPolygonIteration( + const std::vector& poly, + unordered_map& outerTris, + std::vector& trianglesToReuse, + std::vector& iterations) +{ + IndexSizeType iA, iB; + TriInd iT, iParent; + Index iInParent; + assert(!iterations.empty()); + tie(iA, iB, iT, iParent, iInParent) = iterations.back(); + iterations.pop_back(); + assert(iB - iA > 1 && iT != noNeighbor && iParent != noNeighbor); + Triangle& t = triangles[iT]; + // find Delaunay point + const IndexSizeType iC = findDelaunayPoint(poly, iA, iB); + + const VertInd a = poly[iA]; + const VertInd b = poly[iB]; + const VertInd c = poly[iC]; + + // split pseudo-polygon in two parts and triangulate them + // note: second part needs to be pushed on stack first to be processed first + + // second part: points after the Delaunay point + if(iB - iC > 1) + { + assert(!trianglesToReuse.empty()); + const TriInd iNext = trianglesToReuse.back(); + trianglesToReuse.pop_back(); + iterations.push_back(make_tuple(iC, iB, iNext, iT, Index(1))); + } + else // pseudo-poly is reduced to a single outer edge + { + const Edge outerEdge(b, c); + const TriInd outerTri = outerTris.at(outerEdge); + if(outerTri != noNeighbor) + { + assert(outerTri != iT); + t.neighbors[1] = outerTri; + changeNeighbor(outerTri, c, b, iT); + } + else + outerTris.at(outerEdge) = iT; + } + // first part: points before the Delaunay point + if(iC - iA > 1) + { // add next triangle and add another iteration + assert(!trianglesToReuse.empty()); + const TriInd iNext = trianglesToReuse.back(); + trianglesToReuse.pop_back(); + iterations.push_back(make_tuple(iA, iC, iNext, iT, Index(2))); + } + else + { // pseudo-poly is reduced to a single outer edge + const Edge outerEdge(c, a); + const TriInd outerTri = outerTris.at(outerEdge); + if(outerTri != noNeighbor) + { + assert(outerTri != iT); + t.neighbors[2] = outerTri; + changeNeighbor(outerTri, c, a, iT); + } + else + outerTris.at(outerEdge) = iT; + } + // Finalize triangle + // note: only when triangle is finalized to we add it as a neighbor to + // parent to maintain triangulation topology consistency + triangles[iParent].neighbors[iInParent] = iT; + t.neighbors[0] = iParent; + t.vertices = arr3(a, b, c); + setAdjacentTriangle(c, iT); +} + +template +IndexSizeType Triangulation::findDelaunayPoint( + const std::vector& poly, + const IndexSizeType iA, + const IndexSizeType iB) const +{ + assert(iB - iA > 1); + const V2d& a = vertices[poly[iA]]; + const V2d& b = vertices[poly[iB]]; + IndexSizeType out = iA + 1; + const V2d* c = &vertices[poly[out]]; // caching for better performance + for(IndexSizeType i = iA + 1; i < iB; ++i) + { + const V2d& v = vertices[poly[i]]; + if(isInCircumcircle(v, a, b, *c)) + { + out = i; + c = &v; + } + } + assert(out > iA && out < iB); // point is between ends + return out; +} + +template +void Triangulation::insertVertices( + const std::vector >& newVertices) +{ + return insertVertices( + newVertices.begin(), newVertices.end(), getX_V2d, getY_V2d); +} + +template +bool Triangulation::isFinalized() const +{ + return m_vertTris.empty() && !vertices.empty(); +} + +template +unordered_map +Triangulation::peelLayer( + std::stack seeds, + const LayerDepth layerDepth, + std::vector& triDepths) const +{ + unordered_map behindBoundary; + while(!seeds.empty()) + { + const TriInd iT = seeds.top(); + seeds.pop(); + triDepths[iT] = std::min(triDepths[iT], layerDepth); + behindBoundary.erase(iT); + const Triangle& t = triangles[iT]; + for(Index i(0); i < Index(3); ++i) + { + const Edge opEdge(t.vertices[ccw(i)], t.vertices[cw(i)]); + const TriInd iN = t.neighbors[opoNbr(i)]; + if(iN == noNeighbor || triDepths[iN] <= layerDepth) + continue; + if(fixedEdges.count(opEdge)) + { + const unordered_map::const_iterator cit = + overlapCount.find(opEdge); + const LayerDepth triDepth = cit == overlapCount.end() + ? layerDepth + 1 + : layerDepth + cit->second + 1; + behindBoundary[iN] = triDepth; + continue; + } + seeds.push(iN); + } + } + return behindBoundary; +} + +template +std::vector +Triangulation::calculateTriangleDepths() const +{ + std::vector triDepths( + triangles.size(), std::numeric_limits::max()); + std::stack seeds(TriDeque(1, m_vertTris[0])); + LayerDepth layerDepth = 0; + LayerDepth deepestSeedDepth = 0; + + unordered_map seedsByDepth; + do + { + const unordered_map& newSeeds = + peelLayer(seeds, layerDepth, triDepths); + + seedsByDepth.erase(layerDepth); + typedef unordered_map::const_iterator Iter; + for(Iter it = newSeeds.begin(); it != newSeeds.end(); ++it) + { + deepestSeedDepth = std::max(deepestSeedDepth, it->second); + seedsByDepth[it->second].insert(it->first); + } + const TriIndUSet& nextLayerSeeds = seedsByDepth[layerDepth + 1]; + seeds = std::stack( + TriDeque(nextLayerSeeds.begin(), nextLayerSeeds.end())); + ++layerDepth; + } while(!seeds.empty() || deepestSeedDepth > layerDepth); + + return triDepths; +} + +#ifdef CDT_ENABLE_CALLBACK_HANDLER +template +void Triangulation::setCallbackHandler( + ICallbackHandler* callbackHandler) +{ + m_callbackHandler = callbackHandler; +} +#endif + +template +void Triangulation::insertVertices_AsProvided( + VertInd superGeomVertCount) +{ + for(VertInd iV = superGeomVertCount; iV < vertices.size(); ++iV) + { +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler && m_callbackHandler->isAbortCalculation()) + { + return; + } +#endif + insertVertex(iV); + } +} + +template +void Triangulation::insertVertices_Randomized( + VertInd superGeomVertCount) +{ + std::size_t vertexCount = vertices.size() - superGeomVertCount; + std::vector ii(vertexCount); + detail::iota(ii.begin(), ii.end(), superGeomVertCount); + detail::random_shuffle(ii.begin(), ii.end()); + for(std::vector::iterator it = ii.begin(); it != ii.end(); ++it) + { +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler && m_callbackHandler->isAbortCalculation()) + { + return; + } +#endif + insertVertex(*it); + } +} + +namespace detail +{ + +// log2 implementation backwards compatible with pre c++11 +template +inline double log2_bc(T x) +{ +#ifdef CDT_CXX11_IS_SUPPORTED + return std::log2(x); +#else + static double log2_constant = std::log(2.0); + return std::log(static_cast(x)) / log2_constant; +#endif +} + +/// Since KD-tree bulk load builds a balanced tree the maximum length of a +/// queue can be pre-calculated: it is calculated as size of a completely +/// filled tree layer plus the number of the nodes on a completely filled +/// layer that have two children. +inline std::size_t maxQueueLengthBFSKDTree(const std::size_t vertexCount) +{ + const int filledLayerPow2 = + static_cast(std::floor(log2_bc(vertexCount)) - 1); + const std::size_t nodesInFilledTree = + static_cast(std::pow(2., filledLayerPow2 + 1) - 1); + const std::size_t nodesInLastFilledLayer = + static_cast(std::pow(2., filledLayerPow2)); + const std::size_t nodesInLastLayer = vertexCount - nodesInFilledTree; + return nodesInLastLayer >= nodesInLastFilledLayer + ? nodesInLastFilledLayer + nodesInLastLayer - + nodesInLastFilledLayer + : nodesInLastFilledLayer; +} + +template +class FixedCapacityQueue +{ +public: + FixedCapacityQueue(const std::size_t capacity) + : m_vec(capacity) + , m_front(m_vec.begin()) + , m_back(m_vec.begin()) + , m_size(0) + {} + bool empty() const + { + return m_size == 0; + } + const T& front() const + { + return *m_front; + } + void pop() + { + assert(m_size > 0); + ++m_front; + if(m_front == m_vec.end()) + m_front = m_vec.begin(); + --m_size; + } + void push(const T& t) + { + assert(m_size < m_vec.size()); + *m_back = t; + ++m_back; + if(m_back == m_vec.end()) + m_back = m_vec.begin(); + ++m_size; + } +#ifdef CDT_CXX11_IS_SUPPORTED + void push(const T&& t) + { + assert(m_size < m_vec.size()); + *m_back = t; + ++m_back; + if(m_back == m_vec.end()) + m_back = m_vec.begin(); + ++m_size; + } +#endif +private: + std::vector m_vec; + typename std::vector::iterator m_front; + typename std::vector::iterator m_back; + std::size_t m_size; +}; + +template +class less_than_x +{ + const std::vector >& m_vertices; + +public: + less_than_x(const std::vector >& vertices) + : m_vertices(vertices) + {} + bool operator()(const VertInd a, const VertInd b) const + { + return m_vertices[a].x < m_vertices[b].x; + } +}; + +template +class less_than_y +{ + const std::vector >& m_vertices; + +public: + less_than_y(const std::vector >& vertices) + : m_vertices(vertices) + {} + bool operator()(const VertInd a, const VertInd b) const + { + return m_vertices[a].y < m_vertices[b].y; + } +}; + +} // namespace detail + +template +void Triangulation::insertVertices_KDTreeBFS( + VertInd superGeomVertCount, + Box2d box) +{ + // calculate original indices + const VertInd vertexCount(vertices.size() - superGeomVertCount); + if(vertexCount <= VertInd(0)) + return; + std::vector ii(vertexCount); + detail::iota(ii.begin(), ii.end(), superGeomVertCount); + + typedef std::vector::iterator It; + detail::FixedCapacityQueue, V2d, VertInd> > queue( + detail::maxQueueLengthBFSKDTree(vertexCount)); + queue.push(make_tuple(ii.begin(), ii.end(), box.min, box.max, VertInd(0))); + + It first, last; + V2d newBoxMin, newBoxMax; + VertInd parent, mid; + + const detail::less_than_x cmpX(vertices); + const detail::less_than_y cmpY(vertices); + + while(!queue.empty()) + { +#ifdef CDT_ENABLE_CALLBACK_HANDLER + if(m_callbackHandler && m_callbackHandler->isAbortCalculation()) + { + return; + } +#endif + tie(first, last, box.min, box.max, parent) = queue.front(); + queue.pop(); + assert(first != last); + + const std::ptrdiff_t len = std::distance(first, last); + if(len == 1) + { + insertVertex(*first, parent); + continue; + } + const It midIt = first + len / 2; + if(box.max.x - box.min.x >= box.max.y - box.min.y) + { + detail::portable_nth_element(first, midIt, last, cmpX); + mid = *midIt; + const T split = vertices[mid].x; + newBoxMin.x = split; + newBoxMin.y = box.min.y; + newBoxMax.x = split; + newBoxMax.y = box.max.y; + } + else + { + detail::portable_nth_element(first, midIt, last, cmpY); + mid = *midIt; + const T split = vertices[mid].y; + newBoxMin.x = box.min.x; + newBoxMin.y = split; + newBoxMax.x = box.max.x; + newBoxMax.y = split; + } + insertVertex(mid, parent); + if(first != midIt) + { + queue.push(make_tuple(first, midIt, box.min, newBoxMax, mid)); + } + if(midIt + 1 != last) + { + queue.push(make_tuple(midIt + 1, last, newBoxMin, box.max, mid)); + } + } +} + +template +std::pair Triangulation::edgeTriangles( + const VertInd a, + const VertInd b) const +{ + const TriInd triStart = m_vertTris[a]; + assert(triStart != noNeighbor); + TriInd iT = triStart, iTNext = triStart; + VertInd iV = noVertex; + do + { + const Triangle& t = triangles[iT]; + tie(iTNext, iV) = t.next(a); + assert(iTNext != noNeighbor); + if(iV == b) + { + return std::make_pair(iT, iTNext); + } + iT = iTNext; + } while(iT != triStart); + return std::make_pair(noNeighbor, noNeighbor); +} + +template +bool Triangulation::hasEdge( + const VertInd a, + const VertInd b) const +{ + return edgeTriangles(a, b).first != invalidIndexSizeType; +} + +template +void Triangulation::setAdjacentTriangle( + const VertInd v, + const TriInd t) +{ + assert(t != noNeighbor); + m_vertTris[v] = t; + assert( + triangles[t].vertices[0] == v || triangles[t].vertices[1] == v || + triangles[t].vertices[2] == v); +} + +template +void Triangulation::pivotVertexTriangleCW(const VertInd v) +{ + assert(m_vertTris[v] != noNeighbor); + m_vertTris[v] = triangles[m_vertTris[v]].next(v).first; + assert(m_vertTris[v] != noNeighbor); + assert( + triangles[m_vertTris[v]].vertices[0] == v || + triangles[m_vertTris[v]].vertices[1] == v || + triangles[m_vertTris[v]].vertices[2] == v); +} + +template +void Triangulation::tryAddVertexToLocator(const VertInd v) +{ + if(!m_nearPtLocator.empty()) // only if locator is initialized already + m_nearPtLocator.addPoint(v, vertices); +} + +template +void Triangulation::tryInitNearestPointLocator() +{ + if(!vertices.empty() && m_nearPtLocator.empty()) + { + m_nearPtLocator.initialize(vertices); + } +} + +} // namespace CDT diff --git a/src/isct/cdt/portable_nth_element.hpp b/src/isct/cdt/portable_nth_element.hpp new file mode 100644 index 00000000..d560f29a --- /dev/null +++ b/src/isct/cdt/portable_nth_element.hpp @@ -0,0 +1,313 @@ +// This code is copied from LLVM's libc++ +// https://github.com/llvm-mirror/libcxx/blob/4dde9ccef57d50e50620408a0b7a902f0aba803e/include/algorithm +// It is needed to provide portable nth_element on different platforms + +// -*- C++ -*- +//===-------------------------- algorithm ---------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#ifndef CDT_PORTABLE_NTH_ELEMENT +#define CDT_PORTABLE_NTH_ELEMENT + +#include +#include +#ifdef CDT_CXX11_IS_SUPPORTED +#include +#else +#include +#endif + +namespace CDT +{ +namespace detail +{ + +// sort + +// stable, 2-3 compares, 0-2 swaps + +template +unsigned +sort3(ForwardIterator x, ForwardIterator y, ForwardIterator z, Compare c) +{ + unsigned r = 0; + if(!c(*y, *x)) // if x <= y + { + if(!c(*z, *y)) // if y <= z + return r; // x <= y && y <= z + // x <= y && y > z + std::swap(*y, *z); // x <= z && y < z + r = 1; + if(c(*y, *x)) // if x > y + { + std::swap(*x, *y); // x < y && y <= z + r = 2; + } + return r; // x <= y && y < z + } + if(c(*z, *y)) // x > y, if y > z + { + std::swap(*x, *z); // x < y && y < z + r = 1; + return r; + } + std::swap(*x, *y); // x > y && y <= z + r = 1; // x < y && x <= z + if(c(*z, *y)) // if y > z + { + std::swap(*y, *z); // x <= y && y < z + r = 2; + } + return r; +} // x <= y && y <= z + +// Assumes size > 0 +template +void selection_sort( + BirdirectionalIterator first, + BirdirectionalIterator last, + Compare comp) +{ + BirdirectionalIterator lm1 = last; + for(--lm1; first != lm1; ++first) + { +#ifdef CDT_CXX11_IS_SUPPORTED + BirdirectionalIterator i = std::min_element< + BirdirectionalIterator, + typename std::add_lvalue_reference::type>( + first, last, comp); +#else + BirdirectionalIterator i = std::min_element< + BirdirectionalIterator, + typename boost::add_lvalue_reference::type>( + first, last, comp); +#endif + if(i != first) + std::swap(*first, *i); + } +} + +// nth_element + +template +void nth_element( + RandomAccessIterator first, + RandomAccessIterator nth, + RandomAccessIterator last, + Compare comp) +{ + // Compare is known to be a reference type + typedef typename std::iterator_traits::difference_type + difference_type; + const difference_type limit = 7; + while(true) + { + restart: + if(nth == last) + return; + difference_type len = last - first; + switch(len) + { + case 0: + case 1: + return; + case 2: + if(comp(*--last, *first)) + std::swap(*first, *last); + return; + case 3: { + RandomAccessIterator m = first; + detail::sort3(first, ++m, --last, comp); + return; + } + } + if(len <= limit) + { + detail::selection_sort(first, last, comp); + return; + } + // len > limit >= 3 + RandomAccessIterator m = first + len / 2; + RandomAccessIterator lm1 = last; + unsigned n_swaps = detail::sort3(first, m, --lm1, comp); + // *m is median + // partition [first, m) < *m and *m <= [m, last) + // (this inhibits tossing elements equivalent to m around + // unnecessarily) + RandomAccessIterator i = first; + RandomAccessIterator j = lm1; + // j points beyond range to be tested, *lm1 is known to be <= *m + // The search going up is known to be guarded but the search coming + // down isn't. Prime the downward search with a guard. + if(!comp(*i, *m)) // if *first == *m + { + // *first == *m, *first doesn't go in first part + // manually guard downward moving j against i + while(true) + { + if(i == --j) + { + // *first == *m, *m <= all other elements + // Parition instead into [first, i) == *first and + // *first < [i, last) + ++i; // first + 1 + j = last; + if(!comp(*first, *--j)) // we need a guard if + // *first == *(last-1) + { + while(true) + { + if(i == j) + return; // [first, last) all equivalent + // elements + if(comp(*first, *i)) + { + std::swap(*i, *j); + ++n_swaps; + ++i; + break; + } + ++i; + } + } + // [first, i) == *first and *first < [j, + // last) and j == last - 1 + if(i == j) + return; + while(true) + { + while(!comp(*first, *i)) + ++i; + while(comp(*first, *--j)) + ; + if(i >= j) + break; + std::swap(*i, *j); + ++n_swaps; + ++i; + } + // [first, i) == *first and *first < [i, + // last) The first part is sorted, + if(nth < i) + return; + // nth_element the secod part + // nth_element(i, nth, last, comp); + first = i; + goto restart; + } + if(comp(*j, *m)) + { + std::swap(*i, *j); + ++n_swaps; + break; // found guard for downward moving j, now use + // unguarded partition + } + } + } + ++i; + // j points beyond range to be tested, *lm1 is known to be <= *m + // if not yet partitioned... + if(i < j) + { + // known that *(i - 1) < *m + while(true) + { + // m still guards upward moving i + while(comp(*i, *m)) + ++i; + // It is now known that a guard exists for downward moving + // j + while(!comp(*--j, *m)) + ; + if(i >= j) + break; + std::swap(*i, *j); + ++n_swaps; + // It is known that m != j + // If m just moved, follow it + if(m == i) + m = j; + ++i; + } + } + // [first, i) < *m and *m <= [i, last) + if(i != m && comp(*m, *i)) + { + std::swap(*i, *m); + ++n_swaps; + } + // [first, i) < *i and *i <= [i+1, last) + if(nth == i) + return; + if(n_swaps == 0) + { + // We were given a perfectly partitioned sequence. Coincidence? + if(nth < i) + { + // Check for [first, i) already sorted + j = m = first; + while(++j != i) + { + if(comp(*j, *m)) + // not yet sorted, so sort + goto not_sorted; + m = j; + } + // [first, i) sorted + return; + } + else + { + // Check for [i, last) already sorted + j = m = i; + while(++j != last) + { + if(comp(*j, *m)) + // not yet sorted, so sort + goto not_sorted; + m = j; + } + // [i, last) sorted + return; + } + } + not_sorted: + // nth_element on range containing nth + if(nth < i) + { + // nth_element(first, nth, i, comp); + last = i; + } + else + { + // nth_element(i+1, nth, last, comp); + first = ++i; + } + } +} + +template +inline void portable_nth_element( + _RandomAccessIterator first, + _RandomAccessIterator nth, + _RandomAccessIterator last, + _Compare comp) +{ +#ifdef CDT_CXX11_IS_SUPPORTED + detail::nth_element::type>( + first, nth, last, comp); +#else + detail::nth_element::type>( + first, nth, last, comp); +#endif +} + +} // namespace detail +} // namespace CDT + +#endif // CDT_PORTABLE_NTH_ELEMENT diff --git a/src/isct/cdt/predicates.h b/src/isct/cdt/predicates.h new file mode 100644 index 00000000..bcdd3a2f --- /dev/null +++ b/src/isct/cdt/predicates.h @@ -0,0 +1,915 @@ +/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * + * * + * Copyright (c) 2019, William C. Lenthe * + * All rights reserved. * + * * + * Redistribution and use in source and binary forms, with or without * + * modification, are permitted provided that the following conditions are met: * + * * + * 1. Redistributions of source code must retain the above copyright notice, this * + * list of conditions and the following disclaimer. * + * * + * 2. Redistributions in binary form must reproduce the above copyright notice, * + * this list of conditions and the following disclaimer in the documentation * + * and/or other materials provided with the distribution. * + * * + * 3. Neither the name of the copyright holder nor the names of its * + * contributors may be used to endorse or promote products derived from * + * this software without specific prior written permission. * + * * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" * + * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE * + * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE * + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR * + * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER * + * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, * + * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * + * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. * + * * + * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ + +#ifndef PREDICATES_H_INCLUDED +#define PREDICATES_H_INCLUDED + +//@reference: https://www.cs.cmu.edu/~quake/robust.html + +namespace predicates { + //@brief: geometric predicates using arbitrary precision arithmetic + //@note : these are provided primarily for illustrative purposes and adaptive routines should be preferred + namespace exact { + //@brief : determine if the 2d point c is above, on, or below the line defined by a and b + //@param ax: X-coordinate of a + //@param ay: Y-coordinate of a + //@param bx: X-coordinate of b + //@param by: Y-coordinate of b + //@param cx: X-coordinate of c + //@param cy: Y-coordinate of c + //@return : determinant of {{ax - cx, ay - cy}, {bx - cx, by - cy}} + //@note : positive, 0, negative result for c above, on, or below the line defined by a -> b + template T orient2d(T const ax, T const ay, T const bx, T const by, T const cx, T const cy); + + //@brief : determine if the 2d point c is above, on, or below the line defined by a and b + //@param pa: pointer to a as {x, y} + //@param pb: pointer to b as {x, y} + //@param pc: pointer to c as {x, y} + //@return : determinant of {{ax - cx, ay - cy}, {bx - cx, by - cy}} + //@note : positive, 0, negative result for c above, on, or below the line defined by a -> b + template T orient2d(T const*const pa, T const*const pb, T const*const pc); + + //@brief : determine if the 2d point d is inside, on, or outside the circle defined by a, b, and c + //@param ax: X-coordinate of a + //@param ay: Y-coordinate of a + //@param bx: X-coordinate of b + //@param by: Y-coordinate of b + //@param cx: X-coordinate of c + //@param cy: Y-coordinate of c + //@param dx: X-coordinate of d + //@param dy: Y-coordinate of d + //@return : determinant of {{ax - dx, ay - dy, (ax - dx)^2 + (ay - dy)^2}, {bx - dx, by - dy, (bx - dx)^2 + (by - dy)^2}, {cx - dx, cy - dy, (cx - dx)^2 + (cy - dy)^2}} + //@note : positive, 0, negative result for d inside, on, or outside the circle defined by a, b, and c + template T incircle(T const ax, T const ay, T const bx, T const by, T const cx, T const cy, T const dx, T const dy); + + //@brief : determine if the 2d point d is inside, on, or outside the circle defined by a, b, and c + //@param pa: pointer to a as {x, y} + //@param pb: pointer to b as {x, y} + //@param pc: pointer to c as {x, y} + //@param pc: pointer to d as {x, y} + //@return : determinant of {{ax - dx, ay - dy, (ax - dx)^2 + (ay - dy)^2}, {bx - dx, by - dy, (bx - dx)^2 + (by - dy)^2}, {cx - dx, cy - dy, (cx - dx)^2 + (cy - dy)^2}} + //@note : positive, 0, negative result for d inside, on, or outside the circle defined by a, b, and c + template T incircle(T const*const pa, T const*const pb, T const*const pc, T const*const pd); + + //@brief : determine if the 3d point d is above, on, or below the plane defined by a, b, and c + //@param pa: pointer to a as {x, y, z} + //@param pb: pointer to b as {x, y, z} + //@param pc: pointer to c as {x, y, z} + //@param pd: pointer to d as {x, y, z} + //@return : determinant of {{ax - dx, ay - dy, az - dz}, {bx - dx, by - dy, bz - dz}, {cx - dx, cy - dy, cz - dz}} + //@note : positive, 0, negative result for c above, on, or below the plane defined by a, b, and c + template T orient3d(T const*const pa, T const*const pb, T const*const pc, T const*const pd); + + //@brief : determine if the 3d point e is inside, on, or outside the sphere defined by a, b, c, and d + //@param pa: pointer to a as {x, y, z} + //@param pb: pointer to b as {x, y, z} + //@param pc: pointer to c as {x, y, z} + //@param pd: pointer to d as {x, y, z} + //@param pe: pointer to e as {x, y, z} + //@return : determinant of {{ax - ex, ay - ey, az - ez, (ax - ex)^2 + (ay - ey)^2 + (az - ez)^2}, {bx - ex, by - ey, bz - ez, (bx - ex)^2 + (by - ey)^2 + (bz - ez)^2}, {cx - ex, cy - ey, cz - ez, (cx - ex)^2 + (cy - ey)^2 + (cz - ez)^2}, {dx - ex, dy - ey, dz - ez, (dx - ex)^2 + (dy - ey)^2 + (dz - ez)^2}} + //@note : positive, 0, negative result for d inside, on, or outside the circle defined by a, b, and c + template T insphere(T const*const pa, T const*const pb, T const*const pc, T const*const pd, T const*const pe); + } + + //@brief: geometric predicates using normal floating point arithmetic but falling back to arbitrary precision when needed + //@note : these should have the same accuracy but are significantly faster when determinants are large + namespace adaptive { + //@brief : determine if the 2d point c is above, on, or below the line defined by a and b + //@param ax: X-coordinate of a + //@param ay: Y-coordinate of a + //@param bx: X-coordinate of b + //@param by: Y-coordinate of b + //@param cx: X-coordinate of c + //@param cy: Y-coordinate of c + //@return : determinant of {{ax - cx, ay - cy}, {bx - cx, by - cy}} + //@note : positive, 0, negative result for c above, on, or below the line defined by a -> b + template T orient2d(T const ax, T const ay, T const bx, T const by, T const cx, T const cy); + + //@brief : determine if the 2d point c is above, on, or below the line defined by a and b + //@param pa: pointer to a as {x, y} + //@param pb: pointer to b as {x, y} + //@param pc: pointer to c as {x, y} + //@return : determinant of {{ax - cx, ay - cy}, {bx - cx, by - cy}} + //@note : positive, 0, negative result for c above, on, or below the line defined by a -> b + template T orient2d(T const*const pa, T const*const pb, T const*const pc); + + //@brief : determine if the 2d point d is inside, on, or outside the circle defined by a, b, and c + //@param ax: X-coordinate of a + //@param ay: Y-coordinate of a + //@param bx: X-coordinate of b + //@param by: Y-coordinate of b + //@param cx: X-coordinate of c + //@param cy: Y-coordinate of c + //@param dx: X-coordinate of d + //@param dy: Y-coordinate of d + //@return : determinant of {{ax - dx, ay - dy, (ax - dx)^2 + (ay - dy)^2}, {bx - dx, by - dy, (bx - dx)^2 + (by - dy)^2}, {cx - dx, cy - dy, (cx - dx)^2 + (cy - dy)^2}} + //@note : positive, 0, negative result for d inside, on, or outside the circle defined by a, b, and c + template T incircle(T const ax, T const ay, T const bx, T const by, T const cx, T const cy, T const dx, T const dy); + + //@brief : determine if the 2d point d is inside, on, or outside the circle defined by a, b, and c + //@param pa: pointer to a as {x, y} + //@param pb: pointer to b as {x, y} + //@param pc: pointer to c as {x, y} + //@param pc: pointer to d as {x, y} + //@return : determinant of {{ax - dx, ay - dy, (ax - dx)^2 + (ay - dy)^2}, {bx - dx, by - dy, (bx - dx)^2 + (by - dy)^2}, {cx - dx, cy - dy, (cx - dx)^2 + (cy - dy)^2}} + //@note : positive, 0, negative result for d inside, on, or outside the circle defined by a, b, and c + template T incircle(T const*const pa, T const*const pb, T const*const pc, T const*const pd); + + //@brief : determine if the 3d point d is above, on, or below the plane defined by a, b, and c + //@param pa: pointer to a as {x, y, z} + //@param pb: pointer to b as {x, y, z} + //@param pc: pointer to c as {x, y, z} + //@param pd: pointer to d as {x, y, z} + //@return : determinant of {{ax - dx, ay - dy, az - dz}, {bx - dx, by - dy, bz - dz}, {cx - dx, cy - dy, cz - dz}} + //@note : positive, 0, negative result for c above, on, or below the plane defined by a, b, and c + template T orient3d(T const*const pa, T const*const pb, T const*const pc, T const*const pd); + + //@brief : determine if the 3d point e is inside, on, or outside the sphere defined by a, b, c, and d + //@param pa: pointer to a as {x, y, z} + //@param pb: pointer to b as {x, y, z} + //@param pc: pointer to c as {x, y, z} + //@param pd: pointer to d as {x, y, z} + //@param pe: pointer to e as {x, y, z} + //@return : determinant of {{ax - ex, ay - ey, az - ez, (ax - ex)^2 + (ay - ey)^2 + (az - ez)^2}, {bx - ex, by - ey, bz - ez, (bx - ex)^2 + (by - ey)^2 + (bz - ez)^2}, {cx - ex, cy - ey, cz - ez, (cx - ex)^2 + (cy - ey)^2 + (cz - ez)^2}, {dx - ex, dy - ey, dz - ez, (dx - ex)^2 + (dy - ey)^2 + (dz - ez)^2}} + //@note : positive, 0, negative result for d inside, on, or outside the circle defined by a, b, and c + template T insphere(T const*const pa, T const*const pb, T const*const pc, T const*const pd, T const*const pe); + } +} + +#include //abs, fma +#include +#include //pair +#include //accumulate +#include //transform, copy_n, merge +#include //negate + +// a macro based static assert for pre c++11 +#define PREDICATES_PORTABLE_STATIC_ASSERT(condition, message) typedef char message[(condition) ? 1 : -1] + +// check if c++11 is supported +#if !defined(__cplusplus) && !defined(_MSC_VER) + PREDICATES_PORTABLE_STATIC_ASSERT(false, couldnt_parse_cxx_standard) +#endif +#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900) + #define PREDICATES_CXX11_IS_SUPPORTED +#endif + +// choose to use c++11 features or their backports +#ifdef PREDICATES_CXX11_IS_SUPPORTED +#include +#include // is_same, enable_if +#undef PREDICATES_PORTABLE_STATIC_ASSERT +#define PREDICATES_TOKEN_TO_STRING1(x) #x +#define PREDICATES_TOKEN_TO_STRING(x) PREDICATES_TOKEN_TO_STRING1(x) +#define PREDICATES_PORTABLE_STATIC_ASSERT(condition, message) static_assert(condition, PREDICATES_TOKEN_TO_STRING(message)) +namespace predicates { +namespace stdx { + using std::array; + using std::copy_n; +} +#else +namespace predicates { +namespace stdx { + // array + template + class array { + T buff[N]; + public: + T& operator[](const size_t& i) { return buff[i]; } + const T& operator[](const size_t& i) const { return buff[i]; } + + T * data() { return buff; } + T const * data() const { return buff; } + + T * begin() { return buff; } + T const * cbegin() const { return buff; } + }; + // copy_n + template< class InputIt, class Size, class OutputIt> + OutputIt copy_n(InputIt first, Size count, OutputIt result) + { + if (count > 0) { + *result++ = *first; + for (Size i = 1; i < count; ++i) { + *result++ = *++first; + } + } + return result; + } +} +#endif // PREDICATES_CXX11_IS_SUPPORTED + +namespace detail { + template class ExpansionBase; + + //@brief: class to exactly represent the result of a sequence of arithmetic operations as an sequence of values that sum to the result + template + class Expansion : private ExpansionBase, public stdx::array { + private: + public: + size_t m_size; + template friend class ExpansionBase;//access for base class + template friend class Expansion;//access for expansions of different size + + Expansion() : m_size(0) {} + template Expansion& operator=(const Expansion& e) { + PREDICATES_PORTABLE_STATIC_ASSERT(M <= N, cannot_assign_a_larger_expansion_to_a_smaller_expansion); + stdx::copy_n(e.cbegin(), e.size(), stdx::array::begin()); + m_size = e.size(); + return *this; + } + + //vector like convenience functions + size_t size() const {return m_size;} + bool empty() const {return 0 == m_size;} + void push_back(const T v) {stdx::array::operator[](m_size++) = v;} + + public: + //estimates of expansion value + T mostSignificant() const {return empty() ? T(0) : stdx::array::operator[](m_size - 1);} + T estimate() const {return std::accumulate(stdx::array::cbegin(), stdx::array::cbegin() + size(), T(0));} + + template Expansion operator+(const Expansion& f) const { + Expansion h; + h.m_size = ExpansionBase::ExpansionSum(this->data(), this->size(), f.data(), f.size(), h.data()); + return h; + } + + void negate() {std::transform(stdx::array::cbegin(), stdx::array::cbegin() + size(), stdx::array::begin(), std::negate());} + Expansion operator-() const {Expansion e = *this; e.negate(); return e;} + template Expansion operator-(const Expansion& f) const {return operator+(-f);} + + Expansion operator*(const T b) const { + Expansion h; + h.m_size = ExpansionBase::ScaleExpansion(this->data(), this->size(), b, h.data()); + return h; + } + }; + +// See: https://stackoverflow.com/a/40765925/1597714 +// Standard defines: https://en.cppreference.com/w/cpp/numeric/math/fma +#if defined(__FMA__) || defined(__FMA4__) || defined(__AVX2__) || (defined(FP_FAST_FMA) && defined(FP_FAST_FMAF)) +#define PREDICATES_FAST_FMA 1 +#endif + + //@brief : helper function to sort by absolute value + //@param a: lhs item to compare + //@param b: rhs item to compare + //@return : true if |a| < |b| + //@note : defined since lambda functions aren't allow in c++03 + template bool absLess(const T& a, const T& b) {return std::abs(a) < std::abs(b);} + + template + class ExpansionBase { + private: + static const T Splitter; + + PREDICATES_PORTABLE_STATIC_ASSERT(std::numeric_limits::is_iec559, Requires_IEC_559_IEEE_754_floating_point_type); + PREDICATES_PORTABLE_STATIC_ASSERT(2 == std::numeric_limits::radix, Requires_base_2_floating_point_type); + + //combine result + roundoff error into expansion + static inline Expansion MakeExpansion(const T value, const T tail) { + Expansion e; + if(T(0) != tail) e.push_back(tail); + if(T(0) != value) e.push_back(value); + return e; + } + + protected: + //add 2 expansions + static size_t ExpansionSum(T const * const e, const size_t n, T const * const f, const size_t m, T * const h) { + std::merge(e, e + n, f, f + m, h, absLess); + if(m == 0) return n; + if(n == 0) return m; + size_t hIndex = 0; + T Q = h[0]; + T Qnew = h[1] + Q; + T hh = FastPlusTail(h[1], Q, Qnew); + Q = Qnew; + if(T(0) != hh) h[hIndex++] = hh; + for(size_t g = 2; g != n + m; ++g) { + Qnew = Q + h[g]; + hh = PlusTail(Q, h[g], Qnew); + Q = Qnew; + if(T(0) != hh) h[hIndex++] = hh; + } + if(T(0) != Q) h[hIndex++] = Q; + return hIndex; + } + + //scale an expansion by a constant + static size_t ScaleExpansion(T const * const e, const size_t n, const T b, T * const h) { + if(n == 0 || T(0) == b) return 0; + size_t hIndex = 0; + T Q = e[0] * b; + const std::pair bSplit = Split(b); + T hh = MultTailPreSplit(e[0], b, bSplit, Q); + if(T(0) != hh) h[hIndex++] = hh; + for(size_t eIndex = 1; eIndex < n; ++eIndex) { + T Ti = e[eIndex] * b; + T ti = MultTailPreSplit(e[eIndex], b, bSplit, Ti); + T Qi = Q + ti; + hh = PlusTail(Q, ti, Qi); + if(T(0) != hh) h[hIndex++] = hh; + Q = Ti + Qi; + hh = FastPlusTail(Ti, Qi, Q); + if(T(0) != hh) h[hIndex++] = hh; + } + if(T(0) != Q) h[hIndex++] = Q; + return hIndex; + } + + public: + //roundoff error of x = a + b + static inline T PlusTail(const T a, const T b, const T x) { + const T bVirtual = x - a; + const T aVirtual = x - bVirtual; + const T bRoundoff = b - bVirtual; + const T aRoundoff = a - aVirtual; + return aRoundoff + bRoundoff; + } + + //roundoff error of x = a + b if |a| > |b| + static inline T FastPlusTail(const T a, const T b, const T x) { + const T bVirtual = x - a; + return b - bVirtual; + } + + //roundoff error of x = a - b + static inline T MinusTail(const T a, const T b, const T x) { + const T bVirtual = a - x; + const T aVirtual = x + bVirtual; + const T bRoundoff = bVirtual - b; + const T aRoundoff = a - aVirtual; + return aRoundoff + bRoundoff; + } + + //split a into 2 nonoverlapping values + static inline std::pair Split(const T a) { + const T c = a * Splitter; + const T aBig = c - a; + const T aHi = c - aBig; + return std::pair(aHi, a - aHi); + } + + //roundoff error of x = a * b via dekkers product + static inline T DekkersProduct(const T /*a*/, const std::pair aSplit, const T /*b*/, const std::pair bSplit, const T p) { + T y = p - T(aSplit.first * bSplit.first); + y -= T(aSplit.second * bSplit.first); + y -= T(aSplit.first * bSplit.second); + return T(aSplit.second * bSplit.second) - y; + } + + //roundoff error of x = a * b +#if defined(PREDICATES_CXX11_IS_SUPPORTED) && defined(PREDICATES_FAST_FMA) + static T MultTail(const T a, const T b, const T p) {return std::fma(a, b, -p);} + static T MultTailPreSplit(const T a, const T b, const std::pair /*bSplit*/, const T p) {return std::fma(a, b, -p);} +#else + static T MultTail(const T a, const T b, const T p) {return DekkersProduct(a, Split(a), b, Split(b), p);} + static T MultTailPreSplit(const T a, const T b, const std::pair bSplit, const T p) {return DekkersProduct(a, Split(a), b, bSplit, p);} +#endif + //expand a + b + static inline Expansion Plus(const T a, const T b) { + const T x = a + b; + return MakeExpansion(x, PlusTail(a, b, x)); + } + + //expand a - b + static inline Expansion Minus(const T a, const T b) {return Plus(a, -b);} + + //expand a * b + static inline Expansion Mult(const T a, const T b) { + const T x = a * b; + return MakeExpansion(x, MultTail(a, b, x)); + } + + //expand the determinant of {{ax, ay}, {bx, by}} (unrolled Mult(ax, by) - Mult(ay, bx)) + static inline Expansion TwoTwoDiff(const T ax, const T by, const T ay, const T bx) { + const T axby1 = ax * by; + const T axby0 = MultTail(ax, by, axby1); + const T bxay1 = bx * ay; + const T bxay0 = MultTail(bx, ay, bxay1); + const T _i0 = axby0 - bxay0; + const T x0 = MinusTail(axby0, bxay0, _i0); + const T _j = axby1 + _i0; + const T _0 = PlusTail(axby1, _i0, _j); + const T _i1 = _0 - bxay1; + const T x1 = MinusTail(_0, bxay1, _i1); + const T x3 = _j + _i1; + const T x2 = PlusTail(_j, _i1, x3); + Expansion e; + if(T(0) != x0) e.push_back(x0); + if(T(0) != x1) e.push_back(x1); + if(T(0) != x2) e.push_back(x2); + if(T(0) != x3) e.push_back(x3); + return e; + } + + //TwoTwoDiff checking for zeros to avoid extra splitting + static inline Expansion TwoTwoDiffZeroCheck(const T ax, const T by, const T ay, const T bx) { + Expansion e; + if(T(0) == ax && T(0) == ay) return e; + else if(T(0) == ax) e = Mult(ay, bx); + else if(T(0) == ay) e = Mult(ax, by); + else e = TwoTwoDiff(ax, by, ay, bx); + return e; + } + + //(a * b) * c checking for zeros + static inline Expansion ThreeProd(const T a, const T b, const T c) {return (T(0) == a || T(0) == b || T(0) == c) ? Expansion() : Mult(a, b) * c;} + }; + + template const T ExpansionBase::Splitter = +#ifdef PREDICATES_CXX11_IS_SUPPORTED + static_cast(std::exp2(std::numeric_limits::digits/2 + 1)); +#else + static_cast(std::ldexp(T(1), std::numeric_limits::digits/2 + 1)); +#endif +} + + namespace exact { + template T orient2d(T const ax, T const ay, T const bx, T const by, T const cx, T const cy) + { + const detail::Expansion aterms = detail::ExpansionBase::TwoTwoDiff(ax, by, ax, cy); + const detail::Expansion bterms = detail::ExpansionBase::TwoTwoDiff(bx, cy, bx, ay); + const detail::Expansion cterms = detail::ExpansionBase::TwoTwoDiff(cx, ay, cx, by); + const detail::Expansion w = aterms + bterms + cterms; + return w.mostSignificant(); + } + + template T orient2d(T const*const pa, T const*const pb, T const*const pc) { + return orient2d(pa[0], pa[1], pb[0], pb[1], pc[0], pc[1]); + } + + template T incircle(T const ax, T const ay, T const bx, T const by, T const cx, T const cy, T const dx, T const dy) { + const detail::Expansion ab = detail::ExpansionBase::TwoTwoDiff(ax, by, bx, ay); + const detail::Expansion bc = detail::ExpansionBase::TwoTwoDiff(bx, cy, cx, by); + const detail::Expansion cd = detail::ExpansionBase::TwoTwoDiff(cx, dy, dx, cy); + const detail::Expansion da = detail::ExpansionBase::TwoTwoDiff(dx, ay, ax, dy); + const detail::Expansion ac = detail::ExpansionBase::TwoTwoDiff(ax, cy, cx, ay); + const detail::Expansion bd = detail::ExpansionBase::TwoTwoDiff(bx, dy, dx, by); + + const detail::Expansion abc = ab + bc - ac; + const detail::Expansion bcd = bc + cd - bd; + const detail::Expansion cda = cd + da + ac; + const detail::Expansion dab = da + ab + bd; + + const detail::Expansion adet = bcd * ax * ax + bcd * ay * ay; + const detail::Expansion bdet = cda * bx * -bx + cda * by * -by; + const detail::Expansion cdet = dab * cx * cx + dab * cy * cy; + const detail::Expansion ddet = abc * dx * -dx + abc * dy * -dy; + + const detail::Expansion deter = (adet + bdet) + (cdet + ddet); + return deter.mostSignificant(); + } + + template T incircle(T const*const pa, T const*const pb, T const*const pc, T const*const pd) { + return incircle(pa[0], pa[1], pb[0], pb[1], pc[0], pc[1], pd[0], pd[1]); + } + + //@brief : determine if the 3d point d is above, on, or below the plane defined by a, b, and c + //@param pa: pointer to a as {x, y, z} + //@param pb: pointer to b as {x, y, z} + //@param pc: pointer to c as {x, y, z} + //@param pd: pointer to d as {x, y, z} + //@return : determinant of {{ax - dx, ay - dy, az - dz}, {bx - dx, by - dy, bz - dz}, {cx - dx, cy - dy, cz - dz}} + //@note : positive, 0, negative result for c above, on, or below the plane defined by a, b, and c + template T orient3d(T const*const pa, T const*const pb, T const*const pc, T const*const pd) { + const detail::Expansion ab = detail::ExpansionBase::TwoTwoDiff(pa[0], pb[1], pb[0], pa[1]); + const detail::Expansion bc = detail::ExpansionBase::TwoTwoDiff(pb[0], pc[1], pc[0], pb[1]); + const detail::Expansion cd = detail::ExpansionBase::TwoTwoDiff(pc[0], pd[1], pd[0], pc[1]); + const detail::Expansion da = detail::ExpansionBase::TwoTwoDiff(pd[0], pa[1], pa[0], pd[1]); + const detail::Expansion ac = detail::ExpansionBase::TwoTwoDiff(pa[0], pc[1], pc[0], pa[1]); + const detail::Expansion bd = detail::ExpansionBase::TwoTwoDiff(pb[0], pd[1], pd[0], pb[1]); + + const detail::Expansion abc = ab + bc - ac; + const detail::Expansion bcd = bc + cd - bd; + const detail::Expansion cda = cd + da + ac; + const detail::Expansion dab = da + ab + bd; + + const detail::Expansion adet = bcd * pa[2]; + const detail::Expansion bdet = cda * -pb[2]; + const detail::Expansion cdet = dab * pc[2]; + const detail::Expansion ddet = abc * -pd[2]; + + const detail::Expansion deter = (adet + bdet) + (cdet + ddet); + return deter.mostSignificant(); + } + + //@brief : determine if the 3d point e is inside, on, or outside the sphere defined by a, b, c, and d + //@param pa: pointer to a as {x, y, z} + //@param pb: pointer to b as {x, y, z} + //@param pc: pointer to c as {x, y, z} + //@param pd: pointer to d as {x, y, z} + //@param pe: pointer to e as {x, y, z} + //@return : determinant of {{ax - ex, ay - ey, az - ez, (ax - ex)^2 + (ay - ey)^2 + (az - ez)^2}, {bx - ex, by - ey, bz - ez, (bx - ex)^2 + (by - ey)^2 + (bz - ez)^2}, {cx - ex, cy - ey, cz - ez, (cx - ex)^2 + (cy - ey)^2 + (cz - ez)^2}, {dx - ex, dy - ey, dz - ez, (dx - ex)^2 + (dy - ey)^2 + (dz - ez)^2}} + //@note : positive, 0, negative result for d inside, on, or outside the circle defined by a, b, and c + template T insphere(T const*const pa, T const*const pb, T const*const pc, T const*const pd, T const*const pe) { + const detail::Expansion ab = detail::ExpansionBase::TwoTwoDiff(pa[0], pb[1], pb[0], pa[1]); + const detail::Expansion bc = detail::ExpansionBase::TwoTwoDiff(pb[0], pc[1], pc[0], pb[1]); + const detail::Expansion cd = detail::ExpansionBase::TwoTwoDiff(pc[0], pd[1], pd[0], pc[1]); + const detail::Expansion de = detail::ExpansionBase::TwoTwoDiff(pd[0], pe[1], pe[0], pd[1]); + const detail::Expansion ea = detail::ExpansionBase::TwoTwoDiff(pe[0], pa[1], pa[0], pe[1]); + const detail::Expansion ac = detail::ExpansionBase::TwoTwoDiff(pa[0], pc[1], pc[0], pa[1]); + const detail::Expansion bd = detail::ExpansionBase::TwoTwoDiff(pb[0], pd[1], pd[0], pb[1]); + const detail::Expansion ce = detail::ExpansionBase::TwoTwoDiff(pc[0], pe[1], pe[0], pc[1]); + const detail::Expansion da = detail::ExpansionBase::TwoTwoDiff(pd[0], pa[1], pa[0], pd[1]); + const detail::Expansion eb = detail::ExpansionBase::TwoTwoDiff(pe[0], pb[1], pb[0], pe[1]); + + const detail::Expansion abc = bc * pa[2] + ac * -pb[2] + ab * pc[2]; + const detail::Expansion bcd = cd * pb[2] + bd * -pc[2] + bc * pd[2]; + const detail::Expansion cde = de * pc[2] + ce * -pd[2] + cd * pe[2]; + const detail::Expansion dea = ea * pd[2] + da * -pe[2] + de * pa[2]; + const detail::Expansion eab = ab * pe[2] + eb * -pa[2] + ea * pb[2]; + const detail::Expansion abd = bd * pa[2] + da * pb[2] + ab * pd[2]; + const detail::Expansion bce = ce * pb[2] + eb * pc[2] + bc * pe[2]; + const detail::Expansion cda = da * pc[2] + ac * pd[2] + cd * pa[2]; + const detail::Expansion deb = eb * pd[2] + bd * pe[2] + de * pb[2]; + const detail::Expansion eac = ac * pe[2] + ce * pa[2] + ea * pc[2]; + + const detail::Expansion bcde = (cde + bce) - (deb + bcd); + const detail::Expansion cdea = (dea + cda) - (eac + cde); + const detail::Expansion deab = (eab + deb) - (abd + dea); + const detail::Expansion eabc = (abc + eac) - (bce + eab); + const detail::Expansion abcd = (bcd + abd) - (cda + abc); + + const detail::Expansion adet = bcde * pa[0] * pa[0] + bcde * pa[1] * pa[1] + bcde * pa[2] * pa[2]; + const detail::Expansion bdet = cdea * pb[0] * pb[0] + cdea * pb[1] * pb[1] + cdea * pb[2] * pb[2]; + const detail::Expansion cdet = deab * pc[0] * pc[0] + deab * pc[1] * pc[1] + deab * pc[2] * pc[2]; + const detail::Expansion ddet = eabc * pd[0] * pd[0] + eabc * pd[1] * pd[1] + eabc * pd[2] * pd[2]; + const detail::Expansion edet = abcd * pe[0] * pe[0] + abcd * pe[1] * pe[1] + abcd * pe[2] * pe[2]; + + const detail::Expansion deter = (adet + bdet) + ((cdet + ddet) + edet); + return deter.mostSignificant(); + } + } + + template + const T& Epsilon() + { + static const T epsilon = +#ifdef PREDICATES_CXX11_IS_SUPPORTED + static_cast(std::exp2(-std::numeric_limits::digits)); +#else + static_cast(std::ldexp(T(1), -std::numeric_limits::digits)); +#endif + return epsilon; + } + + template + class Constants { + public: + static const T epsilon, resulterrbound; + static const T ccwerrboundA, ccwerrboundB, ccwerrboundC; + static const T o3derrboundA, o3derrboundB, o3derrboundC; + static const T iccerrboundA, iccerrboundB, iccerrboundC; + static const T isperrboundA, isperrboundB, isperrboundC; + }; + + template const T Constants::epsilon = Epsilon(); + template const T Constants::resulterrbound = (T( 3) + T( 8) * Epsilon()) * Epsilon(); + template const T Constants::ccwerrboundA = (T( 3) + T( 16) * Epsilon()) * Epsilon(); + template const T Constants::ccwerrboundB = (T( 2) + T( 12) * Epsilon()) * Epsilon(); + template const T Constants::ccwerrboundC = (T( 9) + T( 64) * Epsilon()) * Epsilon() * Epsilon(); + template const T Constants::o3derrboundA = (T( 7) + T( 56) * Epsilon()) * Epsilon(); + template const T Constants::o3derrboundB = (T( 3) + T( 28) * Epsilon()) * Epsilon(); + template const T Constants::o3derrboundC = (T(26) + T( 288) * Epsilon()) * Epsilon() * Epsilon(); + template const T Constants::iccerrboundA = (T(10) + T( 96) * Epsilon()) * Epsilon(); + template const T Constants::iccerrboundB = (T( 4) + T( 48) * Epsilon()) * Epsilon(); + template const T Constants::iccerrboundC = (T(44) + T( 576) * Epsilon()) * Epsilon() * Epsilon(); + template const T Constants::isperrboundA = (T(16) + T( 224) * Epsilon()) * Epsilon(); + template const T Constants::isperrboundB = (T( 5) + T( 72) * Epsilon()) * Epsilon(); + template const T Constants::isperrboundC = (T(71) + T(1408) * Epsilon()) * Epsilon() * Epsilon(); + + namespace adaptive { + template T orient2d(T const ax, T const ay, T const bx, T const by, T const cx, T const cy) { + const T acx = ax - cx; + const T bcx = bx - cx; + const T acy = ay - cy; + const T bcy = by - cy; + const T detleft = acx * bcy; + const T detright = acy * bcx; + T det = detleft - detright; + if((detleft < 0) != (detright < 0)) return det; + if(T(0) == detleft || T(0) == detright) return det; + + const T detsum = std::abs(detleft + detright); + T errbound = Constants::ccwerrboundA * detsum; + if(std::abs(det) >= std::abs(errbound)) return det; + + const detail::Expansion B = detail::ExpansionBase::TwoTwoDiff(acx, bcy, acy, bcx); + det = B.estimate(); + errbound = Constants::ccwerrboundB * detsum; + if(std::abs(det) >= std::abs(errbound)) return det; + + const T acxtail = detail::ExpansionBase::MinusTail(ax, cx, acx); + const T bcxtail = detail::ExpansionBase::MinusTail(bx, cx, bcx); + const T acytail = detail::ExpansionBase::MinusTail(ay, cy, acy); + const T bcytail = detail::ExpansionBase::MinusTail(by, cy, bcy); + if(T(0) == acxtail && T(0) == bcxtail && T(0) == acytail && T(0) == bcytail) return det; + + errbound = Constants::ccwerrboundC * detsum + Constants::resulterrbound * std::abs(det); + det += (acx * bcytail + bcy * acxtail) - (acy * bcxtail + bcx * acytail); + if(std::abs(det) >= std::abs(errbound)) return det; + + const detail::Expansion D = ((B + detail::ExpansionBase::TwoTwoDiff(acxtail, bcy, acytail, bcx)) + detail::ExpansionBase::TwoTwoDiff(acx, bcytail, acy, bcxtail)) + detail::ExpansionBase::TwoTwoDiff(acxtail, bcytail, acytail, bcxtail); + return D.mostSignificant(); + } + + template T orient2d(T const*const pa, T const*const pb, T const*const pc) { + return orient2d(pa[0], pa[1], pb[0], pb[1], pc[0], pc[1]); + } + + template T incircle(T const ax, T const ay, T const bx, T const by, T const cx, T const cy, T const dx, T const dy) { + const T adx = ax - dx; + const T bdx = bx - dx; + const T cdx = cx - dx; + const T ady = ay - dy; + const T bdy = by - dy; + const T cdy = cy - dy; + const T bdxcdy = bdx * cdy; + const T cdxbdy = cdx * bdy; + const T cdxady = cdx * ady; + const T adxcdy = adx * cdy; + const T adxbdy = adx * bdy; + const T bdxady = bdx * ady; + const T alift = adx * adx + ady * ady; + const T blift = bdx * bdx + bdy * bdy; + const T clift = cdx * cdx + cdy * cdy; + T det = alift * (bdxcdy - cdxbdy) + blift * (cdxady - adxcdy) + clift * (adxbdy - bdxady); + const T permanent = (std::abs(bdxcdy) + std::abs(cdxbdy)) * alift + + (std::abs(cdxady) + std::abs(adxcdy)) * blift + + (std::abs(adxbdy) + std::abs(bdxady)) * clift; + T errbound = Constants::iccerrboundA * permanent; + if(std::abs(det) >= std::abs(errbound)) return det; + + const detail::Expansion bc = detail::ExpansionBase::TwoTwoDiff(bdx, cdy, cdx, bdy); + const detail::Expansion ca = detail::ExpansionBase::TwoTwoDiff(cdx, ady, adx, cdy); + const detail::Expansion ab = detail::ExpansionBase::TwoTwoDiff(adx, bdy, bdx, ady); + const detail::Expansion adet = bc * adx * adx + bc * ady * ady; + const detail::Expansion bdet = ca * bdx * bdx + ca * bdy * bdy; + const detail::Expansion cdet = ab * cdx * cdx + ab * cdy * cdy; + const detail::Expansion fin1 = adet + bdet + cdet; + det = fin1.estimate(); + errbound = Constants::iccerrboundB * permanent; + if(std::abs(det) >= std::abs(errbound)) return det; + + const T adxtail = detail::ExpansionBase::MinusTail(ax, dx, adx); + const T adytail = detail::ExpansionBase::MinusTail(ay, dy, ady); + const T bdxtail = detail::ExpansionBase::MinusTail(bx, dx, bdx); + const T bdytail = detail::ExpansionBase::MinusTail(by, dy, bdy); + const T cdxtail = detail::ExpansionBase::MinusTail(cx, dx, cdx); + const T cdytail = detail::ExpansionBase::MinusTail(cy, dy, cdy); + if(T(0) == adxtail && T(0) == bdxtail && T(0) == cdxtail && T(0) == adytail && T(0) == bdytail && T(0) == cdytail) return det; + + errbound = Constants::iccerrboundC * permanent + Constants::resulterrbound * std::abs(det); + det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail) - (bdy * cdxtail + cdx * bdytail)) + + (bdx * cdy - bdy * cdx) * (adx * adxtail + ady * adytail) * T(2)) + + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail) - (cdy * adxtail + adx * cdytail)) + + (cdx * ady - cdy * adx) * (bdx * bdxtail + bdy * bdytail) * T(2)) + + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail) - (ady * bdxtail + bdx * adytail)) + + (adx * bdy - ady * bdx) * (cdx * cdxtail + cdy * cdytail) * T(2)); + if(std::abs(det) >= std::abs(errbound)) return det; + return exact::incircle(ax, ay, bx, by, cx, cy, dx, dy); + } + + template T incircle(T const*const pa, T const*const pb, T const*const pc, T const*const pd) { + return incircle(pa[0], pa[1], pb[0], pb[1], pc[0], pc[1], pd[0], pd[1]); + } + + //@brief : determine if the 3d point d is above, on, or below the plane defined by a, b, and c + //@param pa: pointer to a as {x, y, z} + //@param pb: pointer to b as {x, y, z} + //@param pc: pointer to c as {x, y, z} + //@param pd: pointer to d as {x, y, z} + //@return : determinant of {{ax - dx, ay - dy, az - dz}, {bx - dx, by - dy, bz - dz}, {cx - dx, cy - dy, cz - dz}} + //@note : positive, 0, negative result for c above, on, or below the plane defined by a, b, and c + template T orient3d(T const*const pa, T const*const pb, T const*const pc, T const*const pd) { + const T adx = pa[0] - pd[0]; + const T bdx = pb[0] - pd[0]; + const T cdx = pc[0] - pd[0]; + const T ady = pa[1] - pd[1]; + const T bdy = pb[1] - pd[1]; + const T cdy = pc[1] - pd[1]; + const T adz = pa[2] - pd[2]; + const T bdz = pb[2] - pd[2]; + const T cdz = pc[2] - pd[2]; + const T bdxcdy = bdx * cdy; + const T cdxbdy = cdx * bdy; + const T cdxady = cdx * ady; + const T adxcdy = adx * cdy; + const T adxbdy = adx * bdy; + const T bdxady = bdx * ady; + T det = adz * (bdxcdy - cdxbdy) + bdz * (cdxady - adxcdy) + cdz * (adxbdy - bdxady); + const T permanent = (std::abs(bdxcdy) + std::abs(cdxbdy)) * std::abs(adz) + (std::abs(cdxady) + std::abs(adxcdy)) * std::abs(bdz) + (std::abs(adxbdy) + std::abs(bdxady)) * std::abs(cdz); + T errbound = Constants::o3derrboundA * permanent; + if(std::abs(det) >= std::abs(errbound)) return det; + + const detail::Expansion bc = detail::ExpansionBase::TwoTwoDiff(bdx, cdy, cdx, bdy); + const detail::Expansion ca = detail::ExpansionBase::TwoTwoDiff(cdx, ady, adx, cdy); + const detail::Expansion ab = detail::ExpansionBase::TwoTwoDiff(adx, bdy, bdx, ady); + const detail::Expansion fin1 = (bc * adz + ca * bdz) + ab * cdz; + det = fin1.estimate(); + errbound = Constants::o3derrboundB * permanent; + if(std::abs(det) >= std::abs(errbound)) return det; + + const T adxtail = detail::ExpansionBase::MinusTail(pa[0], pd[0], adx); + const T bdxtail = detail::ExpansionBase::MinusTail(pb[0], pd[0], bdx); + const T cdxtail = detail::ExpansionBase::MinusTail(pc[0], pd[0], cdx); + const T adytail = detail::ExpansionBase::MinusTail(pa[1], pd[1], ady); + const T bdytail = detail::ExpansionBase::MinusTail(pb[1], pd[1], bdy); + const T cdytail = detail::ExpansionBase::MinusTail(pc[1], pd[1], cdy); + const T adztail = detail::ExpansionBase::MinusTail(pa[2], pd[2], adz); + const T bdztail = detail::ExpansionBase::MinusTail(pb[2], pd[2], bdz); + const T cdztail = detail::ExpansionBase::MinusTail(pc[2], pd[2], cdz); + if(T(0) == adxtail && T(0) == adytail && T(0) == adztail && + T(0) == bdxtail && T(0) == bdytail && T(0) == bdztail && + T(0) == cdxtail && T(0) == cdytail && T(0) == cdztail) return det; + + errbound = Constants::o3derrboundC * permanent + Constants::resulterrbound * std::abs(det); + det += (adz * ((bdx * cdytail + cdy * bdxtail) - (bdy * cdxtail + cdx * bdytail)) + adztail * (bdx * cdy - bdy * cdx)) + + (bdz * ((cdx * adytail + ady * cdxtail) - (cdy * adxtail + adx * cdytail)) + bdztail * (cdx * ady - cdy * adx)) + + (cdz * ((adx * bdytail + bdy * adxtail) - (ady * bdxtail + bdx * adytail)) + cdztail * (adx * bdy - ady * bdx)); + if(std::abs(det) >= std::abs(errbound)) return det; + + const detail::Expansion bct = detail::ExpansionBase::TwoTwoDiffZeroCheck(bdxtail, cdy, bdytail, cdx) + detail::ExpansionBase::TwoTwoDiffZeroCheck(cdytail, bdx, cdxtail, bdy); + const detail::Expansion cat = detail::ExpansionBase::TwoTwoDiffZeroCheck(cdxtail, ady, cdytail, adx) + detail::ExpansionBase::TwoTwoDiffZeroCheck(adytail, cdx, adxtail, cdy); + const detail::Expansion abt = detail::ExpansionBase::TwoTwoDiffZeroCheck(adxtail, bdy, adytail, bdx) + detail::ExpansionBase::TwoTwoDiffZeroCheck(bdytail, adx, bdxtail, ady); + const detail::Expansion fin2 = fin1 + bct * adz + cat * bdz + abt * cdz + bc * adztail + ca * bdztail + ab * cdztail + + detail::ExpansionBase::ThreeProd( adxtail, bdytail, cdz) + detail::ExpansionBase::ThreeProd( adxtail, bdytail, cdztail) + + detail::ExpansionBase::ThreeProd(-adxtail, cdytail, bdz) + detail::ExpansionBase::ThreeProd(-adxtail, cdytail, bdztail) + + detail::ExpansionBase::ThreeProd( bdxtail, cdytail, adz) + detail::ExpansionBase::ThreeProd( bdxtail, cdytail, adztail) + + detail::ExpansionBase::ThreeProd(-bdxtail, adytail, cdz) + detail::ExpansionBase::ThreeProd(-bdxtail, adytail, cdztail) + + detail::ExpansionBase::ThreeProd( cdxtail, adytail, bdz) + detail::ExpansionBase::ThreeProd( cdxtail, adytail, bdztail) + + detail::ExpansionBase::ThreeProd(-cdxtail, bdytail, adz) + detail::ExpansionBase::ThreeProd(-cdxtail, bdytail, adztail) + + bct * adztail + cat * bdztail + abt * cdztail; + return fin2.mostSignificant(); + } + + //@brief : determine if the 3d point e is inside, on, or outside the sphere defined by a, b, c, and d + //@param pa: pointer to a as {x, y, z} + //@param pb: pointer to b as {x, y, z} + //@param pc: pointer to c as {x, y, z} + //@param pd: pointer to d as {x, y, z} + //@param pe: pointer to e as {x, y, z} + //@return : determinant of {{ax - ex, ay - ey, az - ez, (ax - ex)^2 + (ay - ey)^2 + (az - ez)^2}, {bx - ex, by - ey, bz - ez, (bx - ex)^2 + (by - ey)^2 + (bz - ez)^2}, {cx - ex, cy - ey, cz - ez, (cx - ex)^2 + (cy - ey)^2 + (cz - ez)^2}, {dx - ex, dy - ey, dz - ez, (dx - ex)^2 + (dy - ey)^2 + (dz - ez)^2}} + //@note : positive, 0, negative result for d inside, on, or outside the circle defined by a, b, and c + template T insphere(T const*const pa, T const*const pb, T const*const pc, T const*const pd, T const*const pe) { + T permanent; + const T aex = pa[0] - pe[0]; + const T bex = pb[0] - pe[0]; + const T cex = pc[0] - pe[0]; + const T dex = pd[0] - pe[0]; + const T aey = pa[1] - pe[1]; + const T bey = pb[1] - pe[1]; + const T cey = pc[1] - pe[1]; + const T dey = pd[1] - pe[1]; + const T aez = pa[2] - pe[2]; + const T bez = pb[2] - pe[2]; + const T cez = pc[2] - pe[2]; + const T dez = pd[2] - pe[2]; + { + const T aexbey = aex * bey; + const T bexaey = bex * aey; + const T bexcey = bex * cey; + const T cexbey = cex * bey; + const T cexdey = cex * dey; + const T dexcey = dex * cey; + const T dexaey = dex * aey; + const T aexdey = aex * dey; + const T aexcey = aex * cey; + const T cexaey = cex * aey; + const T bexdey = bex * dey; + const T dexbey = dex * bey; + const T ab = aexbey - bexaey; + const T bc = bexcey - cexbey; + const T cd = cexdey - dexcey; + const T da = dexaey - aexdey; + const T ac = aexcey - cexaey; + const T bd = bexdey - dexbey; + const T abc = aez * bc - bez * ac + cez * ab; + const T bcd = bez * cd - cez * bd + dez * bc; + const T cda = cez * da + dez * ac + aez * cd; + const T dab = dez * ab + aez * bd + bez * da; + const T alift = aex * aex + aey * aey + aez * aez; + const T blift = bex * bex + bey * bey + bez * bez; + const T clift = cex * cex + cey * cey + cez * cez; + const T dlift = dex * dex + dey * dey + dez * dez; + const T det = (dlift * abc - clift * dab) + (blift * cda - alift * bcd); + const T aezplus = std::abs(aez); + const T bezplus = std::abs(bez); + const T cezplus = std::abs(cez); + const T dezplus = std::abs(dez); + const T aexbeyplus = std::abs(aexbey); + const T bexaeyplus = std::abs(bexaey); + const T bexceyplus = std::abs(bexcey); + const T cexbeyplus = std::abs(cexbey); + const T cexdeyplus = std::abs(cexdey); + const T dexceyplus = std::abs(dexcey); + const T dexaeyplus = std::abs(dexaey); + const T aexdeyplus = std::abs(aexdey); + const T aexceyplus = std::abs(aexcey); + const T cexaeyplus = std::abs(cexaey); + const T bexdeyplus = std::abs(bexdey); + const T dexbeyplus = std::abs(dexbey); + permanent = ((cexdeyplus + dexceyplus) * bezplus + (dexbeyplus + bexdeyplus) * cezplus + (bexceyplus + cexbeyplus) * dezplus) * alift + + ((dexaeyplus + aexdeyplus) * cezplus + (aexceyplus + cexaeyplus) * dezplus + (cexdeyplus + dexceyplus) * aezplus) * blift + + ((aexbeyplus + bexaeyplus) * dezplus + (bexdeyplus + dexbeyplus) * aezplus + (dexaeyplus + aexdeyplus) * bezplus) * clift + + ((bexceyplus + cexbeyplus) * aezplus + (cexaeyplus + aexceyplus) * bezplus + (aexbeyplus + bexaeyplus) * cezplus) * dlift; + const T errbound = Constants::isperrboundA * permanent; + if(std::abs(det) >= std::abs(errbound)) return det; + } + + const detail::Expansion ab = detail::ExpansionBase::TwoTwoDiff(aex, bey, bex, aey); + const detail::Expansion bc = detail::ExpansionBase::TwoTwoDiff(bex, cey, cex, bey); + const detail::Expansion cd = detail::ExpansionBase::TwoTwoDiff(cex, dey, dex, cey); + const detail::Expansion da = detail::ExpansionBase::TwoTwoDiff(dex, aey, aex, dey); + const detail::Expansion ac = detail::ExpansionBase::TwoTwoDiff(aex, cey, cex, aey); + const detail::Expansion bd = detail::ExpansionBase::TwoTwoDiff(bex, dey, dex, bey); + const detail::Expansion temp24a = bc * dez + (cd * bez + bd * -cez); + const detail::Expansion temp24b = cd * aez + (da * cez + ac * dez); + const detail::Expansion temp24c = da * bez + (ab * dez + bd * aez); + const detail::Expansion temp24d = ab * cez + (bc * aez + ac * -bez); + const detail::Expansion adet = temp24a * aex * -aex + temp24a * aey * -aey + temp24a * aez * -aez; + const detail::Expansion bdet = temp24b * bex * bex + temp24b * bey * bey + temp24b * bez * bez; + const detail::Expansion cdet = temp24c * cex * -cex + temp24c * cey * -cey + temp24c * cez * -cez; + const detail::Expansion ddet = temp24d * dex * dex + temp24d * dey * dey + temp24d * dez * dez; + const detail::Expansion fin1 = (adet + bdet) + (cdet + ddet); + T det = fin1.estimate(); + T errbound = Constants::isperrboundB * permanent; + if(std::abs(det) >= std::abs(errbound)) return det; + + const T aextail = detail::ExpansionBase::MinusTail(pa[0], pe[0], aex); + const T aeytail = detail::ExpansionBase::MinusTail(pa[1], pe[1], aey); + const T aeztail = detail::ExpansionBase::MinusTail(pa[2], pe[2], aez); + const T bextail = detail::ExpansionBase::MinusTail(pb[0], pe[0], bex); + const T beytail = detail::ExpansionBase::MinusTail(pb[1], pe[1], bey); + const T beztail = detail::ExpansionBase::MinusTail(pb[2], pe[2], bez); + const T cextail = detail::ExpansionBase::MinusTail(pc[0], pe[0], cex); + const T ceytail = detail::ExpansionBase::MinusTail(pc[1], pe[1], cey); + const T ceztail = detail::ExpansionBase::MinusTail(pc[2], pe[2], cez); + const T dextail = detail::ExpansionBase::MinusTail(pd[0], pe[0], dex); + const T deytail = detail::ExpansionBase::MinusTail(pd[1], pe[1], dey); + const T deztail = detail::ExpansionBase::MinusTail(pd[2], pe[2], dez); + if (T(0) == aextail && T(0) == aeytail && T(0) == aeztail && + T(0) == bextail && T(0) == beytail && T(0) == beztail && + T(0) == cextail && T(0) == ceytail && T(0) == ceztail && + T(0) == dextail && T(0) == deytail && T(0) == deztail) return det; + + errbound = Constants::isperrboundC * permanent + Constants::resulterrbound * std::abs(det); + const T abeps = (aex * beytail + bey * aextail) - (aey * bextail + bex * aeytail); + const T bceps = (bex * ceytail + cey * bextail) - (bey * cextail + cex * beytail); + const T cdeps = (cex * deytail + dey * cextail) - (cey * dextail + dex * ceytail); + const T daeps = (dex * aeytail + aey * dextail) - (dey * aextail + aex * deytail); + const T aceps = (aex * ceytail + cey * aextail) - (aey * cextail + cex * aeytail); + const T bdeps = (bex * deytail + dey * bextail) - (bey * dextail + dex * beytail); + const T ab3 = ab.mostSignificant(); + const T bc3 = bc.mostSignificant(); + const T cd3 = cd.mostSignificant(); + const T da3 = da.mostSignificant(); + const T ac3 = ac.mostSignificant(); + const T bd3 = bd.mostSignificant(); + det += ( ( (bex * bex + bey * bey + bez * bez) * ((cez * daeps + dez * aceps + aez * cdeps) + (ceztail * da3 + deztail * ac3 + aeztail * cd3)) + + (dex * dex + dey * dey + dez * dez) * ((aez * bceps - bez * aceps + cez * abeps) + (aeztail * bc3 - beztail * ac3 + ceztail * ab3)) ) + - ( (aex * aex + aey * aey + aez * aez) * ((bez * cdeps - cez * bdeps + dez * bceps) + (beztail * cd3 - ceztail * bd3 + deztail * bc3)) + + (cex * cex + cey * cey + cez * cez) * ((dez * abeps + aez * bdeps + bez * daeps) + (deztail * ab3 + aeztail * bd3 + beztail * da3)) ) ) + + T(2) * ( ( (bex * bextail + bey * beytail + bez * beztail) * (cez * da3 + dez * ac3 + aez * cd3) + + (dex * dextail + dey * deytail + dez * deztail) * (aez * bc3 - bez * ac3 + cez * ab3)) + - ( (aex * aextail + aey * aeytail + aez * aeztail) * (bez * cd3 - cez * bd3 + dez * bc3) + + (cex * cextail + cey * ceytail + cez * ceztail) * (dez * ab3 + aez * bd3 + bez * da3))); + if(std::abs(det) >= std::abs(errbound)) return det; + return exact::insphere(pa, pb, pc, pd, pe); + } + } +} + +#endif diff --git a/src/isct/cdt/remove_at.hpp b/src/isct/cdt/remove_at.hpp new file mode 100644 index 00000000..8b960b58 --- /dev/null +++ b/src/isct/cdt/remove_at.hpp @@ -0,0 +1,55 @@ +#ifndef REMOVE_AT_HPP +#define REMOVE_AT_HPP + +// check if c++11 is supported +#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900) +#define REMOVE_AT_CXX11_IS_SUPPORTED +#elif !defined(__cplusplus) && !defined(_MSC_VER) +typedef char couldnt_parse_cxx_standard[-1]; +#endif + +#include +#include + +/*! + * Remove elements in the range [first; last) with indices from the sorted + * unique range [ii_first, ii_last) + */ +template +inline ForwardIt remove_at( + ForwardIt first, + ForwardIt last, + SortUniqIndsFwdIt ii_first, + SortUniqIndsFwdIt ii_last) +{ + if(ii_first == ii_last) // no indices-to-remove are given + return last; + typedef typename std::iterator_traits::difference_type diff_t; + typedef typename std::iterator_traits::value_type ind_t; + ForwardIt destination = first + static_cast(*ii_first); + while(ii_first != ii_last) + { + // advance to an index after a chunk of elements-to-keep + for(ind_t cur = *ii_first++; ii_first != ii_last; ++ii_first) + { + const ind_t nxt = *ii_first; + if(nxt - cur > 1) + break; + cur = nxt; + } + // move the chunk of elements-to-keep to new destination + const ForwardIt source_first = + first + static_cast(*(ii_first - 1)) + 1; + const ForwardIt source_last = + ii_first != ii_last ? first + static_cast(*ii_first) : last; +#ifdef REMOVE_AT_CXX11_IS_SUPPORTED + std::move(source_first, source_last, destination); +#else + std::copy(source_first, source_last, destination); // c++98 version +#endif + destination += source_last - source_first; + } + return destination; +} + +#endif // REMOVE_AT_HPP diff --git a/src/isct/triangle.c b/src/isct/triangle.c deleted file mode 100644 index 08dcc87e..00000000 --- a/src/isct/triangle.c +++ /dev/null @@ -1,16005 +0,0 @@ -/*****************************************************************************/ -/* */ -/* 888888888 ,o, / 888 */ -/* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */ -/* 888 888 888 88b 888 888 888 888 888 d888 88b */ -/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */ -/* 888 888 888 C888 888 888 888 / 888 q888 */ -/* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */ -/* "8oo8D */ -/* */ -/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */ -/* (triangle.c) */ -/* */ -/* Version 1.6 */ -/* July 28, 2005 */ -/* */ -/* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */ -/* Jonathan Richard Shewchuk */ -/* 2360 Woolsey #H */ -/* Berkeley, California 94705-1927 */ -/* jrs@cs.berkeley.edu */ -/* */ -/* This program may be freely redistributed under the condition that the */ -/* copyright notices (including this entire header and the copyright */ -/* notice printed when the `-h' switch is selected) are not removed, and */ -/* no compensation is received. Private, research, and institutional */ -/* use is free. You may distribute modified versions of this code UNDER */ -/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */ -/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */ -/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */ -/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */ -/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */ -/* WITH THE AUTHOR. (If you are not directly supplying this code to a */ -/* customer, and you are instead telling them how they can obtain it for */ -/* free, then you are not required to make any arrangement with me.) */ -/* */ -/* Hypertext instructions for Triangle are available on the Web at */ -/* */ -/* http://www.cs.cmu.edu/~quake/triangle.html */ -/* */ -/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */ -/* whatsoever. This code is provided "as-is". Use at your own risk. */ -/* */ -/* Some of the references listed below are marked with an asterisk. [*] */ -/* These references are available for downloading from the Web page */ -/* */ -/* http://www.cs.cmu.edu/~quake/triangle.research.html */ -/* */ -/* Three papers discussing aspects of Triangle are available. A short */ -/* overview appears in "Triangle: Engineering a 2D Quality Mesh */ -/* Generator and Delaunay Triangulator," in Applied Computational */ -/* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */ -/* Manocha, editors, Lecture Notes in Computer Science volume 1148, */ -/* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */ -/* Workshop on Applied Computational Geometry). [*] */ -/* */ -/* The algorithms are discussed in the greatest detail in "Delaunay */ -/* Refinement Algorithms for Triangular Mesh Generation," Computational */ -/* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */ -/* */ -/* More detail about the data structures may be found in my dissertation: */ -/* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */ -/* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */ -/* Pittsburgh, Pennsylvania, 18 May 1997. [*] */ -/* */ -/* Triangle was created as part of the Quake Project in the School of */ -/* Computer Science at Carnegie Mellon University. For further */ -/* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */ -/* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */ -/* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */ -/* Media on Parallel Computers," Computer Methods in Applied Mechanics */ -/* and Engineering 152(1-2):85-102, 22 January 1998. */ -/* */ -/* Triangle's Delaunay refinement algorithm for quality mesh generation is */ -/* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */ -/* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */ -/* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */ -/* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */ -/* Annual Symposium on Computational Geometry (San Diego, California), */ -/* pages 274-280, Association for Computing Machinery, May 1993, */ -/* http://portal.acm.org/citation.cfm?id=161150 . */ -/* */ -/* The Delaunay refinement algorithm has been modified so that it meshes */ -/* domains with small input angles well, as described in Gary L. Miller, */ -/* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */ -/* Algorithm Works," Twelfth International Meshing Roundtable, pages */ -/* 91-102, Sandia National Laboratories, September 2003. [*] */ -/* */ -/* My implementation of the divide-and-conquer and incremental Delaunay */ -/* triangulation algorithms follows closely the presentation of Guibas */ -/* and Stolfi, even though I use a triangle-based data structure instead */ -/* of their quad-edge data structure. (In fact, I originally implemented */ -/* Triangle using the quad-edge data structure, but the switch to a */ -/* triangle-based data structure sped Triangle by a factor of two.) The */ -/* mesh manipulation primitives and the two aforementioned Delaunay */ -/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */ -/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */ -/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */ -/* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/ -/* */ -/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */ -/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */ -/* Delaunay Triangulation," International Journal of Computer and */ -/* Information Science 9(3):219-242, 1980. Triangle's improvement of the */ -/* divide-and-conquer algorithm by alternating between vertical and */ -/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */ -/* Conquer Algorithm for Constructing Delaunay Triangulations," */ -/* Algorithmica 2(2):137-151, 1987. */ -/* */ -/* The incremental insertion algorithm was first proposed by C. L. Lawson, */ -/* "Software for C1 Surface Interpolation," in Mathematical Software III, */ -/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */ -/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */ -/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */ -/* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */ -/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */ -/* ACM, May 1996. [*] If I were to randomize the order of vertex */ -/* insertion (I currently don't bother), their result combined with the */ -/* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */ -/* Random Sampling in Computational Geometry II," Discrete & */ -/* Computational Geometry 4(1):387-421, 1989, would yield an expected */ -/* O(n^{4/3}) bound on running time. */ -/* */ -/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */ -/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */ -/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */ -/* boundary of the triangulation are maintained in a splay tree for the */ -/* purpose of point location. Splay trees are described by Daniel */ -/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */ -/* Trees," Journal of the ACM 32(3):652-686, July 1985, */ -/* http://portal.acm.org/citation.cfm?id=3835 . */ -/* */ -/* The algorithms for exact computation of the signs of determinants are */ -/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */ -/* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */ -/* Computational Geometry 18(3):305-363, October 1997. (Also available */ -/* as Technical Report CMU-CS-96-140, School of Computer Science, */ -/* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */ -/* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */ -/* Adaptive Floating-Point Geometric Predicates," Proceedings of the */ -/* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */ -/* Many of the ideas for my exact arithmetic routines originate with */ -/* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */ -/* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */ -/* Computer Society Press, 1991. [*] Many of the ideas for the correct */ -/* evaluation of the signs of determinants are taken from Steven Fortune */ -/* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */ -/* tional Geometry," Proceedings of the Ninth Annual Symposium on */ -/* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */ -/* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */ -/* lations," International Journal of Computational Geometry & Applica- */ -/* tions 5(1-2):193-213, March-June 1995. */ -/* */ -/* The method of inserting new vertices off-center (not precisely at the */ -/* circumcenter of every poor-quality triangle) is from Alper Ungor, */ -/* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal */ -/* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN */ -/* 2004 (Buenos Aires, Argentina), April 2004. */ -/* */ -/* For definitions of and results involving Delaunay triangulations, */ -/* constrained and conforming versions thereof, and other aspects of */ -/* triangular mesh generation, see the excellent survey by Marshall Bern */ -/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */ -/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */ -/* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */ -/* */ -/* The time for incrementally adding PSLG (planar straight line graph) */ -/* segments to create a constrained Delaunay triangulation is probably */ -/* O(t^2) per segment in the worst case and O(t) per segment in the */ -/* common case, where t is the number of triangles that intersect the */ -/* segment before it is inserted. This doesn't count point location, */ -/* which can be much more expensive. I could improve this to O(d log d) */ -/* time, but d is usually quite small, so it's not worth the bother. */ -/* (This note does not apply when the -s switch is used, invoking a */ -/* different method is used to insert segments.) */ -/* */ -/* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */ -/* in the worst case and O(d) in the common case, where d is the degree */ -/* of the vertex being deleted. I could improve this to O(d log d) time, */ -/* but d is usually quite small, so it's not worth the bother. */ -/* */ -/* Ruppert's Delaunay refinement algorithm typically generates triangles */ -/* at a linear rate (constant time per triangle) after the initial */ -/* triangulation is formed. There may be pathological cases where */ -/* quadratic time is required, but these never arise in practice. */ -/* */ -/* The geometric predicates (circumcenter calculations, segment */ -/* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */ -/* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . */ -/* */ -/* If you make any improvements to this code, please please please let me */ -/* know, so that I may obtain the improvements. Even if you don't change */ -/* the code, I'd still love to hear what it's being used for. */ -/* */ -/*****************************************************************************/ - -/* For single precision (which will save some memory and reduce paging), */ -/* define the symbol SINGLE by using the -DSINGLE compiler switch or by */ -/* writing "#define SINGLE" below. */ -/* */ -/* For double precision (which will allow you to refine meshes to a smaller */ -/* edge length), leave SINGLE undefined. */ -/* */ -/* Double precision uses more memory, but improves the resolution of the */ -/* meshes you can generate with Triangle. It also reduces the likelihood */ -/* of a floating exception due to overflow. Finally, it is much faster */ -/* than single precision on 64-bit architectures like the DEC Alpha. I */ -/* recommend double precision unless you want to generate a mesh for which */ -/* you do not have enough memory. */ - -/* #define SINGLE */ - -#ifdef SINGLE -#define REAL float -#else /* not SINGLE */ -#define REAL double -#endif /* not SINGLE */ - -/* If yours is not a Unix system, define the NO_TIMER compiler switch to */ -/* remove the Unix-specific timing code. */ - -/* #define NO_TIMER */ - -/* To insert lots of self-checks for internal errors, define the SELF_CHECK */ -/* symbol. This will slow down the program significantly. It is best to */ -/* define the symbol using the -DSELF_CHECK compiler switch, but you could */ -/* write "#define SELF_CHECK" below. If you are modifying this code, I */ -/* recommend you turn self-checks on until your work is debugged. */ - -/* #define SELF_CHECK */ - -/* To compile Triangle as a callable object library (triangle.o), define the */ -/* TRILIBRARY symbol. Read the file triangle.h for details on how to call */ -/* the procedure triangulate() that results. */ - -/* #define TRILIBRARY */ - -/* It is possible to generate a smaller version of Triangle using one or */ -/* both of the following symbols. Define the REDUCED symbol to eliminate */ -/* all features that are primarily of research interest; specifically, the */ -/* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */ -/* all meshing algorithms above and beyond constrained Delaunay */ -/* triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s */ -/* switches. These reductions are most likely to be useful when */ -/* generating an object library (triangle.o) by defining the TRILIBRARY */ -/* symbol. */ - -/* #define REDUCED */ -/* #define CDT_ONLY */ - -/* On some machines, my exact arithmetic routines might be defeated by the */ -/* use of internal extended precision floating-point registers. The best */ -/* way to solve this problem is to set the floating-point registers to use */ -/* single or double precision internally. On 80x86 processors, this may */ -/* be accomplished by setting the CPU86 symbol for the Microsoft C */ -/* compiler, or the LINUX symbol for the gcc compiler running on Linux. */ -/* */ -/* An inferior solution is to declare certain values as `volatile', thus */ -/* forcing them to be stored to memory and rounded off. Unfortunately, */ -/* this solution might slow Triangle down quite a bit. To use volatile */ -/* values, write "#define INEXACT volatile" below. Normally, however, */ -/* INEXACT should be defined to be nothing. ("#define INEXACT".) */ -/* */ -/* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */ -/* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */ -/* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */ -/* available as Section 6.6 of my dissertation). */ - -/* #define CPU86 */ -/* #define LINUX */ - -#define INEXACT /* Nothing */ -/* #define INEXACT volatile */ - -/* Maximum number of characters in a file name (including the null). */ - -#define FILENAMESIZE 2048 - -/* Maximum number of characters in a line read from a file (including the */ -/* null). */ - -#define INPUTLINESIZE 1024 - -/* For efficiency, a variety of data structures are allocated in bulk. The */ -/* following constants determine how many of each structure is allocated */ -/* at once. */ - -#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */ -#define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */ -#define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */ -#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */ -/* Number of encroached subsegments allocated at once. */ -#define BADSUBSEGPERBLOCK 252 -/* Number of skinny triangles allocated at once. */ -#define BADTRIPERBLOCK 4092 -/* Number of flipped triangles allocated at once. */ -#define FLIPSTACKERPERBLOCK 252 -/* Number of splay tree nodes allocated at once. */ -#define SPLAYNODEPERBLOCK 508 - -/* The vertex types. A DEADVERTEX has been deleted entirely. An */ -/* UNDEADVERTEX is not part of the mesh, but is written to the output */ -/* .node file and affects the node indexing in the other output files. */ - -#define INPUTVERTEX 0 -#define SEGMENTVERTEX 1 -#define FREEVERTEX 2 -#define DEADVERTEX -32768 -#define UNDEADVERTEX -32767 - -/* The next line is used to outsmart some very stupid compilers. If your */ -/* compiler is smarter, feel free to replace the "int" with "void". */ -/* Not that it matters. */ - -#define VOID int - -/* Two constants for algorithms based on random sampling. Both constants */ -/* have been chosen empirically to optimize their respective algorithms. */ - -/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */ -/* how large a random sample of triangles to inspect. */ - -#define SAMPLEFACTOR 11 - -/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */ -/* of boundary edges should be maintained in the splay tree for point */ -/* location on the front. */ - -#define SAMPLERATE 10 - -/* A number that speaks for itself, every kissable digit. */ - -#define PI 3.141592653589793238462643383279502884197169399375105820974944592308 - -/* Another fave. */ - -#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732 - -/* And here's one for those of you who are intimidated by math. */ - -#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333 - -#include -#include -#include -#include -#ifndef NO_TIMER -#include -#endif /* not NO_TIMER */ -#ifdef CPU86 -#include -#endif /* CPU86 */ -#ifdef LINUX -#include -#endif /* LINUX */ -#ifdef TRILIBRARY -#include "triangle.h" -#endif /* TRILIBRARY */ - -/* A few forward declarations. */ - -#ifndef TRILIBRARY -char *readline(); -char *findfield(); -#endif /* not TRILIBRARY */ - -/* Labels that signify the result of point location. The result of a */ -/* search indicates that the point falls in the interior of a triangle, on */ -/* an edge, on a vertex, or outside the mesh. */ - -enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE}; - -/* Labels that signify the result of vertex insertion. The result indicates */ -/* that the vertex was inserted with complete success, was inserted but */ -/* encroaches upon a subsegment, was not inserted because it lies on a */ -/* segment, or was not inserted because another vertex occupies the same */ -/* location. */ - -enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX, - DUPLICATEVERTEX}; - -/* Labels that signify the result of direction finding. The result */ -/* indicates that a segment connecting the two query points falls within */ -/* the direction triangle, along the left edge of the direction triangle, */ -/* or along the right edge of the direction triangle. */ - -enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR}; - -/*****************************************************************************/ -/* */ -/* The basic mesh data structures */ -/* */ -/* There are three: vertices, triangles, and subsegments (abbreviated */ -/* `subseg'). These three data structures, linked by pointers, comprise */ -/* the mesh. A vertex simply represents a mesh vertex and its properties. */ -/* A triangle is a triangle. A subsegment is a special data structure used */ -/* to represent an impenetrable edge of the mesh (perhaps on the outer */ -/* boundary, on the boundary of a hole, or part of an internal boundary */ -/* separating two triangulated regions). Subsegments represent boundaries, */ -/* defined by the user, that triangles may not lie across. */ -/* */ -/* A triangle consists of a list of three vertices, a list of three */ -/* adjoining triangles, a list of three adjoining subsegments (when */ -/* segments exist), an arbitrary number of optional user-defined */ -/* floating-point attributes, and an optional area constraint. The latter */ -/* is an upper bound on the permissible area of each triangle in a region, */ -/* used for mesh refinement. */ -/* */ -/* For a triangle on a boundary of the mesh, some or all of the neighboring */ -/* triangles may not be present. For a triangle in the interior of the */ -/* mesh, often no neighboring subsegments are present. Such absent */ -/* triangles and subsegments are never represented by NULL pointers; they */ -/* are represented by two special records: `dummytri', the triangle that */ -/* fills "outer space", and `dummysub', the omnipresent subsegment. */ -/* `dummytri' and `dummysub' are used for several reasons; for instance, */ -/* they can be dereferenced and their contents examined without violating */ -/* protected memory. */ -/* */ -/* However, it is important to understand that a triangle includes other */ -/* information as well. The pointers to adjoining vertices, triangles, and */ -/* subsegments are ordered in a way that indicates their geometric relation */ -/* to each other. Furthermore, each of these pointers contains orientation */ -/* information. Each pointer to an adjoining triangle indicates which face */ -/* of that triangle is contacted. Similarly, each pointer to an adjoining */ -/* subsegment indicates which side of that subsegment is contacted, and how */ -/* the subsegment is oriented relative to the triangle. */ -/* */ -/* The data structure representing a subsegment may be thought to be */ -/* abutting the edge of one or two triangle data structures: either */ -/* sandwiched between two triangles, or resting against one triangle on an */ -/* exterior boundary or hole boundary. */ -/* */ -/* A subsegment consists of a list of four vertices--the vertices of the */ -/* subsegment, and the vertices of the segment it is a part of--a list of */ -/* two adjoining subsegments, and a list of two adjoining triangles. One */ -/* of the two adjoining triangles may not be present (though there should */ -/* always be one), and neighboring subsegments might not be present. */ -/* Subsegments also store a user-defined integer "boundary marker". */ -/* Typically, this integer is used to indicate what boundary conditions are */ -/* to be applied at that location in a finite element simulation. */ -/* */ -/* Like triangles, subsegments maintain information about the relative */ -/* orientation of neighboring objects. */ -/* */ -/* Vertices are relatively simple. A vertex is a list of floating-point */ -/* numbers, starting with the x, and y coordinates, followed by an */ -/* arbitrary number of optional user-defined floating-point attributes, */ -/* followed by an integer boundary marker. During the segment insertion */ -/* phase, there is also a pointer from each vertex to a triangle that may */ -/* contain it. Each pointer is not always correct, but when one is, it */ -/* speeds up segment insertion. These pointers are assigned values once */ -/* at the beginning of the segment insertion phase, and are not used or */ -/* updated except during this phase. Edge flipping during segment */ -/* insertion will render some of them incorrect. Hence, don't rely upon */ -/* them for anything. */ -/* */ -/* Other than the exception mentioned above, vertices have no information */ -/* about what triangles, subfacets, or subsegments they are linked to. */ -/* */ -/*****************************************************************************/ - -/*****************************************************************************/ -/* */ -/* Handles */ -/* */ -/* The oriented triangle (`otri') and oriented subsegment (`osub') data */ -/* structures defined below do not themselves store any part of the mesh. */ -/* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */ -/* */ -/* Oriented triangles and oriented subsegments will usually be referred to */ -/* as "handles." A handle is essentially a pointer into the mesh; it */ -/* allows you to "hold" one particular part of the mesh. Handles are used */ -/* to specify the regions in which one is traversing and modifying the mesh.*/ -/* A single `triangle' may be held by many handles, or none at all. (The */ -/* latter case is not a memory leak, because the triangle is still */ -/* connected to other triangles in the mesh.) */ -/* */ -/* An `otri' is a handle that holds a triangle. It holds a specific edge */ -/* of the triangle. An `osub' is a handle that holds a subsegment. It */ -/* holds either the left or right side of the subsegment. */ -/* */ -/* Navigation about the mesh is accomplished through a set of mesh */ -/* manipulation primitives, further below. Many of these primitives take */ -/* a handle and produce a new handle that holds the mesh near the first */ -/* handle. Other primitives take two handles and glue the corresponding */ -/* parts of the mesh together. The orientation of the handles is */ -/* important. For instance, when two triangles are glued together by the */ -/* bond() primitive, they are glued at the edges on which the handles lie. */ -/* */ -/* Because vertices have no information about which triangles they are */ -/* attached to, I commonly represent a vertex by use of a handle whose */ -/* origin is the vertex. A single handle can simultaneously represent a */ -/* triangle, an edge, and a vertex. */ -/* */ -/*****************************************************************************/ - -/* The triangle data structure. Each triangle contains three pointers to */ -/* adjoining triangles, plus three pointers to vertices, plus three */ -/* pointers to subsegments (declared below; these pointers are usually */ -/* `dummysub'). It may or may not also contain user-defined attributes */ -/* and/or a floating-point "area constraint." It may also contain extra */ -/* pointers for nodes, when the user asks for high-order elements. */ -/* Because the size and structure of a `triangle' is not decided until */ -/* runtime, I haven't simply declared the type `triangle' as a struct. */ - -typedef REAL **triangle; /* Really: typedef triangle *triangle */ - -/* An oriented triangle: includes a pointer to a triangle and orientation. */ -/* The orientation denotes an edge of the triangle. Hence, there are */ -/* three possible orientations. By convention, each edge always points */ -/* counterclockwise about the corresponding triangle. */ - -struct otri { - triangle *tri; - int orient; /* Ranges from 0 to 2. */ -}; - -/* The subsegment data structure. Each subsegment contains two pointers to */ -/* adjoining subsegments, plus four pointers to vertices, plus two */ -/* pointers to adjoining triangles, plus one boundary marker, plus one */ -/* segment number. */ - -typedef REAL **subseg; /* Really: typedef subseg *subseg */ - -/* An oriented subsegment: includes a pointer to a subsegment and an */ -/* orientation. The orientation denotes a side of the edge. Hence, there */ -/* are two possible orientations. By convention, the edge is always */ -/* directed so that the "side" denoted is the right side of the edge. */ - -struct osub { - subseg *ss; - int ssorient; /* Ranges from 0 to 1. */ -}; - -/* The vertex data structure. Each vertex is actually an array of REALs. */ -/* The number of REALs is unknown until runtime. An integer boundary */ -/* marker, and sometimes a pointer to a triangle, is appended after the */ -/* REALs. */ - -typedef REAL *vertex; - -/* A queue used to store encroached subsegments. Each subsegment's vertices */ -/* are stored so that we can check whether a subsegment is still the same. */ - -struct badsubseg { - subseg encsubseg; /* An encroached subsegment. */ - vertex subsegorg, subsegdest; /* Its two vertices. */ -}; - -/* A queue used to store bad triangles. The key is the square of the cosine */ -/* of the smallest angle of the triangle. Each triangle's vertices are */ -/* stored so that one can check whether a triangle is still the same. */ - -struct badtriang { - triangle poortri; /* A skinny or too-large triangle. */ - REAL key; /* cos^2 of smallest (apical) angle. */ - vertex triangorg, triangdest, triangapex; /* Its three vertices. */ - struct badtriang *nexttriang; /* Pointer to next bad triangle. */ -}; - -/* A stack of triangles flipped during the most recent vertex insertion. */ -/* The stack is used to undo the vertex insertion if the vertex encroaches */ -/* upon a subsegment. */ - -struct flipstacker { - triangle flippedtri; /* A recently flipped triangle. */ - struct flipstacker *prevflip; /* Previous flip in the stack. */ -}; - -/* A node in a heap used to store events for the sweepline Delaunay */ -/* algorithm. Nodes do not point directly to their parents or children in */ -/* the heap. Instead, each node knows its position in the heap, and can */ -/* look up its parent and children in a separate array. The `eventptr' */ -/* points either to a `vertex' or to a triangle (in encoded format, so */ -/* that an orientation is included). In the latter case, the origin of */ -/* the oriented triangle is the apex of a "circle event" of the sweepline */ -/* algorithm. To distinguish site events from circle events, all circle */ -/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */ - -struct event { - REAL xkey, ykey; /* Coordinates of the event. */ - VOID *eventptr; /* Can be a vertex or the location of a circle event. */ - int heapposition; /* Marks this event's position in the heap. */ -}; - -/* A node in the splay tree. Each node holds an oriented ghost triangle */ -/* that represents a boundary edge of the growing triangulation. When a */ -/* circle event covers two boundary edges with a triangle, so that they */ -/* are no longer boundary edges, those edges are not immediately deleted */ -/* from the tree; rather, they are lazily deleted when they are next */ -/* encountered. (Since only a random sample of boundary edges are kept */ -/* in the tree, lazy deletion is faster.) `keydest' is used to verify */ -/* that a triangle is still the same as when it entered the splay tree; if */ -/* it has been rotated (due to a circle event), it no longer represents a */ -/* boundary edge and should be deleted. */ - -struct splaynode { - struct otri keyedge; /* Lprev of an edge on the front. */ - vertex keydest; /* Used to verify that splay node is still live. */ - struct splaynode *lchild, *rchild; /* Children in splay tree. */ -}; - -/* A type used to allocate memory. firstblock is the first block of items. */ -/* nowblock is the block from which items are currently being allocated. */ -/* nextitem points to the next slab of free memory for an item. */ -/* deaditemstack is the head of a linked list (stack) of deallocated items */ -/* that can be recycled. unallocateditems is the number of items that */ -/* remain to be allocated from nowblock. */ -/* */ -/* Traversal is the process of walking through the entire list of items, and */ -/* is separate from allocation. Note that a traversal will visit items on */ -/* the "deaditemstack" stack as well as live items. pathblock points to */ -/* the block currently being traversed. pathitem points to the next item */ -/* to be traversed. pathitemsleft is the number of items that remain to */ -/* be traversed in pathblock. */ -/* */ -/* alignbytes determines how new records should be aligned in memory. */ -/* itembytes is the length of a record in bytes (after rounding up). */ -/* itemsperblock is the number of items allocated at once in a single */ -/* block. itemsfirstblock is the number of items in the first block, */ -/* which can vary from the others. items is the number of currently */ -/* allocated items. maxitems is the maximum number of items that have */ -/* been allocated at once; it is the current number of items plus the */ -/* number of records kept on deaditemstack. */ - -struct memorypool { - VOID **firstblock, **nowblock; - VOID *nextitem; - VOID *deaditemstack; - VOID **pathblock; - VOID *pathitem; - int alignbytes; - int itembytes; - int itemsperblock; - int itemsfirstblock; - long items, maxitems; - int unallocateditems; - int pathitemsleft; -}; - - -/* Global constants. */ - -REAL splitter; /* Used to split REAL factors for exact multiplication. */ -REAL epsilon; /* Floating-point machine epsilon. */ -REAL resulterrbound; -REAL ccwerrboundA, ccwerrboundB, ccwerrboundC; -REAL iccerrboundA, iccerrboundB, iccerrboundC; -REAL o3derrboundA, o3derrboundB, o3derrboundC; - -/* Random number seed is not constant, but I've made it global anyway. */ - -unsigned long randomseed; /* Current random number seed. */ - - -/* Mesh data structure. Triangle operates on only one mesh, but the mesh */ -/* structure is used (instead of global variables) to allow reentrancy. */ - -struct mesh { - -/* Variables used to allocate memory for triangles, subsegments, vertices, */ -/* viri (triangles being eaten), encroached segments, bad (skinny or too */ -/* large) triangles, and splay tree nodes. */ - - struct memorypool triangles; - struct memorypool subsegs; - struct memorypool vertices; - struct memorypool viri; - struct memorypool badsubsegs; - struct memorypool badtriangles; - struct memorypool flipstackers; - struct memorypool splaynodes; - -/* Variables that maintain the bad triangle queues. The queues are */ -/* ordered from 4095 (highest priority) to 0 (lowest priority). */ - - struct badtriang *queuefront[4096]; - struct badtriang *queuetail[4096]; - int nextnonemptyq[4096]; - int firstnonemptyq; - -/* Variable that maintains the stack of recently flipped triangles. */ - - struct flipstacker *lastflip; - -/* Other variables. */ - - REAL xmin, xmax, ymin, ymax; /* x and y bounds. */ - REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */ - int invertices; /* Number of input vertices. */ - int inelements; /* Number of input triangles. */ - int insegments; /* Number of input segments. */ - int holes; /* Number of input holes. */ - int regions; /* Number of input regions. */ - int undeads; /* Number of input vertices that don't appear in the mesh. */ - long edges; /* Number of output edges. */ - int mesh_dim; /* Dimension (ought to be 2). */ - int nextras; /* Number of attributes per vertex. */ - int eextras; /* Number of attributes per triangle. */ - long hullsize; /* Number of edges in convex hull. */ - int steinerleft; /* Number of Steiner points not yet used. */ - int vertexmarkindex; /* Index to find boundary marker of a vertex. */ - int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */ - int highorderindex; /* Index to find extra nodes for high-order elements. */ - int elemattribindex; /* Index to find attributes of a triangle. */ - int areaboundindex; /* Index to find area bound of a triangle. */ - int checksegments; /* Are there segments in the triangulation yet? */ - int checkquality; /* Has quality triangulation begun yet? */ - int readnodefile; /* Has a .node file been read? */ - long samples; /* Number of random samples for point location. */ - - long incirclecount; /* Number of incircle tests performed. */ - long counterclockcount; /* Number of counterclockwise tests performed. */ - long orient3dcount; /* Number of 3D orientation tests performed. */ - long hyperbolacount; /* Number of right-of-hyperbola tests performed. */ - long circumcentercount; /* Number of circumcenter calculations performed. */ - long circletopcount; /* Number of circle top calculations performed. */ - -/* Triangular bounding box vertices. */ - - vertex infvertex1, infvertex2, infvertex3; - -/* Pointer to the `triangle' that occupies all of "outer space." */ - - triangle *dummytri; - triangle *dummytribase; /* Keep base address so we can free() it later. */ - -/* Pointer to the omnipresent subsegment. Referenced by any triangle or */ -/* subsegment that isn't really connected to a subsegment at that */ -/* location. */ - - subseg *dummysub; - subseg *dummysubbase; /* Keep base address so we can free() it later. */ - -/* Pointer to a recently visited triangle. Improves point location if */ -/* proximate vertices are inserted sequentially. */ - - struct otri recenttri; - -}; /* End of `struct mesh'. */ - - -/* Data structure for command line switches and file names. This structure */ -/* is used (instead of global variables) to allow reentrancy. */ - -struct behavior { - -/* Switches for the triangulator. */ -/* poly: -p switch. refine: -r switch. */ -/* quality: -q switch. */ -/* minangle: minimum angle bound, specified after -q switch. */ -/* goodangle: cosine squared of minangle. */ -/* offconstant: constant used to place off-center Steiner points. */ -/* vararea: -a switch without number. */ -/* fixedarea: -a switch with number. */ -/* maxarea: maximum area bound, specified after -a switch. */ -/* usertest: -u switch. */ -/* regionattrib: -A switch. convex: -c switch. */ -/* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */ -/* firstnumber: inverse of -z switch. All items are numbered starting */ -/* from `firstnumber'. */ -/* edgesout: -e switch. voronoi: -v switch. */ -/* neighbors: -n switch. geomview: -g switch. */ -/* nobound: -B switch. nopolywritten: -P switch. */ -/* nonodewritten: -N switch. noelewritten: -E switch. */ -/* noiterationnum: -I switch. noholes: -O switch. */ -/* noexact: -X switch. */ -/* order: element order, specified after -o switch. */ -/* nobisect: count of how often -Y switch is selected. */ -/* steiner: maximum number of Steiner points, specified after -S switch. */ -/* incremental: -i switch. sweepline: -F switch. */ -/* dwyer: inverse of -l switch. */ -/* splitseg: -s switch. */ -/* conformdel: -D switch. docheck: -C switch. */ -/* quiet: -Q switch. verbose: count of how often -V switch is selected. */ -/* usesegments: -p, -r, -q, or -c switch; determines whether segments are */ -/* used at all. */ -/* */ -/* Read the instructions to find out the meaning of these switches. */ - - int poly, refine, quality, vararea, fixedarea, usertest; - int regionattrib, convex, weighted, jettison; - int firstnumber; - int edgesout, voronoi, neighbors, geomview; - int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum; - int noholes, noexact, conformdel; - int incremental, sweepline, dwyer; - int splitseg; - int docheck; - int quiet, verbose; - int usesegments; - int order; - int nobisect; - int steiner; - REAL minangle, goodangle, offconstant; - REAL maxarea; - -/* Variables for file names. */ - -#ifndef TRILIBRARY - char innodefilename[FILENAMESIZE]; - char inelefilename[FILENAMESIZE]; - char inpolyfilename[FILENAMESIZE]; - char areafilename[FILENAMESIZE]; - char outnodefilename[FILENAMESIZE]; - char outelefilename[FILENAMESIZE]; - char outpolyfilename[FILENAMESIZE]; - char edgefilename[FILENAMESIZE]; - char vnodefilename[FILENAMESIZE]; - char vedgefilename[FILENAMESIZE]; - char neighborfilename[FILENAMESIZE]; - char offfilename[FILENAMESIZE]; -#endif /* not TRILIBRARY */ - -}; /* End of `struct behavior'. */ - - -/*****************************************************************************/ -/* */ -/* Mesh manipulation primitives. Each triangle contains three pointers to */ -/* other triangles, with orientations. Each pointer points not to the */ -/* first byte of a triangle, but to one of the first three bytes of a */ -/* triangle. It is necessary to extract both the triangle itself and the */ -/* orientation. To save memory, I keep both pieces of information in one */ -/* pointer. To make this possible, I assume that all triangles are aligned */ -/* to four-byte boundaries. The decode() routine below decodes a pointer, */ -/* extracting an orientation (in the range 0 to 2) and a pointer to the */ -/* beginning of a triangle. The encode() routine compresses a pointer to a */ -/* triangle and an orientation into a single pointer. My assumptions that */ -/* triangles are four-byte-aligned and that the `unsigned long' type is */ -/* long enough to hold a pointer are two of the few kludges in this program.*/ -/* */ -/* Subsegments are manipulated similarly. A pointer to a subsegment */ -/* carries both an address and an orientation in the range 0 to 1. */ -/* */ -/* The other primitives take an oriented triangle or oriented subsegment, */ -/* and return an oriented triangle or oriented subsegment or vertex; or */ -/* they change the connections in the data structure. */ -/* */ -/* Below, triangles and subsegments are denoted by their vertices. The */ -/* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */ -/* c. These vertices occur in counterclockwise order about the triangle. */ -/* The handle abc may simultaneously denote vertex a, edge ab, and triangle */ -/* abc. */ -/* */ -/* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */ -/* b. If ab is thought to be directed upward (with b directly above a), */ -/* then the handle ab is thought to grasp the right side of ab, and may */ -/* simultaneously denote vertex a and edge ab. */ -/* */ -/* An asterisk (*) denotes a vertex whose identity is unknown. */ -/* */ -/* Given this notation, a partial list of mesh manipulation primitives */ -/* follows. */ -/* */ -/* */ -/* For triangles: */ -/* */ -/* sym: Find the abutting triangle; same edge. */ -/* sym(abc) -> ba* */ -/* */ -/* lnext: Find the next edge (counterclockwise) of a triangle. */ -/* lnext(abc) -> bca */ -/* */ -/* lprev: Find the previous edge (clockwise) of a triangle. */ -/* lprev(abc) -> cab */ -/* */ -/* onext: Find the next edge counterclockwise with the same origin. */ -/* onext(abc) -> ac* */ -/* */ -/* oprev: Find the next edge clockwise with the same origin. */ -/* oprev(abc) -> a*b */ -/* */ -/* dnext: Find the next edge counterclockwise with the same destination. */ -/* dnext(abc) -> *ba */ -/* */ -/* dprev: Find the next edge clockwise with the same destination. */ -/* dprev(abc) -> cb* */ -/* */ -/* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */ -/* rnext(abc) -> *a* */ -/* */ -/* rprev: Find the previous edge (clockwise) of the adjacent triangle. */ -/* rprev(abc) -> b** */ -/* */ -/* org: Origin dest: Destination apex: Apex */ -/* org(abc) -> a dest(abc) -> b apex(abc) -> c */ -/* */ -/* bond: Bond two triangles together at the resepective handles. */ -/* bond(abc, bad) */ -/* */ -/* */ -/* For subsegments: */ -/* */ -/* ssym: Reverse the orientation of a subsegment. */ -/* ssym(ab) -> ba */ -/* */ -/* spivot: Find adjoining subsegment with the same origin. */ -/* spivot(ab) -> a* */ -/* */ -/* snext: Find next subsegment in sequence. */ -/* snext(ab) -> b* */ -/* */ -/* sorg: Origin sdest: Destination */ -/* sorg(ab) -> a sdest(ab) -> b */ -/* */ -/* sbond: Bond two subsegments together at the respective origins. */ -/* sbond(ab, ac) */ -/* */ -/* */ -/* For interacting tetrahedra and subfacets: */ -/* */ -/* tspivot: Find a subsegment abutting a triangle. */ -/* tspivot(abc) -> ba */ -/* */ -/* stpivot: Find a triangle abutting a subsegment. */ -/* stpivot(ab) -> ba* */ -/* */ -/* tsbond: Bond a triangle to a subsegment. */ -/* tsbond(abc, ba) */ -/* */ -/*****************************************************************************/ - -/********* Mesh manipulation primitives begin here *********/ -/** **/ -/** **/ - -/* Fast lookup arrays to speed some of the mesh manipulation primitives. */ - -int plus1mod3[3] = {1, 2, 0}; -int minus1mod3[3] = {2, 0, 1}; - -/********* Primitives for triangles *********/ -/* */ -/* */ - -/* decode() converts a pointer to an oriented triangle. The orientation is */ -/* extracted from the two least significant bits of the pointer. */ - -#define decode(ptr, otri) \ - (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \ - (otri).tri = (triangle *) \ - ((unsigned long) (ptr) ^ (unsigned long) (otri).orient) - -/* encode() compresses an oriented triangle into a single pointer. It */ -/* relies on the assumption that all triangles are aligned to four-byte */ -/* boundaries, so the two least significant bits of (otri).tri are zero. */ - -#define encode(otri) \ - (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient) - -/* The following handle manipulation primitives are all described by Guibas */ -/* and Stolfi. However, Guibas and Stolfi use an edge-based data */ -/* structure, whereas I use a triangle-based data structure. */ - -/* sym() finds the abutting triangle, on the same edge. Note that the edge */ -/* direction is necessarily reversed, because the handle specified by an */ -/* oriented triangle is directed counterclockwise around the triangle. */ - -#define sym(otri1, otri2) \ - ptr = (otri1).tri[(otri1).orient]; \ - decode(ptr, otri2); - -#define symself(otri) \ - ptr = (otri).tri[(otri).orient]; \ - decode(ptr, otri); - -/* lnext() finds the next edge (counterclockwise) of a triangle. */ - -#define lnext(otri1, otri2) \ - (otri2).tri = (otri1).tri; \ - (otri2).orient = plus1mod3[(otri1).orient] - -#define lnextself(otri) \ - (otri).orient = plus1mod3[(otri).orient] - -/* lprev() finds the previous edge (clockwise) of a triangle. */ - -#define lprev(otri1, otri2) \ - (otri2).tri = (otri1).tri; \ - (otri2).orient = minus1mod3[(otri1).orient] - -#define lprevself(otri) \ - (otri).orient = minus1mod3[(otri).orient] - -/* onext() spins counterclockwise around a vertex; that is, it finds the */ -/* next edge with the same origin in the counterclockwise direction. This */ -/* edge is part of a different triangle. */ - -#define onext(otri1, otri2) \ - lprev(otri1, otri2); \ - symself(otri2); - -#define onextself(otri) \ - lprevself(otri); \ - symself(otri); - -/* oprev() spins clockwise around a vertex; that is, it finds the next edge */ -/* with the same origin in the clockwise direction. This edge is part of */ -/* a different triangle. */ - -#define oprev(otri1, otri2) \ - sym(otri1, otri2); \ - lnextself(otri2); - -#define oprevself(otri) \ - symself(otri); \ - lnextself(otri); - -/* dnext() spins counterclockwise around a vertex; that is, it finds the */ -/* next edge with the same destination in the counterclockwise direction. */ -/* This edge is part of a different triangle. */ - -#define dnext(otri1, otri2) \ - sym(otri1, otri2); \ - lprevself(otri2); - -#define dnextself(otri) \ - symself(otri); \ - lprevself(otri); - -/* dprev() spins clockwise around a vertex; that is, it finds the next edge */ -/* with the same destination in the clockwise direction. This edge is */ -/* part of a different triangle. */ - -#define dprev(otri1, otri2) \ - lnext(otri1, otri2); \ - symself(otri2); - -#define dprevself(otri) \ - lnextself(otri); \ - symself(otri); - -/* rnext() moves one edge counterclockwise about the adjacent triangle. */ -/* (It's best understood by reading Guibas and Stolfi. It involves */ -/* changing triangles twice.) */ - -#define rnext(otri1, otri2) \ - sym(otri1, otri2); \ - lnextself(otri2); \ - symself(otri2); - -#define rnextself(otri) \ - symself(otri); \ - lnextself(otri); \ - symself(otri); - -/* rprev() moves one edge clockwise about the adjacent triangle. */ -/* (It's best understood by reading Guibas and Stolfi. It involves */ -/* changing triangles twice.) */ - -#define rprev(otri1, otri2) \ - sym(otri1, otri2); \ - lprevself(otri2); \ - symself(otri2); - -#define rprevself(otri) \ - symself(otri); \ - lprevself(otri); \ - symself(otri); - -/* These primitives determine or set the origin, destination, or apex of a */ -/* triangle. */ - -#define org(otri, vertexptr) \ - vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3] - -#define dest(otri, vertexptr) \ - vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3] - -#define apex(otri, vertexptr) \ - vertexptr = (vertex) (otri).tri[(otri).orient + 3] - -#define setorg(otri, vertexptr) \ - (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr - -#define setdest(otri, vertexptr) \ - (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr - -#define setapex(otri, vertexptr) \ - (otri).tri[(otri).orient + 3] = (triangle) vertexptr - -/* Bond two triangles together. */ - -#define bond(otri1, otri2) \ - (otri1).tri[(otri1).orient] = encode(otri2); \ - (otri2).tri[(otri2).orient] = encode(otri1) - -/* Dissolve a bond (from one side). Note that the other triangle will still */ -/* think it's connected to this triangle. Usually, however, the other */ -/* triangle is being deleted entirely, or bonded to another triangle, so */ -/* it doesn't matter. */ - -#define dissolve(otri) \ - (otri).tri[(otri).orient] = (triangle) m->dummytri - -/* Copy an oriented triangle. */ - -#define otricopy(otri1, otri2) \ - (otri2).tri = (otri1).tri; \ - (otri2).orient = (otri1).orient - -/* Test for equality of oriented triangles. */ - -#define otriequal(otri1, otri2) \ - (((otri1).tri == (otri2).tri) && \ - ((otri1).orient == (otri2).orient)) - -/* Primitives to infect or cure a triangle with the virus. These rely on */ -/* the assumption that all subsegments are aligned to four-byte boundaries.*/ - -#define infect(otri) \ - (otri).tri[6] = (triangle) \ - ((unsigned long) (otri).tri[6] | (unsigned long) 2l) - -#define uninfect(otri) \ - (otri).tri[6] = (triangle) \ - ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l) - -/* Test a triangle for viral infection. */ - -#define infected(otri) \ - (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l) - -/* Check or set a triangle's attributes. */ - -#define elemattribute(otri, attnum) \ - ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] - -#define setelemattribute(otri, attnum, value) \ - ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value - -/* Check or set a triangle's maximum area bound. */ - -#define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex] - -#define setareabound(otri, value) \ - ((REAL *) (otri).tri)[m->areaboundindex] = value - -/* Check or set a triangle's deallocation. Its second pointer is set to */ -/* NULL to indicate that it is not allocated. (Its first pointer is used */ -/* for the stack of dead items.) Its fourth pointer (its first vertex) */ -/* is set to NULL in case a `badtriang' structure points to it. */ - -#define deadtri(tria) ((tria)[1] == (triangle) NULL) - -#define killtri(tria) \ - (tria)[1] = (triangle) NULL; \ - (tria)[3] = (triangle) NULL - -/********* Primitives for subsegments *********/ -/* */ -/* */ - -/* sdecode() converts a pointer to an oriented subsegment. The orientation */ -/* is extracted from the least significant bit of the pointer. The two */ -/* least significant bits (one for orientation, one for viral infection) */ -/* are masked out to produce the real pointer. */ - -#define sdecode(sptr, osub) \ - (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \ - (osub).ss = (subseg *) \ - ((unsigned long) (sptr) & ~ (unsigned long) 3l) - -/* sencode() compresses an oriented subsegment into a single pointer. It */ -/* relies on the assumption that all subsegments are aligned to two-byte */ -/* boundaries, so the least significant bit of (osub).ss is zero. */ - -#define sencode(osub) \ - (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient) - -/* ssym() toggles the orientation of a subsegment. */ - -#define ssym(osub1, osub2) \ - (osub2).ss = (osub1).ss; \ - (osub2).ssorient = 1 - (osub1).ssorient - -#define ssymself(osub) \ - (osub).ssorient = 1 - (osub).ssorient - -/* spivot() finds the other subsegment (from the same segment) that shares */ -/* the same origin. */ - -#define spivot(osub1, osub2) \ - sptr = (osub1).ss[(osub1).ssorient]; \ - sdecode(sptr, osub2) - -#define spivotself(osub) \ - sptr = (osub).ss[(osub).ssorient]; \ - sdecode(sptr, osub) - -/* snext() finds the next subsegment (from the same segment) in sequence; */ -/* one whose origin is the input subsegment's destination. */ - -#define snext(osub1, osub2) \ - sptr = (osub1).ss[1 - (osub1).ssorient]; \ - sdecode(sptr, osub2) - -#define snextself(osub) \ - sptr = (osub).ss[1 - (osub).ssorient]; \ - sdecode(sptr, osub) - -/* These primitives determine or set the origin or destination of a */ -/* subsegment or the segment that includes it. */ - -#define sorg(osub, vertexptr) \ - vertexptr = (vertex) (osub).ss[2 + (osub).ssorient] - -#define sdest(osub, vertexptr) \ - vertexptr = (vertex) (osub).ss[3 - (osub).ssorient] - -#define setsorg(osub, vertexptr) \ - (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr - -#define setsdest(osub, vertexptr) \ - (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr - -#define segorg(osub, vertexptr) \ - vertexptr = (vertex) (osub).ss[4 + (osub).ssorient] - -#define segdest(osub, vertexptr) \ - vertexptr = (vertex) (osub).ss[5 - (osub).ssorient] - -#define setsegorg(osub, vertexptr) \ - (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr - -#define setsegdest(osub, vertexptr) \ - (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr - -/* These primitives read or set a boundary marker. Boundary markers are */ -/* used to hold user-defined tags for setting boundary conditions in */ -/* finite element solvers. */ - -#define mark(osub) (* (int *) ((osub).ss + 8)) - -#define setmark(osub, value) \ - * (int *) ((osub).ss + 8) = value - -/* Bond two subsegments together. */ - -#define sbond(osub1, osub2) \ - (osub1).ss[(osub1).ssorient] = sencode(osub2); \ - (osub2).ss[(osub2).ssorient] = sencode(osub1) - -/* Dissolve a subsegment bond (from one side). Note that the other */ -/* subsegment will still think it's connected to this subsegment. */ - -#define sdissolve(osub) \ - (osub).ss[(osub).ssorient] = (subseg) m->dummysub - -/* Copy a subsegment. */ - -#define subsegcopy(osub1, osub2) \ - (osub2).ss = (osub1).ss; \ - (osub2).ssorient = (osub1).ssorient - -/* Test for equality of subsegments. */ - -#define subsegequal(osub1, osub2) \ - (((osub1).ss == (osub2).ss) && \ - ((osub1).ssorient == (osub2).ssorient)) - -/* Check or set a subsegment's deallocation. Its second pointer is set to */ -/* NULL to indicate that it is not allocated. (Its first pointer is used */ -/* for the stack of dead items.) Its third pointer (its first vertex) */ -/* is set to NULL in case a `badsubseg' structure points to it. */ - -#define deadsubseg(sub) ((sub)[1] == (subseg) NULL) - -#define killsubseg(sub) \ - (sub)[1] = (subseg) NULL; \ - (sub)[2] = (subseg) NULL - -/********* Primitives for interacting triangles and subsegments *********/ -/* */ -/* */ - -/* tspivot() finds a subsegment abutting a triangle. */ - -#define tspivot(otri, osub) \ - sptr = (subseg) (otri).tri[6 + (otri).orient]; \ - sdecode(sptr, osub) - -/* stpivot() finds a triangle abutting a subsegment. It requires that the */ -/* variable `ptr' of type `triangle' be defined. */ - -#define stpivot(osub, otri) \ - ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \ - decode(ptr, otri) - -/* Bond a triangle to a subsegment. */ - -#define tsbond(otri, osub) \ - (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \ - (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri) - -/* Dissolve a bond (from the triangle side). */ - -#define tsdissolve(otri) \ - (otri).tri[6 + (otri).orient] = (triangle) m->dummysub - -/* Dissolve a bond (from the subsegment side). */ - -#define stdissolve(osub) \ - (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri - -/********* Primitives for vertices *********/ -/* */ -/* */ - -#define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex] - -#define setvertexmark(vx, value) \ - ((int *) (vx))[m->vertexmarkindex] = value - -#define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1] - -#define setvertextype(vx, value) \ - ((int *) (vx))[m->vertexmarkindex + 1] = value - -#define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex] - -#define setvertex2tri(vx, value) \ - ((triangle *) (vx))[m->vertex2triindex] = value - -/** **/ -/** **/ -/********* Mesh manipulation primitives end here *********/ - -/********* User-defined triangle evaluation routine begins here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* triunsuitable() Determine if a triangle is unsuitable, and thus must */ -/* be further refined. */ -/* */ -/* You may write your own procedure that decides whether or not a selected */ -/* triangle is too big (and needs to be refined). There are two ways to do */ -/* this. */ -/* */ -/* (1) Modify the procedure `triunsuitable' below, then recompile */ -/* Triangle. */ -/* */ -/* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */ -/* to this file, or by using the appropriate compiler switch). This way, */ -/* you can compile triangle.c separately from your test. Write your own */ -/* `triunsuitable' procedure in a separate C file (using the same prototype */ -/* as below). Compile it and link the object code with triangle.o. */ -/* */ -/* This procedure returns 1 if the triangle is too large and should be */ -/* refined; 0 otherwise. */ -/* */ -/*****************************************************************************/ - -#ifdef EXTERNAL_TEST - -int triunsuitable(); - -#else /* not EXTERNAL_TEST */ - -#ifdef ANSI_DECLARATORS -int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area) -#else /* not ANSI_DECLARATORS */ -int triunsuitable(triorg, tridest, triapex, area) -vertex triorg; /* The triangle's origin vertex. */ -vertex tridest; /* The triangle's destination vertex. */ -vertex triapex; /* The triangle's apex vertex. */ -REAL area; /* The area of the triangle. */ -#endif /* not ANSI_DECLARATORS */ - -{ - REAL dxoa, dxda, dxod; - REAL dyoa, dyda, dyod; - REAL oalen, dalen, odlen; - REAL maxlen; - - dxoa = triorg[0] - triapex[0]; - dyoa = triorg[1] - triapex[1]; - dxda = tridest[0] - triapex[0]; - dyda = tridest[1] - triapex[1]; - dxod = triorg[0] - tridest[0]; - dyod = triorg[1] - tridest[1]; - /* Find the squares of the lengths of the triangle's three edges. */ - oalen = dxoa * dxoa + dyoa * dyoa; - dalen = dxda * dxda + dyda * dyda; - odlen = dxod * dxod + dyod * dyod; - /* Find the square of the length of the longest edge. */ - maxlen = (dalen > oalen) ? dalen : oalen; - maxlen = (odlen > maxlen) ? odlen : maxlen; - - if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) { - return 1; - } else { - return 0; - } -} - -#endif /* not EXTERNAL_TEST */ - -/** **/ -/** **/ -/********* User-defined triangle evaluation routine ends here *********/ - -/********* Memory allocation and program exit wrappers begin here *********/ -/** **/ -/** **/ - -#ifdef ANSI_DECLARATORS -void triexit(int status) -#else /* not ANSI_DECLARATORS */ -void triexit(status) -int status; -#endif /* not ANSI_DECLARATORS */ - -{ - exit(status); -} - -#ifdef ANSI_DECLARATORS -VOID *trimalloc(int size) -#else /* not ANSI_DECLARATORS */ -VOID *trimalloc(size) -int size; -#endif /* not ANSI_DECLARATORS */ - -{ - VOID *memptr; - - memptr = (VOID *) malloc((unsigned int) size); - if (memptr == (VOID *) NULL) { - printf("Error: Out of memory.\n"); - triexit(1); - } - return(memptr); -} - -#ifdef ANSI_DECLARATORS -void trifree(void *memptr) -#else /* not ANSI_DECLARATORS */ -void trifree(memptr) -VOID *memptr; -#endif /* not ANSI_DECLARATORS */ -{ - free(memptr); -} - -/** **/ -/** **/ -/********* Memory allocation and program exit wrappers end here *********/ - -/********* User interaction routines begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* syntax() Print list of command line switches. */ -/* */ -/*****************************************************************************/ - -#ifndef TRILIBRARY - -void syntax() -{ -#ifdef CDT_ONLY -#ifdef REDUCED - printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n"); -#else /* not REDUCED */ - printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n"); -#endif /* not REDUCED */ -#else /* not CDT_ONLY */ -#ifdef REDUCED - printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n"); -#else /* not REDUCED */ - printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n"); -#endif /* not REDUCED */ -#endif /* not CDT_ONLY */ - - printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n"); -#ifndef CDT_ONLY - printf(" -r Refines a previously generated mesh.\n"); - printf( - " -q Quality mesh generation. A minimum angle may be specified.\n"); - printf(" -a Applies a maximum triangle area constraint.\n"); - printf(" -u Applies a user-defined triangle constraint.\n"); -#endif /* not CDT_ONLY */ - printf( - " -A Applies attributes to identify triangles in certain regions.\n"); - printf(" -c Encloses the convex hull with segments.\n"); -#ifndef CDT_ONLY - printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n"); -#endif /* not CDT_ONLY */ -/* - printf(" -w Weighted Delaunay triangulation.\n"); - printf(" -W Regular triangulation (lower hull of a height field).\n"); -*/ - printf(" -j Jettison unused vertices from output .node file.\n"); - printf(" -e Generates an edge list.\n"); - printf(" -v Generates a Voronoi diagram.\n"); - printf(" -n Generates a list of triangle neighbors.\n"); - printf(" -g Generates an .off file for Geomview.\n"); - printf(" -B Suppresses output of boundary information.\n"); - printf(" -P Suppresses output of .poly file.\n"); - printf(" -N Suppresses output of .node file.\n"); - printf(" -E Suppresses output of .ele file.\n"); - printf(" -I Suppresses mesh iteration numbers.\n"); - printf(" -O Ignores holes in .poly file.\n"); - printf(" -X Suppresses use of exact arithmetic.\n"); - printf(" -z Numbers all items starting from zero (rather than one).\n"); - printf(" -o2 Generates second-order subparametric elements.\n"); -#ifndef CDT_ONLY - printf(" -Y Suppresses boundary segment splitting.\n"); - printf(" -S Specifies maximum number of added Steiner points.\n"); -#endif /* not CDT_ONLY */ -#ifndef REDUCED - printf(" -i Uses incremental method, rather than divide-and-conquer.\n"); - printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n"); -#endif /* not REDUCED */ - printf(" -l Uses vertical cuts only, rather than alternating cuts.\n"); -#ifndef REDUCED -#ifndef CDT_ONLY - printf( - " -s Force segments into mesh by splitting (instead of using CDT).\n"); -#endif /* not CDT_ONLY */ - printf(" -C Check consistency of final mesh.\n"); -#endif /* not REDUCED */ - printf(" -Q Quiet: No terminal output except errors.\n"); - printf(" -V Verbose: Detailed information on what I'm doing.\n"); - printf(" -h Help: Detailed instructions for Triangle.\n"); - triexit(0); -} - -#endif /* not TRILIBRARY */ - -/*****************************************************************************/ -/* */ -/* info() Print out complete instructions. */ -/* */ -/*****************************************************************************/ - -#ifndef TRILIBRARY - -void info() -{ - printf("Triangle\n"); - printf( -"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n"); - printf("Version 1.6\n\n"); - printf( -"Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n"); - printf("2360 Woolsey #H / Berkeley, California 94705-1927\n"); - printf("Bugs/comments to jrs@cs.berkeley.edu\n"); - printf( -"Created as part of the Quake project (tools for earthquake simulation).\n"); - printf( -"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n"); - printf("There is no warranty whatsoever. Use at your own risk.\n"); -#ifdef SINGLE - printf("This executable is compiled for single precision arithmetic.\n\n\n"); -#else /* not SINGLE */ - printf("This executable is compiled for double precision arithmetic.\n\n\n"); -#endif /* not SINGLE */ - printf( -"Triangle generates exact Delaunay triangulations, constrained Delaunay\n"); - printf( -"triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n"); - printf( -"high-quality triangular meshes. The latter can be generated with no small\n" -); - printf( -"or large angles, and are thus suitable for finite element analysis. If no\n" -); - printf( -"command line switch is specified, your .node input file is read, and the\n"); - printf( -"Delaunay triangulation is returned in .node and .ele output files. The\n"); - printf("command syntax is:\n\n"); - printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n"); - printf( -"Underscores indicate that numbers may optionally follow certain switches.\n"); - printf( -"Do not leave any space between a switch and its numeric parameter.\n"); - printf( -"input_file must be a file with extension .node, or extension .poly if the\n"); - printf( -"-p switch is used. If -r is used, you must supply .node and .ele files,\n"); - printf( -"and possibly a .poly file and an .area file as well. The formats of these\n" -); - printf("files are described below.\n\n"); - printf("Command Line Switches:\n\n"); - printf( -" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n" -); - printf( -" vertices, segments, holes, regional attributes, and regional area\n"); - printf( -" constraints. Generates a constrained Delaunay triangulation (CDT)\n" -); - printf( -" fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n"); - printf( -" constrained Delaunay triangulation (CCDT). If you want a truly\n"); - printf( -" Delaunay (not just constrained Delaunay) triangulation, use -D as\n"); - printf( -" well. When -p is not used, Triangle reads a .node file by default.\n" -); - printf( -" -r Refines a previously generated mesh. The mesh is read from a .node\n" -); - printf( -" file and an .ele file. If -p is also used, a .poly file is read\n"); - printf( -" and used to constrain segments in the mesh. If -a is also used\n"); - printf( -" (with no number following), an .area file is read and used to\n"); - printf( -" impose area constraints on the mesh. Further details on refinement\n" -); - printf(" appear below.\n"); - printf( -" -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n"); - printf( -" Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n" -); - printf( -" ensure that all angles are between 20 and 140 degrees. An\n"); - printf( -" alternative bound on the minimum angle, replacing 20 degrees, may\n"); - printf( -" be specified after the `q'. The specified angle may include a\n"); - printf( -" decimal point, but not exponential notation. Note that a bound of\n" -); - printf( -" theta degrees on the smallest angle also implies a bound of\n"); - printf( -" (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n" -); - printf( -" degrees or smaller, Triangle is mathematically guaranteed to\n"); - printf( -" terminate (assuming infinite precision arithmetic--Triangle may\n"); - printf( -" fail to terminate if you run out of precision). In practice,\n"); - printf( -" Triangle often succeeds for minimum angles up to 34 degrees. For\n"); - printf( -" some meshes, however, you might need to reduce the minimum angle to\n" -); - printf( -" avoid problems associated with insufficient floating-point\n"); - printf(" precision.\n"); - printf( -" -a Imposes a maximum triangle area. If a number follows the `a', no\n"); - printf( -" triangle is generated whose area is larger than that number. If no\n" -); - printf( -" number is specified, an .area file (if -r is used) or .poly file\n"); - printf( -" (if -r is not used) specifies a set of maximum area constraints.\n"); - printf( -" An .area file contains a separate area constraint for each\n"); - printf( -" triangle, and is useful for refining a finite element mesh based on\n" -); - printf( -" a posteriori error estimates. A .poly file can optionally contain\n" -); - printf( -" an area constraint for each segment-bounded region, thereby\n"); - printf( -" controlling triangle densities in a first triangulation of a PSLG.\n" -); - printf( -" You can impose both a fixed area constraint and a varying area\n"); - printf( -" constraint by invoking the -a switch twice, once with and once\n"); - printf( -" without a number following. Each area specified may include a\n"); - printf(" decimal point.\n"); - printf( -" -u Imposes a user-defined constraint on triangle size. There are two\n" -); - printf( -" ways to use this feature. One is to edit the triunsuitable()\n"); - printf( -" procedure in triangle.c to encode any constraint you like, then\n"); - printf( -" recompile Triangle. The other is to compile triangle.c with the\n"); - printf( -" EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n"); - printf( -" link Triangle with a separate object file that implements\n"); - printf( -" triunsuitable(). In either case, the -u switch causes the user-\n"); - printf(" defined test to be applied to every triangle.\n"); - printf( -" -A Assigns an additional floating-point attribute to each triangle\n"); - printf( -" that identifies what segment-bounded region each triangle belongs\n"); - printf( -" to. Attributes are assigned to regions by the .poly file. If a\n"); - printf( -" region is not explicitly marked by the .poly file, triangles in\n"); - printf( -" that region are assigned an attribute of zero. The -A switch has\n"); - printf( -" an effect only when the -p switch is used and the -r switch is not.\n" -); - printf( -" -c Creates segments on the convex hull of the triangulation. If you\n"); - printf( -" are triangulating a vertex set, this switch causes a .poly file to\n" -); - printf( -" be written, containing all edges of the convex hull. If you are\n"); - printf( -" triangulating a PSLG, this switch specifies that the whole convex\n"); - printf( -" hull of the PSLG should be triangulated, regardless of what\n"); - printf( -" segments the PSLG has. If you do not use this switch when\n"); - printf( -" triangulating a PSLG, Triangle assumes that you have identified the\n" -); - printf( -" region to be triangulated by surrounding it with segments of the\n"); - printf( -" input PSLG. Beware: if you are not careful, this switch can cause\n" -); - printf( -" the introduction of an extremely thin angle between a PSLG segment\n" -); - printf( -" and a convex hull segment, which can cause overrefinement (and\n"); - printf( -" possibly failure if Triangle runs out of precision). If you are\n"); - printf( -" refining a mesh, the -c switch works differently: it causes a\n"); - printf( -" .poly file to be written containing the boundary edges of the mesh\n" -); - printf(" (useful if no .poly file was read).\n"); - printf( -" -D Conforming Delaunay triangulation: use this switch if you want to\n" -); - printf( -" ensure that all the triangles in the mesh are Delaunay, and not\n"); - printf( -" merely constrained Delaunay; or if you want to ensure that all the\n" -); - printf( -" Voronoi vertices lie within the triangulation. (Some finite volume\n" -); - printf( -" methods have this requirement.) This switch invokes Ruppert's\n"); - printf( -" original algorithm, which splits every subsegment whose diametral\n"); - printf( -" circle is encroached. It usually increases the number of vertices\n" -); - printf(" and triangles.\n"); - printf( -" -j Jettisons vertices that are not part of the final triangulation\n"); - printf( -" from the output .node file. By default, Triangle copies all\n"); - printf( -" vertices in the input .node file to the output .node file, in the\n"); - printf( -" same order, so their indices do not change. The -j switch prevents\n" -); - printf( -" duplicated input vertices, or vertices `eaten' by holes, from\n"); - printf( -" appearing in the output .node file. Thus, if two input vertices\n"); - printf( -" have exactly the same coordinates, only the first appears in the\n"); - printf( -" output. If any vertices are jettisoned, the vertex numbering in\n"); - printf( -" the output .node file differs from that of the input .node file.\n"); - printf( -" -e Outputs (to an .edge file) a list of edges of the triangulation.\n"); - printf( -" -v Outputs the Voronoi diagram associated with the triangulation.\n"); - printf( -" Does not attempt to detect degeneracies, so some Voronoi vertices\n"); - printf( -" may be duplicated. See the discussion of Voronoi diagrams below.\n"); - printf( -" -n Outputs (to a .neigh file) a list of triangles neighboring each\n"); - printf(" triangle.\n"); - printf( -" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n" -); - printf(" viewing with the Geometry Center's Geomview package.\n"); - printf( -" -B No boundary markers in the output .node, .poly, and .edge output\n"); - printf( -" files. See the detailed discussion of boundary markers below.\n"); - printf( -" -P No output .poly file. Saves disk space, but you lose the ability\n"); - printf( -" to maintain constraining segments on later refinements of the mesh.\n" -); - printf(" -N No output .node file.\n"); - printf(" -E No output .ele file.\n"); - printf( -" -I No iteration numbers. Suppresses the output of .node and .poly\n"); - printf( -" files, so your input files won't be overwritten. (If your input is\n" -); - printf( -" a .poly file only, a .node file is written.) Cannot be used with\n"); - printf( -" the -r switch, because that would overwrite your input .ele file.\n"); - printf( -" Shouldn't be used with the -q, -a, -u, or -s switch if you are\n"); - printf( -" using a .node file for input, because no .node file is written, so\n" -); - printf(" there is no record of any added Steiner points.\n"); - printf(" -O No holes. Ignores the holes in the .poly file.\n"); - printf( -" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n" -); - printf( -" arithmetic for certain tests if it thinks the inexact tests are not\n" -); - printf( -" accurate enough. Exact arithmetic ensures the robustness of the\n"); - printf( -" triangulation algorithms, despite floating-point roundoff error.\n"); - printf( -" Disabling exact arithmetic with the -X switch causes a small\n"); - printf( -" improvement in speed and creates the possibility that Triangle will\n" -); - printf(" fail to produce a valid mesh. Not recommended.\n"); - printf( -" -z Numbers all items starting from zero (rather than one). Note that\n" -); - printf( -" this switch is normally overridden by the value used to number the\n" -); - printf( -" first vertex of the input .node or .poly file. However, this\n"); - printf( -" switch is useful when calling Triangle from another program.\n"); - printf( -" -o2 Generates second-order subparametric elements with six nodes each.\n" -); - printf( -" -Y No new vertices on the boundary. This switch is useful when the\n"); - printf( -" mesh boundary must be preserved so that it conforms to some\n"); - printf( -" adjacent mesh. Be forewarned that you will probably sacrifice much\n" -); - printf( -" of the quality of the mesh; Triangle will try, but the resulting\n"); - printf( -" mesh may contain poorly shaped triangles. Works well if all the\n"); - printf( -" boundary vertices are closely spaced. Specify this switch twice\n"); - printf( -" (`-YY') to prevent all segment splitting, including internal\n"); - printf(" boundaries.\n"); - printf( -" -S Specifies the maximum number of Steiner points (vertices that are\n"); - printf( -" not in the input, but are added to meet the constraints on minimum\n" -); - printf( -" angle and maximum area). The default is to allow an unlimited\n"); - printf( -" number. If you specify this switch with no number after it,\n"); - printf( -" the limit is set to zero. Triangle always adds vertices at segment\n" -); - printf( -" intersections, even if it needs to use more vertices than the limit\n" -); - printf( -" you set. When Triangle inserts segments by splitting (-s), it\n"); - printf( -" always adds enough vertices to ensure that all the segments of the\n" -); - printf(" PLSG are recovered, ignoring the limit if necessary.\n"); - printf( -" -i Uses an incremental rather than a divide-and-conquer algorithm to\n"); - printf( -" construct a Delaunay triangulation. Try it if the divide-and-\n"); - printf(" conquer algorithm fails.\n"); - printf( -" -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n"); - printf( -" triangulation. Warning: does not use exact arithmetic for all\n"); - printf(" calculations. An exact result is not guaranteed.\n"); - printf( -" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n"); - printf( -" default, Triangle alternates between vertical and horizontal cuts,\n" -); - printf( -" which usually improve the speed except with vertex sets that are\n"); - printf( -" small or short and wide. This switch is primarily of theoretical\n"); - printf(" interest.\n"); - printf( -" -s Specifies that segments should be forced into the triangulation by\n" -); - printf( -" recursively splitting them at their midpoints, rather than by\n"); - printf( -" generating a constrained Delaunay triangulation. Segment splitting\n" -); - printf( -" is true to Ruppert's original algorithm, but can create needlessly\n" -); - printf( -" small triangles. This switch is primarily of theoretical interest.\n" -); - printf( -" -C Check the consistency of the final mesh. Uses exact arithmetic for\n" -); - printf( -" checking, even if the -X switch is used. Useful if you suspect\n"); - printf(" Triangle is buggy.\n"); - printf( -" -Q Quiet: Suppresses all explanation of what Triangle is doing,\n"); - printf(" unless an error occurs.\n"); - printf( -" -V Verbose: Gives detailed information about what Triangle is doing.\n" -); - printf( -" Add more `V's for increasing amount of detail. `-V' is most\n"); - printf( -" useful; itgives information on algorithmic progress and much more\n"); - printf( -" detailed statistics. `-VV' gives vertex-by-vertex details, and\n"); - printf( -" prints so much that Triangle runs much more slowly. `-VVVV' gives\n" -); - printf(" information only a debugger could love.\n"); - printf(" -h Help: Displays these instructions.\n"); - printf("\n"); - printf("Definitions:\n"); - printf("\n"); - printf( -" A Delaunay triangulation of a vertex set is a triangulation whose\n"); - printf( -" vertices are the vertex set, that covers the convex hull of the vertex\n"); - printf( -" set. A Delaunay triangulation has the property that no vertex lies\n"); - printf( -" inside the circumscribing circle (circle that passes through all three\n"); - printf(" vertices) of any triangle in the triangulation.\n\n"); - printf( -" A Voronoi diagram of a vertex set is a subdivision of the plane into\n"); - printf( -" polygonal cells (some of which may be unbounded, meaning infinitely\n"); - printf( -" large), where each cell is the set of points in the plane that are closer\n" -); - printf( -" to some input vertex than to any other input vertex. The Voronoi diagram\n" -); - printf(" is a geometric dual of the Delaunay triangulation.\n\n"); - printf( -" A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n"); - printf( -" Segments are simply edges, whose endpoints are all vertices in the PSLG.\n" -); - printf( -" Segments may intersect each other only at their endpoints. The file\n"); - printf(" format for PSLGs (.poly files) is described below.\n\n"); - printf( -" A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n"); - printf( -" Delaunay triangulation, but each PSLG segment is present as a single edge\n" -); - printf( -" of the CDT. (A constrained Delaunay triangulation is not truly a\n"); - printf( -" Delaunay triangulation, because some of its triangles might not be\n"); - printf( -" Delaunay.) By definition, a CDT does not have any vertices other than\n"); - printf( -" those specified in the input PSLG. Depending on context, a CDT might\n"); - printf( -" cover the convex hull of the PSLG, or it might cover only a segment-\n"); - printf(" bounded region (e.g. a polygon).\n\n"); - printf( -" A conforming Delaunay triangulation of a PSLG is a triangulation in which\n" -); - printf( -" each triangle is truly Delaunay, and each PSLG segment is represented by\n" -); - printf( -" a linear contiguous sequence of edges of the triangulation. New vertices\n" -); - printf( -" (not part of the PSLG) may appear, and each input segment may have been\n"); - printf( -" subdivided into shorter edges (subsegments) by these additional vertices.\n" -); - printf( -" The new vertices are frequently necessary to maintain the Delaunay\n"); - printf(" property while ensuring that every segment is represented.\n\n"); - printf( -" A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n"); - printf( -" triangulation of a PSLG whose triangles are constrained Delaunay. New\n"); - printf(" vertices may appear, and input segments may be subdivided into\n"); - printf( -" subsegments, but not to guarantee that segments are respected; rather, to\n" -); - printf( -" improve the quality of the triangles. The high-quality meshes produced\n"); - printf( -" by the -q switch are usually CCDTs, but can be made conforming Delaunay\n"); - printf(" with the -D switch.\n\n"); - printf("File Formats:\n\n"); - printf( -" All files may contain comments prefixed by the character '#'. Vertices,\n" -); - printf( -" triangles, edges, holes, and maximum area constraints must be numbered\n"); - printf( -" consecutively, starting from either 1 or 0. Whichever you choose, all\n"); - printf( -" input files must be consistent; if the vertices are numbered from 1, so\n"); - printf( -" must be all other objects. Triangle automatically detects your choice\n"); - printf( -" while reading the .node (or .poly) file. (When calling Triangle from\n"); - printf( -" another program, use the -z switch if you wish to number objects from\n"); - printf(" zero.) Examples of these file formats are given below.\n\n"); - printf(" .node files:\n"); - printf( -" First line: <# of vertices> <# of attributes>\n" -); - printf( -" <# of boundary markers (0 or 1)>\n" -); - printf( -" Remaining lines: [attributes] [boundary marker]\n"); - printf("\n"); - printf( -" The attributes, which are typically floating-point values of physical\n"); - printf( -" quantities (such as mass or conductivity) associated with the nodes of\n" -); - printf( -" a finite element mesh, are copied unchanged to the output mesh. If -q,\n" -); - printf( -" -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n" -); - printf(" has attributes assigned to it by linear interpolation.\n\n"); - printf( -" If the fourth entry of the first line is `1', the last column of the\n"); - printf( -" remainder of the file is assumed to contain boundary markers. Boundary\n" -); - printf( -" markers are used to identify boundary vertices and vertices resting on\n" -); - printf( -" PSLG segments; a complete description appears in a section below. The\n" -); - printf( -" .node file produced by Triangle contains boundary markers in the last\n"); - printf(" column unless they are suppressed by the -B switch.\n\n"); - printf(" .ele files:\n"); - printf( -" First line: <# of triangles> <# of attributes>\n"); - printf( -" Remaining lines: ... [attributes]\n"); - printf("\n"); - printf( -" Nodes are indices into the corresponding .node file. The first three\n"); - printf( -" nodes are the corner vertices, and are listed in counterclockwise order\n" -); - printf( -" around each triangle. (The remaining nodes, if any, depend on the type\n" -); - printf(" of finite element used.)\n\n"); - printf( -" The attributes are just like those of .node files. Because there is no\n" -); - printf( -" simple mapping from input to output triangles, Triangle attempts to\n"); - printf( -" interpolate attributes, and may cause a lot of diffusion of attributes\n" -); - printf( -" among nearby triangles as the triangulation is refined. Attributes do\n" -); - printf(" not diffuse across segments, so attributes used to identify\n"); - printf(" segment-bounded regions remain intact.\n\n"); - printf( -" In .ele files produced by Triangle, each triangular element has three\n"); - printf( -" nodes (vertices) unless the -o2 switch is used, in which case\n"); - printf( -" subparametric quadratic elements with six nodes each are generated.\n"); - printf( -" The first three nodes are the corners in counterclockwise order, and\n"); - printf( -" the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n"); - printf( -" opposite the first, second, and third vertices, respectively.\n"); - printf("\n"); - printf(" .poly files:\n"); - printf( -" First line: <# of vertices> <# of attributes>\n" -); - printf( -" <# of boundary markers (0 or 1)>\n" -); - printf( -" Following lines: [attributes] [boundary marker]\n"); - printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); - printf( -" Following lines: [boundary marker]\n"); - printf(" One line: <# of holes>\n"); - printf(" Following lines: \n"); - printf( -" Optional line: <# of regional attributes and/or area constraints>\n"); - printf( -" Optional following lines: \n"); - printf("\n"); - printf( -" A .poly file represents a PSLG, as well as some additional information.\n" -); - printf( -" The first section lists all the vertices, and is identical to the\n"); - printf( -" format of .node files. <# of vertices> may be set to zero to indicate\n" -); - printf( -" that the vertices are listed in a separate .node file; .poly files\n"); - printf( -" produced by Triangle always have this format. A vertex set represented\n" -); - printf( -" this way has the advantage that it may easily be triangulated with or\n"); - printf( -" without segments (depending on whether the -p switch is invoked).\n"); - printf("\n"); - printf( -" The second section lists the segments. Segments are edges whose\n"); - printf( -" presence in the triangulation is enforced. (Depending on the choice of\n" -); - printf( -" switches, segment might be subdivided into smaller edges). Each\n"); - printf( -" segment is specified by listing the indices of its two endpoints. This\n" -); - printf( -" means that you must include its endpoints in the vertex list. Each\n"); - printf(" segment, like each point, may have a boundary marker.\n\n"); - printf( -" If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n" -); - printf( -" Delaunay triangulation (CDT), in which each segment appears as a single\n" -); - printf( -" edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n" -); - printf( -" produces a conforming constrained Delaunay triangulation (CCDT), in\n"); - printf( -" which segments may be subdivided into smaller edges. If -D is\n"); - printf( -" selected, Triangle produces a conforming Delaunay triangulation, so\n"); - printf( -" that every triangle is Delaunay, and not just constrained Delaunay.\n"); - printf("\n"); - printf( -" The third section lists holes (and concavities, if -c is selected) in\n"); - printf( -" the triangulation. Holes are specified by identifying a point inside\n"); - printf( -" each hole. After the triangulation is formed, Triangle creates holes\n"); - printf( -" by eating triangles, spreading out from each hole point until its\n"); - printf( -" progress is blocked by segments in the PSLG. You must be careful to\n"); - printf( -" enclose each hole in segments, or your whole triangulation might be\n"); - printf( -" eaten away. If the two triangles abutting a segment are eaten, the\n"); - printf( -" segment itself is also eaten. Do not place a hole directly on a\n"); - printf(" segment; if you do, Triangle chooses one side of the segment\n"); - printf(" arbitrarily.\n\n"); - printf( -" The optional fourth section lists regional attributes (to be assigned\n"); - printf( -" to all triangles in a region) and regional constraints on the maximum\n"); - printf( -" triangle area. Triangle reads this section only if the -A switch is\n"); - printf( -" used or the -a switch is used without a number following it, and the -r\n" -); - printf( -" switch is not used. Regional attributes and area constraints are\n"); - printf( -" propagated in the same manner as holes: you specify a point for each\n"); - printf( -" attribute and/or constraint, and the attribute and/or constraint\n"); - printf( -" affects the whole region (bounded by segments) containing the point.\n"); - printf( -" If two values are written on a line after the x and y coordinate, the\n"); - printf( -" first such value is assumed to be a regional attribute (but is only\n"); - printf( -" applied if the -A switch is selected), and the second value is assumed\n" -); - printf( -" to be a regional area constraint (but is only applied if the -a switch\n" -); - printf( -" is selected). You may specify just one value after the coordinates,\n"); - printf( -" which can serve as both an attribute and an area constraint, depending\n" -); - printf( -" on the choice of switches. If you are using the -A and -a switches\n"); - printf( -" simultaneously and wish to assign an attribute to some region without\n"); - printf(" imposing an area constraint, use a negative maximum area.\n\n"); - printf( -" When a triangulation is created from a .poly file, you must either\n"); - printf( -" enclose the entire region to be triangulated in PSLG segments, or\n"); - printf( -" use the -c switch, which automatically creates extra segments that\n"); - printf( -" enclose the convex hull of the PSLG. If you do not use the -c switch,\n" -); - printf( -" Triangle eats all triangles that are not enclosed by segments; if you\n"); - printf( -" are not careful, your whole triangulation may be eaten away. If you do\n" -); - printf( -" use the -c switch, you can still produce concavities by the appropriate\n" -); - printf( -" placement of holes just inside the boundary of the convex hull.\n"); - printf("\n"); - printf( -" An ideal PSLG has no intersecting segments, nor any vertices that lie\n"); - printf( -" upon segments (except, of course, the endpoints of each segment). You\n" -); - printf( -" aren't required to make your .poly files ideal, but you should be aware\n" -); - printf( -" of what can go wrong. Segment intersections are relatively safe--\n"); - printf( -" Triangle calculates the intersection points for you and adds them to\n"); - printf( -" the triangulation--as long as your machine's floating-point precision\n"); - printf( -" doesn't become a problem. You are tempting the fates if you have three\n" -); - printf( -" segments that cross at the same location, and expect Triangle to figure\n" -); - printf( -" out where the intersection point is. Thanks to floating-point roundoff\n" -); - printf( -" error, Triangle will probably decide that the three segments intersect\n" -); - printf( -" at three different points, and you will find a minuscule triangle in\n"); - printf( -" your output--unless Triangle tries to refine the tiny triangle, uses\n"); - printf( -" up the last bit of machine precision, and fails to terminate at all.\n"); - printf( -" You're better off putting the intersection point in the input files,\n"); - printf( -" and manually breaking up each segment into two. Similarly, if you\n"); - printf( -" place a vertex at the middle of a segment, and hope that Triangle will\n" -); - printf( -" break up the segment at that vertex, you might get lucky. On the other\n" -); - printf( -" hand, Triangle might decide that the vertex doesn't lie precisely on\n"); - printf( -" the segment, and you'll have a needle-sharp triangle in your output--or\n" -); - printf(" a lot of tiny triangles if you're generating a quality mesh.\n"); - printf("\n"); - printf( -" When Triangle reads a .poly file, it also writes a .poly file, which\n"); - printf( -" includes all the subsegments--the edges that are parts of input\n"); - printf( -" segments. If the -c switch is used, the output .poly file also\n"); - printf( -" includes all of the edges on the convex hull. Hence, the output .poly\n" -); - printf( -" file is useful for finding edges associated with input segments and for\n" -); - printf( -" setting boundary conditions in finite element simulations. Moreover,\n"); - printf( -" you will need the output .poly file if you plan to refine the output\n"); - printf( -" mesh, and don't want segments to be missing in later triangulations.\n"); - printf("\n"); - printf(" .area files:\n"); - printf(" First line: <# of triangles>\n"); - printf(" Following lines: \n"); - printf("\n"); - printf( -" An .area file associates with each triangle a maximum area that is used\n" -); - printf( -" for mesh refinement. As with other file formats, every triangle must\n"); - printf( -" be represented, and the triangles must be numbered consecutively. A\n"); - printf( -" triangle may be left unconstrained by assigning it a negative maximum\n"); - printf(" area.\n\n"); - printf(" .edge files:\n"); - printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n"); - printf( -" Following lines: [boundary marker]\n"); - printf("\n"); - printf( -" Endpoints are indices into the corresponding .node file. Triangle can\n" -); - printf( -" produce .edge files (use the -e switch), but cannot read them. The\n"); - printf( -" optional column of boundary markers is suppressed by the -B switch.\n"); - printf("\n"); - printf( -" In Voronoi diagrams, one also finds a special kind of edge that is an\n"); - printf( -" infinite ray with only one endpoint. For these edges, a different\n"); - printf(" format is used:\n\n"); - printf(" -1 \n\n"); - printf( -" The `direction' is a floating-point vector that indicates the direction\n" -); - printf(" of the infinite ray.\n\n"); - printf(" .neigh files:\n"); - printf( -" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n" -); - printf( -" Following lines: \n"); - printf("\n"); - printf( -" Neighbors are indices into the corresponding .ele file. An index of -1\n" -); - printf( -" indicates no neighbor (because the triangle is on an exterior\n"); - printf( -" boundary). The first neighbor of triangle i is opposite the first\n"); - printf(" corner of triangle i, and so on.\n\n"); - printf( -" Triangle can produce .neigh files (use the -n switch), but cannot read\n" -); - printf(" them.\n\n"); - printf("Boundary Markers:\n\n"); - printf( -" Boundary markers are tags used mainly to identify which output vertices\n"); - printf( -" and edges are associated with which PSLG segment, and to identify which\n"); - printf( -" vertices and edges occur on a boundary of the triangulation. A common\n"); - printf( -" use is to determine where boundary conditions should be applied to a\n"); - printf( -" finite element mesh. You can prevent boundary markers from being written\n" -); - printf(" into files produced by Triangle by using the -B switch.\n\n"); - printf( -" The boundary marker associated with each segment in an output .poly file\n" -); - printf(" and each edge in an output .edge file is chosen as follows:\n"); - printf( -" - If an output edge is part or all of a PSLG segment with a nonzero\n"); - printf( -" boundary marker, then the edge is assigned the same marker.\n"); - printf( -" - Otherwise, if the edge lies on a boundary of the triangulation\n"); - printf( -" (even the boundary of a hole), then the edge is assigned the marker\n"); - printf(" one (1).\n"); - printf(" - Otherwise, the edge is assigned the marker zero (0).\n"); - printf( -" The boundary marker associated with each vertex in an output .node file\n"); - printf(" is chosen as follows:\n"); - printf( -" - If a vertex is assigned a nonzero boundary marker in the input file,\n" -); - printf( -" then it is assigned the same marker in the output .node file.\n"); - printf( -" - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n"); - printf( -" endpoint of the segment) with a nonzero boundary marker, then the\n"); - printf( -" vertex is assigned the same marker. If the vertex lies on several\n"); - printf(" such segments, one of the markers is chosen arbitrarily.\n"); - printf( -" - Otherwise, if the vertex occurs on a boundary of the triangulation,\n"); - printf(" then the vertex is assigned the marker one (1).\n"); - printf(" - Otherwise, the vertex is assigned the marker zero (0).\n"); - printf("\n"); - printf( -" If you want Triangle to determine for you which vertices and edges are on\n" -); - printf( -" the boundary, assign them the boundary marker zero (or use no markers at\n" -); - printf( -" all) in your input files. In the output files, all boundary vertices,\n"); - printf(" edges, and segments will be assigned the value one.\n\n"); - printf("Triangulation Iteration Numbers:\n\n"); - printf( -" Because Triangle can read and refine its own triangulations, input\n"); - printf( -" and output files have iteration numbers. For instance, Triangle might\n"); - printf( -" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n"); - printf( -" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n"); - printf(" mesh.4.poly. Files with no iteration number are treated as if\n"); - printf( -" their iteration number is zero; hence, Triangle might read the file\n"); - printf( -" points.node, triangulate it, and produce the files points.1.node and\n"); - printf(" points.1.ele.\n\n"); - printf( -" Iteration numbers allow you to create a sequence of successively finer\n"); - printf( -" meshes suitable for multigrid methods. They also allow you to produce a\n" -); - printf( -" sequence of meshes using error estimate-driven mesh refinement.\n"); - printf("\n"); - printf( -" If you're not using refinement or quality meshing, and you don't like\n"); - printf( -" iteration numbers, use the -I switch to disable them. This switch also\n"); - printf( -" disables output of .node and .poly files to prevent your input files from\n" -); - printf( -" being overwritten. (If the input is a .poly file that contains its own\n"); - printf( -" points, a .node file is written. This can be quite convenient for\n"); - printf(" computing CDTs or quality meshes.)\n\n"); - printf("Examples of How to Use Triangle:\n\n"); - printf( -" `triangle dots' reads vertices from dots.node, and writes their Delaunay\n" -); - printf( -" triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n"); - printf( -" to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n"); - printf( -" instead. (No additional .node file is needed, so none is written.)\n"); - printf("\n"); - printf( -" `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n"); - printf( -" object.1.node, if the vertices are omitted from object.1.poly) and writes\n" -); - printf( -" its constrained Delaunay triangulation to object.2.node and object.2.ele.\n" -); - printf( -" The segments are copied to object.2.poly, and all edges are written to\n"); - printf(" object.2.edge.\n\n"); - printf( -" `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n" -); - printf( -" object.node), generates a mesh whose angles are all between 31.5 and 117\n" -); - printf( -" degrees and whose triangles all have areas of 0.1 or less, and writes the\n" -); - printf( -" mesh to object.1.node and object.1.ele. Each segment may be broken up\n"); - printf(" into multiple subsegments; these are written to object.1.poly.\n"); - printf("\n"); - printf( -" Here is a sample file `box.poly' describing a square with a square hole:\n" -); - printf("\n"); - printf( -" # A box with eight vertices in 2D, no attributes, one boundary marker.\n" -); - printf(" 8 2 0 1\n"); - printf(" # Outer box has these vertices:\n"); - printf(" 1 0 0 0\n"); - printf(" 2 0 3 0\n"); - printf(" 3 3 0 0\n"); - printf(" 4 3 3 33 # A special marker for this vertex.\n"); - printf(" # Inner square has these vertices:\n"); - printf(" 5 1 1 0\n"); - printf(" 6 1 2 0\n"); - printf(" 7 2 1 0\n"); - printf(" 8 2 2 0\n"); - printf(" # Five segments with boundary markers.\n"); - printf(" 5 1\n"); - printf(" 1 1 2 5 # Left side of outer box.\n"); - printf(" # Square hole has these segments:\n"); - printf(" 2 5 7 0\n"); - printf(" 3 7 8 0\n"); - printf(" 4 8 6 10\n"); - printf(" 5 6 5 0\n"); - printf(" # One hole in the middle of the inner square.\n"); - printf(" 1\n"); - printf(" 1 1.5 1.5\n"); - printf("\n"); - printf( -" Note that some segments are missing from the outer square, so you must\n"); - printf( -" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n" -); - printf( -" file `box.1.node', with twelve vertices. The last four vertices were\n"); - printf( -" added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n"); - printf( -" from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n"); - printf( -" other vertices but 4 have been marked to indicate that they lie on a\n"); - printf(" boundary.\n\n"); - printf(" 12 2 0 1\n"); - printf(" 1 0 0 5\n"); - printf(" 2 0 3 5\n"); - printf(" 3 3 0 1\n"); - printf(" 4 3 3 33\n"); - printf(" 5 1 1 1\n"); - printf(" 6 1 2 10\n"); - printf(" 7 2 1 1\n"); - printf(" 8 2 2 10\n"); - printf(" 9 0 1.5 5\n"); - printf(" 10 1.5 0 1\n"); - printf(" 11 3 1.5 1\n"); - printf(" 12 1.5 3 1\n"); - printf(" # Generated by triangle -pqc box.poly\n"); - printf("\n"); - printf(" Here is the output file `box.1.ele', with twelve triangles.\n"); - printf("\n"); - printf(" 12 3 0\n"); - printf(" 1 5 6 9\n"); - printf(" 2 10 3 7\n"); - printf(" 3 6 8 12\n"); - printf(" 4 9 1 5\n"); - printf(" 5 6 2 9\n"); - printf(" 6 7 3 11\n"); - printf(" 7 11 4 8\n"); - printf(" 8 7 5 10\n"); - printf(" 9 12 2 6\n"); - printf(" 10 8 7 11\n"); - printf(" 11 5 1 10\n"); - printf(" 12 8 4 12\n"); - printf(" # Generated by triangle -pqc box.poly\n\n"); - printf( -" Here is the output file `box.1.poly'. Note that segments have been added\n" -); - printf( -" to represent the convex hull, and some segments have been subdivided by\n"); - printf( -" newly added vertices. Note also that <# of vertices> is set to zero to\n"); - printf(" indicate that the vertices should be read from the .node file.\n"); - printf("\n"); - printf(" 0 2 0 1\n"); - printf(" 12 1\n"); - printf(" 1 1 9 5\n"); - printf(" 2 5 7 1\n"); - printf(" 3 8 7 1\n"); - printf(" 4 6 8 10\n"); - printf(" 5 5 6 1\n"); - printf(" 6 3 10 1\n"); - printf(" 7 4 11 1\n"); - printf(" 8 2 12 1\n"); - printf(" 9 9 2 5\n"); - printf(" 10 10 1 1\n"); - printf(" 11 11 3 1\n"); - printf(" 12 12 4 1\n"); - printf(" 1\n"); - printf(" 1 1.5 1.5\n"); - printf(" # Generated by triangle -pqc box.poly\n"); - printf("\n"); - printf("Refinement and Area Constraints:\n"); - printf("\n"); - printf( -" The -r switch causes a mesh (.node and .ele files) to be read and\n"); - printf( -" refined. If the -p switch is also used, a .poly file is read and used to\n" -); - printf( -" specify edges that are constrained and cannot be eliminated (although\n"); - printf( -" they can be subdivided into smaller edges) by the refinement process.\n"); - printf("\n"); - printf( -" When you refine a mesh, you generally want to impose tighter constraints.\n" -); - printf( -" One way to accomplish this is to use -q with a larger angle, or -a\n"); - printf( -" followed by a smaller area than you used to generate the mesh you are\n"); - printf( -" refining. Another way to do this is to create an .area file, which\n"); - printf( -" specifies a maximum area for each triangle, and use the -a switch\n"); - printf( -" (without a number following). Each triangle's area constraint is applied\n" -); - printf( -" to that triangle. Area constraints tend to diffuse as the mesh is\n"); - printf( -" refined, so if there are large variations in area constraint between\n"); - printf( -" adjacent triangles, you may not get the results you want. In that case,\n" -); - printf( -" consider instead using the -u switch and writing a C procedure that\n"); - printf(" determines which triangles are too large.\n\n"); - printf( -" If you are refining a mesh composed of linear (three-node) elements, the\n" -); - printf( -" output mesh contains all the nodes present in the input mesh, in the same\n" -); - printf( -" order, with new nodes added at the end of the .node file. However, the\n"); - printf( -" refinement is not hierarchical: there is no guarantee that each output\n"); - printf( -" element is contained in a single input element. Often, an output element\n" -); - printf( -" can overlap two or three input elements, and some input edges are not\n"); - printf( -" present in the output mesh. Hence, a sequence of refined meshes forms a\n" -); - printf( -" hierarchy of nodes, but not a hierarchy of elements. If you refine a\n"); - printf( -" mesh of higher-order elements, the hierarchical property applies only to\n" -); - printf( -" the nodes at the corners of an element; the midpoint nodes on each edge\n"); - printf(" are discarded before the mesh is refined.\n\n"); - printf( -" Maximum area constraints in .poly files operate differently from those in\n" -); - printf( -" .area files. A maximum area in a .poly file applies to the whole\n"); - printf( -" (segment-bounded) region in which a point falls, whereas a maximum area\n"); - printf( -" in an .area file applies to only one triangle. Area constraints in .poly\n" -); - printf( -" files are used only when a mesh is first generated, whereas area\n"); - printf( -" constraints in .area files are used only to refine an existing mesh, and\n" -); - printf( -" are typically based on a posteriori error estimates resulting from a\n"); - printf(" finite element simulation on that mesh.\n\n"); - printf( -" `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n"); - printf( -" refines the triangulation to enforce a 25 degree minimum angle, and then\n" -); - printf( -" writes the refined triangulation to object.2.node and object.2.ele.\n"); - printf("\n"); - printf( -" `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n" -); - printf( -" After reconstructing the mesh and its subsegments, Triangle refines the\n"); - printf( -" mesh so that no triangle has area greater than 6.2, and furthermore the\n"); - printf( -" triangles satisfy the maximum area constraints in z.3.area. No angle\n"); - printf( -" bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n" -); - printf(" z.4.poly.\n\n"); - printf( -" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n"); - printf( -" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n"); - printf(" suitable for multigrid.\n\n"); - printf("Convex Hulls and Mesh Boundaries:\n\n"); - printf( -" If the input is a vertex set (not a PSLG), Triangle produces its convex\n"); - printf( -" hull as a by-product in the output .poly file if you use the -c switch.\n"); - printf( -" There are faster algorithms for finding a two-dimensional convex hull\n"); - printf(" than triangulation, of course, but this one comes for free.\n\n"); - printf( -" If the input is an unconstrained mesh (you are using the -r switch but\n"); - printf( -" not the -p switch), Triangle produces a list of its boundary edges\n"); - printf( -" (including hole boundaries) as a by-product when you use the -c switch.\n"); - printf( -" If you also use the -p switch, the output .poly file contains all the\n"); - printf(" segments from the input .poly file as well.\n\n"); - printf("Voronoi Diagrams:\n\n"); - printf( -" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n"); - printf( -" .v.edge. For example, `triangle -v points' reads points.node, produces\n"); - printf( -" its Delaunay triangulation in points.1.node and points.1.ele, and\n"); - printf( -" produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n" -); - printf( -" .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"); - printf( -" file contains a list of all Voronoi edges, some of which may be infinite\n" -); - printf( -" rays. (The choice of filenames makes it easy to run the set of Voronoi\n"); - printf(" vertices through Triangle, if so desired.)\n\n"); - printf( -" This implementation does not use exact arithmetic to compute the Voronoi\n" -); - printf( -" vertices, and does not check whether neighboring vertices are identical.\n" -); - printf( -" Be forewarned that if the Delaunay triangulation is degenerate or\n"); - printf( -" near-degenerate, the Voronoi diagram may have duplicate vertices or\n"); - printf(" crossing edges.\n\n"); - printf( -" The result is a valid Voronoi diagram only if Triangle's output is a true\n" -); - printf( -" Delaunay triangulation. The Voronoi output is usually meaningless (and\n"); - printf( -" may contain crossing edges and other pathology) if the output is a CDT or\n" -); - printf( -" CCDT, or if it has holes or concavities. If the triangulated domain is\n"); - printf( -" convex and has no holes, you can use -D switch to force Triangle to\n"); - printf( -" construct a conforming Delaunay triangulation instead of a CCDT, so the\n"); - printf(" Voronoi diagram will be valid.\n\n"); - printf("Mesh Topology:\n\n"); - printf( -" You may wish to know which triangles are adjacent to a certain Delaunay\n"); - printf( -" edge in an .edge file, which Voronoi cells are adjacent to a certain\n"); - printf( -" Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n"); - printf( -" each other. All of this information can be found by cross-referencing\n"); - printf( -" output files with the recollection that the Delaunay triangulation and\n"); - printf(" the Voronoi diagram are planar duals.\n\n"); - printf( -" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n"); - printf( -" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n"); - printf( -" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n"); - printf( -" vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n"); - printf(" of vertex k of the corresponding .node file.\n\n"); - printf( -" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n"); - printf( -" vertices of the corresponding Voronoi edge. If the endpoints of a\n"); - printf( -" Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n" -); - printf( -" and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n" -); - printf( -" respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n" -); - printf( -" at the endpoints of the corresponding Delaunay edge. If the endpoints of\n" -); - printf( -" a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n" -); - printf( -" adjoin the right and left sides of the corresponding Voronoi edge,\n"); - printf( -" respectively. To find which Voronoi cells are adjacent to each other,\n"); - printf(" just read the list of Delaunay edges.\n\n"); - printf( -" Triangle does not write a list of the edges adjoining each Voronoi cell,\n" -); - printf( -" but you can reconstructed it straightforwardly. For instance, to find\n"); - printf( -" all the edges of Voronoi cell 1, search the output .edge file for every\n"); - printf( -" edge that has input vertex 1 as an endpoint. The corresponding dual\n"); - printf( -" edges in the output .v.edge file form the boundary of Voronoi cell 1.\n"); - printf("\n"); - printf( -" For each Voronoi vertex, the .neigh file gives a list of the three\n"); - printf( -" Voronoi vertices attached to it. You might find this more convenient\n"); - printf(" than the .v.edge file.\n\n"); - printf("Quadratic Elements:\n\n"); - printf( -" Triangle generates meshes with subparametric quadratic elements if the\n"); - printf( -" -o2 switch is specified. Quadratic elements have six nodes per element,\n" -); - printf( -" rather than three. `Subparametric' means that the edges of the triangles\n" -); - printf( -" are always straight, so that subparametric quadratic elements are\n"); - printf( -" geometrically identical to linear elements, even though they can be used\n" -); - printf( -" with quadratic interpolating functions. The three extra nodes of an\n"); - printf( -" element fall at the midpoints of the three edges, with the fourth, fifth,\n" -); - printf( -" and sixth nodes appearing opposite the first, second, and third corners\n"); - printf(" respectively.\n\n"); - printf("Domains with Small Angles:\n\n"); - printf( -" If two input segments adjoin each other at a small angle, clearly the -q\n" -); - printf( -" switch cannot remove the small angle. Moreover, Triangle may have no\n"); - printf( -" choice but to generate additional triangles whose smallest angles are\n"); - printf( -" smaller than the specified bound. However, these triangles only appear\n"); - printf( -" between input segments separated by small angles. Moreover, if you\n"); - printf( -" request a minimum angle of theta degrees, Triangle will generally produce\n" -); - printf( -" no angle larger than 180 - 2 theta, even if it is forced to compromise on\n" -); - printf(" the minimum angle.\n\n"); - printf("Statistics:\n\n"); - printf( -" After generating a mesh, Triangle prints a count of entities in the\n"); - printf( -" output mesh, including the number of vertices, triangles, edges, exterior\n" -); - printf( -" boundary edges (i.e. subsegments on the boundary of the triangulation,\n"); - printf( -" including hole boundaries), interior boundary edges (i.e. subsegments of\n" -); - printf( -" input segments not on the boundary), and total subsegments. If you've\n"); - printf( -" forgotten the statistics for an existing mesh, run Triangle on that mesh\n" -); - printf( -" with the -rNEP switches to read the mesh and print the statistics without\n" -); - printf( -" writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n"); - printf("\n"); - printf( -" The -V switch produces extended statistics, including a rough estimate\n"); - printf( -" of memory use, the number of calls to geometric predicates, and\n"); - printf( -" histograms of the angles and the aspect ratios of the triangles in the\n"); - printf(" mesh.\n\n"); - printf("Exact Arithmetic:\n\n"); - printf( -" Triangle uses adaptive exact arithmetic to perform what computational\n"); - printf( -" geometers call the `orientation' and `incircle' tests. If the floating-\n" -); - printf( -" point arithmetic of your machine conforms to the IEEE 754 standard (as\n"); - printf( -" most workstations do), and does not use extended precision internal\n"); - printf( -" floating-point registers, then your output is guaranteed to be an\n"); - printf( -" absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n" -); - printf( -" error notwithstanding. The word `adaptive' implies that these arithmetic\n" -); - printf( -" routines compute the result only to the precision necessary to guarantee\n" -); - printf( -" correctness, so they are usually nearly as fast as their approximate\n"); - printf(" counterparts.\n\n"); - printf( -" May CPUs, including Intel x86 processors, have extended precision\n"); - printf( -" floating-point registers. These must be reconfigured so their precision\n" -); - printf( -" is reduced to memory precision. Triangle does this if it is compiled\n"); - printf(" correctly. See the makefile for details.\n\n"); - printf( -" The exact tests can be disabled with the -X switch. On most inputs, this\n" -); - printf( -" switch reduces the computation time by about eight percent--it's not\n"); - printf( -" worth the risk. There are rare difficult inputs (having many collinear\n"); - printf( -" and cocircular vertices), however, for which the difference in speed\n"); - printf( -" could be a factor of two. Be forewarned that these are precisely the\n"); - printf( -" inputs most likely to cause errors if you use the -X switch. Hence, the\n" -); - printf(" -X switch is not recommended.\n\n"); - printf( -" Unfortunately, the exact tests don't solve every numerical problem.\n"); - printf( -" Exact arithmetic is not used to compute the positions of new vertices,\n"); - printf( -" because the bit complexity of vertex coordinates would grow without\n"); - printf( -" bound. Hence, segment intersections aren't computed exactly; in very\n"); - printf( -" unusual cases, roundoff error in computing an intersection point might\n"); - printf( -" actually lead to an inverted triangle and an invalid triangulation.\n"); - printf( -" (This is one reason to specify your own intersection points in your .poly\n" -); - printf( -" files.) Similarly, exact arithmetic is not used to compute the vertices\n" -); - printf(" of the Voronoi diagram.\n\n"); - printf( -" Another pair of problems not solved by the exact arithmetic routines is\n"); - printf( -" underflow and overflow. If Triangle is compiled for double precision\n"); - printf( -" arithmetic, I believe that Triangle's geometric predicates work correctly\n" -); - printf( -" if the exponent of every input coordinate falls in the range [-148, 201].\n" -); - printf( -" Underflow can silently prevent the orientation and incircle tests from\n"); - printf( -" being performed exactly, while overflow typically causes a floating\n"); - printf(" exception.\n\n"); - printf("Calling Triangle from Another Program:\n\n"); - printf(" Read the file triangle.h for details.\n\n"); - printf("Troubleshooting:\n\n"); - printf(" Please read this section before mailing me bugs.\n\n"); - printf(" `My output mesh has no triangles!'\n\n"); - printf( -" If you're using a PSLG, you've probably failed to specify a proper set\n" -); - printf( -" of bounding segments, or forgotten to use the -c switch. Or you may\n"); - printf( -" have placed a hole badly, thereby eating all your triangles. To test\n"); - printf(" these possibilities, try again with the -c and -O switches.\n"); - printf( -" Alternatively, all your input vertices may be collinear, in which case\n" -); - printf(" you can hardly expect to triangulate them.\n\n"); - printf(" `Triangle doesn't terminate, or just crashes.'\n\n"); - printf( -" Bad things can happen when triangles get so small that the distance\n"); - printf( -" between their vertices isn't much larger than the precision of your\n"); - printf( -" machine's arithmetic. If you've compiled Triangle for single-precision\n" -); - printf( -" arithmetic, you might do better by recompiling it for double-precision.\n" -); - printf( -" Then again, you might just have to settle for more lenient constraints\n" -); - printf( -" on the minimum angle and the maximum area than you had planned.\n"); - printf("\n"); - printf( -" You can minimize precision problems by ensuring that the origin lies\n"); - printf( -" inside your vertex set, or even inside the densest part of your\n"); - printf( -" mesh. If you're triangulating an object whose x-coordinates all fall\n"); - printf( -" between 6247133 and 6247134, you're not leaving much floating-point\n"); - printf(" precision for Triangle to work with.\n\n"); - printf( -" Precision problems can occur covertly if the input PSLG contains two\n"); - printf( -" segments that meet (or intersect) at an extremely small angle, or if\n"); - printf( -" such an angle is introduced by the -c switch. If you don't realize\n"); - printf( -" that a tiny angle is being formed, you might never discover why\n"); - printf( -" Triangle is crashing. To check for this possibility, use the -S switch\n" -); - printf( -" (with an appropriate limit on the number of Steiner points, found by\n"); - printf( -" trial-and-error) to stop Triangle early, and view the output .poly file\n" -); - printf( -" with Show Me (described below). Look carefully for regions where dense\n" -); - printf( -" clusters of vertices are forming and for small angles between segments.\n" -); - printf( -" Zoom in closely, as such segments might look like a single segment from\n" -); - printf(" a distance.\n\n"); - printf( -" If some of the input values are too large, Triangle may suffer a\n"); - printf( -" floating exception due to overflow when attempting to perform an\n"); - printf( -" orientation or incircle test. (Read the section on exact arithmetic\n"); - printf( -" above.) Again, I recommend compiling Triangle for double (rather\n"); - printf(" than single) precision arithmetic.\n\n"); - printf( -" Unexpected problems can arise if you use quality meshing (-q, -a, or\n"); - printf( -" -u) with an input that is not segment-bounded--that is, if your input\n"); - printf( -" is a vertex set, or you're using the -c switch. If the convex hull of\n" -); - printf( -" your input vertices has collinear vertices on its boundary, an input\n"); - printf( -" vertex that you think lies on the convex hull might actually lie just\n"); - printf( -" inside the convex hull. If so, the vertex and the nearby convex hull\n"); - printf( -" edge form an extremely thin triangle. When Triangle tries to refine\n"); - printf( -" the mesh to enforce angle and area constraints, Triangle might generate\n" -); - printf( -" extremely tiny triangles, or it might fail because of insufficient\n"); - printf(" floating-point precision.\n\n"); - printf( -" `The numbering of the output vertices doesn't match the input vertices.'\n" -); - printf("\n"); - printf( -" You may have had duplicate input vertices, or you may have eaten some\n"); - printf( -" of your input vertices with a hole, or by placing them outside the area\n" -); - printf( -" enclosed by segments. In any case, you can solve the problem by not\n"); - printf(" using the -j switch.\n\n"); - printf( -" `Triangle executes without incident, but when I look at the resulting\n"); - printf( -" mesh, it has overlapping triangles or other geometric inconsistencies.'\n"); - printf("\n"); - printf( -" If you select the -X switch, Triangle occasionally makes mistakes due\n"); - printf( -" to floating-point roundoff error. Although these errors are rare,\n"); - printf( -" don't use the -X switch. If you still have problems, please report the\n" -); - printf(" bug.\n\n"); - printf( -" `Triangle executes without incident, but when I look at the resulting\n"); - printf(" Voronoi diagram, it has overlapping edges or other geometric\n"); - printf(" inconsistencies.'\n"); - printf("\n"); - printf( -" If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n" -); - printf( -" diagram if the domain you are triangulating is convex and free of\n"); - printf( -" holes, and you use the -D switch to construct a conforming Delaunay\n"); - printf(" triangulation (instead of a CDT or CCDT).\n\n"); - printf( -" Strange things can happen if you've taken liberties with your PSLG. Do\n"); - printf( -" you have a vertex lying in the middle of a segment? Triangle sometimes\n"); - printf( -" copes poorly with that sort of thing. Do you want to lay out a collinear\n" -); - printf( -" row of evenly spaced, segment-connected vertices? Have you simply\n"); - printf( -" defined one long segment connecting the leftmost vertex to the rightmost\n" -); - printf( -" vertex, and a bunch of vertices lying along it? This method occasionally\n" -); - printf( -" works, especially with horizontal and vertical lines, but often it\n"); - printf( -" doesn't, and you'll have to connect each adjacent pair of vertices with a\n" -); - printf(" separate segment. If you don't like it, tough.\n\n"); - printf( -" Furthermore, if you have segments that intersect other than at their\n"); - printf( -" endpoints, try not to let the intersections fall extremely close to PSLG\n" -); - printf(" vertices or each other.\n\n"); - printf( -" If you have problems refining a triangulation not produced by Triangle:\n"); - printf( -" Are you sure the triangulation is geometrically valid? Is it formatted\n"); - printf( -" correctly for Triangle? Are the triangles all listed so the first three\n" -); - printf( -" vertices are their corners in counterclockwise order? Are all of the\n"); - printf( -" triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n" -); - printf(" assumes that it starts with a CDT.\n\n"); - printf("Show Me:\n\n"); - printf( -" Triangle comes with a separate program named `Show Me', whose primary\n"); - printf( -" purpose is to draw meshes on your screen or in PostScript. Its secondary\n" -); - printf( -" purpose is to check the validity of your input files, and do so more\n"); - printf( -" thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n"); - printf( -" you have the X Windows system. Sorry, Microsoft Windows users.\n"); - printf("\n"); - printf("Triangle on the Web:\n"); - printf("\n"); - printf(" To see an illustrated version of these instructions, check out\n"); - printf("\n"); - printf(" http://www.cs.cmu.edu/~quake/triangle.html\n"); - printf("\n"); - printf("A Brief Plea:\n"); - printf("\n"); - printf( -" If you use Triangle, and especially if you use it to accomplish real\n"); - printf( -" work, I would like very much to hear from you. A short letter or email\n"); - printf( -" (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n" -); - printf( -" to me. The more people I know are using this program, the more easily I\n" -); - printf( -" can justify spending time on improvements, which in turn will benefit\n"); - printf( -" you. Also, I can put you on a list to receive email whenever a new\n"); - printf(" version of Triangle is available.\n\n"); - printf( -" If you use a mesh generated by Triangle in a publication, please include\n" -); - printf( -" an acknowledgment as well. And please spell Triangle with a capital `T'!\n" -); - printf( -" If you want to include a citation, use `Jonathan Richard Shewchuk,\n"); - printf( -" ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n"); - printf( -" Triangulator,'' in Applied Computational Geometry: Towards Geometric\n"); - printf( -" Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n"); - printf( -" Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n"); - printf( -" Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n" -); - printf(" Geometry.)'\n\n"); - printf("Research credit:\n\n"); - printf( -" Of course, I can take credit for only a fraction of the ideas that made\n"); - printf( -" this mesh generator possible. Triangle owes its existence to the efforts\n" -); - printf( -" of many fine computational geometers and other researchers, including\n"); - printf( -" Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n" -); - printf( -" Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n"); - printf( -" Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n"); - printf( -" Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n"); - printf( -" Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n" -); - printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n"); - printf( -" Walkington, and Binhai Zhu. See the comments at the beginning of the\n"); - printf(" source code for references.\n\n"); - triexit(0); -} - -#endif /* not TRILIBRARY */ - -/*****************************************************************************/ -/* */ -/* internalerror() Ask the user to send me the defective product. Exit. */ -/* */ -/*****************************************************************************/ - -void internalerror() -{ - printf(" Please report this bug to jrs@cs.berkeley.edu\n"); - printf(" Include the message above, your input data set, and the exact\n"); - printf(" command line you used to run Triangle.\n"); - triexit(1); -} - -/*****************************************************************************/ -/* */ -/* parsecommandline() Read the command line, identify switches, and set */ -/* up options and file names. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void parsecommandline(int argc, char **argv, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void parsecommandline(argc, argv, b) -int argc; -char **argv; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ -#ifdef TRILIBRARY -#define STARTINDEX 0 -#else /* not TRILIBRARY */ -#define STARTINDEX 1 - int increment; - int meshnumber; -#endif /* not TRILIBRARY */ - int i, j, k; - char workstring[FILENAMESIZE]; - - b->poly = b->refine = b->quality = 0; - b->vararea = b->fixedarea = b->usertest = 0; - b->regionattrib = b->convex = b->weighted = b->jettison = 0; - b->firstnumber = 1; - b->edgesout = b->voronoi = b->neighbors = b->geomview = 0; - b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0; - b->noiterationnum = 0; - b->noholes = b->noexact = 0; - b->incremental = b->sweepline = 0; - b->dwyer = 1; - b->splitseg = 0; - b->docheck = 0; - b->nobisect = 0; - b->conformdel = 0; - b->steiner = -1; - b->order = 1; - b->minangle = 0.0; - b->maxarea = -1.0; - b->quiet = b->verbose = 0; -#ifndef TRILIBRARY - b->innodefilename[0] = '\0'; -#endif /* not TRILIBRARY */ - - for (i = STARTINDEX; i < argc; i++) { -#ifndef TRILIBRARY - if (argv[i][0] == '-') { -#endif /* not TRILIBRARY */ - for (j = STARTINDEX; argv[i][j] != '\0'; j++) { - if (argv[i][j] == 'p') { - b->poly = 1; - } -#ifndef CDT_ONLY - if (argv[i][j] == 'r') { - b->refine = 1; - } - if (argv[i][j] == 'q') { - b->quality = 1; - if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || - (argv[i][j + 1] == '.')) { - k = 0; - while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || - (argv[i][j + 1] == '.')) { - j++; - workstring[k] = argv[i][j]; - k++; - } - workstring[k] = '\0'; - b->minangle = (REAL) strtod(workstring, (char **) NULL); - } else { - b->minangle = 20.0; - } - } - if (argv[i][j] == 'a') { - b->quality = 1; - if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || - (argv[i][j + 1] == '.')) { - b->fixedarea = 1; - k = 0; - while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || - (argv[i][j + 1] == '.')) { - j++; - workstring[k] = argv[i][j]; - k++; - } - workstring[k] = '\0'; - b->maxarea = (REAL) strtod(workstring, (char **) NULL); - if (b->maxarea <= 0.0) { - printf("Error: Maximum area must be greater than zero.\n"); - triexit(1); - } - } else { - b->vararea = 1; - } - } - if (argv[i][j] == 'u') { - b->quality = 1; - b->usertest = 1; - } -#endif /* not CDT_ONLY */ - if (argv[i][j] == 'A') { - b->regionattrib = 1; - } - if (argv[i][j] == 'c') { - b->convex = 1; - } - if (argv[i][j] == 'w') { - b->weighted = 1; - } - if (argv[i][j] == 'W') { - b->weighted = 2; - } - if (argv[i][j] == 'j') { - b->jettison = 1; - } - if (argv[i][j] == 'z') { - b->firstnumber = 0; - } - if (argv[i][j] == 'e') { - b->edgesout = 1; - } - if (argv[i][j] == 'v') { - b->voronoi = 1; - } - if (argv[i][j] == 'n') { - b->neighbors = 1; - } - if (argv[i][j] == 'g') { - b->geomview = 1; - } - if (argv[i][j] == 'B') { - b->nobound = 1; - } - if (argv[i][j] == 'P') { - b->nopolywritten = 1; - } - if (argv[i][j] == 'N') { - b->nonodewritten = 1; - } - if (argv[i][j] == 'E') { - b->noelewritten = 1; - } -#ifndef TRILIBRARY - if (argv[i][j] == 'I') { - b->noiterationnum = 1; - } -#endif /* not TRILIBRARY */ - if (argv[i][j] == 'O') { - b->noholes = 1; - } - if (argv[i][j] == 'X') { - b->noexact = 1; - } - if (argv[i][j] == 'o') { - if (argv[i][j + 1] == '2') { - j++; - b->order = 2; - } - } -#ifndef CDT_ONLY - if (argv[i][j] == 'Y') { - b->nobisect++; - } - if (argv[i][j] == 'S') { - b->steiner = 0; - while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { - j++; - b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0'); - } - } -#endif /* not CDT_ONLY */ -#ifndef REDUCED - if (argv[i][j] == 'i') { - b->incremental = 1; - } - if (argv[i][j] == 'F') { - b->sweepline = 1; - } -#endif /* not REDUCED */ - if (argv[i][j] == 'l') { - b->dwyer = 0; - } -#ifndef REDUCED -#ifndef CDT_ONLY - if (argv[i][j] == 's') { - b->splitseg = 1; - } - if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) { - b->quality = 1; - b->conformdel = 1; - } -#endif /* not CDT_ONLY */ - if (argv[i][j] == 'C') { - b->docheck = 1; - } -#endif /* not REDUCED */ - if (argv[i][j] == 'Q') { - b->quiet = 1; - } - if (argv[i][j] == 'V') { - b->verbose++; - } -#ifndef TRILIBRARY - if ((argv[i][j] == 'h') || (argv[i][j] == 'H') || - (argv[i][j] == '?')) { - info(); - } -#endif /* not TRILIBRARY */ - } -#ifndef TRILIBRARY - } else { - strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1); - b->innodefilename[FILENAMESIZE - 1] = '\0'; - } -#endif /* not TRILIBRARY */ - } -#ifndef TRILIBRARY - if (b->innodefilename[0] == '\0') { - syntax(); - } - if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) { - b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; - } - if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) { - b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; - b->poly = 1; - } -#ifndef CDT_ONLY - if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) { - b->innodefilename[strlen(b->innodefilename) - 4] = '\0'; - b->refine = 1; - } - if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) { - b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; - b->refine = 1; - b->quality = 1; - b->vararea = 1; - } -#endif /* not CDT_ONLY */ -#endif /* not TRILIBRARY */ - b->usesegments = b->poly || b->refine || b->quality || b->convex; - b->goodangle = cos(b->minangle * PI / 180.0); - if (b->goodangle == 1.0) { - b->offconstant = 0.0; - } else { - b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle)); - } - b->goodangle *= b->goodangle; - if (b->refine && b->noiterationnum) { - printf( - "Error: You cannot use the -I switch when refining a triangulation.\n"); - triexit(1); - } - /* Be careful not to allocate space for element area constraints that */ - /* will never be assigned any value (other than the default -1.0). */ - if (!b->refine && !b->poly) { - b->vararea = 0; - } - /* Be careful not to add an extra attribute to each element unless the */ - /* input supports it (PSLG in, but not refining a preexisting mesh). */ - if (b->refine || !b->poly) { - b->regionattrib = 0; - } - /* Regular/weighted triangulations are incompatible with PSLGs */ - /* and meshing. */ - if (b->weighted && (b->poly || b->quality)) { - b->weighted = 0; - if (!b->quiet) { - printf("Warning: weighted triangulations (-w, -W) are incompatible\n"); - printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n" - ); - } - } - if (b->jettison && b->nonodewritten && !b->quiet) { - printf("Warning: -j and -N switches are somewhat incompatible.\n"); - printf(" If any vertices are jettisoned, you will need the output\n"); - printf(" .node file to reconstruct the new node indices."); - } - -#ifndef TRILIBRARY - strcpy(b->inpolyfilename, b->innodefilename); - strcpy(b->inelefilename, b->innodefilename); - strcpy(b->areafilename, b->innodefilename); - increment = 0; - strcpy(workstring, b->innodefilename); - j = 1; - while (workstring[j] != '\0') { - if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) { - increment = j + 1; - } - j++; - } - meshnumber = 0; - if (increment > 0) { - j = increment; - do { - if ((workstring[j] >= '0') && (workstring[j] <= '9')) { - meshnumber = meshnumber * 10 + (int) (workstring[j] - '0'); - } else { - increment = 0; - } - j++; - } while (workstring[j] != '\0'); - } - if (b->noiterationnum) { - strcpy(b->outnodefilename, b->innodefilename); - strcpy(b->outelefilename, b->innodefilename); - strcpy(b->edgefilename, b->innodefilename); - strcpy(b->vnodefilename, b->innodefilename); - strcpy(b->vedgefilename, b->innodefilename); - strcpy(b->neighborfilename, b->innodefilename); - strcpy(b->offfilename, b->innodefilename); - strcat(b->outnodefilename, ".node"); - strcat(b->outelefilename, ".ele"); - strcat(b->edgefilename, ".edge"); - strcat(b->vnodefilename, ".v.node"); - strcat(b->vedgefilename, ".v.edge"); - strcat(b->neighborfilename, ".neigh"); - strcat(b->offfilename, ".off"); - } else if (increment == 0) { - strcpy(b->outnodefilename, b->innodefilename); - strcpy(b->outpolyfilename, b->innodefilename); - strcpy(b->outelefilename, b->innodefilename); - strcpy(b->edgefilename, b->innodefilename); - strcpy(b->vnodefilename, b->innodefilename); - strcpy(b->vedgefilename, b->innodefilename); - strcpy(b->neighborfilename, b->innodefilename); - strcpy(b->offfilename, b->innodefilename); - strcat(b->outnodefilename, ".1.node"); - strcat(b->outpolyfilename, ".1.poly"); - strcat(b->outelefilename, ".1.ele"); - strcat(b->edgefilename, ".1.edge"); - strcat(b->vnodefilename, ".1.v.node"); - strcat(b->vedgefilename, ".1.v.edge"); - strcat(b->neighborfilename, ".1.neigh"); - strcat(b->offfilename, ".1.off"); - } else { - workstring[increment] = '%'; - workstring[increment + 1] = 'd'; - workstring[increment + 2] = '\0'; - sprintf(b->outnodefilename, workstring, meshnumber + 1); - strcpy(b->outpolyfilename, b->outnodefilename); - strcpy(b->outelefilename, b->outnodefilename); - strcpy(b->edgefilename, b->outnodefilename); - strcpy(b->vnodefilename, b->outnodefilename); - strcpy(b->vedgefilename, b->outnodefilename); - strcpy(b->neighborfilename, b->outnodefilename); - strcpy(b->offfilename, b->outnodefilename); - strcat(b->outnodefilename, ".node"); - strcat(b->outpolyfilename, ".poly"); - strcat(b->outelefilename, ".ele"); - strcat(b->edgefilename, ".edge"); - strcat(b->vnodefilename, ".v.node"); - strcat(b->vedgefilename, ".v.edge"); - strcat(b->neighborfilename, ".neigh"); - strcat(b->offfilename, ".off"); - } - strcat(b->innodefilename, ".node"); - strcat(b->inpolyfilename, ".poly"); - strcat(b->inelefilename, ".ele"); - strcat(b->areafilename, ".area"); -#endif /* not TRILIBRARY */ -} - -/** **/ -/** **/ -/********* User interaction routines begin here *********/ - -/********* Debugging routines begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* printtriangle() Print out the details of an oriented triangle. */ -/* */ -/* I originally wrote this procedure to simplify debugging; it can be */ -/* called directly from the debugger, and presents information about an */ -/* oriented triangle in digestible form. It's also used when the */ -/* highest level of verbosity (`-VVV') is specified. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void printtriangle(struct mesh *m, struct behavior *b, struct otri *t) -#else /* not ANSI_DECLARATORS */ -void printtriangle(m, b, t) -struct mesh *m; -struct behavior *b; -struct otri *t; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri printtri; - struct osub printsh; - vertex printvertex; - - printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri, - t->orient); - decode(t->tri[0], printtri); - if (printtri.tri == m->dummytri) { - printf(" [0] = Outer space\n"); - } else { - printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri, - printtri.orient); - } - decode(t->tri[1], printtri); - if (printtri.tri == m->dummytri) { - printf(" [1] = Outer space\n"); - } else { - printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri, - printtri.orient); - } - decode(t->tri[2], printtri); - if (printtri.tri == m->dummytri) { - printf(" [2] = Outer space\n"); - } else { - printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri, - printtri.orient); - } - - org(*t, printvertex); - if (printvertex == (vertex) NULL) - printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3); - else - printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", - (t->orient + 1) % 3 + 3, (unsigned long) printvertex, - printvertex[0], printvertex[1]); - dest(*t, printvertex); - if (printvertex == (vertex) NULL) - printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3); - else - printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", - (t->orient + 2) % 3 + 3, (unsigned long) printvertex, - printvertex[0], printvertex[1]); - apex(*t, printvertex); - if (printvertex == (vertex) NULL) - printf(" Apex [%d] = NULL\n", t->orient + 3); - else - printf(" Apex [%d] = x%lx (%.12g, %.12g)\n", - t->orient + 3, (unsigned long) printvertex, - printvertex[0], printvertex[1]); - - if (b->usesegments) { - sdecode(t->tri[6], printsh); - if (printsh.ss != m->dummysub) { - printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss, - printsh.ssorient); - } - sdecode(t->tri[7], printsh); - if (printsh.ss != m->dummysub) { - printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss, - printsh.ssorient); - } - sdecode(t->tri[8], printsh); - if (printsh.ss != m->dummysub) { - printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss, - printsh.ssorient); - } - } - - if (b->vararea) { - printf(" Area constraint: %.4g\n", areabound(*t)); - } -} - -/*****************************************************************************/ -/* */ -/* printsubseg() Print out the details of an oriented subsegment. */ -/* */ -/* I originally wrote this procedure to simplify debugging; it can be */ -/* called directly from the debugger, and presents information about an */ -/* oriented subsegment in digestible form. It's also used when the highest */ -/* level of verbosity (`-VVV') is specified. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void printsubseg(struct mesh *m, struct behavior *b, struct osub *s) -#else /* not ANSI_DECLARATORS */ -void printsubseg(m, b, s) -struct mesh *m; -struct behavior *b; -struct osub *s; -#endif /* not ANSI_DECLARATORS */ - -{ - struct osub printsh; - struct otri printtri; - vertex printvertex; - - printf("subsegment x%lx with orientation %d and mark %d:\n", - (unsigned long) s->ss, s->ssorient, mark(*s)); - sdecode(s->ss[0], printsh); - if (printsh.ss == m->dummysub) { - printf(" [0] = No subsegment\n"); - } else { - printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss, - printsh.ssorient); - } - sdecode(s->ss[1], printsh); - if (printsh.ss == m->dummysub) { - printf(" [1] = No subsegment\n"); - } else { - printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss, - printsh.ssorient); - } - - sorg(*s, printvertex); - if (printvertex == (vertex) NULL) - printf(" Origin[%d] = NULL\n", 2 + s->ssorient); - else - printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", - 2 + s->ssorient, (unsigned long) printvertex, - printvertex[0], printvertex[1]); - sdest(*s, printvertex); - if (printvertex == (vertex) NULL) - printf(" Dest [%d] = NULL\n", 3 - s->ssorient); - else - printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", - 3 - s->ssorient, (unsigned long) printvertex, - printvertex[0], printvertex[1]); - - decode(s->ss[6], printtri); - if (printtri.tri == m->dummytri) { - printf(" [6] = Outer space\n"); - } else { - printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri, - printtri.orient); - } - decode(s->ss[7], printtri); - if (printtri.tri == m->dummytri) { - printf(" [7] = Outer space\n"); - } else { - printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri, - printtri.orient); - } - - segorg(*s, printvertex); - if (printvertex == (vertex) NULL) - printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient); - else - printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n", - 4 + s->ssorient, (unsigned long) printvertex, - printvertex[0], printvertex[1]); - segdest(*s, printvertex); - if (printvertex == (vertex) NULL) - printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient); - else - printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n", - 5 - s->ssorient, (unsigned long) printvertex, - printvertex[0], printvertex[1]); -} - -/** **/ -/** **/ -/********* Debugging routines end here *********/ - -/********* Memory management routines begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* poolzero() Set all of a pool's fields to zero. */ -/* */ -/* This procedure should never be called on a pool that has any memory */ -/* allocated to it, as that memory would leak. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void poolzero(struct memorypool *pool) -#else /* not ANSI_DECLARATORS */ -void poolzero(pool) -struct memorypool *pool; -#endif /* not ANSI_DECLARATORS */ - -{ - pool->firstblock = (VOID **) NULL; - pool->nowblock = (VOID **) NULL; - pool->nextitem = (VOID *) NULL; - pool->deaditemstack = (VOID *) NULL; - pool->pathblock = (VOID **) NULL; - pool->pathitem = (VOID *) NULL; - pool->alignbytes = 0; - pool->itembytes = 0; - pool->itemsperblock = 0; - pool->itemsfirstblock = 0; - pool->items = 0; - pool->maxitems = 0; - pool->unallocateditems = 0; - pool->pathitemsleft = 0; -} - -/*****************************************************************************/ -/* */ -/* poolrestart() Deallocate all items in a pool. */ -/* */ -/* The pool is returned to its starting state, except that no memory is */ -/* freed to the operating system. Rather, the previously allocated blocks */ -/* are ready to be reused. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void poolrestart(struct memorypool *pool) -#else /* not ANSI_DECLARATORS */ -void poolrestart(pool) -struct memorypool *pool; -#endif /* not ANSI_DECLARATORS */ - -{ - unsigned long alignptr; - - pool->items = 0; - pool->maxitems = 0; - - /* Set the currently active block. */ - pool->nowblock = pool->firstblock; - /* Find the first item in the pool. Increment by the size of (VOID *). */ - alignptr = (unsigned long) (pool->nowblock + 1); - /* Align the item on an `alignbytes'-byte boundary. */ - pool->nextitem = (VOID *) - (alignptr + (unsigned long) pool->alignbytes - - (alignptr % (unsigned long) pool->alignbytes)); - /* There are lots of unallocated items left in this block. */ - pool->unallocateditems = pool->itemsfirstblock; - /* The stack of deallocated items is empty. */ - pool->deaditemstack = (VOID *) NULL; -} - -/*****************************************************************************/ -/* */ -/* poolinit() Initialize a pool of memory for allocation of items. */ -/* */ -/* This routine initializes the machinery for allocating items. A `pool' */ -/* is created whose records have size at least `bytecount'. Items will be */ -/* allocated in `itemcount'-item blocks. Each item is assumed to be a */ -/* collection of words, and either pointers or floating-point values are */ -/* assumed to be the "primary" word type. (The "primary" word type is used */ -/* to determine alignment of items.) If `alignment' isn't zero, all items */ -/* will be `alignment'-byte aligned in memory. `alignment' must be either */ -/* a multiple or a factor of the primary word size; powers of two are safe. */ -/* `alignment' is normally used to create a few unused bits at the bottom */ -/* of each item's pointer, in which information may be stored. */ -/* */ -/* Don't change this routine unless you understand it. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void poolinit(struct memorypool *pool, int bytecount, int itemcount, - int firstitemcount, int alignment) -#else /* not ANSI_DECLARATORS */ -void poolinit(pool, bytecount, itemcount, firstitemcount, alignment) -struct memorypool *pool; -int bytecount; -int itemcount; -int firstitemcount; -int alignment; -#endif /* not ANSI_DECLARATORS */ - -{ - /* Find the proper alignment, which must be at least as large as: */ - /* - The parameter `alignment'. */ - /* - sizeof(VOID *), so the stack of dead items can be maintained */ - /* without unaligned accesses. */ - if (alignment > sizeof(VOID *)) { - pool->alignbytes = alignment; - } else { - pool->alignbytes = sizeof(VOID *); - } - pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) * - pool->alignbytes; - pool->itemsperblock = itemcount; - if (firstitemcount == 0) { - pool->itemsfirstblock = itemcount; - } else { - pool->itemsfirstblock = firstitemcount; - } - - /* Allocate a block of items. Space for `itemsfirstblock' items and one */ - /* pointer (to point to the next block) are allocated, as well as space */ - /* to ensure alignment of the items. */ - pool->firstblock = (VOID **) - trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) + - pool->alignbytes); - /* Set the next block pointer to NULL. */ - *(pool->firstblock) = (VOID *) NULL; - poolrestart(pool); -} - -/*****************************************************************************/ -/* */ -/* pooldeinit() Free to the operating system all memory taken by a pool. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void pooldeinit(struct memorypool *pool) -#else /* not ANSI_DECLARATORS */ -void pooldeinit(pool) -struct memorypool *pool; -#endif /* not ANSI_DECLARATORS */ - -{ - while (pool->firstblock != (VOID **) NULL) { - pool->nowblock = (VOID **) *(pool->firstblock); - trifree((VOID *) pool->firstblock); - pool->firstblock = pool->nowblock; - } -} - -/*****************************************************************************/ -/* */ -/* poolalloc() Allocate space for an item. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -VOID *poolalloc(struct memorypool *pool) -#else /* not ANSI_DECLARATORS */ -VOID *poolalloc(pool) -struct memorypool *pool; -#endif /* not ANSI_DECLARATORS */ - -{ - VOID *newitem; - VOID **newblock; - unsigned long alignptr; - - /* First check the linked list of dead items. If the list is not */ - /* empty, allocate an item from the list rather than a fresh one. */ - if (pool->deaditemstack != (VOID *) NULL) { - newitem = pool->deaditemstack; /* Take first item in list. */ - pool->deaditemstack = * (VOID **) pool->deaditemstack; - } else { - /* Check if there are any free items left in the current block. */ - if (pool->unallocateditems == 0) { - /* Check if another block must be allocated. */ - if (*(pool->nowblock) == (VOID *) NULL) { - /* Allocate a new block of items, pointed to by the previous block. */ - newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes + - (int) sizeof(VOID *) + - pool->alignbytes); - *(pool->nowblock) = (VOID *) newblock; - /* The next block pointer is NULL. */ - *newblock = (VOID *) NULL; - } - - /* Move to the new block. */ - pool->nowblock = (VOID **) *(pool->nowblock); - /* Find the first item in the block. */ - /* Increment by the size of (VOID *). */ - alignptr = (unsigned long) (pool->nowblock + 1); - /* Align the item on an `alignbytes'-byte boundary. */ - pool->nextitem = (VOID *) - (alignptr + (unsigned long) pool->alignbytes - - (alignptr % (unsigned long) pool->alignbytes)); - /* There are lots of unallocated items left in this block. */ - pool->unallocateditems = pool->itemsperblock; - } - - /* Allocate a new item. */ - newitem = pool->nextitem; - /* Advance `nextitem' pointer to next free item in block. */ - pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes); - pool->unallocateditems--; - pool->maxitems++; - } - pool->items++; - return newitem; -} - -/*****************************************************************************/ -/* */ -/* pooldealloc() Deallocate space for an item. */ -/* */ -/* The deallocated space is stored in a queue for later reuse. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void pooldealloc(struct memorypool *pool, VOID *dyingitem) -#else /* not ANSI_DECLARATORS */ -void pooldealloc(pool, dyingitem) -struct memorypool *pool; -VOID *dyingitem; -#endif /* not ANSI_DECLARATORS */ - -{ - /* Push freshly killed item onto stack. */ - *((VOID **) dyingitem) = pool->deaditemstack; - pool->deaditemstack = dyingitem; - pool->items--; -} - -/*****************************************************************************/ -/* */ -/* traversalinit() Prepare to traverse the entire list of items. */ -/* */ -/* This routine is used in conjunction with traverse(). */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void traversalinit(struct memorypool *pool) -#else /* not ANSI_DECLARATORS */ -void traversalinit(pool) -struct memorypool *pool; -#endif /* not ANSI_DECLARATORS */ - -{ - unsigned long alignptr; - - /* Begin the traversal in the first block. */ - pool->pathblock = pool->firstblock; - /* Find the first item in the block. Increment by the size of (VOID *). */ - alignptr = (unsigned long) (pool->pathblock + 1); - /* Align with item on an `alignbytes'-byte boundary. */ - pool->pathitem = (VOID *) - (alignptr + (unsigned long) pool->alignbytes - - (alignptr % (unsigned long) pool->alignbytes)); - /* Set the number of items left in the current block. */ - pool->pathitemsleft = pool->itemsfirstblock; -} - -/*****************************************************************************/ -/* */ -/* traverse() Find the next item in the list. */ -/* */ -/* This routine is used in conjunction with traversalinit(). Be forewarned */ -/* that this routine successively returns all items in the list, including */ -/* deallocated ones on the deaditemqueue. It's up to you to figure out */ -/* which ones are actually dead. Why? I don't want to allocate extra */ -/* space just to demarcate dead items. It can usually be done more */ -/* space-efficiently by a routine that knows something about the structure */ -/* of the item. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -VOID *traverse(struct memorypool *pool) -#else /* not ANSI_DECLARATORS */ -VOID *traverse(pool) -struct memorypool *pool; -#endif /* not ANSI_DECLARATORS */ - -{ - VOID *newitem; - unsigned long alignptr; - - /* Stop upon exhausting the list of items. */ - if (pool->pathitem == pool->nextitem) { - return (VOID *) NULL; - } - - /* Check whether any untraversed items remain in the current block. */ - if (pool->pathitemsleft == 0) { - /* Find the next block. */ - pool->pathblock = (VOID **) *(pool->pathblock); - /* Find the first item in the block. Increment by the size of (VOID *). */ - alignptr = (unsigned long) (pool->pathblock + 1); - /* Align with item on an `alignbytes'-byte boundary. */ - pool->pathitem = (VOID *) - (alignptr + (unsigned long) pool->alignbytes - - (alignptr % (unsigned long) pool->alignbytes)); - /* Set the number of items left in the current block. */ - pool->pathitemsleft = pool->itemsperblock; - } - - newitem = pool->pathitem; - /* Find the next item in the block. */ - pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes); - pool->pathitemsleft--; - return newitem; -} - -/*****************************************************************************/ -/* */ -/* dummyinit() Initialize the triangle that fills "outer space" and the */ -/* omnipresent subsegment. */ -/* */ -/* The triangle that fills "outer space," called `dummytri', is pointed to */ -/* by every triangle and subsegment on a boundary (be it outer or inner) of */ -/* the triangulation. Also, `dummytri' points to one of the triangles on */ -/* the convex hull (until the holes and concavities are carved), making it */ -/* possible to find a starting triangle for point location. */ -/* */ -/* The omnipresent subsegment, `dummysub', is pointed to by every triangle */ -/* or subsegment that doesn't have a full complement of real subsegments */ -/* to point to. */ -/* */ -/* `dummytri' and `dummysub' are generally required to fulfill only a few */ -/* invariants: their vertices must remain NULL and `dummytri' must always */ -/* be bonded (at offset zero) to some triangle on the convex hull of the */ -/* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */ -/* `dummysub' may change willy-nilly. This makes it possible to avoid */ -/* writing a good deal of special-case code (in the edge flip, for example) */ -/* for dealing with the boundary of the mesh, places where no subsegment is */ -/* present, and so forth. Other entities are frequently bonded to */ -/* `dummytri' and `dummysub' as if they were real mesh entities, with no */ -/* harm done. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes, - int subsegbytes) -#else /* not ANSI_DECLARATORS */ -void dummyinit(m, b, trianglebytes, subsegbytes) -struct mesh *m; -struct behavior *b; -int trianglebytes; -int subsegbytes; -#endif /* not ANSI_DECLARATORS */ - -{ - unsigned long alignptr; - - /* Set up `dummytri', the `triangle' that occupies "outer space." */ - m->dummytribase = (triangle *) trimalloc(trianglebytes + - m->triangles.alignbytes); - /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */ - alignptr = (unsigned long) m->dummytribase; - m->dummytri = (triangle *) - (alignptr + (unsigned long) m->triangles.alignbytes - - (alignptr % (unsigned long) m->triangles.alignbytes)); - /* Initialize the three adjoining triangles to be "outer space." These */ - /* will eventually be changed by various bonding operations, but their */ - /* values don't really matter, as long as they can legally be */ - /* dereferenced. */ - m->dummytri[0] = (triangle) m->dummytri; - m->dummytri[1] = (triangle) m->dummytri; - m->dummytri[2] = (triangle) m->dummytri; - /* Three NULL vertices. */ - m->dummytri[3] = (triangle) NULL; - m->dummytri[4] = (triangle) NULL; - m->dummytri[5] = (triangle) NULL; - - if (b->usesegments) { - /* Set up `dummysub', the omnipresent subsegment pointed to by any */ - /* triangle side or subsegment end that isn't attached to a real */ - /* subsegment. */ - m->dummysubbase = (subseg *) trimalloc(subsegbytes + - m->subsegs.alignbytes); - /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */ - alignptr = (unsigned long) m->dummysubbase; - m->dummysub = (subseg *) - (alignptr + (unsigned long) m->subsegs.alignbytes - - (alignptr % (unsigned long) m->subsegs.alignbytes)); - /* Initialize the two adjoining subsegments to be the omnipresent */ - /* subsegment. These will eventually be changed by various bonding */ - /* operations, but their values don't really matter, as long as they */ - /* can legally be dereferenced. */ - m->dummysub[0] = (subseg) m->dummysub; - m->dummysub[1] = (subseg) m->dummysub; - /* Four NULL vertices. */ - m->dummysub[2] = (subseg) NULL; - m->dummysub[3] = (subseg) NULL; - m->dummysub[4] = (subseg) NULL; - m->dummysub[5] = (subseg) NULL; - /* Initialize the two adjoining triangles to be "outer space." */ - m->dummysub[6] = (subseg) m->dummytri; - m->dummysub[7] = (subseg) m->dummytri; - /* Set the boundary marker to zero. */ - * (int *) (m->dummysub + 8) = 0; - - /* Initialize the three adjoining subsegments of `dummytri' to be */ - /* the omnipresent subsegment. */ - m->dummytri[6] = (triangle) m->dummysub; - m->dummytri[7] = (triangle) m->dummysub; - m->dummytri[8] = (triangle) m->dummysub; - } -} - -/*****************************************************************************/ -/* */ -/* initializevertexpool() Calculate the size of the vertex data structure */ -/* and initialize its memory pool. */ -/* */ -/* This routine also computes the `vertexmarkindex' and `vertex2triindex' */ -/* indices used to find values within each vertex. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void initializevertexpool(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void initializevertexpool(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - int vertexsize; - - /* The index within each vertex at which the boundary marker is found, */ - /* followed by the vertex type. Ensure the vertex marker is aligned to */ - /* a sizeof(int)-byte address. */ - m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) + - sizeof(int) - 1) / - sizeof(int); - vertexsize = (m->vertexmarkindex + 2) * sizeof(int); - if (b->poly) { - /* The index within each vertex at which a triangle pointer is found. */ - /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */ - m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) / - sizeof(triangle); - vertexsize = (m->vertex2triindex + 1) * sizeof(triangle); - } - - /* Initialize the pool of vertices. */ - poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK, - m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK, - sizeof(REAL)); -} - -/*****************************************************************************/ -/* */ -/* initializetrisubpools() Calculate the sizes of the triangle and */ -/* subsegment data structures and initialize */ -/* their memory pools. */ -/* */ -/* This routine also computes the `highorderindex', `elemattribindex', and */ -/* `areaboundindex' indices used to find values within each triangle. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void initializetrisubpools(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void initializetrisubpools(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - int trisize; - - /* The index within each triangle at which the extra nodes (above three) */ - /* associated with high order elements are found. There are three */ - /* pointers to other triangles, three pointers to corners, and possibly */ - /* three pointers to subsegments before the extra nodes. */ - m->highorderindex = 6 + (b->usesegments * 3); - /* The number of bytes occupied by a triangle. */ - trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) * - sizeof(triangle); - /* The index within each triangle at which its attributes are found, */ - /* where the index is measured in REALs. */ - m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL); - /* The index within each triangle at which the maximum area constraint */ - /* is found, where the index is measured in REALs. Note that if the */ - /* `regionattrib' flag is set, an additional attribute will be added. */ - m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib; - /* If triangle attributes or an area bound are needed, increase the number */ - /* of bytes occupied by a triangle. */ - if (b->vararea) { - trisize = (m->areaboundindex + 1) * sizeof(REAL); - } else if (m->eextras + b->regionattrib > 0) { - trisize = m->areaboundindex * sizeof(REAL); - } - /* If a Voronoi diagram or triangle neighbor graph is requested, make */ - /* sure there's room to store an integer index in each triangle. This */ - /* integer index can occupy the same space as the subsegment pointers */ - /* or attributes or area constraint or extra nodes. */ - if ((b->voronoi || b->neighbors) && - (trisize < 6 * sizeof(triangle) + sizeof(int))) { - trisize = 6 * sizeof(triangle) + sizeof(int); - } - - /* Having determined the memory size of a triangle, initialize the pool. */ - poolinit(&m->triangles, trisize, TRIPERBLOCK, - (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) : - TRIPERBLOCK, 4); - - if (b->usesegments) { - /* Initialize the pool of subsegments. Take into account all eight */ - /* pointers and one boundary marker. */ - poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int), - SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4); - - /* Initialize the "outer space" triangle and omnipresent subsegment. */ - dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes); - } else { - /* Initialize the "outer space" triangle. */ - dummyinit(m, b, m->triangles.itembytes, 0); - } -} - -/*****************************************************************************/ -/* */ -/* triangledealloc() Deallocate space for a triangle, marking it dead. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void triangledealloc(struct mesh *m, triangle *dyingtriangle) -#else /* not ANSI_DECLARATORS */ -void triangledealloc(m, dyingtriangle) -struct mesh *m; -triangle *dyingtriangle; -#endif /* not ANSI_DECLARATORS */ - -{ - /* Mark the triangle as dead. This makes it possible to detect dead */ - /* triangles when traversing the list of all triangles. */ - killtri(dyingtriangle); - pooldealloc(&m->triangles, (VOID *) dyingtriangle); -} - -/*****************************************************************************/ -/* */ -/* triangletraverse() Traverse the triangles, skipping dead ones. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -triangle *triangletraverse(struct mesh *m) -#else /* not ANSI_DECLARATORS */ -triangle *triangletraverse(m) -struct mesh *m; -#endif /* not ANSI_DECLARATORS */ - -{ - triangle *newtriangle; - - do { - newtriangle = (triangle *) traverse(&m->triangles); - if (newtriangle == (triangle *) NULL) { - return (triangle *) NULL; - } - } while (deadtri(newtriangle)); /* Skip dead ones. */ - return newtriangle; -} - -/*****************************************************************************/ -/* */ -/* subsegdealloc() Deallocate space for a subsegment, marking it dead. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void subsegdealloc(struct mesh *m, subseg *dyingsubseg) -#else /* not ANSI_DECLARATORS */ -void subsegdealloc(m, dyingsubseg) -struct mesh *m; -subseg *dyingsubseg; -#endif /* not ANSI_DECLARATORS */ - -{ - /* Mark the subsegment as dead. This makes it possible to detect dead */ - /* subsegments when traversing the list of all subsegments. */ - killsubseg(dyingsubseg); - pooldealloc(&m->subsegs, (VOID *) dyingsubseg); -} - -/*****************************************************************************/ -/* */ -/* subsegtraverse() Traverse the subsegments, skipping dead ones. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -subseg *subsegtraverse(struct mesh *m) -#else /* not ANSI_DECLARATORS */ -subseg *subsegtraverse(m) -struct mesh *m; -#endif /* not ANSI_DECLARATORS */ - -{ - subseg *newsubseg; - - do { - newsubseg = (subseg *) traverse(&m->subsegs); - if (newsubseg == (subseg *) NULL) { - return (subseg *) NULL; - } - } while (deadsubseg(newsubseg)); /* Skip dead ones. */ - return newsubseg; -} - -/*****************************************************************************/ -/* */ -/* vertexdealloc() Deallocate space for a vertex, marking it dead. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void vertexdealloc(struct mesh *m, vertex dyingvertex) -#else /* not ANSI_DECLARATORS */ -void vertexdealloc(m, dyingvertex) -struct mesh *m; -vertex dyingvertex; -#endif /* not ANSI_DECLARATORS */ - -{ - /* Mark the vertex as dead. This makes it possible to detect dead */ - /* vertices when traversing the list of all vertices. */ - setvertextype(dyingvertex, DEADVERTEX); - pooldealloc(&m->vertices, (VOID *) dyingvertex); -} - -/*****************************************************************************/ -/* */ -/* vertextraverse() Traverse the vertices, skipping dead ones. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -vertex vertextraverse(struct mesh *m) -#else /* not ANSI_DECLARATORS */ -vertex vertextraverse(m) -struct mesh *m; -#endif /* not ANSI_DECLARATORS */ - -{ - vertex newvertex; - - do { - newvertex = (vertex) traverse(&m->vertices); - if (newvertex == (vertex) NULL) { - return (vertex) NULL; - } - } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */ - return newvertex; -} - -/*****************************************************************************/ -/* */ -/* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */ -/* dead. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg) -#else /* not ANSI_DECLARATORS */ -void badsubsegdealloc(m, dyingseg) -struct mesh *m; -struct badsubseg *dyingseg; -#endif /* not ANSI_DECLARATORS */ - -{ - /* Set subsegment's origin to NULL. This makes it possible to detect dead */ - /* badsubsegs when traversing the list of all badsubsegs . */ - dyingseg->subsegorg = (vertex) NULL; - pooldealloc(&m->badsubsegs, (VOID *) dyingseg); -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -struct badsubseg *badsubsegtraverse(struct mesh *m) -#else /* not ANSI_DECLARATORS */ -struct badsubseg *badsubsegtraverse(m) -struct mesh *m; -#endif /* not ANSI_DECLARATORS */ - -{ - struct badsubseg *newseg; - - do { - newseg = (struct badsubseg *) traverse(&m->badsubsegs); - if (newseg == (struct badsubseg *) NULL) { - return (struct badsubseg *) NULL; - } - } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */ - return newseg; -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* getvertex() Get a specific vertex, by number, from the list. */ -/* */ -/* The first vertex is number 'firstnumber'. */ -/* */ -/* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */ -/* is large). I don't care to take the trouble to make it work in constant */ -/* time. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -vertex getvertex(struct mesh *m, struct behavior *b, int number) -#else /* not ANSI_DECLARATORS */ -vertex getvertex(m, b, number) -struct mesh *m; -struct behavior *b; -int number; -#endif /* not ANSI_DECLARATORS */ - -{ - VOID **getblock; - char *foundvertex; - unsigned long alignptr; - int current; - - getblock = m->vertices.firstblock; - current = b->firstnumber; - - /* Find the right block. */ - if (current + m->vertices.itemsfirstblock <= number) { - getblock = (VOID **) *getblock; - current += m->vertices.itemsfirstblock; - while (current + m->vertices.itemsperblock <= number) { - getblock = (VOID **) *getblock; - current += m->vertices.itemsperblock; - } - } - - /* Now find the right vertex. */ - alignptr = (unsigned long) (getblock + 1); - foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes - - (alignptr % (unsigned long) m->vertices.alignbytes)); - return (vertex) (foundvertex + m->vertices.itembytes * (number - current)); -} - -/*****************************************************************************/ -/* */ -/* triangledeinit() Free all remaining allocated memory. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void triangledeinit(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void triangledeinit(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - pooldeinit(&m->triangles); - trifree((VOID *) m->dummytribase); - if (b->usesegments) { - pooldeinit(&m->subsegs); - trifree((VOID *) m->dummysubbase); - } - pooldeinit(&m->vertices); -#ifndef CDT_ONLY - if (b->quality) { - pooldeinit(&m->badsubsegs); - if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) { - pooldeinit(&m->badtriangles); - pooldeinit(&m->flipstackers); - } - } -#endif /* not CDT_ONLY */ -} - -/** **/ -/** **/ -/********* Memory management routines end here *********/ - -/********* Constructors begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* maketriangle() Create a new triangle with orientation zero. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri) -#else /* not ANSI_DECLARATORS */ -void maketriangle(m, b, newotri) -struct mesh *m; -struct behavior *b; -struct otri *newotri; -#endif /* not ANSI_DECLARATORS */ - -{ - int i; - - newotri->tri = (triangle *) poolalloc(&m->triangles); - /* Initialize the three adjoining triangles to be "outer space". */ - newotri->tri[0] = (triangle) m->dummytri; - newotri->tri[1] = (triangle) m->dummytri; - newotri->tri[2] = (triangle) m->dummytri; - /* Three NULL vertices. */ - newotri->tri[3] = (triangle) NULL; - newotri->tri[4] = (triangle) NULL; - newotri->tri[5] = (triangle) NULL; - if (b->usesegments) { - /* Initialize the three adjoining subsegments to be the omnipresent */ - /* subsegment. */ - newotri->tri[6] = (triangle) m->dummysub; - newotri->tri[7] = (triangle) m->dummysub; - newotri->tri[8] = (triangle) m->dummysub; - } - for (i = 0; i < m->eextras; i++) { - setelemattribute(*newotri, i, 0.0); - } - if (b->vararea) { - setareabound(*newotri, -1.0); - } - - newotri->orient = 0; -} - -/*****************************************************************************/ -/* */ -/* makesubseg() Create a new subsegment with orientation zero. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void makesubseg(struct mesh *m, struct osub *newsubseg) -#else /* not ANSI_DECLARATORS */ -void makesubseg(m, newsubseg) -struct mesh *m; -struct osub *newsubseg; -#endif /* not ANSI_DECLARATORS */ - -{ - newsubseg->ss = (subseg *) poolalloc(&m->subsegs); - /* Initialize the two adjoining subsegments to be the omnipresent */ - /* subsegment. */ - newsubseg->ss[0] = (subseg) m->dummysub; - newsubseg->ss[1] = (subseg) m->dummysub; - /* Four NULL vertices. */ - newsubseg->ss[2] = (subseg) NULL; - newsubseg->ss[3] = (subseg) NULL; - newsubseg->ss[4] = (subseg) NULL; - newsubseg->ss[5] = (subseg) NULL; - /* Initialize the two adjoining triangles to be "outer space." */ - newsubseg->ss[6] = (subseg) m->dummytri; - newsubseg->ss[7] = (subseg) m->dummytri; - /* Set the boundary marker to zero. */ - setmark(*newsubseg, 0); - - newsubseg->ssorient = 0; -} - -/** **/ -/** **/ -/********* Constructors end here *********/ - -/********* Geometric primitives begin here *********/ -/** **/ -/** **/ - -/* The adaptive exact arithmetic geometric predicates implemented herein are */ -/* described in detail in my paper, "Adaptive Precision Floating-Point */ -/* Arithmetic and Fast Robust Geometric Predicates." See the header for a */ -/* full citation. */ - -/* Which of the following two methods of finding the absolute values is */ -/* fastest is compiler-dependent. A few compilers can inline and optimize */ -/* the fabs() call; but most will incur the overhead of a function call, */ -/* which is disastrously slow. A faster way on IEEE machines might be to */ -/* mask the appropriate bit, but that's difficult to do in C without */ -/* forcing the value to be stored to memory (rather than be kept in the */ -/* register to which the optimizer assigned it). */ - -#define Absolute(a) ((a) >= 0.0 ? (a) : -(a)) -/* #define Absolute(a) fabs(a) */ - -/* Many of the operations are broken up into two pieces, a main part that */ -/* performs an approximate operation, and a "tail" that computes the */ -/* roundoff error of that operation. */ -/* */ -/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */ -/* Split(), and Two_Product() are all implemented as described in the */ -/* reference. Each of these macros requires certain variables to be */ -/* defined in the calling routine. The variables `bvirt', `c', `abig', */ -/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */ -/* they store the result of an operation that may incur roundoff error. */ -/* The input parameter `x' (or the highest numbered `x_' parameter) must */ -/* also be declared `INEXACT'. */ - -#define Fast_Two_Sum_Tail(a, b, x, y) \ - bvirt = x - a; \ - y = b - bvirt - -#define Fast_Two_Sum(a, b, x, y) \ - x = (REAL) (a + b); \ - Fast_Two_Sum_Tail(a, b, x, y) - -#define Two_Sum_Tail(a, b, x, y) \ - bvirt = (REAL) (x - a); \ - avirt = x - bvirt; \ - bround = b - bvirt; \ - around = a - avirt; \ - y = around + bround - -#define Two_Sum(a, b, x, y) \ - x = (REAL) (a + b); \ - Two_Sum_Tail(a, b, x, y) - -#define Two_Diff_Tail(a, b, x, y) \ - bvirt = (REAL) (a - x); \ - avirt = x + bvirt; \ - bround = bvirt - b; \ - around = a - avirt; \ - y = around + bround - -#define Two_Diff(a, b, x, y) \ - x = (REAL) (a - b); \ - Two_Diff_Tail(a, b, x, y) - -#define Split(a, ahi, alo) \ - c = (REAL) (splitter * a); \ - abig = (REAL) (c - a); \ - ahi = c - abig; \ - alo = a - ahi - -#define Two_Product_Tail(a, b, x, y) \ - Split(a, ahi, alo); \ - Split(b, bhi, blo); \ - err1 = x - (ahi * bhi); \ - err2 = err1 - (alo * bhi); \ - err3 = err2 - (ahi * blo); \ - y = (alo * blo) - err3 - -#define Two_Product(a, b, x, y) \ - x = (REAL) (a * b); \ - Two_Product_Tail(a, b, x, y) - -/* Two_Product_Presplit() is Two_Product() where one of the inputs has */ -/* already been split. Avoids redundant splitting. */ - -#define Two_Product_Presplit(a, b, bhi, blo, x, y) \ - x = (REAL) (a * b); \ - Split(a, ahi, alo); \ - err1 = x - (ahi * bhi); \ - err2 = err1 - (alo * bhi); \ - err3 = err2 - (ahi * blo); \ - y = (alo * blo) - err3 - -/* Square() can be done more quickly than Two_Product(). */ - -#define Square_Tail(a, x, y) \ - Split(a, ahi, alo); \ - err1 = x - (ahi * ahi); \ - err3 = err1 - ((ahi + ahi) * alo); \ - y = (alo * alo) - err3 - -#define Square(a, x, y) \ - x = (REAL) (a * a); \ - Square_Tail(a, x, y) - -/* Macros for summing expansions of various fixed lengths. These are all */ -/* unrolled versions of Expansion_Sum(). */ - -#define Two_One_Sum(a1, a0, b, x2, x1, x0) \ - Two_Sum(a0, b , _i, x0); \ - Two_Sum(a1, _i, x2, x1) - -#define Two_One_Diff(a1, a0, b, x2, x1, x0) \ - Two_Diff(a0, b , _i, x0); \ - Two_Sum( a1, _i, x2, x1) - -#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \ - Two_One_Sum(a1, a0, b0, _j, _0, x0); \ - Two_One_Sum(_j, _0, b1, x3, x2, x1) - -#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \ - Two_One_Diff(a1, a0, b0, _j, _0, x0); \ - Two_One_Diff(_j, _0, b1, x3, x2, x1) - -/* Macro for multiplying a two-component expansion by a single component. */ - -#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \ - Split(b, bhi, blo); \ - Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \ - Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \ - Two_Sum(_i, _0, _k, x1); \ - Fast_Two_Sum(_j, _k, x3, x2) - -/*****************************************************************************/ -/* */ -/* exactinit() Initialize the variables used for exact arithmetic. */ -/* */ -/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */ -/* floating-point arithmetic. `epsilon' bounds the relative roundoff */ -/* error. It is used for floating-point error analysis. */ -/* */ -/* `splitter' is used to split floating-point numbers into two half- */ -/* length significands for exact multiplication. */ -/* */ -/* I imagine that a highly optimizing compiler might be too smart for its */ -/* own good, and somehow cause this routine to fail, if it pretends that */ -/* floating-point arithmetic is too much like real arithmetic. */ -/* */ -/* Don't change this routine unless you fully understand it. */ -/* */ -/*****************************************************************************/ - -void exactinit() -{ - REAL half; - REAL check, lastcheck; - int every_other; -#ifdef LINUX - int cword; -#endif /* LINUX */ - -#ifdef CPU86 -#ifdef SINGLE - _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */ -#else /* not SINGLE */ - _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */ -#endif /* not SINGLE */ -#endif /* CPU86 */ -#ifdef LINUX -#ifdef SINGLE - /* cword = 4223; */ - cword = 4210; /* set FPU control word for single precision */ -#else /* not SINGLE */ - /* cword = 4735; */ - cword = 4722; /* set FPU control word for double precision */ -#endif /* not SINGLE */ - _FPU_SETCW(cword); -#endif /* LINUX */ - - every_other = 1; - half = 0.5; - epsilon = 1.0; - splitter = 1.0; - check = 1.0; - /* Repeatedly divide `epsilon' by two until it is too small to add to */ - /* one without causing roundoff. (Also check if the sum is equal to */ - /* the previous sum, for machines that round up instead of using exact */ - /* rounding. Not that these routines will work on such machines.) */ - do { - lastcheck = check; - epsilon *= half; - if (every_other) { - splitter *= 2.0; - } - every_other = !every_other; - check = 1.0 + epsilon; - } while ((check != 1.0) && (check != lastcheck)); - splitter += 1.0; - /* Error bounds for orientation and incircle tests. */ - resulterrbound = (3.0 + 8.0 * epsilon) * epsilon; - ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon; - ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon; - ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon; - iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon; - iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon; - iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon; - o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon; - o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon; - o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon; -} - -/*****************************************************************************/ -/* */ -/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */ -/* components from the output expansion. */ -/* */ -/* Sets h = e + f. See my Robust Predicates paper for details. */ -/* */ -/* If round-to-even is used (as with IEEE 754), maintains the strongly */ -/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */ -/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */ -/* properties. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h) -#else /* not ANSI_DECLARATORS */ -int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */ -int elen; -REAL *e; -int flen; -REAL *f; -REAL *h; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL Q; - INEXACT REAL Qnew; - INEXACT REAL hh; - INEXACT REAL bvirt; - REAL avirt, bround, around; - int eindex, findex, hindex; - REAL enow, fnow; - - enow = e[0]; - fnow = f[0]; - eindex = findex = 0; - if ((fnow > enow) == (fnow > -enow)) { - Q = enow; - enow = e[++eindex]; - } else { - Q = fnow; - fnow = f[++findex]; - } - hindex = 0; - if ((eindex < elen) && (findex < flen)) { - if ((fnow > enow) == (fnow > -enow)) { - Fast_Two_Sum(enow, Q, Qnew, hh); - enow = e[++eindex]; - } else { - Fast_Two_Sum(fnow, Q, Qnew, hh); - fnow = f[++findex]; - } - Q = Qnew; - if (hh != 0.0) { - h[hindex++] = hh; - } - while ((eindex < elen) && (findex < flen)) { - if ((fnow > enow) == (fnow > -enow)) { - Two_Sum(Q, enow, Qnew, hh); - enow = e[++eindex]; - } else { - Two_Sum(Q, fnow, Qnew, hh); - fnow = f[++findex]; - } - Q = Qnew; - if (hh != 0.0) { - h[hindex++] = hh; - } - } - } - while (eindex < elen) { - Two_Sum(Q, enow, Qnew, hh); - enow = e[++eindex]; - Q = Qnew; - if (hh != 0.0) { - h[hindex++] = hh; - } - } - while (findex < flen) { - Two_Sum(Q, fnow, Qnew, hh); - fnow = f[++findex]; - Q = Qnew; - if (hh != 0.0) { - h[hindex++] = hh; - } - } - if ((Q != 0.0) || (hindex == 0)) { - h[hindex++] = Q; - } - return hindex; -} - -/*****************************************************************************/ -/* */ -/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */ -/* eliminating zero components from the */ -/* output expansion. */ -/* */ -/* Sets h = be. See my Robust Predicates paper for details. */ -/* */ -/* Maintains the nonoverlapping property. If round-to-even is used (as */ -/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */ -/* properties as well. (That is, if e has one of these properties, so */ -/* will h.) */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h) -#else /* not ANSI_DECLARATORS */ -int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */ -int elen; -REAL *e; -REAL b; -REAL *h; -#endif /* not ANSI_DECLARATORS */ - -{ - INEXACT REAL Q, sum; - REAL hh; - INEXACT REAL product1; - REAL product0; - int eindex, hindex; - REAL enow; - INEXACT REAL bvirt; - REAL avirt, bround, around; - INEXACT REAL c; - INEXACT REAL abig; - REAL ahi, alo, bhi, blo; - REAL err1, err2, err3; - - Split(b, bhi, blo); - Two_Product_Presplit(e[0], b, bhi, blo, Q, hh); - hindex = 0; - if (hh != 0) { - h[hindex++] = hh; - } - for (eindex = 1; eindex < elen; eindex++) { - enow = e[eindex]; - Two_Product_Presplit(enow, b, bhi, blo, product1, product0); - Two_Sum(Q, product0, sum, hh); - if (hh != 0) { - h[hindex++] = hh; - } - Fast_Two_Sum(product1, sum, Q, hh); - if (hh != 0) { - h[hindex++] = hh; - } - } - if ((Q != 0.0) || (hindex == 0)) { - h[hindex++] = Q; - } - return hindex; -} - -/*****************************************************************************/ -/* */ -/* estimate() Produce a one-word estimate of an expansion's value. */ -/* */ -/* See my Robust Predicates paper for details. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -REAL estimate(int elen, REAL *e) -#else /* not ANSI_DECLARATORS */ -REAL estimate(elen, e) -int elen; -REAL *e; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL Q; - int eindex; - - Q = e[0]; - for (eindex = 1; eindex < elen; eindex++) { - Q += e[eindex]; - } - return Q; -} - -/*****************************************************************************/ -/* */ -/* counterclockwise() Return a positive value if the points pa, pb, and */ -/* pc occur in counterclockwise order; a negative */ -/* value if they occur in clockwise order; and zero */ -/* if they are collinear. The result is also a rough */ -/* approximation of twice the signed area of the */ -/* triangle defined by the three points. */ -/* */ -/* Uses exact arithmetic if necessary to ensure a correct answer. The */ -/* result returned is the determinant of a matrix. This determinant is */ -/* computed adaptively, in the sense that exact arithmetic is used only to */ -/* the degree it is needed to ensure that the returned value has the */ -/* correct sign. Hence, this function is usually quite fast, but will run */ -/* more slowly when the input points are collinear or nearly so. */ -/* */ -/* See my Robust Predicates paper for details. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum) -#else /* not ANSI_DECLARATORS */ -REAL counterclockwiseadapt(pa, pb, pc, detsum) -vertex pa; -vertex pb; -vertex pc; -REAL detsum; -#endif /* not ANSI_DECLARATORS */ - -{ - INEXACT REAL acx, acy, bcx, bcy; - REAL acxtail, acytail, bcxtail, bcytail; - INEXACT REAL detleft, detright; - REAL detlefttail, detrighttail; - REAL det, errbound; - REAL B[4], C1[8], C2[12], D[16]; - INEXACT REAL B3; - int C1length, C2length, Dlength; - REAL u[4]; - INEXACT REAL u3; - INEXACT REAL s1, t1; - REAL s0, t0; - - INEXACT REAL bvirt; - REAL avirt, bround, around; - INEXACT REAL c; - INEXACT REAL abig; - REAL ahi, alo, bhi, blo; - REAL err1, err2, err3; - INEXACT REAL _i, _j; - REAL _0; - - acx = (REAL) (pa[0] - pc[0]); - bcx = (REAL) (pb[0] - pc[0]); - acy = (REAL) (pa[1] - pc[1]); - bcy = (REAL) (pb[1] - pc[1]); - - Two_Product(acx, bcy, detleft, detlefttail); - Two_Product(acy, bcx, detright, detrighttail); - - Two_Two_Diff(detleft, detlefttail, detright, detrighttail, - B3, B[2], B[1], B[0]); - B[3] = B3; - - det = estimate(4, B); - errbound = ccwerrboundB * detsum; - if ((det >= errbound) || (-det >= errbound)) { - return det; - } - - Two_Diff_Tail(pa[0], pc[0], acx, acxtail); - Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail); - Two_Diff_Tail(pa[1], pc[1], acy, acytail); - Two_Diff_Tail(pb[1], pc[1], bcy, bcytail); - - if ((acxtail == 0.0) && (acytail == 0.0) - && (bcxtail == 0.0) && (bcytail == 0.0)) { - return det; - } - - errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det); - det += (acx * bcytail + bcy * acxtail) - - (acy * bcxtail + bcx * acytail); - if ((det >= errbound) || (-det >= errbound)) { - return det; - } - - Two_Product(acxtail, bcy, s1, s0); - Two_Product(acytail, bcx, t1, t0); - Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); - u[3] = u3; - C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1); - - Two_Product(acx, bcytail, s1, s0); - Two_Product(acy, bcxtail, t1, t0); - Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); - u[3] = u3; - C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2); - - Two_Product(acxtail, bcytail, s1, s0); - Two_Product(acytail, bcxtail, t1, t0); - Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); - u[3] = u3; - Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D); - - return(D[Dlength - 1]); -} - -#ifdef ANSI_DECLARATORS -REAL counterclockwise(struct mesh *m, struct behavior *b, - vertex pa, vertex pb, vertex pc) -#else /* not ANSI_DECLARATORS */ -REAL counterclockwise(m, b, pa, pb, pc) -struct mesh *m; -struct behavior *b; -vertex pa; -vertex pb; -vertex pc; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL detleft, detright, det; - REAL detsum, errbound; - - m->counterclockcount++; - - detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]); - detright = (pa[1] - pc[1]) * (pb[0] - pc[0]); - det = detleft - detright; - - if (b->noexact) { - return det; - } - - if (detleft > 0.0) { - if (detright <= 0.0) { - return det; - } else { - detsum = detleft + detright; - } - } else if (detleft < 0.0) { - if (detright >= 0.0) { - return det; - } else { - detsum = -detleft - detright; - } - } else { - return det; - } - - errbound = ccwerrboundA * detsum; - if ((det >= errbound) || (-det >= errbound)) { - return det; - } - - return counterclockwiseadapt(pa, pb, pc, detsum); -} - -/*****************************************************************************/ -/* */ -/* incircle() Return a positive value if the point pd lies inside the */ -/* circle passing through pa, pb, and pc; a negative value if */ -/* it lies outside; and zero if the four points are cocircular.*/ -/* The points pa, pb, and pc must be in counterclockwise */ -/* order, or the sign of the result will be reversed. */ -/* */ -/* Uses exact arithmetic if necessary to ensure a correct answer. The */ -/* result returned is the determinant of a matrix. This determinant is */ -/* computed adaptively, in the sense that exact arithmetic is used only to */ -/* the degree it is needed to ensure that the returned value has the */ -/* correct sign. Hence, this function is usually quite fast, but will run */ -/* more slowly when the input points are cocircular or nearly so. */ -/* */ -/* See my Robust Predicates paper for details. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent) -#else /* not ANSI_DECLARATORS */ -REAL incircleadapt(pa, pb, pc, pd, permanent) -vertex pa; -vertex pb; -vertex pc; -vertex pd; -REAL permanent; -#endif /* not ANSI_DECLARATORS */ - -{ - INEXACT REAL adx, bdx, cdx, ady, bdy, cdy; - REAL det, errbound; - - INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; - REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; - REAL bc[4], ca[4], ab[4]; - INEXACT REAL bc3, ca3, ab3; - REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32]; - int axbclen, axxbclen, aybclen, ayybclen, alen; - REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32]; - int bxcalen, bxxcalen, bycalen, byycalen, blen; - REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32]; - int cxablen, cxxablen, cyablen, cyyablen, clen; - REAL abdet[64]; - int ablen; - REAL fin1[1152], fin2[1152]; - REAL *finnow, *finother, *finswap; - int finlength; - - REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail; - INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1; - REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0; - REAL aa[4], bb[4], cc[4]; - INEXACT REAL aa3, bb3, cc3; - INEXACT REAL ti1, tj1; - REAL ti0, tj0; - REAL u[4], v[4]; - INEXACT REAL u3, v3; - REAL temp8[8], temp16a[16], temp16b[16], temp16c[16]; - REAL temp32a[32], temp32b[32], temp48[48], temp64[64]; - int temp8len, temp16alen, temp16blen, temp16clen; - int temp32alen, temp32blen, temp48len, temp64len; - REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8]; - int axtbblen, axtcclen, aytbblen, aytcclen; - REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8]; - int bxtaalen, bxtcclen, bytaalen, bytcclen; - REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8]; - int cxtaalen, cxtbblen, cytaalen, cytbblen; - REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8]; - int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen; - REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16]; - int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen; - REAL axtbctt[8], aytbctt[8], bxtcatt[8]; - REAL bytcatt[8], cxtabtt[8], cytabtt[8]; - int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen; - REAL abt[8], bct[8], cat[8]; - int abtlen, bctlen, catlen; - REAL abtt[4], bctt[4], catt[4]; - int abttlen, bcttlen, cattlen; - INEXACT REAL abtt3, bctt3, catt3; - REAL negate; - - INEXACT REAL bvirt; - REAL avirt, bround, around; - INEXACT REAL c; - INEXACT REAL abig; - REAL ahi, alo, bhi, blo; - REAL err1, err2, err3; - INEXACT REAL _i, _j; - REAL _0; - - adx = (REAL) (pa[0] - pd[0]); - bdx = (REAL) (pb[0] - pd[0]); - cdx = (REAL) (pc[0] - pd[0]); - ady = (REAL) (pa[1] - pd[1]); - bdy = (REAL) (pb[1] - pd[1]); - cdy = (REAL) (pc[1] - pd[1]); - - Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); - Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); - Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); - bc[3] = bc3; - axbclen = scale_expansion_zeroelim(4, bc, adx, axbc); - axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc); - aybclen = scale_expansion_zeroelim(4, bc, ady, aybc); - ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc); - alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet); - - Two_Product(cdx, ady, cdxady1, cdxady0); - Two_Product(adx, cdy, adxcdy1, adxcdy0); - Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); - ca[3] = ca3; - bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca); - bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca); - bycalen = scale_expansion_zeroelim(4, ca, bdy, byca); - byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca); - blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet); - - Two_Product(adx, bdy, adxbdy1, adxbdy0); - Two_Product(bdx, ady, bdxady1, bdxady0); - Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); - ab[3] = ab3; - cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab); - cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab); - cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab); - cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab); - clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet); - - ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); - finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); - - det = estimate(finlength, fin1); - errbound = iccerrboundB * permanent; - if ((det >= errbound) || (-det >= errbound)) { - return det; - } - - Two_Diff_Tail(pa[0], pd[0], adx, adxtail); - Two_Diff_Tail(pa[1], pd[1], ady, adytail); - Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); - Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); - Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); - Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); - if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) - && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) { - return det; - } - - errbound = iccerrboundC * permanent + resulterrbound * Absolute(det); - det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail) - - (bdy * cdxtail + cdx * bdytail)) - + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx)) - + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail) - - (cdy * adxtail + adx * cdytail)) - + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx)) - + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail) - - (ady * bdxtail + bdx * adytail)) - + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx)); - if ((det >= errbound) || (-det >= errbound)) { - return det; - } - - finnow = fin1; - finother = fin2; - - if ((bdxtail != 0.0) || (bdytail != 0.0) - || (cdxtail != 0.0) || (cdytail != 0.0)) { - Square(adx, adxadx1, adxadx0); - Square(ady, adyady1, adyady0); - Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]); - aa[3] = aa3; - } - if ((cdxtail != 0.0) || (cdytail != 0.0) - || (adxtail != 0.0) || (adytail != 0.0)) { - Square(bdx, bdxbdx1, bdxbdx0); - Square(bdy, bdybdy1, bdybdy0); - Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]); - bb[3] = bb3; - } - if ((adxtail != 0.0) || (adytail != 0.0) - || (bdxtail != 0.0) || (bdytail != 0.0)) { - Square(cdx, cdxcdx1, cdxcdx0); - Square(cdy, cdycdy1, cdycdy0); - Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]); - cc[3] = cc3; - } - - if (adxtail != 0.0) { - axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc); - temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx, - temp16a); - - axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc); - temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b); - - axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb); - temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c); - - temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (adytail != 0.0) { - aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc); - temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady, - temp16a); - - aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb); - temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b); - - aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc); - temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c); - - temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (bdxtail != 0.0) { - bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca); - temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx, - temp16a); - - bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa); - temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b); - - bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc); - temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c); - - temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (bdytail != 0.0) { - bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca); - temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy, - temp16a); - - bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc); - temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b); - - bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa); - temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c); - - temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (cdxtail != 0.0) { - cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab); - temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx, - temp16a); - - cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb); - temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b); - - cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa); - temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c); - - temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (cdytail != 0.0) { - cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab); - temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy, - temp16a); - - cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa); - temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b); - - cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb); - temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c); - - temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - - if ((adxtail != 0.0) || (adytail != 0.0)) { - if ((bdxtail != 0.0) || (bdytail != 0.0) - || (cdxtail != 0.0) || (cdytail != 0.0)) { - Two_Product(bdxtail, cdy, ti1, ti0); - Two_Product(bdx, cdytail, tj1, tj0); - Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); - u[3] = u3; - negate = -bdy; - Two_Product(cdxtail, negate, ti1, ti0); - negate = -bdytail; - Two_Product(cdx, negate, tj1, tj0); - Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); - v[3] = v3; - bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct); - - Two_Product(bdxtail, cdytail, ti1, ti0); - Two_Product(cdxtail, bdytail, tj1, tj0); - Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]); - bctt[3] = bctt3; - bcttlen = 4; - } else { - bct[0] = 0.0; - bctlen = 1; - bctt[0] = 0.0; - bcttlen = 1; - } - - if (adxtail != 0.0) { - temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a); - axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct); - temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx, - temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - if (bdytail != 0.0) { - temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8); - temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, - temp16a); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, - temp16a, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (cdytail != 0.0) { - temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8); - temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, - temp16a); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, - temp16a, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - - temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail, - temp32a); - axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt); - temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx, - temp16a); - temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail, - temp16b); - temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32b); - temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, - temp32blen, temp32b, temp64); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, - temp64, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (adytail != 0.0) { - temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a); - aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct); - temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady, - temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - - - temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail, - temp32a); - aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt); - temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady, - temp16a); - temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail, - temp16b); - temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32b); - temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, - temp32blen, temp32b, temp64); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, - temp64, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - if ((bdxtail != 0.0) || (bdytail != 0.0)) { - if ((cdxtail != 0.0) || (cdytail != 0.0) - || (adxtail != 0.0) || (adytail != 0.0)) { - Two_Product(cdxtail, ady, ti1, ti0); - Two_Product(cdx, adytail, tj1, tj0); - Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); - u[3] = u3; - negate = -cdy; - Two_Product(adxtail, negate, ti1, ti0); - negate = -cdytail; - Two_Product(adx, negate, tj1, tj0); - Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); - v[3] = v3; - catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat); - - Two_Product(cdxtail, adytail, ti1, ti0); - Two_Product(adxtail, cdytail, tj1, tj0); - Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]); - catt[3] = catt3; - cattlen = 4; - } else { - cat[0] = 0.0; - catlen = 1; - catt[0] = 0.0; - cattlen = 1; - } - - if (bdxtail != 0.0) { - temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a); - bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat); - temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx, - temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - if (cdytail != 0.0) { - temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8); - temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, - temp16a); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, - temp16a, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (adytail != 0.0) { - temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8); - temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, - temp16a); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, - temp16a, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - - temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail, - temp32a); - bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt); - temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx, - temp16a); - temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail, - temp16b); - temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32b); - temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, - temp32blen, temp32b, temp64); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, - temp64, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (bdytail != 0.0) { - temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a); - bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat); - temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy, - temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - - - temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail, - temp32a); - bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt); - temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy, - temp16a); - temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail, - temp16b); - temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32b); - temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, - temp32blen, temp32b, temp64); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, - temp64, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - if ((cdxtail != 0.0) || (cdytail != 0.0)) { - if ((adxtail != 0.0) || (adytail != 0.0) - || (bdxtail != 0.0) || (bdytail != 0.0)) { - Two_Product(adxtail, bdy, ti1, ti0); - Two_Product(adx, bdytail, tj1, tj0); - Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); - u[3] = u3; - negate = -ady; - Two_Product(bdxtail, negate, ti1, ti0); - negate = -adytail; - Two_Product(bdx, negate, tj1, tj0); - Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); - v[3] = v3; - abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt); - - Two_Product(adxtail, bdytail, ti1, ti0); - Two_Product(bdxtail, adytail, tj1, tj0); - Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]); - abtt[3] = abtt3; - abttlen = 4; - } else { - abt[0] = 0.0; - abtlen = 1; - abtt[0] = 0.0; - abttlen = 1; - } - - if (cdxtail != 0.0) { - temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a); - cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt); - temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx, - temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - if (adytail != 0.0) { - temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8); - temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, - temp16a); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, - temp16a, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (bdytail != 0.0) { - temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8); - temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, - temp16a); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, - temp16a, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - - temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail, - temp32a); - cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt); - temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx, - temp16a); - temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail, - temp16b); - temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32b); - temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, - temp32blen, temp32b, temp64); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, - temp64, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (cdytail != 0.0) { - temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a); - cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt); - temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy, - temp32a); - temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp32alen, temp32a, temp48); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, - temp48, finother); - finswap = finnow; finnow = finother; finother = finswap; - - - temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail, - temp32a); - cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt); - temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy, - temp16a); - temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail, - temp16b); - temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, - temp16blen, temp16b, temp32b); - temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, - temp32blen, temp32b, temp64); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, - temp64, finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - - return finnow[finlength - 1]; -} - -#ifdef ANSI_DECLARATORS -REAL incircle(struct mesh *m, struct behavior *b, - vertex pa, vertex pb, vertex pc, vertex pd) -#else /* not ANSI_DECLARATORS */ -REAL incircle(m, b, pa, pb, pc, pd) -struct mesh *m; -struct behavior *b; -vertex pa; -vertex pb; -vertex pc; -vertex pd; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL adx, bdx, cdx, ady, bdy, cdy; - REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; - REAL alift, blift, clift; - REAL det; - REAL permanent, errbound; - - m->incirclecount++; - - adx = pa[0] - pd[0]; - bdx = pb[0] - pd[0]; - cdx = pc[0] - pd[0]; - ady = pa[1] - pd[1]; - bdy = pb[1] - pd[1]; - cdy = pc[1] - pd[1]; - - bdxcdy = bdx * cdy; - cdxbdy = cdx * bdy; - alift = adx * adx + ady * ady; - - cdxady = cdx * ady; - adxcdy = adx * cdy; - blift = bdx * bdx + bdy * bdy; - - adxbdy = adx * bdy; - bdxady = bdx * ady; - clift = cdx * cdx + cdy * cdy; - - det = alift * (bdxcdy - cdxbdy) - + blift * (cdxady - adxcdy) - + clift * (adxbdy - bdxady); - - if (b->noexact) { - return det; - } - - permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift - + (Absolute(cdxady) + Absolute(adxcdy)) * blift - + (Absolute(adxbdy) + Absolute(bdxady)) * clift; - errbound = iccerrboundA * permanent; - if ((det > errbound) || (-det > errbound)) { - return det; - } - - return incircleadapt(pa, pb, pc, pd, permanent); -} - -/*****************************************************************************/ -/* */ -/* orient3d() Return a positive value if the point pd lies below the */ -/* plane passing through pa, pb, and pc; "below" is defined so */ -/* that pa, pb, and pc appear in counterclockwise order when */ -/* viewed from above the plane. Returns a negative value if */ -/* pd lies above the plane. Returns zero if the points are */ -/* coplanar. The result is also a rough approximation of six */ -/* times the signed volume of the tetrahedron defined by the */ -/* four points. */ -/* */ -/* Uses exact arithmetic if necessary to ensure a correct answer. The */ -/* result returned is the determinant of a matrix. This determinant is */ -/* computed adaptively, in the sense that exact arithmetic is used only to */ -/* the degree it is needed to ensure that the returned value has the */ -/* correct sign. Hence, this function is usually quite fast, but will run */ -/* more slowly when the input points are coplanar or nearly so. */ -/* */ -/* See my Robust Predicates paper for details. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd, - REAL aheight, REAL bheight, REAL cheight, REAL dheight, - REAL permanent) -#else /* not ANSI_DECLARATORS */ -REAL orient3dadapt(pa, pb, pc, pd, - aheight, bheight, cheight, dheight, permanent) -vertex pa; -vertex pb; -vertex pc; -vertex pd; -REAL aheight; -REAL bheight; -REAL cheight; -REAL dheight; -REAL permanent; -#endif /* not ANSI_DECLARATORS */ - -{ - INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; - REAL det, errbound; - - INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; - REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; - REAL bc[4], ca[4], ab[4]; - INEXACT REAL bc3, ca3, ab3; - REAL adet[8], bdet[8], cdet[8]; - int alen, blen, clen; - REAL abdet[16]; - int ablen; - REAL *finnow, *finother, *finswap; - REAL fin1[192], fin2[192]; - int finlength; - - REAL adxtail, bdxtail, cdxtail; - REAL adytail, bdytail, cdytail; - REAL adheighttail, bdheighttail, cdheighttail; - INEXACT REAL at_blarge, at_clarge; - INEXACT REAL bt_clarge, bt_alarge; - INEXACT REAL ct_alarge, ct_blarge; - REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4]; - int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen; - INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1; - INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1; - REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0; - REAL adxt_cdy0, adxt_bdy0, bdxt_ady0; - INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1; - INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1; - REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0; - REAL adyt_cdx0, adyt_bdx0, bdyt_adx0; - REAL bct[8], cat[8], abt[8]; - int bctlen, catlen, abtlen; - INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1; - INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1; - REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0; - REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0; - REAL u[4], v[12], w[16]; - INEXACT REAL u3; - int vlength, wlength; - REAL negate; - - INEXACT REAL bvirt; - REAL avirt, bround, around; - INEXACT REAL c; - INEXACT REAL abig; - REAL ahi, alo, bhi, blo; - REAL err1, err2, err3; - INEXACT REAL _i, _j, _k; - REAL _0; - - adx = (REAL) (pa[0] - pd[0]); - bdx = (REAL) (pb[0] - pd[0]); - cdx = (REAL) (pc[0] - pd[0]); - ady = (REAL) (pa[1] - pd[1]); - bdy = (REAL) (pb[1] - pd[1]); - cdy = (REAL) (pc[1] - pd[1]); - adheight = (REAL) (aheight - dheight); - bdheight = (REAL) (bheight - dheight); - cdheight = (REAL) (cheight - dheight); - - Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); - Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); - Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); - bc[3] = bc3; - alen = scale_expansion_zeroelim(4, bc, adheight, adet); - - Two_Product(cdx, ady, cdxady1, cdxady0); - Two_Product(adx, cdy, adxcdy1, adxcdy0); - Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); - ca[3] = ca3; - blen = scale_expansion_zeroelim(4, ca, bdheight, bdet); - - Two_Product(adx, bdy, adxbdy1, adxbdy0); - Two_Product(bdx, ady, bdxady1, bdxady0); - Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); - ab[3] = ab3; - clen = scale_expansion_zeroelim(4, ab, cdheight, cdet); - - ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); - finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); - - det = estimate(finlength, fin1); - errbound = o3derrboundB * permanent; - if ((det >= errbound) || (-det >= errbound)) { - return det; - } - - Two_Diff_Tail(pa[0], pd[0], adx, adxtail); - Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); - Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); - Two_Diff_Tail(pa[1], pd[1], ady, adytail); - Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); - Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); - Two_Diff_Tail(aheight, dheight, adheight, adheighttail); - Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail); - Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail); - - if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) && - (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) && - (adheighttail == 0.0) && - (bdheighttail == 0.0) && - (cdheighttail == 0.0)) { - return det; - } - - errbound = o3derrboundC * permanent + resulterrbound * Absolute(det); - det += (adheight * ((bdx * cdytail + cdy * bdxtail) - - (bdy * cdxtail + cdx * bdytail)) + - adheighttail * (bdx * cdy - bdy * cdx)) + - (bdheight * ((cdx * adytail + ady * cdxtail) - - (cdy * adxtail + adx * cdytail)) + - bdheighttail * (cdx * ady - cdy * adx)) + - (cdheight * ((adx * bdytail + bdy * adxtail) - - (ady * bdxtail + bdx * adytail)) + - cdheighttail * (adx * bdy - ady * bdx)); - if ((det >= errbound) || (-det >= errbound)) { - return det; - } - - finnow = fin1; - finother = fin2; - - if (adxtail == 0.0) { - if (adytail == 0.0) { - at_b[0] = 0.0; - at_blen = 1; - at_c[0] = 0.0; - at_clen = 1; - } else { - negate = -adytail; - Two_Product(negate, bdx, at_blarge, at_b[0]); - at_b[1] = at_blarge; - at_blen = 2; - Two_Product(adytail, cdx, at_clarge, at_c[0]); - at_c[1] = at_clarge; - at_clen = 2; - } - } else { - if (adytail == 0.0) { - Two_Product(adxtail, bdy, at_blarge, at_b[0]); - at_b[1] = at_blarge; - at_blen = 2; - negate = -adxtail; - Two_Product(negate, cdy, at_clarge, at_c[0]); - at_c[1] = at_clarge; - at_clen = 2; - } else { - Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0); - Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0); - Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0, - at_blarge, at_b[2], at_b[1], at_b[0]); - at_b[3] = at_blarge; - at_blen = 4; - Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0); - Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0); - Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0, - at_clarge, at_c[2], at_c[1], at_c[0]); - at_c[3] = at_clarge; - at_clen = 4; - } - } - if (bdxtail == 0.0) { - if (bdytail == 0.0) { - bt_c[0] = 0.0; - bt_clen = 1; - bt_a[0] = 0.0; - bt_alen = 1; - } else { - negate = -bdytail; - Two_Product(negate, cdx, bt_clarge, bt_c[0]); - bt_c[1] = bt_clarge; - bt_clen = 2; - Two_Product(bdytail, adx, bt_alarge, bt_a[0]); - bt_a[1] = bt_alarge; - bt_alen = 2; - } - } else { - if (bdytail == 0.0) { - Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]); - bt_c[1] = bt_clarge; - bt_clen = 2; - negate = -bdxtail; - Two_Product(negate, ady, bt_alarge, bt_a[0]); - bt_a[1] = bt_alarge; - bt_alen = 2; - } else { - Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0); - Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0); - Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0, - bt_clarge, bt_c[2], bt_c[1], bt_c[0]); - bt_c[3] = bt_clarge; - bt_clen = 4; - Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0); - Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0); - Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0, - bt_alarge, bt_a[2], bt_a[1], bt_a[0]); - bt_a[3] = bt_alarge; - bt_alen = 4; - } - } - if (cdxtail == 0.0) { - if (cdytail == 0.0) { - ct_a[0] = 0.0; - ct_alen = 1; - ct_b[0] = 0.0; - ct_blen = 1; - } else { - negate = -cdytail; - Two_Product(negate, adx, ct_alarge, ct_a[0]); - ct_a[1] = ct_alarge; - ct_alen = 2; - Two_Product(cdytail, bdx, ct_blarge, ct_b[0]); - ct_b[1] = ct_blarge; - ct_blen = 2; - } - } else { - if (cdytail == 0.0) { - Two_Product(cdxtail, ady, ct_alarge, ct_a[0]); - ct_a[1] = ct_alarge; - ct_alen = 2; - negate = -cdxtail; - Two_Product(negate, bdy, ct_blarge, ct_b[0]); - ct_b[1] = ct_blarge; - ct_blen = 2; - } else { - Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0); - Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0); - Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0, - ct_alarge, ct_a[2], ct_a[1], ct_a[0]); - ct_a[3] = ct_alarge; - ct_alen = 4; - Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0); - Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0); - Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0, - ct_blarge, ct_b[2], ct_b[1], ct_b[0]); - ct_b[3] = ct_blarge; - ct_blen = 4; - } - } - - bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct); - wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, - finother); - finswap = finnow; finnow = finother; finother = finswap; - - catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat); - wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, - finother); - finswap = finnow; finnow = finother; finother = finswap; - - abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt); - wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, - finother); - finswap = finnow; finnow = finother; finother = finswap; - - if (adheighttail != 0.0) { - vlength = scale_expansion_zeroelim(4, bc, adheighttail, v); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (bdheighttail != 0.0) { - vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (cdheighttail != 0.0) { - vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - - if (adxtail != 0.0) { - if (bdytail != 0.0) { - Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0); - Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - if (cdheighttail != 0.0) { - Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail, - u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - if (cdytail != 0.0) { - negate = -adxtail; - Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0); - Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - if (bdheighttail != 0.0) { - Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail, - u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - } - if (bdxtail != 0.0) { - if (cdytail != 0.0) { - Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0); - Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - if (adheighttail != 0.0) { - Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail, - u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - if (adytail != 0.0) { - negate = -bdxtail; - Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0); - Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - if (cdheighttail != 0.0) { - Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail, - u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - } - if (cdxtail != 0.0) { - if (adytail != 0.0) { - Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0); - Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - if (bdheighttail != 0.0) { - Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail, - u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - if (bdytail != 0.0) { - negate = -cdxtail; - Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0); - Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - if (adheighttail != 0.0) { - Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail, - u3, u[2], u[1], u[0]); - u[3] = u3; - finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - } - } - - if (adheighttail != 0.0) { - wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (bdheighttail != 0.0) { - wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - if (cdheighttail != 0.0) { - wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w); - finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, - finother); - finswap = finnow; finnow = finother; finother = finswap; - } - - return finnow[finlength - 1]; -} - -#ifdef ANSI_DECLARATORS -REAL orient3d(struct mesh *m, struct behavior *b, - vertex pa, vertex pb, vertex pc, vertex pd, - REAL aheight, REAL bheight, REAL cheight, REAL dheight) -#else /* not ANSI_DECLARATORS */ -REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight) -struct mesh *m; -struct behavior *b; -vertex pa; -vertex pb; -vertex pc; -vertex pd; -REAL aheight; -REAL bheight; -REAL cheight; -REAL dheight; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; - REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; - REAL det; - REAL permanent, errbound; - - m->orient3dcount++; - - adx = pa[0] - pd[0]; - bdx = pb[0] - pd[0]; - cdx = pc[0] - pd[0]; - ady = pa[1] - pd[1]; - bdy = pb[1] - pd[1]; - cdy = pc[1] - pd[1]; - adheight = aheight - dheight; - bdheight = bheight - dheight; - cdheight = cheight - dheight; - - bdxcdy = bdx * cdy; - cdxbdy = cdx * bdy; - - cdxady = cdx * ady; - adxcdy = adx * cdy; - - adxbdy = adx * bdy; - bdxady = bdx * ady; - - det = adheight * (bdxcdy - cdxbdy) - + bdheight * (cdxady - adxcdy) - + cdheight * (adxbdy - bdxady); - - if (b->noexact) { - return det; - } - - permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight) - + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight) - + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight); - errbound = o3derrboundA * permanent; - if ((det > errbound) || (-det > errbound)) { - return det; - } - - return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight, - permanent); -} - -/*****************************************************************************/ -/* */ -/* nonregular() Return a positive value if the point pd is incompatible */ -/* with the circle or plane passing through pa, pb, and pc */ -/* (meaning that pd is inside the circle or below the */ -/* plane); a negative value if it is compatible; and zero if */ -/* the four points are cocircular/coplanar. The points pa, */ -/* pb, and pc must be in counterclockwise order, or the sign */ -/* of the result will be reversed. */ -/* */ -/* If the -w switch is used, the points are lifted onto the parabolic */ -/* lifting map, then they are dropped according to their weights, then the */ -/* 3D orientation test is applied. If the -W switch is used, the points' */ -/* heights are already provided, so the 3D orientation test is applied */ -/* directly. If neither switch is used, the incircle test is applied. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -REAL nonregular(struct mesh *m, struct behavior *b, - vertex pa, vertex pb, vertex pc, vertex pd) -#else /* not ANSI_DECLARATORS */ -REAL nonregular(m, b, pa, pb, pc, pd) -struct mesh *m; -struct behavior *b; -vertex pa; -vertex pb; -vertex pc; -vertex pd; -#endif /* not ANSI_DECLARATORS */ - -{ - if (b->weighted == 0) { - return incircle(m, b, pa, pb, pc, pd); - } else if (b->weighted == 1) { - return orient3d(m, b, pa, pb, pc, pd, - pa[0] * pa[0] + pa[1] * pa[1] - pa[2], - pb[0] * pb[0] + pb[1] * pb[1] - pb[2], - pc[0] * pc[0] + pc[1] * pc[1] - pc[2], - pd[0] * pd[0] + pd[1] * pd[1] - pd[2]); - } else { - return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]); - } -} - -/*****************************************************************************/ -/* */ -/* findcircumcenter() Find the circumcenter of a triangle. */ -/* */ -/* The result is returned both in terms of x-y coordinates and xi-eta */ -/* (barycentric) coordinates. The xi-eta coordinate system is defined in */ -/* terms of the triangle: the origin of the triangle is the origin of the */ -/* coordinate system; the destination of the triangle is one unit along the */ -/* xi axis; and the apex of the triangle is one unit along the eta axis. */ -/* This procedure also returns the square of the length of the triangle's */ -/* shortest edge. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void findcircumcenter(struct mesh *m, struct behavior *b, - vertex torg, vertex tdest, vertex tapex, - vertex circumcenter, REAL *xi, REAL *eta, int offcenter) -#else /* not ANSI_DECLARATORS */ -void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta, - offcenter) -struct mesh *m; -struct behavior *b; -vertex torg; -vertex tdest; -vertex tapex; -vertex circumcenter; -REAL *xi; -REAL *eta; -int offcenter; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL xdo, ydo, xao, yao; - REAL dodist, aodist, dadist; - REAL denominator; - REAL dx, dy, dxoff, dyoff; - - m->circumcentercount++; - - /* Compute the circumcenter of the triangle. */ - xdo = tdest[0] - torg[0]; - ydo = tdest[1] - torg[1]; - xao = tapex[0] - torg[0]; - yao = tapex[1] - torg[1]; - dodist = xdo * xdo + ydo * ydo; - aodist = xao * xao + yao * yao; - dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) + - (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]); - if (b->noexact) { - denominator = 0.5 / (xdo * yao - xao * ydo); - } else { - /* Use the counterclockwise() routine to ensure a positive (and */ - /* reasonably accurate) result, avoiding any possibility of */ - /* division by zero. */ - denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg); - /* Don't count the above as an orientation test. */ - m->counterclockcount--; - } - dx = (yao * dodist - ydo * aodist) * denominator; - dy = (xdo * aodist - xao * dodist) * denominator; - - /* Find the (squared) length of the triangle's shortest edge. This */ - /* serves as a conservative estimate of the insertion radius of the */ - /* circumcenter's parent. The estimate is used to ensure that */ - /* the algorithm terminates even if very small angles appear in */ - /* the input PSLG. */ - if ((dodist < aodist) && (dodist < dadist)) { - if (offcenter && (b->offconstant > 0.0)) { - /* Find the position of the off-center, as described by Alper Ungor. */ - dxoff = 0.5 * xdo - b->offconstant * ydo; - dyoff = 0.5 * ydo + b->offconstant * xdo; - /* If the off-center is closer to the origin than the */ - /* circumcenter, use the off-center instead. */ - if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) { - dx = dxoff; - dy = dyoff; - } - } - } else if (aodist < dadist) { - if (offcenter && (b->offconstant > 0.0)) { - dxoff = 0.5 * xao + b->offconstant * yao; - dyoff = 0.5 * yao - b->offconstant * xao; - /* If the off-center is closer to the origin than the */ - /* circumcenter, use the off-center instead. */ - if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) { - dx = dxoff; - dy = dyoff; - } - } - } else { - if (offcenter && (b->offconstant > 0.0)) { - dxoff = 0.5 * (tapex[0] - tdest[0]) - - b->offconstant * (tapex[1] - tdest[1]); - dyoff = 0.5 * (tapex[1] - tdest[1]) + - b->offconstant * (tapex[0] - tdest[0]); - /* If the off-center is closer to the destination than the */ - /* circumcenter, use the off-center instead. */ - if (dxoff * dxoff + dyoff * dyoff < - (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) { - dx = xdo + dxoff; - dy = ydo + dyoff; - } - } - } - - circumcenter[0] = torg[0] + dx; - circumcenter[1] = torg[1] + dy; - - /* To interpolate vertex attributes for the new vertex inserted at */ - /* the circumcenter, define a coordinate system with a xi-axis, */ - /* directed from the triangle's origin to its destination, and */ - /* an eta-axis, directed from its origin to its apex. */ - /* Calculate the xi and eta coordinates of the circumcenter. */ - *xi = (yao * dx - xao * dy) * (2.0 * denominator); - *eta = (xdo * dy - ydo * dx) * (2.0 * denominator); -} - -/** **/ -/** **/ -/********* Geometric primitives end here *********/ - -/*****************************************************************************/ -/* */ -/* triangleinit() Initialize some variables. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void triangleinit(struct mesh *m) -#else /* not ANSI_DECLARATORS */ -void triangleinit(m) -struct mesh *m; -#endif /* not ANSI_DECLARATORS */ - -{ - poolzero(&m->vertices); - poolzero(&m->triangles); - poolzero(&m->subsegs); - poolzero(&m->viri); - poolzero(&m->badsubsegs); - poolzero(&m->badtriangles); - poolzero(&m->flipstackers); - poolzero(&m->splaynodes); - - m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */ - m->undeads = 0; /* No eliminated input vertices yet. */ - m->samples = 1; /* Point location should take at least one sample. */ - m->checksegments = 0; /* There are no segments in the triangulation yet. */ - m->checkquality = 0; /* The quality triangulation stage has not begun. */ - m->incirclecount = m->counterclockcount = m->orient3dcount = 0; - m->hyperbolacount = m->circletopcount = m->circumcentercount = 0; - randomseed = 1; - - exactinit(); /* Initialize exact arithmetic constants. */ -} - -/*****************************************************************************/ -/* */ -/* randomnation() Generate a random number between 0 and `choices' - 1. */ -/* */ -/* This is a simple linear congruential random number generator. Hence, it */ -/* is a bad random number generator, but good enough for most randomized */ -/* geometric algorithms. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -unsigned long randomnation(unsigned int choices) -#else /* not ANSI_DECLARATORS */ -unsigned long randomnation(choices) -unsigned int choices; -#endif /* not ANSI_DECLARATORS */ - -{ - randomseed = (randomseed * 1366l + 150889l) % 714025l; - return randomseed / (714025l / choices + 1); -} - -/********* Mesh quality testing routines begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* checkmesh() Test the mesh for topological consistency. */ -/* */ -/*****************************************************************************/ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -void checkmesh(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void checkmesh(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri triangleloop; - struct otri oppotri, oppooppotri; - vertex triorg, tridest, triapex; - vertex oppoorg, oppodest; - int horrors; - int saveexact; - triangle ptr; /* Temporary variable used by sym(). */ - - /* Temporarily turn on exact arithmetic if it's off. */ - saveexact = b->noexact; - b->noexact = 0; - if (!b->quiet) { - printf(" Checking consistency of mesh...\n"); - } - horrors = 0; - /* Run through the list of triangles, checking each one. */ - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - while (triangleloop.tri != (triangle *) NULL) { - /* Check all three edges of the triangle. */ - for (triangleloop.orient = 0; triangleloop.orient < 3; - triangleloop.orient++) { - org(triangleloop, triorg); - dest(triangleloop, tridest); - if (triangleloop.orient == 0) { /* Only test for inversion once. */ - /* Test if the triangle is flat or inverted. */ - apex(triangleloop, triapex); - if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) { - printf(" !! !! Inverted "); - printtriangle(m, b, &triangleloop); - horrors++; - } - } - /* Find the neighboring triangle on this edge. */ - sym(triangleloop, oppotri); - if (oppotri.tri != m->dummytri) { - /* Check that the triangle's neighbor knows it's a neighbor. */ - sym(oppotri, oppooppotri); - if ((triangleloop.tri != oppooppotri.tri) - || (triangleloop.orient != oppooppotri.orient)) { - printf(" !! !! Asymmetric triangle-triangle bond:\n"); - if (triangleloop.tri == oppooppotri.tri) { - printf(" (Right triangle, wrong orientation)\n"); - } - printf(" First "); - printtriangle(m, b, &triangleloop); - printf(" Second (nonreciprocating) "); - printtriangle(m, b, &oppotri); - horrors++; - } - /* Check that both triangles agree on the identities */ - /* of their shared vertices. */ - org(oppotri, oppoorg); - dest(oppotri, oppodest); - if ((triorg != oppodest) || (tridest != oppoorg)) { - printf(" !! !! Mismatched edge coordinates between two triangles:\n" - ); - printf(" First mismatched "); - printtriangle(m, b, &triangleloop); - printf(" Second mismatched "); - printtriangle(m, b, &oppotri); - horrors++; - } - } - } - triangleloop.tri = triangletraverse(m); - } - if (horrors == 0) { - if (!b->quiet) { - printf(" In my studied opinion, the mesh appears to be consistent.\n"); - } - } else if (horrors == 1) { - printf(" !! !! !! !! Precisely one festering wound discovered.\n"); - } else { - printf(" !! !! !! !! %d abominations witnessed.\n", horrors); - } - /* Restore the status of exact arithmetic. */ - b->noexact = saveexact; -} - -#endif /* not REDUCED */ - -/*****************************************************************************/ -/* */ -/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */ -/* */ -/*****************************************************************************/ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -void checkdelaunay(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void checkdelaunay(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri triangleloop; - struct otri oppotri; - struct osub opposubseg; - vertex triorg, tridest, triapex; - vertex oppoapex; - int shouldbedelaunay; - int horrors; - int saveexact; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - /* Temporarily turn on exact arithmetic if it's off. */ - saveexact = b->noexact; - b->noexact = 0; - if (!b->quiet) { - printf(" Checking Delaunay property of mesh...\n"); - } - horrors = 0; - /* Run through the list of triangles, checking each one. */ - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - while (triangleloop.tri != (triangle *) NULL) { - /* Check all three edges of the triangle. */ - for (triangleloop.orient = 0; triangleloop.orient < 3; - triangleloop.orient++) { - org(triangleloop, triorg); - dest(triangleloop, tridest); - apex(triangleloop, triapex); - sym(triangleloop, oppotri); - apex(oppotri, oppoapex); - /* Only test that the edge is locally Delaunay if there is an */ - /* adjoining triangle whose pointer is larger (to ensure that */ - /* each pair isn't tested twice). */ - shouldbedelaunay = (oppotri.tri != m->dummytri) && - !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) && - (triorg != m->infvertex1) && (triorg != m->infvertex2) && - (triorg != m->infvertex3) && - (tridest != m->infvertex1) && (tridest != m->infvertex2) && - (tridest != m->infvertex3) && - (triapex != m->infvertex1) && (triapex != m->infvertex2) && - (triapex != m->infvertex3) && - (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) && - (oppoapex != m->infvertex3); - if (m->checksegments && shouldbedelaunay) { - /* If a subsegment separates the triangles, then the edge is */ - /* constrained, so no local Delaunay test should be done. */ - tspivot(triangleloop, opposubseg); - if (opposubseg.ss != m->dummysub){ - shouldbedelaunay = 0; - } - } - if (shouldbedelaunay) { - if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) { - if (!b->weighted) { - printf(" !! !! Non-Delaunay pair of triangles:\n"); - printf(" First non-Delaunay "); - printtriangle(m, b, &triangleloop); - printf(" Second non-Delaunay "); - } else { - printf(" !! !! Non-regular pair of triangles:\n"); - printf(" First non-regular "); - printtriangle(m, b, &triangleloop); - printf(" Second non-regular "); - } - printtriangle(m, b, &oppotri); - horrors++; - } - } - } - triangleloop.tri = triangletraverse(m); - } - if (horrors == 0) { - if (!b->quiet) { - printf( - " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n"); - } - } else if (horrors == 1) { - printf( - " !! !! !! !! Precisely one terrifying transgression identified.\n"); - } else { - printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors); - } - /* Restore the status of exact arithmetic. */ - b->noexact = saveexact; -} - -#endif /* not REDUCED */ - -/*****************************************************************************/ -/* */ -/* enqueuebadtriang() Add a bad triangle data structure to the end of a */ -/* queue. */ -/* */ -/* The queue is actually a set of 4096 queues. I use multiple queues to */ -/* give priority to smaller angles. I originally implemented a heap, but */ -/* the queues are faster by a larger margin than I'd suspected. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void enqueuebadtriang(struct mesh *m, struct behavior *b, - struct badtriang *badtri) -#else /* not ANSI_DECLARATORS */ -void enqueuebadtriang(m, b, badtri) -struct mesh *m; -struct behavior *b; -struct badtriang *badtri; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL length, multiplier; - int exponent, expincrement; - int queuenumber; - int posexponent; - int i; - - if (b->verbose > 2) { - printf(" Queueing bad triangle:\n"); - printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", - badtri->triangorg[0], badtri->triangorg[1], - badtri->triangdest[0], badtri->triangdest[1], - badtri->triangapex[0], badtri->triangapex[1]); - } - - /* Determine the appropriate queue to put the bad triangle into. */ - /* Recall that the key is the square of its shortest edge length. */ - if (badtri->key >= 1.0) { - length = badtri->key; - posexponent = 1; - } else { - /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */ - /* fact and use the reciprocal of `badtri->key', which is > 1.0. */ - length = 1.0 / badtri->key; - posexponent = 0; - } - /* `length' is approximately 2.0 to what exponent? The following code */ - /* determines the answer in time logarithmic in the exponent. */ - exponent = 0; - while (length > 2.0) { - /* Find an approximation by repeated squaring of two. */ - expincrement = 1; - multiplier = 0.5; - while (length * multiplier * multiplier > 1.0) { - expincrement *= 2; - multiplier *= multiplier; - } - /* Reduce the value of `length', then iterate if necessary. */ - exponent += expincrement; - length *= multiplier; - } - /* `length' is approximately squareroot(2.0) to what exponent? */ - exponent = 2.0 * exponent + (length > SQUAREROOTTWO); - /* `exponent' is now in the range 0...2047 for IEEE double precision. */ - /* Choose a queue in the range 0...4095. The shortest edges have the */ - /* highest priority (queue 4095). */ - if (posexponent) { - queuenumber = 2047 - exponent; - } else { - queuenumber = 2048 + exponent; - } - - /* Are we inserting into an empty queue? */ - if (m->queuefront[queuenumber] == (struct badtriang *) NULL) { - /* Yes, we are inserting into an empty queue. */ - /* Will this become the highest-priority queue? */ - if (queuenumber > m->firstnonemptyq) { - /* Yes, this is the highest-priority queue. */ - m->nextnonemptyq[queuenumber] = m->firstnonemptyq; - m->firstnonemptyq = queuenumber; - } else { - /* No, this is not the highest-priority queue. */ - /* Find the queue with next higher priority. */ - i = queuenumber + 1; - while (m->queuefront[i] == (struct badtriang *) NULL) { - i++; - } - /* Mark the newly nonempty queue as following a higher-priority queue. */ - m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i]; - m->nextnonemptyq[i] = queuenumber; - } - /* Put the bad triangle at the beginning of the (empty) queue. */ - m->queuefront[queuenumber] = badtri; - } else { - /* Add the bad triangle to the end of an already nonempty queue. */ - m->queuetail[queuenumber]->nexttriang = badtri; - } - /* Maintain a pointer to the last triangle of the queue. */ - m->queuetail[queuenumber] = badtri; - /* Newly enqueued bad triangle has no successor in the queue. */ - badtri->nexttriang = (struct badtriang *) NULL; -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* enqueuebadtri() Add a bad triangle to the end of a queue. */ -/* */ -/* Allocates a badtriang data structure for the triangle, then passes it to */ -/* enqueuebadtriang(). */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri, - REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest) -#else /* not ANSI_DECLARATORS */ -void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest) -struct mesh *m; -struct behavior *b; -struct otri *enqtri; -REAL minedge; -vertex enqapex; -vertex enqorg; -vertex enqdest; -#endif /* not ANSI_DECLARATORS */ - -{ - struct badtriang *newbad; - - /* Allocate space for the bad triangle. */ - newbad = (struct badtriang *) poolalloc(&m->badtriangles); - newbad->poortri = encode(*enqtri); - newbad->key = minedge; - newbad->triangapex = enqapex; - newbad->triangorg = enqorg; - newbad->triangdest = enqdest; - enqueuebadtriang(m, b, newbad); -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* dequeuebadtriang() Remove a triangle from the front of the queue. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -struct badtriang *dequeuebadtriang(struct mesh *m) -#else /* not ANSI_DECLARATORS */ -struct badtriang *dequeuebadtriang(m) -struct mesh *m; -#endif /* not ANSI_DECLARATORS */ - -{ - struct badtriang *result; - - /* If no queues are nonempty, return NULL. */ - if (m->firstnonemptyq < 0) { - return (struct badtriang *) NULL; - } - /* Find the first triangle of the highest-priority queue. */ - result = m->queuefront[m->firstnonemptyq]; - /* Remove the triangle from the queue. */ - m->queuefront[m->firstnonemptyq] = result->nexttriang; - /* If this queue is now empty, note the new highest-priority */ - /* nonempty queue. */ - if (result == m->queuetail[m->firstnonemptyq]) { - m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq]; - } - return result; -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* checkseg4encroach() Check a subsegment to see if it is encroached; add */ -/* it to the list if it is. */ -/* */ -/* A subsegment is encroached if there is a vertex in its diametral lens. */ -/* For Ruppert's algorithm (-D switch), the "diametral lens" is the */ -/* diametral circle. For Chew's algorithm (default), the diametral lens is */ -/* just big enough to enclose two isosceles triangles whose bases are the */ -/* subsegment. Each of the two isosceles triangles has two angles equal */ -/* to `b->minangle'. */ -/* */ -/* Chew's algorithm does not require diametral lenses at all--but they save */ -/* time. Any vertex inside a subsegment's diametral lens implies that the */ -/* triangle adjoining the subsegment will be too skinny, so it's only a */ -/* matter of time before the encroaching vertex is deleted by Chew's */ -/* algorithm. It's faster to simply not insert the doomed vertex in the */ -/* first place, which is why I use diametral lenses with Chew's algorithm. */ -/* */ -/* Returns a nonzero value if the subsegment is encroached. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -int checkseg4encroach(struct mesh *m, struct behavior *b, - struct osub *testsubseg) -#else /* not ANSI_DECLARATORS */ -int checkseg4encroach(m, b, testsubseg) -struct mesh *m; -struct behavior *b; -struct osub *testsubseg; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri neighbortri; - struct osub testsym; - struct badsubseg *encroachedseg; - REAL dotproduct; - int encroached; - int sides; - vertex eorg, edest, eapex; - triangle ptr; /* Temporary variable used by stpivot(). */ - - encroached = 0; - sides = 0; - - sorg(*testsubseg, eorg); - sdest(*testsubseg, edest); - /* Check one neighbor of the subsegment. */ - stpivot(*testsubseg, neighbortri); - /* Does the neighbor exist, or is this a boundary edge? */ - if (neighbortri.tri != m->dummytri) { - sides++; - /* Find a vertex opposite this subsegment. */ - apex(neighbortri, eapex); - /* Check whether the apex is in the diametral lens of the subsegment */ - /* (the diametral circle if `conformdel' is set). A dot product */ - /* of two sides of the triangle is used to check whether the angle */ - /* at the apex is greater than (180 - 2 `minangle') degrees (for */ - /* lenses; 90 degrees for diametral circles). */ - dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + - (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); - if (dotproduct < 0.0) { - if (b->conformdel || - (dotproduct * dotproduct >= - (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) * - ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + - (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * - ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + - (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { - encroached = 1; - } - } - } - /* Check the other neighbor of the subsegment. */ - ssym(*testsubseg, testsym); - stpivot(testsym, neighbortri); - /* Does the neighbor exist, or is this a boundary edge? */ - if (neighbortri.tri != m->dummytri) { - sides++; - /* Find the other vertex opposite this subsegment. */ - apex(neighbortri, eapex); - /* Check whether the apex is in the diametral lens of the subsegment */ - /* (or the diametral circle, if `conformdel' is set). */ - dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + - (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); - if (dotproduct < 0.0) { - if (b->conformdel || - (dotproduct * dotproduct >= - (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) * - ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + - (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * - ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + - (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { - encroached += 2; - } - } - } - - if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) { - if (b->verbose > 2) { - printf( - " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", - eorg[0], eorg[1], edest[0], edest[1]); - } - /* Add the subsegment to the list of encroached subsegments. */ - /* Be sure to get the orientation right. */ - encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs); - if (encroached == 1) { - encroachedseg->encsubseg = sencode(*testsubseg); - encroachedseg->subsegorg = eorg; - encroachedseg->subsegdest = edest; - } else { - encroachedseg->encsubseg = sencode(testsym); - encroachedseg->subsegorg = edest; - encroachedseg->subsegdest = eorg; - } - } - - return encroached; -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* testtriangle() Test a triangle for quality and size. */ -/* */ -/* Tests a triangle to see if it satisfies the minimum angle condition and */ -/* the maximum area condition. Triangles that aren't up to spec are added */ -/* to the bad triangle queue. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri) -#else /* not ANSI_DECLARATORS */ -void testtriangle(m, b, testtri) -struct mesh *m; -struct behavior *b; -struct otri *testtri; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri tri1, tri2; - struct osub testsub; - vertex torg, tdest, tapex; - vertex base1, base2; - vertex org1, dest1, org2, dest2; - vertex joinvertex; - REAL dxod, dyod, dxda, dyda, dxao, dyao; - REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2; - REAL apexlen, orglen, destlen, minedge; - REAL angle; - REAL area; - REAL dist1, dist2; - subseg sptr; /* Temporary variable used by tspivot(). */ - triangle ptr; /* Temporary variable used by oprev() and dnext(). */ - - org(*testtri, torg); - dest(*testtri, tdest); - apex(*testtri, tapex); - dxod = torg[0] - tdest[0]; - dyod = torg[1] - tdest[1]; - dxda = tdest[0] - tapex[0]; - dyda = tdest[1] - tapex[1]; - dxao = tapex[0] - torg[0]; - dyao = tapex[1] - torg[1]; - dxod2 = dxod * dxod; - dyod2 = dyod * dyod; - dxda2 = dxda * dxda; - dyda2 = dyda * dyda; - dxao2 = dxao * dxao; - dyao2 = dyao * dyao; - /* Find the lengths of the triangle's three edges. */ - apexlen = dxod2 + dyod2; - orglen = dxda2 + dyda2; - destlen = dxao2 + dyao2; - - if ((apexlen < orglen) && (apexlen < destlen)) { - /* The edge opposite the apex is shortest. */ - minedge = apexlen; - /* Find the square of the cosine of the angle at the apex. */ - angle = dxda * dxao + dyda * dyao; - angle = angle * angle / (orglen * destlen); - base1 = torg; - base2 = tdest; - otricopy(*testtri, tri1); - } else if (orglen < destlen) { - /* The edge opposite the origin is shortest. */ - minedge = orglen; - /* Find the square of the cosine of the angle at the origin. */ - angle = dxod * dxao + dyod * dyao; - angle = angle * angle / (apexlen * destlen); - base1 = tdest; - base2 = tapex; - lnext(*testtri, tri1); - } else { - /* The edge opposite the destination is shortest. */ - minedge = destlen; - /* Find the square of the cosine of the angle at the destination. */ - angle = dxod * dxda + dyod * dyda; - angle = angle * angle / (apexlen * orglen); - base1 = tapex; - base2 = torg; - lprev(*testtri, tri1); - } - - if (b->vararea || b->fixedarea || b->usertest) { - /* Check whether the area is larger than permitted. */ - area = 0.5 * (dxod * dyda - dyod * dxda); - if (b->fixedarea && (area > b->maxarea)) { - /* Add this triangle to the list of bad triangles. */ - enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); - return; - } - - /* Nonpositive area constraints are treated as unconstrained. */ - if ((b->vararea) && (area > areabound(*testtri)) && - (areabound(*testtri) > 0.0)) { - /* Add this triangle to the list of bad triangles. */ - enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); - return; - } - - if (b->usertest) { - /* Check whether the user thinks this triangle is too large. */ - if (triunsuitable(torg, tdest, tapex, area)) { - enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); - return; - } - } - } - - /* Check whether the angle is smaller than permitted. */ - if (angle > b->goodangle) { - /* Use the rules of Miller, Pav, and Walkington to decide that certain */ - /* triangles should not be split, even if they have bad angles. */ - /* A skinny triangle is not split if its shortest edge subtends a */ - /* small input angle, and both endpoints of the edge lie on a */ - /* concentric circular shell. For convenience, I make a small */ - /* adjustment to that rule: I check if the endpoints of the edge */ - /* both lie in segment interiors, equidistant from the apex where */ - /* the two segments meet. */ - /* First, check if both points lie in segment interiors. */ - if ((vertextype(base1) == SEGMENTVERTEX) && - (vertextype(base2) == SEGMENTVERTEX)) { - /* Check if both points lie in a common segment. If they do, the */ - /* skinny triangle is enqueued to be split as usual. */ - tspivot(tri1, testsub); - if (testsub.ss == m->dummysub) { - /* No common segment. Find a subsegment that contains `torg'. */ - otricopy(tri1, tri2); - do { - oprevself(tri1); - tspivot(tri1, testsub); - } while (testsub.ss == m->dummysub); - /* Find the endpoints of the containing segment. */ - segorg(testsub, org1); - segdest(testsub, dest1); - /* Find a subsegment that contains `tdest'. */ - do { - dnextself(tri2); - tspivot(tri2, testsub); - } while (testsub.ss == m->dummysub); - /* Find the endpoints of the containing segment. */ - segorg(testsub, org2); - segdest(testsub, dest2); - /* Check if the two containing segments have an endpoint in common. */ - joinvertex = (vertex) NULL; - if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) { - joinvertex = dest1; - } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) { - joinvertex = org1; - } - if (joinvertex != (vertex) NULL) { - /* Compute the distance from the common endpoint (of the two */ - /* segments) to each of the endpoints of the shortest edge. */ - dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) + - (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1])); - dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) + - (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1])); - /* If the two distances are equal, don't split the triangle. */ - if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) { - /* Return now to avoid enqueueing the bad triangle. */ - return; - } - } - } - } - - /* Add this triangle to the list of bad triangles. */ - enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); - } -} - -#endif /* not CDT_ONLY */ - -/** **/ -/** **/ -/********* Mesh quality testing routines end here *********/ - -/********* Point location routines begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* makevertexmap() Construct a mapping from vertices to triangles to */ -/* improve the speed of point location for segment */ -/* insertion. */ -/* */ -/* Traverses all the triangles, and provides each corner of each triangle */ -/* with a pointer to that triangle. Of course, pointers will be */ -/* overwritten by other pointers because (almost) each vertex is a corner */ -/* of several triangles, but in the end every vertex will point to some */ -/* triangle that contains it. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void makevertexmap(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void makevertexmap(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri triangleloop; - vertex triorg; - - if (b->verbose) { - printf(" Constructing mapping from vertices to triangles.\n"); - } - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - while (triangleloop.tri != (triangle *) NULL) { - /* Check all three vertices of the triangle. */ - for (triangleloop.orient = 0; triangleloop.orient < 3; - triangleloop.orient++) { - org(triangleloop, triorg); - setvertex2tri(triorg, encode(triangleloop)); - } - triangleloop.tri = triangletraverse(m); - } -} - -/*****************************************************************************/ -/* */ -/* preciselocate() Find a triangle or edge containing a given point. */ -/* */ -/* Begins its search from `searchtri'. It is important that `searchtri' */ -/* be a handle with the property that `searchpoint' is strictly to the left */ -/* of the edge denoted by `searchtri', or is collinear with that edge and */ -/* does not intersect that edge. (In particular, `searchpoint' should not */ -/* be the origin or destination of that edge.) */ -/* */ -/* These conditions are imposed because preciselocate() is normally used in */ -/* one of two situations: */ -/* */ -/* (1) To try to find the location to insert a new point. Normally, we */ -/* know an edge that the point is strictly to the left of. In the */ -/* incremental Delaunay algorithm, that edge is a bounding box edge. */ -/* In Ruppert's Delaunay refinement algorithm for quality meshing, */ -/* that edge is the shortest edge of the triangle whose circumcenter */ -/* is being inserted. */ -/* */ -/* (2) To try to find an existing point. In this case, any edge on the */ -/* convex hull is a good starting edge. You must screen out the */ -/* possibility that the vertex sought is an endpoint of the starting */ -/* edge before you call preciselocate(). */ -/* */ -/* On completion, `searchtri' is a triangle that contains `searchpoint'. */ -/* */ -/* This implementation differs from that given by Guibas and Stolfi. It */ -/* walks from triangle to triangle, crossing an edge only if `searchpoint' */ -/* is on the other side of the line containing that edge. After entering */ -/* a triangle, there are two edges by which one can leave that triangle. */ -/* If both edges are valid (`searchpoint' is on the other side of both */ -/* edges), one of the two is chosen by drawing a line perpendicular to */ -/* the entry edge (whose endpoints are `forg' and `fdest') passing through */ -/* `fapex'. Depending on which side of this perpendicular `searchpoint' */ -/* falls on, an exit edge is chosen. */ -/* */ -/* This implementation is empirically faster than the Guibas and Stolfi */ -/* point location routine (which I originally used), which tends to spiral */ -/* in toward its target. */ -/* */ -/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ -/* is a handle whose origin is the existing vertex. */ -/* */ -/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ -/* handle whose primary edge is the edge on which the point lies. */ -/* */ -/* Returns INTRIANGLE if the point lies strictly within a triangle. */ -/* `searchtri' is a handle on the triangle that contains the point. */ -/* */ -/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ -/* handle whose primary edge the point is to the right of. This might */ -/* occur when the circumcenter of a triangle falls just slightly outside */ -/* the mesh due to floating-point roundoff error. It also occurs when */ -/* seeking a hole or region point that a foolish user has placed outside */ -/* the mesh. */ -/* */ -/* If `stopatsubsegment' is nonzero, the search will stop if it tries to */ -/* walk through a subsegment, and will return OUTSIDE. */ -/* */ -/* WARNING: This routine is designed for convex triangulations, and will */ -/* not generally work after the holes and concavities have been carved. */ -/* However, it can still be used to find the circumcenter of a triangle, as */ -/* long as the search is begun from the triangle in question. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -enum locateresult preciselocate(struct mesh *m, struct behavior *b, - vertex searchpoint, struct otri *searchtri, - int stopatsubsegment) -#else /* not ANSI_DECLARATORS */ -enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment) -struct mesh *m; -struct behavior *b; -vertex searchpoint; -struct otri *searchtri; -int stopatsubsegment; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri backtracktri; - struct osub checkedge; - vertex forg, fdest, fapex; - REAL orgorient, destorient; - int moveleft; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - if (b->verbose > 2) { - printf(" Searching for point (%.12g, %.12g).\n", - searchpoint[0], searchpoint[1]); - } - /* Where are we? */ - org(*searchtri, forg); - dest(*searchtri, fdest); - apex(*searchtri, fapex); - while (1) { - if (b->verbose > 2) { - printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", - forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]); - } - /* Check whether the apex is the point we seek. */ - if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) { - lprevself(*searchtri); - return ONVERTEX; - } - /* Does the point lie on the other side of the line defined by the */ - /* triangle edge opposite the triangle's destination? */ - destorient = counterclockwise(m, b, forg, fapex, searchpoint); - /* Does the point lie on the other side of the line defined by the */ - /* triangle edge opposite the triangle's origin? */ - orgorient = counterclockwise(m, b, fapex, fdest, searchpoint); - if (destorient > 0.0) { - if (orgorient > 0.0) { - /* Move left if the inner product of (fapex - searchpoint) and */ - /* (fdest - forg) is positive. This is equivalent to drawing */ - /* a line perpendicular to the line (forg, fdest) and passing */ - /* through `fapex', and determining which side of this line */ - /* `searchpoint' falls on. */ - moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) + - (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0; - } else { - moveleft = 1; - } - } else { - if (orgorient > 0.0) { - moveleft = 0; - } else { - /* The point we seek must be on the boundary of or inside this */ - /* triangle. */ - if (destorient == 0.0) { - lprevself(*searchtri); - return ONEDGE; - } - if (orgorient == 0.0) { - lnextself(*searchtri); - return ONEDGE; - } - return INTRIANGLE; - } - } - - /* Move to another triangle. Leave a trace `backtracktri' in case */ - /* floating-point roundoff or some such bogey causes us to walk */ - /* off a boundary of the triangulation. */ - if (moveleft) { - lprev(*searchtri, backtracktri); - fdest = fapex; - } else { - lnext(*searchtri, backtracktri); - forg = fapex; - } - sym(backtracktri, *searchtri); - - if (m->checksegments && stopatsubsegment) { - /* Check for walking through a subsegment. */ - tspivot(backtracktri, checkedge); - if (checkedge.ss != m->dummysub) { - /* Go back to the last triangle. */ - otricopy(backtracktri, *searchtri); - return OUTSIDE; - } - } - /* Check for walking right out of the triangulation. */ - if (searchtri->tri == m->dummytri) { - /* Go back to the last triangle. */ - otricopy(backtracktri, *searchtri); - return OUTSIDE; - } - - apex(*searchtri, fapex); - } -} - -/*****************************************************************************/ -/* */ -/* locate() Find a triangle or edge containing a given point. */ -/* */ -/* Searching begins from one of: the input `searchtri', a recently */ -/* encountered triangle `recenttri', or from a triangle chosen from a */ -/* random sample. The choice is made by determining which triangle's */ -/* origin is closest to the point we are searching for. Normally, */ -/* `searchtri' should be a handle on the convex hull of the triangulation. */ -/* */ -/* Details on the random sampling method can be found in the Mucke, Saias, */ -/* and Zhu paper cited in the header of this code. */ -/* */ -/* On completion, `searchtri' is a triangle that contains `searchpoint'. */ -/* */ -/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ -/* is a handle whose origin is the existing vertex. */ -/* */ -/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ -/* handle whose primary edge is the edge on which the point lies. */ -/* */ -/* Returns INTRIANGLE if the point lies strictly within a triangle. */ -/* `searchtri' is a handle on the triangle that contains the point. */ -/* */ -/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ -/* handle whose primary edge the point is to the right of. This might */ -/* occur when the circumcenter of a triangle falls just slightly outside */ -/* the mesh due to floating-point roundoff error. It also occurs when */ -/* seeking a hole or region point that a foolish user has placed outside */ -/* the mesh. */ -/* */ -/* WARNING: This routine is designed for convex triangulations, and will */ -/* not generally work after the holes and concavities have been carved. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -enum locateresult locate(struct mesh *m, struct behavior *b, - vertex searchpoint, struct otri *searchtri) -#else /* not ANSI_DECLARATORS */ -enum locateresult locate(m, b, searchpoint, searchtri) -struct mesh *m; -struct behavior *b; -vertex searchpoint; -struct otri *searchtri; -#endif /* not ANSI_DECLARATORS */ - -{ - VOID **sampleblock; - char *firsttri; - struct otri sampletri; - vertex torg, tdest; - unsigned long alignptr; - REAL searchdist, dist; - REAL ahead; - long samplesperblock, totalsamplesleft, samplesleft; - long population, totalpopulation; - triangle ptr; /* Temporary variable used by sym(). */ - - if (b->verbose > 2) { - printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n", - searchpoint[0], searchpoint[1]); - } - /* Record the distance from the suggested starting triangle to the */ - /* point we seek. */ - org(*searchtri, torg); - searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + - (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); - if (b->verbose > 2) { - printf(" Boundary triangle has origin (%.12g, %.12g).\n", - torg[0], torg[1]); - } - - /* If a recently encountered triangle has been recorded and has not been */ - /* deallocated, test it as a good starting point. */ - if (m->recenttri.tri != (triangle *) NULL) { - if (!deadtri(m->recenttri.tri)) { - org(m->recenttri, torg); - if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { - otricopy(m->recenttri, *searchtri); - return ONVERTEX; - } - dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + - (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); - if (dist < searchdist) { - otricopy(m->recenttri, *searchtri); - searchdist = dist; - if (b->verbose > 2) { - printf(" Choosing recent triangle with origin (%.12g, %.12g).\n", - torg[0], torg[1]); - } - } - } - } - - /* The number of random samples taken is proportional to the cube root of */ - /* the number of triangles in the mesh. The next bit of code assumes */ - /* that the number of triangles increases monotonically (or at least */ - /* doesn't decrease enough to matter). */ - while (SAMPLEFACTOR * m->samples * m->samples * m->samples < - m->triangles.items) { - m->samples++; - } - - /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */ - /* from each block of triangles (except the first)--until we meet the */ - /* sample quota. The ceiling means that blocks at the end might be */ - /* neglected, but I don't care. */ - samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1; - /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */ - /* from the first block of triangles. */ - samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) / - m->triangles.maxitems + 1; - totalsamplesleft = m->samples; - population = m->triangles.itemsfirstblock; - totalpopulation = m->triangles.maxitems; - sampleblock = m->triangles.firstblock; - sampletri.orient = 0; - while (totalsamplesleft > 0) { - /* If we're in the last block, `population' needs to be corrected. */ - if (population > totalpopulation) { - population = totalpopulation; - } - /* Find a pointer to the first triangle in the block. */ - alignptr = (unsigned long) (sampleblock + 1); - firsttri = (char *) (alignptr + - (unsigned long) m->triangles.alignbytes - - (alignptr % - (unsigned long) m->triangles.alignbytes)); - - /* Choose `samplesleft' randomly sampled triangles in this block. */ - do { - sampletri.tri = (triangle *) (firsttri + - (randomnation((unsigned int) population) * - m->triangles.itembytes)); - if (!deadtri(sampletri.tri)) { - org(sampletri, torg); - dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + - (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); - if (dist < searchdist) { - otricopy(sampletri, *searchtri); - searchdist = dist; - if (b->verbose > 2) { - printf(" Choosing triangle with origin (%.12g, %.12g).\n", - torg[0], torg[1]); - } - } - } - - samplesleft--; - totalsamplesleft--; - } while ((samplesleft > 0) && (totalsamplesleft > 0)); - - if (totalsamplesleft > 0) { - sampleblock = (VOID **) *sampleblock; - samplesleft = samplesperblock; - totalpopulation -= population; - population = TRIPERBLOCK; - } - } - - /* Where are we? */ - org(*searchtri, torg); - dest(*searchtri, tdest); - /* Check the starting triangle's vertices. */ - if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { - return ONVERTEX; - } - if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) { - lnextself(*searchtri); - return ONVERTEX; - } - /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */ - ahead = counterclockwise(m, b, torg, tdest, searchpoint); - if (ahead < 0.0) { - /* Turn around so that `searchpoint' is to the left of the */ - /* edge specified by `searchtri'. */ - symself(*searchtri); - } else if (ahead == 0.0) { - /* Check if `searchpoint' is between `torg' and `tdest'. */ - if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) && - ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) { - return ONEDGE; - } - } - return preciselocate(m, b, searchpoint, searchtri, 0); -} - -/** **/ -/** **/ -/********* Point location routines end here *********/ - -/********* Mesh transformation routines begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* insertsubseg() Create a new subsegment and insert it between two */ -/* triangles. */ -/* */ -/* The new subsegment is inserted at the edge described by the handle */ -/* `tri'. Its vertices are properly initialized. The marker `subsegmark' */ -/* is applied to the subsegment and, if appropriate, its vertices. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri, - int subsegmark) -#else /* not ANSI_DECLARATORS */ -void insertsubseg(m, b, tri, subsegmark) -struct mesh *m; -struct behavior *b; -struct otri *tri; /* Edge at which to insert the new subsegment. */ -int subsegmark; /* Marker for the new subsegment. */ -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri oppotri; - struct osub newsubseg; - vertex triorg, tridest; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - org(*tri, triorg); - dest(*tri, tridest); - /* Mark vertices if possible. */ - if (vertexmark(triorg) == 0) { - setvertexmark(triorg, subsegmark); - } - if (vertexmark(tridest) == 0) { - setvertexmark(tridest, subsegmark); - } - /* Check if there's already a subsegment here. */ - tspivot(*tri, newsubseg); - if (newsubseg.ss == m->dummysub) { - /* Make new subsegment and initialize its vertices. */ - makesubseg(m, &newsubseg); - setsorg(newsubseg, tridest); - setsdest(newsubseg, triorg); - setsegorg(newsubseg, tridest); - setsegdest(newsubseg, triorg); - /* Bond new subsegment to the two triangles it is sandwiched between. */ - /* Note that the facing triangle `oppotri' might be equal to */ - /* `dummytri' (outer space), but the new subsegment is bonded to it */ - /* all the same. */ - tsbond(*tri, newsubseg); - sym(*tri, oppotri); - ssymself(newsubseg); - tsbond(oppotri, newsubseg); - setmark(newsubseg, subsegmark); - if (b->verbose > 2) { - printf(" Inserting new "); - printsubseg(m, b, &newsubseg); - } - } else { - if (mark(newsubseg) == 0) { - setmark(newsubseg, subsegmark); - } - } -} - -/*****************************************************************************/ -/* */ -/* Terminology */ -/* */ -/* A "local transformation" replaces a small set of triangles with another */ -/* set of triangles. This may or may not involve inserting or deleting a */ -/* vertex. */ -/* */ -/* The term "casing" is used to describe the set of triangles that are */ -/* attached to the triangles being transformed, but are not transformed */ -/* themselves. Think of the casing as a fixed hollow structure inside */ -/* which all the action happens. A "casing" is only defined relative to */ -/* a single transformation; each occurrence of a transformation will */ -/* involve a different casing. */ -/* */ -/*****************************************************************************/ - -/*****************************************************************************/ -/* */ -/* flip() Transform two triangles to two different triangles by flipping */ -/* an edge counterclockwise within a quadrilateral. */ -/* */ -/* Imagine the original triangles, abc and bad, oriented so that the */ -/* shared edge ab lies in a horizontal plane, with the vertex b on the left */ -/* and the vertex a on the right. The vertex c lies below the edge, and */ -/* the vertex d lies above the edge. The `flipedge' handle holds the edge */ -/* ab of triangle abc, and is directed left, from vertex a to vertex b. */ -/* */ -/* The triangles abc and bad are deleted and replaced by the triangles cdb */ -/* and dca. The triangles that represent abc and bad are NOT deallocated; */ -/* they are reused for dca and cdb, respectively. Hence, any handles that */ -/* may have held the original triangles are still valid, although not */ -/* directed as they were before. */ -/* */ -/* Upon completion of this routine, the `flipedge' handle holds the edge */ -/* dc of triangle dca, and is directed down, from vertex d to vertex c. */ -/* (Hence, the two triangles have rotated counterclockwise.) */ -/* */ -/* WARNING: This transformation is geometrically valid only if the */ -/* quadrilateral adbc is convex. Furthermore, this transformation is */ -/* valid only if there is not a subsegment between the triangles abc and */ -/* bad. This routine does not check either of these preconditions, and */ -/* it is the responsibility of the calling routine to ensure that they are */ -/* met. If they are not, the streets shall be filled with wailing and */ -/* gnashing of teeth. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void flip(struct mesh *m, struct behavior *b, struct otri *flipedge) -#else /* not ANSI_DECLARATORS */ -void flip(m, b, flipedge) -struct mesh *m; -struct behavior *b; -struct otri *flipedge; /* Handle for the triangle abc. */ -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri botleft, botright; - struct otri topleft, topright; - struct otri top; - struct otri botlcasing, botrcasing; - struct otri toplcasing, toprcasing; - struct osub botlsubseg, botrsubseg; - struct osub toplsubseg, toprsubseg; - vertex leftvertex, rightvertex, botvertex; - vertex farvertex; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - /* Identify the vertices of the quadrilateral. */ - org(*flipedge, rightvertex); - dest(*flipedge, leftvertex); - apex(*flipedge, botvertex); - sym(*flipedge, top); -#ifdef SELF_CHECK - if (top.tri == m->dummytri) { - printf("Internal error in flip(): Attempt to flip on boundary.\n"); - lnextself(*flipedge); - return; - } - if (m->checksegments) { - tspivot(*flipedge, toplsubseg); - if (toplsubseg.ss != m->dummysub) { - printf("Internal error in flip(): Attempt to flip a segment.\n"); - lnextself(*flipedge); - return; - } - } -#endif /* SELF_CHECK */ - apex(top, farvertex); - - /* Identify the casing of the quadrilateral. */ - lprev(top, topleft); - sym(topleft, toplcasing); - lnext(top, topright); - sym(topright, toprcasing); - lnext(*flipedge, botleft); - sym(botleft, botlcasing); - lprev(*flipedge, botright); - sym(botright, botrcasing); - /* Rotate the quadrilateral one-quarter turn counterclockwise. */ - bond(topleft, botlcasing); - bond(botleft, botrcasing); - bond(botright, toprcasing); - bond(topright, toplcasing); - - if (m->checksegments) { - /* Check for subsegments and rebond them to the quadrilateral. */ - tspivot(topleft, toplsubseg); - tspivot(botleft, botlsubseg); - tspivot(botright, botrsubseg); - tspivot(topright, toprsubseg); - if (toplsubseg.ss == m->dummysub) { - tsdissolve(topright); - } else { - tsbond(topright, toplsubseg); - } - if (botlsubseg.ss == m->dummysub) { - tsdissolve(topleft); - } else { - tsbond(topleft, botlsubseg); - } - if (botrsubseg.ss == m->dummysub) { - tsdissolve(botleft); - } else { - tsbond(botleft, botrsubseg); - } - if (toprsubseg.ss == m->dummysub) { - tsdissolve(botright); - } else { - tsbond(botright, toprsubseg); - } - } - - /* New vertex assignments for the rotated quadrilateral. */ - setorg(*flipedge, farvertex); - setdest(*flipedge, botvertex); - setapex(*flipedge, rightvertex); - setorg(top, botvertex); - setdest(top, farvertex); - setapex(top, leftvertex); - if (b->verbose > 2) { - printf(" Edge flip results in left "); - printtriangle(m, b, &top); - printf(" and right "); - printtriangle(m, b, flipedge); - } -} - -/*****************************************************************************/ -/* */ -/* unflip() Transform two triangles to two different triangles by */ -/* flipping an edge clockwise within a quadrilateral. Reverses */ -/* the flip() operation so that the data structures representing */ -/* the triangles are back where they were before the flip(). */ -/* */ -/* Imagine the original triangles, abc and bad, oriented so that the */ -/* shared edge ab lies in a horizontal plane, with the vertex b on the left */ -/* and the vertex a on the right. The vertex c lies below the edge, and */ -/* the vertex d lies above the edge. The `flipedge' handle holds the edge */ -/* ab of triangle abc, and is directed left, from vertex a to vertex b. */ -/* */ -/* The triangles abc and bad are deleted and replaced by the triangles cdb */ -/* and dca. The triangles that represent abc and bad are NOT deallocated; */ -/* they are reused for cdb and dca, respectively. Hence, any handles that */ -/* may have held the original triangles are still valid, although not */ -/* directed as they were before. */ -/* */ -/* Upon completion of this routine, the `flipedge' handle holds the edge */ -/* cd of triangle cdb, and is directed up, from vertex c to vertex d. */ -/* (Hence, the two triangles have rotated clockwise.) */ -/* */ -/* WARNING: This transformation is geometrically valid only if the */ -/* quadrilateral adbc is convex. Furthermore, this transformation is */ -/* valid only if there is not a subsegment between the triangles abc and */ -/* bad. This routine does not check either of these preconditions, and */ -/* it is the responsibility of the calling routine to ensure that they are */ -/* met. If they are not, the streets shall be filled with wailing and */ -/* gnashing of teeth. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge) -#else /* not ANSI_DECLARATORS */ -void unflip(m, b, flipedge) -struct mesh *m; -struct behavior *b; -struct otri *flipedge; /* Handle for the triangle abc. */ -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri botleft, botright; - struct otri topleft, topright; - struct otri top; - struct otri botlcasing, botrcasing; - struct otri toplcasing, toprcasing; - struct osub botlsubseg, botrsubseg; - struct osub toplsubseg, toprsubseg; - vertex leftvertex, rightvertex, botvertex; - vertex farvertex; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - /* Identify the vertices of the quadrilateral. */ - org(*flipedge, rightvertex); - dest(*flipedge, leftvertex); - apex(*flipedge, botvertex); - sym(*flipedge, top); -#ifdef SELF_CHECK - if (top.tri == m->dummytri) { - printf("Internal error in unflip(): Attempt to flip on boundary.\n"); - lnextself(*flipedge); - return; - } - if (m->checksegments) { - tspivot(*flipedge, toplsubseg); - if (toplsubseg.ss != m->dummysub) { - printf("Internal error in unflip(): Attempt to flip a subsegment.\n"); - lnextself(*flipedge); - return; - } - } -#endif /* SELF_CHECK */ - apex(top, farvertex); - - /* Identify the casing of the quadrilateral. */ - lprev(top, topleft); - sym(topleft, toplcasing); - lnext(top, topright); - sym(topright, toprcasing); - lnext(*flipedge, botleft); - sym(botleft, botlcasing); - lprev(*flipedge, botright); - sym(botright, botrcasing); - /* Rotate the quadrilateral one-quarter turn clockwise. */ - bond(topleft, toprcasing); - bond(botleft, toplcasing); - bond(botright, botlcasing); - bond(topright, botrcasing); - - if (m->checksegments) { - /* Check for subsegments and rebond them to the quadrilateral. */ - tspivot(topleft, toplsubseg); - tspivot(botleft, botlsubseg); - tspivot(botright, botrsubseg); - tspivot(topright, toprsubseg); - if (toplsubseg.ss == m->dummysub) { - tsdissolve(botleft); - } else { - tsbond(botleft, toplsubseg); - } - if (botlsubseg.ss == m->dummysub) { - tsdissolve(botright); - } else { - tsbond(botright, botlsubseg); - } - if (botrsubseg.ss == m->dummysub) { - tsdissolve(topright); - } else { - tsbond(topright, botrsubseg); - } - if (toprsubseg.ss == m->dummysub) { - tsdissolve(topleft); - } else { - tsbond(topleft, toprsubseg); - } - } - - /* New vertex assignments for the rotated quadrilateral. */ - setorg(*flipedge, botvertex); - setdest(*flipedge, farvertex); - setapex(*flipedge, leftvertex); - setorg(top, farvertex); - setdest(top, botvertex); - setapex(top, rightvertex); - if (b->verbose > 2) { - printf(" Edge unflip results in left "); - printtriangle(m, b, flipedge); - printf(" and right "); - printtriangle(m, b, &top); - } -} - -/*****************************************************************************/ -/* */ -/* insertvertex() Insert a vertex into a Delaunay triangulation, */ -/* performing flips as necessary to maintain the Delaunay */ -/* property. */ -/* */ -/* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */ -/* the search for the containing triangle begins from `searchtri'. If */ -/* `searchtri.tri' is NULL, a full point location procedure is called. */ -/* If `insertvertex' is found inside a triangle, the triangle is split into */ -/* three; if `insertvertex' lies on an edge, the edge is split in two, */ -/* thereby splitting the two adjacent triangles into four. Edge flips are */ -/* used to restore the Delaunay property. If `insertvertex' lies on an */ -/* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */ -/* returned. On return, `searchtri' is set to a handle whose origin is the */ -/* existing vertex. */ -/* */ -/* Normally, the parameter `splitseg' is set to NULL, implying that no */ -/* subsegment should be split. In this case, if `insertvertex' is found to */ -/* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */ -/* returned. On return, `searchtri' is set to a handle whose primary edge */ -/* is the violated subsegment. */ -/* */ -/* If the calling routine wishes to split a subsegment by inserting a */ -/* vertex in it, the parameter `splitseg' should be that subsegment. In */ -/* this case, `searchtri' MUST be the triangle handle reached by pivoting */ -/* from that subsegment; no point location is done. */ -/* */ -/* `segmentflaws' and `triflaws' are flags that indicate whether or not */ -/* there should be checks for the creation of encroached subsegments or bad */ -/* quality triangles. If a newly inserted vertex encroaches upon */ -/* subsegments, these subsegments are added to the list of subsegments to */ -/* be split if `segmentflaws' is set. If bad triangles are created, these */ -/* are added to the queue if `triflaws' is set. */ -/* */ -/* If a duplicate vertex or violated segment does not prevent the vertex */ -/* from being inserted, the return value will be ENCROACHINGVERTEX if the */ -/* vertex encroaches upon a subsegment (and checking is enabled), or */ -/* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */ -/* handle whose origin is the newly inserted vertex. */ -/* */ -/* insertvertex() does not use flip() for reasons of speed; some */ -/* information can be reused from edge flip to edge flip, like the */ -/* locations of subsegments. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b, - vertex newvertex, struct otri *searchtri, - struct osub *splitseg, - int segmentflaws, int triflaws) -#else /* not ANSI_DECLARATORS */ -enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg, - segmentflaws, triflaws) -struct mesh *m; -struct behavior *b; -vertex newvertex; -struct otri *searchtri; -struct osub *splitseg; -int segmentflaws; -int triflaws; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri horiz; - struct otri top; - struct otri botleft, botright; - struct otri topleft, topright; - struct otri newbotleft, newbotright; - struct otri newtopright; - struct otri botlcasing, botrcasing; - struct otri toplcasing, toprcasing; - struct otri testtri; - struct osub botlsubseg, botrsubseg; - struct osub toplsubseg, toprsubseg; - struct osub brokensubseg; - struct osub checksubseg; - struct osub rightsubseg; - struct osub newsubseg; - struct badsubseg *encroached; - struct flipstacker *newflip; - vertex first; - vertex leftvertex, rightvertex, botvertex, topvertex, farvertex; - vertex segmentorg, segmentdest; - REAL attrib; - REAL area; - enum insertvertexresult success; - enum locateresult intersect; - int doflip; - int mirrorflag; - int enq; - int i; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by spivot() and tspivot(). */ - - if (b->verbose > 1) { - printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); - } - - if (splitseg == (struct osub *) NULL) { - /* Find the location of the vertex to be inserted. Check if a good */ - /* starting triangle has already been provided by the caller. */ - if (searchtri->tri == m->dummytri) { - /* Find a boundary triangle. */ - horiz.tri = m->dummytri; - horiz.orient = 0; - symself(horiz); - /* Search for a triangle containing `newvertex'. */ - intersect = locate(m, b, newvertex, &horiz); - } else { - /* Start searching from the triangle provided by the caller. */ - otricopy(*searchtri, horiz); - intersect = preciselocate(m, b, newvertex, &horiz, 1); - } - } else { - /* The calling routine provides the subsegment in which */ - /* the vertex is inserted. */ - otricopy(*searchtri, horiz); - intersect = ONEDGE; - } - - if (intersect == ONVERTEX) { - /* There's already a vertex there. Return in `searchtri' a triangle */ - /* whose origin is the existing vertex. */ - otricopy(horiz, *searchtri); - otricopy(horiz, m->recenttri); - return DUPLICATEVERTEX; - } - if ((intersect == ONEDGE) || (intersect == OUTSIDE)) { - /* The vertex falls on an edge or boundary. */ - if (m->checksegments && (splitseg == (struct osub *) NULL)) { - /* Check whether the vertex falls on a subsegment. */ - tspivot(horiz, brokensubseg); - if (brokensubseg.ss != m->dummysub) { - /* The vertex falls on a subsegment, and hence will not be inserted. */ - if (segmentflaws) { - enq = b->nobisect != 2; - if (enq && (b->nobisect == 1)) { - /* This subsegment may be split only if it is an */ - /* internal boundary. */ - sym(horiz, testtri); - enq = testtri.tri != m->dummytri; - } - if (enq) { - /* Add the subsegment to the list of encroached subsegments. */ - encroached = (struct badsubseg *) poolalloc(&m->badsubsegs); - encroached->encsubseg = sencode(brokensubseg); - sorg(brokensubseg, encroached->subsegorg); - sdest(brokensubseg, encroached->subsegdest); - if (b->verbose > 2) { - printf( - " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", - encroached->subsegorg[0], encroached->subsegorg[1], - encroached->subsegdest[0], encroached->subsegdest[1]); - } - } - } - /* Return a handle whose primary edge contains the vertex, */ - /* which has not been inserted. */ - otricopy(horiz, *searchtri); - otricopy(horiz, m->recenttri); - return VIOLATINGVERTEX; - } - } - - /* Insert the vertex on an edge, dividing one triangle into two (if */ - /* the edge lies on a boundary) or two triangles into four. */ - lprev(horiz, botright); - sym(botright, botrcasing); - sym(horiz, topright); - /* Is there a second triangle? (Or does this edge lie on a boundary?) */ - mirrorflag = topright.tri != m->dummytri; - if (mirrorflag) { - lnextself(topright); - sym(topright, toprcasing); - maketriangle(m, b, &newtopright); - } else { - /* Splitting a boundary edge increases the number of boundary edges. */ - m->hullsize++; - } - maketriangle(m, b, &newbotright); - - /* Set the vertices of changed and new triangles. */ - org(horiz, rightvertex); - dest(horiz, leftvertex); - apex(horiz, botvertex); - setorg(newbotright, botvertex); - setdest(newbotright, rightvertex); - setapex(newbotright, newvertex); - setorg(horiz, newvertex); - for (i = 0; i < m->eextras; i++) { - /* Set the element attributes of a new triangle. */ - setelemattribute(newbotright, i, elemattribute(botright, i)); - } - if (b->vararea) { - /* Set the area constraint of a new triangle. */ - setareabound(newbotright, areabound(botright)); - } - if (mirrorflag) { - dest(topright, topvertex); - setorg(newtopright, rightvertex); - setdest(newtopright, topvertex); - setapex(newtopright, newvertex); - setorg(topright, newvertex); - for (i = 0; i < m->eextras; i++) { - /* Set the element attributes of another new triangle. */ - setelemattribute(newtopright, i, elemattribute(topright, i)); - } - if (b->vararea) { - /* Set the area constraint of another new triangle. */ - setareabound(newtopright, areabound(topright)); - } - } - - /* There may be subsegments that need to be bonded */ - /* to the new triangle(s). */ - if (m->checksegments) { - tspivot(botright, botrsubseg); - if (botrsubseg.ss != m->dummysub) { - tsdissolve(botright); - tsbond(newbotright, botrsubseg); - } - if (mirrorflag) { - tspivot(topright, toprsubseg); - if (toprsubseg.ss != m->dummysub) { - tsdissolve(topright); - tsbond(newtopright, toprsubseg); - } - } - } - - /* Bond the new triangle(s) to the surrounding triangles. */ - bond(newbotright, botrcasing); - lprevself(newbotright); - bond(newbotright, botright); - lprevself(newbotright); - if (mirrorflag) { - bond(newtopright, toprcasing); - lnextself(newtopright); - bond(newtopright, topright); - lnextself(newtopright); - bond(newtopright, newbotright); - } - - if (splitseg != (struct osub *) NULL) { - /* Split the subsegment into two. */ - setsdest(*splitseg, newvertex); - segorg(*splitseg, segmentorg); - segdest(*splitseg, segmentdest); - ssymself(*splitseg); - spivot(*splitseg, rightsubseg); - insertsubseg(m, b, &newbotright, mark(*splitseg)); - tspivot(newbotright, newsubseg); - setsegorg(newsubseg, segmentorg); - setsegdest(newsubseg, segmentdest); - sbond(*splitseg, newsubseg); - ssymself(newsubseg); - sbond(newsubseg, rightsubseg); - ssymself(*splitseg); - /* Transfer the subsegment's boundary marker to the vertex */ - /* if required. */ - if (vertexmark(newvertex) == 0) { - setvertexmark(newvertex, mark(*splitseg)); - } - } - - if (m->checkquality) { - poolrestart(&m->flipstackers); - m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); - m->lastflip->flippedtri = encode(horiz); - m->lastflip->prevflip = (struct flipstacker *) &insertvertex; - } - -#ifdef SELF_CHECK - if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf( - " Clockwise triangle prior to edge vertex insertion (bottom).\n"); - } - if (mirrorflag) { - if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle prior to edge vertex insertion (top).\n"); - } - if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf( - " Clockwise triangle after edge vertex insertion (top right).\n"); - } - if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf( - " Clockwise triangle after edge vertex insertion (top left).\n"); - } - } - if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf( - " Clockwise triangle after edge vertex insertion (bottom left).\n"); - } - if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf( - " Clockwise triangle after edge vertex insertion (bottom right).\n"); - } -#endif /* SELF_CHECK */ - if (b->verbose > 2) { - printf(" Updating bottom left "); - printtriangle(m, b, &botright); - if (mirrorflag) { - printf(" Updating top left "); - printtriangle(m, b, &topright); - printf(" Creating top right "); - printtriangle(m, b, &newtopright); - } - printf(" Creating bottom right "); - printtriangle(m, b, &newbotright); - } - - /* Position `horiz' on the first edge to check for */ - /* the Delaunay property. */ - lnextself(horiz); - } else { - /* Insert the vertex in a triangle, splitting it into three. */ - lnext(horiz, botleft); - lprev(horiz, botright); - sym(botleft, botlcasing); - sym(botright, botrcasing); - maketriangle(m, b, &newbotleft); - maketriangle(m, b, &newbotright); - - /* Set the vertices of changed and new triangles. */ - org(horiz, rightvertex); - dest(horiz, leftvertex); - apex(horiz, botvertex); - setorg(newbotleft, leftvertex); - setdest(newbotleft, botvertex); - setapex(newbotleft, newvertex); - setorg(newbotright, botvertex); - setdest(newbotright, rightvertex); - setapex(newbotright, newvertex); - setapex(horiz, newvertex); - for (i = 0; i < m->eextras; i++) { - /* Set the element attributes of the new triangles. */ - attrib = elemattribute(horiz, i); - setelemattribute(newbotleft, i, attrib); - setelemattribute(newbotright, i, attrib); - } - if (b->vararea) { - /* Set the area constraint of the new triangles. */ - area = areabound(horiz); - setareabound(newbotleft, area); - setareabound(newbotright, area); - } - - /* There may be subsegments that need to be bonded */ - /* to the new triangles. */ - if (m->checksegments) { - tspivot(botleft, botlsubseg); - if (botlsubseg.ss != m->dummysub) { - tsdissolve(botleft); - tsbond(newbotleft, botlsubseg); - } - tspivot(botright, botrsubseg); - if (botrsubseg.ss != m->dummysub) { - tsdissolve(botright); - tsbond(newbotright, botrsubseg); - } - } - - /* Bond the new triangles to the surrounding triangles. */ - bond(newbotleft, botlcasing); - bond(newbotright, botrcasing); - lnextself(newbotleft); - lprevself(newbotright); - bond(newbotleft, newbotright); - lnextself(newbotleft); - bond(botleft, newbotleft); - lprevself(newbotright); - bond(botright, newbotright); - - if (m->checkquality) { - poolrestart(&m->flipstackers); - m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); - m->lastflip->flippedtri = encode(horiz); - m->lastflip->prevflip = (struct flipstacker *) NULL; - } - -#ifdef SELF_CHECK - if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle prior to vertex insertion.\n"); - } - if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle after vertex insertion (top).\n"); - } - if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle after vertex insertion (left).\n"); - } - if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle after vertex insertion (right).\n"); - } -#endif /* SELF_CHECK */ - if (b->verbose > 2) { - printf(" Updating top "); - printtriangle(m, b, &horiz); - printf(" Creating left "); - printtriangle(m, b, &newbotleft); - printf(" Creating right "); - printtriangle(m, b, &newbotright); - } - } - - /* The insertion is successful by default, unless an encroached */ - /* subsegment is found. */ - success = SUCCESSFULVERTEX; - /* Circle around the newly inserted vertex, checking each edge opposite */ - /* it for the Delaunay property. Non-Delaunay edges are flipped. */ - /* `horiz' is always the edge being checked. `first' marks where to */ - /* stop circling. */ - org(horiz, first); - rightvertex = first; - dest(horiz, leftvertex); - /* Circle until finished. */ - while (1) { - /* By default, the edge will be flipped. */ - doflip = 1; - - if (m->checksegments) { - /* Check for a subsegment, which cannot be flipped. */ - tspivot(horiz, checksubseg); - if (checksubseg.ss != m->dummysub) { - /* The edge is a subsegment and cannot be flipped. */ - doflip = 0; -#ifndef CDT_ONLY - if (segmentflaws) { - /* Does the new vertex encroach upon this subsegment? */ - if (checkseg4encroach(m, b, &checksubseg)) { - success = ENCROACHINGVERTEX; - } - } -#endif /* not CDT_ONLY */ - } - } - - if (doflip) { - /* Check if the edge is a boundary edge. */ - sym(horiz, top); - if (top.tri == m->dummytri) { - /* The edge is a boundary edge and cannot be flipped. */ - doflip = 0; - } else { - /* Find the vertex on the other side of the edge. */ - apex(top, farvertex); - /* In the incremental Delaunay triangulation algorithm, any of */ - /* `leftvertex', `rightvertex', and `farvertex' could be vertices */ - /* of the triangular bounding box. These vertices must be */ - /* treated as if they are infinitely distant, even though their */ - /* "coordinates" are not. */ - if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) || - (leftvertex == m->infvertex3)) { - /* `leftvertex' is infinitely distant. Check the convexity of */ - /* the boundary of the triangulation. 'farvertex' might be */ - /* infinite as well, but trust me, this same condition should */ - /* be applied. */ - doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex) - > 0.0; - } else if ((rightvertex == m->infvertex1) || - (rightvertex == m->infvertex2) || - (rightvertex == m->infvertex3)) { - /* `rightvertex' is infinitely distant. Check the convexity of */ - /* the boundary of the triangulation. 'farvertex' might be */ - /* infinite as well, but trust me, this same condition should */ - /* be applied. */ - doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex) - > 0.0; - } else if ((farvertex == m->infvertex1) || - (farvertex == m->infvertex2) || - (farvertex == m->infvertex3)) { - /* `farvertex' is infinitely distant and cannot be inside */ - /* the circumcircle of the triangle `horiz'. */ - doflip = 0; - } else { - /* Test whether the edge is locally Delaunay. */ - doflip = incircle(m, b, leftvertex, newvertex, rightvertex, - farvertex) > 0.0; - } - if (doflip) { - /* We made it! Flip the edge `horiz' by rotating its containing */ - /* quadrilateral (the two triangles adjacent to `horiz'). */ - /* Identify the casing of the quadrilateral. */ - lprev(top, topleft); - sym(topleft, toplcasing); - lnext(top, topright); - sym(topright, toprcasing); - lnext(horiz, botleft); - sym(botleft, botlcasing); - lprev(horiz, botright); - sym(botright, botrcasing); - /* Rotate the quadrilateral one-quarter turn counterclockwise. */ - bond(topleft, botlcasing); - bond(botleft, botrcasing); - bond(botright, toprcasing); - bond(topright, toplcasing); - if (m->checksegments) { - /* Check for subsegments and rebond them to the quadrilateral. */ - tspivot(topleft, toplsubseg); - tspivot(botleft, botlsubseg); - tspivot(botright, botrsubseg); - tspivot(topright, toprsubseg); - if (toplsubseg.ss == m->dummysub) { - tsdissolve(topright); - } else { - tsbond(topright, toplsubseg); - } - if (botlsubseg.ss == m->dummysub) { - tsdissolve(topleft); - } else { - tsbond(topleft, botlsubseg); - } - if (botrsubseg.ss == m->dummysub) { - tsdissolve(botleft); - } else { - tsbond(botleft, botrsubseg); - } - if (toprsubseg.ss == m->dummysub) { - tsdissolve(botright); - } else { - tsbond(botright, toprsubseg); - } - } - /* New vertex assignments for the rotated quadrilateral. */ - setorg(horiz, farvertex); - setdest(horiz, newvertex); - setapex(horiz, rightvertex); - setorg(top, newvertex); - setdest(top, farvertex); - setapex(top, leftvertex); - for (i = 0; i < m->eextras; i++) { - /* Take the average of the two triangles' attributes. */ - attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i)); - setelemattribute(top, i, attrib); - setelemattribute(horiz, i, attrib); - } - if (b->vararea) { - if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) { - area = -1.0; - } else { - /* Take the average of the two triangles' area constraints. */ - /* This prevents small area constraints from migrating a */ - /* long, long way from their original location due to flips. */ - area = 0.5 * (areabound(top) + areabound(horiz)); - } - setareabound(top, area); - setareabound(horiz, area); - } - - if (m->checkquality) { - newflip = (struct flipstacker *) poolalloc(&m->flipstackers); - newflip->flippedtri = encode(horiz); - newflip->prevflip = m->lastflip; - m->lastflip = newflip; - } - -#ifdef SELF_CHECK - if (newvertex != (vertex) NULL) { - if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) < - 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle prior to edge flip (bottom).\n"); - } - /* The following test has been removed because constrainededge() */ - /* sometimes generates inverted triangles that insertvertex() */ - /* removes. */ -/* - if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) < - 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle prior to edge flip (top).\n"); - } -*/ - if (counterclockwise(m, b, farvertex, leftvertex, newvertex) < - 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle after edge flip (left).\n"); - } - if (counterclockwise(m, b, newvertex, rightvertex, farvertex) < - 0.0) { - printf("Internal error in insertvertex():\n"); - printf(" Clockwise triangle after edge flip (right).\n"); - } - } -#endif /* SELF_CHECK */ - if (b->verbose > 2) { - printf(" Edge flip results in left "); - lnextself(topleft); - printtriangle(m, b, &topleft); - printf(" and right "); - printtriangle(m, b, &horiz); - } - /* On the next iterations, consider the two edges that were */ - /* exposed (this is, are now visible to the newly inserted */ - /* vertex) by the edge flip. */ - lprevself(horiz); - leftvertex = farvertex; - } - } - } - if (!doflip) { - /* The handle `horiz' is accepted as locally Delaunay. */ -#ifndef CDT_ONLY - if (triflaws) { - /* Check the triangle `horiz' for quality. */ - testtriangle(m, b, &horiz); - } -#endif /* not CDT_ONLY */ - /* Look for the next edge around the newly inserted vertex. */ - lnextself(horiz); - sym(horiz, testtri); - /* Check for finishing a complete revolution about the new vertex, or */ - /* falling outside of the triangulation. The latter will happen */ - /* when a vertex is inserted at a boundary. */ - if ((leftvertex == first) || (testtri.tri == m->dummytri)) { - /* We're done. Return a triangle whose origin is the new vertex. */ - lnext(horiz, *searchtri); - lnext(horiz, m->recenttri); - return success; - } - /* Finish finding the next edge around the newly inserted vertex. */ - lnext(testtri, horiz); - rightvertex = leftvertex; - dest(horiz, leftvertex); - } - } -} - -/*****************************************************************************/ -/* */ -/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */ -/* has a certain "nice" shape. This includes the */ -/* polygons that result from deletion of a vertex or */ -/* insertion of a segment. */ -/* */ -/* This is a conceptually difficult routine. The starting assumption is */ -/* that we have a polygon with n sides. n - 1 of these sides are currently */ -/* represented as edges in the mesh. One side, called the "base", need not */ -/* be. */ -/* */ -/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */ -/* triangles that share a common origin. For each of these triangles, the */ -/* edge opposite the origin is one of the sides of the polygon. The */ -/* primary edge of each triangle is the edge directed from the origin to */ -/* the destination; note that this is not the same edge that is a side of */ -/* the polygon. `firstedge' is the primary edge of the first triangle. */ -/* From there, the triangles follow in counterclockwise order about the */ -/* polygon, until `lastedge', the primary edge of the last triangle. */ -/* `firstedge' and `lastedge' are probably connected to other triangles */ -/* beyond the extremes of the fan, but their identity is not important, as */ -/* long as the fan remains connected to them. */ -/* */ -/* Imagine the polygon oriented so that its base is at the bottom. This */ -/* puts `firstedge' on the far right, and `lastedge' on the far left. */ -/* The right vertex of the base is the destination of `firstedge', and the */ -/* left vertex of the base is the apex of `lastedge'. */ -/* */ -/* The challenge now is to find the right sequence of edge flips to */ -/* transform the fan into a Delaunay triangulation of the polygon. Each */ -/* edge flip effectively removes one triangle from the fan, committing it */ -/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */ -/* is set, the final flip will be performed, resulting in a fan of one */ -/* (useless?) triangle. If `doflip' is not set, the final flip is not */ -/* performed, resulting in a fan of two triangles, and an unfinished */ -/* triangular polygon that is not yet filled out with a single triangle. */ -/* On completion of the routine, `lastedge' is the last remaining triangle, */ -/* or the leftmost of the last two. */ -/* */ -/* Although the flips are performed in the order described above, the */ -/* decisions about what flips to perform are made in precisely the reverse */ -/* order. The recursive triangulatepolygon() procedure makes a decision, */ -/* uses up to two recursive calls to triangulate the "subproblems" */ -/* (polygons with fewer edges), and then performs an edge flip. */ -/* */ -/* The "decision" it makes is which vertex of the polygon should be */ -/* connected to the base. This decision is made by testing every possible */ -/* vertex. Once the best vertex is found, the two edges that connect this */ -/* vertex to the base become the bases for two smaller polygons. These */ -/* are triangulated recursively. Unfortunately, this approach can take */ -/* O(n^2) time not only in the worst case, but in many common cases. It's */ -/* rarely a big deal for vertex deletion, where n is rarely larger than */ -/* ten, but it could be a big deal for segment insertion, especially if */ -/* there's a lot of long segments that each cut many triangles. I ought to */ -/* code a faster algorithm some day. */ -/* */ -/* The `edgecount' parameter is the number of sides of the polygon, */ -/* including its base. `triflaws' is a flag that determines whether the */ -/* new triangles should be tested for quality, and enqueued if they are */ -/* bad. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void triangulatepolygon(struct mesh *m, struct behavior *b, - struct otri *firstedge, struct otri *lastedge, - int edgecount, int doflip, int triflaws) -#else /* not ANSI_DECLARATORS */ -void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws) -struct mesh *m; -struct behavior *b; -struct otri *firstedge; -struct otri *lastedge; -int edgecount; -int doflip; -int triflaws; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri testtri; - struct otri besttri; - struct otri tempedge; - vertex leftbasevertex, rightbasevertex; - vertex testvertex; - vertex bestvertex; - int bestnumber; - int i; - triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ - - /* Identify the base vertices. */ - apex(*lastedge, leftbasevertex); - dest(*firstedge, rightbasevertex); - if (b->verbose > 2) { - printf(" Triangulating interior polygon at edge\n"); - printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0], - leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]); - } - /* Find the best vertex to connect the base to. */ - onext(*firstedge, besttri); - dest(besttri, bestvertex); - otricopy(besttri, testtri); - bestnumber = 1; - for (i = 2; i <= edgecount - 2; i++) { - onextself(testtri); - dest(testtri, testvertex); - /* Is this a better vertex? */ - if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex, - testvertex) > 0.0) { - otricopy(testtri, besttri); - bestvertex = testvertex; - bestnumber = i; - } - } - if (b->verbose > 2) { - printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0], - bestvertex[1]); - } - if (bestnumber > 1) { - /* Recursively triangulate the smaller polygon on the right. */ - oprev(besttri, tempedge); - triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1, - triflaws); - } - if (bestnumber < edgecount - 2) { - /* Recursively triangulate the smaller polygon on the left. */ - sym(besttri, tempedge); - triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1, - triflaws); - /* Find `besttri' again; it may have been lost to edge flips. */ - sym(tempedge, besttri); - } - if (doflip) { - /* Do one final edge flip. */ - flip(m, b, &besttri); -#ifndef CDT_ONLY - if (triflaws) { - /* Check the quality of the newly committed triangle. */ - sym(besttri, testtri); - testtriangle(m, b, &testtri); - } -#endif /* not CDT_ONLY */ - } - /* Return the base triangle. */ - otricopy(besttri, *lastedge); -} - -/*****************************************************************************/ -/* */ -/* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */ -/* that the triangulation remains Delaunay. */ -/* */ -/* The origin of `deltri' is deleted. The union of the triangles adjacent */ -/* to this vertex is a polygon, for which the Delaunay triangulation is */ -/* found. Two triangles are removed from the mesh. */ -/* */ -/* Only interior vertices that do not lie on segments or boundaries may be */ -/* deleted. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri) -#else /* not ANSI_DECLARATORS */ -void deletevertex(m, b, deltri) -struct mesh *m; -struct behavior *b; -struct otri *deltri; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri countingtri; - struct otri firstedge, lastedge; - struct otri deltriright; - struct otri lefttri, righttri; - struct otri leftcasing, rightcasing; - struct osub leftsubseg, rightsubseg; - vertex delvertex; - vertex neworg; - int edgecount; - triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - org(*deltri, delvertex); - if (b->verbose > 1) { - printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]); - } - vertexdealloc(m, delvertex); - - /* Count the degree of the vertex being deleted. */ - onext(*deltri, countingtri); - edgecount = 1; - while (!otriequal(*deltri, countingtri)) { -#ifdef SELF_CHECK - if (countingtri.tri == m->dummytri) { - printf("Internal error in deletevertex():\n"); - printf(" Attempt to delete boundary vertex.\n"); - internalerror(); - } -#endif /* SELF_CHECK */ - edgecount++; - onextself(countingtri); - } - -#ifdef SELF_CHECK - if (edgecount < 3) { - printf("Internal error in deletevertex():\n Vertex has degree %d.\n", - edgecount); - internalerror(); - } -#endif /* SELF_CHECK */ - if (edgecount > 3) { - /* Triangulate the polygon defined by the union of all triangles */ - /* adjacent to the vertex being deleted. Check the quality of */ - /* the resulting triangles. */ - onext(*deltri, firstedge); - oprev(*deltri, lastedge); - triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0, - !b->nobisect); - } - /* Splice out two triangles. */ - lprev(*deltri, deltriright); - dnext(*deltri, lefttri); - sym(lefttri, leftcasing); - oprev(deltriright, righttri); - sym(righttri, rightcasing); - bond(*deltri, leftcasing); - bond(deltriright, rightcasing); - tspivot(lefttri, leftsubseg); - if (leftsubseg.ss != m->dummysub) { - tsbond(*deltri, leftsubseg); - } - tspivot(righttri, rightsubseg); - if (rightsubseg.ss != m->dummysub) { - tsbond(deltriright, rightsubseg); - } - - /* Set the new origin of `deltri' and check its quality. */ - org(lefttri, neworg); - setorg(*deltri, neworg); - if (!b->nobisect) { - testtriangle(m, b, deltri); - } - - /* Delete the two spliced-out triangles. */ - triangledealloc(m, lefttri.tri); - triangledealloc(m, righttri.tri); -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* undovertex() Undo the most recent vertex insertion. */ -/* */ -/* Walks through the list of transformations (flips and a vertex insertion) */ -/* in the reverse of the order in which they were done, and undoes them. */ -/* The inserted vertex is removed from the triangulation and deallocated. */ -/* Two triangles (possibly just one) are also deallocated. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void undovertex(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void undovertex(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri fliptri; - struct otri botleft, botright, topright; - struct otri botlcasing, botrcasing, toprcasing; - struct otri gluetri; - struct osub botlsubseg, botrsubseg, toprsubseg; - vertex botvertex, rightvertex; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - /* Walk through the list of transformations (flips and a vertex insertion) */ - /* in the reverse of the order in which they were done, and undo them. */ - while (m->lastflip != (struct flipstacker *) NULL) { - /* Find a triangle involved in the last unreversed transformation. */ - decode(m->lastflip->flippedtri, fliptri); - - /* We are reversing one of three transformations: a trisection of one */ - /* triangle into three (by inserting a vertex in the triangle), a */ - /* bisection of two triangles into four (by inserting a vertex in an */ - /* edge), or an edge flip. */ - if (m->lastflip->prevflip == (struct flipstacker *) NULL) { - /* Restore a triangle that was split into three triangles, */ - /* so it is again one triangle. */ - dprev(fliptri, botleft); - lnextself(botleft); - onext(fliptri, botright); - lprevself(botright); - sym(botleft, botlcasing); - sym(botright, botrcasing); - dest(botleft, botvertex); - - setapex(fliptri, botvertex); - lnextself(fliptri); - bond(fliptri, botlcasing); - tspivot(botleft, botlsubseg); - tsbond(fliptri, botlsubseg); - lnextself(fliptri); - bond(fliptri, botrcasing); - tspivot(botright, botrsubseg); - tsbond(fliptri, botrsubseg); - - /* Delete the two spliced-out triangles. */ - triangledealloc(m, botleft.tri); - triangledealloc(m, botright.tri); - } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) { - /* Restore two triangles that were split into four triangles, */ - /* so they are again two triangles. */ - lprev(fliptri, gluetri); - sym(gluetri, botright); - lnextself(botright); - sym(botright, botrcasing); - dest(botright, rightvertex); - - setorg(fliptri, rightvertex); - bond(gluetri, botrcasing); - tspivot(botright, botrsubseg); - tsbond(gluetri, botrsubseg); - - /* Delete the spliced-out triangle. */ - triangledealloc(m, botright.tri); - - sym(fliptri, gluetri); - if (gluetri.tri != m->dummytri) { - lnextself(gluetri); - dnext(gluetri, topright); - sym(topright, toprcasing); - - setorg(gluetri, rightvertex); - bond(gluetri, toprcasing); - tspivot(topright, toprsubseg); - tsbond(gluetri, toprsubseg); - - /* Delete the spliced-out triangle. */ - triangledealloc(m, topright.tri); - } - - /* This is the end of the list, sneakily encoded. */ - m->lastflip->prevflip = (struct flipstacker *) NULL; - } else { - /* Undo an edge flip. */ - unflip(m, b, &fliptri); - } - - /* Go on and process the next transformation. */ - m->lastflip = m->lastflip->prevflip; - } -} - -#endif /* not CDT_ONLY */ - -/** **/ -/** **/ -/********* Mesh transformation routines end here *********/ - -/********* Divide-and-conquer Delaunay triangulation begins here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* The divide-and-conquer bounding box */ -/* */ -/* I originally implemented the divide-and-conquer and incremental Delaunay */ -/* triangulations using the edge-based data structure presented by Guibas */ -/* and Stolfi. Switching to a triangle-based data structure doubled the */ -/* speed. However, I had to think of a few extra tricks to maintain the */ -/* elegance of the original algorithms. */ -/* */ -/* The "bounding box" used by my variant of the divide-and-conquer */ -/* algorithm uses one triangle for each edge of the convex hull of the */ -/* triangulation. These bounding triangles all share a common apical */ -/* vertex, which is represented by NULL and which represents nothing. */ -/* The bounding triangles are linked in a circular fan about this NULL */ -/* vertex, and the edges on the convex hull of the triangulation appear */ -/* opposite the NULL vertex. You might find it easiest to imagine that */ -/* the NULL vertex is a point in 3D space behind the center of the */ -/* triangulation, and that the bounding triangles form a sort of cone. */ -/* */ -/* This bounding box makes it easy to represent degenerate cases. For */ -/* instance, the triangulation of two vertices is a single edge. This edge */ -/* is represented by two bounding box triangles, one on each "side" of the */ -/* edge. These triangles are also linked together in a fan about the NULL */ -/* vertex. */ -/* */ -/* The bounding box also makes it easy to traverse the convex hull, as the */ -/* divide-and-conquer algorithm needs to do. */ -/* */ -/*****************************************************************************/ - -/*****************************************************************************/ -/* */ -/* vertexsort() Sort an array of vertices by x-coordinate, using the */ -/* y-coordinate as a secondary key. */ -/* */ -/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */ -/* the usual quicksort mistakes. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void vertexsort(vertex *sortarray, int arraysize) -#else /* not ANSI_DECLARATORS */ -void vertexsort(sortarray, arraysize) -vertex *sortarray; -int arraysize; -#endif /* not ANSI_DECLARATORS */ - -{ - int left, right; - int pivot; - REAL pivotx, pivoty; - vertex temp; - - if (arraysize == 2) { - /* Recursive base case. */ - if ((sortarray[0][0] > sortarray[1][0]) || - ((sortarray[0][0] == sortarray[1][0]) && - (sortarray[0][1] > sortarray[1][1]))) { - temp = sortarray[1]; - sortarray[1] = sortarray[0]; - sortarray[0] = temp; - } - return; - } - /* Choose a random pivot to split the array. */ - pivot = (int) randomnation((unsigned int) arraysize); - pivotx = sortarray[pivot][0]; - pivoty = sortarray[pivot][1]; - /* Split the array. */ - left = -1; - right = arraysize; - while (left < right) { - /* Search for a vertex whose x-coordinate is too large for the left. */ - do { - left++; - } while ((left <= right) && ((sortarray[left][0] < pivotx) || - ((sortarray[left][0] == pivotx) && - (sortarray[left][1] < pivoty)))); - /* Search for a vertex whose x-coordinate is too small for the right. */ - do { - right--; - } while ((left <= right) && ((sortarray[right][0] > pivotx) || - ((sortarray[right][0] == pivotx) && - (sortarray[right][1] > pivoty)))); - if (left < right) { - /* Swap the left and right vertices. */ - temp = sortarray[left]; - sortarray[left] = sortarray[right]; - sortarray[right] = temp; - } - } - if (left > 1) { - /* Recursively sort the left subset. */ - vertexsort(sortarray, left); - } - if (right < arraysize - 2) { - /* Recursively sort the right subset. */ - vertexsort(&sortarray[right + 1], arraysize - right - 1); - } -} - -/*****************************************************************************/ -/* */ -/* vertexmedian() An order statistic algorithm, almost. Shuffles an */ -/* array of vertices so that the first `median' vertices */ -/* occur lexicographically before the remaining vertices. */ -/* */ -/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */ -/* if axis == 1. Very similar to the vertexsort() procedure, but runs in */ -/* randomized linear time. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void vertexmedian(vertex *sortarray, int arraysize, int median, int axis) -#else /* not ANSI_DECLARATORS */ -void vertexmedian(sortarray, arraysize, median, axis) -vertex *sortarray; -int arraysize; -int median; -int axis; -#endif /* not ANSI_DECLARATORS */ - -{ - int left, right; - int pivot; - REAL pivot1, pivot2; - vertex temp; - - if (arraysize == 2) { - /* Recursive base case. */ - if ((sortarray[0][axis] > sortarray[1][axis]) || - ((sortarray[0][axis] == sortarray[1][axis]) && - (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) { - temp = sortarray[1]; - sortarray[1] = sortarray[0]; - sortarray[0] = temp; - } - return; - } - /* Choose a random pivot to split the array. */ - pivot = (int) randomnation((unsigned int) arraysize); - pivot1 = sortarray[pivot][axis]; - pivot2 = sortarray[pivot][1 - axis]; - /* Split the array. */ - left = -1; - right = arraysize; - while (left < right) { - /* Search for a vertex whose x-coordinate is too large for the left. */ - do { - left++; - } while ((left <= right) && ((sortarray[left][axis] < pivot1) || - ((sortarray[left][axis] == pivot1) && - (sortarray[left][1 - axis] < pivot2)))); - /* Search for a vertex whose x-coordinate is too small for the right. */ - do { - right--; - } while ((left <= right) && ((sortarray[right][axis] > pivot1) || - ((sortarray[right][axis] == pivot1) && - (sortarray[right][1 - axis] > pivot2)))); - if (left < right) { - /* Swap the left and right vertices. */ - temp = sortarray[left]; - sortarray[left] = sortarray[right]; - sortarray[right] = temp; - } - } - /* Unlike in vertexsort(), at most one of the following */ - /* conditionals is true. */ - if (left > median) { - /* Recursively shuffle the left subset. */ - vertexmedian(sortarray, left, median, axis); - } - if (right < median - 1) { - /* Recursively shuffle the right subset. */ - vertexmedian(&sortarray[right + 1], arraysize - right - 1, - median - right - 1, axis); - } -} - -/*****************************************************************************/ -/* */ -/* alternateaxes() Sorts the vertices as appropriate for the divide-and- */ -/* conquer algorithm with alternating cuts. */ -/* */ -/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */ -/* For the base case, subsets containing only two or three vertices are */ -/* always sorted by x-coordinate. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void alternateaxes(vertex *sortarray, int arraysize, int axis) -#else /* not ANSI_DECLARATORS */ -void alternateaxes(sortarray, arraysize, axis) -vertex *sortarray; -int arraysize; -int axis; -#endif /* not ANSI_DECLARATORS */ - -{ - int divider; - - divider = arraysize >> 1; - if (arraysize <= 3) { - /* Recursive base case: subsets of two or three vertices will be */ - /* handled specially, and should always be sorted by x-coordinate. */ - axis = 0; - } - /* Partition with a horizontal or vertical cut. */ - vertexmedian(sortarray, arraysize, divider, axis); - /* Recursively partition the subsets with a cross cut. */ - if (arraysize - divider >= 2) { - if (divider >= 2) { - alternateaxes(sortarray, divider, 1 - axis); - } - alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis); - } -} - -/*****************************************************************************/ -/* */ -/* mergehulls() Merge two adjacent Delaunay triangulations into a */ -/* single Delaunay triangulation. */ -/* */ -/* This is similar to the algorithm given by Guibas and Stolfi, but uses */ -/* a triangle-based, rather than edge-based, data structure. */ -/* */ -/* The algorithm walks up the gap between the two triangulations, knitting */ -/* them together. As they are merged, some of their bounding triangles */ -/* are converted into real triangles of the triangulation. The procedure */ -/* pulls each hull's bounding triangles apart, then knits them together */ -/* like the teeth of two gears. The Delaunay property determines, at each */ -/* step, whether the next "tooth" is a bounding triangle of the left hull */ -/* or the right. When a bounding triangle becomes real, its apex is */ -/* changed from NULL to a real vertex. */ -/* */ -/* Only two new triangles need to be allocated. These become new bounding */ -/* triangles at the top and bottom of the seam. They are used to connect */ -/* the remaining bounding triangles (those that have not been converted */ -/* into real triangles) into a single fan. */ -/* */ -/* On entry, `farleft' and `innerleft' are bounding triangles of the left */ -/* triangulation. The origin of `farleft' is the leftmost vertex, and */ -/* the destination of `innerleft' is the rightmost vertex of the */ -/* triangulation. Similarly, `innerright' and `farright' are bounding */ -/* triangles of the right triangulation. The origin of `innerright' and */ -/* destination of `farright' are the leftmost and rightmost vertices. */ -/* */ -/* On completion, the origin of `farleft' is the leftmost vertex of the */ -/* merged triangulation, and the destination of `farright' is the rightmost */ -/* vertex. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft, - struct otri *innerleft, struct otri *innerright, - struct otri *farright, int axis) -#else /* not ANSI_DECLARATORS */ -void mergehulls(m, b, farleft, innerleft, innerright, farright, axis) -struct mesh *m; -struct behavior *b; -struct otri *farleft; -struct otri *innerleft; -struct otri *innerright; -struct otri *farright; -int axis; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri leftcand, rightcand; - struct otri baseedge; - struct otri nextedge; - struct otri sidecasing, topcasing, outercasing; - struct otri checkedge; - vertex innerleftdest; - vertex innerrightorg; - vertex innerleftapex, innerrightapex; - vertex farleftpt, farrightpt; - vertex farleftapex, farrightapex; - vertex lowerleft, lowerright; - vertex upperleft, upperright; - vertex nextapex; - vertex checkvertex; - int changemade; - int badedge; - int leftfinished, rightfinished; - triangle ptr; /* Temporary variable used by sym(). */ - - dest(*innerleft, innerleftdest); - apex(*innerleft, innerleftapex); - org(*innerright, innerrightorg); - apex(*innerright, innerrightapex); - /* Special treatment for horizontal cuts. */ - if (b->dwyer && (axis == 1)) { - org(*farleft, farleftpt); - apex(*farleft, farleftapex); - dest(*farright, farrightpt); - apex(*farright, farrightapex); - /* The pointers to the extremal vertices are shifted to point to the */ - /* topmost and bottommost vertex of each hull, rather than the */ - /* leftmost and rightmost vertices. */ - while (farleftapex[1] < farleftpt[1]) { - lnextself(*farleft); - symself(*farleft); - farleftpt = farleftapex; - apex(*farleft, farleftapex); - } - sym(*innerleft, checkedge); - apex(checkedge, checkvertex); - while (checkvertex[1] > innerleftdest[1]) { - lnext(checkedge, *innerleft); - innerleftapex = innerleftdest; - innerleftdest = checkvertex; - sym(*innerleft, checkedge); - apex(checkedge, checkvertex); - } - while (innerrightapex[1] < innerrightorg[1]) { - lnextself(*innerright); - symself(*innerright); - innerrightorg = innerrightapex; - apex(*innerright, innerrightapex); - } - sym(*farright, checkedge); - apex(checkedge, checkvertex); - while (checkvertex[1] > farrightpt[1]) { - lnext(checkedge, *farright); - farrightapex = farrightpt; - farrightpt = checkvertex; - sym(*farright, checkedge); - apex(checkedge, checkvertex); - } - } - /* Find a line tangent to and below both hulls. */ - do { - changemade = 0; - /* Make innerleftdest the "bottommost" vertex of the left hull. */ - if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) > - 0.0) { - lprevself(*innerleft); - symself(*innerleft); - innerleftdest = innerleftapex; - apex(*innerleft, innerleftapex); - changemade = 1; - } - /* Make innerrightorg the "bottommost" vertex of the right hull. */ - if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) > - 0.0) { - lnextself(*innerright); - symself(*innerright); - innerrightorg = innerrightapex; - apex(*innerright, innerrightapex); - changemade = 1; - } - } while (changemade); - /* Find the two candidates to be the next "gear tooth." */ - sym(*innerleft, leftcand); - sym(*innerright, rightcand); - /* Create the bottom new bounding triangle. */ - maketriangle(m, b, &baseedge); - /* Connect it to the bounding boxes of the left and right triangulations. */ - bond(baseedge, *innerleft); - lnextself(baseedge); - bond(baseedge, *innerright); - lnextself(baseedge); - setorg(baseedge, innerrightorg); - setdest(baseedge, innerleftdest); - /* Apex is intentionally left NULL. */ - if (b->verbose > 2) { - printf(" Creating base bounding "); - printtriangle(m, b, &baseedge); - } - /* Fix the extreme triangles if necessary. */ - org(*farleft, farleftpt); - if (innerleftdest == farleftpt) { - lnext(baseedge, *farleft); - } - dest(*farright, farrightpt); - if (innerrightorg == farrightpt) { - lprev(baseedge, *farright); - } - /* The vertices of the current knitting edge. */ - lowerleft = innerleftdest; - lowerright = innerrightorg; - /* The candidate vertices for knitting. */ - apex(leftcand, upperleft); - apex(rightcand, upperright); - /* Walk up the gap between the two triangulations, knitting them together. */ - while (1) { - /* Have we reached the top? (This isn't quite the right question, */ - /* because even though the left triangulation might seem finished now, */ - /* moving up on the right triangulation might reveal a new vertex of */ - /* the left triangulation. And vice-versa.) */ - leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <= - 0.0; - rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright) - <= 0.0; - if (leftfinished && rightfinished) { - /* Create the top new bounding triangle. */ - maketriangle(m, b, &nextedge); - setorg(nextedge, lowerleft); - setdest(nextedge, lowerright); - /* Apex is intentionally left NULL. */ - /* Connect it to the bounding boxes of the two triangulations. */ - bond(nextedge, baseedge); - lnextself(nextedge); - bond(nextedge, rightcand); - lnextself(nextedge); - bond(nextedge, leftcand); - if (b->verbose > 2) { - printf(" Creating top bounding "); - printtriangle(m, b, &nextedge); - } - /* Special treatment for horizontal cuts. */ - if (b->dwyer && (axis == 1)) { - org(*farleft, farleftpt); - apex(*farleft, farleftapex); - dest(*farright, farrightpt); - apex(*farright, farrightapex); - sym(*farleft, checkedge); - apex(checkedge, checkvertex); - /* The pointers to the extremal vertices are restored to the */ - /* leftmost and rightmost vertices (rather than topmost and */ - /* bottommost). */ - while (checkvertex[0] < farleftpt[0]) { - lprev(checkedge, *farleft); - farleftapex = farleftpt; - farleftpt = checkvertex; - sym(*farleft, checkedge); - apex(checkedge, checkvertex); - } - while (farrightapex[0] > farrightpt[0]) { - lprevself(*farright); - symself(*farright); - farrightpt = farrightapex; - apex(*farright, farrightapex); - } - } - return; - } - /* Consider eliminating edges from the left triangulation. */ - if (!leftfinished) { - /* What vertex would be exposed if an edge were deleted? */ - lprev(leftcand, nextedge); - symself(nextedge); - apex(nextedge, nextapex); - /* If nextapex is NULL, then no vertex would be exposed; the */ - /* triangulation would have been eaten right through. */ - if (nextapex != (vertex) NULL) { - /* Check whether the edge is Delaunay. */ - badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) > - 0.0; - while (badedge) { - /* Eliminate the edge with an edge flip. As a result, the */ - /* left triangulation will have one more boundary triangle. */ - lnextself(nextedge); - sym(nextedge, topcasing); - lnextself(nextedge); - sym(nextedge, sidecasing); - bond(nextedge, topcasing); - bond(leftcand, sidecasing); - lnextself(leftcand); - sym(leftcand, outercasing); - lprevself(nextedge); - bond(nextedge, outercasing); - /* Correct the vertices to reflect the edge flip. */ - setorg(leftcand, lowerleft); - setdest(leftcand, NULL); - setapex(leftcand, nextapex); - setorg(nextedge, NULL); - setdest(nextedge, upperleft); - setapex(nextedge, nextapex); - /* Consider the newly exposed vertex. */ - upperleft = nextapex; - /* What vertex would be exposed if another edge were deleted? */ - otricopy(sidecasing, nextedge); - apex(nextedge, nextapex); - if (nextapex != (vertex) NULL) { - /* Check whether the edge is Delaunay. */ - badedge = incircle(m, b, lowerleft, lowerright, upperleft, - nextapex) > 0.0; - } else { - /* Avoid eating right through the triangulation. */ - badedge = 0; - } - } - } - } - /* Consider eliminating edges from the right triangulation. */ - if (!rightfinished) { - /* What vertex would be exposed if an edge were deleted? */ - lnext(rightcand, nextedge); - symself(nextedge); - apex(nextedge, nextapex); - /* If nextapex is NULL, then no vertex would be exposed; the */ - /* triangulation would have been eaten right through. */ - if (nextapex != (vertex) NULL) { - /* Check whether the edge is Delaunay. */ - badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) > - 0.0; - while (badedge) { - /* Eliminate the edge with an edge flip. As a result, the */ - /* right triangulation will have one more boundary triangle. */ - lprevself(nextedge); - sym(nextedge, topcasing); - lprevself(nextedge); - sym(nextedge, sidecasing); - bond(nextedge, topcasing); - bond(rightcand, sidecasing); - lprevself(rightcand); - sym(rightcand, outercasing); - lnextself(nextedge); - bond(nextedge, outercasing); - /* Correct the vertices to reflect the edge flip. */ - setorg(rightcand, NULL); - setdest(rightcand, lowerright); - setapex(rightcand, nextapex); - setorg(nextedge, upperright); - setdest(nextedge, NULL); - setapex(nextedge, nextapex); - /* Consider the newly exposed vertex. */ - upperright = nextapex; - /* What vertex would be exposed if another edge were deleted? */ - otricopy(sidecasing, nextedge); - apex(nextedge, nextapex); - if (nextapex != (vertex) NULL) { - /* Check whether the edge is Delaunay. */ - badedge = incircle(m, b, lowerleft, lowerright, upperright, - nextapex) > 0.0; - } else { - /* Avoid eating right through the triangulation. */ - badedge = 0; - } - } - } - } - if (leftfinished || (!rightfinished && - (incircle(m, b, upperleft, lowerleft, lowerright, upperright) > - 0.0))) { - /* Knit the triangulations, adding an edge from `lowerleft' */ - /* to `upperright'. */ - bond(baseedge, rightcand); - lprev(rightcand, baseedge); - setdest(baseedge, lowerleft); - lowerright = upperright; - sym(baseedge, rightcand); - apex(rightcand, upperright); - } else { - /* Knit the triangulations, adding an edge from `upperleft' */ - /* to `lowerright'. */ - bond(baseedge, leftcand); - lnext(leftcand, baseedge); - setorg(baseedge, lowerright); - lowerleft = upperleft; - sym(baseedge, leftcand); - apex(leftcand, upperleft); - } - if (b->verbose > 2) { - printf(" Connecting "); - printtriangle(m, b, &baseedge); - } - } -} - -/*****************************************************************************/ -/* */ -/* divconqrecurse() Recursively form a Delaunay triangulation by the */ -/* divide-and-conquer method. */ -/* */ -/* Recursively breaks down the problem into smaller pieces, which are */ -/* knitted together by mergehulls(). The base cases (problems of two or */ -/* three vertices) are handled specially here. */ -/* */ -/* On completion, `farleft' and `farright' are bounding triangles such that */ -/* the origin of `farleft' is the leftmost vertex (breaking ties by */ -/* choosing the highest leftmost vertex), and the destination of */ -/* `farright' is the rightmost vertex (breaking ties by choosing the */ -/* lowest rightmost vertex). */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray, - int vertices, int axis, - struct otri *farleft, struct otri *farright) -#else /* not ANSI_DECLARATORS */ -void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright) -struct mesh *m; -struct behavior *b; -vertex *sortarray; -int vertices; -int axis; -struct otri *farleft; -struct otri *farright; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri midtri, tri1, tri2, tri3; - struct otri innerleft, innerright; - REAL area; - int divider; - - if (b->verbose > 2) { - printf(" Triangulating %d vertices.\n", vertices); - } - if (vertices == 2) { - /* The triangulation of two vertices is an edge. An edge is */ - /* represented by two bounding triangles. */ - maketriangle(m, b, farleft); - setorg(*farleft, sortarray[0]); - setdest(*farleft, sortarray[1]); - /* The apex is intentionally left NULL. */ - maketriangle(m, b, farright); - setorg(*farright, sortarray[1]); - setdest(*farright, sortarray[0]); - /* The apex is intentionally left NULL. */ - bond(*farleft, *farright); - lprevself(*farleft); - lnextself(*farright); - bond(*farleft, *farright); - lprevself(*farleft); - lnextself(*farright); - bond(*farleft, *farright); - if (b->verbose > 2) { - printf(" Creating "); - printtriangle(m, b, farleft); - printf(" Creating "); - printtriangle(m, b, farright); - } - /* Ensure that the origin of `farleft' is sortarray[0]. */ - lprev(*farright, *farleft); - return; - } else if (vertices == 3) { - /* The triangulation of three vertices is either a triangle (with */ - /* three bounding triangles) or two edges (with four bounding */ - /* triangles). In either case, four triangles are created. */ - maketriangle(m, b, &midtri); - maketriangle(m, b, &tri1); - maketriangle(m, b, &tri2); - maketriangle(m, b, &tri3); - area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]); - if (area == 0.0) { - /* Three collinear vertices; the triangulation is two edges. */ - setorg(midtri, sortarray[0]); - setdest(midtri, sortarray[1]); - setorg(tri1, sortarray[1]); - setdest(tri1, sortarray[0]); - setorg(tri2, sortarray[2]); - setdest(tri2, sortarray[1]); - setorg(tri3, sortarray[1]); - setdest(tri3, sortarray[2]); - /* All apices are intentionally left NULL. */ - bond(midtri, tri1); - bond(tri2, tri3); - lnextself(midtri); - lprevself(tri1); - lnextself(tri2); - lprevself(tri3); - bond(midtri, tri3); - bond(tri1, tri2); - lnextself(midtri); - lprevself(tri1); - lnextself(tri2); - lprevself(tri3); - bond(midtri, tri1); - bond(tri2, tri3); - /* Ensure that the origin of `farleft' is sortarray[0]. */ - otricopy(tri1, *farleft); - /* Ensure that the destination of `farright' is sortarray[2]. */ - otricopy(tri2, *farright); - } else { - /* The three vertices are not collinear; the triangulation is one */ - /* triangle, namely `midtri'. */ - setorg(midtri, sortarray[0]); - setdest(tri1, sortarray[0]); - setorg(tri3, sortarray[0]); - /* Apices of tri1, tri2, and tri3 are left NULL. */ - if (area > 0.0) { - /* The vertices are in counterclockwise order. */ - setdest(midtri, sortarray[1]); - setorg(tri1, sortarray[1]); - setdest(tri2, sortarray[1]); - setapex(midtri, sortarray[2]); - setorg(tri2, sortarray[2]); - setdest(tri3, sortarray[2]); - } else { - /* The vertices are in clockwise order. */ - setdest(midtri, sortarray[2]); - setorg(tri1, sortarray[2]); - setdest(tri2, sortarray[2]); - setapex(midtri, sortarray[1]); - setorg(tri2, sortarray[1]); - setdest(tri3, sortarray[1]); - } - /* The topology does not depend on how the vertices are ordered. */ - bond(midtri, tri1); - lnextself(midtri); - bond(midtri, tri2); - lnextself(midtri); - bond(midtri, tri3); - lprevself(tri1); - lnextself(tri2); - bond(tri1, tri2); - lprevself(tri1); - lprevself(tri3); - bond(tri1, tri3); - lnextself(tri2); - lprevself(tri3); - bond(tri2, tri3); - /* Ensure that the origin of `farleft' is sortarray[0]. */ - otricopy(tri1, *farleft); - /* Ensure that the destination of `farright' is sortarray[2]. */ - if (area > 0.0) { - otricopy(tri2, *farright); - } else { - lnext(*farleft, *farright); - } - } - if (b->verbose > 2) { - printf(" Creating "); - printtriangle(m, b, &midtri); - printf(" Creating "); - printtriangle(m, b, &tri1); - printf(" Creating "); - printtriangle(m, b, &tri2); - printf(" Creating "); - printtriangle(m, b, &tri3); - } - return; - } else { - /* Split the vertices in half. */ - divider = vertices >> 1; - /* Recursively triangulate each half. */ - divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft); - divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis, - &innerright, farright); - if (b->verbose > 1) { - printf(" Joining triangulations with %d and %d vertices.\n", divider, - vertices - divider); - } - /* Merge the two triangulations into one. */ - mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis); - } -} - -#ifdef ANSI_DECLARATORS -long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost) -#else /* not ANSI_DECLARATORS */ -long removeghosts(m, b, startghost) -struct mesh *m; -struct behavior *b; -struct otri *startghost; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri searchedge; - struct otri dissolveedge; - struct otri deadtriangle; - vertex markorg; - long hullsize; - triangle ptr; /* Temporary variable used by sym(). */ - - if (b->verbose) { - printf(" Removing ghost triangles.\n"); - } - /* Find an edge on the convex hull to start point location from. */ - lprev(*startghost, searchedge); - symself(searchedge); - m->dummytri[0] = encode(searchedge); - /* Remove the bounding box and count the convex hull edges. */ - otricopy(*startghost, dissolveedge); - hullsize = 0; - do { - hullsize++; - lnext(dissolveedge, deadtriangle); - lprevself(dissolveedge); - symself(dissolveedge); - /* If no PSLG is involved, set the boundary markers of all the vertices */ - /* on the convex hull. If a PSLG is used, this step is done later. */ - if (!b->poly) { - /* Watch out for the case where all the input vertices are collinear. */ - if (dissolveedge.tri != m->dummytri) { - org(dissolveedge, markorg); - if (vertexmark(markorg) == 0) { - setvertexmark(markorg, 1); - } - } - } - /* Remove a bounding triangle from a convex hull triangle. */ - dissolve(dissolveedge); - /* Find the next bounding triangle. */ - sym(deadtriangle, dissolveedge); - /* Delete the bounding triangle. */ - triangledealloc(m, deadtriangle.tri); - } while (!otriequal(dissolveedge, *startghost)); - return hullsize; -} - -/*****************************************************************************/ -/* */ -/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */ -/* conquer method. */ -/* */ -/* Sorts the vertices, calls a recursive procedure to triangulate them, and */ -/* removes the bounding box, setting boundary markers as appropriate. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -long divconqdelaunay(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -long divconqdelaunay(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - vertex *sortarray; - struct otri hullleft, hullright; - int divider; - int i, j; - - if (b->verbose) { - printf(" Sorting vertices.\n"); - } - - /* Allocate an array of pointers to vertices for sorting. */ - sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex)); - traversalinit(&m->vertices); - for (i = 0; i < m->invertices; i++) { - sortarray[i] = vertextraverse(m); - } - /* Sort the vertices. */ - vertexsort(sortarray, m->invertices); - /* Discard duplicate vertices, which can really mess up the algorithm. */ - i = 0; - for (j = 1; j < m->invertices; j++) { - if ((sortarray[i][0] == sortarray[j][0]) - && (sortarray[i][1] == sortarray[j][1])) { - if (!b->quiet) { - printf( -"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", - sortarray[j][0], sortarray[j][1]); - } - setvertextype(sortarray[j], UNDEADVERTEX); - m->undeads++; - } else { - i++; - sortarray[i] = sortarray[j]; - } - } - i++; - if (b->dwyer) { - /* Re-sort the array of vertices to accommodate alternating cuts. */ - divider = i >> 1; - if (i - divider >= 2) { - if (divider >= 2) { - alternateaxes(sortarray, divider, 1); - } - alternateaxes(&sortarray[divider], i - divider, 1); - } - } - - if (b->verbose) { - printf(" Forming triangulation.\n"); - } - - /* Form the Delaunay triangulation. */ - divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright); - trifree((VOID *) sortarray); - - return removeghosts(m, b, &hullleft); -} - -/** **/ -/** **/ -/********* Divide-and-conquer Delaunay triangulation ends here *********/ - -/********* Incremental Delaunay triangulation begins here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* boundingbox() Form an "infinite" bounding triangle to insert vertices */ -/* into. */ -/* */ -/* The vertices at "infinity" are assigned finite coordinates, which are */ -/* used by the point location routines, but (mostly) ignored by the */ -/* Delaunay edge flip routines. */ -/* */ -/*****************************************************************************/ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -void boundingbox(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void boundingbox(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri inftri; /* Handle for the triangular bounding box. */ - REAL width; - - if (b->verbose) { - printf(" Creating triangular bounding box.\n"); - } - /* Find the width (or height, whichever is larger) of the triangulation. */ - width = m->xmax - m->xmin; - if (m->ymax - m->ymin > width) { - width = m->ymax - m->ymin; - } - if (width == 0.0) { - width = 1.0; - } - /* Create the vertices of the bounding box. */ - m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes); - m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes); - m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes); - m->infvertex1[0] = m->xmin - 50.0 * width; - m->infvertex1[1] = m->ymin - 40.0 * width; - m->infvertex2[0] = m->xmax + 50.0 * width; - m->infvertex2[1] = m->ymin - 40.0 * width; - m->infvertex3[0] = 0.5 * (m->xmin + m->xmax); - m->infvertex3[1] = m->ymax + 60.0 * width; - - /* Create the bounding box. */ - maketriangle(m, b, &inftri); - setorg(inftri, m->infvertex1); - setdest(inftri, m->infvertex2); - setapex(inftri, m->infvertex3); - /* Link dummytri to the bounding box so we can always find an */ - /* edge to begin searching (point location) from. */ - m->dummytri[0] = (triangle) inftri.tri; - if (b->verbose > 2) { - printf(" Creating "); - printtriangle(m, b, &inftri); - } -} - -#endif /* not REDUCED */ - -/*****************************************************************************/ -/* */ -/* removebox() Remove the "infinite" bounding triangle, setting boundary */ -/* markers as appropriate. */ -/* */ -/* The triangular bounding box has three boundary triangles (one for each */ -/* side of the bounding box), and a bunch of triangles fanning out from */ -/* the three bounding box vertices (one triangle for each edge of the */ -/* convex hull of the inner mesh). This routine removes these triangles. */ -/* */ -/* Returns the number of edges on the convex hull of the triangulation. */ -/* */ -/*****************************************************************************/ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -long removebox(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -long removebox(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri deadtriangle; - struct otri searchedge; - struct otri checkedge; - struct otri nextedge, finaledge, dissolveedge; - vertex markorg; - long hullsize; - triangle ptr; /* Temporary variable used by sym(). */ - - if (b->verbose) { - printf(" Removing triangular bounding box.\n"); - } - /* Find a boundary triangle. */ - nextedge.tri = m->dummytri; - nextedge.orient = 0; - symself(nextedge); - /* Mark a place to stop. */ - lprev(nextedge, finaledge); - lnextself(nextedge); - symself(nextedge); - /* Find a triangle (on the boundary of the vertex set) that isn't */ - /* a bounding box triangle. */ - lprev(nextedge, searchedge); - symself(searchedge); - /* Check whether nextedge is another boundary triangle */ - /* adjacent to the first one. */ - lnext(nextedge, checkedge); - symself(checkedge); - if (checkedge.tri == m->dummytri) { - /* Go on to the next triangle. There are only three boundary */ - /* triangles, and this next triangle cannot be the third one, */ - /* so it's safe to stop here. */ - lprevself(searchedge); - symself(searchedge); - } - /* Find a new boundary edge to search from, as the current search */ - /* edge lies on a bounding box triangle and will be deleted. */ - m->dummytri[0] = encode(searchedge); - hullsize = -2l; - while (!otriequal(nextedge, finaledge)) { - hullsize++; - lprev(nextedge, dissolveedge); - symself(dissolveedge); - /* If not using a PSLG, the vertices should be marked now. */ - /* (If using a PSLG, markhull() will do the job.) */ - if (!b->poly) { - /* Be careful! One must check for the case where all the input */ - /* vertices are collinear, and thus all the triangles are part of */ - /* the bounding box. Otherwise, the setvertexmark() call below */ - /* will cause a bad pointer reference. */ - if (dissolveedge.tri != m->dummytri) { - org(dissolveedge, markorg); - if (vertexmark(markorg) == 0) { - setvertexmark(markorg, 1); - } - } - } - /* Disconnect the bounding box triangle from the mesh triangle. */ - dissolve(dissolveedge); - lnext(nextedge, deadtriangle); - sym(deadtriangle, nextedge); - /* Get rid of the bounding box triangle. */ - triangledealloc(m, deadtriangle.tri); - /* Do we need to turn the corner? */ - if (nextedge.tri == m->dummytri) { - /* Turn the corner. */ - otricopy(dissolveedge, nextedge); - } - } - triangledealloc(m, finaledge.tri); - - trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */ - trifree((VOID *) m->infvertex2); - trifree((VOID *) m->infvertex3); - - return hullsize; -} - -#endif /* not REDUCED */ - -/*****************************************************************************/ -/* */ -/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */ -/* inserting vertices. */ -/* */ -/* Returns the number of edges on the convex hull of the triangulation. */ -/* */ -/*****************************************************************************/ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -long incrementaldelaunay(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -long incrementaldelaunay(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri starttri; - vertex vertexloop; - - /* Create a triangular bounding box. */ - boundingbox(m, b); - if (b->verbose) { - printf(" Incrementally inserting vertices.\n"); - } - traversalinit(&m->vertices); - vertexloop = vertextraverse(m); - while (vertexloop != (vertex) NULL) { - starttri.tri = m->dummytri; - if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0) - == DUPLICATEVERTEX) { - if (!b->quiet) { - printf( -"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", - vertexloop[0], vertexloop[1]); - } - setvertextype(vertexloop, UNDEADVERTEX); - m->undeads++; - } - vertexloop = vertextraverse(m); - } - /* Remove the bounding box. */ - return removebox(m, b); -} - -#endif /* not REDUCED */ - -/** **/ -/** **/ -/********* Incremental Delaunay triangulation ends here *********/ - -/********* Sweepline Delaunay triangulation begins here *********/ -/** **/ -/** **/ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -void eventheapinsert(struct event **heap, int heapsize, struct event *newevent) -#else /* not ANSI_DECLARATORS */ -void eventheapinsert(heap, heapsize, newevent) -struct event **heap; -int heapsize; -struct event *newevent; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL eventx, eventy; - int eventnum; - int parent; - int notdone; - - eventx = newevent->xkey; - eventy = newevent->ykey; - eventnum = heapsize; - notdone = eventnum > 0; - while (notdone) { - parent = (eventnum - 1) >> 1; - if ((heap[parent]->ykey < eventy) || - ((heap[parent]->ykey == eventy) - && (heap[parent]->xkey <= eventx))) { - notdone = 0; - } else { - heap[eventnum] = heap[parent]; - heap[eventnum]->heapposition = eventnum; - - eventnum = parent; - notdone = eventnum > 0; - } - } - heap[eventnum] = newevent; - newevent->heapposition = eventnum; -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -void eventheapify(struct event **heap, int heapsize, int eventnum) -#else /* not ANSI_DECLARATORS */ -void eventheapify(heap, heapsize, eventnum) -struct event **heap; -int heapsize; -int eventnum; -#endif /* not ANSI_DECLARATORS */ - -{ - struct event *thisevent; - REAL eventx, eventy; - int leftchild, rightchild; - int smallest; - int notdone; - - thisevent = heap[eventnum]; - eventx = thisevent->xkey; - eventy = thisevent->ykey; - leftchild = 2 * eventnum + 1; - notdone = leftchild < heapsize; - while (notdone) { - if ((heap[leftchild]->ykey < eventy) || - ((heap[leftchild]->ykey == eventy) - && (heap[leftchild]->xkey < eventx))) { - smallest = leftchild; - } else { - smallest = eventnum; - } - rightchild = leftchild + 1; - if (rightchild < heapsize) { - if ((heap[rightchild]->ykey < heap[smallest]->ykey) || - ((heap[rightchild]->ykey == heap[smallest]->ykey) - && (heap[rightchild]->xkey < heap[smallest]->xkey))) { - smallest = rightchild; - } - } - if (smallest == eventnum) { - notdone = 0; - } else { - heap[eventnum] = heap[smallest]; - heap[eventnum]->heapposition = eventnum; - heap[smallest] = thisevent; - thisevent->heapposition = smallest; - - eventnum = smallest; - leftchild = 2 * eventnum + 1; - notdone = leftchild < heapsize; - } - } -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -void eventheapdelete(struct event **heap, int heapsize, int eventnum) -#else /* not ANSI_DECLARATORS */ -void eventheapdelete(heap, heapsize, eventnum) -struct event **heap; -int heapsize; -int eventnum; -#endif /* not ANSI_DECLARATORS */ - -{ - struct event *moveevent; - REAL eventx, eventy; - int parent; - int notdone; - - moveevent = heap[heapsize - 1]; - if (eventnum > 0) { - eventx = moveevent->xkey; - eventy = moveevent->ykey; - do { - parent = (eventnum - 1) >> 1; - if ((heap[parent]->ykey < eventy) || - ((heap[parent]->ykey == eventy) - && (heap[parent]->xkey <= eventx))) { - notdone = 0; - } else { - heap[eventnum] = heap[parent]; - heap[eventnum]->heapposition = eventnum; - - eventnum = parent; - notdone = eventnum > 0; - } - } while (notdone); - } - heap[eventnum] = moveevent; - moveevent->heapposition = eventnum; - eventheapify(heap, heapsize - 1, eventnum); -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -void createeventheap(struct mesh *m, struct event ***eventheap, - struct event **events, struct event **freeevents) -#else /* not ANSI_DECLARATORS */ -void createeventheap(m, eventheap, events, freeevents) -struct mesh *m; -struct event ***eventheap; -struct event **events; -struct event **freeevents; -#endif /* not ANSI_DECLARATORS */ - -{ - vertex thisvertex; - int maxevents; - int i; - - maxevents = (3 * m->invertices) / 2; - *eventheap = (struct event **) trimalloc(maxevents * - (int) sizeof(struct event *)); - *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event)); - traversalinit(&m->vertices); - for (i = 0; i < m->invertices; i++) { - thisvertex = vertextraverse(m); - (*events)[i].eventptr = (VOID *) thisvertex; - (*events)[i].xkey = thisvertex[0]; - (*events)[i].ykey = thisvertex[1]; - eventheapinsert(*eventheap, i, *events + i); - } - *freeevents = (struct event *) NULL; - for (i = maxevents - 1; i >= m->invertices; i--) { - (*events)[i].eventptr = (VOID *) *freeevents; - *freeevents = *events + i; - } -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite) -#else /* not ANSI_DECLARATORS */ -int rightofhyperbola(m, fronttri, newsite) -struct mesh *m; -struct otri *fronttri; -vertex newsite; -#endif /* not ANSI_DECLARATORS */ - -{ - vertex leftvertex, rightvertex; - REAL dxa, dya, dxb, dyb; - - m->hyperbolacount++; - - dest(*fronttri, leftvertex); - apex(*fronttri, rightvertex); - if ((leftvertex[1] < rightvertex[1]) || - ((leftvertex[1] == rightvertex[1]) && - (leftvertex[0] < rightvertex[0]))) { - if (newsite[0] >= rightvertex[0]) { - return 1; - } - } else { - if (newsite[0] <= leftvertex[0]) { - return 0; - } - } - dxa = leftvertex[0] - newsite[0]; - dya = leftvertex[1] - newsite[1]; - dxb = rightvertex[0] - newsite[0]; - dyb = rightvertex[1] - newsite[1]; - return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya); -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc) -#else /* not ANSI_DECLARATORS */ -REAL circletop(m, pa, pb, pc, ccwabc) -struct mesh *m; -vertex pa; -vertex pb; -vertex pc; -REAL ccwabc; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL xac, yac, xbc, ybc, xab, yab; - REAL aclen2, bclen2, ablen2; - - m->circletopcount++; - - xac = pa[0] - pc[0]; - yac = pa[1] - pc[1]; - xbc = pb[0] - pc[0]; - ybc = pb[1] - pc[1]; - xab = pa[0] - pb[0]; - yab = pa[1] - pb[1]; - aclen2 = xac * xac + yac * yac; - bclen2 = xbc * xbc + ybc * ybc; - ablen2 = xab * xab + yab * yab; - return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2)) - / (2.0 * ccwabc); -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -void check4deadevent(struct otri *checktri, struct event **freeevents, - struct event **eventheap, int *heapsize) -#else /* not ANSI_DECLARATORS */ -void check4deadevent(checktri, freeevents, eventheap, heapsize) -struct otri *checktri; -struct event **freeevents; -struct event **eventheap; -int *heapsize; -#endif /* not ANSI_DECLARATORS */ - -{ - struct event *deadevent; - vertex eventvertex; - int eventnum; - - org(*checktri, eventvertex); - if (eventvertex != (vertex) NULL) { - deadevent = (struct event *) eventvertex; - eventnum = deadevent->heapposition; - deadevent->eventptr = (VOID *) *freeevents; - *freeevents = deadevent; - eventheapdelete(eventheap, *heapsize, eventnum); - (*heapsize)--; - setorg(*checktri, NULL); - } -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -struct splaynode *splay(struct mesh *m, struct splaynode *splaytree, - vertex searchpoint, struct otri *searchtri) -#else /* not ANSI_DECLARATORS */ -struct splaynode *splay(m, splaytree, searchpoint, searchtri) -struct mesh *m; -struct splaynode *splaytree; -vertex searchpoint; -struct otri *searchtri; -#endif /* not ANSI_DECLARATORS */ - -{ - struct splaynode *child, *grandchild; - struct splaynode *lefttree, *righttree; - struct splaynode *leftright; - vertex checkvertex; - int rightofroot, rightofchild; - - if (splaytree == (struct splaynode *) NULL) { - return (struct splaynode *) NULL; - } - dest(splaytree->keyedge, checkvertex); - if (checkvertex == splaytree->keydest) { - rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint); - if (rightofroot) { - otricopy(splaytree->keyedge, *searchtri); - child = splaytree->rchild; - } else { - child = splaytree->lchild; - } - if (child == (struct splaynode *) NULL) { - return splaytree; - } - dest(child->keyedge, checkvertex); - if (checkvertex != child->keydest) { - child = splay(m, child, searchpoint, searchtri); - if (child == (struct splaynode *) NULL) { - if (rightofroot) { - splaytree->rchild = (struct splaynode *) NULL; - } else { - splaytree->lchild = (struct splaynode *) NULL; - } - return splaytree; - } - } - rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint); - if (rightofchild) { - otricopy(child->keyedge, *searchtri); - grandchild = splay(m, child->rchild, searchpoint, searchtri); - child->rchild = grandchild; - } else { - grandchild = splay(m, child->lchild, searchpoint, searchtri); - child->lchild = grandchild; - } - if (grandchild == (struct splaynode *) NULL) { - if (rightofroot) { - splaytree->rchild = child->lchild; - child->lchild = splaytree; - } else { - splaytree->lchild = child->rchild; - child->rchild = splaytree; - } - return child; - } - if (rightofchild) { - if (rightofroot) { - splaytree->rchild = child->lchild; - child->lchild = splaytree; - } else { - splaytree->lchild = grandchild->rchild; - grandchild->rchild = splaytree; - } - child->rchild = grandchild->lchild; - grandchild->lchild = child; - } else { - if (rightofroot) { - splaytree->rchild = grandchild->lchild; - grandchild->lchild = splaytree; - } else { - splaytree->lchild = child->rchild; - child->rchild = splaytree; - } - child->lchild = grandchild->rchild; - grandchild->rchild = child; - } - return grandchild; - } else { - lefttree = splay(m, splaytree->lchild, searchpoint, searchtri); - righttree = splay(m, splaytree->rchild, searchpoint, searchtri); - - pooldealloc(&m->splaynodes, (VOID *) splaytree); - if (lefttree == (struct splaynode *) NULL) { - return righttree; - } else if (righttree == (struct splaynode *) NULL) { - return lefttree; - } else if (lefttree->rchild == (struct splaynode *) NULL) { - lefttree->rchild = righttree->lchild; - righttree->lchild = lefttree; - return righttree; - } else if (righttree->lchild == (struct splaynode *) NULL) { - righttree->lchild = lefttree->rchild; - lefttree->rchild = righttree; - return lefttree; - } else { -/* printf("Holy Toledo!!!\n"); */ - leftright = lefttree->rchild; - while (leftright->rchild != (struct splaynode *) NULL) { - leftright = leftright->rchild; - } - leftright->rchild = righttree; - return lefttree; - } - } -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot, - struct otri *newkey, vertex searchpoint) -#else /* not ANSI_DECLARATORS */ -struct splaynode *splayinsert(m, splayroot, newkey, searchpoint) -struct mesh *m; -struct splaynode *splayroot; -struct otri *newkey; -vertex searchpoint; -#endif /* not ANSI_DECLARATORS */ - -{ - struct splaynode *newsplaynode; - - newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes); - otricopy(*newkey, newsplaynode->keyedge); - dest(*newkey, newsplaynode->keydest); - if (splayroot == (struct splaynode *) NULL) { - newsplaynode->lchild = (struct splaynode *) NULL; - newsplaynode->rchild = (struct splaynode *) NULL; - } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) { - newsplaynode->lchild = splayroot; - newsplaynode->rchild = splayroot->rchild; - splayroot->rchild = (struct splaynode *) NULL; - } else { - newsplaynode->lchild = splayroot->lchild; - newsplaynode->rchild = splayroot; - splayroot->lchild = (struct splaynode *) NULL; - } - return newsplaynode; -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -struct splaynode *circletopinsert(struct mesh *m, struct behavior *b, - struct splaynode *splayroot, - struct otri *newkey, - vertex pa, vertex pb, vertex pc, REAL topy) -#else /* not ANSI_DECLARATORS */ -struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy) -struct mesh *m; -struct behavior *b; -struct splaynode *splayroot; -struct otri *newkey; -vertex pa; -vertex pb; -vertex pc; -REAL topy; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL ccwabc; - REAL xac, yac, xbc, ybc; - REAL aclen2, bclen2; - REAL searchpoint[2]; - struct otri dummytri; - - ccwabc = counterclockwise(m, b, pa, pb, pc); - xac = pa[0] - pc[0]; - yac = pa[1] - pc[1]; - xbc = pb[0] - pc[0]; - ybc = pb[1] - pc[1]; - aclen2 = xac * xac + yac * yac; - bclen2 = xbc * xbc + ybc * ybc; - searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc); - searchpoint[1] = topy; - return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri), - newkey, (vertex) searchpoint); -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot, - struct otri *bottommost, vertex searchvertex, - struct otri *searchtri, int *farright) -#else /* not ANSI_DECLARATORS */ -struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex, - searchtri, farright) -struct mesh *m; -struct splaynode *splayroot; -struct otri *bottommost; -vertex searchvertex; -struct otri *searchtri; -int *farright; -#endif /* not ANSI_DECLARATORS */ - -{ - int farrightflag; - triangle ptr; /* Temporary variable used by onext(). */ - - otricopy(*bottommost, *searchtri); - splayroot = splay(m, splayroot, searchvertex, searchtri); - - farrightflag = 0; - while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) { - onextself(*searchtri); - farrightflag = otriequal(*searchtri, *bottommost); - } - *farright = farrightflag; - return splayroot; -} - -#endif /* not REDUCED */ - -#ifndef REDUCED - -#ifdef ANSI_DECLARATORS -long sweeplinedelaunay(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -long sweeplinedelaunay(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct event **eventheap; - struct event *events; - struct event *freeevents; - struct event *nextevent; - struct event *newevent; - struct splaynode *splayroot; - struct otri bottommost; - struct otri searchtri; - struct otri fliptri; - struct otri lefttri, righttri, farlefttri, farrighttri; - struct otri inserttri; - vertex firstvertex, secondvertex; - vertex nextvertex, lastvertex; - vertex connectvertex; - vertex leftvertex, midvertex, rightvertex; - REAL lefttest, righttest; - int heapsize; - int check4events, farrightflag; - triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ - - poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK, - SPLAYNODEPERBLOCK, 0); - splayroot = (struct splaynode *) NULL; - - if (b->verbose) { - printf(" Placing vertices in event heap.\n"); - } - createeventheap(m, &eventheap, &events, &freeevents); - heapsize = m->invertices; - - if (b->verbose) { - printf(" Forming triangulation.\n"); - } - maketriangle(m, b, &lefttri); - maketriangle(m, b, &righttri); - bond(lefttri, righttri); - lnextself(lefttri); - lprevself(righttri); - bond(lefttri, righttri); - lnextself(lefttri); - lprevself(righttri); - bond(lefttri, righttri); - firstvertex = (vertex) eventheap[0]->eventptr; - eventheap[0]->eventptr = (VOID *) freeevents; - freeevents = eventheap[0]; - eventheapdelete(eventheap, heapsize, 0); - heapsize--; - do { - if (heapsize == 0) { - printf("Error: Input vertices are all identical.\n"); - triexit(1); - } - secondvertex = (vertex) eventheap[0]->eventptr; - eventheap[0]->eventptr = (VOID *) freeevents; - freeevents = eventheap[0]; - eventheapdelete(eventheap, heapsize, 0); - heapsize--; - if ((firstvertex[0] == secondvertex[0]) && - (firstvertex[1] == secondvertex[1])) { - if (!b->quiet) { - printf( -"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", - secondvertex[0], secondvertex[1]); - } - setvertextype(secondvertex, UNDEADVERTEX); - m->undeads++; - } - } while ((firstvertex[0] == secondvertex[0]) && - (firstvertex[1] == secondvertex[1])); - setorg(lefttri, firstvertex); - setdest(lefttri, secondvertex); - setorg(righttri, secondvertex); - setdest(righttri, firstvertex); - lprev(lefttri, bottommost); - lastvertex = secondvertex; - while (heapsize > 0) { - nextevent = eventheap[0]; - eventheapdelete(eventheap, heapsize, 0); - heapsize--; - check4events = 1; - if (nextevent->xkey < m->xmin) { - decode(nextevent->eventptr, fliptri); - oprev(fliptri, farlefttri); - check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize); - onext(fliptri, farrighttri); - check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize); - - if (otriequal(farlefttri, bottommost)) { - lprev(fliptri, bottommost); - } - flip(m, b, &fliptri); - setapex(fliptri, NULL); - lprev(fliptri, lefttri); - lnext(fliptri, righttri); - sym(lefttri, farlefttri); - - if (randomnation(SAMPLERATE) == 0) { - symself(fliptri); - dest(fliptri, leftvertex); - apex(fliptri, midvertex); - org(fliptri, rightvertex); - splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex, - midvertex, rightvertex, nextevent->ykey); - } - } else { - nextvertex = (vertex) nextevent->eventptr; - if ((nextvertex[0] == lastvertex[0]) && - (nextvertex[1] == lastvertex[1])) { - if (!b->quiet) { - printf( -"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", - nextvertex[0], nextvertex[1]); - } - setvertextype(nextvertex, UNDEADVERTEX); - m->undeads++; - check4events = 0; - } else { - lastvertex = nextvertex; - - splayroot = frontlocate(m, splayroot, &bottommost, nextvertex, - &searchtri, &farrightflag); -/* - otricopy(bottommost, searchtri); - farrightflag = 0; - while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) { - onextself(searchtri); - farrightflag = otriequal(searchtri, bottommost); - } -*/ - - check4deadevent(&searchtri, &freeevents, eventheap, &heapsize); - - otricopy(searchtri, farrighttri); - sym(searchtri, farlefttri); - maketriangle(m, b, &lefttri); - maketriangle(m, b, &righttri); - dest(farrighttri, connectvertex); - setorg(lefttri, connectvertex); - setdest(lefttri, nextvertex); - setorg(righttri, nextvertex); - setdest(righttri, connectvertex); - bond(lefttri, righttri); - lnextself(lefttri); - lprevself(righttri); - bond(lefttri, righttri); - lnextself(lefttri); - lprevself(righttri); - bond(lefttri, farlefttri); - bond(righttri, farrighttri); - if (!farrightflag && otriequal(farrighttri, bottommost)) { - otricopy(lefttri, bottommost); - } - - if (randomnation(SAMPLERATE) == 0) { - splayroot = splayinsert(m, splayroot, &lefttri, nextvertex); - } else if (randomnation(SAMPLERATE) == 0) { - lnext(righttri, inserttri); - splayroot = splayinsert(m, splayroot, &inserttri, nextvertex); - } - } - } - nextevent->eventptr = (VOID *) freeevents; - freeevents = nextevent; - - if (check4events) { - apex(farlefttri, leftvertex); - dest(lefttri, midvertex); - apex(lefttri, rightvertex); - lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); - if (lefttest > 0.0) { - newevent = freeevents; - freeevents = (struct event *) freeevents->eventptr; - newevent->xkey = m->xminextreme; - newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, - lefttest); - newevent->eventptr = (VOID *) encode(lefttri); - eventheapinsert(eventheap, heapsize, newevent); - heapsize++; - setorg(lefttri, newevent); - } - apex(righttri, leftvertex); - org(righttri, midvertex); - apex(farrighttri, rightvertex); - righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); - if (righttest > 0.0) { - newevent = freeevents; - freeevents = (struct event *) freeevents->eventptr; - newevent->xkey = m->xminextreme; - newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, - righttest); - newevent->eventptr = (VOID *) encode(farrighttri); - eventheapinsert(eventheap, heapsize, newevent); - heapsize++; - setorg(farrighttri, newevent); - } - } - } - - pooldeinit(&m->splaynodes); - lprevself(bottommost); - return removeghosts(m, b, &bottommost); -} - -#endif /* not REDUCED */ - -/** **/ -/** **/ -/********* Sweepline Delaunay triangulation ends here *********/ - -/********* General mesh construction routines begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* delaunay() Form a Delaunay triangulation. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -long delaunay(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -long delaunay(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - long hulledges; - - m->eextras = 0; - initializetrisubpools(m, b); - -#ifdef REDUCED - if (!b->quiet) { - printf( - "Constructing Delaunay triangulation by divide-and-conquer method.\n"); - } - hulledges = divconqdelaunay(m, b); -#else /* not REDUCED */ - if (!b->quiet) { - printf("Constructing Delaunay triangulation "); - if (b->incremental) { - printf("by incremental method.\n"); - } else if (b->sweepline) { - printf("by sweepline method.\n"); - } else { - printf("by divide-and-conquer method.\n"); - } - } - if (b->incremental) { - hulledges = incrementaldelaunay(m, b); - } else if (b->sweepline) { - hulledges = sweeplinedelaunay(m, b); - } else { - hulledges = divconqdelaunay(m, b); - } -#endif /* not REDUCED */ - - if (m->triangles.items == 0) { - /* The input vertices were all collinear, so there are no triangles. */ - return 0l; - } else { - return hulledges; - } -} - -/*****************************************************************************/ -/* */ -/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */ -/* .poly) file. Used when the -r switch is used. */ -/* */ -/* Reads an .ele file and reconstructs the original mesh. If the -p switch */ -/* is used, this procedure will also read a .poly file and reconstruct the */ -/* subsegments of the original mesh. If the -a switch is used, this */ -/* procedure will also read an .area file and set a maximum area constraint */ -/* on each triangle. */ -/* */ -/* Vertices that are not corners of triangles, such as nodes on edges of */ -/* subparametric elements, are discarded. */ -/* */ -/* This routine finds the adjacencies between triangles (and subsegments) */ -/* by forming one stack of triangles for each vertex. Each triangle is on */ -/* three different stacks simultaneously. Each triangle's subsegment */ -/* pointers are used to link the items in each stack. This memory-saving */ -/* feature makes the code harder to read. The most important thing to keep */ -/* in mind is that each triangle is removed from a stack precisely when */ -/* the corresponding pointer is adjusted to refer to a subsegment rather */ -/* than the next triangle of the stack. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist, - REAL *triangleattriblist, REAL *trianglearealist, - int elements, int corners, int attribs, - int *segmentlist,int *segmentmarkerlist, int numberofsegments) -#else /* not ANSI_DECLARATORS */ -int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist, - elements, corners, attribs, segmentlist, segmentmarkerlist, - numberofsegments) -struct mesh *m; -struct behavior *b; -int *trianglelist; -REAL *triangleattriblist; -REAL *trianglearealist; -int elements; -int corners; -int attribs; -int *segmentlist; -int *segmentmarkerlist; -int numberofsegments; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -long reconstruct(struct mesh *m, struct behavior *b, char *elefilename, - char *areafilename, char *polyfilename, FILE *polyfile) -#else /* not ANSI_DECLARATORS */ -long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile) -struct mesh *m; -struct behavior *b; -char *elefilename; -char *areafilename; -char *polyfilename; -FILE *polyfile; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ -#ifdef TRILIBRARY - int vertexindex; - int attribindex; -#else /* not TRILIBRARY */ - FILE *elefile; - FILE *areafile; - char inputline[INPUTLINESIZE]; - char *stringptr; - int areaelements; -#endif /* not TRILIBRARY */ - struct otri triangleloop; - struct otri triangleleft; - struct otri checktri; - struct otri checkleft; - struct otri checkneighbor; - struct osub subsegloop; - triangle *vertexarray; - triangle *prevlink; - triangle nexttri; - vertex tdest, tapex; - vertex checkdest, checkapex; - vertex shorg; - vertex killvertex; - vertex segmentorg, segmentdest; - REAL area; - int corner[3]; - int end[2]; - int killvertexindex; - int incorners; - int segmentmarkers; - int boundmarker; - int aroundvertex; - long hullsize; - int notfound; - long elementnumber, segmentnumber; - int i, j; - triangle ptr; /* Temporary variable used by sym(). */ - -#ifdef TRILIBRARY - m->inelements = elements; - incorners = corners; - if (incorners < 3) { - printf("Error: Triangles must have at least 3 vertices.\n"); - triexit(1); - } - m->eextras = attribs; -#else /* not TRILIBRARY */ - /* Read the triangles from an .ele file. */ - if (!b->quiet) { - printf("Opening %s.\n", elefilename); - } - elefile = fopen(elefilename, "r"); - if (elefile == (FILE *) NULL) { - printf(" Error: Cannot access file %s.\n", elefilename); - triexit(1); - } - /* Read number of triangles, number of vertices per triangle, and */ - /* number of triangle attributes from .ele file. */ - stringptr = readline(inputline, elefile, elefilename); - m->inelements = (int) strtol(stringptr, &stringptr, 0); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - incorners = 3; - } else { - incorners = (int) strtol(stringptr, &stringptr, 0); - if (incorners < 3) { - printf("Error: Triangles in %s must have at least 3 vertices.\n", - elefilename); - triexit(1); - } - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - m->eextras = 0; - } else { - m->eextras = (int) strtol(stringptr, &stringptr, 0); - } -#endif /* not TRILIBRARY */ - - initializetrisubpools(m, b); - - /* Create the triangles. */ - for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) { - maketriangle(m, b, &triangleloop); - /* Mark the triangle as living. */ - triangleloop.tri[3] = (triangle) triangleloop.tri; - } - - segmentmarkers = 0; - if (b->poly) { -#ifdef TRILIBRARY - m->insegments = numberofsegments; - segmentmarkers = segmentmarkerlist != (int *) NULL; -#else /* not TRILIBRARY */ - /* Read number of segments and number of segment */ - /* boundary markers from .poly file. */ - stringptr = readline(inputline, polyfile, b->inpolyfilename); - m->insegments = (int) strtol(stringptr, &stringptr, 0); - stringptr = findfield(stringptr); - if (*stringptr != '\0') { - segmentmarkers = (int) strtol(stringptr, &stringptr, 0); - } -#endif /* not TRILIBRARY */ - - /* Create the subsegments. */ - for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) { - makesubseg(m, &subsegloop); - /* Mark the subsegment as living. */ - subsegloop.ss[2] = (subseg) subsegloop.ss; - } - } - -#ifdef TRILIBRARY - vertexindex = 0; - attribindex = 0; -#else /* not TRILIBRARY */ - if (b->vararea) { - /* Open an .area file, check for consistency with the .ele file. */ - if (!b->quiet) { - printf("Opening %s.\n", areafilename); - } - areafile = fopen(areafilename, "r"); - if (areafile == (FILE *) NULL) { - printf(" Error: Cannot access file %s.\n", areafilename); - triexit(1); - } - stringptr = readline(inputline, areafile, areafilename); - areaelements = (int) strtol(stringptr, &stringptr, 0); - if (areaelements != m->inelements) { - printf("Error: %s and %s disagree on number of triangles.\n", - elefilename, areafilename); - triexit(1); - } - } -#endif /* not TRILIBRARY */ - - if (!b->quiet) { - printf("Reconstructing mesh.\n"); - } - /* Allocate a temporary array that maps each vertex to some adjacent */ - /* triangle. I took care to allocate all the permanent memory for */ - /* triangles and subsegments first. */ - vertexarray = (triangle *) trimalloc(m->vertices.items * - (int) sizeof(triangle)); - /* Each vertex is initially unrepresented. */ - for (i = 0; i < m->vertices.items; i++) { - vertexarray[i] = (triangle) m->dummytri; - } - - if (b->verbose) { - printf(" Assembling triangles.\n"); - } - /* Read the triangles from the .ele file, and link */ - /* together those that share an edge. */ - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - elementnumber = b->firstnumber; - while (triangleloop.tri != (triangle *) NULL) { -#ifdef TRILIBRARY - /* Copy the triangle's three corners. */ - for (j = 0; j < 3; j++) { - corner[j] = trianglelist[vertexindex++]; - if ((corner[j] < b->firstnumber) || - (corner[j] >= b->firstnumber + m->invertices)) { - printf("Error: Triangle %ld has an invalid vertex index.\n", - elementnumber); - triexit(1); - } - } -#else /* not TRILIBRARY */ - /* Read triangle number and the triangle's three corners. */ - stringptr = readline(inputline, elefile, elefilename); - for (j = 0; j < 3; j++) { - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Triangle %ld is missing vertex %d in %s.\n", - elementnumber, j + 1, elefilename); - triexit(1); - } else { - corner[j] = (int) strtol(stringptr, &stringptr, 0); - if ((corner[j] < b->firstnumber) || - (corner[j] >= b->firstnumber + m->invertices)) { - printf("Error: Triangle %ld has an invalid vertex index.\n", - elementnumber); - triexit(1); - } - } - } -#endif /* not TRILIBRARY */ - - /* Find out about (and throw away) extra nodes. */ - for (j = 3; j < incorners; j++) { -#ifdef TRILIBRARY - killvertexindex = trianglelist[vertexindex++]; -#else /* not TRILIBRARY */ - stringptr = findfield(stringptr); - if (*stringptr != '\0') { - killvertexindex = (int) strtol(stringptr, &stringptr, 0); -#endif /* not TRILIBRARY */ - if ((killvertexindex >= b->firstnumber) && - (killvertexindex < b->firstnumber + m->invertices)) { - /* Delete the non-corner vertex if it's not already deleted. */ - killvertex = getvertex(m, b, killvertexindex); - if (vertextype(killvertex) != DEADVERTEX) { - vertexdealloc(m, killvertex); - } - } -#ifndef TRILIBRARY - } -#endif /* not TRILIBRARY */ - } - - /* Read the triangle's attributes. */ - for (j = 0; j < m->eextras; j++) { -#ifdef TRILIBRARY - setelemattribute(triangleloop, j, triangleattriblist[attribindex++]); -#else /* not TRILIBRARY */ - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - setelemattribute(triangleloop, j, 0); - } else { - setelemattribute(triangleloop, j, - (REAL) strtod(stringptr, &stringptr)); - } -#endif /* not TRILIBRARY */ - } - - if (b->vararea) { -#ifdef TRILIBRARY - area = trianglearealist[elementnumber - b->firstnumber]; -#else /* not TRILIBRARY */ - /* Read an area constraint from the .area file. */ - stringptr = readline(inputline, areafile, areafilename); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - area = -1.0; /* No constraint on this triangle. */ - } else { - area = (REAL) strtod(stringptr, &stringptr); - } -#endif /* not TRILIBRARY */ - setareabound(triangleloop, area); - } - - /* Set the triangle's vertices. */ - triangleloop.orient = 0; - setorg(triangleloop, getvertex(m, b, corner[0])); - setdest(triangleloop, getvertex(m, b, corner[1])); - setapex(triangleloop, getvertex(m, b, corner[2])); - /* Try linking the triangle to others that share these vertices. */ - for (triangleloop.orient = 0; triangleloop.orient < 3; - triangleloop.orient++) { - /* Take the number for the origin of triangleloop. */ - aroundvertex = corner[triangleloop.orient]; - /* Look for other triangles having this vertex. */ - nexttri = vertexarray[aroundvertex - b->firstnumber]; - /* Link the current triangle to the next one in the stack. */ - triangleloop.tri[6 + triangleloop.orient] = nexttri; - /* Push the current triangle onto the stack. */ - vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop); - decode(nexttri, checktri); - if (checktri.tri != m->dummytri) { - dest(triangleloop, tdest); - apex(triangleloop, tapex); - /* Look for other triangles that share an edge. */ - do { - dest(checktri, checkdest); - apex(checktri, checkapex); - if (tapex == checkdest) { - /* The two triangles share an edge; bond them together. */ - lprev(triangleloop, triangleleft); - bond(triangleleft, checktri); - } - if (tdest == checkapex) { - /* The two triangles share an edge; bond them together. */ - lprev(checktri, checkleft); - bond(triangleloop, checkleft); - } - /* Find the next triangle in the stack. */ - nexttri = checktri.tri[6 + checktri.orient]; - decode(nexttri, checktri); - } while (checktri.tri != m->dummytri); - } - } - triangleloop.tri = triangletraverse(m); - elementnumber++; - } - -#ifdef TRILIBRARY - vertexindex = 0; -#else /* not TRILIBRARY */ - fclose(elefile); - if (b->vararea) { - fclose(areafile); - } -#endif /* not TRILIBRARY */ - - hullsize = 0; /* Prepare to count the boundary edges. */ - if (b->poly) { - if (b->verbose) { - printf(" Marking segments in triangulation.\n"); - } - /* Read the segments from the .poly file, and link them */ - /* to their neighboring triangles. */ - boundmarker = 0; - traversalinit(&m->subsegs); - subsegloop.ss = subsegtraverse(m); - segmentnumber = b->firstnumber; - while (subsegloop.ss != (subseg *) NULL) { -#ifdef TRILIBRARY - end[0] = segmentlist[vertexindex++]; - end[1] = segmentlist[vertexindex++]; - if (segmentmarkers) { - boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber]; - } -#else /* not TRILIBRARY */ - /* Read the endpoints of each segment, and possibly a boundary marker. */ - stringptr = readline(inputline, polyfile, b->inpolyfilename); - /* Skip the first (segment number) field. */ - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber, - polyfilename); - triexit(1); - } else { - end[0] = (int) strtol(stringptr, &stringptr, 0); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Segment %ld is missing its second endpoint in %s.\n", - segmentnumber, polyfilename); - triexit(1); - } else { - end[1] = (int) strtol(stringptr, &stringptr, 0); - } - if (segmentmarkers) { - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - boundmarker = 0; - } else { - boundmarker = (int) strtol(stringptr, &stringptr, 0); - } - } -#endif /* not TRILIBRARY */ - for (j = 0; j < 2; j++) { - if ((end[j] < b->firstnumber) || - (end[j] >= b->firstnumber + m->invertices)) { - printf("Error: Segment %ld has an invalid vertex index.\n", - segmentnumber); - triexit(1); - } - } - - /* set the subsegment's vertices. */ - subsegloop.ssorient = 0; - segmentorg = getvertex(m, b, end[0]); - segmentdest = getvertex(m, b, end[1]); - setsorg(subsegloop, segmentorg); - setsdest(subsegloop, segmentdest); - setsegorg(subsegloop, segmentorg); - setsegdest(subsegloop, segmentdest); - setmark(subsegloop, boundmarker); - /* Try linking the subsegment to triangles that share these vertices. */ - for (subsegloop.ssorient = 0; subsegloop.ssorient < 2; - subsegloop.ssorient++) { - /* Take the number for the destination of subsegloop. */ - aroundvertex = end[1 - subsegloop.ssorient]; - /* Look for triangles having this vertex. */ - prevlink = &vertexarray[aroundvertex - b->firstnumber]; - nexttri = vertexarray[aroundvertex - b->firstnumber]; - decode(nexttri, checktri); - sorg(subsegloop, shorg); - notfound = 1; - /* Look for triangles having this edge. Note that I'm only */ - /* comparing each triangle's destination with the subsegment; */ - /* each triangle's apex is handled through a different vertex. */ - /* Because each triangle appears on three vertices' lists, each */ - /* occurrence of a triangle on a list can (and does) represent */ - /* an edge. In this way, most edges are represented twice, and */ - /* every triangle-subsegment bond is represented once. */ - while (notfound && (checktri.tri != m->dummytri)) { - dest(checktri, checkdest); - if (shorg == checkdest) { - /* We have a match. Remove this triangle from the list. */ - *prevlink = checktri.tri[6 + checktri.orient]; - /* Bond the subsegment to the triangle. */ - tsbond(checktri, subsegloop); - /* Check if this is a boundary edge. */ - sym(checktri, checkneighbor); - if (checkneighbor.tri == m->dummytri) { - /* The next line doesn't insert a subsegment (because there's */ - /* already one there), but it sets the boundary markers of */ - /* the existing subsegment and its vertices. */ - insertsubseg(m, b, &checktri, 1); - hullsize++; - } - notfound = 0; - } - /* Find the next triangle in the stack. */ - prevlink = &checktri.tri[6 + checktri.orient]; - nexttri = checktri.tri[6 + checktri.orient]; - decode(nexttri, checktri); - } - } - subsegloop.ss = subsegtraverse(m); - segmentnumber++; - } - } - - /* Mark the remaining edges as not being attached to any subsegment. */ - /* Also, count the (yet uncounted) boundary edges. */ - for (i = 0; i < m->vertices.items; i++) { - /* Search the stack of triangles adjacent to a vertex. */ - nexttri = vertexarray[i]; - decode(nexttri, checktri); - while (checktri.tri != m->dummytri) { - /* Find the next triangle in the stack before this */ - /* information gets overwritten. */ - nexttri = checktri.tri[6 + checktri.orient]; - /* No adjacent subsegment. (This overwrites the stack info.) */ - tsdissolve(checktri); - sym(checktri, checkneighbor); - if (checkneighbor.tri == m->dummytri) { - insertsubseg(m, b, &checktri, 1); - hullsize++; - } - decode(nexttri, checktri); - } - } - - trifree((VOID *) vertexarray); - return hullsize; -} - -#endif /* not CDT_ONLY */ - -/** **/ -/** **/ -/********* General mesh construction routines end here *********/ - -/********* Segment insertion begins here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* finddirection() Find the first triangle on the path from one point */ -/* to another. */ -/* */ -/* Finds the triangle that intersects a line segment drawn from the */ -/* origin of `searchtri' to the point `searchpoint', and returns the result */ -/* in `searchtri'. The origin of `searchtri' does not change, even though */ -/* the triangle returned may differ from the one passed in. This routine */ -/* is used to find the direction to move in to get from one point to */ -/* another. */ -/* */ -/* The return value notes whether the destination or apex of the found */ -/* triangle is collinear with the two points in question. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -enum finddirectionresult finddirection(struct mesh *m, struct behavior *b, - struct otri *searchtri, - vertex searchpoint) -#else /* not ANSI_DECLARATORS */ -enum finddirectionresult finddirection(m, b, searchtri, searchpoint) -struct mesh *m; -struct behavior *b; -struct otri *searchtri; -vertex searchpoint; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri checktri; - vertex startvertex; - vertex leftvertex, rightvertex; - REAL leftccw, rightccw; - int leftflag, rightflag; - triangle ptr; /* Temporary variable used by onext() and oprev(). */ - - org(*searchtri, startvertex); - dest(*searchtri, rightvertex); - apex(*searchtri, leftvertex); - /* Is `searchpoint' to the left? */ - leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); - leftflag = leftccw > 0.0; - /* Is `searchpoint' to the right? */ - rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); - rightflag = rightccw > 0.0; - if (leftflag && rightflag) { - /* `searchtri' faces directly away from `searchpoint'. We could go left */ - /* or right. Ask whether it's a triangle or a boundary on the left. */ - onext(*searchtri, checktri); - if (checktri.tri == m->dummytri) { - leftflag = 0; - } else { - rightflag = 0; - } - } - while (leftflag) { - /* Turn left until satisfied. */ - onextself(*searchtri); - if (searchtri->tri == m->dummytri) { - printf("Internal error in finddirection(): Unable to find a\n"); - printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], - startvertex[1]); - printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); - internalerror(); - } - apex(*searchtri, leftvertex); - rightccw = leftccw; - leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); - leftflag = leftccw > 0.0; - } - while (rightflag) { - /* Turn right until satisfied. */ - oprevself(*searchtri); - if (searchtri->tri == m->dummytri) { - printf("Internal error in finddirection(): Unable to find a\n"); - printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], - startvertex[1]); - printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); - internalerror(); - } - dest(*searchtri, rightvertex); - leftccw = rightccw; - rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); - rightflag = rightccw > 0.0; - } - if (leftccw == 0.0) { - return LEFTCOLLINEAR; - } else if (rightccw == 0.0) { - return RIGHTCOLLINEAR; - } else { - return WITHIN; - } -} - -/*****************************************************************************/ -/* */ -/* segmentintersection() Find the intersection of an existing segment */ -/* and a segment that is being inserted. Insert */ -/* a vertex at the intersection, splitting an */ -/* existing subsegment. */ -/* */ -/* The segment being inserted connects the apex of splittri to endpoint2. */ -/* splitsubseg is the subsegment being split, and MUST adjoin splittri. */ -/* Hence, endpoints of the subsegment being split are the origin and */ -/* destination of splittri. */ -/* */ -/* On completion, splittri is a handle having the newly inserted */ -/* intersection point as its origin, and endpoint1 as its destination. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void segmentintersection(struct mesh *m, struct behavior *b, - struct otri *splittri, struct osub *splitsubseg, - vertex endpoint2) -#else /* not ANSI_DECLARATORS */ -void segmentintersection(m, b, splittri, splitsubseg, endpoint2) -struct mesh *m; -struct behavior *b; -struct otri *splittri; -struct osub *splitsubseg; -vertex endpoint2; -#endif /* not ANSI_DECLARATORS */ - -{ - struct osub opposubseg; - vertex endpoint1; - vertex torg, tdest; - vertex leftvertex, rightvertex; - vertex newvertex; - enum insertvertexresult success; - enum finddirectionresult collinear; - REAL ex, ey; - REAL tx, ty; - REAL etx, ety; - REAL split, denom; - int i; - triangle ptr; /* Temporary variable used by onext(). */ - subseg sptr; /* Temporary variable used by snext(). */ - - /* Find the other three segment endpoints. */ - apex(*splittri, endpoint1); - org(*splittri, torg); - dest(*splittri, tdest); - /* Segment intersection formulae; see the Antonio reference. */ - tx = tdest[0] - torg[0]; - ty = tdest[1] - torg[1]; - ex = endpoint2[0] - endpoint1[0]; - ey = endpoint2[1] - endpoint1[1]; - etx = torg[0] - endpoint2[0]; - ety = torg[1] - endpoint2[1]; - denom = ty * ex - tx * ey; - if (denom == 0.0) { - printf("Internal error in segmentintersection():"); - printf(" Attempt to find intersection of parallel segments.\n"); - internalerror(); - } - split = (ey * etx - ex * ety) / denom; - /* Create the new vertex. */ - newvertex = (vertex) poolalloc(&m->vertices); - /* Interpolate its coordinate and attributes. */ - for (i = 0; i < 2 + m->nextras; i++) { - newvertex[i] = torg[i] + split * (tdest[i] - torg[i]); - } - setvertexmark(newvertex, mark(*splitsubseg)); - setvertextype(newvertex, INPUTVERTEX); - if (b->verbose > 1) { - printf( - " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", - torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]); - } - /* Insert the intersection vertex. This should always succeed. */ - success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0); - if (success != SUCCESSFULVERTEX) { - printf("Internal error in segmentintersection():\n"); - printf(" Failure to split a segment.\n"); - internalerror(); - } - /* Record a triangle whose origin is the new vertex. */ - setvertex2tri(newvertex, encode(*splittri)); - if (m->steinerleft > 0) { - m->steinerleft--; - } - - /* Divide the segment into two, and correct the segment endpoints. */ - ssymself(*splitsubseg); - spivot(*splitsubseg, opposubseg); - sdissolve(*splitsubseg); - sdissolve(opposubseg); - do { - setsegorg(*splitsubseg, newvertex); - snextself(*splitsubseg); - } while (splitsubseg->ss != m->dummysub); - do { - setsegorg(opposubseg, newvertex); - snextself(opposubseg); - } while (opposubseg.ss != m->dummysub); - - /* Inserting the vertex may have caused edge flips. We wish to rediscover */ - /* the edge connecting endpoint1 to the new intersection vertex. */ - collinear = finddirection(m, b, splittri, endpoint1); - dest(*splittri, rightvertex); - apex(*splittri, leftvertex); - if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) { - onextself(*splittri); - } else if ((rightvertex[0] != endpoint1[0]) || - (rightvertex[1] != endpoint1[1])) { - printf("Internal error in segmentintersection():\n"); - printf(" Topological inconsistency after splitting a segment.\n"); - internalerror(); - } - /* `splittri' should have destination endpoint1. */ -} - -/*****************************************************************************/ -/* */ -/* scoutsegment() Scout the first triangle on the path from one endpoint */ -/* to another, and check for completion (reaching the */ -/* second endpoint), a collinear vertex, or the */ -/* intersection of two segments. */ -/* */ -/* Returns one if the entire segment is successfully inserted, and zero if */ -/* the job must be finished by conformingedge() or constrainededge(). */ -/* */ -/* If the first triangle on the path has the second endpoint as its */ -/* destination or apex, a subsegment is inserted and the job is done. */ -/* */ -/* If the first triangle on the path has a destination or apex that lies on */ -/* the segment, a subsegment is inserted connecting the first endpoint to */ -/* the collinear vertex, and the search is continued from the collinear */ -/* vertex. */ -/* */ -/* If the first triangle on the path has a subsegment opposite its origin, */ -/* then there is a segment that intersects the segment being inserted. */ -/* Their intersection vertex is inserted, splitting the subsegment. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri, - vertex endpoint2, int newmark) -#else /* not ANSI_DECLARATORS */ -int scoutsegment(m, b, searchtri, endpoint2, newmark) -struct mesh *m; -struct behavior *b; -struct otri *searchtri; -vertex endpoint2; -int newmark; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri crosstri; - struct osub crosssubseg; - vertex leftvertex, rightvertex; - enum finddirectionresult collinear; - subseg sptr; /* Temporary variable used by tspivot(). */ - - collinear = finddirection(m, b, searchtri, endpoint2); - dest(*searchtri, rightvertex); - apex(*searchtri, leftvertex); - if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) || - ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) { - /* The segment is already an edge in the mesh. */ - if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) { - lprevself(*searchtri); - } - /* Insert a subsegment, if there isn't already one there. */ - insertsubseg(m, b, searchtri, newmark); - return 1; - } else if (collinear == LEFTCOLLINEAR) { - /* We've collided with a vertex between the segment's endpoints. */ - /* Make the collinear vertex be the triangle's origin. */ - lprevself(*searchtri); - insertsubseg(m, b, searchtri, newmark); - /* Insert the remainder of the segment. */ - return scoutsegment(m, b, searchtri, endpoint2, newmark); - } else if (collinear == RIGHTCOLLINEAR) { - /* We've collided with a vertex between the segment's endpoints. */ - insertsubseg(m, b, searchtri, newmark); - /* Make the collinear vertex be the triangle's origin. */ - lnextself(*searchtri); - /* Insert the remainder of the segment. */ - return scoutsegment(m, b, searchtri, endpoint2, newmark); - } else { - lnext(*searchtri, crosstri); - tspivot(crosstri, crosssubseg); - /* Check for a crossing segment. */ - if (crosssubseg.ss == m->dummysub) { - return 0; - } else { - /* Insert a vertex at the intersection. */ - segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2); - otricopy(crosstri, *searchtri); - insertsubseg(m, b, searchtri, newmark); - /* Insert the remainder of the segment. */ - return scoutsegment(m, b, searchtri, endpoint2, newmark); - } - } -} - -/*****************************************************************************/ -/* */ -/* conformingedge() Force a segment into a conforming Delaunay */ -/* triangulation by inserting a vertex at its midpoint, */ -/* and recursively forcing in the two half-segments if */ -/* necessary. */ -/* */ -/* Generates a sequence of subsegments connecting `endpoint1' to */ -/* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */ -/* to each new splitting vertex and subsegment. */ -/* */ -/* Note that conformingedge() does not always maintain the conforming */ -/* Delaunay property. Once inserted, segments are locked into place; */ -/* vertices inserted later (to force other segments in) may render these */ -/* fixed segments non-Delaunay. The conforming Delaunay property will be */ -/* restored by enforcequality() by splitting encroached subsegments. */ -/* */ -/*****************************************************************************/ - -#ifndef REDUCED -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void conformingedge(struct mesh *m, struct behavior *b, - vertex endpoint1, vertex endpoint2, int newmark) -#else /* not ANSI_DECLARATORS */ -void conformingedge(m, b, endpoint1, endpoint2, newmark) -struct mesh *m; -struct behavior *b; -vertex endpoint1; -vertex endpoint2; -int newmark; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri searchtri1, searchtri2; - struct osub brokensubseg; - vertex newvertex; - vertex midvertex1, midvertex2; - enum insertvertexresult success; - int i; - subseg sptr; /* Temporary variable used by tspivot(). */ - - if (b->verbose > 2) { - printf("Forcing segment into triangulation by recursive splitting:\n"); - printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1], - endpoint2[0], endpoint2[1]); - } - /* Create a new vertex to insert in the middle of the segment. */ - newvertex = (vertex) poolalloc(&m->vertices); - /* Interpolate coordinates and attributes. */ - for (i = 0; i < 2 + m->nextras; i++) { - newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]); - } - setvertexmark(newvertex, newmark); - setvertextype(newvertex, SEGMENTVERTEX); - /* No known triangle to search from. */ - searchtri1.tri = m->dummytri; - /* Attempt to insert the new vertex. */ - success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL, - 0, 0); - if (success == DUPLICATEVERTEX) { - if (b->verbose > 2) { - printf(" Segment intersects existing vertex (%.12g, %.12g).\n", - newvertex[0], newvertex[1]); - } - /* Use the vertex that's already there. */ - vertexdealloc(m, newvertex); - org(searchtri1, newvertex); - } else { - if (success == VIOLATINGVERTEX) { - if (b->verbose > 2) { - printf(" Two segments intersect at (%.12g, %.12g).\n", - newvertex[0], newvertex[1]); - } - /* By fluke, we've landed right on another segment. Split it. */ - tspivot(searchtri1, brokensubseg); - success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg, - 0, 0); - if (success != SUCCESSFULVERTEX) { - printf("Internal error in conformingedge():\n"); - printf(" Failure to split a segment.\n"); - internalerror(); - } - } - /* The vertex has been inserted successfully. */ - if (m->steinerleft > 0) { - m->steinerleft--; - } - } - otricopy(searchtri1, searchtri2); - /* `searchtri1' and `searchtri2' are fastened at their origins to */ - /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */ - /* respectively. First, we must get `searchtri2' out of the way so it */ - /* won't be invalidated during the insertion of the first half of the */ - /* segment. */ - finddirection(m, b, &searchtri2, endpoint2); - if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) { - /* The origin of searchtri1 may have changed if a collision with an */ - /* intervening vertex on the segment occurred. */ - org(searchtri1, midvertex1); - conformingedge(m, b, midvertex1, endpoint1, newmark); - } - if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) { - /* The origin of searchtri2 may have changed if a collision with an */ - /* intervening vertex on the segment occurred. */ - org(searchtri2, midvertex2); - conformingedge(m, b, midvertex2, endpoint2, newmark); - } -} - -#endif /* not CDT_ONLY */ -#endif /* not REDUCED */ - -/*****************************************************************************/ -/* */ -/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */ -/* recursively from an existing vertex. Pay special */ -/* attention to stacking inverted triangles. */ -/* */ -/* This is a support routine for inserting segments into a constrained */ -/* Delaunay triangulation. */ -/* */ -/* The origin of fixuptri is treated as if it has just been inserted, and */ -/* the local Delaunay condition needs to be enforced. It is only enforced */ -/* in one sector, however, that being the angular range defined by */ -/* fixuptri. */ -/* */ -/* This routine also needs to make decisions regarding the "stacking" of */ -/* triangles. (Read the description of constrainededge() below before */ -/* reading on here, so you understand the algorithm.) If the position of */ -/* the new vertex (the origin of fixuptri) indicates that the vertex before */ -/* it on the polygon is a reflex vertex, then "stack" the triangle by */ -/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */ -/* triangles are identified.) */ -/* */ -/* Otherwise, check whether the vertex before that was a reflex vertex. */ -/* If so, perform an edge flip, thereby eliminating an inverted triangle */ -/* (popping it off the stack). The edge flip may result in the creation */ -/* of a new inverted triangle, depending on whether or not the new vertex */ -/* is visible to the vertex three edges behind on the polygon. */ -/* */ -/* If neither of the two vertices behind the new vertex are reflex */ -/* vertices, fixuptri and fartri, the triangle opposite it, are not */ -/* inverted; hence, ensure that the edge between them is locally Delaunay. */ -/* */ -/* `leftside' indicates whether or not fixuptri is to the left of the */ -/* segment being inserted. (Imagine that the segment is pointing up from */ -/* endpoint1 to endpoint2.) */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void delaunayfixup(struct mesh *m, struct behavior *b, - struct otri *fixuptri, int leftside) -#else /* not ANSI_DECLARATORS */ -void delaunayfixup(m, b, fixuptri, leftside) -struct mesh *m; -struct behavior *b; -struct otri *fixuptri; -int leftside; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri neartri; - struct otri fartri; - struct osub faredge; - vertex nearvertex, leftvertex, rightvertex, farvertex; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - lnext(*fixuptri, neartri); - sym(neartri, fartri); - /* Check if the edge opposite the origin of fixuptri can be flipped. */ - if (fartri.tri == m->dummytri) { - return; - } - tspivot(neartri, faredge); - if (faredge.ss != m->dummysub) { - return; - } - /* Find all the relevant vertices. */ - apex(neartri, nearvertex); - org(neartri, leftvertex); - dest(neartri, rightvertex); - apex(fartri, farvertex); - /* Check whether the previous polygon vertex is a reflex vertex. */ - if (leftside) { - if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) { - /* leftvertex is a reflex vertex too. Nothing can */ - /* be done until a convex section is found. */ - return; - } - } else { - if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) { - /* rightvertex is a reflex vertex too. Nothing can */ - /* be done until a convex section is found. */ - return; - } - } - if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) { - /* fartri is not an inverted triangle, and farvertex is not a reflex */ - /* vertex. As there are no reflex vertices, fixuptri isn't an */ - /* inverted triangle, either. Hence, test the edge between the */ - /* triangles to ensure it is locally Delaunay. */ - if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <= - 0.0) { - return; - } - /* Not locally Delaunay; go on to an edge flip. */ - } /* else fartri is inverted; remove it from the stack by flipping. */ - flip(m, b, &neartri); - lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */ - /* Recursively process the two triangles that result from the flip. */ - delaunayfixup(m, b, fixuptri, leftside); - delaunayfixup(m, b, &fartri, leftside); -} - -/*****************************************************************************/ -/* */ -/* constrainededge() Force a segment into a constrained Delaunay */ -/* triangulation by deleting the triangles it */ -/* intersects, and triangulating the polygons that */ -/* form on each side of it. */ -/* */ -/* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */ -/* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */ -/* boundary marker of the segment. */ -/* */ -/* To insert a segment, every triangle whose interior intersects the */ -/* segment is deleted. The union of these deleted triangles is a polygon */ -/* (which is not necessarily monotone, but is close enough), which is */ -/* divided into two polygons by the new segment. This routine's task is */ -/* to generate the Delaunay triangulation of these two polygons. */ -/* */ -/* You might think of this routine's behavior as a two-step process. The */ -/* first step is to walk from endpoint1 to endpoint2, flipping each edge */ -/* encountered. This step creates a fan of edges connected to endpoint1, */ -/* including the desired edge to endpoint2. The second step enforces the */ -/* Delaunay condition on each side of the segment in an incremental manner: */ -/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */ -/* independently on each side of the segment), each vertex is "enforced" */ -/* as if it had just been inserted, but affecting only the previous */ -/* vertices. The result is the same as if the vertices had been inserted */ -/* in the order they appear on the polygon, so the result is Delaunay. */ -/* */ -/* In truth, constrainededge() interleaves these two steps. The procedure */ -/* walks from endpoint1 to endpoint2, and each time an edge is encountered */ -/* and flipped, the newly exposed vertex (at the far end of the flipped */ -/* edge) is "enforced" upon the previously flipped edges, usually affecting */ -/* only one side of the polygon (depending upon which side of the segment */ -/* the vertex falls on). */ -/* */ -/* The algorithm is complicated by the need to handle polygons that are not */ -/* convex. Although the polygon is not necessarily monotone, it can be */ -/* triangulated in a manner similar to the stack-based algorithms for */ -/* monotone polygons. For each reflex vertex (local concavity) of the */ -/* polygon, there will be an inverted triangle formed by one of the edge */ -/* flips. (An inverted triangle is one with negative area - that is, its */ -/* vertices are arranged in clockwise order - and is best thought of as a */ -/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */ -/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */ -/* later. */ -/* */ -/* A reflex vertex is popped from the stack when a vertex is inserted that */ -/* is visible to the reflex vertex. (However, if the vertex behind the */ -/* reflex vertex is not visible to the reflex vertex, a new inverted */ -/* triangle will take its place on the stack.) These details are handled */ -/* by the delaunayfixup() routine above. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void constrainededge(struct mesh *m, struct behavior *b, - struct otri *starttri, vertex endpoint2, int newmark) -#else /* not ANSI_DECLARATORS */ -void constrainededge(m, b, starttri, endpoint2, newmark) -struct mesh *m; -struct behavior *b; -struct otri *starttri; -vertex endpoint2; -int newmark; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri fixuptri, fixuptri2; - struct osub crosssubseg; - vertex endpoint1; - vertex farvertex; - REAL area; - int collision; - int done; - triangle ptr; /* Temporary variable used by sym() and oprev(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - org(*starttri, endpoint1); - lnext(*starttri, fixuptri); - flip(m, b, &fixuptri); - /* `collision' indicates whether we have found a vertex directly */ - /* between endpoint1 and endpoint2. */ - collision = 0; - done = 0; - do { - org(fixuptri, farvertex); - /* `farvertex' is the extreme point of the polygon we are "digging" */ - /* to get from endpoint1 to endpoint2. */ - if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) { - oprev(fixuptri, fixuptri2); - /* Enforce the Delaunay condition around endpoint2. */ - delaunayfixup(m, b, &fixuptri, 0); - delaunayfixup(m, b, &fixuptri2, 1); - done = 1; - } else { - /* Check whether farvertex is to the left or right of the segment */ - /* being inserted, to decide which edge of fixuptri to dig */ - /* through next. */ - area = counterclockwise(m, b, endpoint1, endpoint2, farvertex); - if (area == 0.0) { - /* We've collided with a vertex between endpoint1 and endpoint2. */ - collision = 1; - oprev(fixuptri, fixuptri2); - /* Enforce the Delaunay condition around farvertex. */ - delaunayfixup(m, b, &fixuptri, 0); - delaunayfixup(m, b, &fixuptri2, 1); - done = 1; - } else { - if (area > 0.0) { /* farvertex is to the left of the segment. */ - oprev(fixuptri, fixuptri2); - /* Enforce the Delaunay condition around farvertex, on the */ - /* left side of the segment only. */ - delaunayfixup(m, b, &fixuptri2, 1); - /* Flip the edge that crosses the segment. After the edge is */ - /* flipped, one of its endpoints is the fan vertex, and the */ - /* destination of fixuptri is the fan vertex. */ - lprevself(fixuptri); - } else { /* farvertex is to the right of the segment. */ - delaunayfixup(m, b, &fixuptri, 0); - /* Flip the edge that crosses the segment. After the edge is */ - /* flipped, one of its endpoints is the fan vertex, and the */ - /* destination of fixuptri is the fan vertex. */ - oprevself(fixuptri); - } - /* Check for two intersecting segments. */ - tspivot(fixuptri, crosssubseg); - if (crosssubseg.ss == m->dummysub) { - flip(m, b, &fixuptri); /* May create inverted triangle at left. */ - } else { - /* We've collided with a segment between endpoint1 and endpoint2. */ - collision = 1; - /* Insert a vertex at the intersection. */ - segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2); - done = 1; - } - } - } - } while (!done); - /* Insert a subsegment to make the segment permanent. */ - insertsubseg(m, b, &fixuptri, newmark); - /* If there was a collision with an interceding vertex, install another */ - /* segment connecting that vertex with endpoint2. */ - if (collision) { - /* Insert the remainder of the segment. */ - if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) { - constrainededge(m, b, &fixuptri, endpoint2, newmark); - } - } -} - -/*****************************************************************************/ -/* */ -/* insertsegment() Insert a PSLG segment into a triangulation. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void insertsegment(struct mesh *m, struct behavior *b, - vertex endpoint1, vertex endpoint2, int newmark) -#else /* not ANSI_DECLARATORS */ -void insertsegment(m, b, endpoint1, endpoint2, newmark) -struct mesh *m; -struct behavior *b; -vertex endpoint1; -vertex endpoint2; -int newmark; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri searchtri1, searchtri2; - triangle encodedtri; - vertex checkvertex; - triangle ptr; /* Temporary variable used by sym(). */ - - if (b->verbose > 1) { - printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n", - endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]); - } - - /* Find a triangle whose origin is the segment's first endpoint. */ - checkvertex = (vertex) NULL; - encodedtri = vertex2tri(endpoint1); - if (encodedtri != (triangle) NULL) { - decode(encodedtri, searchtri1); - org(searchtri1, checkvertex); - } - if (checkvertex != endpoint1) { - /* Find a boundary triangle to search from. */ - searchtri1.tri = m->dummytri; - searchtri1.orient = 0; - symself(searchtri1); - /* Search for the segment's first endpoint by point location. */ - if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) { - printf( - "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); - printf(" (%.12g, %.12g) in triangulation.\n", - endpoint1[0], endpoint1[1]); - internalerror(); - } - } - /* Remember this triangle to improve subsequent point location. */ - otricopy(searchtri1, m->recenttri); - /* Scout the beginnings of a path from the first endpoint */ - /* toward the second. */ - if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) { - /* The segment was easily inserted. */ - return; - } - /* The first endpoint may have changed if a collision with an intervening */ - /* vertex on the segment occurred. */ - org(searchtri1, endpoint1); - - /* Find a triangle whose origin is the segment's second endpoint. */ - checkvertex = (vertex) NULL; - encodedtri = vertex2tri(endpoint2); - if (encodedtri != (triangle) NULL) { - decode(encodedtri, searchtri2); - org(searchtri2, checkvertex); - } - if (checkvertex != endpoint2) { - /* Find a boundary triangle to search from. */ - searchtri2.tri = m->dummytri; - searchtri2.orient = 0; - symself(searchtri2); - /* Search for the segment's second endpoint by point location. */ - if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) { - printf( - "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); - printf(" (%.12g, %.12g) in triangulation.\n", - endpoint2[0], endpoint2[1]); - internalerror(); - } - } - /* Remember this triangle to improve subsequent point location. */ - otricopy(searchtri2, m->recenttri); - /* Scout the beginnings of a path from the second endpoint */ - /* toward the first. */ - if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) { - /* The segment was easily inserted. */ - return; - } - /* The second endpoint may have changed if a collision with an intervening */ - /* vertex on the segment occurred. */ - org(searchtri2, endpoint2); - -#ifndef REDUCED -#ifndef CDT_ONLY - if (b->splitseg) { - /* Insert vertices to force the segment into the triangulation. */ - conformingedge(m, b, endpoint1, endpoint2, newmark); - } else { -#endif /* not CDT_ONLY */ -#endif /* not REDUCED */ - /* Insert the segment directly into the triangulation. */ - constrainededge(m, b, &searchtri1, endpoint2, newmark); -#ifndef REDUCED -#ifndef CDT_ONLY - } -#endif /* not CDT_ONLY */ -#endif /* not REDUCED */ -} - -/*****************************************************************************/ -/* */ -/* markhull() Cover the convex hull of a triangulation with subsegments. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void markhull(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void markhull(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri hulltri; - struct otri nexttri; - struct otri starttri; - triangle ptr; /* Temporary variable used by sym() and oprev(). */ - - /* Find a triangle handle on the hull. */ - hulltri.tri = m->dummytri; - hulltri.orient = 0; - symself(hulltri); - /* Remember where we started so we know when to stop. */ - otricopy(hulltri, starttri); - /* Go once counterclockwise around the convex hull. */ - do { - /* Create a subsegment if there isn't already one here. */ - insertsubseg(m, b, &hulltri, 1); - /* To find the next hull edge, go clockwise around the next vertex. */ - lnextself(hulltri); - oprev(hulltri, nexttri); - while (nexttri.tri != m->dummytri) { - otricopy(nexttri, hulltri); - oprev(hulltri, nexttri); - } - } while (!otriequal(hulltri, starttri)); -} - -/*****************************************************************************/ -/* */ -/* formskeleton() Create the segments of a triangulation, including PSLG */ -/* segments and edges on the convex hull. */ -/* */ -/* The PSLG segments are read from a .poly file. The return value is the */ -/* number of segments in the file. */ -/* */ -/*****************************************************************************/ - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist, - int *segmentmarkerlist, int numberofsegments) -#else /* not ANSI_DECLARATORS */ -void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments) -struct mesh *m; -struct behavior *b; -int *segmentlist; -int *segmentmarkerlist; -int numberofsegments; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -void formskeleton(struct mesh *m, struct behavior *b, - FILE *polyfile, char *polyfilename) -#else /* not ANSI_DECLARATORS */ -void formskeleton(m, b, polyfile, polyfilename) -struct mesh *m; -struct behavior *b; -FILE *polyfile; -char *polyfilename; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ -#ifdef TRILIBRARY - char polyfilename[6]; - int index; -#else /* not TRILIBRARY */ - char inputline[INPUTLINESIZE]; - char *stringptr; -#endif /* not TRILIBRARY */ - vertex endpoint1, endpoint2; - int segmentmarkers; - int end1, end2; - int boundmarker; - int i; - - if (b->poly) { - if (!b->quiet) { - printf("Recovering segments in Delaunay triangulation.\n"); - } -#ifdef TRILIBRARY - strcpy(polyfilename, "input"); - m->insegments = numberofsegments; - segmentmarkers = segmentmarkerlist != (int *) NULL; - index = 0; -#else /* not TRILIBRARY */ - /* Read the segments from a .poly file. */ - /* Read number of segments and number of boundary markers. */ - stringptr = readline(inputline, polyfile, polyfilename); - m->insegments = (int) strtol(stringptr, &stringptr, 0); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - segmentmarkers = 0; - } else { - segmentmarkers = (int) strtol(stringptr, &stringptr, 0); - } -#endif /* not TRILIBRARY */ - /* If the input vertices are collinear, there is no triangulation, */ - /* so don't try to insert segments. */ - if (m->triangles.items == 0) { - return; - } - - /* If segments are to be inserted, compute a mapping */ - /* from vertices to triangles. */ - if (m->insegments > 0) { - makevertexmap(m, b); - if (b->verbose) { - printf(" Recovering PSLG segments.\n"); - } - } - - boundmarker = 0; - /* Read and insert the segments. */ - for (i = 0; i < m->insegments; i++) { -#ifdef TRILIBRARY - end1 = segmentlist[index++]; - end2 = segmentlist[index++]; - if (segmentmarkers) { - boundmarker = segmentmarkerlist[i]; - } -#else /* not TRILIBRARY */ - stringptr = readline(inputline, polyfile, b->inpolyfilename); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Segment %d has no endpoints in %s.\n", - b->firstnumber + i, polyfilename); - triexit(1); - } else { - end1 = (int) strtol(stringptr, &stringptr, 0); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Segment %d is missing its second endpoint in %s.\n", - b->firstnumber + i, polyfilename); - triexit(1); - } else { - end2 = (int) strtol(stringptr, &stringptr, 0); - } - if (segmentmarkers) { - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - boundmarker = 0; - } else { - boundmarker = (int) strtol(stringptr, &stringptr, 0); - } - } -#endif /* not TRILIBRARY */ - if ((end1 < b->firstnumber) || - (end1 >= b->firstnumber + m->invertices)) { - if (!b->quiet) { - printf("Warning: Invalid first endpoint of segment %d in %s.\n", - b->firstnumber + i, polyfilename); - } - } else if ((end2 < b->firstnumber) || - (end2 >= b->firstnumber + m->invertices)) { - if (!b->quiet) { - printf("Warning: Invalid second endpoint of segment %d in %s.\n", - b->firstnumber + i, polyfilename); - } - } else { - /* Find the vertices numbered `end1' and `end2'. */ - endpoint1 = getvertex(m, b, end1); - endpoint2 = getvertex(m, b, end2); - if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) { - if (!b->quiet) { - printf("Warning: Endpoints of segment %d are coincident in %s.\n", - b->firstnumber + i, polyfilename); - } - } else { - insertsegment(m, b, endpoint1, endpoint2, boundmarker); - } - } - } - } else { - m->insegments = 0; - } - if (b->convex || !b->poly) { - /* Enclose the convex hull with subsegments. */ - if (b->verbose) { - printf(" Enclosing convex hull with segments.\n"); - } - markhull(m, b); - } -} - -/** **/ -/** **/ -/********* Segment insertion ends here *********/ - -/********* Carving out holes and concavities begins here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* infecthull() Virally infect all of the triangles of the convex hull */ -/* that are not protected by subsegments. Where there are */ -/* subsegments, set boundary markers as appropriate. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void infecthull(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void infecthull(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri hulltri; - struct otri nexttri; - struct otri starttri; - struct osub hullsubseg; - triangle **deadtriangle; - vertex horg, hdest; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - if (b->verbose) { - printf(" Marking concavities (external triangles) for elimination.\n"); - } - /* Find a triangle handle on the hull. */ - hulltri.tri = m->dummytri; - hulltri.orient = 0; - symself(hulltri); - /* Remember where we started so we know when to stop. */ - otricopy(hulltri, starttri); - /* Go once counterclockwise around the convex hull. */ - do { - /* Ignore triangles that are already infected. */ - if (!infected(hulltri)) { - /* Is the triangle protected by a subsegment? */ - tspivot(hulltri, hullsubseg); - if (hullsubseg.ss == m->dummysub) { - /* The triangle is not protected; infect it. */ - if (!infected(hulltri)) { - infect(hulltri); - deadtriangle = (triangle **) poolalloc(&m->viri); - *deadtriangle = hulltri.tri; - } - } else { - /* The triangle is protected; set boundary markers if appropriate. */ - if (mark(hullsubseg) == 0) { - setmark(hullsubseg, 1); - org(hulltri, horg); - dest(hulltri, hdest); - if (vertexmark(horg) == 0) { - setvertexmark(horg, 1); - } - if (vertexmark(hdest) == 0) { - setvertexmark(hdest, 1); - } - } - } - } - /* To find the next hull edge, go clockwise around the next vertex. */ - lnextself(hulltri); - oprev(hulltri, nexttri); - while (nexttri.tri != m->dummytri) { - otricopy(nexttri, hulltri); - oprev(hulltri, nexttri); - } - } while (!otriequal(hulltri, starttri)); -} - -/*****************************************************************************/ -/* */ -/* plague() Spread the virus from all infected triangles to any neighbors */ -/* not protected by subsegments. Delete all infected triangles. */ -/* */ -/* This is the procedure that actually creates holes and concavities. */ -/* */ -/* This procedure operates in two phases. The first phase identifies all */ -/* the triangles that will die, and marks them as infected. They are */ -/* marked to ensure that each triangle is added to the virus pool only */ -/* once, so the procedure will terminate. */ -/* */ -/* The second phase actually eliminates the infected triangles. It also */ -/* eliminates orphaned vertices. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void plague(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void plague(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri testtri; - struct otri neighbor; - triangle **virusloop; - triangle **deadtriangle; - struct osub neighborsubseg; - vertex testvertex; - vertex norg, ndest; - vertex deadorg, deaddest, deadapex; - int killorg; - triangle ptr; /* Temporary variable used by sym() and onext(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - if (b->verbose) { - printf(" Marking neighbors of marked triangles.\n"); - } - /* Loop through all the infected triangles, spreading the virus to */ - /* their neighbors, then to their neighbors' neighbors. */ - traversalinit(&m->viri); - virusloop = (triangle **) traverse(&m->viri); - while (virusloop != (triangle **) NULL) { - testtri.tri = *virusloop; - /* A triangle is marked as infected by messing with one of its pointers */ - /* to subsegments, setting it to an illegal value. Hence, we have to */ - /* temporarily uninfect this triangle so that we can examine its */ - /* adjacent subsegments. */ - uninfect(testtri); - if (b->verbose > 2) { - /* Assign the triangle an orientation for convenience in */ - /* checking its vertices. */ - testtri.orient = 0; - org(testtri, deadorg); - dest(testtri, deaddest); - apex(testtri, deadapex); - printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", - deadorg[0], deadorg[1], deaddest[0], deaddest[1], - deadapex[0], deadapex[1]); - } - /* Check each of the triangle's three neighbors. */ - for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { - /* Find the neighbor. */ - sym(testtri, neighbor); - /* Check for a subsegment between the triangle and its neighbor. */ - tspivot(testtri, neighborsubseg); - /* Check if the neighbor is nonexistent or already infected. */ - if ((neighbor.tri == m->dummytri) || infected(neighbor)) { - if (neighborsubseg.ss != m->dummysub) { - /* There is a subsegment separating the triangle from its */ - /* neighbor, but both triangles are dying, so the subsegment */ - /* dies too. */ - subsegdealloc(m, neighborsubseg.ss); - if (neighbor.tri != m->dummytri) { - /* Make sure the subsegment doesn't get deallocated again */ - /* later when the infected neighbor is visited. */ - uninfect(neighbor); - tsdissolve(neighbor); - infect(neighbor); - } - } - } else { /* The neighbor exists and is not infected. */ - if (neighborsubseg.ss == m->dummysub) { - /* There is no subsegment protecting the neighbor, so */ - /* the neighbor becomes infected. */ - if (b->verbose > 2) { - org(neighbor, deadorg); - dest(neighbor, deaddest); - apex(neighbor, deadapex); - printf( - " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", - deadorg[0], deadorg[1], deaddest[0], deaddest[1], - deadapex[0], deadapex[1]); - } - infect(neighbor); - /* Ensure that the neighbor's neighbors will be infected. */ - deadtriangle = (triangle **) poolalloc(&m->viri); - *deadtriangle = neighbor.tri; - } else { /* The neighbor is protected by a subsegment. */ - /* Remove this triangle from the subsegment. */ - stdissolve(neighborsubseg); - /* The subsegment becomes a boundary. Set markers accordingly. */ - if (mark(neighborsubseg) == 0) { - setmark(neighborsubseg, 1); - } - org(neighbor, norg); - dest(neighbor, ndest); - if (vertexmark(norg) == 0) { - setvertexmark(norg, 1); - } - if (vertexmark(ndest) == 0) { - setvertexmark(ndest, 1); - } - } - } - } - /* Remark the triangle as infected, so it doesn't get added to the */ - /* virus pool again. */ - infect(testtri); - virusloop = (triangle **) traverse(&m->viri); - } - - if (b->verbose) { - printf(" Deleting marked triangles.\n"); - } - - traversalinit(&m->viri); - virusloop = (triangle **) traverse(&m->viri); - while (virusloop != (triangle **) NULL) { - testtri.tri = *virusloop; - - /* Check each of the three corners of the triangle for elimination. */ - /* This is done by walking around each vertex, checking if it is */ - /* still connected to at least one live triangle. */ - for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { - org(testtri, testvertex); - /* Check if the vertex has already been tested. */ - if (testvertex != (vertex) NULL) { - killorg = 1; - /* Mark the corner of the triangle as having been tested. */ - setorg(testtri, NULL); - /* Walk counterclockwise about the vertex. */ - onext(testtri, neighbor); - /* Stop upon reaching a boundary or the starting triangle. */ - while ((neighbor.tri != m->dummytri) && - (!otriequal(neighbor, testtri))) { - if (infected(neighbor)) { - /* Mark the corner of this triangle as having been tested. */ - setorg(neighbor, NULL); - } else { - /* A live triangle. The vertex survives. */ - killorg = 0; - } - /* Walk counterclockwise about the vertex. */ - onextself(neighbor); - } - /* If we reached a boundary, we must walk clockwise as well. */ - if (neighbor.tri == m->dummytri) { - /* Walk clockwise about the vertex. */ - oprev(testtri, neighbor); - /* Stop upon reaching a boundary. */ - while (neighbor.tri != m->dummytri) { - if (infected(neighbor)) { - /* Mark the corner of this triangle as having been tested. */ - setorg(neighbor, NULL); - } else { - /* A live triangle. The vertex survives. */ - killorg = 0; - } - /* Walk clockwise about the vertex. */ - oprevself(neighbor); - } - } - if (killorg) { - if (b->verbose > 1) { - printf(" Deleting vertex (%.12g, %.12g)\n", - testvertex[0], testvertex[1]); - } - setvertextype(testvertex, UNDEADVERTEX); - m->undeads++; - } - } - } - - /* Record changes in the number of boundary edges, and disconnect */ - /* dead triangles from their neighbors. */ - for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { - sym(testtri, neighbor); - if (neighbor.tri == m->dummytri) { - /* There is no neighboring triangle on this edge, so this edge */ - /* is a boundary edge. This triangle is being deleted, so this */ - /* boundary edge is deleted. */ - m->hullsize--; - } else { - /* Disconnect the triangle from its neighbor. */ - dissolve(neighbor); - /* There is a neighboring triangle on this edge, so this edge */ - /* becomes a boundary edge when this triangle is deleted. */ - m->hullsize++; - } - } - /* Return the dead triangle to the pool of triangles. */ - triangledealloc(m, testtri.tri); - virusloop = (triangle **) traverse(&m->viri); - } - /* Empty the virus pool. */ - poolrestart(&m->viri); -} - -/*****************************************************************************/ -/* */ -/* regionplague() Spread regional attributes and/or area constraints */ -/* (from a .poly file) throughout the mesh. */ -/* */ -/* This procedure operates in two phases. The first phase spreads an */ -/* attribute and/or an area constraint through a (segment-bounded) region. */ -/* The triangles are marked to ensure that each triangle is added to the */ -/* virus pool only once, so the procedure will terminate. */ -/* */ -/* The second phase uninfects all infected triangles, returning them to */ -/* normal. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void regionplague(struct mesh *m, struct behavior *b, - REAL attribute, REAL area) -#else /* not ANSI_DECLARATORS */ -void regionplague(m, b, attribute, area) -struct mesh *m; -struct behavior *b; -REAL attribute; -REAL area; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri testtri; - struct otri neighbor; - triangle **virusloop; - triangle **regiontri; - struct osub neighborsubseg; - vertex regionorg, regiondest, regionapex; - triangle ptr; /* Temporary variable used by sym() and onext(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - if (b->verbose > 1) { - printf(" Marking neighbors of marked triangles.\n"); - } - /* Loop through all the infected triangles, spreading the attribute */ - /* and/or area constraint to their neighbors, then to their neighbors' */ - /* neighbors. */ - traversalinit(&m->viri); - virusloop = (triangle **) traverse(&m->viri); - while (virusloop != (triangle **) NULL) { - testtri.tri = *virusloop; - /* A triangle is marked as infected by messing with one of its pointers */ - /* to subsegments, setting it to an illegal value. Hence, we have to */ - /* temporarily uninfect this triangle so that we can examine its */ - /* adjacent subsegments. */ - uninfect(testtri); - if (b->regionattrib) { - /* Set an attribute. */ - setelemattribute(testtri, m->eextras, attribute); - } - if (b->vararea) { - /* Set an area constraint. */ - setareabound(testtri, area); - } - if (b->verbose > 2) { - /* Assign the triangle an orientation for convenience in */ - /* checking its vertices. */ - testtri.orient = 0; - org(testtri, regionorg); - dest(testtri, regiondest); - apex(testtri, regionapex); - printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", - regionorg[0], regionorg[1], regiondest[0], regiondest[1], - regionapex[0], regionapex[1]); - } - /* Check each of the triangle's three neighbors. */ - for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { - /* Find the neighbor. */ - sym(testtri, neighbor); - /* Check for a subsegment between the triangle and its neighbor. */ - tspivot(testtri, neighborsubseg); - /* Make sure the neighbor exists, is not already infected, and */ - /* isn't protected by a subsegment. */ - if ((neighbor.tri != m->dummytri) && !infected(neighbor) - && (neighborsubseg.ss == m->dummysub)) { - if (b->verbose > 2) { - org(neighbor, regionorg); - dest(neighbor, regiondest); - apex(neighbor, regionapex); - printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", - regionorg[0], regionorg[1], regiondest[0], regiondest[1], - regionapex[0], regionapex[1]); - } - /* Infect the neighbor. */ - infect(neighbor); - /* Ensure that the neighbor's neighbors will be infected. */ - regiontri = (triangle **) poolalloc(&m->viri); - *regiontri = neighbor.tri; - } - } - /* Remark the triangle as infected, so it doesn't get added to the */ - /* virus pool again. */ - infect(testtri); - virusloop = (triangle **) traverse(&m->viri); - } - - /* Uninfect all triangles. */ - if (b->verbose > 1) { - printf(" Unmarking marked triangles.\n"); - } - traversalinit(&m->viri); - virusloop = (triangle **) traverse(&m->viri); - while (virusloop != (triangle **) NULL) { - testtri.tri = *virusloop; - uninfect(testtri); - virusloop = (triangle **) traverse(&m->viri); - } - /* Empty the virus pool. */ - poolrestart(&m->viri); -} - -/*****************************************************************************/ -/* */ -/* carveholes() Find the holes and infect them. Find the area */ -/* constraints and infect them. Infect the convex hull. */ -/* Spread the infection and kill triangles. Spread the */ -/* area constraints. */ -/* */ -/* This routine mainly calls other routines to carry out all these */ -/* functions. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes, - REAL *regionlist, int regions) -#else /* not ANSI_DECLARATORS */ -void carveholes(m, b, holelist, holes, regionlist, regions) -struct mesh *m; -struct behavior *b; -REAL *holelist; -int holes; -REAL *regionlist; -int regions; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri searchtri; - struct otri triangleloop; - struct otri *regiontris; - triangle **holetri; - triangle **regiontri; - vertex searchorg, searchdest; - enum locateresult intersect; - int i; - triangle ptr; /* Temporary variable used by sym(). */ - - if (!(b->quiet || (b->noholes && b->convex))) { - printf("Removing unwanted triangles.\n"); - if (b->verbose && (holes > 0)) { - printf(" Marking holes for elimination.\n"); - } - } - - if (regions > 0) { - /* Allocate storage for the triangles in which region points fall. */ - regiontris = (struct otri *) trimalloc(regions * - (int) sizeof(struct otri)); - } else { - regiontris = (struct otri *) NULL; - } - - if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { - /* Initialize a pool of viri to be used for holes, concavities, */ - /* regional attributes, and/or regional area constraints. */ - poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0); - } - - if (!b->convex) { - /* Mark as infected any unprotected triangles on the boundary. */ - /* This is one way by which concavities are created. */ - infecthull(m, b); - } - - if ((holes > 0) && !b->noholes) { - /* Infect each triangle in which a hole lies. */ - for (i = 0; i < 2 * holes; i += 2) { - /* Ignore holes that aren't within the bounds of the mesh. */ - if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax) - && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) { - /* Start searching from some triangle on the outer boundary. */ - searchtri.tri = m->dummytri; - searchtri.orient = 0; - symself(searchtri); - /* Ensure that the hole is to the left of this boundary edge; */ - /* otherwise, locate() will falsely report that the hole */ - /* falls within the starting triangle. */ - org(searchtri, searchorg); - dest(searchtri, searchdest); - if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) > - 0.0) { - /* Find a triangle that contains the hole. */ - intersect = locate(m, b, &holelist[i], &searchtri); - if ((intersect != OUTSIDE) && (!infected(searchtri))) { - /* Infect the triangle. This is done by marking the triangle */ - /* as infected and including the triangle in the virus pool. */ - infect(searchtri); - holetri = (triangle **) poolalloc(&m->viri); - *holetri = searchtri.tri; - } - } - } - } - } - - /* Now, we have to find all the regions BEFORE we carve the holes, because */ - /* locate() won't work when the triangulation is no longer convex. */ - /* (Incidentally, this is the reason why regional attributes and area */ - /* constraints can't be used when refining a preexisting mesh, which */ - /* might not be convex; they can only be used with a freshly */ - /* triangulated PSLG.) */ - if (regions > 0) { - /* Find the starting triangle for each region. */ - for (i = 0; i < regions; i++) { - regiontris[i].tri = m->dummytri; - /* Ignore region points that aren't within the bounds of the mesh. */ - if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) && - (regionlist[4 * i + 1] >= m->ymin) && - (regionlist[4 * i + 1] <= m->ymax)) { - /* Start searching from some triangle on the outer boundary. */ - searchtri.tri = m->dummytri; - searchtri.orient = 0; - symself(searchtri); - /* Ensure that the region point is to the left of this boundary */ - /* edge; otherwise, locate() will falsely report that the */ - /* region point falls within the starting triangle. */ - org(searchtri, searchorg); - dest(searchtri, searchdest); - if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) > - 0.0) { - /* Find a triangle that contains the region point. */ - intersect = locate(m, b, ®ionlist[4 * i], &searchtri); - if ((intersect != OUTSIDE) && (!infected(searchtri))) { - /* Record the triangle for processing after the */ - /* holes have been carved. */ - otricopy(searchtri, regiontris[i]); - } - } - } - } - } - - if (m->viri.items > 0) { - /* Carve the holes and concavities. */ - plague(m, b); - } - /* The virus pool should be empty now. */ - - if (regions > 0) { - if (!b->quiet) { - if (b->regionattrib) { - if (b->vararea) { - printf("Spreading regional attributes and area constraints.\n"); - } else { - printf("Spreading regional attributes.\n"); - } - } else { - printf("Spreading regional area constraints.\n"); - } - } - if (b->regionattrib && !b->refine) { - /* Assign every triangle a regional attribute of zero. */ - traversalinit(&m->triangles); - triangleloop.orient = 0; - triangleloop.tri = triangletraverse(m); - while (triangleloop.tri != (triangle *) NULL) { - setelemattribute(triangleloop, m->eextras, 0.0); - triangleloop.tri = triangletraverse(m); - } - } - for (i = 0; i < regions; i++) { - if (regiontris[i].tri != m->dummytri) { - /* Make sure the triangle under consideration still exists. */ - /* It may have been eaten by the virus. */ - if (!deadtri(regiontris[i].tri)) { - /* Put one triangle in the virus pool. */ - infect(regiontris[i]); - regiontri = (triangle **) poolalloc(&m->viri); - *regiontri = regiontris[i].tri; - /* Apply one region's attribute and/or area constraint. */ - regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]); - /* The virus pool should be empty now. */ - } - } - } - if (b->regionattrib && !b->refine) { - /* Note the fact that each triangle has an additional attribute. */ - m->eextras++; - } - } - - /* Free up memory. */ - if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { - pooldeinit(&m->viri); - } - if (regions > 0) { - trifree((VOID *) regiontris); - } -} - -/** **/ -/** **/ -/********* Carving out holes and concavities ends here *********/ - -/********* Mesh quality maintenance begins here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* tallyencs() Traverse the entire list of subsegments, and check each */ -/* to see if it is encroached. If so, add it to the list. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void tallyencs(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void tallyencs(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct osub subsegloop; - int dummy; - - traversalinit(&m->subsegs); - subsegloop.ssorient = 0; - subsegloop.ss = subsegtraverse(m); - while (subsegloop.ss != (subseg *) NULL) { - /* If the segment is encroached, add it to the list. */ - dummy = checkseg4encroach(m, b, &subsegloop); - subsegloop.ss = subsegtraverse(m); - } -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* precisionerror() Print an error message for precision problems. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -void precisionerror() -{ - printf("Try increasing the area criterion and/or reducing the minimum\n"); - printf(" allowable angle so that tiny triangles are not created.\n"); -#ifdef SINGLE - printf("Alternatively, try recompiling me with double precision\n"); - printf(" arithmetic (by removing \"#define SINGLE\" from the\n"); - printf(" source file or \"-DSINGLE\" from the makefile).\n"); -#endif /* SINGLE */ -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* splitencsegs() Split all the encroached subsegments. */ -/* */ -/* Each encroached subsegment is repaired by splitting it - inserting a */ -/* vertex at or near its midpoint. Newly inserted vertices may encroach */ -/* upon other subsegments; these are also repaired. */ -/* */ -/* `triflaws' is a flag that specifies whether one should take note of new */ -/* bad triangles that result from inserting vertices to repair encroached */ -/* subsegments. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void splitencsegs(struct mesh *m, struct behavior *b, int triflaws) -#else /* not ANSI_DECLARATORS */ -void splitencsegs(m, b, triflaws) -struct mesh *m; -struct behavior *b; -int triflaws; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri enctri; - struct otri testtri; - struct osub testsh; - struct osub currentenc; - struct badsubseg *encloop; - vertex eorg, edest, eapex; - vertex newvertex; - enum insertvertexresult success; - REAL segmentlength, nearestpoweroftwo; - REAL split; - REAL multiplier, divisor; - int acuteorg, acuteorg2, acutedest, acutedest2; - int dummy; - int i; - triangle ptr; /* Temporary variable used by stpivot(). */ - subseg sptr; /* Temporary variable used by snext(). */ - - /* Note that steinerleft == -1 if an unlimited number */ - /* of Steiner points is allowed. */ - while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) { - traversalinit(&m->badsubsegs); - encloop = badsubsegtraverse(m); - while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) { - sdecode(encloop->encsubseg, currentenc); - sorg(currentenc, eorg); - sdest(currentenc, edest); - /* Make sure that this segment is still the same segment it was */ - /* when it was determined to be encroached. If the segment was */ - /* enqueued multiple times (because several newly inserted */ - /* vertices encroached it), it may have already been split. */ - if (!deadsubseg(currentenc.ss) && - (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) { - /* To decide where to split a segment, we need to know if the */ - /* segment shares an endpoint with an adjacent segment. */ - /* The concern is that, if we simply split every encroached */ - /* segment in its center, two adjacent segments with a small */ - /* angle between them might lead to an infinite loop; each */ - /* vertex added to split one segment will encroach upon the */ - /* other segment, which must then be split with a vertex that */ - /* will encroach upon the first segment, and so on forever. */ - /* To avoid this, imagine a set of concentric circles, whose */ - /* radii are powers of two, about each segment endpoint. */ - /* These concentric circles determine where the segment is */ - /* split. (If both endpoints are shared with adjacent */ - /* segments, split the segment in the middle, and apply the */ - /* concentric circles for later splittings.) */ - - /* Is the origin shared with another segment? */ - stpivot(currentenc, enctri); - lnext(enctri, testtri); - tspivot(testtri, testsh); - acuteorg = testsh.ss != m->dummysub; - /* Is the destination shared with another segment? */ - lnextself(testtri); - tspivot(testtri, testsh); - acutedest = testsh.ss != m->dummysub; - - /* If we're using Chew's algorithm (rather than Ruppert's) */ - /* to define encroachment, delete free vertices from the */ - /* subsegment's diametral circle. */ - if (!b->conformdel && !acuteorg && !acutedest) { - apex(enctri, eapex); - while ((vertextype(eapex) == FREEVERTEX) && - ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + - (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) { - deletevertex(m, b, &testtri); - stpivot(currentenc, enctri); - apex(enctri, eapex); - lprev(enctri, testtri); - } - } - - /* Now, check the other side of the segment, if there's a triangle */ - /* there. */ - sym(enctri, testtri); - if (testtri.tri != m->dummytri) { - /* Is the destination shared with another segment? */ - lnextself(testtri); - tspivot(testtri, testsh); - acutedest2 = testsh.ss != m->dummysub; - acutedest = acutedest || acutedest2; - /* Is the origin shared with another segment? */ - lnextself(testtri); - tspivot(testtri, testsh); - acuteorg2 = testsh.ss != m->dummysub; - acuteorg = acuteorg || acuteorg2; - - /* Delete free vertices from the subsegment's diametral circle. */ - if (!b->conformdel && !acuteorg2 && !acutedest2) { - org(testtri, eapex); - while ((vertextype(eapex) == FREEVERTEX) && - ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + - (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) { - deletevertex(m, b, &testtri); - sym(enctri, testtri); - apex(testtri, eapex); - lprevself(testtri); - } - } - } - - /* Use the concentric circles if exactly one endpoint is shared */ - /* with another adjacent segment. */ - if (acuteorg || acutedest) { - segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) + - (edest[1] - eorg[1]) * (edest[1] - eorg[1])); - /* Find the power of two that most evenly splits the segment. */ - /* The worst case is a 2:1 ratio between subsegment lengths. */ - nearestpoweroftwo = 1.0; - while (segmentlength > 3.0 * nearestpoweroftwo) { - nearestpoweroftwo *= 2.0; - } - while (segmentlength < 1.5 * nearestpoweroftwo) { - nearestpoweroftwo *= 0.5; - } - /* Where do we split the segment? */ - split = nearestpoweroftwo / segmentlength; - if (acutedest) { - split = 1.0 - split; - } - } else { - /* If we're not worried about adjacent segments, split */ - /* this segment in the middle. */ - split = 0.5; - } - - /* Create the new vertex. */ - newvertex = (vertex) poolalloc(&m->vertices); - /* Interpolate its coordinate and attributes. */ - for (i = 0; i < 2 + m->nextras; i++) { - newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]); - } - - if (!b->noexact) { - /* Roundoff in the above calculation may yield a `newvertex' */ - /* that is not precisely collinear with `eorg' and `edest'. */ - /* Improve collinearity by one step of iterative refinement. */ - multiplier = counterclockwise(m, b, eorg, edest, newvertex); - divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) + - (eorg[1] - edest[1]) * (eorg[1] - edest[1])); - if ((multiplier != 0.0) && (divisor != 0.0)) { - multiplier = multiplier / divisor; - /* Watch out for NANs. */ - if (multiplier == multiplier) { - newvertex[0] += multiplier * (edest[1] - eorg[1]); - newvertex[1] += multiplier * (eorg[0] - edest[0]); - } - } - } - - setvertexmark(newvertex, mark(currentenc)); - setvertextype(newvertex, SEGMENTVERTEX); - if (b->verbose > 1) { - printf( - " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", - eorg[0], eorg[1], edest[0], edest[1], - newvertex[0], newvertex[1]); - } - /* Check whether the new vertex lies on an endpoint. */ - if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) || - ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) { - printf("Error: Ran out of precision at (%.12g, %.12g).\n", - newvertex[0], newvertex[1]); - printf("I attempted to split a segment to a smaller size than\n"); - printf(" can be accommodated by the finite precision of\n"); - printf(" floating point arithmetic.\n"); - precisionerror(); - triexit(1); - } - /* Insert the splitting vertex. This should always succeed. */ - success = insertvertex(m, b, newvertex, &enctri, ¤tenc, - 1, triflaws); - if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) { - printf("Internal error in splitencsegs():\n"); - printf(" Failure to split a segment.\n"); - internalerror(); - } - if (m->steinerleft > 0) { - m->steinerleft--; - } - /* Check the two new subsegments to see if they're encroached. */ - dummy = checkseg4encroach(m, b, ¤tenc); - snextself(currentenc); - dummy = checkseg4encroach(m, b, ¤tenc); - } - - badsubsegdealloc(m, encloop); - encloop = badsubsegtraverse(m); - } - } -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* tallyfaces() Test every triangle in the mesh for quality measures. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void tallyfaces(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void tallyfaces(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri triangleloop; - - if (b->verbose) { - printf(" Making a list of bad triangles.\n"); - } - traversalinit(&m->triangles); - triangleloop.orient = 0; - triangleloop.tri = triangletraverse(m); - while (triangleloop.tri != (triangle *) NULL) { - /* If the triangle is bad, enqueue it. */ - testtriangle(m, b, &triangleloop); - triangleloop.tri = triangletraverse(m); - } -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* splittriangle() Inserts a vertex at the circumcenter of a triangle. */ -/* Deletes the newly inserted vertex if it encroaches */ -/* upon a segment. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void splittriangle(struct mesh *m, struct behavior *b, - struct badtriang *badtri) -#else /* not ANSI_DECLARATORS */ -void splittriangle(m, b, badtri) -struct mesh *m; -struct behavior *b; -struct badtriang *badtri; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri badotri; - vertex borg, bdest, bapex; - vertex newvertex; - REAL xi, eta; - enum insertvertexresult success; - int errorflag; - int i; - - decode(badtri->poortri, badotri); - org(badotri, borg); - dest(badotri, bdest); - apex(badotri, bapex); - /* Make sure that this triangle is still the same triangle it was */ - /* when it was tested and determined to be of bad quality. */ - /* Subsequent transformations may have made it a different triangle. */ - if (!deadtri(badotri.tri) && (borg == badtri->triangorg) && - (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) { - if (b->verbose > 1) { - printf(" Splitting this triangle at its circumcenter:\n"); - printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0], - borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); - } - - errorflag = 0; - /* Create a new vertex at the triangle's circumcenter. */ - newvertex = (vertex) poolalloc(&m->vertices); - findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1); - - /* Check whether the new vertex lies on a triangle vertex. */ - if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) || - ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) || - ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) { - if (!b->quiet) { - printf( - "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", - newvertex[0], newvertex[1]); - errorflag = 1; - } - vertexdealloc(m, newvertex); - } else { - for (i = 2; i < 2 + m->nextras; i++) { - /* Interpolate the vertex attributes at the circumcenter. */ - newvertex[i] = borg[i] + xi * (bdest[i] - borg[i]) - + eta * (bapex[i] - borg[i]); - } - /* The new vertex must be in the interior, and therefore is a */ - /* free vertex with a marker of zero. */ - setvertexmark(newvertex, 0); - setvertextype(newvertex, FREEVERTEX); - - /* Ensure that the handle `badotri' does not represent the longest */ - /* edge of the triangle. This ensures that the circumcenter must */ - /* fall to the left of this edge, so point location will work. */ - /* (If the angle org-apex-dest exceeds 90 degrees, then the */ - /* circumcenter lies outside the org-dest edge, and eta is */ - /* negative. Roundoff error might prevent eta from being */ - /* negative when it should be, so I test eta against xi.) */ - if (eta < xi) { - lprevself(badotri); - } - - /* Insert the circumcenter, searching from the edge of the triangle, */ - /* and maintain the Delaunay property of the triangulation. */ - success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL, - 1, 1); - if (success == SUCCESSFULVERTEX) { - if (m->steinerleft > 0) { - m->steinerleft--; - } - } else if (success == ENCROACHINGVERTEX) { - /* If the newly inserted vertex encroaches upon a subsegment, */ - /* delete the new vertex. */ - undovertex(m, b); - if (b->verbose > 1) { - printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); - } - vertexdealloc(m, newvertex); - } else if (success == VIOLATINGVERTEX) { - /* Failed to insert the new vertex, but some subsegment was */ - /* marked as being encroached. */ - vertexdealloc(m, newvertex); - } else { /* success == DUPLICATEVERTEX */ - /* Couldn't insert the new vertex because a vertex is already there. */ - if (!b->quiet) { - printf( - "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", - newvertex[0], newvertex[1]); - errorflag = 1; - } - vertexdealloc(m, newvertex); - } - } - if (errorflag) { - if (b->verbose) { - printf(" The new vertex is at the circumcenter of triangle\n"); - printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", - borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); - } - printf("This probably means that I am trying to refine triangles\n"); - printf(" to a smaller size than can be accommodated by the finite\n"); - printf(" precision of floating point arithmetic. (You can be\n"); - printf(" sure of this if I fail to terminate.)\n"); - precisionerror(); - } - } -} - -#endif /* not CDT_ONLY */ - -/*****************************************************************************/ -/* */ -/* enforcequality() Remove all the encroached subsegments and bad */ -/* triangles from the triangulation. */ -/* */ -/*****************************************************************************/ - -#ifndef CDT_ONLY - -#ifdef ANSI_DECLARATORS -void enforcequality(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void enforcequality(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct badtriang *badtri; - int i; - - if (!b->quiet) { - printf("Adding Steiner points to enforce quality.\n"); - } - /* Initialize the pool of encroached subsegments. */ - poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK, - BADSUBSEGPERBLOCK, 0); - if (b->verbose) { - printf(" Looking for encroached subsegments.\n"); - } - /* Test all segments to see if they're encroached. */ - tallyencs(m, b); - if (b->verbose && (m->badsubsegs.items > 0)) { - printf(" Splitting encroached subsegments.\n"); - } - /* Fix encroached subsegments without noting bad triangles. */ - splitencsegs(m, b, 0); - /* At this point, if we haven't run out of Steiner points, the */ - /* triangulation should be (conforming) Delaunay. */ - - /* Next, we worry about enforcing triangle quality. */ - if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) { - /* Initialize the pool of bad triangles. */ - poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK, - BADTRIPERBLOCK, 0); - /* Initialize the queues of bad triangles. */ - for (i = 0; i < 4096; i++) { - m->queuefront[i] = (struct badtriang *) NULL; - } - m->firstnonemptyq = -1; - /* Test all triangles to see if they're bad. */ - tallyfaces(m, b); - /* Initialize the pool of recently flipped triangles. */ - poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK, - FLIPSTACKERPERBLOCK, 0); - m->checkquality = 1; - if (b->verbose) { - printf(" Splitting bad triangles.\n"); - } - while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) { - /* Fix one bad triangle by inserting a vertex at its circumcenter. */ - badtri = dequeuebadtriang(m); - splittriangle(m, b, badtri); - if (m->badsubsegs.items > 0) { - /* Put bad triangle back in queue for another try later. */ - enqueuebadtriang(m, b, badtri); - /* Fix any encroached subsegments that resulted. */ - /* Record any new bad triangles that result. */ - splitencsegs(m, b, 1); - } else { - /* Return the bad triangle to the pool. */ - pooldealloc(&m->badtriangles, (VOID *) badtri); - } - } - } - /* At this point, if the "-D" switch was selected and we haven't run out */ - /* of Steiner points, the triangulation should be (conforming) Delaunay */ - /* and have no low-quality triangles. */ - - /* Might we have run out of Steiner points too soon? */ - if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) && - (m->steinerleft == 0)) { - printf("\nWarning: I ran out of Steiner points, but the mesh has\n"); - if (m->badsubsegs.items == 1) { - printf(" one encroached subsegment, and therefore might not be truly\n" - ); - } else { - printf(" %ld encroached subsegments, and therefore might not be truly\n" - , m->badsubsegs.items); - } - printf(" Delaunay. If the Delaunay property is important to you,\n"); - printf(" try increasing the number of Steiner points (controlled by\n"); - printf(" the -S switch) slightly and try again.\n\n"); - } -} - -#endif /* not CDT_ONLY */ - -/** **/ -/** **/ -/********* Mesh quality maintenance ends here *********/ - -/*****************************************************************************/ -/* */ -/* highorder() Create extra nodes for quadratic subparametric elements. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void highorder(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void highorder(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri triangleloop, trisym; - struct osub checkmark; - vertex newvertex; - vertex torg, tdest; - int i; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - - if (!b->quiet) { - printf("Adding vertices for second-order triangles.\n"); - } - /* The following line ensures that dead items in the pool of nodes */ - /* cannot be allocated for the extra nodes associated with high */ - /* order elements. This ensures that the primary nodes (at the */ - /* corners of elements) will occur earlier in the output files, and */ - /* have lower indices, than the extra nodes. */ - m->vertices.deaditemstack = (VOID *) NULL; - - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - /* To loop over the set of edges, loop over all triangles, and look at */ - /* the three edges of each triangle. If there isn't another triangle */ - /* adjacent to the edge, operate on the edge. If there is another */ - /* adjacent triangle, operate on the edge only if the current triangle */ - /* has a smaller pointer than its neighbor. This way, each edge is */ - /* considered only once. */ - while (triangleloop.tri != (triangle *) NULL) { - for (triangleloop.orient = 0; triangleloop.orient < 3; - triangleloop.orient++) { - sym(triangleloop, trisym); - if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { - org(triangleloop, torg); - dest(triangleloop, tdest); - /* Create a new node in the middle of the edge. Interpolate */ - /* its attributes. */ - newvertex = (vertex) poolalloc(&m->vertices); - for (i = 0; i < 2 + m->nextras; i++) { - newvertex[i] = 0.5 * (torg[i] + tdest[i]); - } - /* Set the new node's marker to zero or one, depending on */ - /* whether it lies on a boundary. */ - setvertexmark(newvertex, trisym.tri == m->dummytri); - setvertextype(newvertex, - trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX); - if (b->usesegments) { - tspivot(triangleloop, checkmark); - /* If this edge is a segment, transfer the marker to the new node. */ - if (checkmark.ss != m->dummysub) { - setvertexmark(newvertex, mark(checkmark)); - setvertextype(newvertex, SEGMENTVERTEX); - } - } - if (b->verbose > 1) { - printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]); - } - /* Record the new node in the (one or two) adjacent elements. */ - triangleloop.tri[m->highorderindex + triangleloop.orient] = - (triangle) newvertex; - if (trisym.tri != m->dummytri) { - trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex; - } - } - } - triangleloop.tri = triangletraverse(m); - } -} - -/********* File I/O routines begin here *********/ -/** **/ -/** **/ - -/*****************************************************************************/ -/* */ -/* readline() Read a nonempty line from a file. */ -/* */ -/* A line is considered "nonempty" if it contains something that looks like */ -/* a number. Comments (prefaced by `#') are ignored. */ -/* */ -/*****************************************************************************/ - -#ifndef TRILIBRARY - -#ifdef ANSI_DECLARATORS -char *readline(char *string, FILE *infile, char *infilename) -#else /* not ANSI_DECLARATORS */ -char *readline(string, infile, infilename) -char *string; -FILE *infile; -char *infilename; -#endif /* not ANSI_DECLARATORS */ - -{ - char *result; - - /* Search for something that looks like a number. */ - do { - result = fgets(string, INPUTLINESIZE, infile); - if (result == (char *) NULL) { - printf(" Error: Unexpected end of file in %s.\n", infilename); - triexit(1); - } - /* Skip anything that doesn't look like a number, a comment, */ - /* or the end of a line. */ - while ((*result != '\0') && (*result != '#') - && (*result != '.') && (*result != '+') && (*result != '-') - && ((*result < '0') || (*result > '9'))) { - result++; - } - /* If it's a comment or end of line, read another line and try again. */ - } while ((*result == '#') || (*result == '\0')); - return result; -} - -#endif /* not TRILIBRARY */ - -/*****************************************************************************/ -/* */ -/* findfield() Find the next field of a string. */ -/* */ -/* Jumps past the current field by searching for whitespace, then jumps */ -/* past the whitespace to find the next field. */ -/* */ -/*****************************************************************************/ - -#ifndef TRILIBRARY - -#ifdef ANSI_DECLARATORS -char *findfield(char *string) -#else /* not ANSI_DECLARATORS */ -char *findfield(string) -char *string; -#endif /* not ANSI_DECLARATORS */ - -{ - char *result; - - result = string; - /* Skip the current field. Stop upon reaching whitespace. */ - while ((*result != '\0') && (*result != '#') - && (*result != ' ') && (*result != '\t')) { - result++; - } - /* Now skip the whitespace and anything else that doesn't look like a */ - /* number, a comment, or the end of a line. */ - while ((*result != '\0') && (*result != '#') - && (*result != '.') && (*result != '+') && (*result != '-') - && ((*result < '0') || (*result > '9'))) { - result++; - } - /* Check for a comment (prefixed with `#'). */ - if (*result == '#') { - *result = '\0'; - } - return result; -} - -#endif /* not TRILIBRARY */ - -/*****************************************************************************/ -/* */ -/* readnodes() Read the vertices from a file, which may be a .node or */ -/* .poly file. */ -/* */ -/*****************************************************************************/ - -#ifndef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void readnodes(struct mesh *m, struct behavior *b, char *nodefilename, - char *polyfilename, FILE **polyfile) -#else /* not ANSI_DECLARATORS */ -void readnodes(m, b, nodefilename, polyfilename, polyfile) -struct mesh *m; -struct behavior *b; -char *nodefilename; -char *polyfilename; -FILE **polyfile; -#endif /* not ANSI_DECLARATORS */ - -{ - FILE *infile; - vertex vertexloop; - char inputline[INPUTLINESIZE]; - char *stringptr; - char *infilename; - REAL x, y; - int firstnode; - int nodemarkers; - int currentmarker; - int i, j; - - if (b->poly) { - /* Read the vertices from a .poly file. */ - if (!b->quiet) { - printf("Opening %s.\n", polyfilename); - } - *polyfile = fopen(polyfilename, "r"); - if (*polyfile == (FILE *) NULL) { - printf(" Error: Cannot access file %s.\n", polyfilename); - triexit(1); - } - /* Read number of vertices, number of dimensions, number of vertex */ - /* attributes, and number of boundary markers. */ - stringptr = readline(inputline, *polyfile, polyfilename); - m->invertices = (int) strtol(stringptr, &stringptr, 0); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - m->mesh_dim = 2; - } else { - m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - m->nextras = 0; - } else { - m->nextras = (int) strtol(stringptr, &stringptr, 0); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - nodemarkers = 0; - } else { - nodemarkers = (int) strtol(stringptr, &stringptr, 0); - } - if (m->invertices > 0) { - infile = *polyfile; - infilename = polyfilename; - m->readnodefile = 0; - } else { - /* If the .poly file claims there are zero vertices, that means that */ - /* the vertices should be read from a separate .node file. */ - m->readnodefile = 1; - infilename = nodefilename; - } - } else { - m->readnodefile = 1; - infilename = nodefilename; - *polyfile = (FILE *) NULL; - } - - if (m->readnodefile) { - /* Read the vertices from a .node file. */ - if (!b->quiet) { - printf("Opening %s.\n", nodefilename); - } - infile = fopen(nodefilename, "r"); - if (infile == (FILE *) NULL) { - printf(" Error: Cannot access file %s.\n", nodefilename); - triexit(1); - } - /* Read number of vertices, number of dimensions, number of vertex */ - /* attributes, and number of boundary markers. */ - stringptr = readline(inputline, infile, nodefilename); - m->invertices = (int) strtol(stringptr, &stringptr, 0); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - m->mesh_dim = 2; - } else { - m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - m->nextras = 0; - } else { - m->nextras = (int) strtol(stringptr, &stringptr, 0); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - nodemarkers = 0; - } else { - nodemarkers = (int) strtol(stringptr, &stringptr, 0); - } - } - - if (m->invertices < 3) { - printf("Error: Input must have at least three input vertices.\n"); - triexit(1); - } - if (m->mesh_dim != 2) { - printf("Error: Triangle only works with two-dimensional meshes.\n"); - triexit(1); - } - if (m->nextras == 0) { - b->weighted = 0; - } - - initializevertexpool(m, b); - - /* Read the vertices. */ - for (i = 0; i < m->invertices; i++) { - vertexloop = (vertex) poolalloc(&m->vertices); - stringptr = readline(inputline, infile, infilename); - if (i == 0) { - firstnode = (int) strtol(stringptr, &stringptr, 0); - if ((firstnode == 0) || (firstnode == 1)) { - b->firstnumber = firstnode; - } - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i); - triexit(1); - } - x = (REAL) strtod(stringptr, &stringptr); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i); - triexit(1); - } - y = (REAL) strtod(stringptr, &stringptr); - vertexloop[0] = x; - vertexloop[1] = y; - /* Read the vertex attributes. */ - for (j = 2; j < 2 + m->nextras; j++) { - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - vertexloop[j] = 0.0; - } else { - vertexloop[j] = (REAL) strtod(stringptr, &stringptr); - } - } - if (nodemarkers) { - /* Read a vertex marker. */ - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - setvertexmark(vertexloop, 0); - } else { - currentmarker = (int) strtol(stringptr, &stringptr, 0); - setvertexmark(vertexloop, currentmarker); - } - } else { - /* If no markers are specified in the file, they default to zero. */ - setvertexmark(vertexloop, 0); - } - setvertextype(vertexloop, INPUTVERTEX); - /* Determine the smallest and largest x and y coordinates. */ - if (i == 0) { - m->xmin = m->xmax = x; - m->ymin = m->ymax = y; - } else { - m->xmin = (x < m->xmin) ? x : m->xmin; - m->xmax = (x > m->xmax) ? x : m->xmax; - m->ymin = (y < m->ymin) ? y : m->ymin; - m->ymax = (y > m->ymax) ? y : m->ymax; - } - } - if (m->readnodefile) { - fclose(infile); - } - - /* Nonexistent x value used as a flag to mark circle events in sweepline */ - /* Delaunay algorithm. */ - m->xminextreme = 10 * m->xmin - 9 * m->xmax; -} - -#endif /* not TRILIBRARY */ - -/*****************************************************************************/ -/* */ -/* transfernodes() Read the vertices from memory. */ -/* */ -/*****************************************************************************/ - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist, - REAL *pointattriblist, int *pointmarkerlist, - int numberofpoints, int numberofpointattribs) -#else /* not ANSI_DECLARATORS */ -void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist, - numberofpoints, numberofpointattribs) -struct mesh *m; -struct behavior *b; -REAL *pointlist; -REAL *pointattriblist; -int *pointmarkerlist; -int numberofpoints; -int numberofpointattribs; -#endif /* not ANSI_DECLARATORS */ - -{ - vertex vertexloop; - REAL x, y; - int i, j; - int coordindex; - int attribindex; - - m->invertices = numberofpoints; - m->mesh_dim = 2; - m->nextras = numberofpointattribs; - m->readnodefile = 0; - if (m->invertices < 3) { - printf("Error: Input must have at least three input vertices.\n"); - triexit(1); - } - if (m->nextras == 0) { - b->weighted = 0; - } - - initializevertexpool(m, b); - - /* Read the vertices. */ - coordindex = 0; - attribindex = 0; - for (i = 0; i < m->invertices; i++) { - vertexloop = (vertex) poolalloc(&m->vertices); - /* Read the vertex coordinates. */ - x = vertexloop[0] = pointlist[coordindex++]; - y = vertexloop[1] = pointlist[coordindex++]; - /* Read the vertex attributes. */ - for (j = 0; j < numberofpointattribs; j++) { - vertexloop[2 + j] = pointattriblist[attribindex++]; - } - if (pointmarkerlist != (int *) NULL) { - /* Read a vertex marker. */ - setvertexmark(vertexloop, pointmarkerlist[i]); - } else { - /* If no markers are specified, they default to zero. */ - setvertexmark(vertexloop, 0); - } - setvertextype(vertexloop, INPUTVERTEX); - /* Determine the smallest and largest x and y coordinates. */ - if (i == 0) { - m->xmin = m->xmax = x; - m->ymin = m->ymax = y; - } else { - m->xmin = (x < m->xmin) ? x : m->xmin; - m->xmax = (x > m->xmax) ? x : m->xmax; - m->ymin = (y < m->ymin) ? y : m->ymin; - m->ymax = (y > m->ymax) ? y : m->ymax; - } - } - - /* Nonexistent x value used as a flag to mark circle events in sweepline */ - /* Delaunay algorithm. */ - m->xminextreme = 10 * m->xmin - 9 * m->xmax; -} - -#endif /* TRILIBRARY */ - -/*****************************************************************************/ -/* */ -/* readholes() Read the holes, and possibly regional attributes and area */ -/* constraints, from a .poly file. */ -/* */ -/*****************************************************************************/ - -#ifndef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void readholes(struct mesh *m, struct behavior *b, - FILE *polyfile, char *polyfilename, REAL **hlist, int *holes, - REAL **rlist, int *regions) -#else /* not ANSI_DECLARATORS */ -void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions) -struct mesh *m; -struct behavior *b; -FILE *polyfile; -char *polyfilename; -REAL **hlist; -int *holes; -REAL **rlist; -int *regions; -#endif /* not ANSI_DECLARATORS */ - -{ - REAL *holelist; - REAL *regionlist; - char inputline[INPUTLINESIZE]; - char *stringptr; - int index; - int i; - - /* Read the holes. */ - stringptr = readline(inputline, polyfile, polyfilename); - *holes = (int) strtol(stringptr, &stringptr, 0); - if (*holes > 0) { - holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL)); - *hlist = holelist; - for (i = 0; i < 2 * *holes; i += 2) { - stringptr = readline(inputline, polyfile, polyfilename); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Hole %d has no x coordinate.\n", - b->firstnumber + (i >> 1)); - triexit(1); - } else { - holelist[i] = (REAL) strtod(stringptr, &stringptr); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Hole %d has no y coordinate.\n", - b->firstnumber + (i >> 1)); - triexit(1); - } else { - holelist[i + 1] = (REAL) strtod(stringptr, &stringptr); - } - } - } else { - *hlist = (REAL *) NULL; - } - -#ifndef CDT_ONLY - if ((b->regionattrib || b->vararea) && !b->refine) { - /* Read the area constraints. */ - stringptr = readline(inputline, polyfile, polyfilename); - *regions = (int) strtol(stringptr, &stringptr, 0); - if (*regions > 0) { - regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL)); - *rlist = regionlist; - index = 0; - for (i = 0; i < *regions; i++) { - stringptr = readline(inputline, polyfile, polyfilename); - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Region %d has no x coordinate.\n", - b->firstnumber + i); - triexit(1); - } else { - regionlist[index++] = (REAL) strtod(stringptr, &stringptr); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf("Error: Region %d has no y coordinate.\n", - b->firstnumber + i); - triexit(1); - } else { - regionlist[index++] = (REAL) strtod(stringptr, &stringptr); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - printf( - "Error: Region %d has no region attribute or area constraint.\n", - b->firstnumber + i); - triexit(1); - } else { - regionlist[index++] = (REAL) strtod(stringptr, &stringptr); - } - stringptr = findfield(stringptr); - if (*stringptr == '\0') { - regionlist[index] = regionlist[index - 1]; - } else { - regionlist[index] = (REAL) strtod(stringptr, &stringptr); - } - index++; - } - } - } else { - /* Set `*regions' to zero to avoid an accidental free() later. */ - *regions = 0; - *rlist = (REAL *) NULL; - } -#endif /* not CDT_ONLY */ - - fclose(polyfile); -} - -#endif /* not TRILIBRARY */ - -/*****************************************************************************/ -/* */ -/* finishfile() Write the command line to the output file so the user */ -/* can remember how the file was generated. Close the file. */ -/* */ -/*****************************************************************************/ - -#ifndef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void finishfile(FILE *outfile, int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -void finishfile(outfile, argc, argv) -FILE *outfile; -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -{ - int i; - - fprintf(outfile, "# Generated by"); - for (i = 0; i < argc; i++) { - fprintf(outfile, " "); - fputs(argv[i], outfile); - } - fprintf(outfile, "\n"); - fclose(outfile); -} - -#endif /* not TRILIBRARY */ - -/*****************************************************************************/ -/* */ -/* writenodes() Number the vertices and write them to a .node file. */ -/* */ -/* To save memory, the vertex numbers are written over the boundary markers */ -/* after the vertices are written to a file. */ -/* */ -/*****************************************************************************/ - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist, - REAL **pointattriblist, int **pointmarkerlist) -#else /* not ANSI_DECLARATORS */ -void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist) -struct mesh *m; -struct behavior *b; -REAL **pointlist; -REAL **pointattriblist; -int **pointmarkerlist; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -void writenodes(struct mesh *m, struct behavior *b, char *nodefilename, - int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -void writenodes(m, b, nodefilename, argc, argv) -struct mesh *m; -struct behavior *b; -char *nodefilename; -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ -#ifdef TRILIBRARY - REAL *plist; - REAL *palist; - int *pmlist; - int coordindex; - int attribindex; -#else /* not TRILIBRARY */ - FILE *outfile; -#endif /* not TRILIBRARY */ - vertex vertexloop; - long outvertices; - int vertexnumber; - int i; - - if (b->jettison) { - outvertices = m->vertices.items - m->undeads; - } else { - outvertices = m->vertices.items; - } - -#ifdef TRILIBRARY - if (!b->quiet) { - printf("Writing vertices.\n"); - } - /* Allocate memory for output vertices if necessary. */ - if (*pointlist == (REAL *) NULL) { - *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL))); - } - /* Allocate memory for output vertex attributes if necessary. */ - if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) { - *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras * - sizeof(REAL))); - } - /* Allocate memory for output vertex markers if necessary. */ - if (!b->nobound && (*pointmarkerlist == (int *) NULL)) { - *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int))); - } - plist = *pointlist; - palist = *pointattriblist; - pmlist = *pointmarkerlist; - coordindex = 0; - attribindex = 0; -#else /* not TRILIBRARY */ - if (!b->quiet) { - printf("Writing %s.\n", nodefilename); - } - outfile = fopen(nodefilename, "w"); - if (outfile == (FILE *) NULL) { - printf(" Error: Cannot create file %s.\n", nodefilename); - triexit(1); - } - /* Number of vertices, number of dimensions, number of vertex attributes, */ - /* and number of boundary markers (zero or one). */ - fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim, - m->nextras, 1 - b->nobound); -#endif /* not TRILIBRARY */ - - traversalinit(&m->vertices); - vertexnumber = b->firstnumber; - vertexloop = vertextraverse(m); - while (vertexloop != (vertex) NULL) { - if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { -#ifdef TRILIBRARY - /* X and y coordinates. */ - plist[coordindex++] = vertexloop[0]; - plist[coordindex++] = vertexloop[1]; - /* Vertex attributes. */ - for (i = 0; i < m->nextras; i++) { - palist[attribindex++] = vertexloop[2 + i]; - } - if (!b->nobound) { - /* Copy the boundary marker. */ - pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop); - } -#else /* not TRILIBRARY */ - /* Vertex number, x and y coordinates. */ - fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0], - vertexloop[1]); - for (i = 0; i < m->nextras; i++) { - /* Write an attribute. */ - fprintf(outfile, " %.17g", vertexloop[i + 2]); - } - if (b->nobound) { - fprintf(outfile, "\n"); - } else { - /* Write the boundary marker. */ - fprintf(outfile, " %d\n", vertexmark(vertexloop)); - } -#endif /* not TRILIBRARY */ - - setvertexmark(vertexloop, vertexnumber); - vertexnumber++; - } - vertexloop = vertextraverse(m); - } - -#ifndef TRILIBRARY - finishfile(outfile, argc, argv); -#endif /* not TRILIBRARY */ -} - -/*****************************************************************************/ -/* */ -/* numbernodes() Number the vertices. */ -/* */ -/* Each vertex is assigned a marker equal to its number. */ -/* */ -/* Used when writenodes() is not called because no .node file is written. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void numbernodes(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void numbernodes(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - vertex vertexloop; - int vertexnumber; - - traversalinit(&m->vertices); - vertexnumber = b->firstnumber; - vertexloop = vertextraverse(m); - while (vertexloop != (vertex) NULL) { - setvertexmark(vertexloop, vertexnumber); - if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { - vertexnumber++; - } - vertexloop = vertextraverse(m); - } -} - -/*****************************************************************************/ -/* */ -/* writeelements() Write the triangles to an .ele file. */ -/* */ -/*****************************************************************************/ - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void writeelements(struct mesh *m, struct behavior *b, - int **trianglelist, REAL **triangleattriblist) -#else /* not ANSI_DECLARATORS */ -void writeelements(m, b, trianglelist, triangleattriblist) -struct mesh *m; -struct behavior *b; -int **trianglelist; -REAL **triangleattriblist; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -void writeelements(struct mesh *m, struct behavior *b, char *elefilename, - int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -void writeelements(m, b, elefilename, argc, argv) -struct mesh *m; -struct behavior *b; -char *elefilename; -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ -#ifdef TRILIBRARY - int *tlist; - REAL *talist; - int vertexindex; - int attribindex; -#else /* not TRILIBRARY */ - FILE *outfile; -#endif /* not TRILIBRARY */ - struct otri triangleloop; - vertex p1, p2, p3; - vertex mid1, mid2, mid3; - long elementnumber; - int i; - -#ifdef TRILIBRARY - if (!b->quiet) { - printf("Writing triangles.\n"); - } - /* Allocate memory for output triangles if necessary. */ - if (*trianglelist == (int *) NULL) { - *trianglelist = (int *) trimalloc((int) (m->triangles.items * - ((b->order + 1) * (b->order + 2) / - 2) * sizeof(int))); - } - /* Allocate memory for output triangle attributes if necessary. */ - if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) { - *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items * - m->eextras * - sizeof(REAL))); - } - tlist = *trianglelist; - talist = *triangleattriblist; - vertexindex = 0; - attribindex = 0; -#else /* not TRILIBRARY */ - if (!b->quiet) { - printf("Writing %s.\n", elefilename); - } - outfile = fopen(elefilename, "w"); - if (outfile == (FILE *) NULL) { - printf(" Error: Cannot create file %s.\n", elefilename); - triexit(1); - } - /* Number of triangles, vertices per triangle, attributes per triangle. */ - fprintf(outfile, "%ld %d %d\n", m->triangles.items, - (b->order + 1) * (b->order + 2) / 2, m->eextras); -#endif /* not TRILIBRARY */ - - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - triangleloop.orient = 0; - elementnumber = b->firstnumber; - while (triangleloop.tri != (triangle *) NULL) { - org(triangleloop, p1); - dest(triangleloop, p2); - apex(triangleloop, p3); - if (b->order == 1) { -#ifdef TRILIBRARY - tlist[vertexindex++] = vertexmark(p1); - tlist[vertexindex++] = vertexmark(p2); - tlist[vertexindex++] = vertexmark(p3); -#else /* not TRILIBRARY */ - /* Triangle number, indices for three vertices. */ - fprintf(outfile, "%4ld %4d %4d %4d", elementnumber, - vertexmark(p1), vertexmark(p2), vertexmark(p3)); -#endif /* not TRILIBRARY */ - } else { - mid1 = (vertex) triangleloop.tri[m->highorderindex + 1]; - mid2 = (vertex) triangleloop.tri[m->highorderindex + 2]; - mid3 = (vertex) triangleloop.tri[m->highorderindex]; -#ifdef TRILIBRARY - tlist[vertexindex++] = vertexmark(p1); - tlist[vertexindex++] = vertexmark(p2); - tlist[vertexindex++] = vertexmark(p3); - tlist[vertexindex++] = vertexmark(mid1); - tlist[vertexindex++] = vertexmark(mid2); - tlist[vertexindex++] = vertexmark(mid3); -#else /* not TRILIBRARY */ - /* Triangle number, indices for six vertices. */ - fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber, - vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1), - vertexmark(mid2), vertexmark(mid3)); -#endif /* not TRILIBRARY */ - } - -#ifdef TRILIBRARY - for (i = 0; i < m->eextras; i++) { - talist[attribindex++] = elemattribute(triangleloop, i); - } -#else /* not TRILIBRARY */ - for (i = 0; i < m->eextras; i++) { - fprintf(outfile, " %.17g", elemattribute(triangleloop, i)); - } - fprintf(outfile, "\n"); -#endif /* not TRILIBRARY */ - - triangleloop.tri = triangletraverse(m); - elementnumber++; - } - -#ifndef TRILIBRARY - finishfile(outfile, argc, argv); -#endif /* not TRILIBRARY */ -} - -/*****************************************************************************/ -/* */ -/* writepoly() Write the segments and holes to a .poly file. */ -/* */ -/*****************************************************************************/ - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void writepoly(struct mesh *m, struct behavior *b, - int **segmentlist, int **segmentmarkerlist) -#else /* not ANSI_DECLARATORS */ -void writepoly(m, b, segmentlist, segmentmarkerlist) -struct mesh *m; -struct behavior *b; -int **segmentlist; -int **segmentmarkerlist; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -void writepoly(struct mesh *m, struct behavior *b, char *polyfilename, - REAL *holelist, int holes, REAL *regionlist, int regions, - int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions, - argc, argv) -struct mesh *m; -struct behavior *b; -char *polyfilename; -REAL *holelist; -int holes; -REAL *regionlist; -int regions; -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ -#ifdef TRILIBRARY - int *slist; - int *smlist; - int index; -#else /* not TRILIBRARY */ - FILE *outfile; - long holenumber, regionnumber; -#endif /* not TRILIBRARY */ - struct osub subsegloop; - vertex endpoint1, endpoint2; - long subsegnumber; - -#ifdef TRILIBRARY - if (!b->quiet) { - printf("Writing segments.\n"); - } - /* Allocate memory for output segments if necessary. */ - if (*segmentlist == (int *) NULL) { - *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 * - sizeof(int))); - } - /* Allocate memory for output segment markers if necessary. */ - if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) { - *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items * - sizeof(int))); - } - slist = *segmentlist; - smlist = *segmentmarkerlist; - index = 0; -#else /* not TRILIBRARY */ - if (!b->quiet) { - printf("Writing %s.\n", polyfilename); - } - outfile = fopen(polyfilename, "w"); - if (outfile == (FILE *) NULL) { - printf(" Error: Cannot create file %s.\n", polyfilename); - triexit(1); - } - /* The zero indicates that the vertices are in a separate .node file. */ - /* Followed by number of dimensions, number of vertex attributes, */ - /* and number of boundary markers (zero or one). */ - fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras, - 1 - b->nobound); - /* Number of segments, number of boundary markers (zero or one). */ - fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound); -#endif /* not TRILIBRARY */ - - traversalinit(&m->subsegs); - subsegloop.ss = subsegtraverse(m); - subsegloop.ssorient = 0; - subsegnumber = b->firstnumber; - while (subsegloop.ss != (subseg *) NULL) { - sorg(subsegloop, endpoint1); - sdest(subsegloop, endpoint2); -#ifdef TRILIBRARY - /* Copy indices of the segment's two endpoints. */ - slist[index++] = vertexmark(endpoint1); - slist[index++] = vertexmark(endpoint2); - if (!b->nobound) { - /* Copy the boundary marker. */ - smlist[subsegnumber - b->firstnumber] = mark(subsegloop); - } -#else /* not TRILIBRARY */ - /* Segment number, indices of its two endpoints, and possibly a marker. */ - if (b->nobound) { - fprintf(outfile, "%4ld %4d %4d\n", subsegnumber, - vertexmark(endpoint1), vertexmark(endpoint2)); - } else { - fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber, - vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop)); - } -#endif /* not TRILIBRARY */ - - subsegloop.ss = subsegtraverse(m); - subsegnumber++; - } - -#ifndef TRILIBRARY -#ifndef CDT_ONLY - fprintf(outfile, "%d\n", holes); - if (holes > 0) { - for (holenumber = 0; holenumber < holes; holenumber++) { - /* Hole number, x and y coordinates. */ - fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber, - holelist[2 * holenumber], holelist[2 * holenumber + 1]); - } - } - if (regions > 0) { - fprintf(outfile, "%d\n", regions); - for (regionnumber = 0; regionnumber < regions; regionnumber++) { - /* Region number, x and y coordinates, attribute, maximum area. */ - fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n", - b->firstnumber + regionnumber, - regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1], - regionlist[4 * regionnumber + 2], - regionlist[4 * regionnumber + 3]); - } - } -#endif /* not CDT_ONLY */ - - finishfile(outfile, argc, argv); -#endif /* not TRILIBRARY */ -} - -/*****************************************************************************/ -/* */ -/* writeedges() Write the edges to an .edge file. */ -/* */ -/*****************************************************************************/ - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void writeedges(struct mesh *m, struct behavior *b, - int **edgelist, int **edgemarkerlist) -#else /* not ANSI_DECLARATORS */ -void writeedges(m, b, edgelist, edgemarkerlist) -struct mesh *m; -struct behavior *b; -int **edgelist; -int **edgemarkerlist; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -void writeedges(struct mesh *m, struct behavior *b, char *edgefilename, - int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -void writeedges(m, b, edgefilename, argc, argv) -struct mesh *m; -struct behavior *b; -char *edgefilename; -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ -#ifdef TRILIBRARY - int *elist; - int *emlist; - int index; -#else /* not TRILIBRARY */ - FILE *outfile; -#endif /* not TRILIBRARY */ - struct otri triangleloop, trisym; - struct osub checkmark; - vertex p1, p2; - long edgenumber; - triangle ptr; /* Temporary variable used by sym(). */ - subseg sptr; /* Temporary variable used by tspivot(). */ - -#ifdef TRILIBRARY - if (!b->quiet) { - printf("Writing edges.\n"); - } - /* Allocate memory for edges if necessary. */ - if (*edgelist == (int *) NULL) { - *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int))); - } - /* Allocate memory for edge markers if necessary. */ - if (!b->nobound && (*edgemarkerlist == (int *) NULL)) { - *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int))); - } - elist = *edgelist; - emlist = *edgemarkerlist; - index = 0; -#else /* not TRILIBRARY */ - if (!b->quiet) { - printf("Writing %s.\n", edgefilename); - } - outfile = fopen(edgefilename, "w"); - if (outfile == (FILE *) NULL) { - printf(" Error: Cannot create file %s.\n", edgefilename); - triexit(1); - } - /* Number of edges, number of boundary markers (zero or one). */ - fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound); -#endif /* not TRILIBRARY */ - - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - edgenumber = b->firstnumber; - /* To loop over the set of edges, loop over all triangles, and look at */ - /* the three edges of each triangle. If there isn't another triangle */ - /* adjacent to the edge, operate on the edge. If there is another */ - /* adjacent triangle, operate on the edge only if the current triangle */ - /* has a smaller pointer than its neighbor. This way, each edge is */ - /* considered only once. */ - while (triangleloop.tri != (triangle *) NULL) { - for (triangleloop.orient = 0; triangleloop.orient < 3; - triangleloop.orient++) { - sym(triangleloop, trisym); - if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { - org(triangleloop, p1); - dest(triangleloop, p2); -#ifdef TRILIBRARY - elist[index++] = vertexmark(p1); - elist[index++] = vertexmark(p2); -#endif /* TRILIBRARY */ - if (b->nobound) { -#ifndef TRILIBRARY - /* Edge number, indices of two endpoints. */ - fprintf(outfile, "%4ld %d %d\n", edgenumber, - vertexmark(p1), vertexmark(p2)); -#endif /* not TRILIBRARY */ - } else { - /* Edge number, indices of two endpoints, and a boundary marker. */ - /* If there's no subsegment, the boundary marker is zero. */ - if (b->usesegments) { - tspivot(triangleloop, checkmark); - if (checkmark.ss == m->dummysub) { -#ifdef TRILIBRARY - emlist[edgenumber - b->firstnumber] = 0; -#else /* not TRILIBRARY */ - fprintf(outfile, "%4ld %d %d %d\n", edgenumber, - vertexmark(p1), vertexmark(p2), 0); -#endif /* not TRILIBRARY */ - } else { -#ifdef TRILIBRARY - emlist[edgenumber - b->firstnumber] = mark(checkmark); -#else /* not TRILIBRARY */ - fprintf(outfile, "%4ld %d %d %d\n", edgenumber, - vertexmark(p1), vertexmark(p2), mark(checkmark)); -#endif /* not TRILIBRARY */ - } - } else { -#ifdef TRILIBRARY - emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri; -#else /* not TRILIBRARY */ - fprintf(outfile, "%4ld %d %d %d\n", edgenumber, - vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri); -#endif /* not TRILIBRARY */ - } - } - edgenumber++; - } - } - triangleloop.tri = triangletraverse(m); - } - -#ifndef TRILIBRARY - finishfile(outfile, argc, argv); -#endif /* not TRILIBRARY */ -} - -/*****************************************************************************/ -/* */ -/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */ -/* file. */ -/* */ -/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */ -/* Hence, the Voronoi vertices are listed by traversing the Delaunay */ -/* triangles, and the Voronoi edges are listed by traversing the Delaunay */ -/* edges. */ -/* */ -/* WARNING: In order to assign numbers to the Voronoi vertices, this */ -/* procedure messes up the subsegments or the extra nodes of every */ -/* element. Hence, you should call this procedure last. */ -/* */ -/*****************************************************************************/ - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist, - REAL **vpointattriblist, int **vpointmarkerlist, - int **vedgelist, int **vedgemarkerlist, REAL **vnormlist) -#else /* not ANSI_DECLARATORS */ -void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist, - vedgelist, vedgemarkerlist, vnormlist) -struct mesh *m; -struct behavior *b; -REAL **vpointlist; -REAL **vpointattriblist; -int **vpointmarkerlist; -int **vedgelist; -int **vedgemarkerlist; -REAL **vnormlist; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename, - char *vedgefilename, int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv) -struct mesh *m; -struct behavior *b; -char *vnodefilename; -char *vedgefilename; -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ -#ifdef TRILIBRARY - REAL *plist; - REAL *palist; - int *elist; - REAL *normlist; - int coordindex; - int attribindex; -#else /* not TRILIBRARY */ - FILE *outfile; -#endif /* not TRILIBRARY */ - struct otri triangleloop, trisym; - vertex torg, tdest, tapex; - REAL circumcenter[2]; - REAL xi, eta; - long vnodenumber, vedgenumber; - int p1, p2; - int i; - triangle ptr; /* Temporary variable used by sym(). */ - -#ifdef TRILIBRARY - if (!b->quiet) { - printf("Writing Voronoi vertices.\n"); - } - /* Allocate memory for Voronoi vertices if necessary. */ - if (*vpointlist == (REAL *) NULL) { - *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 * - sizeof(REAL))); - } - /* Allocate memory for Voronoi vertex attributes if necessary. */ - if (*vpointattriblist == (REAL *) NULL) { - *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items * - m->nextras * sizeof(REAL))); - } - *vpointmarkerlist = (int *) NULL; - plist = *vpointlist; - palist = *vpointattriblist; - coordindex = 0; - attribindex = 0; -#else /* not TRILIBRARY */ - if (!b->quiet) { - printf("Writing %s.\n", vnodefilename); - } - outfile = fopen(vnodefilename, "w"); - if (outfile == (FILE *) NULL) { - printf(" Error: Cannot create file %s.\n", vnodefilename); - triexit(1); - } - /* Number of triangles, two dimensions, number of vertex attributes, */ - /* no markers. */ - fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0); -#endif /* not TRILIBRARY */ - - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - triangleloop.orient = 0; - vnodenumber = b->firstnumber; - while (triangleloop.tri != (triangle *) NULL) { - org(triangleloop, torg); - dest(triangleloop, tdest); - apex(triangleloop, tapex); - findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0); -#ifdef TRILIBRARY - /* X and y coordinates. */ - plist[coordindex++] = circumcenter[0]; - plist[coordindex++] = circumcenter[1]; - for (i = 2; i < 2 + m->nextras; i++) { - /* Interpolate the vertex attributes at the circumcenter. */ - palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i]) - + eta * (tapex[i] - torg[i]); - } -#else /* not TRILIBRARY */ - /* Voronoi vertex number, x and y coordinates. */ - fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0], - circumcenter[1]); - for (i = 2; i < 2 + m->nextras; i++) { - /* Interpolate the vertex attributes at the circumcenter. */ - fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i]) - + eta * (tapex[i] - torg[i])); - } - fprintf(outfile, "\n"); -#endif /* not TRILIBRARY */ - - * (int *) (triangleloop.tri + 6) = (int) vnodenumber; - triangleloop.tri = triangletraverse(m); - vnodenumber++; - } - -#ifndef TRILIBRARY - finishfile(outfile, argc, argv); -#endif /* not TRILIBRARY */ - -#ifdef TRILIBRARY - if (!b->quiet) { - printf("Writing Voronoi edges.\n"); - } - /* Allocate memory for output Voronoi edges if necessary. */ - if (*vedgelist == (int *) NULL) { - *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int))); - } - *vedgemarkerlist = (int *) NULL; - /* Allocate memory for output Voronoi norms if necessary. */ - if (*vnormlist == (REAL *) NULL) { - *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL))); - } - elist = *vedgelist; - normlist = *vnormlist; - coordindex = 0; -#else /* not TRILIBRARY */ - if (!b->quiet) { - printf("Writing %s.\n", vedgefilename); - } - outfile = fopen(vedgefilename, "w"); - if (outfile == (FILE *) NULL) { - printf(" Error: Cannot create file %s.\n", vedgefilename); - triexit(1); - } - /* Number of edges, zero boundary markers. */ - fprintf(outfile, "%ld %d\n", m->edges, 0); -#endif /* not TRILIBRARY */ - - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - vedgenumber = b->firstnumber; - /* To loop over the set of edges, loop over all triangles, and look at */ - /* the three edges of each triangle. If there isn't another triangle */ - /* adjacent to the edge, operate on the edge. If there is another */ - /* adjacent triangle, operate on the edge only if the current triangle */ - /* has a smaller pointer than its neighbor. This way, each edge is */ - /* considered only once. */ - while (triangleloop.tri != (triangle *) NULL) { - for (triangleloop.orient = 0; triangleloop.orient < 3; - triangleloop.orient++) { - sym(triangleloop, trisym); - if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { - /* Find the number of this triangle (and Voronoi vertex). */ - p1 = * (int *) (triangleloop.tri + 6); - if (trisym.tri == m->dummytri) { - org(triangleloop, torg); - dest(triangleloop, tdest); -#ifdef TRILIBRARY - /* Copy an infinite ray. Index of one endpoint, and -1. */ - elist[coordindex] = p1; - normlist[coordindex++] = tdest[1] - torg[1]; - elist[coordindex] = -1; - normlist[coordindex++] = torg[0] - tdest[0]; -#else /* not TRILIBRARY */ - /* Write an infinite ray. Edge number, index of one endpoint, -1, */ - /* and x and y coordinates of a vector representing the */ - /* direction of the ray. */ - fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber, - p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]); -#endif /* not TRILIBRARY */ - } else { - /* Find the number of the adjacent triangle (and Voronoi vertex). */ - p2 = * (int *) (trisym.tri + 6); - /* Finite edge. Write indices of two endpoints. */ -#ifdef TRILIBRARY - elist[coordindex] = p1; - normlist[coordindex++] = 0.0; - elist[coordindex] = p2; - normlist[coordindex++] = 0.0; -#else /* not TRILIBRARY */ - fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2); -#endif /* not TRILIBRARY */ - } - vedgenumber++; - } - } - triangleloop.tri = triangletraverse(m); - } - -#ifndef TRILIBRARY - finishfile(outfile, argc, argv); -#endif /* not TRILIBRARY */ -} - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist) -#else /* not ANSI_DECLARATORS */ -void writeneighbors(m, b, neighborlist) -struct mesh *m; -struct behavior *b; -int **neighborlist; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename, - int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -void writeneighbors(m, b, neighborfilename, argc, argv) -struct mesh *m; -struct behavior *b; -char *neighborfilename; -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ -#ifdef TRILIBRARY - int *nlist; - int index; -#else /* not TRILIBRARY */ - FILE *outfile; -#endif /* not TRILIBRARY */ - struct otri triangleloop, trisym; - long elementnumber; - int neighbor1, neighbor2, neighbor3; - triangle ptr; /* Temporary variable used by sym(). */ - -#ifdef TRILIBRARY - if (!b->quiet) { - printf("Writing neighbors.\n"); - } - /* Allocate memory for neighbors if necessary. */ - if (*neighborlist == (int *) NULL) { - *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 * - sizeof(int))); - } - nlist = *neighborlist; - index = 0; -#else /* not TRILIBRARY */ - if (!b->quiet) { - printf("Writing %s.\n", neighborfilename); - } - outfile = fopen(neighborfilename, "w"); - if (outfile == (FILE *) NULL) { - printf(" Error: Cannot create file %s.\n", neighborfilename); - triexit(1); - } - /* Number of triangles, three neighbors per triangle. */ - fprintf(outfile, "%ld %d\n", m->triangles.items, 3); -#endif /* not TRILIBRARY */ - - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - triangleloop.orient = 0; - elementnumber = b->firstnumber; - while (triangleloop.tri != (triangle *) NULL) { - * (int *) (triangleloop.tri + 6) = (int) elementnumber; - triangleloop.tri = triangletraverse(m); - elementnumber++; - } - * (int *) (m->dummytri + 6) = -1; - - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - elementnumber = b->firstnumber; - while (triangleloop.tri != (triangle *) NULL) { - triangleloop.orient = 1; - sym(triangleloop, trisym); - neighbor1 = * (int *) (trisym.tri + 6); - triangleloop.orient = 2; - sym(triangleloop, trisym); - neighbor2 = * (int *) (trisym.tri + 6); - triangleloop.orient = 0; - sym(triangleloop, trisym); - neighbor3 = * (int *) (trisym.tri + 6); -#ifdef TRILIBRARY - nlist[index++] = neighbor1; - nlist[index++] = neighbor2; - nlist[index++] = neighbor3; -#else /* not TRILIBRARY */ - /* Triangle number, neighboring triangle numbers. */ - fprintf(outfile, "%4ld %d %d %d\n", elementnumber, - neighbor1, neighbor2, neighbor3); -#endif /* not TRILIBRARY */ - - triangleloop.tri = triangletraverse(m); - elementnumber++; - } - -#ifndef TRILIBRARY - finishfile(outfile, argc, argv); -#endif /* not TRILIBRARY */ -} - -/*****************************************************************************/ -/* */ -/* writeoff() Write the triangulation to an .off file. */ -/* */ -/* OFF stands for the Object File Format, a format used by the Geometry */ -/* Center's Geomview package. */ -/* */ -/*****************************************************************************/ - -#ifndef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void writeoff(struct mesh *m, struct behavior *b, char *offfilename, - int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -void writeoff(m, b, offfilename, argc, argv) -struct mesh *m; -struct behavior *b; -char *offfilename; -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -{ - FILE *outfile; - struct otri triangleloop; - vertex vertexloop; - vertex p1, p2, p3; - long outvertices; - - if (!b->quiet) { - printf("Writing %s.\n", offfilename); - } - - if (b->jettison) { - outvertices = m->vertices.items - m->undeads; - } else { - outvertices = m->vertices.items; - } - - outfile = fopen(offfilename, "w"); - if (outfile == (FILE *) NULL) { - printf(" Error: Cannot create file %s.\n", offfilename); - triexit(1); - } - /* Number of vertices, triangles, and edges. */ - fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items, - m->edges); - - /* Write the vertices. */ - traversalinit(&m->vertices); - vertexloop = vertextraverse(m); - while (vertexloop != (vertex) NULL) { - if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { - /* The "0.0" is here because the OFF format uses 3D coordinates. */ - fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1], - 0.0); - } - vertexloop = vertextraverse(m); - } - - /* Write the triangles. */ - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - triangleloop.orient = 0; - while (triangleloop.tri != (triangle *) NULL) { - org(triangleloop, p1); - dest(triangleloop, p2); - apex(triangleloop, p3); - /* The "3" means a three-vertex polygon. */ - fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber, - vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber); - triangleloop.tri = triangletraverse(m); - } - finishfile(outfile, argc, argv); -} - -#endif /* not TRILIBRARY */ - -/** **/ -/** **/ -/********* File I/O routines end here *********/ - -/*****************************************************************************/ -/* */ -/* quality_statistics() Print statistics about the quality of the mesh. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void quality_statistics(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void quality_statistics(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - struct otri triangleloop; - vertex p[3]; - REAL cossquaretable[8]; - REAL ratiotable[16]; - REAL dx[3], dy[3]; - REAL edgelength[3]; - REAL dotproduct; - REAL cossquare; - REAL triarea; - REAL shortest, longest; - REAL trilongest2; - REAL smallestarea, biggestarea; - REAL triminaltitude2; - REAL minaltitude; - REAL triaspect2; - REAL worstaspect; - REAL smallestangle, biggestangle; - REAL radconst, degconst; - int angletable[18]; - int aspecttable[16]; - int aspectindex; - int tendegree; - int acutebiggest; - int i, ii, j, k; - - printf("Mesh quality statistics:\n\n"); - radconst = PI / 18.0; - degconst = 180.0 / PI; - for (i = 0; i < 8; i++) { - cossquaretable[i] = cos(radconst * (REAL) (i + 1)); - cossquaretable[i] = cossquaretable[i] * cossquaretable[i]; - } - for (i = 0; i < 18; i++) { - angletable[i] = 0; - } - - ratiotable[0] = 1.5; ratiotable[1] = 2.0; - ratiotable[2] = 2.5; ratiotable[3] = 3.0; - ratiotable[4] = 4.0; ratiotable[5] = 6.0; - ratiotable[6] = 10.0; ratiotable[7] = 15.0; - ratiotable[8] = 25.0; ratiotable[9] = 50.0; - ratiotable[10] = 100.0; ratiotable[11] = 300.0; - ratiotable[12] = 1000.0; ratiotable[13] = 10000.0; - ratiotable[14] = 100000.0; ratiotable[15] = 0.0; - for (i = 0; i < 16; i++) { - aspecttable[i] = 0; - } - - worstaspect = 0.0; - minaltitude = m->xmax - m->xmin + m->ymax - m->ymin; - minaltitude = minaltitude * minaltitude; - shortest = minaltitude; - longest = 0.0; - smallestarea = minaltitude; - biggestarea = 0.0; - worstaspect = 0.0; - smallestangle = 0.0; - biggestangle = 2.0; - acutebiggest = 1; - - traversalinit(&m->triangles); - triangleloop.tri = triangletraverse(m); - triangleloop.orient = 0; - while (triangleloop.tri != (triangle *) NULL) { - org(triangleloop, p[0]); - dest(triangleloop, p[1]); - apex(triangleloop, p[2]); - trilongest2 = 0.0; - - for (i = 0; i < 3; i++) { - j = plus1mod3[i]; - k = minus1mod3[i]; - dx[i] = p[j][0] - p[k][0]; - dy[i] = p[j][1] - p[k][1]; - edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i]; - if (edgelength[i] > trilongest2) { - trilongest2 = edgelength[i]; - } - if (edgelength[i] > longest) { - longest = edgelength[i]; - } - if (edgelength[i] < shortest) { - shortest = edgelength[i]; - } - } - - triarea = counterclockwise(m, b, p[0], p[1], p[2]); - if (triarea < smallestarea) { - smallestarea = triarea; - } - if (triarea > biggestarea) { - biggestarea = triarea; - } - triminaltitude2 = triarea * triarea / trilongest2; - if (triminaltitude2 < minaltitude) { - minaltitude = triminaltitude2; - } - triaspect2 = trilongest2 / triminaltitude2; - if (triaspect2 > worstaspect) { - worstaspect = triaspect2; - } - aspectindex = 0; - while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex]) - && (aspectindex < 15)) { - aspectindex++; - } - aspecttable[aspectindex]++; - - for (i = 0; i < 3; i++) { - j = plus1mod3[i]; - k = minus1mod3[i]; - dotproduct = dx[j] * dx[k] + dy[j] * dy[k]; - cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]); - tendegree = 8; - for (ii = 7; ii >= 0; ii--) { - if (cossquare > cossquaretable[ii]) { - tendegree = ii; - } - } - if (dotproduct <= 0.0) { - angletable[tendegree]++; - if (cossquare > smallestangle) { - smallestangle = cossquare; - } - if (acutebiggest && (cossquare < biggestangle)) { - biggestangle = cossquare; - } - } else { - angletable[17 - tendegree]++; - if (acutebiggest || (cossquare > biggestangle)) { - biggestangle = cossquare; - acutebiggest = 0; - } - } - } - triangleloop.tri = triangletraverse(m); - } - - shortest = sqrt(shortest); - longest = sqrt(longest); - minaltitude = sqrt(minaltitude); - worstaspect = sqrt(worstaspect); - smallestarea *= 0.5; - biggestarea *= 0.5; - if (smallestangle >= 1.0) { - smallestangle = 0.0; - } else { - smallestangle = degconst * acos(sqrt(smallestangle)); - } - if (biggestangle >= 1.0) { - biggestangle = 180.0; - } else { - if (acutebiggest) { - biggestangle = degconst * acos(sqrt(biggestangle)); - } else { - biggestangle = 180.0 - degconst * acos(sqrt(biggestangle)); - } - } - - printf(" Smallest area: %16.5g | Largest area: %16.5g\n", - smallestarea, biggestarea); - printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n", - shortest, longest); - printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n", - minaltitude, worstaspect); - - printf(" Triangle aspect ratio histogram:\n"); - printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", - ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8], - aspecttable[8]); - for (i = 1; i < 7; i++) { - printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", - ratiotable[i - 1], ratiotable[i], aspecttable[i], - ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]); - } - printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n", - ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14], - aspecttable[15]); - printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n"); - - printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n", - smallestangle, biggestangle); - - printf(" Angle histogram:\n"); - for (i = 0; i < 9; i++) { - printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n", - i * 10, i * 10 + 10, angletable[i], - i * 10 + 90, i * 10 + 100, angletable[i + 9]); - } - printf("\n"); -} - -/*****************************************************************************/ -/* */ -/* statistics() Print all sorts of cool facts. */ -/* */ -/*****************************************************************************/ - -#ifdef ANSI_DECLARATORS -void statistics(struct mesh *m, struct behavior *b) -#else /* not ANSI_DECLARATORS */ -void statistics(m, b) -struct mesh *m; -struct behavior *b; -#endif /* not ANSI_DECLARATORS */ - -{ - printf("\nStatistics:\n\n"); - printf(" Input vertices: %d\n", m->invertices); - if (b->refine) { - printf(" Input triangles: %d\n", m->inelements); - } - if (b->poly) { - printf(" Input segments: %d\n", m->insegments); - if (!b->refine) { - printf(" Input holes: %d\n", m->holes); - } - } - - printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads); - printf(" Mesh triangles: %ld\n", m->triangles.items); - printf(" Mesh edges: %ld\n", m->edges); - printf(" Mesh exterior boundary edges: %ld\n", m->hullsize); - if (b->poly || b->refine) { - printf(" Mesh interior boundary edges: %ld\n", - m->subsegs.items - m->hullsize); - printf(" Mesh subsegments (constrained edges): %ld\n", - m->subsegs.items); - } - printf("\n"); - - if (b->verbose) { - quality_statistics(m, b); - printf("Memory allocation statistics:\n\n"); - printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems); - printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems); - if (m->subsegs.maxitems > 0) { - printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems); - } - if (m->viri.maxitems > 0) { - printf(" Maximum number of viri: %ld\n", m->viri.maxitems); - } - if (m->badsubsegs.maxitems > 0) { - printf(" Maximum number of encroached subsegments: %ld\n", - m->badsubsegs.maxitems); - } - if (m->badtriangles.maxitems > 0) { - printf(" Maximum number of bad triangles: %ld\n", - m->badtriangles.maxitems); - } - if (m->flipstackers.maxitems > 0) { - printf(" Maximum number of stacked triangle flips: %ld\n", - m->flipstackers.maxitems); - } - if (m->splaynodes.maxitems > 0) { - printf(" Maximum number of splay tree nodes: %ld\n", - m->splaynodes.maxitems); - } - printf(" Approximate heap memory use (bytes): %ld\n\n", - m->vertices.maxitems * m->vertices.itembytes + - m->triangles.maxitems * m->triangles.itembytes + - m->subsegs.maxitems * m->subsegs.itembytes + - m->viri.maxitems * m->viri.itembytes + - m->badsubsegs.maxitems * m->badsubsegs.itembytes + - m->badtriangles.maxitems * m->badtriangles.itembytes + - m->flipstackers.maxitems * m->flipstackers.itembytes + - m->splaynodes.maxitems * m->splaynodes.itembytes); - - printf("Algorithmic statistics:\n\n"); - if (!b->weighted) { - printf(" Number of incircle tests: %ld\n", m->incirclecount); - } else { - printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount); - } - printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount); - if (m->hyperbolacount > 0) { - printf(" Number of right-of-hyperbola tests: %ld\n", - m->hyperbolacount); - } - if (m->circletopcount > 0) { - printf(" Number of circle top computations: %ld\n", - m->circletopcount); - } - if (m->circumcentercount > 0) { - printf(" Number of triangle circumcenter computations: %ld\n", - m->circumcentercount); - } - printf("\n"); - } -} - -/*****************************************************************************/ -/* */ -/* main() or triangulate() Gosh, do everything. */ -/* */ -/* The sequence is roughly as follows. Many of these steps can be skipped, */ -/* depending on the command line switches. */ -/* */ -/* - Initialize constants and parse the command line. */ -/* - Read the vertices from a file and either */ -/* - triangulate them (no -r), or */ -/* - read an old mesh from files and reconstruct it (-r). */ -/* - Insert the PSLG segments (-p), and possibly segments on the convex */ -/* hull (-c). */ -/* - Read the holes (-p), regional attributes (-pA), and regional area */ -/* constraints (-pa). Carve the holes and concavities, and spread the */ -/* regional attributes and area constraints. */ -/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */ -/* Also enforce the conforming Delaunay property (-q and -a). */ -/* - Compute the number of edges in the resulting mesh. */ -/* - Promote the mesh's linear triangles to higher order elements (-o). */ -/* - Write the output files and print the statistics. */ -/* - Check the consistency and Delaunay property of the mesh (-C). */ -/* */ -/*****************************************************************************/ - -#ifdef TRILIBRARY - -#ifdef ANSI_DECLARATORS -void triangulate(char *triswitches, struct triangulateio *in, - struct triangulateio *out, struct triangulateio *vorout) -#else /* not ANSI_DECLARATORS */ -void triangulate(triswitches, in, out, vorout) -char *triswitches; -struct triangulateio *in; -struct triangulateio *out; -struct triangulateio *vorout; -#endif /* not ANSI_DECLARATORS */ - -#else /* not TRILIBRARY */ - -#ifdef ANSI_DECLARATORS -int main(int argc, char **argv) -#else /* not ANSI_DECLARATORS */ -int main(argc, argv) -int argc; -char **argv; -#endif /* not ANSI_DECLARATORS */ - -#endif /* not TRILIBRARY */ - -{ - struct mesh m; - struct behavior b; - REAL *holearray; /* Array of holes. */ - REAL *regionarray; /* Array of regional attributes and area constraints. */ -#ifndef TRILIBRARY - FILE *polyfile; -#endif /* not TRILIBRARY */ -#ifndef NO_TIMER - /* Variables for timing the performance of Triangle. The types are */ - /* defined in sys/time.h. */ - struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6; - struct timezone tz; -#endif /* not NO_TIMER */ - -#ifndef NO_TIMER - gettimeofday(&tv0, &tz); -#endif /* not NO_TIMER */ - - triangleinit(&m); -#ifdef TRILIBRARY - parsecommandline(1, &triswitches, &b); -#else /* not TRILIBRARY */ - parsecommandline(argc, argv, &b); -#endif /* not TRILIBRARY */ - m.steinerleft = b.steiner; - -#ifdef TRILIBRARY - transfernodes(&m, &b, in->pointlist, in->pointattributelist, - in->pointmarkerlist, in->numberofpoints, - in->numberofpointattributes); -#else /* not TRILIBRARY */ - readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile); -#endif /* not TRILIBRARY */ - -#ifndef NO_TIMER - if (!b.quiet) { - gettimeofday(&tv1, &tz); - } -#endif /* not NO_TIMER */ - -#ifdef CDT_ONLY - m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ -#else /* not CDT_ONLY */ - if (b.refine) { - /* Read and reconstruct a mesh. */ -#ifdef TRILIBRARY - m.hullsize = reconstruct(&m, &b, in->trianglelist, - in->triangleattributelist, in->trianglearealist, - in->numberoftriangles, in->numberofcorners, - in->numberoftriangleattributes, - in->segmentlist, in->segmentmarkerlist, - in->numberofsegments); -#else /* not TRILIBRARY */ - m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename, - b.inpolyfilename, polyfile); -#endif /* not TRILIBRARY */ - } else { - m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ - } -#endif /* not CDT_ONLY */ - -#ifndef NO_TIMER - if (!b.quiet) { - gettimeofday(&tv2, &tz); - if (b.refine) { - printf("Mesh reconstruction"); - } else { - printf("Delaunay"); - } - printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) + - (tv2.tv_usec - tv1.tv_usec) / 1000l); - } -#endif /* not NO_TIMER */ - - /* Ensure that no vertex can be mistaken for a triangular bounding */ - /* box vertex in insertvertex(). */ - m.infvertex1 = (vertex) NULL; - m.infvertex2 = (vertex) NULL; - m.infvertex3 = (vertex) NULL; - - if (b.usesegments) { - m.checksegments = 1; /* Segments will be introduced next. */ - if (!b.refine) { - /* Insert PSLG segments and/or convex hull segments. */ -#ifdef TRILIBRARY - formskeleton(&m, &b, in->segmentlist, - in->segmentmarkerlist, in->numberofsegments); -#else /* not TRILIBRARY */ - formskeleton(&m, &b, polyfile, b.inpolyfilename); -#endif /* not TRILIBRARY */ - } - } - -#ifndef NO_TIMER - if (!b.quiet) { - gettimeofday(&tv3, &tz); - if (b.usesegments && !b.refine) { - printf("Segment milliseconds: %ld\n", - 1000l * (tv3.tv_sec - tv2.tv_sec) + - (tv3.tv_usec - tv2.tv_usec) / 1000l); - } - } -#endif /* not NO_TIMER */ - - if (b.poly && (m.triangles.items > 0)) { -#ifdef TRILIBRARY - holearray = in->holelist; - m.holes = in->numberofholes; - regionarray = in->regionlist; - m.regions = in->numberofregions; -#else /* not TRILIBRARY */ - readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes, - ®ionarray, &m.regions); -#endif /* not TRILIBRARY */ - if (!b.refine) { - /* Carve out holes and concavities. */ - carveholes(&m, &b, holearray, m.holes, regionarray, m.regions); - } - } else { - /* Without a PSLG, there can be no holes or regional attributes */ - /* or area constraints. The following are set to zero to avoid */ - /* an accidental free() later. */ - m.holes = 0; - m.regions = 0; - } - -#ifndef NO_TIMER - if (!b.quiet) { - gettimeofday(&tv4, &tz); - if (b.poly && !b.refine) { - printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) + - (tv4.tv_usec - tv3.tv_usec) / 1000l); - } - } -#endif /* not NO_TIMER */ - -#ifndef CDT_ONLY - if (b.quality && (m.triangles.items > 0)) { - enforcequality(&m, &b); /* Enforce angle and area constraints. */ - } -#endif /* not CDT_ONLY */ - -#ifndef NO_TIMER - if (!b.quiet) { - gettimeofday(&tv5, &tz); -#ifndef CDT_ONLY - if (b.quality) { - printf("Quality milliseconds: %ld\n", - 1000l * (tv5.tv_sec - tv4.tv_sec) + - (tv5.tv_usec - tv4.tv_usec) / 1000l); - } -#endif /* not CDT_ONLY */ - } -#endif /* not NO_TIMER */ - - /* Calculate the number of edges. */ - m.edges = (3l * m.triangles.items + m.hullsize) / 2l; - - if (b.order > 1) { - highorder(&m, &b); /* Promote elements to higher polynomial order. */ - } - if (!b.quiet) { - printf("\n"); - } - -#ifdef TRILIBRARY - if (b.jettison) { - out->numberofpoints = m.vertices.items - m.undeads; - } else { - out->numberofpoints = m.vertices.items; - } - out->numberofpointattributes = m.nextras; - out->numberoftriangles = m.triangles.items; - out->numberofcorners = (b.order + 1) * (b.order + 2) / 2; - out->numberoftriangleattributes = m.eextras; - out->numberofedges = m.edges; - if (b.usesegments) { - out->numberofsegments = m.subsegs.items; - } else { - out->numberofsegments = m.hullsize; - } - if (vorout != (struct triangulateio *) NULL) { - vorout->numberofpoints = m.triangles.items; - vorout->numberofpointattributes = m.nextras; - vorout->numberofedges = m.edges; - } -#endif /* TRILIBRARY */ - /* If not using iteration numbers, don't write a .node file if one was */ - /* read, because the original one would be overwritten! */ - if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) { - if (!b.quiet) { -#ifdef TRILIBRARY - printf("NOT writing vertices.\n"); -#else /* not TRILIBRARY */ - printf("NOT writing a .node file.\n"); -#endif /* not TRILIBRARY */ - } - numbernodes(&m, &b); /* We must remember to number the vertices. */ - } else { - /* writenodes() numbers the vertices too. */ -#ifdef TRILIBRARY - writenodes(&m, &b, &out->pointlist, &out->pointattributelist, - &out->pointmarkerlist); -#else /* not TRILIBRARY */ - writenodes(&m, &b, b.outnodefilename, argc, argv); -#endif /* TRILIBRARY */ - } - if (b.noelewritten) { - if (!b.quiet) { -#ifdef TRILIBRARY - printf("NOT writing triangles.\n"); -#else /* not TRILIBRARY */ - printf("NOT writing an .ele file.\n"); -#endif /* not TRILIBRARY */ - } - } else { -#ifdef TRILIBRARY - writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist); -#else /* not TRILIBRARY */ - writeelements(&m, &b, b.outelefilename, argc, argv); -#endif /* not TRILIBRARY */ - } - /* The -c switch (convex switch) causes a PSLG to be written */ - /* even if none was read. */ - if (b.poly || b.convex) { - /* If not using iteration numbers, don't overwrite the .poly file. */ - if (b.nopolywritten || b.noiterationnum) { - if (!b.quiet) { -#ifdef TRILIBRARY - printf("NOT writing segments.\n"); -#else /* not TRILIBRARY */ - printf("NOT writing a .poly file.\n"); -#endif /* not TRILIBRARY */ - } - } else { -#ifdef TRILIBRARY - writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist); - out->numberofholes = m.holes; - out->numberofregions = m.regions; - if (b.poly) { - out->holelist = in->holelist; - out->regionlist = in->regionlist; - } else { - out->holelist = (REAL *) NULL; - out->regionlist = (REAL *) NULL; - } -#else /* not TRILIBRARY */ - writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray, - m.regions, argc, argv); -#endif /* not TRILIBRARY */ - } - } -#ifndef TRILIBRARY -#ifndef CDT_ONLY - if (m.regions > 0) { - trifree((VOID *) regionarray); - } -#endif /* not CDT_ONLY */ - if (m.holes > 0) { - trifree((VOID *) holearray); - } - if (b.geomview) { - writeoff(&m, &b, b.offfilename, argc, argv); - } -#endif /* not TRILIBRARY */ - if (b.edgesout) { -#ifdef TRILIBRARY - writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist); -#else /* not TRILIBRARY */ - writeedges(&m, &b, b.edgefilename, argc, argv); -#endif /* not TRILIBRARY */ - } - if (b.voronoi) { -#ifdef TRILIBRARY - writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist, - &vorout->pointmarkerlist, &vorout->edgelist, - &vorout->edgemarkerlist, &vorout->normlist); -#else /* not TRILIBRARY */ - writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv); -#endif /* not TRILIBRARY */ - } - if (b.neighbors) { -#ifdef TRILIBRARY - writeneighbors(&m, &b, &out->neighborlist); -#else /* not TRILIBRARY */ - writeneighbors(&m, &b, b.neighborfilename, argc, argv); -#endif /* not TRILIBRARY */ - } - - if (!b.quiet) { -#ifndef NO_TIMER - gettimeofday(&tv6, &tz); - printf("\nOutput milliseconds: %ld\n", - 1000l * (tv6.tv_sec - tv5.tv_sec) + - (tv6.tv_usec - tv5.tv_usec) / 1000l); - printf("Total running milliseconds: %ld\n", - 1000l * (tv6.tv_sec - tv0.tv_sec) + - (tv6.tv_usec - tv0.tv_usec) / 1000l); -#endif /* not NO_TIMER */ - - statistics(&m, &b); - } - -#ifndef REDUCED - if (b.docheck) { - checkmesh(&m, &b); - checkdelaunay(&m, &b); - } -#endif /* not REDUCED */ - - triangledeinit(&m, &b); -#ifndef TRILIBRARY - return 0; -#endif /* not TRILIBRARY */ -} diff --git a/src/isct/triangle.h b/src/isct/triangle.h deleted file mode 100644 index dbf087a1..00000000 --- a/src/isct/triangle.h +++ /dev/null @@ -1,289 +0,0 @@ -/*****************************************************************************/ -/* */ -/* (triangle.h) */ -/* */ -/* Include file for programs that call Triangle. */ -/* */ -/* Accompanies Triangle Version 1.6 */ -/* July 28, 2005 */ -/* */ -/* Copyright 1996, 2005 */ -/* Jonathan Richard Shewchuk */ -/* 2360 Woolsey #H */ -/* Berkeley, California 94705-1927 */ -/* jrs@cs.berkeley.edu */ -/* */ -/*****************************************************************************/ - -/*****************************************************************************/ -/* */ -/* How to call Triangle from another program */ -/* */ -/* */ -/* If you haven't read Triangle's instructions (run "triangle -h" to read */ -/* them), you won't understand what follows. */ -/* */ -/* Triangle must be compiled into an object file (triangle.o) with the */ -/* TRILIBRARY symbol defined (generally by using the -DTRILIBRARY compiler */ -/* switch). The makefile included with Triangle will do this for you if */ -/* you run "make trilibrary". The resulting object file can be called via */ -/* the procedure triangulate(). */ -/* */ -/* If the size of the object file is important to you, you may wish to */ -/* generate a reduced version of triangle.o. The REDUCED symbol gets rid */ -/* of all features that are primarily of research interest. Specifically, */ -/* the -DREDUCED switch eliminates Triangle's -i, -F, -s, and -C switches. */ -/* The CDT_ONLY symbol gets rid of all meshing algorithms above and beyond */ -/* constrained Delaunay triangulation. Specifically, the -DCDT_ONLY switch */ -/* eliminates Triangle's -r, -q, -a, -u, -D, -Y, -S, and -s switches. */ -/* */ -/* IMPORTANT: These definitions (TRILIBRARY, REDUCED, CDT_ONLY) must be */ -/* made in the makefile or in triangle.c itself. Putting these definitions */ -/* in this file (triangle.h) will not create the desired effect. */ -/* */ -/* */ -/* The calling convention for triangulate() follows. */ -/* */ -/* void triangulate(triswitches, in, out, vorout) */ -/* char *triswitches; */ -/* struct triangulateio *in; */ -/* struct triangulateio *out; */ -/* struct triangulateio *vorout; */ -/* */ -/* `triswitches' is a string containing the command line switches you wish */ -/* to invoke. No initial dash is required. Some suggestions: */ -/* */ -/* - You'll probably find it convenient to use the `z' switch so that */ -/* points (and other items) are numbered from zero. This simplifies */ -/* indexing, because the first item of any type always starts at index */ -/* [0] of the corresponding array, whether that item's number is zero or */ -/* one. */ -/* - You'll probably want to use the `Q' (quiet) switch in your final code, */ -/* but you can take advantage of Triangle's printed output (including the */ -/* `V' switch) while debugging. */ -/* - If you are not using the `q', `a', `u', `D', `j', or `s' switches, */ -/* then the output points will be identical to the input points, except */ -/* possibly for the boundary markers. If you don't need the boundary */ -/* markers, you should use the `N' (no nodes output) switch to save */ -/* memory. (If you do need boundary markers, but need to save memory, a */ -/* good nasty trick is to set out->pointlist equal to in->pointlist */ -/* before calling triangulate(), so that Triangle overwrites the input */ -/* points with identical copies.) */ -/* - The `I' (no iteration numbers) and `g' (.off file output) switches */ -/* have no effect when Triangle is compiled with TRILIBRARY defined. */ -/* */ -/* `in', `out', and `vorout' are descriptions of the input, the output, */ -/* and the Voronoi output. If the `v' (Voronoi output) switch is not used, */ -/* `vorout' may be NULL. `in' and `out' may never be NULL. */ -/* */ -/* Certain fields of the input and output structures must be initialized, */ -/* as described below. */ -/* */ -/*****************************************************************************/ - -/*****************************************************************************/ -/* */ -/* The `triangulateio' structure. */ -/* */ -/* Used to pass data into and out of the triangulate() procedure. */ -/* */ -/* */ -/* Arrays are used to store points, triangles, markers, and so forth. In */ -/* all cases, the first item in any array is stored starting at index [0]. */ -/* However, that item is item number `1' unless the `z' switch is used, in */ -/* which case it is item number `0'. Hence, you may find it easier to */ -/* index points (and triangles in the neighbor list) if you use the `z' */ -/* switch. Unless, of course, you're calling Triangle from a Fortran */ -/* program. */ -/* */ -/* Description of fields (except the `numberof' fields, which are obvious): */ -/* */ -/* `pointlist': An array of point coordinates. The first point's x */ -/* coordinate is at index [0] and its y coordinate at index [1], followed */ -/* by the coordinates of the remaining points. Each point occupies two */ -/* REALs. */ -/* `pointattributelist': An array of point attributes. Each point's */ -/* attributes occupy `numberofpointattributes' REALs. */ -/* `pointmarkerlist': An array of point markers; one int per point. */ -/* */ -/* `trianglelist': An array of triangle corners. The first triangle's */ -/* first corner is at index [0], followed by its other two corners in */ -/* counterclockwise order, followed by any other nodes if the triangle */ -/* represents a nonlinear element. Each triangle occupies */ -/* `numberofcorners' ints. */ -/* `triangleattributelist': An array of triangle attributes. Each */ -/* triangle's attributes occupy `numberoftriangleattributes' REALs. */ -/* `trianglearealist': An array of triangle area constraints; one REAL per */ -/* triangle. Input only. */ -/* `neighborlist': An array of triangle neighbors; three ints per */ -/* triangle. Output only. */ -/* */ -/* `segmentlist': An array of segment endpoints. The first segment's */ -/* endpoints are at indices [0] and [1], followed by the remaining */ -/* segments. Two ints per segment. */ -/* `segmentmarkerlist': An array of segment markers; one int per segment. */ -/* */ -/* `holelist': An array of holes. The first hole's x and y coordinates */ -/* are at indices [0] and [1], followed by the remaining holes. Two */ -/* REALs per hole. Input only, although the pointer is copied to the */ -/* output structure for your convenience. */ -/* */ -/* `regionlist': An array of regional attributes and area constraints. */ -/* The first constraint's x and y coordinates are at indices [0] and [1], */ -/* followed by the regional attribute at index [2], followed by the */ -/* maximum area at index [3], followed by the remaining area constraints. */ -/* Four REALs per area constraint. Note that each regional attribute is */ -/* used only if you select the `A' switch, and each area constraint is */ -/* used only if you select the `a' switch (with no number following), but */ -/* omitting one of these switches does not change the memory layout. */ -/* Input only, although the pointer is copied to the output structure for */ -/* your convenience. */ -/* */ -/* `edgelist': An array of edge endpoints. The first edge's endpoints are */ -/* at indices [0] and [1], followed by the remaining edges. Two ints per */ -/* edge. Output only. */ -/* `edgemarkerlist': An array of edge markers; one int per edge. Output */ -/* only. */ -/* `normlist': An array of normal vectors, used for infinite rays in */ -/* Voronoi diagrams. The first normal vector's x and y magnitudes are */ -/* at indices [0] and [1], followed by the remaining vectors. For each */ -/* finite edge in a Voronoi diagram, the normal vector written is the */ -/* zero vector. Two REALs per edge. Output only. */ -/* */ -/* */ -/* Any input fields that Triangle will examine must be initialized. */ -/* Furthermore, for each output array that Triangle will write to, you */ -/* must either provide space by setting the appropriate pointer to point */ -/* to the space you want the data written to, or you must initialize the */ -/* pointer to NULL, which tells Triangle to allocate space for the results. */ -/* The latter option is preferable, because Triangle always knows exactly */ -/* how much space to allocate. The former option is provided mainly for */ -/* people who need to call Triangle from Fortran code, though it also makes */ -/* possible some nasty space-saving tricks, like writing the output to the */ -/* same arrays as the input. */ -/* */ -/* Triangle will not free() any input or output arrays, including those it */ -/* allocates itself; that's up to you. You should free arrays allocated by */ -/* Triangle by calling the trifree() procedure defined below. (By default, */ -/* trifree() just calls the standard free() library procedure, but */ -/* applications that call triangulate() may replace trimalloc() and */ -/* trifree() in triangle.c to use specialized memory allocators.) */ -/* */ -/* Here's a guide to help you decide which fields you must initialize */ -/* before you call triangulate(). */ -/* */ -/* `in': */ -/* */ -/* - `pointlist' must always point to a list of points; `numberofpoints' */ -/* and `numberofpointattributes' must be properly set. */ -/* `pointmarkerlist' must either be set to NULL (in which case all */ -/* markers default to zero), or must point to a list of markers. If */ -/* `numberofpointattributes' is not zero, `pointattributelist' must */ -/* point to a list of point attributes. */ -/* - If the `r' switch is used, `trianglelist' must point to a list of */ -/* triangles, and `numberoftriangles', `numberofcorners', and */ -/* `numberoftriangleattributes' must be properly set. If */ -/* `numberoftriangleattributes' is not zero, `triangleattributelist' */ -/* must point to a list of triangle attributes. If the `a' switch is */ -/* used (with no number following), `trianglearealist' must point to a */ -/* list of triangle area constraints. `neighborlist' may be ignored. */ -/* - If the `p' switch is used, `segmentlist' must point to a list of */ -/* segments, `numberofsegments' must be properly set, and */ -/* `segmentmarkerlist' must either be set to NULL (in which case all */ -/* markers default to zero), or must point to a list of markers. */ -/* - If the `p' switch is used without the `r' switch, then */ -/* `numberofholes' and `numberofregions' must be properly set. If */ -/* `numberofholes' is not zero, `holelist' must point to a list of */ -/* holes. If `numberofregions' is not zero, `regionlist' must point to */ -/* a list of region constraints. */ -/* - If the `p' switch is used, `holelist', `numberofholes', */ -/* `regionlist', and `numberofregions' is copied to `out'. (You can */ -/* nonetheless get away with not initializing them if the `r' switch is */ -/* used.) */ -/* - `edgelist', `edgemarkerlist', `normlist', and `numberofedges' may be */ -/* ignored. */ -/* */ -/* `out': */ -/* */ -/* - `pointlist' must be initialized (NULL or pointing to memory) unless */ -/* the `N' switch is used. `pointmarkerlist' must be initialized */ -/* unless the `N' or `B' switch is used. If `N' is not used and */ -/* `in->numberofpointattributes' is not zero, `pointattributelist' must */ -/* be initialized. */ -/* - `trianglelist' must be initialized unless the `E' switch is used. */ -/* `neighborlist' must be initialized if the `n' switch is used. If */ -/* the `E' switch is not used and (`in->numberofelementattributes' is */ -/* not zero or the `A' switch is used), `elementattributelist' must be */ -/* initialized. `trianglearealist' may be ignored. */ -/* - `segmentlist' must be initialized if the `p' or `c' switch is used, */ -/* and the `P' switch is not used. `segmentmarkerlist' must also be */ -/* initialized under these circumstances unless the `B' switch is used. */ -/* - `edgelist' must be initialized if the `e' switch is used. */ -/* `edgemarkerlist' must be initialized if the `e' switch is used and */ -/* the `B' switch is not. */ -/* - `holelist', `regionlist', `normlist', and all scalars may be ignored.*/ -/* */ -/* `vorout' (only needed if `v' switch is used): */ -/* */ -/* - `pointlist' must be initialized. If `in->numberofpointattributes' */ -/* is not zero, `pointattributelist' must be initialized. */ -/* `pointmarkerlist' may be ignored. */ -/* - `edgelist' and `normlist' must both be initialized. */ -/* `edgemarkerlist' may be ignored. */ -/* - Everything else may be ignored. */ -/* */ -/* After a call to triangulate(), the valid fields of `out' and `vorout' */ -/* will depend, in an obvious way, on the choice of switches used. Note */ -/* that when the `p' switch is used, the pointers `holelist' and */ -/* `regionlist' are copied from `in' to `out', but no new space is */ -/* allocated; be careful that you don't free() the same array twice. On */ -/* the other hand, Triangle will never copy the `pointlist' pointer (or any */ -/* others); new space is allocated for `out->pointlist', or if the `N' */ -/* switch is used, `out->pointlist' remains uninitialized. */ -/* */ -/* All of the meaningful `numberof' fields will be properly set; for */ -/* instance, `numberofedges' will represent the number of edges in the */ -/* triangulation whether or not the edges were written. If segments are */ -/* not used, `numberofsegments' will indicate the number of boundary edges. */ -/* */ -/*****************************************************************************/ - -struct triangulateio { - REAL *pointlist; /* In / out */ - REAL *pointattributelist; /* In / out */ - int *pointmarkerlist; /* In / out */ - int numberofpoints; /* In / out */ - int numberofpointattributes; /* In / out */ - - int *trianglelist; /* In / out */ - REAL *triangleattributelist; /* In / out */ - REAL *trianglearealist; /* In only */ - int *neighborlist; /* Out only */ - int numberoftriangles; /* In / out */ - int numberofcorners; /* In / out */ - int numberoftriangleattributes; /* In / out */ - - int *segmentlist; /* In / out */ - int *segmentmarkerlist; /* In / out */ - int numberofsegments; /* In / out */ - - REAL *holelist; /* In / pointer to array copied out */ - int numberofholes; /* In / copied out */ - - REAL *regionlist; /* In / pointer to array copied out */ - int numberofregions; /* In / copied out */ - - int *edgelist; /* Out only */ - int *edgemarkerlist; /* Not used with Voronoi diagram; out only */ - REAL *normlist; /* Used only with Voronoi diagram; out only */ - int numberofedges; /* Out only */ -}; - -/*#ifdef ANSI_DECLARATORS*/ -void triangulate(char *, struct triangulateio *, struct triangulateio *, - struct triangulateio *); -void trifree(void *memptr); -/*#else*/ /* not ANSI_DECLARATORS */ -/*void triangulate(); -void trifree();*/ -/*#endif*/ /* not ANSI_DECLARATORS */ diff --git a/src/main.cpp b/src/main.cpp index 93d89c43..a2ccb2f6 100644 --- a/src/main.cpp +++ b/src/main.cpp @@ -42,6 +42,7 @@ using std::ostream; #include "cork.h" +int doremesh=0; void file2corktrimesh( const Files::FileMesh &in, CorkTriMesh *out @@ -165,6 +166,7 @@ void CmdList::printHelp(ostream &out) out << "Welcome to Cork. Usage:" << endl << " > cork [-command arg0 arg1 ... argn]*" << endl << + " if --command is used, a remesh is applied to the output" << endl << "for example," << endl << " > cork -union box0.off box1.off result.off" << endl << "Options:" << endl; @@ -184,6 +186,10 @@ void CmdList::runCommands(std::vector::iterator &arg_it, exit(1); } arg_cmd = arg_cmd.substr(1); + if(arg_cmd[0] == '-') { + doremesh=1; + arg_cmd = arg_cmd.substr(1); + } arg_it++; bool found = true; @@ -217,6 +223,8 @@ genericBinaryOp( CorkTriMesh in0; CorkTriMesh in1; CorkTriMesh out; + + out.remesh=doremesh; if(args == end) { cerr << "too few args" << endl; exit(1); } loadMesh(*args, &in0); @@ -244,7 +252,10 @@ genericBinaryOp( int main(int argc, char *argv[]) { - initRand(); // that's useful + if(argc>=6){ + initRand(atoi(argv[5])); //use the 4th argument to set the seed + }else + initRand(); if(argc < 2) { cout << "Please type 'cork -help' for instructions" << endl; @@ -305,8 +316,39 @@ int main(int argc, char *argv[]) " and output the connected mesh with those\n" " intersections made explicit and connected", genericBinaryOp(resolveIntersections)); - - + cmds.regCmd("first", + "-first in0 in1 out Compute the first mesh in0 cut by the second mesh in1,\n" + " and output the result", + genericBinaryOp(computeFirst)); + cmds.regCmd("second", + "-second in0 in1 out Compute the second mesh in1 cut by the first mesh in0,\n" + " and output the result", + genericBinaryOp(computeSecond)); + + // add cmds + cmds.regCmd("remesh", + "-remesh in out Remesh the input mesh to remove poorly shaped triangles", + [](std::vector::iterator &args, + const std::vector::iterator &end) { + CorkTriMesh in; + CorkTriMesh out; + + if(args == end) { cerr << "too few args" << endl; exit(1); } + loadMesh(*args, &in); + args++; + + remeshTriangles(in, &out); + + if(args == end) { cerr << "too few args" << endl; exit(1); } + saveMesh(*args, out); + args++; + + freeCorkTriMesh(&out); + + delete[] in.vertices; + delete[] in.triangles; + }); + cmds.runCommands(arg_it, args.end()); return 0; diff --git a/src/mesh/mesh.bool.tpp b/src/mesh/mesh.bool.tpp index 6b76c551..0c6e747d 100644 --- a/src/mesh/mesh.bool.tpp +++ b/src/mesh/mesh.bool.tpp @@ -356,17 +356,17 @@ void Mesh::boolXor(Mesh &rhs) }); } - - - - - - - - - - - - - - +template +void Mesh::boolFirst(Mesh &rhs) +{ + BoolProblem bprob(this); + + bprob.doSetup(rhs); + + bprob.doDeleteAndFlip([](byte data) -> typename BoolProblem::TriCode { + if(data == 1) // part of op 1 OUTSIDE op 0 + return BoolProblem::DELETE_TRI; + else // otherwise + return BoolProblem::KEEP_TRI; + }); +} diff --git a/src/mesh/mesh.decl.h b/src/mesh/mesh.decl.h index 0adac06f..fbdf070f 100644 --- a/src/mesh/mesh.decl.h +++ b/src/mesh/mesh.decl.h @@ -212,6 +212,7 @@ class Mesh void boolDiff(Mesh &rhs); void boolIsct(Mesh &rhs); void boolXor(Mesh &rhs); + void boolFirst(Mesh &rhs); private: // Internal Formats struct Tri { @@ -265,8 +266,10 @@ class Mesh uint vid; ShortVec tids; Edata data; - inline EGraphEntry() {} - inline EGraphEntry(uint vid_) : vid(vid_) {} + // value-initialize data; it is filled in by the users of the cache, + // but leaving it indeterminate here trips -Wmaybe-uninitialized + inline EGraphEntry() : vid(0), data() {} + inline EGraphEntry(uint vid_) : vid(vid_), data() {} }; template struct EGraphCache { diff --git a/src/mesh/mesh.isct.tpp b/src/mesh/mesh.isct.tpp index 6c48930a..cc0da55b 100644 --- a/src/mesh/mesh.isct.tpp +++ b/src/mesh/mesh.isct.tpp @@ -33,10 +33,9 @@ #include "aabvh.h" -#define REAL double -extern "C" { -#include "triangle.h" -} +#include + +#include "cdt/CDT.h" struct GenericVertType; struct IsctVertType; @@ -423,57 +422,34 @@ public: uint dim1 = (normdim+2)%3; double sign_flip = (normal.v[normdim] < 0.0)? -1.0 : 1.0; - struct triangulateio in, out; - - /* Define input points. */ - in.numberofpoints = points.size(); - in.numberofpointattributes = 0; - in.pointlist = new REAL[in.numberofpoints * 2]; - in.pointattributelist = nullptr; - in.pointmarkerlist = new int[in.numberofpoints]; - for(int k=0; kcoord.v[dim0]; - in.pointlist[k*2 + 1] = points[k]->coord.v[dim1] * sign_flip; - in.pointmarkerlist[k] = (points[k]->boundary)? 1 : 0; - } - - /* Define the input segments */ - in.numberofsegments = edges.size(); - in.numberofholes = 0;// yes, zero - in.numberofregions = 0;// not using regions - in.segmentlist = new int[in.numberofsegments * 2]; - in.segmentmarkerlist = new int[in.numberofsegments]; - for(int k=0; kends[0]->idx; - in.segmentlist[k*2 + 1] = edges[k]->ends[1]->idx; - in.segmentmarkerlist[k] = (edges[k]->boundary)? 1 : 0; + // solve the constrained Delaunay triangulation problem + // in the 2d projection plane; the domain is a single convex + // triangle, so no exterior/hole cleanup is needed beyond + // removing the super-triangle + std::vector< CDT::V2d > cdtpts(points.size()); + std::vector< CDT::Edge > cdtedges; + + for(uint k=0; kcoord.v[dim0]; + cdtpts[k].y = points[k]->coord.v[dim1] * sign_flip; } - - // to be safe... declare 0 triangle attributes on input - in.numberoftriangles = 0; - in.numberoftriangleattributes = 0; - - /* set for flags.... */ - out.pointlist = nullptr; - out.pointattributelist = nullptr; // not necessary if using -N or 0 attr - out.pointmarkerlist = nullptr; - out.trianglelist = nullptr; // not necessary if using -E - //out.triangleattributelist = null; // not necessary if using -E or 0 attr - //out.trianglearealist = // only needed with -r and -a - //out.neighborlist = null; // only neccesary if -n is used - out.segmentlist = nullptr; // NEED THIS; output segments go here - out.segmentmarkerlist = nullptr; // NEED THIS for OUTPUT SEGMENTS - //out.edgelist = null; // only necessary if -e is used - //out.edgemarkerlist = null; // only necessary if -e is used - - // solve the triangulation problem - char *params = (char*)("pzQYY"); - //char *debug_params = (char*)("pzYYVC"); - triangulate(params, &in, &out, nullptr); - - if(out.numberofpoints != in.numberofpoints) { - std::cout << "out.numberofpoints: " - << out.numberofpoints << std::endl; + cdtedges.reserve(edges.size()); + for(uint k=0; kends[0]->idx, + edges[k]->ends[1]->idx)); + + CDT::Triangulation cdt; + cdt.insertVertices(cdtpts); + cdt.insertEdges(cdtedges); + // discard triangles outside of the closed boundary-edge loop; + // quantized intersection points may fall slightly outside the + // original triangle, and the resulting sliver triangles beyond + // the boundary must not be kept (matches Triangle's -p behavior) + cdt.eraseOuterTriangles(); + + if(cdt.vertices.size() != points.size()) { + std::cout << "cdt.vertices.size(): " + << cdt.vertices.size() << std::endl; std::cout << "points.size(): " << points.size() << std::endl; std::cout << "dumping out the points' coordinates" << std::endl; for(uint k=0; kcoord << " " << gv->idx << std::endl; } - + std::cout << "dumping out the segments" << std::endl; - for(int k=0; kends[0]->idx + << "; " << edges[k]->ends[1]->idx + << " (" << (edges[k]->boundary? 1 : 0) << ") " << std::endl; - + std::cout << "dumping out the solved for triangles now..." << std::endl; - for(int k=0; knewGenericTri(gv0, gv1, gv2); } - - - // clean up after triangulate... - // in free - free(in.pointlist); - free(in.pointmarkerlist); - free(in.segmentlist); - free(in.segmentmarkerlist); - // out free - free(out.pointlist); - //free(out.pointattributelist); - free(out.pointmarkerlist); - free(out.trianglelist); - //free(out.triangleattributelist); - //free(out.trianglearealist); - //free(out.neighborlist); - free(out.segmentlist); - free(out.segmentmarkerlist); - //free(out.edgelist); - //free(out.edgemarkerlist); } private: diff --git a/src/util/prelude.h b/src/util/prelude.h index 00329aad..fb92a0e3 100644 --- a/src/util/prelude.h +++ b/src/util/prelude.h @@ -25,11 +25,13 @@ // +------------------------------------------------------------------------- #pragma once +#define _USE_MATH_DEFINES #include #include #include #include #include +#include #ifndef uint typedef unsigned int uint; @@ -39,6 +41,10 @@ typedef unsigned int uint; typedef unsigned char byte; #endif +#ifndef M_PI +#define M_PI (3.14159265358979323846) +#endif + // *********** // * Logging @@ -150,6 +156,11 @@ inline void initRand() { srand(uint(time(0))); } +inline void initRand(uint seed) { + // currently none! Should seed using clock + srand(seed); +} + inline double drand(double min, double max) { const double invMAX = 1.0/double(RAND_MAX); double rand0to1 = double(std::rand())*invMAX; diff --git a/win/wincork/wincork.vcxproj b/win/wincork/wincork.vcxproj index 92a3fae4..dcc95762 100644 --- a/win/wincork/wincork.vcxproj +++ b/win/wincork/wincork.vcxproj @@ -78,7 +78,12 @@ - + + + + + + @@ -107,10 +112,6 @@ - - NO_TIMER;REDUCED;CDT_ONLY;TRILIBRARY;ANSI_DECLARATORS;%(PreprocessorDefinitions) - NO_TIMER;REDUCED;CDT_ONLY;TRILIBRARY;ANSI_DECLARATORS;%(PreprocessorDefinitions) - diff --git a/win/wincork/wincork.vcxproj.filters b/win/wincork/wincork.vcxproj.filters index 792818b5..3a4c76f6 100644 --- a/win/wincork/wincork.vcxproj.filters +++ b/win/wincork/wincork.vcxproj.filters @@ -105,7 +105,22 @@ Header Files\isct - + + Header Files\isct + + + Header Files\isct + + + Header Files\isct + + + Header Files\isct + + + Header Files\isct + + Header Files\isct @@ -157,9 +172,6 @@ Source Files\isct - - Source Files\isct - Source Files