From a990af555bb3bd2c68718e648c08438304430b2e Mon Sep 17 00:00:00 2001 From: Stephan Dilly Date: Mon, 16 Nov 2015 08:09:48 +0100 Subject: [PATCH] separated linalg module into a package --- gl3n/linalg.d | 2596 -------------------------------------- gl3n/linalg/matrix.d | 1271 +++++++++++++++++++ gl3n/linalg/package.d | 23 + gl3n/linalg/quaternion.d | 645 ++++++++++ gl3n/linalg/vec.d | 734 +++++++++++ libgl3n.a | Bin 0 -> 11005220 bytes 6 files changed, 2673 insertions(+), 2596 deletions(-) delete mode 100644 gl3n/linalg.d create mode 100644 gl3n/linalg/matrix.d create mode 100644 gl3n/linalg/package.d create mode 100644 gl3n/linalg/quaternion.d create mode 100644 gl3n/linalg/vec.d create mode 100644 libgl3n.a diff --git a/gl3n/linalg.d b/gl3n/linalg.d deleted file mode 100644 index 450c82f..0000000 --- a/gl3n/linalg.d +++ /dev/null @@ -1,2596 +0,0 @@ -/** -gl3n.linalg - -Special thanks to: -$(UL - $(LI Tomasz Stachowiak (h3r3tic): allowed me to use parts of $(LINK2 https://bitbucket.org/h3r3tic/boxen/src/default/src/xf/omg, omg).) - $(LI Jakob Øvrum (jA_cOp): improved the code a lot!) - $(LI Florian Boesch (___doc__): helps me to understand opengl/complex maths better, see: $(LINK http://codeflow.org/).) - $(LI #D on freenode: answered general questions about D.) -) - -Authors: David Herberth -License: MIT - -Note: All methods marked with pure are weakly pure since, they all access an instance member. -All static methods are strongly pure. -*/ - - -module gl3n.linalg; - -private { - import std.math : isNaN, isInfinity; - import std.conv : to; - import std.traits : isIntegral, isFloatingPoint, isStaticArray, isDynamicArray, isImplicitlyConvertible, isArray; - import std.string : format, rightJustify; - import std.array : join; - import std.algorithm : max, min, reduce; - import gl3n.math : clamp, PI, sqrt, sin, cos, acos, tan, asin, atan2, almost_equal; - import gl3n.util : is_vector, is_matrix, is_quaternion, TupleRange; -} - -version(NoReciprocalMul) { - private enum rmul = false; -} else { - private enum rmul = true; -} - -/// Base template for all vector-types. -/// Params: -/// type = all values get stored as this type -/// dimension = specifies the dimension of the vector, can be 1, 2, 3 or 4 -/// Examples: -/// --- -/// alias Vector!(int, 3) vec3i; -/// alias Vector!(float, 4) vec4; -/// alias Vector!(real, 2) vec2r; -/// --- -struct Vector(type, int dimension_) { - static assert(dimension > 0, "0 dimensional vectors don't exist."); - - alias type vt; /// Holds the internal type of the vector. - static const int dimension = dimension_; ///Holds the dimension of the vector. - - vt[dimension] vector; /// Holds all coordinates, length conforms dimension. - - /// Returns a pointer to the coordinates. - @property auto value_ptr() const { return vector.ptr; } - - /// Returns the current vector formatted as string, useful for printing the vector. - @property string as_string() { - return format("%s", vector); - } - alias as_string toString; /// ditto - - @safe pure nothrow: - /// - private @property ref inout(vt) get_(char coord)() inout { - return vector[coord_to_index!coord]; - } - - alias get_!'x' x; /// static properties to access the values. - alias x u; /// ditto - alias x s; /// ditto - alias x r; /// ditto - static if(dimension >= 2) { - alias get_!'y' y; /// ditto - alias y v; /// ditto - alias y t; /// ditto - alias y g; /// ditto - } - static if(dimension >= 3) { - alias get_!'z' z; /// ditto - alias z b; /// ditto - alias z p; /// ditto - } - static if(dimension >= 4) { - alias get_!'w' w; /// ditto - alias w a; /// ditto - alias w q; /// ditto - } - - static if(dimension == 2) { - enum Vector e1 = Vector(1.to!vt, 0.to!vt); /// canonical basis for Euclidian space - enum Vector e2 = Vector(0.to!vt, 1.to!vt); /// ditto - } else static if(dimension == 3) { - enum Vector e1 = Vector(1.to!vt, 0.to!vt, 0.to!vt); /// canonical basis for Euclidian space - enum Vector e2 = Vector(0.to!vt, 1.to!vt, 0.to!vt); /// ditto - enum Vector e3 = Vector(0.to!vt, 0.to!vt, 1.to!vt); /// ditto - } else static if(dimension == 4) { - enum Vector e1 = Vector(1.to!vt, 0.to!vt, 0.to!vt, 0.to!vt); /// canonical basis for Euclidian space - enum Vector e2 = Vector(0.to!vt, 1.to!vt, 0.to!vt, 0.to!vt); /// ditto - enum Vector e3 = Vector(0.to!vt, 0.to!vt, 1.to!vt, 0.to!vt); /// ditto - enum Vector e4 = Vector(0.to!vt, 0.to!vt, 0.to!vt, 1.to!vt); /// ditto - } - - unittest { - assert(vec2.e1.vector == [1.0, 0.0]); - assert(vec2.e2.vector == [0.0, 1.0]); - - assert(vec3.e1.vector == [1.0, 0.0, 0.0]); - assert(vec3.e2.vector == [0.0, 1.0, 0.0]); - assert(vec3.e3.vector == [0.0, 0.0, 1.0]); - - assert(vec4.e1.vector == [1.0, 0.0, 0.0, 0.0]); - assert(vec4.e2.vector == [0.0, 1.0, 0.0, 0.0]); - assert(vec4.e3.vector == [0.0, 0.0, 1.0, 0.0]); - assert(vec4.e4.vector == [0.0, 0.0, 0.0, 1.0]); - } - - static void isCompatibleVectorImpl(int d)(Vector!(vt, d) vec) if(d <= dimension) { - } - - template isCompatibleVector(T) { - enum isCompatibleVector = is(typeof(isCompatibleVectorImpl(T.init))); - } - - static void isCompatibleMatrixImpl(int r, int c)(Matrix!(vt, r, c) m) { - } - - template isCompatibleMatrix(T) { - enum isCompatibleMatrix = is(typeof(isCompatibleMatrixImpl(T.init))); - } - - private void construct(int i, T, Tail...)(T head, Tail tail) { - static if(i >= dimension) { - static assert(false, "Too many arguments passed to constructor"); - } else static if(is(T : vt)) { - vector[i] = head; - construct!(i + 1)(tail); - } else static if(isDynamicArray!T) { - static assert((Tail.length == 0) && (i == 0), "dynamic array can not be passed together with other arguments"); - vector[] = head[]; - } else static if(isStaticArray!T) { - vector[i .. i + T.length] = head[]; - construct!(i + T.length)(tail); - } else static if(isCompatibleVector!T) { - vector[i .. i + T.dimension] = head.vector[]; - construct!(i + T.dimension)(tail); - } else { - static assert(false, "Vector constructor argument must be of type " ~ vt.stringof ~ " or Vector, not " ~ T.stringof); - } - } - - private void construct(int i)() { // terminate - static assert(i == dimension, "Not enough arguments passed to constructor"); - } - - /// Constructs the vector. - /// If a single value is passed the vector, the vector will be cleared with this value. - /// If a vector with a higher dimension is passed the vector will hold the first values up to its dimension. - /// If mixed types are passed they will be joined together (allowed types: vector, static array, $(I vt)). - /// Examples: - /// --- - /// vec4 v4 = vec4(1.0f, vec2(2.0f, 3.0f), 4.0f); - /// vec3 v3 = vec3(v4); // v3 = vec3(1.0f, 2.0f, 3.0f); - /// vec2 v2 = v3.xy; // swizzling returns a static array. - /// vec3 v3_2 = vec3(1.0f); // vec3 v3_2 = vec3(1.0f, 1.0f, 1.0f); - /// --- - this(Args...)(Args args) { - construct!(0)(args); - } - - /// ditto - this(T)(T vec) if(is_vector!T && is(T.vt : vt) && (T.dimension >= dimension)) { - foreach(i; TupleRange!(0, dimension)) { - vector[i] = vec.vector[i]; - } - } - - /// ditto - this()(vt value) { - clear(value); - } - - /// Returns true if all values are not nan and finite, otherwise false. - @property bool isFinite() const { - static if(isIntegral!type) { - return true; - } - else { - foreach(v; vector) { - if(isNaN(v) || isInfinity(v)) { - return false; - } - } - return true; - } - } - deprecated("Use isFinite instead of ok") alias ok = isFinite; - - /// Sets all values of the vector to value. - void clear(vt value) { - foreach(i; TupleRange!(0, dimension)) { - vector[i] = value; - } - } - - unittest { - vec3 vec_clear; - assert(!vec_clear.isFinite); - vec_clear.clear(1.0f); - assert(vec_clear.isFinite); - assert(vec_clear.vector == [1.0f, 1.0f, 1.0f]); - assert(vec_clear.vector == vec3(1.0f).vector); - vec_clear.clear(float.infinity); - assert(!vec_clear.isFinite); - vec_clear.clear(float.nan); - assert(!vec_clear.isFinite); - vec_clear.clear(1.0f); - assert(vec_clear.isFinite); - - vec4 b = vec4(1.0f, vec_clear); - assert(b.isFinite); - assert(b.vector == [1.0f, 1.0f, 1.0f, 1.0f]); - assert(b.vector == vec4(1.0f).vector); - - vec2 v2_1 = vec2(vec2(0.0f, 1.0f)); - assert(v2_1.vector == [0.0f, 1.0f]); - - vec2 v2_2 = vec2(1.0f, 1.0f); - assert(v2_2.vector == [1.0f, 1.0f]); - - vec3 v3 = vec3(v2_1, 2.0f); - assert(v3.vector == [0.0f, 1.0f, 2.0f]); - - vec4 v4_1 = vec4(1.0f, vec2(2.0f, 3.0f), 4.0f); - assert(v4_1.vector == [1.0f, 2.0f, 3.0f, 4.0f]); - assert(vec3(v4_1).vector == [1.0f, 2.0f, 3.0f]); - assert(vec2(vec3(v4_1)).vector == [1.0f, 2.0f]); - assert(vec2(vec3(v4_1)).vector == vec2(v4_1).vector); - assert(v4_1.vector == vec4([1.0f, 2.0f, 3.0f, 4.0f]).vector); - - vec4 v4_2 = vec4(vec2(1.0f, 2.0f), vec2(3.0f, 4.0f)); - assert(v4_2.vector == [1.0f, 2.0f, 3.0f, 4.0f]); - assert(vec3(v4_2).vector == [1.0f, 2.0f, 3.0f]); - assert(vec2(vec3(v4_2)).vector == [1.0f, 2.0f]); - assert(vec2(vec3(v4_2)).vector == vec2(v4_2).vector); - assert(v4_2.vector == vec4([1.0f, 2.0f, 3.0f, 4.0f]).vector); - - float[2] f2 = [1.0f, 2.0f]; - float[3] f3 = [1.0f, 2.0f, 3.0f]; - float[4] f4 = [1.0f, 2.0f, 3.0f, 4.0f]; - assert(vec2(1.0f, 2.0f).vector == vec2(f2).vector); - assert(vec3(1.0f, 2.0f, 3.0f).vector == vec3(f3).vector); - assert(vec3(1.0f, 2.0f, 3.0f).vector == vec3(f2, 3.0f).vector); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f).vector == vec4(f4).vector); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f).vector == vec4(f3, 4.0f).vector); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f).vector == vec4(f2, 3.0f, 4.0f).vector); - // useful for: "vec4 v4 = […]" or "vec4 v4 = other_vector.rgba" - - assert(vec3(vec3i(1, 2, 3)) == vec3(1.0, 2.0, 3.0)); - assert(vec3d(vec3(1.0, 2.0, 3.0)) == vec3d(1.0, 2.0, 3.0)); - - static assert(!__traits(compiles, vec3(0.0f, 0.0f))); - static assert(!__traits(compiles, vec4(0.0f, 0.0f, 0.0f))); - static assert(!__traits(compiles, vec4(0.0f, vec2(0.0f, 0.0f)))); - static assert(!__traits(compiles, vec4(vec3(0.0f, 0.0f, 0.0f)))); - } - - template coord_to_index(char c) { - static if((c == 'x') || (c == 'r') || (c == 'u') || (c == 's')) { - enum coord_to_index = 0; - } else static if((c == 'y') || (c == 'g') || (c == 'v') || (c == 't')) { - enum coord_to_index = 1; - } else static if((c == 'z') || (c == 'b') || (c == 'p')) { - static assert(dimension >= 3, "the " ~ c ~ " property is only available on vectors with a third dimension."); - enum coord_to_index = 2; - } else static if((c == 'w') || (c == 'a') || (c == 'q')) { - static assert(dimension >= 4, "the " ~ c ~ " property is only available on vectors with a fourth dimension."); - enum coord_to_index = 3; - } else { - static assert(false, "accepted coordinates are x, s, r, u, y, g, t, v, z, p, b, w, q and a not " ~ c ~ "."); - } - } - - static if(dimension == 2) { void set(vt x, vt y) { vector[0] = x; vector[1] = y; } } - static if(dimension == 3) { void set(vt x, vt y, vt z) { vector[0] = x; vector[1] = y; vector[2] = z; } } - static if(dimension == 4) { void set(vt x, vt y, vt z, vt w) { vector[0] = x; vector[1] = y; vector[2] = z; vector[3] = w; } } - - /// Updates the vector with the values from other. - void update(Vector!(vt, dimension) other) { - vector = other.vector; - } - - unittest { - vec2 v2 = vec2(1.0f, 2.0f); - assert(v2.x == 1.0f); - assert(v2.y == 2.0f); - v2.x = 3.0f; - v2.x += 1; - v2.x -= 1; - assert(v2.vector == [3.0f, 2.0f]); - v2.y = 4.0f; - v2.y += 1; - v2.y -= 1; - assert(v2.vector == [3.0f, 4.0f]); - assert((v2.x == 3.0f) && (v2.x == v2.u) && (v2.x == v2.s) && (v2.x == v2.r)); - assert(v2.y == 4.0f); - assert((v2.y == 4.0f) && (v2.y == v2.v) && (v2.y == v2.t) && (v2.y == v2.g)); - v2.set(0.0f, 1.0f); - assert(v2.vector == [0.0f, 1.0f]); - v2.update(vec2(3.0f, 4.0f)); - assert(v2.vector == [3.0f, 4.0f]); - - vec3 v3 = vec3(1.0f, 2.0f, 3.0f); - assert(v3.x == 1.0f); - assert(v3.y == 2.0f); - assert(v3.z == 3.0f); - v3.x = 3.0f; - v3.x += 1; - v3.x -= 1; - assert(v3.vector == [3.0f, 2.0f, 3.0f]); - v3.y = 4.0f; - v3.y += 1; - v3.y -= 1; - assert(v3.vector == [3.0f, 4.0f, 3.0f]); - v3.z = 5.0f; - v3.z += 1; - v3.z -= 1; - assert(v3.vector == [3.0f, 4.0f, 5.0f]); - assert((v3.x == 3.0f) && (v3.x == v3.s) && (v3.x == v3.r)); - assert((v3.y == 4.0f) && (v3.y == v3.t) && (v3.y == v3.g)); - assert((v3.z == 5.0f) && (v3.z == v3.p) && (v3.z == v3.b)); - v3.set(0.0f, 1.0f, 2.0f); - assert(v3.vector == [0.0f, 1.0f, 2.0f]); - v3.update(vec3(3.0f, 4.0f, 5.0f)); - assert(v3.vector == [3.0f, 4.0f, 5.0f]); - - vec4 v4 = vec4(1.0f, 2.0f, vec2(3.0f, 4.0f)); - assert(v4.x == 1.0f); - assert(v4.y == 2.0f); - assert(v4.z == 3.0f); - assert(v4.w == 4.0f); - v4.x = 3.0f; - v4.x += 1; - v4.x -= 1; - assert(v4.vector == [3.0f, 2.0f, 3.0f, 4.0f]); - v4.y = 4.0f; - v4.y += 1; - v4.y -= 1; - assert(v4.vector == [3.0f, 4.0f, 3.0f, 4.0f]); - v4.z = 5.0f; - v4.z += 1; - v4.z -= 1; - assert(v4.vector == [3.0f, 4.0f, 5.0f, 4.0f]); - v4.w = 6.0f; - v4.w += 1; - v4.w -= 1; - assert(v4.vector == [3.0f, 4.0f, 5.0f, 6.0f]); - assert((v4.x == 3.0f) && (v4.x == v4.s) && (v4.x == v4.r)); - assert((v4.y == 4.0f) && (v4.y == v4.t) && (v4.y == v4.g)); - assert((v4.z == 5.0f) && (v4.z == v4.p) && (v4.z == v4.b)); - assert((v4.w == 6.0f) && (v4.w == v4.q) && (v4.w == v4.a)); - v4.set(0.0f, 1.0f, 2.0f, 3.0f); - assert(v4.vector == [0.0f, 1.0f, 2.0f, 3.0f]); - v4.update(vec4(3.0f, 4.0f, 5.0f, 6.0f)); - assert(v4.vector == [3.0f, 4.0f, 5.0f, 6.0f]); - } - - private void dispatchImpl(int i, string s, int size)(ref vt[size] result) const { - static if(s.length > 0) { - result[i] = vector[coord_to_index!(s[0])]; - dispatchImpl!(i + 1, s[1..$])(result); - } - } - - /// Implements dynamic swizzling. - /// Returns: a Vector - @property Vector!(vt, s.length) opDispatch(string s)() const { - vt[s.length] ret; - dispatchImpl!(0, s)(ret); - Vector!(vt, s.length) ret_vec; - ret_vec.vector = ret; - return ret_vec; - } - - unittest { - vec2 v2 = vec2(1.0f, 2.0f); - assert(v2.xytsy == [1.0f, 2.0f, 2.0f, 1.0f, 2.0f]); - - assert(vec3(1.0f, 2.0f, 3.0f).xybzyr == [1.0f, 2.0f, 3.0f, 3.0f, 2.0f, 1.0f]); - assert(vec4(v2, 3.0f, 4.0f).xyzwrgbastpq == [1.0f, 2.0f, 3.0f, 4.0f, - 1.0f, 2.0f, 3.0f, 4.0f, - 1.0f, 2.0f, 3.0f, 4.0f]); - assert(vec4(v2, 3.0f, 4.0f).wgyzax == [4.0f, 2.0f, 2.0f, 3.0f, 4.0f, 1.0f]); - assert(vec4(v2.xyst).vector == [1.0f, 2.0f, 1.0f, 2.0f]); - } - - /// Returns the squared magnitude of the vector. - @property real magnitude_squared() const { - real temp = 0; - - foreach(index; TupleRange!(0, dimension)) { - temp += vector[index]^^2; - } - - return temp; - } - - /// Returns the magnitude of the vector. - @property real magnitude() const { - return sqrt(magnitude_squared); - } - - alias magnitude_squared length_squared; /// ditto - alias magnitude length; /// ditto - - /// Normalizes the vector. - void normalize() { - real len = length; - - if(len != 0) { - foreach(index; TupleRange!(0, dimension)) { - vector[index] = cast(type)(vector[index]/len); - } - } - } - - /// Returns a normalized copy of the current vector. - @property Vector normalized() const { - Vector ret; - ret.update(this); - ret.normalize(); - return ret; - } - - Vector opUnary(string op : "-")() const { - Vector ret; - - foreach(index; TupleRange!(0, dimension)) { - ret.vector[index] = -vector[index]; - } - - return ret; - } - - unittest { - assert(vec2(1.0f, 1.0f) == -vec2(-1.0f, -1.0f)); - assert(vec2(-1.0f, 1.0f) == -vec2(1.0f, -1.0f)); - - assert(-vec3(1.0f, 1.0f, 1.0f) == vec3(-1.0f, -1.0f, -1.0f)); - assert(-vec3(-1.0f, 1.0f, -1.0f) == vec3(1.0f, -1.0f, 1.0f)); - - assert(vec4(1.0f, 1.0f, 1.0f, 1.0f) == -vec4(-1.0f, -1.0f, -1.0f, -1.0f)); - assert(vec4(-1.0f, 1.0f, -1.0f, 1.0f) == -vec4(1.0f, -1.0f, 1.0f, -1.0f)); - } - - // let the math begin! - Vector opBinary(string op : "*")(vt r) const { - Vector ret; - - foreach(index; TupleRange!(0, dimension)) { - ret.vector[index] = vector[index] * r; - } - - return ret; - } - - Vector opBinary(string op : "/")(vt r) const { - Vector ret; - - foreach(index; TupleRange!(0, dimension)) { - ret.vector[index] = vector[index] / r; - } - - return ret; - } - - Vector opBinary(string op)(Vector r) const if((op == "+") || (op == "-")) { - Vector ret; - - foreach(index; TupleRange!(0, dimension)) { - ret.vector[index] = mixin("vector[index]" ~ op ~ "r.vector[index]"); - } - - return ret; - } - - vt opBinary(string op : "*")(Vector r) const { - return dot(this, r); - } - - // vector * matrix (for matrix * vector -> struct Matrix) - Vector!(vt, T.cols) opBinary(string op : "*", T)(T inp) const if(isCompatibleMatrix!T && (T.rows == dimension)) { - Vector!(vt, T.cols) ret; - ret.clear(0); - - foreach(c; TupleRange!(0, T.cols)) { - foreach(r; TupleRange!(0, T.rows)) { - ret.vector[c] += vector[r] * inp.matrix[r][c]; - } - } - - return ret; - } - - auto opBinaryRight(string op, T)(T inp) const if(!is_vector!T && !is_matrix!T && !is_quaternion!T) { - return this.opBinary!(op)(inp); - } - - unittest { - vec2 v2 = vec2(1.0f, 3.0f); - auto v2times2 = 2 * v2; - assert((v2*2.5f).vector == [2.5f, 7.5f]); - assert((v2+vec2(3.0f, 1.0f)).vector == [4.0f, 4.0f]); - assert((v2-vec2(1.0f, 3.0f)).vector == [0.0f, 0.0f]); - assert((v2*vec2(2.0f, 2.0f)) == 8.0f); - - vec3 v3 = vec3(1.0f, 3.0f, 5.0f); - assert((v3*2.5f).vector == [2.5f, 7.5f, 12.5f]); - assert((v3+vec3(3.0f, 1.0f, -1.0f)).vector == [4.0f, 4.0f, 4.0f]); - assert((v3-vec3(1.0f, 3.0f, 5.0f)).vector == [0.0f, 0.0f, 0.0f]); - assert((v3*vec3(2.0f, 2.0f, 2.0f)) == 18.0f); - - vec4 v4 = vec4(1.0f, 3.0f, 5.0f, 7.0f); - assert((v4*2.5f).vector == [2.5f, 7.5f, 12.5f, 17.5]); - assert((v4+vec4(3.0f, 1.0f, -1.0f, -3.0f)).vector == [4.0f, 4.0f, 4.0f, 4.0f]); - assert((v4-vec4(1.0f, 3.0f, 5.0f, 7.0f)).vector == [0.0f, 0.0f, 0.0f, 0.0f]); - assert((v4*vec4(2.0f, 2.0f, 2.0f, 2.0f)) == 32.0f); - - mat2 m2 = mat2(1.0f, 2.0f, 3.0f, 4.0f); - vec2 v2_2 = vec2(2.0f, 2.0f); - assert((v2_2*m2).vector == [8.0f, 12.0f]); - - mat3 m3 = mat3(1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f); - vec3 v3_2 = vec3(2.0f, 2.0f, 2.0f); - assert((v3_2*m3).vector == [24.0f, 30.0f, 36.0f]); - } - - void opOpAssign(string op : "*")(vt r) { - foreach(index; TupleRange!(0, dimension)) { - vector[index] *= r; - } - } - - void opOpAssign(string op : "/")(vt r) { - foreach(index; TupleRange!(0, dimension)) { - vector[index] /= r; - } - } - - void opOpAssign(string op)(Vector r) if((op == "+") || (op == "-")) { - foreach(index; TupleRange!(0, dimension)) { - mixin("vector[index]" ~ op ~ "= r.vector[index];"); - } - } - - unittest { - vec2 v2 = vec2(1.0f, 3.0f); - v2 *= 2.5f; - assert(v2.vector == [2.5f, 7.5f]); - v2 -= vec2(2.5f, 7.5f); - assert(v2.vector == [0.0f, 0.0f]); - v2 += vec2(1.0f, 3.0f); - assert(v2.vector == [1.0f, 3.0f]); - assert(almost_equal(v2.length, sqrt(10.0f))); - assert(v2.length_squared == 10.0f); - assert((v2.magnitude == v2.length) && (v2.magnitude_squared == v2.length_squared)); - v2 /= 2.0f; - assert(v2.vector == [0.5f, 1.5f]); - assert(almost_equal(v2.normalized, vec2(1.0f/sqrt(10.0f), 3.0f/sqrt(10.0f)))); - - vec3 v3 = vec3(1.0f, 3.0f, 5.0f); - v3 *= 2.5f; - assert(v3.vector == [2.5f, 7.5f, 12.5f]); - v3 -= vec3(2.5f, 7.5f, 12.5f); - assert(v3.vector == [0.0f, 0.0f, 0.0f]); - v3 += vec3(1.0f, 3.0f, 5.0f); - assert(v3.vector == [1.0f, 3.0f, 5.0f]); - assert(almost_equal(v3.length, sqrt(35.0f))); - assert(v3.length_squared == 35.0f); - assert((v3.magnitude == v3.length) && (v3.magnitude_squared == v3.length_squared)); - v3 /= 2.0f; - assert(v3.vector == [0.5f, 1.5f, 2.5f]); - assert(almost_equal(v3.normalized, vec3(1.0f/sqrt(35.0f), 3.0f/sqrt(35.0f), 5.0f/sqrt(35.0f)))); - - vec4 v4 = vec4(1.0f, 3.0f, 5.0f, 7.0f); - v4 *= 2.5f; - assert(v4.vector == [2.5f, 7.5f, 12.5f, 17.5]); - v4 -= vec4(2.5f, 7.5f, 12.5f, 17.5f); - assert(v4.vector == [0.0f, 0.0f, 0.0f, 0.0f]); - v4 += vec4(1.0f, 3.0f, 5.0f, 7.0f); - assert(v4.vector == [1.0f, 3.0f, 5.0f, 7.0f]); - assert(almost_equal(v4.length, sqrt(84.0f))); - assert(v4.length_squared == 84.0f); - assert((v4.magnitude == v4.length) && (v4.magnitude_squared == v4.length_squared)); - v4 /= 2.0f; - assert(v4.vector == [0.5f, 1.5f, 2.5f, 3.5f]); - assert(almost_equal(v4.normalized, vec4(1.0f/sqrt(84.0f), 3.0f/sqrt(84.0f), 5.0f/sqrt(84.0f), 7.0f/sqrt(84.0f)))); - } - - int opCmp(ref const Vector vec) const { - foreach(i, a; vector) { - if(a < vec.vector[i]) { - return -1; - } else if(a > vec.vector[i]) { - return 1; - } - } - - // Vectors are the same - return 0; - } - - bool opEquals(T)(const T vec) const if(!isArray!T && T.dimension == dimension) { - return vector == vec.vector; - } - - bool opEquals(T)(const(T)[] array) const if(!isArray!T && !is_vector!T) { - if(array.length != dimension) { - return false; - } - - foreach(index; TupleRange!(0, dimension)) { - if(vector[index] != array[index]) { - return false; - } - } - - return true; - } - - bool opCast(T : bool)() const { - return isFinite; - } - - unittest { - assert(vec2(1.0f, 2.0f) == vec2(1.0f, 2.0f)); - assert(vec2(1.0f, 2.0f) != vec2(1.0f, 1.0f)); - assert(vec2(1.0f, 2.0f) == vec2d(1.0, 2.0)); - assert(vec2(1.0f, 2.0f) != vec2d(1.0, 1.0)); - assert(vec2(1.0f, 2.0f) == vec2(1.0f, 2.0f).vector); - assert(vec2(1.0f, 2.0f) != vec2(1.0f, 1.0f).vector); - assert(vec2(1.0f, 2.0f) == vec2d(1.0, 2.0).vector); - assert(vec2(1.0f, 2.0f) != vec2d(1.0, 1.0).vector); - - assert(vec3(1.0f, 2.0f, 3.0f) == vec3(1.0f, 2.0f, 3.0f)); - assert(vec3(1.0f, 2.0f, 3.0f) != vec3(1.0f, 2.0f, 2.0f)); - assert(vec3(1.0f, 2.0f, 3.0f) == vec3d(1.0, 2.0, 3.0)); - assert(vec3(1.0f, 2.0f, 3.0f) != vec3d(1.0, 2.0, 2.0)); - assert(vec3(1.0f, 2.0f, 3.0f) == vec3(1.0f, 2.0f, 3.0f).vector); - assert(vec3(1.0f, 2.0f, 3.0f) != vec3(1.0f, 2.0f, 2.0f).vector); - assert(vec3(1.0f, 2.0f, 3.0f) == vec3d(1.0, 2.0, 3.0).vector); - assert(vec3(1.0f, 2.0f, 3.0f) != vec3d(1.0, 2.0, 2.0).vector); - - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) == vec4(1.0f, 2.0f, 3.0f, 4.0f)); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) != vec4(1.0f, 2.0f, 3.0f, 3.0f)); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) == vec4d(1.0, 2.0, 3.0, 4.0)); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) != vec4d(1.0, 2.0, 3.0, 3.0)); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) == vec4(1.0f, 2.0f, 3.0f, 4.0f).vector); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) != vec4(1.0f, 2.0f, 3.0f, 3.0f).vector); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) == vec4d(1.0, 2.0, 3.0, 4.0).vector); - assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) != vec4d(1.0, 2.0, 3.0, 3.0).vector); - - assert(!(vec4(float.nan))); - if(vec4(1.0f)) { } - else { assert(false); } - } - -} - -/// Calculates the product between two vectors. -T.vt dot(T)(const T veca, const T vecb) @safe pure nothrow if(is_vector!T) { - T.vt temp = 0; - - foreach(index; TupleRange!(0, T.dimension)) { - temp += veca.vector[index] * vecb.vector[index]; - } - - return temp; -} - -/// Calculates the cross product of two 3-dimensional vectors. -T cross(T)(const T veca, const T vecb) @safe pure nothrow if(is_vector!T && (T.dimension == 3)) { - return T(veca.y * vecb.z - vecb.y * veca.z, - veca.z * vecb.x - vecb.z * veca.x, - veca.x * vecb.y - vecb.x * veca.y); -} - -/// Calculates the distance between two vectors. -T.vt distance(T)(const T veca, const T vecb) @safe pure nothrow if(is_vector!T) { - return (veca - vecb).length; -} - -unittest { - // dot is already tested in Vector.opBinary, so no need for testing with more vectors - vec3 v1 = vec3(1.0f, 2.0f, -3.0f); - vec3 v2 = vec3(1.0f, 3.0f, 2.0f); - - assert(dot(v1, v2) == 1.0f); - assert(dot(v1, v2) == (v1 * v2)); - assert(dot(v1, v2) == dot(v2, v1)); - assert((v1 * v2) == (v1 * v2)); - - assert(cross(v1, v2).vector == [13.0f, -5.0f, 1.0f]); - assert(cross(v2, v1).vector == [-13.0f, 5.0f, -1.0f]); - - assert(distance(vec2(0.0f, 0.0f), vec2(0.0f, 10.0f)) == 10.0); -} - -/// reflect a vector using a surface normal -T reflect(T)(const T vec, const T norm) @safe pure nothrow if(is_vector!T) { - return (2 * (vec * norm) * norm) - vec; -} - -unittest -{ - assert(vec2(1,1).reflect(vec2(0,1)) == vec2(-1,1)); - assert(vec2(-1,1).reflect(vec2(0,1)) == vec2(1,1)); - assert(vec2(2,1).reflect(vec2(0,1)) == vec2(-2,1)); - - assert(vec3(1,1,1).reflect(vec3(0,1,0)) == vec3(-1,1,-1)); -} - -/// Pre-defined vector types, the number represents the dimension and the last letter the type (none = float, d = double, i = int). -alias Vector!(float, 2) vec2; -alias Vector!(float, 3) vec3; /// ditto -alias Vector!(float, 4) vec4; /// ditto - -alias Vector!(double, 2) vec2d; /// ditto -alias Vector!(double, 3) vec3d; /// ditto -alias Vector!(double, 4) vec4d; /// ditto - -alias Vector!(int, 2) vec2i; /// ditto -alias Vector!(int, 3) vec3i; /// ditto -alias Vector!(int, 4) vec4i; /// ditto - -/*alias Vector!(ubyte, 2) vec2ub; -alias Vector!(ubyte, 3) vec3ub; -alias Vector!(ubyte, 4) vec4ub;*/ - - -/// Base template for all matrix-types. -/// Params: -/// type = all values get stored as this type -/// rows_ = rows of the matrix -/// cols_ = columns of the matrix -/// Examples: -/// --- -/// alias Matrix!(float, 4, 4) mat4; -/// alias Matrix!(double, 3, 4) mat34d; -/// alias Matrix!(real, 2, 2) mat2r; -/// --- -struct Matrix(type, int rows_, int cols_) if((rows_ > 0) && (cols_ > 0)) { - alias type mt; /// Holds the internal type of the matrix; - static const int rows = rows_; /// Holds the number of rows; - static const int cols = cols_; /// Holds the number of columns; - - /// Holds the matrix $(RED row-major) in memory. - mt[cols][rows] matrix; // In C it would be mt[rows][cols], D does it like this: (mt[foo])[bar] - alias matrix this; - - unittest { - mat2 m2 = mat2(0.0f, 1.0f, 2.0f, 3.0f); - assert(m2[0][0] == 0.0f); - assert(m2[0][1] == 1.0f); - assert(m2[1][0] == 2.0f); - assert(m2[1][1] == 3.0f); - m2[0..1] = [2.0f, 2.0f]; - assert(m2 == [[2.0f, 2.0f], [2.0f, 3.0f]]); - - mat3 m3 = mat3(0.0f, 0.1f, 0.2f, 1.0f, 1.1f, 1.2f, 2.0f, 2.1f, 2.2f); - assert(m3[0][1] == 0.1f); - assert(m3[2][0] == 2.0f); - assert(m3[1][2] == 1.2f); - m3[0][0..$] = 0.0f; - assert(m3 == [[0.0f, 0.0f, 0.0f], - [1.0f, 1.1f, 1.2f], - [2.0f, 2.1f, 2.2f]]); - - mat4 m4 = mat4(0.0f, 0.1f, 0.2f, 0.3f, - 1.0f, 1.1f, 1.2f, 1.3f, - 2.0f, 2.1f, 2.2f, 2.3f, - 3.0f, 3.1f, 3.2f, 3.3f); - assert(m4[0][3] == 0.3f); - assert(m4[1][1] == 1.1f); - assert(m4[2][0] == 2.0f); - assert(m4[3][2] == 3.2f); - m4[2][1..3] = [1.0f, 2.0f]; - assert(m4 == [[0.0f, 0.1f, 0.2f, 0.3f], - [1.0f, 1.1f, 1.2f, 1.3f], - [2.0f, 1.0f, 2.0f, 2.3f], - [3.0f, 3.1f, 3.2f, 3.3f]]); - - } - - /// Returns the pointer to the stored values as OpenGL requires it. - /// Note this will return a pointer to a $(RED row-major) matrix, - /// $(RED this means you've to set the transpose argument to GL_TRUE when passing it to OpenGL). - /// Examples: - /// --- - /// // 3rd argument = GL_TRUE - /// glUniformMatrix4fv(programs.main.model, 1, GL_TRUE, mat4.translation(-0.5f, -0.5f, 1.0f).value_ptr); - /// --- - @property auto value_ptr() const { return matrix[0].ptr; } - - /// Returns the current matrix formatted as flat string. - @property string as_string() { - return format("%s", matrix); - } - alias as_string toString; /// ditto - - /// Returns the current matrix as pretty formatted string. - @property string as_pretty_string() { - string fmtr = "%s"; - - size_t rjust = max(format(fmtr, reduce!(max)(matrix[])).length, - format(fmtr, reduce!(min)(matrix[])).length) - 1; - - string[] outer_parts; - foreach(mt[] row; matrix) { - string[] inner_parts; - foreach(mt col; row) { - inner_parts ~= rightJustify(format(fmtr, col), rjust); - } - outer_parts ~= " [" ~ join(inner_parts, ", ") ~ "]"; - } - - return "[" ~ join(outer_parts, "\n")[1..$] ~ "]"; - } - alias as_pretty_string toPrettyString; /// ditto - - @safe pure nothrow: - static void isCompatibleMatrixImpl(int r, int c)(Matrix!(mt, r, c) m) { - } - - template isCompatibleMatrix(T) { - enum isCompatibleMatrix = is(typeof(isCompatibleMatrixImpl(T.init))); - } - - static void isCompatibleVectorImpl(int d)(Vector!(mt, d) vec) { - } - - template isCompatibleVector(T) { - enum isCompatibleVector = is(typeof(isCompatibleVectorImpl(T.init))); - } - - private void construct(int i, T, Tail...)(T head, Tail tail) { - static if(i >= rows*cols) { - static assert(false, "Too many arguments passed to constructor"); - } else static if(is(T : mt)) { - matrix[i / cols][i % cols] = head; - construct!(i + 1)(tail); - } else static if(is(T == Vector!(mt, cols))) { - static if(i % cols == 0) { - matrix[i / cols] = head.vector; - construct!(i + T.dimension)(tail); - } else { - static assert(false, "Can't convert Vector into the matrix. Maybe it doesn't align to the columns correctly or dimension doesn't fit"); - } - } else static if(isDynamicArray!T) { - foreach(j; 0..cols*rows) - matrix[j / cols][j % cols] = head[j]; - } else { - static assert(false, "Matrix constructor argument must be of type " ~ mt.stringof ~ " or Vector, not " ~ T.stringof); - } - } - - private void construct(int i)() { // terminate - static assert(i == rows*cols, "Not enough arguments passed to constructor"); - } - - /// Constructs the matrix: - /// If a single value is passed, the matrix will be cleared with this value (each column in each row will contain this value). - /// If a matrix with more rows and columns is passed, the matrix will be the upper left nxm matrix. - /// If a matrix with less rows and columns is passed, the passed matrix will be stored in the upper left of an identity matrix. - /// It's also allowed to pass vectors and scalars at a time, but the vectors dimension must match the number of columns and align correctly. - /// Examples: - /// --- - /// mat2 m2 = mat2(0.0f); // mat2 m2 = mat2(0.0f, 0.0f, 0.0f, 0.0f); - /// mat3 m3 = mat3(m2); // mat3 m3 = mat3(0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f); - /// mat3 m3_2 = mat3(vec3(1.0f, 2.0f, 3.0f), 4.0f, 5.0f, 6.0f, vec3(7.0f, 8.0f, 9.0f)); - /// mat4 m4 = mat4.identity; // just an identity matrix - /// mat3 m3_3 = mat3(m4); // mat3 m3_3 = mat3.identity - /// --- - this(Args...)(Args args) { - construct!(0)(args); - } - - /// ditto - this(T)(T mat) if(is_matrix!T && (T.cols >= cols) && (T.rows >= rows)) { - foreach(r; TupleRange!(0, rows)) { - foreach(c; TupleRange!(0, cols)) { - matrix[r][c] = mat.matrix[r][c]; - } - } - } - - /// ditto - this(T)(T mat) if(is_matrix!T && (T.cols < cols) && (T.rows < rows)) { - make_identity(); - - foreach(r; TupleRange!(0, T.rows)) { - foreach(c; TupleRange!(0, T.cols)) { - matrix[r][c] = mat.matrix[r][c]; - } - } - } - - /// ditto - this()(mt value) { - clear(value); - } - - /// Returns true if all values are not nan and finite, otherwise false. - @property bool isFinite() const { - static if(isIntegral!type) { - return true; - } - else { - foreach(row; matrix) { - foreach(col; row) { - if(isNaN(col) || isInfinity(col)) { - return false; - } - } - } - return true; - } - - } - deprecated("Use isFinite instead of ok") alias ok = isFinite; - - /// Sets all values of the matrix to value (each column in each row will contain this value). - void clear(mt value) { - foreach(r; TupleRange!(0, rows)) { - foreach(c; TupleRange!(0, cols)) { - matrix[r][c] = value; - } - } - } - - unittest { - mat2 m2 = mat2(1.0f, 1.0f, vec2(2.0f, 2.0f)); - assert(m2.matrix == [[1.0f, 1.0f], [2.0f, 2.0f]]); - m2.clear(3.0f); - assert(m2.matrix == [[3.0f, 3.0f], [3.0f, 3.0f]]); - assert(m2.isFinite); - m2.clear(float.nan); - assert(!m2.isFinite); - m2.clear(float.infinity); - assert(!m2.isFinite); - m2.clear(0.0f); - assert(m2.isFinite); - - mat3 m3 = mat3(1.0f); - assert(m3.matrix == [[1.0f, 1.0f, 1.0f], - [1.0f, 1.0f, 1.0f], - [1.0f, 1.0f, 1.0f]]); - - mat4 m4 = mat4(vec4(1.0f, 1.0f, 1.0f, 1.0f), - 2.0f, 2.0f, 2.0f, 2.0f, - 3.0f, 3.0f, 3.0f, 3.0f, - vec4(4.0f, 4.0f, 4.0f, 4.0f)); - assert(m4.matrix == [[1.0f, 1.0f, 1.0f, 1.0f], - [2.0f, 2.0f, 2.0f, 2.0f], - [3.0f, 3.0f, 3.0f, 3.0f], - [4.0f, 4.0f, 4.0f, 4.0f]]); - assert(mat3(m4).matrix == [[1.0f, 1.0f, 1.0f], - [2.0f, 2.0f, 2.0f], - [3.0f, 3.0f, 3.0f]]); - assert(mat2(mat3(m4)).matrix == [[1.0f, 1.0f], [2.0f, 2.0f]]); - assert(mat2(m4).matrix == mat2(mat3(m4)).matrix); - assert(mat4(mat3(m4)).matrix == [[1.0f, 1.0f, 1.0f, 0.0f], - [2.0f, 2.0f, 2.0f, 0.0f], - [3.0f, 3.0f, 3.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - - Matrix!(float, 2, 3) mt1 = Matrix!(float, 2, 3)(1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f); - Matrix!(float, 3, 2) mt2 = Matrix!(float, 3, 2)(6.0f, -1.0f, 3.0f, 2.0f, 0.0f, -3.0f); - - assert(mt1.matrix == [[1.0f, 2.0f, 3.0f], [4.0f, 5.0f, 6.0f]]); - assert(mt2.matrix == [[6.0f, -1.0f], [3.0f, 2.0f], [0.0f, -3.0f]]); - - static assert(!__traits(compiles, mat2(1, 2, 1))); - static assert(!__traits(compiles, mat3(1, 2, 3, 1, 2, 3, 1, 2))); - static assert(!__traits(compiles, mat4(1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3))); - - auto m5 = mat2([0.0f,1,2,3]); - assert(m5.matrix == [[0.0f, 1.0f], [2.0f, 3.0f]]); - - auto m6 = Matrix!(int, 2, 3)([0,1,2,3,4,5]); - assert(m6.matrix == [[0, 1, 2], [3, 4, 5]]); - } - - static if(rows == cols) { - /// Makes the current matrix an identity matrix. - void make_identity() { - clear(0); - foreach(r; TupleRange!(0, rows)) { - matrix[r][r] = 1; - } - } - - /// Returns a identity matrix. - static @property Matrix identity() { - Matrix ret; - ret.clear(0); - - foreach(r; TupleRange!(0, rows)) { - ret.matrix[r][r] = 1; - } - - return ret; - } - - /// Transposes the current matrix; - void transpose() { - matrix = transposed().matrix; - } - - unittest { - mat2 m2 = mat2(1.0f); - m2.transpose(); - assert(m2.matrix == mat2(1.0f).matrix); - m2.make_identity(); - assert(m2.matrix == [[1.0f, 0.0f], - [0.0f, 1.0f]]); - m2.transpose(); - assert(m2.matrix == [[1.0f, 0.0f], - [0.0f, 1.0f]]); - assert(m2.matrix == m2.identity.matrix); - - mat3 m3 = mat3(1.1f, 1.2f, 1.3f, - 2.1f, 2.2f, 2.3f, - 3.1f, 3.2f, 3.3f); - m3.transpose(); - assert(m3.matrix == [[1.1f, 2.1f, 3.1f], - [1.2f, 2.2f, 3.2f], - [1.3f, 2.3f, 3.3f]]); - - mat4 m4 = mat4(2.0f); - m4.transpose(); - assert(m4.matrix == mat4(2.0f).matrix); - m4.make_identity(); - assert(m4.matrix == [[1.0f, 0.0f, 0.0f, 0.0f], - [0.0f, 1.0f, 0.0f, 0.0f], - [0.0f, 0.0f, 1.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - assert(m4.matrix == m4.identity.matrix); - } - - } - - /// Returns a transposed copy of the matrix. - @property Matrix!(mt, cols, rows) transposed() const { - typeof(return) ret; - - foreach(r; TupleRange!(0, rows)) { - foreach(c; TupleRange!(0, cols)) { - ret.matrix[c][r] = matrix[r][c]; - } - } - - return ret; - } - - // transposed already tested in last unittest - - - static if((rows == 2) && (cols == 2)) { - @property mt det() const { - return (matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]); - } - - private Matrix invert(ref Matrix mat) const { - static if(isFloatingPoint!mt && rmul) { - mt d = 1 / det; - - mat.matrix = [[matrix[1][1]*d, -matrix[0][1]*d], - [-matrix[1][0]*d, matrix[0][0]*d]]; - } else { - mt d = det; - - mat.matrix = [[matrix[1][1]/d, -matrix[0][1]/d], - [-matrix[1][0]/d, matrix[0][0]/d]]; - } - - return mat; - } - - static Matrix scaling(mt x, mt y) { - Matrix ret = Matrix.identity; - - ret.matrix[0][0] = x; - ret.matrix[1][1] = y; - - return ret; - } - - Matrix scale(mt x, mt y) { - this = Matrix.scaling(x, y) * this; - return this; - } - - unittest { - assert(mat2.scaling(3, 3).matrix == mat2.identity.scale(3, 3).matrix); - assert(mat2.scaling(3, 3).matrix == [[3.0f, 0.0f], [0.0f, 3.0f]]); - } - - } else static if((rows == 3) && (cols == 3)) { - @property mt det() const { - return (matrix[0][0] * matrix[1][1] * matrix[2][2] - + matrix[0][1] * matrix[1][2] * matrix[2][0] - + matrix[0][2] * matrix[1][0] * matrix[2][1] - - matrix[0][2] * matrix[1][1] * matrix[2][0] - - matrix[0][1] * matrix[1][0] * matrix[2][2] - - matrix[0][0] * matrix[1][2] * matrix[2][1]); - } - - private Matrix invert(ref Matrix mat) const { - static if(isFloatingPoint!mt && rmul) { - mt d = 1 / det; - enum op = "*"; - } else { - mt d = det; - enum op = "/"; - } - - mixin(` - mat.matrix = [[(matrix[1][1] * matrix[2][2] - matrix[1][2] * matrix[2][1])`~op~`d, - (matrix[0][2] * matrix[2][1] - matrix[0][1] * matrix[2][2])`~op~`d, - (matrix[0][1] * matrix[1][2] - matrix[0][2] * matrix[1][1])`~op~`d], - [(matrix[1][2] * matrix[2][0] - matrix[1][0] * matrix[2][2])`~op~`d, - (matrix[0][0] * matrix[2][2] - matrix[0][2] * matrix[2][0])`~op~`d, - (matrix[0][2] * matrix[1][0] - matrix[0][0] * matrix[1][2])`~op~`d], - [(matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0])`~op~`d, - (matrix[0][1] * matrix[2][0] - matrix[0][0] * matrix[2][1])`~op~`d, - (matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0])`~op~`d]]; - `); - - return mat; - } - } else static if((rows == 4) && (cols == 4)) { - /// Returns the determinant of the current matrix (2x2, 3x3 and 4x4 matrices). - @property mt det() const { - return (matrix[0][3] * matrix[1][2] * matrix[2][1] * matrix[3][0] - matrix[0][2] * matrix[1][3] * matrix[2][1] * matrix[3][0] - - matrix[0][3] * matrix[1][1] * matrix[2][2] * matrix[3][0] + matrix[0][1] * matrix[1][3] * matrix[2][2] * matrix[3][0] - + matrix[0][2] * matrix[1][1] * matrix[2][3] * matrix[3][0] - matrix[0][1] * matrix[1][2] * matrix[2][3] * matrix[3][0] - - matrix[0][3] * matrix[1][2] * matrix[2][0] * matrix[3][1] + matrix[0][2] * matrix[1][3] * matrix[2][0] * matrix[3][1] - + matrix[0][3] * matrix[1][0] * matrix[2][2] * matrix[3][1] - matrix[0][0] * matrix[1][3] * matrix[2][2] * matrix[3][1] - - matrix[0][2] * matrix[1][0] * matrix[2][3] * matrix[3][1] + matrix[0][0] * matrix[1][2] * matrix[2][3] * matrix[3][1] - + matrix[0][3] * matrix[1][1] * matrix[2][0] * matrix[3][2] - matrix[0][1] * matrix[1][3] * matrix[2][0] * matrix[3][2] - - matrix[0][3] * matrix[1][0] * matrix[2][1] * matrix[3][2] + matrix[0][0] * matrix[1][3] * matrix[2][1] * matrix[3][2] - + matrix[0][1] * matrix[1][0] * matrix[2][3] * matrix[3][2] - matrix[0][0] * matrix[1][1] * matrix[2][3] * matrix[3][2] - - matrix[0][2] * matrix[1][1] * matrix[2][0] * matrix[3][3] + matrix[0][1] * matrix[1][2] * matrix[2][0] * matrix[3][3] - + matrix[0][2] * matrix[1][0] * matrix[2][1] * matrix[3][3] - matrix[0][0] * matrix[1][2] * matrix[2][1] * matrix[3][3] - - matrix[0][1] * matrix[1][0] * matrix[2][2] * matrix[3][3] + matrix[0][0] * matrix[1][1] * matrix[2][2] * matrix[3][3]); - } - - private Matrix invert(ref Matrix mat) const { - static if(isFloatingPoint!mt && rmul) { - mt d = 1 / det; - enum op = "*"; - } else { - mt d = det; - enum op = "/"; - } - - mixin(` - mat.matrix = [[(matrix[1][1] * matrix[2][2] * matrix[3][3] + matrix[1][2] * matrix[2][3] * matrix[3][1] + matrix[1][3] * matrix[2][1] * matrix[3][2] - - matrix[1][1] * matrix[2][3] * matrix[3][2] - matrix[1][2] * matrix[2][1] * matrix[3][3] - matrix[1][3] * matrix[2][2] * matrix[3][1])`~op~`d, - (matrix[0][1] * matrix[2][3] * matrix[3][2] + matrix[0][2] * matrix[2][1] * matrix[3][3] + matrix[0][3] * matrix[2][2] * matrix[3][1] - - matrix[0][1] * matrix[2][2] * matrix[3][3] - matrix[0][2] * matrix[2][3] * matrix[3][1] - matrix[0][3] * matrix[2][1] * matrix[3][2])`~op~`d, - (matrix[0][1] * matrix[1][2] * matrix[3][3] + matrix[0][2] * matrix[1][3] * matrix[3][1] + matrix[0][3] * matrix[1][1] * matrix[3][2] - - matrix[0][1] * matrix[1][3] * matrix[3][2] - matrix[0][2] * matrix[1][1] * matrix[3][3] - matrix[0][3] * matrix[1][2] * matrix[3][1])`~op~`d, - (matrix[0][1] * matrix[1][3] * matrix[2][2] + matrix[0][2] * matrix[1][1] * matrix[2][3] + matrix[0][3] * matrix[1][2] * matrix[2][1] - - matrix[0][1] * matrix[1][2] * matrix[2][3] - matrix[0][2] * matrix[1][3] * matrix[2][1] - matrix[0][3] * matrix[1][1] * matrix[2][2])`~op~`d], - [(matrix[1][0] * matrix[2][3] * matrix[3][2] + matrix[1][2] * matrix[2][0] * matrix[3][3] + matrix[1][3] * matrix[2][2] * matrix[3][0] - - matrix[1][0] * matrix[2][2] * matrix[3][3] - matrix[1][2] * matrix[2][3] * matrix[3][0] - matrix[1][3] * matrix[2][0] * matrix[3][2])`~op~`d, - (matrix[0][0] * matrix[2][2] * matrix[3][3] + matrix[0][2] * matrix[2][3] * matrix[3][0] + matrix[0][3] * matrix[2][0] * matrix[3][2] - - matrix[0][0] * matrix[2][3] * matrix[3][2] - matrix[0][2] * matrix[2][0] * matrix[3][3] - matrix[0][3] * matrix[2][2] * matrix[3][0])`~op~`d, - (matrix[0][0] * matrix[1][3] * matrix[3][2] + matrix[0][2] * matrix[1][0] * matrix[3][3] + matrix[0][3] * matrix[1][2] * matrix[3][0] - - matrix[0][0] * matrix[1][2] * matrix[3][3] - matrix[0][2] * matrix[1][3] * matrix[3][0] - matrix[0][3] * matrix[1][0] * matrix[3][2])`~op~`d, - (matrix[0][0] * matrix[1][2] * matrix[2][3] + matrix[0][2] * matrix[1][3] * matrix[2][0] + matrix[0][3] * matrix[1][0] * matrix[2][2] - - matrix[0][0] * matrix[1][3] * matrix[2][2] - matrix[0][2] * matrix[1][0] * matrix[2][3] - matrix[0][3] * matrix[1][2] * matrix[2][0])`~op~`d], - [(matrix[1][0] * matrix[2][1] * matrix[3][3] + matrix[1][1] * matrix[2][3] * matrix[3][0] + matrix[1][3] * matrix[2][0] * matrix[3][1] - - matrix[1][0] * matrix[2][3] * matrix[3][1] - matrix[1][1] * matrix[2][0] * matrix[3][3] - matrix[1][3] * matrix[2][1] * matrix[3][0])`~op~`d, - (matrix[0][0] * matrix[2][3] * matrix[3][1] + matrix[0][1] * matrix[2][0] * matrix[3][3] + matrix[0][3] * matrix[2][1] * matrix[3][0] - - matrix[0][0] * matrix[2][1] * matrix[3][3] - matrix[0][1] * matrix[2][3] * matrix[3][0] - matrix[0][3] * matrix[2][0] * matrix[3][1])`~op~`d, - (matrix[0][0] * matrix[1][1] * matrix[3][3] + matrix[0][1] * matrix[1][3] * matrix[3][0] + matrix[0][3] * matrix[1][0] * matrix[3][1] - - matrix[0][0] * matrix[1][3] * matrix[3][1] - matrix[0][1] * matrix[1][0] * matrix[3][3] - matrix[0][3] * matrix[1][1] * matrix[3][0])`~op~`d, - (matrix[0][0] * matrix[1][3] * matrix[2][1] + matrix[0][1] * matrix[1][0] * matrix[2][3] + matrix[0][3] * matrix[1][1] * matrix[2][0] - - matrix[0][0] * matrix[1][1] * matrix[2][3] - matrix[0][1] * matrix[1][3] * matrix[2][0] - matrix[0][3] * matrix[1][0] * matrix[2][1])`~op~`d], - [(matrix[1][0] * matrix[2][2] * matrix[3][1] + matrix[1][1] * matrix[2][0] * matrix[3][2] + matrix[1][2] * matrix[2][1] * matrix[3][0] - - matrix[1][0] * matrix[2][1] * matrix[3][2] - matrix[1][1] * matrix[2][2] * matrix[3][0] - matrix[1][2] * matrix[2][0] * matrix[3][1])`~op~`d, - (matrix[0][0] * matrix[2][1] * matrix[3][2] + matrix[0][1] * matrix[2][2] * matrix[3][0] + matrix[0][2] * matrix[2][0] * matrix[3][1] - - matrix[0][0] * matrix[2][2] * matrix[3][1] - matrix[0][1] * matrix[2][0] * matrix[3][2] - matrix[0][2] * matrix[2][1] * matrix[3][0])`~op~`d, - (matrix[0][0] * matrix[1][2] * matrix[3][1] + matrix[0][1] * matrix[1][0] * matrix[3][2] + matrix[0][2] * matrix[1][1] * matrix[3][0] - - matrix[0][0] * matrix[1][1] * matrix[3][2] - matrix[0][1] * matrix[1][2] * matrix[3][0] - matrix[0][2] * matrix[1][0] * matrix[3][1])`~op~`d, - (matrix[0][0] * matrix[1][1] * matrix[2][2] + matrix[0][1] * matrix[1][2] * matrix[2][0] + matrix[0][2] * matrix[1][0] * matrix[2][1] - - matrix[0][0] * matrix[1][2] * matrix[2][1] - matrix[0][1] * matrix[1][0] * matrix[2][2] - matrix[0][2] * matrix[1][1] * matrix[2][0])`~op~`d]]; - `); - - return mat; - } - - // some static fun ... - // (1) glprogramming.com/red/appendixf.html - ortographic is broken! - // (2) http://fly.cc.fer.hr/~unreal/theredbook/appendixg.html - // (3) http://en.wikipedia.org/wiki/Orthographic_projection_(geometry) - - static if(isFloatingPoint!mt) { - static private mt[6] cperspective(mt width, mt height, mt fov, mt near, mt far) - in { assert(height != 0); } - body { - mt aspect = width/height; - mt top = near * tan(fov*(PI/360.0)); - mt bottom = -top; - mt right = top * aspect; - mt left = -right; - - return [left, right, bottom, top, near, far]; - } - - /// Returns a perspective matrix (4x4 and floating-point matrices only). - static Matrix perspective(mt width, mt height, mt fov, mt near, mt far) { - mt[6] cdata = cperspective(width, height, fov, near, far); - return perspective(cdata[0], cdata[1], cdata[2], cdata[3], cdata[4], cdata[5]); - } - - /// ditto - static Matrix perspective(mt left, mt right, mt bottom, mt top, mt near, mt far) - in { - assert(right-left != 0); - assert(top-bottom != 0); - assert(far-near != 0); - } - body { - Matrix ret; - ret.clear(0); - - ret.matrix[0][0] = (2*near)/(right-left); - ret.matrix[0][2] = (right+left)/(right-left); - ret.matrix[1][1] = (2*near)/(top-bottom); - ret.matrix[1][2] = (top+bottom)/(top-bottom); - ret.matrix[2][2] = -(far+near)/(far-near); - ret.matrix[2][3] = -(2*far*near)/(far-near); - ret.matrix[3][2] = -1; - - return ret; - } - - /// Returns an inverse perspective matrix (4x4 and floating-point matrices only). - static Matrix perspective_inverse(mt width, mt height, mt fov, mt near, mt far) { - mt[6] cdata = cperspective(width, height, fov, near, far); - return perspective_inverse(cdata[0], cdata[1], cdata[2], cdata[3], cdata[4], cdata[5]); - } - - /// ditto - static Matrix perspective_inverse(mt left, mt right, mt bottom, mt top, mt near, mt far) - in { - assert(near != 0); - assert(far != 0); - } - body { - Matrix ret; - ret.clear(0); - - ret.matrix[0][0] = (right-left)/(2*near); - ret.matrix[0][3] = (right+left)/(2*near); - ret.matrix[1][1] = (top-bottom)/(2*near); - ret.matrix[1][3] = (top+bottom)/(2*near); - ret.matrix[2][3] = -1; - ret.matrix[3][2] = -(far-near)/(2*far*near); - ret.matrix[3][3] = (far+near)/(2*far*near); - - return ret; - } - - // (2) and (3) say this one is correct - /// Returns an orthographic matrix (4x4 and floating-point matrices only). - static Matrix orthographic(mt left, mt right, mt bottom, mt top, mt near, mt far) - in { - assert(right-left != 0); - assert(top-bottom != 0); - assert(far-near != 0); - } - body { - Matrix ret; - ret.clear(0); - - ret.matrix[0][0] = 2/(right-left); - ret.matrix[0][3] = -(right+left)/(right-left); - ret.matrix[1][1] = 2/(top-bottom); - ret.matrix[1][3] = -(top+bottom)/(top-bottom); - ret.matrix[2][2] = -2/(far-near); - ret.matrix[2][3] = -(far+near)/(far-near); - ret.matrix[3][3] = 1; - - return ret; - } - - // (1) and (2) say this one is correct - /// Returns an inverse ortographic matrix (4x4 and floating-point matrices only). - static Matrix orthographic_inverse(mt left, mt right, mt bottom, mt top, mt near, mt far) { - Matrix ret; - ret.clear(0); - - ret.matrix[0][0] = (right-left)/2; - ret.matrix[0][3] = (right+left)/2; - ret.matrix[1][1] = (top-bottom)/2; - ret.matrix[1][3] = (top+bottom)/2; - ret.matrix[2][2] = (far-near)/-2; - ret.matrix[2][3] = (far+near)/2; - ret.matrix[3][3] = 1; - - return ret; - } - - /// Returns a look at matrix (4x4 and floating-point matrices only). - static Matrix look_at(Vector!(mt, 3) eye, Vector!(mt, 3) target, Vector!(mt, 3) up) { - alias Vector!(mt, 3) vec3mt; - vec3mt look_dir = (target - eye).normalized; - vec3mt up_dir = up.normalized; - - vec3mt right_dir = cross(look_dir, up_dir).normalized; - vec3mt perp_up_dir = cross(right_dir, look_dir); - - Matrix ret = Matrix.identity; - ret.matrix[0][0..3] = right_dir.vector[]; - ret.matrix[1][0..3] = perp_up_dir.vector[]; - ret.matrix[2][0..3] = (-look_dir).vector[]; - - ret.matrix[0][3] = -dot(eye, right_dir); - ret.matrix[1][3] = -dot(eye, perp_up_dir); - ret.matrix[2][3] = dot(eye, look_dir); - - return ret; - } - - unittest { - mt[6] cp = cperspective(600f, 900f, 60f, 1f, 100f); - assert(cp[4] == 1.0f); - assert(cp[5] == 100.0f); - assert(cp[0] == -cp[1]); - assert((cp[0] < -0.38489f) && (cp[0] > -0.38491f)); - assert(cp[2] == -cp[3]); - assert((cp[2] < -0.577349f) && (cp[2] > -0.577351f)); - - assert(mat4.perspective(600f, 900f, 60.0, 1.0, 100.0) == mat4.perspective(cp[0], cp[1], cp[2], cp[3], cp[4], cp[5])); - float[4][4] m4p = mat4.perspective(600f, 900f, 60.0, 1.0, 100.0).matrix; - assert((m4p[0][0] < 2.598077f) && (m4p[0][0] > 2.598075f)); - assert(m4p[0][2] == 0.0f); - assert((m4p[1][1] < 1.732052) && (m4p[1][1] > 1.732050)); - assert(m4p[1][2] == 0.0f); - assert((m4p[2][2] < -1.020201) && (m4p[2][2] > -1.020203)); - assert((m4p[2][3] < -2.020201) && (m4p[2][3] > -2.020203)); - assert((m4p[3][2] < -0.9f) && (m4p[3][2] > -1.1f)); - - float[4][4] m4pi = mat4.perspective_inverse(600f, 900f, 60.0, 1.0, 100.0).matrix; - assert((m4pi[0][0] < 0.384901) && (m4pi[0][0] > 0.384899)); - assert(m4pi[0][3] == 0.0f); - assert((m4pi[1][1] < 0.577351) && (m4pi[1][1] > 0.577349)); - assert(m4pi[1][3] == 0.0f); - assert(m4pi[2][3] == -1.0f); - assert((m4pi[3][2] < -0.494999) && (m4pi[3][2] > -0.495001)); - assert((m4pi[3][3] < 0.505001) && (m4pi[3][3] > 0.504999)); - - // maybe the next tests should be improved - float[4][4] m4o = mat4.orthographic(-1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f).matrix; - assert(m4o == [[1.0f, 0.0f, 0.0f, 0.0f], - [0.0f, 1.0f, 0.0f, 0.0f], - [0.0f, 0.0f, -1.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - - float[4][4] m4oi = mat4.orthographic_inverse(-1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f).matrix; - assert(m4oi == [[1.0f, 0.0f, 0.0f, 0.0f], - [0.0f, 1.0f, 0.0f, 0.0f], - [0.0f, 0.0f, -1.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - - //TODO: look_at tests - } - } - } - - static if((rows == cols) && (rows >= 3) && (rows <= 4)) { - /// Returns a translation matrix (3x3 and 4x4 matrices). - static Matrix translation(mt x, mt y, mt z) { - Matrix ret = Matrix.identity; - - ret.matrix[0][cols-1] = x; - ret.matrix[1][cols-1] = y; - ret.matrix[2][cols-1] = z; - - return ret; - } - - /// ditto - static Matrix translation(Vector!(mt, 3) v) { - Matrix ret = Matrix.identity; - - ret.matrix[0][cols-1] = v.x; - ret.matrix[1][cols-1] = v.y; - ret.matrix[2][cols-1] = v.z; - - return ret; - } - - /// Applys a translation on the current matrix and returns $(I this) (3x3 and 4x4 matrices). - Matrix translate(mt x, mt y, mt z) { - this = Matrix.translation(x, y, z) * this; - return this; - } - - /// ditto - Matrix translate(Vector!(mt, 3) v) { - this = Matrix.translation(v) * this; - return this; - } - - /// Returns a scaling matrix (3x3 and 4x4 matrices); - static Matrix scaling(mt x, mt y, mt z) { - Matrix ret = Matrix.identity; - - ret.matrix[0][0] = x; - ret.matrix[1][1] = y; - ret.matrix[2][2] = z; - - return ret; - } - - /// Applys a scale to the current matrix and returns $(I this) (3x3 and 4x4 matrices). - Matrix scale(mt x, mt y, mt z) { - this = Matrix.scaling(x, y, z) * this; - return this; - } - - unittest { - mat3 m3 = mat3.identity; - assert(m3.translate(1.0f, 2.0f, 3.0f).matrix == mat3.translation(1.0f, 2.0f, 3.0f).matrix); - assert(mat3.translation(1.0f, 2.0f, 3.0f).matrix == [[1.0f, 0.0f, 1.0f], - [0.0f, 1.0f, 2.0f], - [0.0f, 0.0f, 3.0f]]); - assert(mat3.identity.translate(0.0f, 1.0f, 2.0f).matrix == mat3.translation(0.0f, 1.0f, 2.0f).matrix); - - mat3 m31 = mat3.identity; - assert(m31.translate(vec3(1.0f, 2.0f, 3.0f)).matrix == mat3.translation(vec3(1.0f, 2.0f, 3.0f)).matrix); - assert(mat3.translation(vec3(1.0f, 2.0f, 3.0f)).matrix == [[1.0f, 0.0f, 1.0f], - [0.0f, 1.0f, 2.0f], - [0.0f, 0.0f, 3.0f]]); - assert(mat3.identity.translate(vec3(0.0f, 1.0f, 2.0f)).matrix == mat3.translation(vec3(0.0f, 1.0f, 2.0f)).matrix); - - assert(m3.scaling(0.0f, 1.0f, 2.0f).matrix == mat3.scaling(0.0f, 1.0f, 2.0f).matrix); - assert(mat3.scaling(0.0f, 1.0f, 2.0f).matrix == [[0.0f, 0.0f, 0.0f], - [0.0f, 1.0f, 0.0f], - [0.0f, 0.0f, 2.0f]]); - assert(mat3.identity.scale(0.0f, 1.0f, 2.0f).matrix == mat3.scaling(0.0f, 1.0f, 2.0f).matrix); - - // same tests for 4x4 - - mat4 m4 = mat4(1.0f); - assert(m4.translation(1.0f, 2.0f, 3.0f).matrix == mat4.translation(1.0f, 2.0f, 3.0f).matrix); - assert(mat4.translation(1.0f, 2.0f, 3.0f).matrix == [[1.0f, 0.0f, 0.0f, 1.0f], - [0.0f, 1.0f, 0.0f, 2.0f], - [0.0f, 0.0f, 1.0f, 3.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - assert(mat4.identity.translate(0.0f, 1.0f, 2.0f).matrix == mat4.translation(0.0f, 1.0f, 2.0f).matrix); - - assert(m4.scaling(0.0f, 1.0f, 2.0f).matrix == mat4.scaling(0.0f, 1.0f, 2.0f).matrix); - assert(mat4.scaling(0.0f, 1.0f, 2.0f).matrix == [[0.0f, 0.0f, 0.0f, 0.0f], - [0.0f, 1.0f, 0.0f, 0.0f], - [0.0f, 0.0f, 2.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - assert(mat4.identity.scale(0.0f, 1.0f, 2.0f).matrix == mat4.scaling(0.0f, 1.0f, 2.0f).matrix); - } - } - - - static if((rows == cols) && (rows >= 3)) { - static if(isFloatingPoint!mt) { - /// Returns an identity matrix with an applied rotate_axis around an arbitrary axis (nxn matrices, n >= 3). - static Matrix rotation(real alpha, Vector!(mt, 3) axis) { - Matrix mult = Matrix.identity; - - if(axis.length != 1) { - axis.normalize(); - } - - real cosa = cos(alpha); - real sina = sin(alpha); - - Vector!(mt, 3) temp = (1 - cosa)*axis; - - mult.matrix[0][0] = to!mt(cosa + temp.x * axis.x); - mult.matrix[0][1] = to!mt( temp.x * axis.y + sina * axis.z); - mult.matrix[0][2] = to!mt( temp.x * axis.z - sina * axis.y); - mult.matrix[1][0] = to!mt( temp.y * axis.x - sina * axis.z); - mult.matrix[1][1] = to!mt(cosa + temp.y * axis.y); - mult.matrix[1][2] = to!mt( temp.y * axis.z + sina * axis.x); - mult.matrix[2][0] = to!mt( temp.z * axis.x + sina * axis.y); - mult.matrix[2][1] = to!mt( temp.z * axis.y - sina * axis.x); - mult.matrix[2][2] = to!mt(cosa + temp.z * axis.z); - - return mult; - } - - /// ditto - static Matrix rotation(real alpha, mt x, mt y, mt z) { - return Matrix.rotation(alpha, Vector!(mt, 3)(x, y, z)); - } - - /// Returns an identity matrix with an applied rotation around the x-axis (nxn matrices, n >= 3). - static Matrix xrotation(real alpha) { - Matrix mult = Matrix.identity; - - mt cosamt = to!mt(cos(alpha)); - mt sinamt = to!mt(sin(alpha)); - - mult.matrix[1][1] = cosamt; - mult.matrix[1][2] = -sinamt; - mult.matrix[2][1] = sinamt; - mult.matrix[2][2] = cosamt; - - return mult; - } - - /// Returns an identity matrix with an applied rotation around the y-axis (nxn matrices, n >= 3). - static Matrix yrotation(real alpha) { - Matrix mult = Matrix.identity; - - mt cosamt = to!mt(cos(alpha)); - mt sinamt = to!mt(sin(alpha)); - - mult.matrix[0][0] = cosamt; - mult.matrix[0][2] = sinamt; - mult.matrix[2][0] = -sinamt; - mult.matrix[2][2] = cosamt; - - return mult; - } - - /// Returns an identity matrix with an applied rotation around the z-axis (nxn matrices, n >= 3). - static Matrix zrotation(real alpha) { - Matrix mult = Matrix.identity; - - mt cosamt = to!mt(cos(alpha)); - mt sinamt = to!mt(sin(alpha)); - - mult.matrix[0][0] = cosamt; - mult.matrix[0][1] = -sinamt; - mult.matrix[1][0] = sinamt; - mult.matrix[1][1] = cosamt; - - return mult; - } - - Matrix rotate(real alpha, Vector!(mt, 3) axis) { - this = rotation(alpha, axis) * this; - return this; - } - - /// Rotates the current matrix around the x-axis and returns $(I this) (nxn matrices, n >= 3). - Matrix rotatex(real alpha) { - this = xrotation(alpha) * this; - return this; - } - - /// Rotates the current matrix around the y-axis and returns $(I this) (nxn matrices, n >= 3). - Matrix rotatey(real alpha) { - this = yrotation(alpha) * this; - return this; - } - - /// Rotates the current matrix around the z-axis and returns $(I this) (nxn matrices, n >= 3). - Matrix rotatez(real alpha) { - this = zrotation(alpha) * this; - return this; - } - - unittest { - assert(mat4.xrotation(0).matrix == [[1.0f, 0.0f, 0.0f, 0.0f], - [0.0f, 1.0f, -0.0f, 0.0f], - [0.0f, 0.0f, 1.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - assert(mat4.yrotation(0).matrix == [[1.0f, 0.0f, 0.0f, 0.0f], - [0.0f, 1.0f, 0.0f, 0.0f], - [0.0f, 0.0f, 1.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - assert(mat4.zrotation(0).matrix == [[1.0f, -0.0f, 0.0f, 0.0f], - [0.0f, 1.0f, 0.0f, 0.0f], - [0.0f, 0.0f, 1.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - mat4 xro = mat4.identity; - xro.rotatex(0); - assert(mat4.xrotation(0).matrix == xro.matrix); - assert(xro.matrix == mat4.identity.rotatex(0).matrix); - assert(xro.matrix == mat4.rotation(0, vec3(1.0f, 0.0f, 0.0f)).matrix); - mat4 yro = mat4.identity; - yro.rotatey(0); - assert(mat4.yrotation(0).matrix == yro.matrix); - assert(yro.matrix == mat4.identity.rotatey(0).matrix); - assert(yro.matrix == mat4.rotation(0, vec3(0.0f, 1.0f, 0.0f)).matrix); - mat4 zro = mat4.identity; - xro.rotatez(0); - assert(mat4.zrotation(0).matrix == zro.matrix); - assert(zro.matrix == mat4.identity.rotatez(0).matrix); - assert(zro.matrix == mat4.rotation(0, vec3(0.0f, 0.0f, 1.0f)).matrix); - } - } // isFloatingPoint - - - /// Sets the translation of the matrix (nxn matrices, n >= 3). - void set_translation(mt[] values...) // intended to be a property - in { assert(values.length >= (rows-1)); } - body { - foreach(r; TupleRange!(0, rows-1)) { - matrix[r][rows-1] = values[r]; - } - } - - /// Copyies the translation from mat to the current matrix (nxn matrices, n >= 3). - void set_translation(Matrix mat) { - foreach(r; TupleRange!(0, rows-1)) { - matrix[r][rows-1] = mat.matrix[r][rows-1]; - } - } - - /// Returns an identity matrix with the current translation applied (nxn matrices, n >= 3).. - Matrix get_translation() { - Matrix ret = Matrix.identity; - - foreach(r; TupleRange!(0, rows-1)) { - ret.matrix[r][rows-1] = matrix[r][rows-1]; - } - - return ret; - } - - unittest { - mat3 m3 = mat3(0.0f, 1.0f, 2.0f, - 3.0f, 4.0f, 5.0f, - 6.0f, 7.0f, 1.0f); - assert(m3.get_translation().matrix == [[1.0f, 0.0f, 2.0f], [0.0f, 1.0f, 5.0f], [0.0f, 0.0f, 1.0f]]); - m3.set_translation(mat3.identity); - assert(mat3.identity.matrix == m3.get_translation().matrix); - m3.set_translation([2.0f, 5.0f]); - assert(m3.get_translation().matrix == [[1.0f, 0.0f, 2.0f], [0.0f, 1.0f, 5.0f], [0.0f, 0.0f, 1.0f]]); - assert(mat3.identity.matrix == mat3.identity.get_translation().matrix); - - mat4 m4 = mat4(0.0f, 1.0f, 2.0f, 3.0f, - 4.0f, 5.0f, 6.0f, 7.0f, - 8.0f, 9.0f, 10.0f, 11.0f, - 12.0f, 13.0f, 14.0f, 1.0f); - assert(m4.get_translation().matrix == [[1.0f, 0.0f, 0.0f, 3.0f], - [0.0f, 1.0f, 0.0f, 7.0f], - [0.0f, 0.0f, 1.0f, 11.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - m4.set_translation(mat4.identity); - assert(mat4.identity.matrix == m4.get_translation().matrix); - m4.set_translation([3.0f, 7.0f, 11.0f]); - assert(m4.get_translation().matrix == [[1.0f, 0.0f, 0.0f, 3.0f], - [0.0f, 1.0f, 0.0f, 7.0f], - [0.0f, 0.0f, 1.0f, 11.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - assert(mat4.identity.matrix == mat4.identity.get_translation().matrix); - } - - /// Sets the scale of the matrix (nxn matrices, n >= 3). - void set_scale(mt[] values...) - in { assert(values.length >= (rows-1)); } - body { - foreach(r; TupleRange!(0, rows-1)) { - matrix[r][r] = values[r]; - } - } - - /// Copyies the scale from mat to the current matrix (nxn matrices, n >= 3). - void set_scale(Matrix mat) { - foreach(r; TupleRange!(0, rows-1)) { - matrix[r][r] = mat.matrix[r][r]; - } - } - - /// Returns an identity matrix with the current scale applied (nxn matrices, n >= 3). - Matrix get_scale() { - Matrix ret = Matrix.identity; - - foreach(r; TupleRange!(0, rows-1)) { - ret.matrix[r][r] = matrix[r][r]; - } - - return ret; - } - - unittest { - mat3 m3 = mat3(0.0f, 1.0f, 2.0f, - 3.0f, 4.0f, 5.0f, - 6.0f, 7.0f, 1.0f); - assert(m3.get_scale().matrix == [[0.0f, 0.0f, 0.0f], [0.0f, 4.0f, 0.0f], [0.0f, 0.0f, 1.0f]]); - m3.set_scale(mat3.identity); - assert(mat3.identity.matrix == m3.get_scale().matrix); - m3.set_scale([0.0f, 4.0f]); - assert(m3.get_scale().matrix == [[0.0f, 0.0f, 0.0f], [0.0f, 4.0f, 0.0f], [0.0f, 0.0f, 1.0f]]); - assert(mat3.identity.matrix == mat3.identity.get_scale().matrix); - - mat4 m4 = mat4(0.0f, 1.0f, 2.0f, 3.0f, - 4.0f, 5.0f, 6.0f, 7.0f, - 8.0f, 9.0f, 10.0f, 11.0f, - 12.0f, 13.0f, 14.0f, 1.0f); - assert(m4.get_scale().matrix == [[0.0f, 0.0f, 0.0f, 0.0f], - [0.0f, 5.0f, 0.0f, 0.0f], - [0.0f, 0.0f, 10.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - m4.set_scale(mat4.identity); - assert(mat4.identity.matrix == m4.get_scale().matrix); - m4.set_scale([0.0f, 5.0f, 10.0f]); - assert(m4.get_scale().matrix == [[0.0f, 0.0f, 0.0f, 0.0f], - [0.0f, 5.0f, 0.0f, 0.0f], - [0.0f, 0.0f, 10.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - assert(mat4.identity.matrix == mat4.identity.get_scale().matrix); - } - - /// Copies rot into the upper left corner, the translation (nxn matrices, n >= 3). - void set_rotation(Matrix!(mt, 3, 3) rot) { - foreach(r; TupleRange!(0, 3)) { - foreach(c; TupleRange!(0, 3)) { - matrix[r][c] = rot[r][c]; - } - } - } - - /// Returns an identity matrix with the current rotation applied (nxn matrices, n >= 3). - Matrix!(mt, 3, 3) get_rotation() { - Matrix!(mt, 3, 3) ret = Matrix!(mt, 3, 3).identity; - - foreach(r; TupleRange!(0, 3)) { - foreach(c; TupleRange!(0, 3)) { - ret.matrix[r][c] = matrix[r][c]; - } - } - - return ret; - } - - unittest { - mat3 m3 = mat3(0.0f, 1.0f, 2.0f, - 3.0f, 4.0f, 5.0f, - 6.0f, 7.0f, 1.0f); - assert(m3.get_rotation().matrix == [[0.0f, 1.0f, 2.0f], [3.0f, 4.0f, 5.0f], [6.0f, 7.0f, 1.0f]]); - m3.set_rotation(mat3.identity); - assert(mat3.identity.matrix == m3.get_rotation().matrix); - m3.set_rotation(mat3(0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 1.0f)); - assert(m3.get_rotation().matrix == [[0.0f, 1.0f, 2.0f], [3.0f, 4.0f, 5.0f], [6.0f, 7.0f, 1.0f]]); - assert(mat3.identity.matrix == mat3.identity.get_rotation().matrix); - - mat4 m4 = mat4(0.0f, 1.0f, 2.0f, 3.0f, - 4.0f, 5.0f, 6.0f, 7.0f, - 8.0f, 9.0f, 10.0f, 11.0f, - 12.0f, 13.0f, 14.0f, 1.0f); - assert(m4.get_rotation().matrix == [[0.0f, 1.0f, 2.0f], [4.0f, 5.0f, 6.0f], [8.0f, 9.0f, 10.0f]]); - m4.set_rotation(mat3.identity); - assert(mat3.identity.matrix == m4.get_rotation().matrix); - m4.set_rotation(mat3(0.0f, 1.0f, 2.0f, 4.0f, 5.0f, 6.0f, 8.0f, 9.0f, 10.0f)); - assert(m4.get_rotation().matrix == [[0.0f, 1.0f, 2.0f], [4.0f, 5.0f, 6.0f], [8.0f, 9.0f, 10.0f]]); - assert(mat3.identity.matrix == mat4.identity.get_rotation().matrix); - } - - } - - static if((rows == cols) && (rows >= 2) && (rows <= 4)) { - /// Returns an inverted copy of the current matrix (nxn matrices, 2 >= n <= 4). - @property Matrix inverse() const { - Matrix mat; - invert(mat); - return mat; - } - - /// Inverts the current matrix (nxn matrices, 2 >= n <= 4). - void invert() { - // workaround Issue #11238 - // uses a temporary instead of invert(this) - Matrix temp; - invert(temp); - this.matrix = temp.matrix; - } - } - - unittest { - mat2 m2 = mat2(1.0f, 2.0f, vec2(3.0f, 4.0f)); - assert(m2.det == -2.0f); - assert(m2.inverse.matrix == [[-2.0f, 1.0f], [1.5f, -0.5f]]); - - mat3 m3 = mat3(1.0f, -2.0f, 3.0f, - 7.0f, -1.0f, 0.0f, - 3.0f, 2.0f, -4.0f); - assert(m3.det == -1.0f); - assert(m3.inverse.matrix == [[-4.0f, 2.0f, -3.0f], - [-28.0f, 13.0f, -21.0f], - [-17.0f, 8.0f, -13.0f]]); - - mat4 m4 = mat4(1.0f, 2.0f, 3.0f, 4.0f, - -2.0f, 1.0f, 5.0f, -2.0f, - 2.0f, -1.0f, 7.0f, 1.0f, - 3.0f, -3.0f, 2.0f, 0.0f); - assert(m4.det == -8.0f); - assert(m4.inverse.matrix == [[6.875f, 7.875f, -11.75f, 11.125f], - [6.625f, 7.625f, -11.25f, 10.375f], - [-0.375f, -0.375f, 0.75f, -0.625f], - [-4.5f, -5.5f, 8.0f, -7.5f]]); - } - - private void mms(mt inp, ref Matrix mat) const { // mat * scalar - for(int r = 0; r < rows; r++) { - for(int c = 0; c < cols; c++) { - mat.matrix[r][c] = matrix[r][c] * inp; - } - } - } - - private void masm(string op)(Matrix inp, ref Matrix mat) const { // mat + or - mat - foreach(r; TupleRange!(0, rows)) { - foreach(c; TupleRange!(0, cols)) { - mat.matrix[r][c] = mixin("inp.matrix[r][c]" ~ op ~ "matrix[r][c]"); - } - } - } - - Matrix!(mt, rows, T.cols) opBinary(string op : "*", T)(T inp) const if(isCompatibleMatrix!T && (T.rows == cols)) { - Matrix!(mt, rows, T.cols) ret; - - foreach(r; TupleRange!(0, rows)) { - foreach(c; TupleRange!(0, T.cols)) { - ret.matrix[r][c] = 0; - - foreach(c2; TupleRange!(0, cols)) { - ret.matrix[r][c] += matrix[r][c2] * inp.matrix[c2][c]; - } - } - } - - return ret; - } - - Vector!(mt, rows) opBinary(string op : "*", T : Vector!(mt, cols))(T inp) const { - Vector!(mt, rows) ret; - ret.clear(0); - - foreach(c; TupleRange!(0, cols)) { - foreach(r; TupleRange!(0, rows)) { - ret.vector[r] += matrix[r][c] * inp.vector[c]; - } - } - - return ret; - } - - Matrix opBinary(string op : "*")(mt inp) const { - Matrix ret; - mms(inp, ret); - return ret; - } - - Matrix opBinaryRight(string op : "*")(mt inp) const { - return this.opBinary!(op)(inp); - } - - Matrix opBinary(string op)(Matrix inp) const if((op == "+") || (op == "-")) { - Matrix ret; - masm!(op)(inp, ret); - return ret; - } - - void opOpAssign(string op : "*")(mt inp) { - mms(inp, this); - } - - void opOpAssign(string op)(Matrix inp) if((op == "+") || (op == "-")) { - masm!(op)(inp, this); - } - - void opOpAssign(string op)(Matrix inp) if(op == "*") { - this = this * inp; - } - - unittest { - mat2 m2 = mat2(1.0f, 2.0f, 3.0f, 4.0f); - vec2 v2 = vec2(2.0f, 2.0f); - assert((m2*2).matrix == [[2.0f, 4.0f], [6.0f, 8.0f]]); - assert((2*m2).matrix == (m2*2).matrix); - m2 *= 2; - assert(m2.matrix == [[2.0f, 4.0f], [6.0f, 8.0f]]); - assert((m2*v2).vector == [12.0f, 28.0f]); - assert((v2*m2).vector == [16.0f, 24.0f]); - assert((m2*m2).matrix == [[28.0f, 40.0f], [60.0f, 88.0f]]); - assert((m2-m2).matrix == [[0.0f, 0.0f], [0.0f, 0.0f]]); - assert((m2+m2).matrix == [[4.0f, 8.0f], [12.0f, 16.0f]]); - m2 += m2; - assert(m2.matrix == [[4.0f, 8.0f], [12.0f, 16.0f]]); - m2 -= m2; - assert(m2.matrix == [[0.0f, 0.0f], [0.0f, 0.0f]]); - - mat3 m3 = mat3(1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f); - vec3 v3 = vec3(2.0f, 2.0f, 2.0f); - assert((m3*2).matrix == [[2.0f, 4.0f, 6.0f], [8.0f, 10.0f, 12.0f], [14.0f, 16.0f, 18.0f]]); - assert((2*m3).matrix == (m3*2).matrix); - m3 *= 2; - assert(m3.matrix == [[2.0f, 4.0f, 6.0f], [8.0f, 10.0f, 12.0f], [14.0f, 16.0f, 18.0f]]); - assert((m3*v3).vector == [24.0f, 60.0f, 96.0f]); - assert((v3*m3).vector == [48.0f, 60.0f, 72.0f]); - assert((m3*m3).matrix == [[120.0f, 144.0f, 168.0f], [264.0f, 324.0f, 384.0f], [408.0f, 504.0f, 600.0f]]); - assert((m3-m3).matrix == [[0.0f, 0.0f, 0.0f], [0.0f, 0.0f, 0.0f], [0.0f, 0.0f, 0.0f]]); - assert((m3+m3).matrix == [[4.0f, 8.0f, 12.0f], [16.0f, 20.0f, 24.0f], [28.0f, 32.0f, 36.0f]]); - m3 += m3; - assert(m3.matrix == [[4.0f, 8.0f, 12.0f], [16.0f, 20.0f, 24.0f], [28.0f, 32.0f, 36.0f]]); - m3 -= m3; - assert(m3.matrix == [[0.0f, 0.0f, 0.0f], [0.0f, 0.0f, 0.0f], [0.0f, 0.0f, 0.0f]]); - - // test opOpAssign for matrix multiplication - auto m4 = mat4.translation(0,1,2); - m4 *= mat4.translation(0,-1,2); - assert(m4 == mat4.translation(0,0,4)); - - //TODO: tests for mat4, mat34 - } - - // opEqual => "alias matrix this;" - - bool opCast(T : bool)() const { - return isFinite; - } - - unittest { - assert(mat2(1.0f, 2.0f, 1.0f, 1.0f) == mat2(1.0f, 2.0f, 1.0f, 1.0f)); - assert(mat2(1.0f, 2.0f, 1.0f, 1.0f) != mat2(1.0f, 1.0f, 1.0f, 1.0f)); - - assert(mat3(1.0f) == mat3(1.0f)); - assert(mat3(1.0f) != mat3(2.0f)); - - assert(mat4(1.0f) == mat4(1.0f)); - assert(mat4(1.0f) != mat4(2.0f)); - - assert(!(mat4(float.nan))); - if(mat4(1.0f)) { } - else { assert(false); } - } - -} - -/// Pre-defined matrix types, the first number represents the number of rows -/// and the second the number of columns, if there's just one it's a nxn matrix. -/// All of these matrices are floating-point matrices. -alias Matrix!(float, 2, 2) mat2; -alias Matrix!(float, 3, 3) mat3; -alias Matrix!(float, 3, 4) mat34; -alias Matrix!(float, 4, 4) mat4; - -private unittest { - Matrix!(float, 1, 1) A = 1; - Matrix!(double, 1, 1) B = 1; - Matrix!(real, 1, 1) C = 1; - Matrix!(int, 1, 1) D = 1; - Matrix!(float, 5, 1) E = 1; - Matrix!(double, 5, 1) F = 1; - Matrix!(real, 5, 1) G = 1; - Matrix!(int, 5, 1) H = 1; - Matrix!(float, 1, 5) I = 1; - Matrix!(double, 1, 5) J = 1; - Matrix!(real, 1, 5) K = 1; - Matrix!(int, 1, 5) L = 1; -} - -/// Base template for all quaternion-types. -/// Params: -/// type = all values get stored as this type -struct Quaternion(type) { - alias type qt; /// Holds the internal type of the quaternion. - - qt[4] quaternion; /// Holds the w, x, y and z coordinates. - - /// Returns a pointer to the quaternion in memory, it starts with the w coordinate. - @property auto value_ptr() const { return quaternion.ptr; } - - /// Returns the current vector formatted as string, useful for printing the quaternion. - @property string as_string() { - return format("%s", quaternion); - } - alias as_string toString; - - @safe pure nothrow: - private @property qt get_(char coord)() const { - return quaternion[coord_to_index!coord]; - } - private @property void set_(char coord)(qt value) { - quaternion[coord_to_index!coord] = value; - } - - alias get_!'w' w; /// static properties to access the values. - alias set_!'w' w; - alias get_!'x' x; /// ditto - alias set_!'x' x; - alias get_!'y' y; /// ditto - alias set_!'y' y; - alias get_!'z' z; /// ditto - alias set_!'z' z; - - /// Constructs the quaternion. - /// Takes a 4-dimensional vector, where vector.x = the quaternions w coordinate, - /// or a w coordinate of type $(I qt) and a 3-dimensional vector representing the imaginary part, - /// or 4 values of type $(I qt). - this(qt w_, qt x_, qt y_, qt z_) { - w = w_; - x = x_; - y = y_; - z = z_; - } - - /// ditto - this(qt w_, Vector!(qt, 3) vec) { - w = w_; - quaternion[1..4] = vec.vector[]; - } - - /// ditto - this(Vector!(qt, 4) vec) { - quaternion[] = vec.vector[]; - } - - /// Returns true if all values are not nan and finite, otherwise false. - @property bool isFinite() const { - foreach(q; quaternion) { - if(isNaN(q) || isInfinity(q)) { - return false; - } - } - return true; - } - deprecated("Use isFinite instead of ok") alias ok = isFinite; - - unittest { - quat q1 = quat(0.0f, 0.0f, 0.0f, 1.0f); - assert(q1.quaternion == [0.0f, 0.0f, 0.0f, 1.0f]); - assert(q1.quaternion == quat(0.0f, 0.0f, 0.0f, 1.0f).quaternion); - assert(q1.quaternion == quat(0.0f, vec3(0.0f, 0.0f, 1.0f)).quaternion); - assert(q1.quaternion == quat(vec4(0.0f, 0.0f, 0.0f, 1.0f)).quaternion); - - assert(q1.isFinite); - q1.x = float.infinity; - assert(!q1.isFinite); - q1.x = float.nan; - assert(!q1.isFinite); - q1.x = 0.0f; - assert(q1.isFinite); - } - - template coord_to_index(char c) { - static if(c == 'w') { - enum coord_to_index = 0; - } else static if(c == 'x') { - enum coord_to_index = 1; - } else static if(c == 'y') { - enum coord_to_index = 2; - } else static if(c == 'z') { - enum coord_to_index = 3; - } else { - static assert(false, "accepted coordinates are x, y, z and w not " ~ c ~ "."); - } - } - - /// Returns the squared magnitude of the quaternion. - @property real magnitude_squared() const { - return to!real(w^^2 + x^^2 + y^^2 + z^^2); - } - - /// Returns the magnitude of the quaternion. - @property real magnitude() const { - return sqrt(magnitude_squared); - } - - /// Returns an identity quaternion (w=1, x=0, y=0, z=0). - static @property Quaternion identity() { - return Quaternion(1, 0, 0, 0); - } - - /// Makes the current quaternion an identity quaternion. - void make_identity() { - w = 1; - x = 0; - y = 0; - z = 0; - } - - /// Inverts the quaternion. - void invert() { - x = -x; - y = -y; - z = -z; - } - alias invert conjugate; /// ditto - - /// Returns an inverted copy of the current quaternion. - @property Quaternion inverse() const { - return Quaternion(w, -x, -y, -z); - } - alias inverse conjugated; /// ditto - - unittest { - quat q1 = quat(1.0f, 1.0f, 1.0f, 1.0f); - - assert(q1.magnitude == 2.0f); - assert(q1.magnitude_squared == 4.0f); - assert(q1.magnitude == quat(0.0f, 0.0f, 2.0f, 0.0f).magnitude); - - quat q2 = quat.identity; - assert(q2.quaternion == [1.0f, 0.0f, 0.0f, 0.0f]); - assert(q2.x == 0.0f); - assert(q2.y == 0.0f); - assert(q2.z == 0.0f); - assert(q2.w == 1.0f); - - assert(q1.inverse.quaternion == [1.0f, -1.0f, -1.0f, -1.0f]); - q1.invert(); - assert(q1.quaternion == [1.0f, -1.0f, -1.0f, -1.0f]); - - q1.make_identity(); - assert(q1.quaternion == q2.quaternion); - - } - - /// Creates a quaternion from a 3x3 matrix. - /// Params: - /// matrix = 3x3 matrix (rotation) - /// Returns: A quaternion representing the rotation (3x3 matrix) - static Quaternion from_matrix(Matrix!(qt, 3, 3) matrix) { - Quaternion ret; - - auto mat = matrix.matrix; - qt trace = mat[0][0] + mat[1][1] + mat[2][2]; - - if(trace > 0) { - real s = 0.5 / sqrt(trace + 1.0f); - - ret.w = to!qt(0.25 / s); - ret.x = to!qt((mat[2][1] - mat[1][2]) * s); - ret.y = to!qt((mat[0][2] - mat[2][0]) * s); - ret.z = to!qt((mat[1][0] - mat[0][1]) * s); - } else if((mat[0][0] > mat[1][1]) && (mat[0][0] > mat[2][2])) { - real s = 2.0 * sqrt(1.0 + mat[0][0] - mat[1][1] - mat[2][2]); - - ret.w = to!qt((mat[2][1] - mat[1][2]) / s); - ret.x = to!qt(0.25f * s); - ret.y = to!qt((mat[0][1] + mat[1][0]) / s); - ret.z = to!qt((mat[0][2] + mat[2][0]) / s); - } else if(mat[1][1] > mat[2][2]) { - real s = 2.0 * sqrt(1 + mat[1][1] - mat[0][0] - mat[2][2]); - - ret.w = to!qt((mat[0][2] - mat[2][0]) / s); - ret.x = to!qt((mat[0][1] + mat[1][0]) / s); - ret.y = to!qt(0.25f * s); - ret.z = to!qt((mat[1][2] + mat[2][1]) / s); - } else { - real s = 2.0 * sqrt(1 + mat[2][2] - mat[0][0] - mat[1][1]); - - ret.w = to!qt((mat[1][0] - mat[0][1]) / s); - ret.x = to!qt((mat[0][2] + mat[2][0]) / s); - ret.y = to!qt((mat[1][2] + mat[2][1]) / s); - ret.z = to!qt(0.25f * s); - } - - return ret; - } - - /// Returns the quaternion as matrix. - /// Params: - /// rows = number of rows of the resulting matrix (min 3) - /// cols = number of columns of the resulting matrix (min 3) - Matrix!(qt, rows, cols) to_matrix(int rows, int cols)() const if((rows >= 3) && (cols >= 3)) { - static if((rows == 3) && (cols == 3)) { - Matrix!(qt, rows, cols) ret; - } else { - Matrix!(qt, rows, cols) ret = Matrix!(qt, rows, cols).identity; - } - - qt xx = x^^2; - qt xy = x * y; - qt xz = x * z; - qt xw = x * w; - qt yy = y^^2; - qt yz = y * z; - qt yw = y * w; - qt zz = z^^2; - qt zw = z * w; - - ret.matrix[0][0] = 1 - 2 * (yy + zz); - ret.matrix[0][1] = 2 * (xy - zw); - ret.matrix[0][2] = 2 * (xz + yw); - - ret.matrix[1][0] = 2 * (xy + zw); - ret.matrix[1][1] = 1 - 2 * (xx + zz); - ret.matrix[1][2] = 2 * (yz - xw); - - ret.matrix[2][0] = 2 * (xz - yw); - ret.matrix[2][1] = 2 * (yz + xw); - ret.matrix[2][2] = 1 - 2 * (xx + yy); - - return ret; - } - - unittest { - quat q1 = quat(4.0f, 1.0f, 2.0f, 3.0f); - - assert(q1.to_matrix!(3, 3).matrix == [[-25.0f, -20.0f, 22.0f], [28.0f, -19.0f, 4.0f], [-10.0f, 20.0f, -9.0f]]); - assert(q1.to_matrix!(4, 4).matrix == [[-25.0f, -20.0f, 22.0f, 0.0f], - [28.0f, -19.0f, 4.0f, 0.0f], - [-10.0f, 20.0f, -9.0f, 0.0f], - [0.0f, 0.0f, 0.0f, 1.0f]]); - assert(quat.identity.to_matrix!(3, 3).matrix == Matrix!(qt, 3, 3).identity.matrix); - assert(q1.quaternion == quat.from_matrix(q1.to_matrix!(3, 3)).quaternion); - - assert(quat(1.0f, 0.0f, 0.0f, 0.0f).quaternion == quat.from_matrix(mat3.identity).quaternion); - - quat q2 = quat.from_matrix(mat3(1.0f, 3.0f, 2.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f)); - assert(q2.x == 0.0f); - assert(almost_equal(q2.y, 0.7071067f)); - assert(almost_equal(q2.z, -1.060660)); - assert(almost_equal(q2.w, 0.7071067f)); - } - - /// Normalizes the current quaternion. - void normalize() { - qt m = to!qt(magnitude); - - if(m != 0) { - w = w / m; - x = x / m; - y = y / m; - z = z / m; - } - } - - /// Returns a normalized copy of the current quaternion. - Quaternion normalized() const { - Quaternion ret; - qt m = to!qt(magnitude); - - if(m != 0) { - ret.w = w / m; - ret.x = x / m; - ret.y = y / m; - ret.z = z / m; - } else { - ret = Quaternion(w, x, y, z); - } - - return ret; - } - - unittest { - quat q1 = quat(1.0f, 2.0f, 3.0f, 4.0f); - quat q2 = quat(1.0f, 2.0f, 3.0f, 4.0f); - - q1.normalize(); - assert(q1.quaternion == q2.normalized.quaternion); - //assert(q1.quaternion == q1.normalized.quaternion); - assert(almost_equal(q1.magnitude, 1.0)); - } - - /// Returns the yaw. - @property real yaw() const { - return atan2(to!real(2.0*(w*z + x*y)), to!real(1.0 - 2.0*(y*y + z*z))); - } - - /// Returns the pitch. - @property real pitch() const { - return asin(to!real(2.0*(w*y - z*x))); - } - - /// Returns the roll. - @property real roll() const { - return atan2(to!real(2.0*(w*x + y*z)), to!real(1.0 - 2.0*(x*x + y*y))); - } - - unittest { - quat q1 = quat.identity; - assert(q1.pitch == 0.0f); - assert(q1.yaw == 0.0f); - assert(q1.roll == 0.0f); - - quat q2 = quat(1.0f, 1.0f, 1.0f, 1.0f); - assert(almost_equal(q2.yaw, q2.roll)); - //assert(almost_equal(q2.yaw, 1.570796f)); - assert(q2.pitch == 0.0f); - - quat q3 = quat(0.1f, 1.9f, 2.1f, 1.3f); - //assert(almost_equal(q3.yaw, 2.4382f)); - assert(isNaN(q3.pitch)); - //assert(almost_equal(q3.roll, 1.67719f)); - } - - /// Returns a quaternion with applied rotation around the x-axis. - static Quaternion xrotation(real alpha) { - Quaternion ret; - - alpha /= 2; - ret.w = to!qt(cos(alpha)); - ret.x = to!qt(sin(alpha)); - ret.y = 0; - ret.z = 0; - - return ret; - } - - /// Returns a quaternion with applied rotation around the y-axis. - static Quaternion yrotation(real alpha) { - Quaternion ret; - - alpha /= 2; - ret.w = to!qt(cos(alpha)); - ret.x = 0; - ret.y = to!qt(sin(alpha)); - ret.z = 0; - - return ret; - } - - /// Returns a quaternion with applied rotation around the z-axis. - static Quaternion zrotation(real alpha) { - Quaternion ret; - - alpha /= 2; - ret.w = to!qt(cos(alpha)); - ret.x = 0; - ret.y = 0; - ret.z = to!qt(sin(alpha)); - - return ret; - } - - /// Returns a quaternion with applied rotation around an axis. - static Quaternion axis_rotation(real alpha, Vector!(qt, 3) axis) { - if(alpha == 0) { - return Quaternion.identity; - } - Quaternion ret; - - alpha /= 2; - qt sinaqt = to!qt(sin(alpha)); - - ret.w = to!qt(cos(alpha)); - ret.x = axis.x * sinaqt; - ret.y = axis.y * sinaqt; - ret.z = axis.z * sinaqt; - - return ret; - } - - /// Creates a quaternion from an euler rotation. - static Quaternion euler_rotation(real roll, real pitch, real yaw) { - Quaternion ret; - - auto cr = cos(roll / 2.0); - auto cp = cos(pitch / 2.0); - auto cy = cos(yaw / 2.0); - auto sr = sin(roll / 2.0); - auto sp = sin(pitch / 2.0); - auto sy = sin(yaw / 2.0); - - ret.w = cr * cp * cy + sr * sp * sy; - ret.x = sr * cp * cy - cr * sp * sy; - ret.y = cr * sp * cy + sr * cp * sy; - ret.z = cr * cp * sy - sr * sp * cy; - - return ret; - } - - unittest { - enum startPitch = 0.1; - enum startYaw = -0.2; - enum startRoll = 0.6; - - auto q = quat.euler_rotation(startRoll,startPitch,startYaw); - - assert(almost_equal(q.pitch,startPitch)); - assert(almost_equal(q.yaw,startYaw)); - assert(almost_equal(q.roll,startRoll)); - } - - /// Rotates the current quaternion around the x-axis and returns $(I this). - Quaternion rotatex(real alpha) { - this = xrotation(alpha) * this; - return this; - } - - /// Rotates the current quaternion around the y-axis and returns $(I this). - Quaternion rotatey(real alpha) { - this = yrotation(alpha) * this; - return this; - } - - /// Rotates the current quaternion around the z-axis and returns $(I this). - Quaternion rotatez(real alpha) { - this = zrotation(alpha) * this; - return this; - } - - /// Rotates the current quaternion around an axis and returns $(I this). - Quaternion rotate_axis(real alpha, Vector!(qt, 3) axis) { - this = axis_rotation(alpha, axis) * this; - return this; - } - - /// Applies an euler rotation to the current quaternion and returns $(I this). - Quaternion rotate_euler(real heading, real attitude, real bank) { - this = euler_rotation(heading, attitude, bank) * this; - return this; - } - - unittest { - assert(quat.xrotation(PI).quaternion[1..4] == [1.0f, 0.0f, 0.0f]); - assert(quat.yrotation(PI).quaternion[1..4] == [0.0f, 1.0f, 0.0f]); - assert(quat.zrotation(PI).quaternion[1..4] == [0.0f, 0.0f, 1.0f]); - assert((quat.xrotation(PI).w == quat.yrotation(PI).w) && (quat.yrotation(PI).w == quat.zrotation(PI).w)); - //assert(quat.rotatex(PI).w == to!(quat.qt)(cos(PI))); - assert(quat.xrotation(PI).quaternion == quat.identity.rotatex(PI).quaternion); - assert(quat.yrotation(PI).quaternion == quat.identity.rotatey(PI).quaternion); - assert(quat.zrotation(PI).quaternion == quat.identity.rotatez(PI).quaternion); - - assert(quat.axis_rotation(PI, vec3(1.0f, 1.0f, 1.0f)).quaternion[1..4] == [1.0f, 1.0f, 1.0f]); - assert(quat.axis_rotation(PI, vec3(1.0f, 1.0f, 1.0f)).w == quat.xrotation(PI).w); - assert(quat.axis_rotation(PI, vec3(1.0f, 1.0f, 1.0f)).quaternion == - quat.identity.rotate_axis(PI, vec3(1.0f, 1.0f, 1.0f)).quaternion); - - quat q1 = quat.euler_rotation(PI, PI, PI); - assert((q1.x > -1e-16) && (q1.x < 1e-16)); - assert((q1.y > -1e-16) && (q1.y < 1e-16)); - assert((q1.z > -1e-16) && (q1.z < 1e-16)); - //assert(q1.w == -1.0f); - assert(quat.euler_rotation(PI, PI, PI).quaternion == quat.identity.rotate_euler(PI, PI, PI).quaternion); - } - - Quaternion opBinary(string op : "*")(Quaternion inp) const { - Quaternion ret; - - ret.w = -x * inp.x - y * inp.y - z * inp.z + w * inp.w; - ret.x = x * inp.w + y * inp.z - z * inp.y + w * inp.x; - ret.y = -x * inp.z + y * inp.w + z * inp.x + w * inp.y; - ret.z = x * inp.y - y * inp.x + z * inp.w + w * inp.z; - - return ret; - } - - auto opBinaryRight(string op, T)(T inp) const if(!is_quaternion!T) { - return this.opBinary!(op)(inp); - } - - Quaternion opBinary(string op)(Quaternion inp) const if((op == "+") || (op == "-")) { - Quaternion ret; - - mixin("ret.w = w" ~ op ~ "inp.w;"); - mixin("ret.x = x" ~ op ~ "inp.x;"); - mixin("ret.y = y" ~ op ~ "inp.y;"); - mixin("ret.z = z" ~ op ~ "inp.z;"); - - return ret; - } - - Vector!(qt, 3) opBinary(string op : "*")(Vector!(qt, 3) inp) const { - Vector!(qt, 3) ret; - - qt ww = w^^2; - qt w2 = w * 2; - qt wx2 = w2 * x; - qt wy2 = w2 * y; - qt wz2 = w2 * z; - qt xx = x^^2; - qt x2 = x * 2; - qt xy2 = x2 * y; - qt xz2 = x2 * z; - qt yy = y^^2; - qt yz2 = 2 * y * z; - qt zz = z * z; - - ret.vector = [ww * inp.x + wy2 * inp.z - wz2 * inp.y + xx * inp.x + - xy2 * inp.y + xz2 * inp.z - zz * inp.x - yy * inp.x, - xy2 * inp.x + yy * inp.y + yz2 * inp.z + wz2 * inp.x - - zz * inp.y + ww * inp.y - wx2 * inp.z - xx * inp.y, - xz2 * inp.x + yz2 * inp.y + zz * inp.z - wy2 * inp.x - - yy * inp.z + wx2 * inp.y - xx * inp.z + ww * inp.z]; - - return ret; - } - - Quaternion opBinary(string op : "*")(qt inp) const { - return Quaternion(w*inp, x*inp, y*inp, z*inp); - } - - void opOpAssign(string op : "*")(Quaternion inp) { - qt w2 = -x * inp.x - y * inp.y - z * inp.z + w * inp.w; - qt x2 = x * inp.w + y * inp.z - z * inp.y + w * inp.x; - qt y2 = -x * inp.z + y * inp.w + z * inp.x + w * inp.y; - qt z2 = x * inp.y - y * inp.x + z * inp.w + w * inp.z; - w = w2; x = x2; y = y2; z = z2; - } - - void opOpAssign(string op)(Quaternion inp) if((op == "+") || (op == "-")) { - mixin("w = w" ~ op ~ "inp.w;"); - mixin("x = x" ~ op ~ "inp.x;"); - mixin("y = y" ~ op ~ "inp.y;"); - mixin("z = z" ~ op ~ "inp.z;"); - } - - void opOpAssign(string op : "*")(qt inp) { - quaternion[0] *= inp; - quaternion[1] *= inp; - quaternion[2] *= inp; - quaternion[3] *= inp; - } - - unittest { - quat q1 = quat.identity; - quat q2 = quat(3.0f, 0.0f, 1.0f, 2.0f); - quat q3 = quat(3.4f, 0.1f, 1.2f, 2.3f); - - assert((q1 * q1).quaternion == q1.quaternion); - assert((q1 * q2).quaternion == q2.quaternion); - assert((q2 * q1).quaternion == q2.quaternion); - quat q4 = q3 * q2; - assert((q2 * q3).quaternion != q4.quaternion); - q3 *= q2; - assert(q4.quaternion == q3.quaternion); - assert(almost_equal(q4.x, 0.4f)); - assert(almost_equal(q4.y, 6.8f)); - assert(almost_equal(q4.z, 13.8f)); - assert(almost_equal(q4.w, 4.4f)); - - quat q5 = quat(1.0f, 2.0f, 3.0f, 4.0f); - quat q6 = quat(3.0f, 1.0f, 6.0f, 2.0f); - - assert((q5 - q6).quaternion == [-2.0f, 1.0f, -3.0f, 2.0f]); - assert((q5 + q6).quaternion == [4.0f, 3.0f, 9.0f, 6.0f]); - assert((q6 - q5).quaternion == [2.0f, -1.0f, 3.0f, -2.0f]); - assert((q6 + q5).quaternion == [4.0f, 3.0f, 9.0f, 6.0f]); - q5 += q6; - assert(q5.quaternion == [4.0f, 3.0f, 9.0f, 6.0f]); - q6 -= q6; - assert(q6.quaternion == [0.0f, 0.0f, 0.0f, 0.0f]); - - quat q7 = quat(2.0f, 2.0f, 2.0f, 2.0f); - assert((q7 * 2).quaternion == [4.0f, 4.0f, 4.0f, 4.0f]); - assert((2 * q7).quaternion == (q7 * 2).quaternion); - q7 *= 2; - assert(q7.quaternion == [4.0f, 4.0f, 4.0f, 4.0f]); - - vec3 v1 = vec3(1.0f, 2.0f, 3.0f); - assert((q1 * v1).vector == v1.vector); - assert((v1 * q1).vector == (q1 * v1).vector); - assert((q2 * v1).vector == [-2.0f, 36.0f, 38.0f]); - } - - int opCmp(ref const Quaternion qua) const { - foreach(i, a; quaternion) { - if(a < qua.quaternion[i]) { - return -1; - } else if(a > qua.quaternion[i]) { - return 1; - } - } - - // Quaternions are the same - return 0; - } - - bool opEquals(const Quaternion qu) const { - return quaternion == qu.quaternion; - } - - bool opCast(T : bool)() const { - return isFinite; - } - - unittest { - assert(quat(1.0f, 2.0f, 3.0f, 4.0f) == quat(1.0f, 2.0f, 3.0f, 4.0f)); - assert(quat(1.0f, 2.0f, 3.0f, 4.0f) != quat(1.0f, 2.0f, 3.0f, 3.0f)); - - assert(!(quat(float.nan, float.nan, float.nan, float.nan))); - if(quat(1.0f, 1.0f, 1.0f, 1.0f)) { } - else { assert(false); } - } - -} - -/// Pre-defined quaternion of type float. -alias Quaternion!(float) quat; diff --git a/gl3n/linalg/matrix.d b/gl3n/linalg/matrix.d new file mode 100644 index 0000000..0939fd5 --- /dev/null +++ b/gl3n/linalg/matrix.d @@ -0,0 +1,1271 @@ +/** +gl3n.linalg.matrix + +Special thanks to: +$(UL + $(LI Tomasz Stachowiak (h3r3tic): allowed me to use parts of $(LINK2 https://bitbucket.org/h3r3tic/boxen/src/default/src/xf/omg, omg).) + $(LI Jakob Øvrum (jA_cOp): improved the code a lot!) + $(LI Florian Boesch (___doc__): helps me to understand opengl/complex maths better, see: $(LINK http://codeflow.org/).) + $(LI #D on freenode: answered general questions about D.) +) + +Authors: David Herberth, Stephan Dilly +License: MIT + +Note: All methods marked with pure are weakly pure since, they all access an instance member. +All static methods are strongly pure. +*/ + +module gl3n.linalg.matrix; + +import gl3n.linalg.vec; +import gl3n.math : PI, sin, cos, tan; + +import std.math : isNaN, isInfinity; +import std.traits : isIntegral; +import std.string : format, rightJustify; +import std.array : join; +import std.algorithm : min, reduce; +import std.traits : isFloatingPoint; + +version(NoReciprocalMul) { + private enum rmul = false; +} else { + private enum rmul = true; +} + +/// Base template for all matrix-types. +/// Params: +/// type = all values get stored as this type +/// rows_ = rows of the matrix +/// cols_ = columns of the matrix +/// Examples: +/// --- +/// alias Matrix!(float, 4, 4) mat4; +/// alias Matrix!(double, 3, 4) mat34d; +/// alias Matrix!(real, 2, 2) mat2r; +/// --- +struct Matrix(type, int rows_, int cols_) if((rows_ > 0) && (cols_ > 0)) { + alias type mt; /// Holds the internal type of the matrix; + static const int rows = rows_; /// Holds the number of rows; + static const int cols = cols_; /// Holds the number of columns; + + /// Holds the matrix $(RED row-major) in memory. + mt[cols][rows] matrix; // In C it would be mt[rows][cols], D does it like this: (mt[foo])[bar] + alias matrix this; + + unittest { + mat2 m2 = mat2(0.0f, 1.0f, 2.0f, 3.0f); + assert(m2[0][0] == 0.0f); + assert(m2[0][1] == 1.0f); + assert(m2[1][0] == 2.0f); + assert(m2[1][1] == 3.0f); + m2[0..1] = [2.0f, 2.0f]; + assert(m2 == [[2.0f, 2.0f], [2.0f, 3.0f]]); + + mat3 m3 = mat3(0.0f, 0.1f, 0.2f, 1.0f, 1.1f, 1.2f, 2.0f, 2.1f, 2.2f); + assert(m3[0][1] == 0.1f); + assert(m3[2][0] == 2.0f); + assert(m3[1][2] == 1.2f); + m3[0][0..$] = 0.0f; + assert(m3 == [[0.0f, 0.0f, 0.0f], + [1.0f, 1.1f, 1.2f], + [2.0f, 2.1f, 2.2f]]); + + mat4 m4 = mat4(0.0f, 0.1f, 0.2f, 0.3f, + 1.0f, 1.1f, 1.2f, 1.3f, + 2.0f, 2.1f, 2.2f, 2.3f, + 3.0f, 3.1f, 3.2f, 3.3f); + assert(m4[0][3] == 0.3f); + assert(m4[1][1] == 1.1f); + assert(m4[2][0] == 2.0f); + assert(m4[3][2] == 3.2f); + m4[2][1..3] = [1.0f, 2.0f]; + assert(m4 == [[0.0f, 0.1f, 0.2f, 0.3f], + [1.0f, 1.1f, 1.2f, 1.3f], + [2.0f, 1.0f, 2.0f, 2.3f], + [3.0f, 3.1f, 3.2f, 3.3f]]); + + } + + /// Returns the pointer to the stored values as OpenGL requires it. + /// Note this will return a pointer to a $(RED row-major) matrix, + /// $(RED this means you've to set the transpose argument to GL_TRUE when passing it to OpenGL). + /// Examples: + /// --- + /// // 3rd argument = GL_TRUE + /// glUniformMatrix4fv(programs.main.model, 1, GL_TRUE, mat4.translation(-0.5f, -0.5f, 1.0f).value_ptr); + /// --- + @property auto value_ptr() const { return matrix[0].ptr; } + + /// Returns the current matrix formatted as flat string. + @property string as_string() { + return format("%s", matrix); + } + alias as_string toString; /// ditto + + /// Returns the current matrix as pretty formatted string. + @property string as_pretty_string() { + string fmtr = "%s"; + + size_t rjust = max(format(fmtr, reduce!(max)(matrix[])).length, + format(fmtr, reduce!(min)(matrix[])).length) - 1; + + string[] outer_parts; + foreach(mt[] row; matrix) { + string[] inner_parts; + foreach(mt col; row) { + inner_parts ~= rightJustify(format(fmtr, col), rjust); + } + outer_parts ~= " [" ~ join(inner_parts, ", ") ~ "]"; + } + + return "[" ~ join(outer_parts, "\n")[1..$] ~ "]"; + } + alias as_pretty_string toPrettyString; /// ditto + + @safe pure nothrow: + static void isCompatibleMatrixImpl(int r, int c)(Matrix!(mt, r, c) m) { + } + + template isCompatibleMatrix(T) { + enum isCompatibleMatrix = is(typeof(isCompatibleMatrixImpl(T.init))); + } + + static void isCompatibleVectorImpl(int d)(Vector!(mt, d) vec) { + } + + template isCompatibleVector(T) { + enum isCompatibleVector = is(typeof(isCompatibleVectorImpl(T.init))); + } + + private void construct(int i, T, Tail...)(T head, Tail tail) { + static if(i >= rows*cols) { + static assert(false, "Too many arguments passed to constructor"); + } else static if(is(T : mt)) { + matrix[i / cols][i % cols] = head; + construct!(i + 1)(tail); + } else static if(is(T == Vector!(mt, cols))) { + static if(i % cols == 0) { + matrix[i / cols] = head.vector; + construct!(i + T.dimension)(tail); + } else { + static assert(false, "Can't convert Vector into the matrix. Maybe it doesn't align to the columns correctly or dimension doesn't fit"); + } + } else static if(isDynamicArray!T) { + foreach(j; 0..cols*rows) + matrix[j / cols][j % cols] = head[j]; + } else { + static assert(false, "Matrix constructor argument must be of type " ~ mt.stringof ~ " or Vector, not " ~ T.stringof); + } + } + + private void construct(int i)() { // terminate + static assert(i == rows*cols, "Not enough arguments passed to constructor"); + } + + /// Constructs the matrix: + /// If a single value is passed, the matrix will be cleared with this value (each column in each row will contain this value). + /// If a matrix with more rows and columns is passed, the matrix will be the upper left nxm matrix. + /// If a matrix with less rows and columns is passed, the passed matrix will be stored in the upper left of an identity matrix. + /// It's also allowed to pass vectors and scalars at a time, but the vectors dimension must match the number of columns and align correctly. + /// Examples: + /// --- + /// mat2 m2 = mat2(0.0f); // mat2 m2 = mat2(0.0f, 0.0f, 0.0f, 0.0f); + /// mat3 m3 = mat3(m2); // mat3 m3 = mat3(0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f); + /// mat3 m3_2 = mat3(vec3(1.0f, 2.0f, 3.0f), 4.0f, 5.0f, 6.0f, vec3(7.0f, 8.0f, 9.0f)); + /// mat4 m4 = mat4.identity; // just an identity matrix + /// mat3 m3_3 = mat3(m4); // mat3 m3_3 = mat3.identity + /// --- + this(Args...)(Args args) { + construct!(0)(args); + } + + /// ditto + this(T)(T mat) if(is_matrix!T && (T.cols >= cols) && (T.rows >= rows)) { + foreach(r; TupleRange!(0, rows)) { + foreach(c; TupleRange!(0, cols)) { + matrix[r][c] = mat.matrix[r][c]; + } + } + } + + /// ditto + this(T)(T mat) if(is_matrix!T && (T.cols < cols) && (T.rows < rows)) { + make_identity(); + + foreach(r; TupleRange!(0, T.rows)) { + foreach(c; TupleRange!(0, T.cols)) { + matrix[r][c] = mat.matrix[r][c]; + } + } + } + + /// ditto + this()(mt value) { + clear(value); + } + + /// Returns true if all values are not nan and finite, otherwise false. + @property bool isFinite() const { + static if(isIntegral!type) { + return true; + } + else { + foreach(row; matrix) { + foreach(col; row) { + if(isNaN(col) || isInfinity(col)) { + return false; + } + } + } + return true; + } + + } + deprecated("Use isFinite instead of ok") alias ok = isFinite; + + /// Sets all values of the matrix to value (each column in each row will contain this value). + void clear(mt value) { + foreach(r; TupleRange!(0, rows)) { + foreach(c; TupleRange!(0, cols)) { + matrix[r][c] = value; + } + } + } + + unittest { + mat2 m2 = mat2(1.0f, 1.0f, vec2(2.0f, 2.0f)); + assert(m2.matrix == [[1.0f, 1.0f], [2.0f, 2.0f]]); + m2.clear(3.0f); + assert(m2.matrix == [[3.0f, 3.0f], [3.0f, 3.0f]]); + assert(m2.isFinite); + m2.clear(float.nan); + assert(!m2.isFinite); + m2.clear(float.infinity); + assert(!m2.isFinite); + m2.clear(0.0f); + assert(m2.isFinite); + + mat3 m3 = mat3(1.0f); + assert(m3.matrix == [[1.0f, 1.0f, 1.0f], + [1.0f, 1.0f, 1.0f], + [1.0f, 1.0f, 1.0f]]); + + mat4 m4 = mat4(vec4(1.0f, 1.0f, 1.0f, 1.0f), + 2.0f, 2.0f, 2.0f, 2.0f, + 3.0f, 3.0f, 3.0f, 3.0f, + vec4(4.0f, 4.0f, 4.0f, 4.0f)); + assert(m4.matrix == [[1.0f, 1.0f, 1.0f, 1.0f], + [2.0f, 2.0f, 2.0f, 2.0f], + [3.0f, 3.0f, 3.0f, 3.0f], + [4.0f, 4.0f, 4.0f, 4.0f]]); + assert(mat3(m4).matrix == [[1.0f, 1.0f, 1.0f], + [2.0f, 2.0f, 2.0f], + [3.0f, 3.0f, 3.0f]]); + assert(mat2(mat3(m4)).matrix == [[1.0f, 1.0f], [2.0f, 2.0f]]); + assert(mat2(m4).matrix == mat2(mat3(m4)).matrix); + assert(mat4(mat3(m4)).matrix == [[1.0f, 1.0f, 1.0f, 0.0f], + [2.0f, 2.0f, 2.0f, 0.0f], + [3.0f, 3.0f, 3.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + + Matrix!(float, 2, 3) mt1 = Matrix!(float, 2, 3)(1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f); + Matrix!(float, 3, 2) mt2 = Matrix!(float, 3, 2)(6.0f, -1.0f, 3.0f, 2.0f, 0.0f, -3.0f); + + assert(mt1.matrix == [[1.0f, 2.0f, 3.0f], [4.0f, 5.0f, 6.0f]]); + assert(mt2.matrix == [[6.0f, -1.0f], [3.0f, 2.0f], [0.0f, -3.0f]]); + + static assert(!__traits(compiles, mat2(1, 2, 1))); + static assert(!__traits(compiles, mat3(1, 2, 3, 1, 2, 3, 1, 2))); + static assert(!__traits(compiles, mat4(1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3))); + + auto m5 = mat2([0.0f,1,2,3]); + assert(m5.matrix == [[0.0f, 1.0f], [2.0f, 3.0f]]); + + auto m6 = Matrix!(int, 2, 3)([0,1,2,3,4,5]); + assert(m6.matrix == [[0, 1, 2], [3, 4, 5]]); + } + + static if(rows == cols) { + /// Makes the current matrix an identity matrix. + void make_identity() { + clear(0); + foreach(r; TupleRange!(0, rows)) { + matrix[r][r] = 1; + } + } + + /// Returns a identity matrix. + static @property Matrix identity() { + Matrix ret; + ret.clear(0); + + foreach(r; TupleRange!(0, rows)) { + ret.matrix[r][r] = 1; + } + + return ret; + } + + /// Transposes the current matrix; + void transpose() { + matrix = transposed().matrix; + } + + unittest { + mat2 m2 = mat2(1.0f); + m2.transpose(); + assert(m2.matrix == mat2(1.0f).matrix); + m2.make_identity(); + assert(m2.matrix == [[1.0f, 0.0f], + [0.0f, 1.0f]]); + m2.transpose(); + assert(m2.matrix == [[1.0f, 0.0f], + [0.0f, 1.0f]]); + assert(m2.matrix == m2.identity.matrix); + + mat3 m3 = mat3(1.1f, 1.2f, 1.3f, + 2.1f, 2.2f, 2.3f, + 3.1f, 3.2f, 3.3f); + m3.transpose(); + assert(m3.matrix == [[1.1f, 2.1f, 3.1f], + [1.2f, 2.2f, 3.2f], + [1.3f, 2.3f, 3.3f]]); + + mat4 m4 = mat4(2.0f); + m4.transpose(); + assert(m4.matrix == mat4(2.0f).matrix); + m4.make_identity(); + assert(m4.matrix == [[1.0f, 0.0f, 0.0f, 0.0f], + [0.0f, 1.0f, 0.0f, 0.0f], + [0.0f, 0.0f, 1.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + assert(m4.matrix == m4.identity.matrix); + } + + } + + /// Returns a transposed copy of the matrix. + @property Matrix!(mt, cols, rows) transposed() const { + typeof(return) ret; + + foreach(r; TupleRange!(0, rows)) { + foreach(c; TupleRange!(0, cols)) { + ret.matrix[c][r] = matrix[r][c]; + } + } + + return ret; + } + + // transposed already tested in last unittest + + + static if((rows == 2) && (cols == 2)) { + @property mt det() const { + return (matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]); + } + + private Matrix invert(ref Matrix mat) const { + static if(isFloatingPoint!mt && rmul) { + mt d = 1 / det; + + mat.matrix = [[matrix[1][1]*d, -matrix[0][1]*d], + [-matrix[1][0]*d, matrix[0][0]*d]]; + } else { + mt d = det; + + mat.matrix = [[matrix[1][1]/d, -matrix[0][1]/d], + [-matrix[1][0]/d, matrix[0][0]/d]]; + } + + return mat; + } + + static Matrix scaling(mt x, mt y) { + Matrix ret = Matrix.identity; + + ret.matrix[0][0] = x; + ret.matrix[1][1] = y; + + return ret; + } + + Matrix scale(mt x, mt y) { + this = Matrix.scaling(x, y) * this; + return this; + } + + unittest { + assert(mat2.scaling(3, 3).matrix == mat2.identity.scale(3, 3).matrix); + assert(mat2.scaling(3, 3).matrix == [[3.0f, 0.0f], [0.0f, 3.0f]]); + } + + } else static if((rows == 3) && (cols == 3)) { + @property mt det() const { + return (matrix[0][0] * matrix[1][1] * matrix[2][2] + + matrix[0][1] * matrix[1][2] * matrix[2][0] + + matrix[0][2] * matrix[1][0] * matrix[2][1] + - matrix[0][2] * matrix[1][1] * matrix[2][0] + - matrix[0][1] * matrix[1][0] * matrix[2][2] + - matrix[0][0] * matrix[1][2] * matrix[2][1]); + } + + private Matrix invert(ref Matrix mat) const { + static if(isFloatingPoint!mt && rmul) { + mt d = 1 / det; + enum op = "*"; + } else { + mt d = det; + enum op = "/"; + } + + mixin(` + mat.matrix = [[(matrix[1][1] * matrix[2][2] - matrix[1][2] * matrix[2][1])`~op~`d, + (matrix[0][2] * matrix[2][1] - matrix[0][1] * matrix[2][2])`~op~`d, + (matrix[0][1] * matrix[1][2] - matrix[0][2] * matrix[1][1])`~op~`d], + [(matrix[1][2] * matrix[2][0] - matrix[1][0] * matrix[2][2])`~op~`d, + (matrix[0][0] * matrix[2][2] - matrix[0][2] * matrix[2][0])`~op~`d, + (matrix[0][2] * matrix[1][0] - matrix[0][0] * matrix[1][2])`~op~`d], + [(matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0])`~op~`d, + (matrix[0][1] * matrix[2][0] - matrix[0][0] * matrix[2][1])`~op~`d, + (matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0])`~op~`d]]; + `); + + return mat; + } + } else static if((rows == 4) && (cols == 4)) { + /// Returns the determinant of the current matrix (2x2, 3x3 and 4x4 matrices). + @property mt det() const { + return (matrix[0][3] * matrix[1][2] * matrix[2][1] * matrix[3][0] - matrix[0][2] * matrix[1][3] * matrix[2][1] * matrix[3][0] + - matrix[0][3] * matrix[1][1] * matrix[2][2] * matrix[3][0] + matrix[0][1] * matrix[1][3] * matrix[2][2] * matrix[3][0] + + matrix[0][2] * matrix[1][1] * matrix[2][3] * matrix[3][0] - matrix[0][1] * matrix[1][2] * matrix[2][3] * matrix[3][0] + - matrix[0][3] * matrix[1][2] * matrix[2][0] * matrix[3][1] + matrix[0][2] * matrix[1][3] * matrix[2][0] * matrix[3][1] + + matrix[0][3] * matrix[1][0] * matrix[2][2] * matrix[3][1] - matrix[0][0] * matrix[1][3] * matrix[2][2] * matrix[3][1] + - matrix[0][2] * matrix[1][0] * matrix[2][3] * matrix[3][1] + matrix[0][0] * matrix[1][2] * matrix[2][3] * matrix[3][1] + + matrix[0][3] * matrix[1][1] * matrix[2][0] * matrix[3][2] - matrix[0][1] * matrix[1][3] * matrix[2][0] * matrix[3][2] + - matrix[0][3] * matrix[1][0] * matrix[2][1] * matrix[3][2] + matrix[0][0] * matrix[1][3] * matrix[2][1] * matrix[3][2] + + matrix[0][1] * matrix[1][0] * matrix[2][3] * matrix[3][2] - matrix[0][0] * matrix[1][1] * matrix[2][3] * matrix[3][2] + - matrix[0][2] * matrix[1][1] * matrix[2][0] * matrix[3][3] + matrix[0][1] * matrix[1][2] * matrix[2][0] * matrix[3][3] + + matrix[0][2] * matrix[1][0] * matrix[2][1] * matrix[3][3] - matrix[0][0] * matrix[1][2] * matrix[2][1] * matrix[3][3] + - matrix[0][1] * matrix[1][0] * matrix[2][2] * matrix[3][3] + matrix[0][0] * matrix[1][1] * matrix[2][2] * matrix[3][3]); + } + + private Matrix invert(ref Matrix mat) const { + static if(isFloatingPoint!mt && rmul) { + mt d = 1 / det; + enum op = "*"; + } else { + mt d = det; + enum op = "/"; + } + + mixin(` + mat.matrix = [[(matrix[1][1] * matrix[2][2] * matrix[3][3] + matrix[1][2] * matrix[2][3] * matrix[3][1] + matrix[1][3] * matrix[2][1] * matrix[3][2] + - matrix[1][1] * matrix[2][3] * matrix[3][2] - matrix[1][2] * matrix[2][1] * matrix[3][3] - matrix[1][3] * matrix[2][2] * matrix[3][1])`~op~`d, + (matrix[0][1] * matrix[2][3] * matrix[3][2] + matrix[0][2] * matrix[2][1] * matrix[3][3] + matrix[0][3] * matrix[2][2] * matrix[3][1] + - matrix[0][1] * matrix[2][2] * matrix[3][3] - matrix[0][2] * matrix[2][3] * matrix[3][1] - matrix[0][3] * matrix[2][1] * matrix[3][2])`~op~`d, + (matrix[0][1] * matrix[1][2] * matrix[3][3] + matrix[0][2] * matrix[1][3] * matrix[3][1] + matrix[0][3] * matrix[1][1] * matrix[3][2] + - matrix[0][1] * matrix[1][3] * matrix[3][2] - matrix[0][2] * matrix[1][1] * matrix[3][3] - matrix[0][3] * matrix[1][2] * matrix[3][1])`~op~`d, + (matrix[0][1] * matrix[1][3] * matrix[2][2] + matrix[0][2] * matrix[1][1] * matrix[2][3] + matrix[0][3] * matrix[1][2] * matrix[2][1] + - matrix[0][1] * matrix[1][2] * matrix[2][3] - matrix[0][2] * matrix[1][3] * matrix[2][1] - matrix[0][3] * matrix[1][1] * matrix[2][2])`~op~`d], + [(matrix[1][0] * matrix[2][3] * matrix[3][2] + matrix[1][2] * matrix[2][0] * matrix[3][3] + matrix[1][3] * matrix[2][2] * matrix[3][0] + - matrix[1][0] * matrix[2][2] * matrix[3][3] - matrix[1][2] * matrix[2][3] * matrix[3][0] - matrix[1][3] * matrix[2][0] * matrix[3][2])`~op~`d, + (matrix[0][0] * matrix[2][2] * matrix[3][3] + matrix[0][2] * matrix[2][3] * matrix[3][0] + matrix[0][3] * matrix[2][0] * matrix[3][2] + - matrix[0][0] * matrix[2][3] * matrix[3][2] - matrix[0][2] * matrix[2][0] * matrix[3][3] - matrix[0][3] * matrix[2][2] * matrix[3][0])`~op~`d, + (matrix[0][0] * matrix[1][3] * matrix[3][2] + matrix[0][2] * matrix[1][0] * matrix[3][3] + matrix[0][3] * matrix[1][2] * matrix[3][0] + - matrix[0][0] * matrix[1][2] * matrix[3][3] - matrix[0][2] * matrix[1][3] * matrix[3][0] - matrix[0][3] * matrix[1][0] * matrix[3][2])`~op~`d, + (matrix[0][0] * matrix[1][2] * matrix[2][3] + matrix[0][2] * matrix[1][3] * matrix[2][0] + matrix[0][3] * matrix[1][0] * matrix[2][2] + - matrix[0][0] * matrix[1][3] * matrix[2][2] - matrix[0][2] * matrix[1][0] * matrix[2][3] - matrix[0][3] * matrix[1][2] * matrix[2][0])`~op~`d], + [(matrix[1][0] * matrix[2][1] * matrix[3][3] + matrix[1][1] * matrix[2][3] * matrix[3][0] + matrix[1][3] * matrix[2][0] * matrix[3][1] + - matrix[1][0] * matrix[2][3] * matrix[3][1] - matrix[1][1] * matrix[2][0] * matrix[3][3] - matrix[1][3] * matrix[2][1] * matrix[3][0])`~op~`d, + (matrix[0][0] * matrix[2][3] * matrix[3][1] + matrix[0][1] * matrix[2][0] * matrix[3][3] + matrix[0][3] * matrix[2][1] * matrix[3][0] + - matrix[0][0] * matrix[2][1] * matrix[3][3] - matrix[0][1] * matrix[2][3] * matrix[3][0] - matrix[0][3] * matrix[2][0] * matrix[3][1])`~op~`d, + (matrix[0][0] * matrix[1][1] * matrix[3][3] + matrix[0][1] * matrix[1][3] * matrix[3][0] + matrix[0][3] * matrix[1][0] * matrix[3][1] + - matrix[0][0] * matrix[1][3] * matrix[3][1] - matrix[0][1] * matrix[1][0] * matrix[3][3] - matrix[0][3] * matrix[1][1] * matrix[3][0])`~op~`d, + (matrix[0][0] * matrix[1][3] * matrix[2][1] + matrix[0][1] * matrix[1][0] * matrix[2][3] + matrix[0][3] * matrix[1][1] * matrix[2][0] + - matrix[0][0] * matrix[1][1] * matrix[2][3] - matrix[0][1] * matrix[1][3] * matrix[2][0] - matrix[0][3] * matrix[1][0] * matrix[2][1])`~op~`d], + [(matrix[1][0] * matrix[2][2] * matrix[3][1] + matrix[1][1] * matrix[2][0] * matrix[3][2] + matrix[1][2] * matrix[2][1] * matrix[3][0] + - matrix[1][0] * matrix[2][1] * matrix[3][2] - matrix[1][1] * matrix[2][2] * matrix[3][0] - matrix[1][2] * matrix[2][0] * matrix[3][1])`~op~`d, + (matrix[0][0] * matrix[2][1] * matrix[3][2] + matrix[0][1] * matrix[2][2] * matrix[3][0] + matrix[0][2] * matrix[2][0] * matrix[3][1] + - matrix[0][0] * matrix[2][2] * matrix[3][1] - matrix[0][1] * matrix[2][0] * matrix[3][2] - matrix[0][2] * matrix[2][1] * matrix[3][0])`~op~`d, + (matrix[0][0] * matrix[1][2] * matrix[3][1] + matrix[0][1] * matrix[1][0] * matrix[3][2] + matrix[0][2] * matrix[1][1] * matrix[3][0] + - matrix[0][0] * matrix[1][1] * matrix[3][2] - matrix[0][1] * matrix[1][2] * matrix[3][0] - matrix[0][2] * matrix[1][0] * matrix[3][1])`~op~`d, + (matrix[0][0] * matrix[1][1] * matrix[2][2] + matrix[0][1] * matrix[1][2] * matrix[2][0] + matrix[0][2] * matrix[1][0] * matrix[2][1] + - matrix[0][0] * matrix[1][2] * matrix[2][1] - matrix[0][1] * matrix[1][0] * matrix[2][2] - matrix[0][2] * matrix[1][1] * matrix[2][0])`~op~`d]]; + `); + + return mat; + } + + // some static fun ... + // (1) glprogramming.com/red/appendixf.html - ortographic is broken! + // (2) http://fly.cc.fer.hr/~unreal/theredbook/appendixg.html + // (3) http://en.wikipedia.org/wiki/Orthographic_projection_(geometry) + + static if(isFloatingPoint!mt) { + static private mt[6] cperspective(mt width, mt height, mt fov, mt near, mt far) + in { assert(height != 0); } + body { + mt aspect = width/height; + mt top = near * tan(fov*(PI/360.0)); + mt bottom = -top; + mt right = top * aspect; + mt left = -right; + + return [left, right, bottom, top, near, far]; + } + + /// Returns a perspective matrix (4x4 and floating-point matrices only). + static Matrix perspective(mt width, mt height, mt fov, mt near, mt far) { + mt[6] cdata = cperspective(width, height, fov, near, far); + return perspective(cdata[0], cdata[1], cdata[2], cdata[3], cdata[4], cdata[5]); + } + + /// ditto + static Matrix perspective(mt left, mt right, mt bottom, mt top, mt near, mt far) + in { + assert(right-left != 0); + assert(top-bottom != 0); + assert(far-near != 0); + } + body { + Matrix ret; + ret.clear(0); + + ret.matrix[0][0] = (2*near)/(right-left); + ret.matrix[0][2] = (right+left)/(right-left); + ret.matrix[1][1] = (2*near)/(top-bottom); + ret.matrix[1][2] = (top+bottom)/(top-bottom); + ret.matrix[2][2] = -(far+near)/(far-near); + ret.matrix[2][3] = -(2*far*near)/(far-near); + ret.matrix[3][2] = -1; + + return ret; + } + + /// Returns an inverse perspective matrix (4x4 and floating-point matrices only). + static Matrix perspective_inverse(mt width, mt height, mt fov, mt near, mt far) { + mt[6] cdata = cperspective(width, height, fov, near, far); + return perspective_inverse(cdata[0], cdata[1], cdata[2], cdata[3], cdata[4], cdata[5]); + } + + /// ditto + static Matrix perspective_inverse(mt left, mt right, mt bottom, mt top, mt near, mt far) + in { + assert(near != 0); + assert(far != 0); + } + body { + Matrix ret; + ret.clear(0); + + ret.matrix[0][0] = (right-left)/(2*near); + ret.matrix[0][3] = (right+left)/(2*near); + ret.matrix[1][1] = (top-bottom)/(2*near); + ret.matrix[1][3] = (top+bottom)/(2*near); + ret.matrix[2][3] = -1; + ret.matrix[3][2] = -(far-near)/(2*far*near); + ret.matrix[3][3] = (far+near)/(2*far*near); + + return ret; + } + + // (2) and (3) say this one is correct + /// Returns an orthographic matrix (4x4 and floating-point matrices only). + static Matrix orthographic(mt left, mt right, mt bottom, mt top, mt near, mt far) + in { + assert(right-left != 0); + assert(top-bottom != 0); + assert(far-near != 0); + } + body { + Matrix ret; + ret.clear(0); + + ret.matrix[0][0] = 2/(right-left); + ret.matrix[0][3] = -(right+left)/(right-left); + ret.matrix[1][1] = 2/(top-bottom); + ret.matrix[1][3] = -(top+bottom)/(top-bottom); + ret.matrix[2][2] = -2/(far-near); + ret.matrix[2][3] = -(far+near)/(far-near); + ret.matrix[3][3] = 1; + + return ret; + } + + // (1) and (2) say this one is correct + /// Returns an inverse ortographic matrix (4x4 and floating-point matrices only). + static Matrix orthographic_inverse(mt left, mt right, mt bottom, mt top, mt near, mt far) { + Matrix ret; + ret.clear(0); + + ret.matrix[0][0] = (right-left)/2; + ret.matrix[0][3] = (right+left)/2; + ret.matrix[1][1] = (top-bottom)/2; + ret.matrix[1][3] = (top+bottom)/2; + ret.matrix[2][2] = (far-near)/-2; + ret.matrix[2][3] = (far+near)/2; + ret.matrix[3][3] = 1; + + return ret; + } + + /// Returns a look at matrix (4x4 and floating-point matrices only). + static Matrix look_at(Vector!(mt, 3) eye, Vector!(mt, 3) target, Vector!(mt, 3) up) { + alias Vector!(mt, 3) vec3mt; + vec3mt look_dir = (target - eye).normalized; + vec3mt up_dir = up.normalized; + + vec3mt right_dir = cross(look_dir, up_dir).normalized; + vec3mt perp_up_dir = cross(right_dir, look_dir); + + Matrix ret = Matrix.identity; + ret.matrix[0][0..3] = right_dir.vector[]; + ret.matrix[1][0..3] = perp_up_dir.vector[]; + ret.matrix[2][0..3] = (-look_dir).vector[]; + + ret.matrix[0][3] = -dot(eye, right_dir); + ret.matrix[1][3] = -dot(eye, perp_up_dir); + ret.matrix[2][3] = dot(eye, look_dir); + + return ret; + } + + unittest { + mt[6] cp = cperspective(600f, 900f, 60f, 1f, 100f); + assert(cp[4] == 1.0f); + assert(cp[5] == 100.0f); + assert(cp[0] == -cp[1]); + assert((cp[0] < -0.38489f) && (cp[0] > -0.38491f)); + assert(cp[2] == -cp[3]); + assert((cp[2] < -0.577349f) && (cp[2] > -0.577351f)); + + assert(mat4.perspective(600f, 900f, 60.0, 1.0, 100.0) == mat4.perspective(cp[0], cp[1], cp[2], cp[3], cp[4], cp[5])); + float[4][4] m4p = mat4.perspective(600f, 900f, 60.0, 1.0, 100.0).matrix; + assert((m4p[0][0] < 2.598077f) && (m4p[0][0] > 2.598075f)); + assert(m4p[0][2] == 0.0f); + assert((m4p[1][1] < 1.732052) && (m4p[1][1] > 1.732050)); + assert(m4p[1][2] == 0.0f); + assert((m4p[2][2] < -1.020201) && (m4p[2][2] > -1.020203)); + assert((m4p[2][3] < -2.020201) && (m4p[2][3] > -2.020203)); + assert((m4p[3][2] < -0.9f) && (m4p[3][2] > -1.1f)); + + float[4][4] m4pi = mat4.perspective_inverse(600f, 900f, 60.0, 1.0, 100.0).matrix; + assert((m4pi[0][0] < 0.384901) && (m4pi[0][0] > 0.384899)); + assert(m4pi[0][3] == 0.0f); + assert((m4pi[1][1] < 0.577351) && (m4pi[1][1] > 0.577349)); + assert(m4pi[1][3] == 0.0f); + assert(m4pi[2][3] == -1.0f); + assert((m4pi[3][2] < -0.494999) && (m4pi[3][2] > -0.495001)); + assert((m4pi[3][3] < 0.505001) && (m4pi[3][3] > 0.504999)); + + // maybe the next tests should be improved + float[4][4] m4o = mat4.orthographic(-1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f).matrix; + assert(m4o == [[1.0f, 0.0f, 0.0f, 0.0f], + [0.0f, 1.0f, 0.0f, 0.0f], + [0.0f, 0.0f, -1.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + + float[4][4] m4oi = mat4.orthographic_inverse(-1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f).matrix; + assert(m4oi == [[1.0f, 0.0f, 0.0f, 0.0f], + [0.0f, 1.0f, 0.0f, 0.0f], + [0.0f, 0.0f, -1.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + + //TODO: look_at tests + } + } + } + + static if((rows == cols) && (rows >= 3) && (rows <= 4)) { + /// Returns a translation matrix (3x3 and 4x4 matrices). + static Matrix translation(mt x, mt y, mt z) { + Matrix ret = Matrix.identity; + + ret.matrix[0][cols-1] = x; + ret.matrix[1][cols-1] = y; + ret.matrix[2][cols-1] = z; + + return ret; + } + + /// ditto + static Matrix translation(Vector!(mt, 3) v) { + Matrix ret = Matrix.identity; + + ret.matrix[0][cols-1] = v.x; + ret.matrix[1][cols-1] = v.y; + ret.matrix[2][cols-1] = v.z; + + return ret; + } + + /// Applys a translation on the current matrix and returns $(I this) (3x3 and 4x4 matrices). + Matrix translate(mt x, mt y, mt z) { + this = Matrix.translation(x, y, z) * this; + return this; + } + + /// ditto + Matrix translate(Vector!(mt, 3) v) { + this = Matrix.translation(v) * this; + return this; + } + + /// Returns a scaling matrix (3x3 and 4x4 matrices); + static Matrix scaling(mt x, mt y, mt z) { + Matrix ret = Matrix.identity; + + ret.matrix[0][0] = x; + ret.matrix[1][1] = y; + ret.matrix[2][2] = z; + + return ret; + } + + /// Applys a scale to the current matrix and returns $(I this) (3x3 and 4x4 matrices). + Matrix scale(mt x, mt y, mt z) { + this = Matrix.scaling(x, y, z) * this; + return this; + } + + unittest { + mat3 m3 = mat3.identity; + assert(m3.translate(1.0f, 2.0f, 3.0f).matrix == mat3.translation(1.0f, 2.0f, 3.0f).matrix); + assert(mat3.translation(1.0f, 2.0f, 3.0f).matrix == [[1.0f, 0.0f, 1.0f], + [0.0f, 1.0f, 2.0f], + [0.0f, 0.0f, 3.0f]]); + assert(mat3.identity.translate(0.0f, 1.0f, 2.0f).matrix == mat3.translation(0.0f, 1.0f, 2.0f).matrix); + + mat3 m31 = mat3.identity; + assert(m31.translate(vec3(1.0f, 2.0f, 3.0f)).matrix == mat3.translation(vec3(1.0f, 2.0f, 3.0f)).matrix); + assert(mat3.translation(vec3(1.0f, 2.0f, 3.0f)).matrix == [[1.0f, 0.0f, 1.0f], + [0.0f, 1.0f, 2.0f], + [0.0f, 0.0f, 3.0f]]); + assert(mat3.identity.translate(vec3(0.0f, 1.0f, 2.0f)).matrix == mat3.translation(vec3(0.0f, 1.0f, 2.0f)).matrix); + + assert(m3.scaling(0.0f, 1.0f, 2.0f).matrix == mat3.scaling(0.0f, 1.0f, 2.0f).matrix); + assert(mat3.scaling(0.0f, 1.0f, 2.0f).matrix == [[0.0f, 0.0f, 0.0f], + [0.0f, 1.0f, 0.0f], + [0.0f, 0.0f, 2.0f]]); + assert(mat3.identity.scale(0.0f, 1.0f, 2.0f).matrix == mat3.scaling(0.0f, 1.0f, 2.0f).matrix); + + // same tests for 4x4 + + mat4 m4 = mat4(1.0f); + assert(m4.translation(1.0f, 2.0f, 3.0f).matrix == mat4.translation(1.0f, 2.0f, 3.0f).matrix); + assert(mat4.translation(1.0f, 2.0f, 3.0f).matrix == [[1.0f, 0.0f, 0.0f, 1.0f], + [0.0f, 1.0f, 0.0f, 2.0f], + [0.0f, 0.0f, 1.0f, 3.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + assert(mat4.identity.translate(0.0f, 1.0f, 2.0f).matrix == mat4.translation(0.0f, 1.0f, 2.0f).matrix); + + assert(m4.scaling(0.0f, 1.0f, 2.0f).matrix == mat4.scaling(0.0f, 1.0f, 2.0f).matrix); + assert(mat4.scaling(0.0f, 1.0f, 2.0f).matrix == [[0.0f, 0.0f, 0.0f, 0.0f], + [0.0f, 1.0f, 0.0f, 0.0f], + [0.0f, 0.0f, 2.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + assert(mat4.identity.scale(0.0f, 1.0f, 2.0f).matrix == mat4.scaling(0.0f, 1.0f, 2.0f).matrix); + } + } + + + static if((rows == cols) && (rows >= 3)) { + static if(isFloatingPoint!mt) { + /// Returns an identity matrix with an applied rotate_axis around an arbitrary axis (nxn matrices, n >= 3). + static Matrix rotation(real alpha, Vector!(mt, 3) axis) { + Matrix mult = Matrix.identity; + + if(axis.length != 1) { + axis.normalize(); + } + + real cosa = cos(alpha); + real sina = sin(alpha); + + Vector!(mt, 3) temp = (1 - cosa)*axis; + + mult.matrix[0][0] = to!mt(cosa + temp.x * axis.x); + mult.matrix[0][1] = to!mt( temp.x * axis.y + sina * axis.z); + mult.matrix[0][2] = to!mt( temp.x * axis.z - sina * axis.y); + mult.matrix[1][0] = to!mt( temp.y * axis.x - sina * axis.z); + mult.matrix[1][1] = to!mt(cosa + temp.y * axis.y); + mult.matrix[1][2] = to!mt( temp.y * axis.z + sina * axis.x); + mult.matrix[2][0] = to!mt( temp.z * axis.x + sina * axis.y); + mult.matrix[2][1] = to!mt( temp.z * axis.y - sina * axis.x); + mult.matrix[2][2] = to!mt(cosa + temp.z * axis.z); + + return mult; + } + + /// ditto + static Matrix rotation(real alpha, mt x, mt y, mt z) { + return Matrix.rotation(alpha, Vector!(mt, 3)(x, y, z)); + } + + /// Returns an identity matrix with an applied rotation around the x-axis (nxn matrices, n >= 3). + static Matrix xrotation(real alpha) { + Matrix mult = Matrix.identity; + + mt cosamt = to!mt(cos(alpha)); + mt sinamt = to!mt(sin(alpha)); + + mult.matrix[1][1] = cosamt; + mult.matrix[1][2] = -sinamt; + mult.matrix[2][1] = sinamt; + mult.matrix[2][2] = cosamt; + + return mult; + } + + /// Returns an identity matrix with an applied rotation around the y-axis (nxn matrices, n >= 3). + static Matrix yrotation(real alpha) { + Matrix mult = Matrix.identity; + + mt cosamt = to!mt(cos(alpha)); + mt sinamt = to!mt(sin(alpha)); + + mult.matrix[0][0] = cosamt; + mult.matrix[0][2] = sinamt; + mult.matrix[2][0] = -sinamt; + mult.matrix[2][2] = cosamt; + + return mult; + } + + /// Returns an identity matrix with an applied rotation around the z-axis (nxn matrices, n >= 3). + static Matrix zrotation(real alpha) { + Matrix mult = Matrix.identity; + + mt cosamt = to!mt(cos(alpha)); + mt sinamt = to!mt(sin(alpha)); + + mult.matrix[0][0] = cosamt; + mult.matrix[0][1] = -sinamt; + mult.matrix[1][0] = sinamt; + mult.matrix[1][1] = cosamt; + + return mult; + } + + Matrix rotate(real alpha, Vector!(mt, 3) axis) { + this = rotation(alpha, axis) * this; + return this; + } + + /// Rotates the current matrix around the x-axis and returns $(I this) (nxn matrices, n >= 3). + Matrix rotatex(real alpha) { + this = xrotation(alpha) * this; + return this; + } + + /// Rotates the current matrix around the y-axis and returns $(I this) (nxn matrices, n >= 3). + Matrix rotatey(real alpha) { + this = yrotation(alpha) * this; + return this; + } + + /// Rotates the current matrix around the z-axis and returns $(I this) (nxn matrices, n >= 3). + Matrix rotatez(real alpha) { + this = zrotation(alpha) * this; + return this; + } + + unittest { + assert(mat4.xrotation(0).matrix == [[1.0f, 0.0f, 0.0f, 0.0f], + [0.0f, 1.0f, -0.0f, 0.0f], + [0.0f, 0.0f, 1.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + assert(mat4.yrotation(0).matrix == [[1.0f, 0.0f, 0.0f, 0.0f], + [0.0f, 1.0f, 0.0f, 0.0f], + [0.0f, 0.0f, 1.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + assert(mat4.zrotation(0).matrix == [[1.0f, -0.0f, 0.0f, 0.0f], + [0.0f, 1.0f, 0.0f, 0.0f], + [0.0f, 0.0f, 1.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + mat4 xro = mat4.identity; + xro.rotatex(0); + assert(mat4.xrotation(0).matrix == xro.matrix); + assert(xro.matrix == mat4.identity.rotatex(0).matrix); + assert(xro.matrix == mat4.rotation(0, vec3(1.0f, 0.0f, 0.0f)).matrix); + mat4 yro = mat4.identity; + yro.rotatey(0); + assert(mat4.yrotation(0).matrix == yro.matrix); + assert(yro.matrix == mat4.identity.rotatey(0).matrix); + assert(yro.matrix == mat4.rotation(0, vec3(0.0f, 1.0f, 0.0f)).matrix); + mat4 zro = mat4.identity; + xro.rotatez(0); + assert(mat4.zrotation(0).matrix == zro.matrix); + assert(zro.matrix == mat4.identity.rotatez(0).matrix); + assert(zro.matrix == mat4.rotation(0, vec3(0.0f, 0.0f, 1.0f)).matrix); + } + } // isFloatingPoint + + + /// Sets the translation of the matrix (nxn matrices, n >= 3). + void set_translation(mt[] values...) // intended to be a property + in { assert(values.length >= (rows-1)); } + body { + foreach(r; TupleRange!(0, rows-1)) { + matrix[r][rows-1] = values[r]; + } + } + + /// Copyies the translation from mat to the current matrix (nxn matrices, n >= 3). + void set_translation(Matrix mat) { + foreach(r; TupleRange!(0, rows-1)) { + matrix[r][rows-1] = mat.matrix[r][rows-1]; + } + } + + /// Returns an identity matrix with the current translation applied (nxn matrices, n >= 3).. + Matrix get_translation() { + Matrix ret = Matrix.identity; + + foreach(r; TupleRange!(0, rows-1)) { + ret.matrix[r][rows-1] = matrix[r][rows-1]; + } + + return ret; + } + + unittest { + mat3 m3 = mat3(0.0f, 1.0f, 2.0f, + 3.0f, 4.0f, 5.0f, + 6.0f, 7.0f, 1.0f); + assert(m3.get_translation().matrix == [[1.0f, 0.0f, 2.0f], [0.0f, 1.0f, 5.0f], [0.0f, 0.0f, 1.0f]]); + m3.set_translation(mat3.identity); + assert(mat3.identity.matrix == m3.get_translation().matrix); + m3.set_translation([2.0f, 5.0f]); + assert(m3.get_translation().matrix == [[1.0f, 0.0f, 2.0f], [0.0f, 1.0f, 5.0f], [0.0f, 0.0f, 1.0f]]); + assert(mat3.identity.matrix == mat3.identity.get_translation().matrix); + + mat4 m4 = mat4(0.0f, 1.0f, 2.0f, 3.0f, + 4.0f, 5.0f, 6.0f, 7.0f, + 8.0f, 9.0f, 10.0f, 11.0f, + 12.0f, 13.0f, 14.0f, 1.0f); + assert(m4.get_translation().matrix == [[1.0f, 0.0f, 0.0f, 3.0f], + [0.0f, 1.0f, 0.0f, 7.0f], + [0.0f, 0.0f, 1.0f, 11.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + m4.set_translation(mat4.identity); + assert(mat4.identity.matrix == m4.get_translation().matrix); + m4.set_translation([3.0f, 7.0f, 11.0f]); + assert(m4.get_translation().matrix == [[1.0f, 0.0f, 0.0f, 3.0f], + [0.0f, 1.0f, 0.0f, 7.0f], + [0.0f, 0.0f, 1.0f, 11.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + assert(mat4.identity.matrix == mat4.identity.get_translation().matrix); + } + + /// Sets the scale of the matrix (nxn matrices, n >= 3). + void set_scale(mt[] values...) + in { assert(values.length >= (rows-1)); } + body { + foreach(r; TupleRange!(0, rows-1)) { + matrix[r][r] = values[r]; + } + } + + /// Copyies the scale from mat to the current matrix (nxn matrices, n >= 3). + void set_scale(Matrix mat) { + foreach(r; TupleRange!(0, rows-1)) { + matrix[r][r] = mat.matrix[r][r]; + } + } + + /// Returns an identity matrix with the current scale applied (nxn matrices, n >= 3). + Matrix get_scale() { + Matrix ret = Matrix.identity; + + foreach(r; TupleRange!(0, rows-1)) { + ret.matrix[r][r] = matrix[r][r]; + } + + return ret; + } + + unittest { + mat3 m3 = mat3(0.0f, 1.0f, 2.0f, + 3.0f, 4.0f, 5.0f, + 6.0f, 7.0f, 1.0f); + assert(m3.get_scale().matrix == [[0.0f, 0.0f, 0.0f], [0.0f, 4.0f, 0.0f], [0.0f, 0.0f, 1.0f]]); + m3.set_scale(mat3.identity); + assert(mat3.identity.matrix == m3.get_scale().matrix); + m3.set_scale([0.0f, 4.0f]); + assert(m3.get_scale().matrix == [[0.0f, 0.0f, 0.0f], [0.0f, 4.0f, 0.0f], [0.0f, 0.0f, 1.0f]]); + assert(mat3.identity.matrix == mat3.identity.get_scale().matrix); + + mat4 m4 = mat4(0.0f, 1.0f, 2.0f, 3.0f, + 4.0f, 5.0f, 6.0f, 7.0f, + 8.0f, 9.0f, 10.0f, 11.0f, + 12.0f, 13.0f, 14.0f, 1.0f); + assert(m4.get_scale().matrix == [[0.0f, 0.0f, 0.0f, 0.0f], + [0.0f, 5.0f, 0.0f, 0.0f], + [0.0f, 0.0f, 10.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + m4.set_scale(mat4.identity); + assert(mat4.identity.matrix == m4.get_scale().matrix); + m4.set_scale([0.0f, 5.0f, 10.0f]); + assert(m4.get_scale().matrix == [[0.0f, 0.0f, 0.0f, 0.0f], + [0.0f, 5.0f, 0.0f, 0.0f], + [0.0f, 0.0f, 10.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + assert(mat4.identity.matrix == mat4.identity.get_scale().matrix); + } + + /// Copies rot into the upper left corner, the translation (nxn matrices, n >= 3). + void set_rotation(Matrix!(mt, 3, 3) rot) { + foreach(r; TupleRange!(0, 3)) { + foreach(c; TupleRange!(0, 3)) { + matrix[r][c] = rot[r][c]; + } + } + } + + /// Returns an identity matrix with the current rotation applied (nxn matrices, n >= 3). + Matrix!(mt, 3, 3) get_rotation() { + Matrix!(mt, 3, 3) ret = Matrix!(mt, 3, 3).identity; + + foreach(r; TupleRange!(0, 3)) { + foreach(c; TupleRange!(0, 3)) { + ret.matrix[r][c] = matrix[r][c]; + } + } + + return ret; + } + + unittest { + mat3 m3 = mat3(0.0f, 1.0f, 2.0f, + 3.0f, 4.0f, 5.0f, + 6.0f, 7.0f, 1.0f); + assert(m3.get_rotation().matrix == [[0.0f, 1.0f, 2.0f], [3.0f, 4.0f, 5.0f], [6.0f, 7.0f, 1.0f]]); + m3.set_rotation(mat3.identity); + assert(mat3.identity.matrix == m3.get_rotation().matrix); + m3.set_rotation(mat3(0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 1.0f)); + assert(m3.get_rotation().matrix == [[0.0f, 1.0f, 2.0f], [3.0f, 4.0f, 5.0f], [6.0f, 7.0f, 1.0f]]); + assert(mat3.identity.matrix == mat3.identity.get_rotation().matrix); + + mat4 m4 = mat4(0.0f, 1.0f, 2.0f, 3.0f, + 4.0f, 5.0f, 6.0f, 7.0f, + 8.0f, 9.0f, 10.0f, 11.0f, + 12.0f, 13.0f, 14.0f, 1.0f); + assert(m4.get_rotation().matrix == [[0.0f, 1.0f, 2.0f], [4.0f, 5.0f, 6.0f], [8.0f, 9.0f, 10.0f]]); + m4.set_rotation(mat3.identity); + assert(mat3.identity.matrix == m4.get_rotation().matrix); + m4.set_rotation(mat3(0.0f, 1.0f, 2.0f, 4.0f, 5.0f, 6.0f, 8.0f, 9.0f, 10.0f)); + assert(m4.get_rotation().matrix == [[0.0f, 1.0f, 2.0f], [4.0f, 5.0f, 6.0f], [8.0f, 9.0f, 10.0f]]); + assert(mat3.identity.matrix == mat4.identity.get_rotation().matrix); + } + + } + + static if((rows == cols) && (rows >= 2) && (rows <= 4)) { + /// Returns an inverted copy of the current matrix (nxn matrices, 2 >= n <= 4). + @property Matrix inverse() const { + Matrix mat; + invert(mat); + return mat; + } + + /// Inverts the current matrix (nxn matrices, 2 >= n <= 4). + void invert() { + // workaround Issue #11238 + // uses a temporary instead of invert(this) + Matrix temp; + invert(temp); + this.matrix = temp.matrix; + } + } + + unittest { + mat2 m2 = mat2(1.0f, 2.0f, vec2(3.0f, 4.0f)); + assert(m2.det == -2.0f); + assert(m2.inverse.matrix == [[-2.0f, 1.0f], [1.5f, -0.5f]]); + + mat3 m3 = mat3(1.0f, -2.0f, 3.0f, + 7.0f, -1.0f, 0.0f, + 3.0f, 2.0f, -4.0f); + assert(m3.det == -1.0f); + assert(m3.inverse.matrix == [[-4.0f, 2.0f, -3.0f], + [-28.0f, 13.0f, -21.0f], + [-17.0f, 8.0f, -13.0f]]); + + mat4 m4 = mat4(1.0f, 2.0f, 3.0f, 4.0f, + -2.0f, 1.0f, 5.0f, -2.0f, + 2.0f, -1.0f, 7.0f, 1.0f, + 3.0f, -3.0f, 2.0f, 0.0f); + assert(m4.det == -8.0f); + assert(m4.inverse.matrix == [[6.875f, 7.875f, -11.75f, 11.125f], + [6.625f, 7.625f, -11.25f, 10.375f], + [-0.375f, -0.375f, 0.75f, -0.625f], + [-4.5f, -5.5f, 8.0f, -7.5f]]); + } + + private void mms(mt inp, ref Matrix mat) const { // mat * scalar + for(int r = 0; r < rows; r++) { + for(int c = 0; c < cols; c++) { + mat.matrix[r][c] = matrix[r][c] * inp; + } + } + } + + private void masm(string op)(Matrix inp, ref Matrix mat) const { // mat + or - mat + foreach(r; TupleRange!(0, rows)) { + foreach(c; TupleRange!(0, cols)) { + mat.matrix[r][c] = mixin("inp.matrix[r][c]" ~ op ~ "matrix[r][c]"); + } + } + } + + Matrix!(mt, rows, T.cols) opBinary(string op : "*", T)(T inp) const if(isCompatibleMatrix!T && (T.rows == cols)) { + Matrix!(mt, rows, T.cols) ret; + + foreach(r; TupleRange!(0, rows)) { + foreach(c; TupleRange!(0, T.cols)) { + ret.matrix[r][c] = 0; + + foreach(c2; TupleRange!(0, cols)) { + ret.matrix[r][c] += matrix[r][c2] * inp.matrix[c2][c]; + } + } + } + + return ret; + } + + Vector!(mt, rows) opBinary(string op : "*", T : Vector!(mt, cols))(T inp) const { + Vector!(mt, rows) ret; + ret.clear(0); + + foreach(c; TupleRange!(0, cols)) { + foreach(r; TupleRange!(0, rows)) { + ret.vector[r] += matrix[r][c] * inp.vector[c]; + } + } + + return ret; + } + + /+Vector!(mt, rows) opBinaryRight(string op : "*", T : Vector!(mt, cols))(T inp) const { + return opBinary!(op,T)(inp); + }+/ + + Matrix opBinary(string op : "*")(mt inp) const { + Matrix ret; + mms(inp, ret); + return ret; + } + + Matrix opBinaryRight(string op : "*")(mt inp) const { + return this.opBinary!(op)(inp); + } + + Matrix opBinary(string op)(Matrix inp) const if((op == "+") || (op == "-")) { + Matrix ret; + masm!(op)(inp, ret); + return ret; + } + + void opOpAssign(string op : "*")(mt inp) { + mms(inp, this); + } + + void opOpAssign(string op)(Matrix inp) if((op == "+") || (op == "-")) { + masm!(op)(inp, this); + } + + void opOpAssign(string op)(Matrix inp) if(op == "*") { + this = this * inp; + } + + unittest { + mat2 m2 = mat2(1.0f, 2.0f, 3.0f, 4.0f); + vec2 v2 = vec2(2.0f, 2.0f); + assert((m2*2).matrix == [[2.0f, 4.0f], [6.0f, 8.0f]]); + assert((2*m2).matrix == (m2*2).matrix); + m2 *= 2; + assert(m2.matrix == [[2.0f, 4.0f], [6.0f, 8.0f]]); + assert((m2*v2).vector == [12.0f, 28.0f]); + assert((v2*m2).vector == [16.0f, 24.0f]); + assert((m2*m2).matrix == [[28.0f, 40.0f], [60.0f, 88.0f]]); + assert((m2-m2).matrix == [[0.0f, 0.0f], [0.0f, 0.0f]]); + assert((m2+m2).matrix == [[4.0f, 8.0f], [12.0f, 16.0f]]); + m2 += m2; + assert(m2.matrix == [[4.0f, 8.0f], [12.0f, 16.0f]]); + m2 -= m2; + assert(m2.matrix == [[0.0f, 0.0f], [0.0f, 0.0f]]); + + mat3 m3 = mat3(1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f); + vec3 v3 = vec3(2.0f, 2.0f, 2.0f); + assert((m3*2).matrix == [[2.0f, 4.0f, 6.0f], [8.0f, 10.0f, 12.0f], [14.0f, 16.0f, 18.0f]]); + assert((2*m3).matrix == (m3*2).matrix); + m3 *= 2; + assert(m3.matrix == [[2.0f, 4.0f, 6.0f], [8.0f, 10.0f, 12.0f], [14.0f, 16.0f, 18.0f]]); + assert((m3*v3).vector == [24.0f, 60.0f, 96.0f]); + assert((v3*m3).vector == [48.0f, 60.0f, 72.0f]); + assert((m3*m3).matrix == [[120.0f, 144.0f, 168.0f], [264.0f, 324.0f, 384.0f], [408.0f, 504.0f, 600.0f]]); + assert((m3-m3).matrix == [[0.0f, 0.0f, 0.0f], [0.0f, 0.0f, 0.0f], [0.0f, 0.0f, 0.0f]]); + assert((m3+m3).matrix == [[4.0f, 8.0f, 12.0f], [16.0f, 20.0f, 24.0f], [28.0f, 32.0f, 36.0f]]); + m3 += m3; + assert(m3.matrix == [[4.0f, 8.0f, 12.0f], [16.0f, 20.0f, 24.0f], [28.0f, 32.0f, 36.0f]]); + m3 -= m3; + assert(m3.matrix == [[0.0f, 0.0f, 0.0f], [0.0f, 0.0f, 0.0f], [0.0f, 0.0f, 0.0f]]); + + // test opOpAssign for matrix multiplication + auto m4 = mat4.translation(0,1,2); + m4 *= mat4.translation(0,-1,2); + assert(m4 == mat4.translation(0,0,4)); + + //TODO: tests for mat4, mat34 + } + + // opEqual => "alias matrix this;" + + bool opCast(T : bool)() const { + return isFinite; + } + + unittest { + assert(mat2(1.0f, 2.0f, 1.0f, 1.0f) == mat2(1.0f, 2.0f, 1.0f, 1.0f)); + assert(mat2(1.0f, 2.0f, 1.0f, 1.0f) != mat2(1.0f, 1.0f, 1.0f, 1.0f)); + + assert(mat3(1.0f) == mat3(1.0f)); + assert(mat3(1.0f) != mat3(2.0f)); + + assert(mat4(1.0f) == mat4(1.0f)); + assert(mat4(1.0f) != mat4(2.0f)); + + assert(!(mat4(float.nan))); + if(mat4(1.0f)) { } + else { assert(false); } + } + +} + +/// Pre-defined matrix types, the first number represents the number of rows +/// and the second the number of columns, if there's just one it's a nxn matrix. +/// All of these matrices are floating-point matrices. +alias Matrix!(float, 2, 2) mat2; +alias Matrix!(float, 3, 3) mat3; +alias Matrix!(float, 3, 4) mat34; +alias Matrix!(float, 4, 4) mat4; + +private unittest { + Matrix!(float, 1, 1) A = 1; + Matrix!(double, 1, 1) B = 1; + Matrix!(real, 1, 1) C = 1; + Matrix!(int, 1, 1) D = 1; + Matrix!(float, 5, 1) E = 1; + Matrix!(double, 5, 1) F = 1; + Matrix!(real, 5, 1) G = 1; + Matrix!(int, 5, 1) H = 1; + Matrix!(float, 1, 5) I = 1; + Matrix!(double, 1, 5) J = 1; + Matrix!(real, 1, 5) K = 1; + Matrix!(int, 1, 5) L = 1; +} diff --git a/gl3n/linalg/package.d b/gl3n/linalg/package.d new file mode 100644 index 0000000..e5472b3 --- /dev/null +++ b/gl3n/linalg/package.d @@ -0,0 +1,23 @@ +/** +gl3n.linalg.matrix + +Special thanks to: +$(UL + $(LI Tomasz Stachowiak (h3r3tic): allowed me to use parts of $(LINK2 https://bitbucket.org/h3r3tic/boxen/src/default/src/xf/omg, omg).) + $(LI Jakob Øvrum (jA_cOp): improved the code a lot!) + $(LI Florian Boesch (___doc__): helps me to understand opengl/complex maths better, see: $(LINK http://codeflow.org/).) + $(LI #D on freenode: answered general questions about D.) +) + +Authors: David Herberth, Stephan Dilly +License: MIT + +Note: All methods marked with pure are weakly pure since, they all access an instance member. +All static methods are strongly pure. +*/ + +module gl3n.linalg; + +public import gl3n.linalg.vec; +public import gl3n.linalg.matrix; +public import gl3n.linalg.quaternion; \ No newline at end of file diff --git a/gl3n/linalg/quaternion.d b/gl3n/linalg/quaternion.d new file mode 100644 index 0000000..01198a4 --- /dev/null +++ b/gl3n/linalg/quaternion.d @@ -0,0 +1,645 @@ +/** +gl3n.linalg.quaternion + +Special thanks to: +$(UL + $(LI Tomasz Stachowiak (h3r3tic): allowed me to use parts of $(LINK2 https://bitbucket.org/h3r3tic/boxen/src/default/src/xf/omg, omg).) + $(LI Jakob Øvrum (jA_cOp): improved the code a lot!) + $(LI Florian Boesch (___doc__): helps me to understand opengl/complex maths better, see: $(LINK http://codeflow.org/).) + $(LI #D on freenode: answered general questions about D.) +) + +Authors: David Herberth, Stephan Dilly +License: MIT + +Note: All methods marked with pure are weakly pure since, they all access an instance member. +All static methods are strongly pure. +*/ + +module gl3n.linalg.quaternion; + +import gl3n.linalg.vec; +import gl3n.linalg.matrix; +import gl3n.math : atan2, asin, almost_equal; + +/// Base template for all quaternion-types. +/// Params: +/// type = all values get stored as this type +struct Quaternion(type) { + alias type qt; /// Holds the internal type of the quaternion. + + qt[4] quaternion; /// Holds the w, x, y and z coordinates. + + /// Returns a pointer to the quaternion in memory, it starts with the w coordinate. + @property auto value_ptr() const { return quaternion.ptr; } + + /// Returns the current vector formatted as string, useful for printing the quaternion. + @property string as_string() { + return format("%s", quaternion); + } + alias as_string toString; + + @safe pure nothrow: + private @property qt get_(char coord)() const { + return quaternion[coord_to_index!coord]; + } + private @property void set_(char coord)(qt value) { + quaternion[coord_to_index!coord] = value; + } + + alias get_!'w' w; /// static properties to access the values. + alias set_!'w' w; + alias get_!'x' x; /// ditto + alias set_!'x' x; + alias get_!'y' y; /// ditto + alias set_!'y' y; + alias get_!'z' z; /// ditto + alias set_!'z' z; + + /// Constructs the quaternion. + /// Takes a 4-dimensional vector, where vector.x = the quaternions w coordinate, + /// or a w coordinate of type $(I qt) and a 3-dimensional vector representing the imaginary part, + /// or 4 values of type $(I qt). + this(qt w_, qt x_, qt y_, qt z_) { + w = w_; + x = x_; + y = y_; + z = z_; + } + + /// ditto + this(qt w_, Vector!(qt, 3) vec) { + w = w_; + quaternion[1..4] = vec.vector[]; + } + + /// ditto + this(Vector!(qt, 4) vec) { + quaternion[] = vec.vector[]; + } + + /// Returns true if all values are not nan and finite, otherwise false. + @property bool isFinite() const { + foreach(q; quaternion) { + if(isNaN(q) || isInfinity(q)) { + return false; + } + } + return true; + } + deprecated("Use isFinite instead of ok") alias ok = isFinite; + + unittest { + quat q1 = quat(0.0f, 0.0f, 0.0f, 1.0f); + assert(q1.quaternion == [0.0f, 0.0f, 0.0f, 1.0f]); + assert(q1.quaternion == quat(0.0f, 0.0f, 0.0f, 1.0f).quaternion); + assert(q1.quaternion == quat(0.0f, vec3(0.0f, 0.0f, 1.0f)).quaternion); + assert(q1.quaternion == quat(vec4(0.0f, 0.0f, 0.0f, 1.0f)).quaternion); + + assert(q1.isFinite); + q1.x = float.infinity; + assert(!q1.isFinite); + q1.x = float.nan; + assert(!q1.isFinite); + q1.x = 0.0f; + assert(q1.isFinite); + } + + template coord_to_index(char c) { + static if(c == 'w') { + enum coord_to_index = 0; + } else static if(c == 'x') { + enum coord_to_index = 1; + } else static if(c == 'y') { + enum coord_to_index = 2; + } else static if(c == 'z') { + enum coord_to_index = 3; + } else { + static assert(false, "accepted coordinates are x, y, z and w not " ~ c ~ "."); + } + } + + /// Returns the squared magnitude of the quaternion. + @property real magnitude_squared() const { + return to!real(w^^2 + x^^2 + y^^2 + z^^2); + } + + /// Returns the magnitude of the quaternion. + @property real magnitude() const { + return sqrt(magnitude_squared); + } + + /// Returns an identity quaternion (w=1, x=0, y=0, z=0). + static @property Quaternion identity() { + return Quaternion(1, 0, 0, 0); + } + + /// Makes the current quaternion an identity quaternion. + void make_identity() { + w = 1; + x = 0; + y = 0; + z = 0; + } + + /// Inverts the quaternion. + void invert() { + x = -x; + y = -y; + z = -z; + } + alias invert conjugate; /// ditto + + /// Returns an inverted copy of the current quaternion. + @property Quaternion inverse() const { + return Quaternion(w, -x, -y, -z); + } + alias inverse conjugated; /// ditto + + unittest { + quat q1 = quat(1.0f, 1.0f, 1.0f, 1.0f); + + assert(q1.magnitude == 2.0f); + assert(q1.magnitude_squared == 4.0f); + assert(q1.magnitude == quat(0.0f, 0.0f, 2.0f, 0.0f).magnitude); + + quat q2 = quat.identity; + assert(q2.quaternion == [1.0f, 0.0f, 0.0f, 0.0f]); + assert(q2.x == 0.0f); + assert(q2.y == 0.0f); + assert(q2.z == 0.0f); + assert(q2.w == 1.0f); + + assert(q1.inverse.quaternion == [1.0f, -1.0f, -1.0f, -1.0f]); + q1.invert(); + assert(q1.quaternion == [1.0f, -1.0f, -1.0f, -1.0f]); + + q1.make_identity(); + assert(q1.quaternion == q2.quaternion); + + } + + /// Creates a quaternion from a 3x3 matrix. + /// Params: + /// matrix = 3x3 matrix (rotation) + /// Returns: A quaternion representing the rotation (3x3 matrix) + static Quaternion from_matrix(Matrix!(qt, 3, 3) matrix) { + Quaternion ret; + + auto mat = matrix.matrix; + qt trace = mat[0][0] + mat[1][1] + mat[2][2]; + + if(trace > 0) { + real s = 0.5 / sqrt(trace + 1.0f); + + ret.w = to!qt(0.25 / s); + ret.x = to!qt((mat[2][1] - mat[1][2]) * s); + ret.y = to!qt((mat[0][2] - mat[2][0]) * s); + ret.z = to!qt((mat[1][0] - mat[0][1]) * s); + } else if((mat[0][0] > mat[1][1]) && (mat[0][0] > mat[2][2])) { + real s = 2.0 * sqrt(1.0 + mat[0][0] - mat[1][1] - mat[2][2]); + + ret.w = to!qt((mat[2][1] - mat[1][2]) / s); + ret.x = to!qt(0.25f * s); + ret.y = to!qt((mat[0][1] + mat[1][0]) / s); + ret.z = to!qt((mat[0][2] + mat[2][0]) / s); + } else if(mat[1][1] > mat[2][2]) { + real s = 2.0 * sqrt(1 + mat[1][1] - mat[0][0] - mat[2][2]); + + ret.w = to!qt((mat[0][2] - mat[2][0]) / s); + ret.x = to!qt((mat[0][1] + mat[1][0]) / s); + ret.y = to!qt(0.25f * s); + ret.z = to!qt((mat[1][2] + mat[2][1]) / s); + } else { + real s = 2.0 * sqrt(1 + mat[2][2] - mat[0][0] - mat[1][1]); + + ret.w = to!qt((mat[1][0] - mat[0][1]) / s); + ret.x = to!qt((mat[0][2] + mat[2][0]) / s); + ret.y = to!qt((mat[1][2] + mat[2][1]) / s); + ret.z = to!qt(0.25f * s); + } + + return ret; + } + + /// Returns the quaternion as matrix. + /// Params: + /// rows = number of rows of the resulting matrix (min 3) + /// cols = number of columns of the resulting matrix (min 3) + Matrix!(qt, rows, cols) to_matrix(int rows, int cols)() const if((rows >= 3) && (cols >= 3)) { + static if((rows == 3) && (cols == 3)) { + Matrix!(qt, rows, cols) ret; + } else { + Matrix!(qt, rows, cols) ret = Matrix!(qt, rows, cols).identity; + } + + qt xx = x^^2; + qt xy = x * y; + qt xz = x * z; + qt xw = x * w; + qt yy = y^^2; + qt yz = y * z; + qt yw = y * w; + qt zz = z^^2; + qt zw = z * w; + + ret.matrix[0][0] = 1 - 2 * (yy + zz); + ret.matrix[0][1] = 2 * (xy - zw); + ret.matrix[0][2] = 2 * (xz + yw); + + ret.matrix[1][0] = 2 * (xy + zw); + ret.matrix[1][1] = 1 - 2 * (xx + zz); + ret.matrix[1][2] = 2 * (yz - xw); + + ret.matrix[2][0] = 2 * (xz - yw); + ret.matrix[2][1] = 2 * (yz + xw); + ret.matrix[2][2] = 1 - 2 * (xx + yy); + + return ret; + } + + unittest { + quat q1 = quat(4.0f, 1.0f, 2.0f, 3.0f); + + assert(q1.to_matrix!(3, 3).matrix == [[-25.0f, -20.0f, 22.0f], [28.0f, -19.0f, 4.0f], [-10.0f, 20.0f, -9.0f]]); + assert(q1.to_matrix!(4, 4).matrix == [[-25.0f, -20.0f, 22.0f, 0.0f], + [28.0f, -19.0f, 4.0f, 0.0f], + [-10.0f, 20.0f, -9.0f, 0.0f], + [0.0f, 0.0f, 0.0f, 1.0f]]); + assert(quat.identity.to_matrix!(3, 3).matrix == Matrix!(qt, 3, 3).identity.matrix); + assert(q1.quaternion == quat.from_matrix(q1.to_matrix!(3, 3)).quaternion); + + assert(quat(1.0f, 0.0f, 0.0f, 0.0f).quaternion == quat.from_matrix(mat3.identity).quaternion); + + quat q2 = quat.from_matrix(mat3(1.0f, 3.0f, 2.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f)); + assert(q2.x == 0.0f); + assert(almost_equal(q2.y, 0.7071067f)); + assert(almost_equal(q2.z, -1.060660)); + assert(almost_equal(q2.w, 0.7071067f)); + } + + /// Normalizes the current quaternion. + void normalize() { + qt m = to!qt(magnitude); + + if(m != 0) { + w = w / m; + x = x / m; + y = y / m; + z = z / m; + } + } + + /// Returns a normalized copy of the current quaternion. + Quaternion normalized() const { + Quaternion ret; + qt m = to!qt(magnitude); + + if(m != 0) { + ret.w = w / m; + ret.x = x / m; + ret.y = y / m; + ret.z = z / m; + } else { + ret = Quaternion(w, x, y, z); + } + + return ret; + } + + unittest { + quat q1 = quat(1.0f, 2.0f, 3.0f, 4.0f); + quat q2 = quat(1.0f, 2.0f, 3.0f, 4.0f); + + q1.normalize(); + assert(q1.quaternion == q2.normalized.quaternion); + //assert(q1.quaternion == q1.normalized.quaternion); + assert(almost_equal(q1.magnitude, 1.0)); + } + + /// Returns the yaw. + @property real yaw() const { + return atan2(to!real(2.0*(w*z + x*y)), to!real(1.0 - 2.0*(y*y + z*z))); + } + + /// Returns the pitch. + @property real pitch() const { + return asin(to!real(2.0*(w*y - z*x))); + } + + /// Returns the roll. + @property real roll() const { + return atan2(to!real(2.0*(w*x + y*z)), to!real(1.0 - 2.0*(x*x + y*y))); + } + + unittest { + quat q1 = quat.identity; + assert(q1.pitch == 0.0f); + assert(q1.yaw == 0.0f); + assert(q1.roll == 0.0f); + + quat q2 = quat(1.0f, 1.0f, 1.0f, 1.0f); + assert(almost_equal(q2.yaw, q2.roll)); + //assert(almost_equal(q2.yaw, 1.570796f)); + assert(q2.pitch == 0.0f); + + quat q3 = quat(0.1f, 1.9f, 2.1f, 1.3f); + //assert(almost_equal(q3.yaw, 2.4382f)); + assert(isNaN(q3.pitch)); + //assert(almost_equal(q3.roll, 1.67719f)); + } + + /// Returns a quaternion with applied rotation around the x-axis. + static Quaternion xrotation(real alpha) { + Quaternion ret; + + alpha /= 2; + ret.w = to!qt(cos(alpha)); + ret.x = to!qt(sin(alpha)); + ret.y = 0; + ret.z = 0; + + return ret; + } + + /// Returns a quaternion with applied rotation around the y-axis. + static Quaternion yrotation(real alpha) { + Quaternion ret; + + alpha /= 2; + ret.w = to!qt(cos(alpha)); + ret.x = 0; + ret.y = to!qt(sin(alpha)); + ret.z = 0; + + return ret; + } + + /// Returns a quaternion with applied rotation around the z-axis. + static Quaternion zrotation(real alpha) { + Quaternion ret; + + alpha /= 2; + ret.w = to!qt(cos(alpha)); + ret.x = 0; + ret.y = 0; + ret.z = to!qt(sin(alpha)); + + return ret; + } + + /// Returns a quaternion with applied rotation around an axis. + static Quaternion axis_rotation(real alpha, Vector!(qt, 3) axis) { + if(alpha == 0) { + return Quaternion.identity; + } + Quaternion ret; + + alpha /= 2; + qt sinaqt = to!qt(sin(alpha)); + + ret.w = to!qt(cos(alpha)); + ret.x = axis.x * sinaqt; + ret.y = axis.y * sinaqt; + ret.z = axis.z * sinaqt; + + return ret; + } + + /// Creates a quaternion from an euler rotation. + static Quaternion euler_rotation(real roll, real pitch, real yaw) { + Quaternion ret; + + auto cr = cos(roll / 2.0); + auto cp = cos(pitch / 2.0); + auto cy = cos(yaw / 2.0); + auto sr = sin(roll / 2.0); + auto sp = sin(pitch / 2.0); + auto sy = sin(yaw / 2.0); + + ret.w = cr * cp * cy + sr * sp * sy; + ret.x = sr * cp * cy - cr * sp * sy; + ret.y = cr * sp * cy + sr * cp * sy; + ret.z = cr * cp * sy - sr * sp * cy; + + return ret; + } + + unittest { + enum startPitch = 0.1; + enum startYaw = -0.2; + enum startRoll = 0.6; + + auto q = quat.euler_rotation(startRoll,startPitch,startYaw); + + assert(almost_equal(q.pitch,startPitch)); + assert(almost_equal(q.yaw,startYaw)); + assert(almost_equal(q.roll,startRoll)); + } + + /// Rotates the current quaternion around the x-axis and returns $(I this). + Quaternion rotatex(real alpha) { + this = xrotation(alpha) * this; + return this; + } + + /// Rotates the current quaternion around the y-axis and returns $(I this). + Quaternion rotatey(real alpha) { + this = yrotation(alpha) * this; + return this; + } + + /// Rotates the current quaternion around the z-axis and returns $(I this). + Quaternion rotatez(real alpha) { + this = zrotation(alpha) * this; + return this; + } + + /// Rotates the current quaternion around an axis and returns $(I this). + Quaternion rotate_axis(real alpha, Vector!(qt, 3) axis) { + this = axis_rotation(alpha, axis) * this; + return this; + } + + /// Applies an euler rotation to the current quaternion and returns $(I this). + Quaternion rotate_euler(real heading, real attitude, real bank) { + this = euler_rotation(heading, attitude, bank) * this; + return this; + } + + unittest { + assert(quat.xrotation(PI).quaternion[1..4] == [1.0f, 0.0f, 0.0f]); + assert(quat.yrotation(PI).quaternion[1..4] == [0.0f, 1.0f, 0.0f]); + assert(quat.zrotation(PI).quaternion[1..4] == [0.0f, 0.0f, 1.0f]); + assert((quat.xrotation(PI).w == quat.yrotation(PI).w) && (quat.yrotation(PI).w == quat.zrotation(PI).w)); + //assert(quat.rotatex(PI).w == to!(quat.qt)(cos(PI))); + assert(quat.xrotation(PI).quaternion == quat.identity.rotatex(PI).quaternion); + assert(quat.yrotation(PI).quaternion == quat.identity.rotatey(PI).quaternion); + assert(quat.zrotation(PI).quaternion == quat.identity.rotatez(PI).quaternion); + + assert(quat.axis_rotation(PI, vec3(1.0f, 1.0f, 1.0f)).quaternion[1..4] == [1.0f, 1.0f, 1.0f]); + assert(quat.axis_rotation(PI, vec3(1.0f, 1.0f, 1.0f)).w == quat.xrotation(PI).w); + assert(quat.axis_rotation(PI, vec3(1.0f, 1.0f, 1.0f)).quaternion == + quat.identity.rotate_axis(PI, vec3(1.0f, 1.0f, 1.0f)).quaternion); + + quat q1 = quat.euler_rotation(PI, PI, PI); + assert((q1.x > -1e-16) && (q1.x < 1e-16)); + assert((q1.y > -1e-16) && (q1.y < 1e-16)); + assert((q1.z > -1e-16) && (q1.z < 1e-16)); + //assert(q1.w == -1.0f); + assert(quat.euler_rotation(PI, PI, PI).quaternion == quat.identity.rotate_euler(PI, PI, PI).quaternion); + } + + Quaternion opBinary(string op : "*")(Quaternion inp) const { + Quaternion ret; + + ret.w = -x * inp.x - y * inp.y - z * inp.z + w * inp.w; + ret.x = x * inp.w + y * inp.z - z * inp.y + w * inp.x; + ret.y = -x * inp.z + y * inp.w + z * inp.x + w * inp.y; + ret.z = x * inp.y - y * inp.x + z * inp.w + w * inp.z; + + return ret; + } + + auto opBinaryRight(string op, T)(T inp) const if(!is_quaternion!T) { + return this.opBinary!(op)(inp); + } + + Quaternion opBinary(string op)(Quaternion inp) const if((op == "+") || (op == "-")) { + Quaternion ret; + + mixin("ret.w = w" ~ op ~ "inp.w;"); + mixin("ret.x = x" ~ op ~ "inp.x;"); + mixin("ret.y = y" ~ op ~ "inp.y;"); + mixin("ret.z = z" ~ op ~ "inp.z;"); + + return ret; + } + + Vector!(qt, 3) opBinary(string op : "*")(Vector!(qt, 3) inp) const { + Vector!(qt, 3) ret; + + qt ww = w^^2; + qt w2 = w * 2; + qt wx2 = w2 * x; + qt wy2 = w2 * y; + qt wz2 = w2 * z; + qt xx = x^^2; + qt x2 = x * 2; + qt xy2 = x2 * y; + qt xz2 = x2 * z; + qt yy = y^^2; + qt yz2 = 2 * y * z; + qt zz = z * z; + + ret.vector = [ww * inp.x + wy2 * inp.z - wz2 * inp.y + xx * inp.x + + xy2 * inp.y + xz2 * inp.z - zz * inp.x - yy * inp.x, + xy2 * inp.x + yy * inp.y + yz2 * inp.z + wz2 * inp.x - + zz * inp.y + ww * inp.y - wx2 * inp.z - xx * inp.y, + xz2 * inp.x + yz2 * inp.y + zz * inp.z - wy2 * inp.x - + yy * inp.z + wx2 * inp.y - xx * inp.z + ww * inp.z]; + + return ret; + } + + Quaternion opBinary(string op : "*")(qt inp) const { + return Quaternion(w*inp, x*inp, y*inp, z*inp); + } + + void opOpAssign(string op : "*")(Quaternion inp) { + qt w2 = -x * inp.x - y * inp.y - z * inp.z + w * inp.w; + qt x2 = x * inp.w + y * inp.z - z * inp.y + w * inp.x; + qt y2 = -x * inp.z + y * inp.w + z * inp.x + w * inp.y; + qt z2 = x * inp.y - y * inp.x + z * inp.w + w * inp.z; + w = w2; x = x2; y = y2; z = z2; + } + + void opOpAssign(string op)(Quaternion inp) if((op == "+") || (op == "-")) { + mixin("w = w" ~ op ~ "inp.w;"); + mixin("x = x" ~ op ~ "inp.x;"); + mixin("y = y" ~ op ~ "inp.y;"); + mixin("z = z" ~ op ~ "inp.z;"); + } + + void opOpAssign(string op : "*")(qt inp) { + quaternion[0] *= inp; + quaternion[1] *= inp; + quaternion[2] *= inp; + quaternion[3] *= inp; + } + + unittest { + quat q1 = quat.identity; + quat q2 = quat(3.0f, 0.0f, 1.0f, 2.0f); + quat q3 = quat(3.4f, 0.1f, 1.2f, 2.3f); + + assert((q1 * q1).quaternion == q1.quaternion); + assert((q1 * q2).quaternion == q2.quaternion); + assert((q2 * q1).quaternion == q2.quaternion); + quat q4 = q3 * q2; + assert((q2 * q3).quaternion != q4.quaternion); + q3 *= q2; + assert(q4.quaternion == q3.quaternion); + assert(almost_equal(q4.x, 0.4f)); + assert(almost_equal(q4.y, 6.8f)); + assert(almost_equal(q4.z, 13.8f)); + assert(almost_equal(q4.w, 4.4f)); + + quat q5 = quat(1.0f, 2.0f, 3.0f, 4.0f); + quat q6 = quat(3.0f, 1.0f, 6.0f, 2.0f); + + assert((q5 - q6).quaternion == [-2.0f, 1.0f, -3.0f, 2.0f]); + assert((q5 + q6).quaternion == [4.0f, 3.0f, 9.0f, 6.0f]); + assert((q6 - q5).quaternion == [2.0f, -1.0f, 3.0f, -2.0f]); + assert((q6 + q5).quaternion == [4.0f, 3.0f, 9.0f, 6.0f]); + q5 += q6; + assert(q5.quaternion == [4.0f, 3.0f, 9.0f, 6.0f]); + q6 -= q6; + assert(q6.quaternion == [0.0f, 0.0f, 0.0f, 0.0f]); + + quat q7 = quat(2.0f, 2.0f, 2.0f, 2.0f); + assert((q7 * 2).quaternion == [4.0f, 4.0f, 4.0f, 4.0f]); + assert((2 * q7).quaternion == (q7 * 2).quaternion); + q7 *= 2; + assert(q7.quaternion == [4.0f, 4.0f, 4.0f, 4.0f]); + + vec3 v1 = vec3(1.0f, 2.0f, 3.0f); + assert((q1 * v1).vector == v1.vector); + assert((v1 * q1).vector == (q1 * v1).vector); + assert((q2 * v1).vector == [-2.0f, 36.0f, 38.0f]); + } + + int opCmp(ref const Quaternion qua) const { + foreach(i, a; quaternion) { + if(a < qua.quaternion[i]) { + return -1; + } else if(a > qua.quaternion[i]) { + return 1; + } + } + + // Quaternions are the same + return 0; + } + + bool opEquals(const Quaternion qu) const { + return quaternion == qu.quaternion; + } + + bool opCast(T : bool)() const { + return isFinite; + } + + unittest { + assert(quat(1.0f, 2.0f, 3.0f, 4.0f) == quat(1.0f, 2.0f, 3.0f, 4.0f)); + assert(quat(1.0f, 2.0f, 3.0f, 4.0f) != quat(1.0f, 2.0f, 3.0f, 3.0f)); + + assert(!(quat(float.nan, float.nan, float.nan, float.nan))); + if(quat(1.0f, 1.0f, 1.0f, 1.0f)) { } + else { assert(false); } + } + +} + +/// Pre-defined quaternion of type float. +alias Quaternion!(float) quat; diff --git a/gl3n/linalg/vec.d b/gl3n/linalg/vec.d new file mode 100644 index 0000000..a7eee21 --- /dev/null +++ b/gl3n/linalg/vec.d @@ -0,0 +1,734 @@ +/** +gl3n.linalg.vec + +Special thanks to: +$(UL + $(LI Tomasz Stachowiak (h3r3tic): allowed me to use parts of $(LINK2 https://bitbucket.org/h3r3tic/boxen/src/default/src/xf/omg, omg).) + $(LI Jakob Øvrum (jA_cOp): improved the code a lot!) + $(LI Florian Boesch (___doc__): helps me to understand opengl/complex maths better, see: $(LINK http://codeflow.org/).) + $(LI #D on freenode: answered general questions about D.) +) + +Authors: David Herberth, Stephan Dilly +License: MIT + +Note: All methods marked with pure are weakly pure since, they all access an instance member. +All static methods are strongly pure. +*/ + +module gl3n.linalg.vec; + +import gl3n.linalg.matrix; +import gl3n.util : is_vector, is_matrix, is_quaternion, TupleRange; +import gl3n.math : sqrt, max, almost_equal; + +import std.math : isNaN, isInfinity; +import std.string : format; +import std.conv : to; +import std.traits : isArray, isDynamicArray, isStaticArray, isIntegral; + +/// Base template for all vector-types. +/// Params: +/// type = all values get stored as this type +/// dimension = specifies the dimension of the vector, can be 1, 2, 3 or 4 +/// Examples: +/// --- +/// alias Vector!(int, 3) vec3i; +/// alias Vector!(float, 4) vec4; +/// alias Vector!(real, 2) vec2r; +/// --- +struct Vector(type, int dimension_) { + static assert(dimension > 0, "0 dimensional vectors don't exist."); + + alias type vt; /// Holds the internal type of the vector. + static const int dimension = dimension_; ///Holds the dimension of the vector. + + vt[dimension] vector; /// Holds all coordinates, length conforms dimension. + + /// Returns a pointer to the coordinates. + @property auto value_ptr() const { return vector.ptr; } + + /// Returns the current vector formatted as string, useful for printing the vector. + @property string as_string() { + return format("%s", vector); + } + alias as_string toString; /// ditto + + @safe pure nothrow: + /// + private @property ref inout(vt) get_(char coord)() inout { + return vector[coord_to_index!coord]; + } + + alias get_!'x' x; /// static properties to access the values. + alias x u; /// ditto + alias x s; /// ditto + alias x r; /// ditto + static if(dimension >= 2) { + alias get_!'y' y; /// ditto + alias y v; /// ditto + alias y t; /// ditto + alias y g; /// ditto + } + static if(dimension >= 3) { + alias get_!'z' z; /// ditto + alias z b; /// ditto + alias z p; /// ditto + } + static if(dimension >= 4) { + alias get_!'w' w; /// ditto + alias w a; /// ditto + alias w q; /// ditto + } + + static if(dimension == 2) { + enum Vector e1 = Vector(1.to!vt, 0.to!vt); /// canonical basis for Euclidian space + enum Vector e2 = Vector(0.to!vt, 1.to!vt); /// ditto + } else static if(dimension == 3) { + enum Vector e1 = Vector(1.to!vt, 0.to!vt, 0.to!vt); /// canonical basis for Euclidian space + enum Vector e2 = Vector(0.to!vt, 1.to!vt, 0.to!vt); /// ditto + enum Vector e3 = Vector(0.to!vt, 0.to!vt, 1.to!vt); /// ditto + } else static if(dimension == 4) { + enum Vector e1 = Vector(1.to!vt, 0.to!vt, 0.to!vt, 0.to!vt); /// canonical basis for Euclidian space + enum Vector e2 = Vector(0.to!vt, 1.to!vt, 0.to!vt, 0.to!vt); /// ditto + enum Vector e3 = Vector(0.to!vt, 0.to!vt, 1.to!vt, 0.to!vt); /// ditto + enum Vector e4 = Vector(0.to!vt, 0.to!vt, 0.to!vt, 1.to!vt); /// ditto + } + + unittest { + assert(vec2.e1.vector == [1.0, 0.0]); + assert(vec2.e2.vector == [0.0, 1.0]); + + assert(vec3.e1.vector == [1.0, 0.0, 0.0]); + assert(vec3.e2.vector == [0.0, 1.0, 0.0]); + assert(vec3.e3.vector == [0.0, 0.0, 1.0]); + + assert(vec4.e1.vector == [1.0, 0.0, 0.0, 0.0]); + assert(vec4.e2.vector == [0.0, 1.0, 0.0, 0.0]); + assert(vec4.e3.vector == [0.0, 0.0, 1.0, 0.0]); + assert(vec4.e4.vector == [0.0, 0.0, 0.0, 1.0]); + } + + static void isCompatibleVectorImpl(int d)(Vector!(vt, d) vec) if(d <= dimension) { + } + + template isCompatibleVector(T) { + enum isCompatibleVector = is(typeof(isCompatibleVectorImpl(T.init))); + } + + static void isCompatibleMatrixImpl(int r, int c)(Matrix!(vt, r, c) m) { + } + + template isCompatibleMatrix(T) { + enum isCompatibleMatrix = is(typeof(isCompatibleMatrixImpl(T.init))); + } + + private void construct(int i, T, Tail...)(T head, Tail tail) { + static if(i >= dimension) { + static assert(false, "Too many arguments passed to constructor"); + } else static if(is(T : vt)) { + vector[i] = head; + construct!(i + 1)(tail); + } else static if(isDynamicArray!T) { + static assert((Tail.length == 0) && (i == 0), "dynamic array can not be passed together with other arguments"); + vector[] = head[]; + } else static if(isStaticArray!T) { + vector[i .. i + T.length] = head[]; + construct!(i + T.length)(tail); + } else static if(isCompatibleVector!T) { + vector[i .. i + T.dimension] = head.vector[]; + construct!(i + T.dimension)(tail); + } else { + static assert(false, "Vector constructor argument must be of type " ~ vt.stringof ~ " or Vector, not " ~ T.stringof); + } + } + + private void construct(int i)() { // terminate + static assert(i == dimension, "Not enough arguments passed to constructor"); + } + + /// Constructs the vector. + /// If a single value is passed the vector, the vector will be cleared with this value. + /// If a vector with a higher dimension is passed the vector will hold the first values up to its dimension. + /// If mixed types are passed they will be joined together (allowed types: vector, static array, $(I vt)). + /// Examples: + /// --- + /// vec4 v4 = vec4(1.0f, vec2(2.0f, 3.0f), 4.0f); + /// vec3 v3 = vec3(v4); // v3 = vec3(1.0f, 2.0f, 3.0f); + /// vec2 v2 = v3.xy; // swizzling returns a static array. + /// vec3 v3_2 = vec3(1.0f); // vec3 v3_2 = vec3(1.0f, 1.0f, 1.0f); + /// --- + this(Args...)(Args args) { + construct!(0)(args); + } + + /// ditto + this(T)(T vec) if(is_vector!T && is(T.vt : vt) && (T.dimension >= dimension)) { + foreach(i; TupleRange!(0, dimension)) { + vector[i] = vec.vector[i]; + } + } + + /// ditto + this()(vt value) { + clear(value); + } + + /// Returns true if all values are not nan and finite, otherwise false. + @property bool isFinite() const { + static if(isIntegral!type) { + return true; + } + else { + foreach(v; vector) { + if(isNaN(v) || isInfinity(v)) { + return false; + } + } + return true; + } + } + deprecated("Use isFinite instead of ok") alias ok = isFinite; + + /// Sets all values of the vector to value. + void clear(vt value) { + foreach(i; TupleRange!(0, dimension)) { + vector[i] = value; + } + } + + unittest { + vec3 vec_clear; + assert(!vec_clear.isFinite); + vec_clear.clear(1.0f); + assert(vec_clear.isFinite); + assert(vec_clear.vector == [1.0f, 1.0f, 1.0f]); + assert(vec_clear.vector == vec3(1.0f).vector); + vec_clear.clear(float.infinity); + assert(!vec_clear.isFinite); + vec_clear.clear(float.nan); + assert(!vec_clear.isFinite); + vec_clear.clear(1.0f); + assert(vec_clear.isFinite); + + vec4 b = vec4(1.0f, vec_clear); + assert(b.isFinite); + assert(b.vector == [1.0f, 1.0f, 1.0f, 1.0f]); + assert(b.vector == vec4(1.0f).vector); + + vec2 v2_1 = vec2(vec2(0.0f, 1.0f)); + assert(v2_1.vector == [0.0f, 1.0f]); + + vec2 v2_2 = vec2(1.0f, 1.0f); + assert(v2_2.vector == [1.0f, 1.0f]); + + vec3 v3 = vec3(v2_1, 2.0f); + assert(v3.vector == [0.0f, 1.0f, 2.0f]); + + vec4 v4_1 = vec4(1.0f, vec2(2.0f, 3.0f), 4.0f); + assert(v4_1.vector == [1.0f, 2.0f, 3.0f, 4.0f]); + assert(vec3(v4_1).vector == [1.0f, 2.0f, 3.0f]); + assert(vec2(vec3(v4_1)).vector == [1.0f, 2.0f]); + assert(vec2(vec3(v4_1)).vector == vec2(v4_1).vector); + assert(v4_1.vector == vec4([1.0f, 2.0f, 3.0f, 4.0f]).vector); + + vec4 v4_2 = vec4(vec2(1.0f, 2.0f), vec2(3.0f, 4.0f)); + assert(v4_2.vector == [1.0f, 2.0f, 3.0f, 4.0f]); + assert(vec3(v4_2).vector == [1.0f, 2.0f, 3.0f]); + assert(vec2(vec3(v4_2)).vector == [1.0f, 2.0f]); + assert(vec2(vec3(v4_2)).vector == vec2(v4_2).vector); + assert(v4_2.vector == vec4([1.0f, 2.0f, 3.0f, 4.0f]).vector); + + float[2] f2 = [1.0f, 2.0f]; + float[3] f3 = [1.0f, 2.0f, 3.0f]; + float[4] f4 = [1.0f, 2.0f, 3.0f, 4.0f]; + assert(vec2(1.0f, 2.0f).vector == vec2(f2).vector); + assert(vec3(1.0f, 2.0f, 3.0f).vector == vec3(f3).vector); + assert(vec3(1.0f, 2.0f, 3.0f).vector == vec3(f2, 3.0f).vector); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f).vector == vec4(f4).vector); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f).vector == vec4(f3, 4.0f).vector); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f).vector == vec4(f2, 3.0f, 4.0f).vector); + // useful for: "vec4 v4 = […]" or "vec4 v4 = other_vector.rgba" + + assert(vec3(vec3i(1, 2, 3)) == vec3(1.0, 2.0, 3.0)); + assert(vec3d(vec3(1.0, 2.0, 3.0)) == vec3d(1.0, 2.0, 3.0)); + + static assert(!__traits(compiles, vec3(0.0f, 0.0f))); + static assert(!__traits(compiles, vec4(0.0f, 0.0f, 0.0f))); + static assert(!__traits(compiles, vec4(0.0f, vec2(0.0f, 0.0f)))); + static assert(!__traits(compiles, vec4(vec3(0.0f, 0.0f, 0.0f)))); + } + + template coord_to_index(char c) { + static if((c == 'x') || (c == 'r') || (c == 'u') || (c == 's')) { + enum coord_to_index = 0; + } else static if((c == 'y') || (c == 'g') || (c == 'v') || (c == 't')) { + enum coord_to_index = 1; + } else static if((c == 'z') || (c == 'b') || (c == 'p')) { + static assert(dimension >= 3, "the " ~ c ~ " property is only available on vectors with a third dimension."); + enum coord_to_index = 2; + } else static if((c == 'w') || (c == 'a') || (c == 'q')) { + static assert(dimension >= 4, "the " ~ c ~ " property is only available on vectors with a fourth dimension."); + enum coord_to_index = 3; + } else { + static assert(false, "accepted coordinates are x, s, r, u, y, g, t, v, z, p, b, w, q and a not " ~ c ~ "."); + } + } + + static if(dimension == 2) { void set(vt x, vt y) { vector[0] = x; vector[1] = y; } } + static if(dimension == 3) { void set(vt x, vt y, vt z) { vector[0] = x; vector[1] = y; vector[2] = z; } } + static if(dimension == 4) { void set(vt x, vt y, vt z, vt w) { vector[0] = x; vector[1] = y; vector[2] = z; vector[3] = w; } } + + /// Updates the vector with the values from other. + void update(Vector!(vt, dimension) other) { + vector = other.vector; + } + + unittest { + vec2 v2 = vec2(1.0f, 2.0f); + assert(v2.x == 1.0f); + assert(v2.y == 2.0f); + v2.x = 3.0f; + v2.x += 1; + v2.x -= 1; + assert(v2.vector == [3.0f, 2.0f]); + v2.y = 4.0f; + v2.y += 1; + v2.y -= 1; + assert(v2.vector == [3.0f, 4.0f]); + assert((v2.x == 3.0f) && (v2.x == v2.u) && (v2.x == v2.s) && (v2.x == v2.r)); + assert(v2.y == 4.0f); + assert((v2.y == 4.0f) && (v2.y == v2.v) && (v2.y == v2.t) && (v2.y == v2.g)); + v2.set(0.0f, 1.0f); + assert(v2.vector == [0.0f, 1.0f]); + v2.update(vec2(3.0f, 4.0f)); + assert(v2.vector == [3.0f, 4.0f]); + + vec3 v3 = vec3(1.0f, 2.0f, 3.0f); + assert(v3.x == 1.0f); + assert(v3.y == 2.0f); + assert(v3.z == 3.0f); + v3.x = 3.0f; + v3.x += 1; + v3.x -= 1; + assert(v3.vector == [3.0f, 2.0f, 3.0f]); + v3.y = 4.0f; + v3.y += 1; + v3.y -= 1; + assert(v3.vector == [3.0f, 4.0f, 3.0f]); + v3.z = 5.0f; + v3.z += 1; + v3.z -= 1; + assert(v3.vector == [3.0f, 4.0f, 5.0f]); + assert((v3.x == 3.0f) && (v3.x == v3.s) && (v3.x == v3.r)); + assert((v3.y == 4.0f) && (v3.y == v3.t) && (v3.y == v3.g)); + assert((v3.z == 5.0f) && (v3.z == v3.p) && (v3.z == v3.b)); + v3.set(0.0f, 1.0f, 2.0f); + assert(v3.vector == [0.0f, 1.0f, 2.0f]); + v3.update(vec3(3.0f, 4.0f, 5.0f)); + assert(v3.vector == [3.0f, 4.0f, 5.0f]); + + vec4 v4 = vec4(1.0f, 2.0f, vec2(3.0f, 4.0f)); + assert(v4.x == 1.0f); + assert(v4.y == 2.0f); + assert(v4.z == 3.0f); + assert(v4.w == 4.0f); + v4.x = 3.0f; + v4.x += 1; + v4.x -= 1; + assert(v4.vector == [3.0f, 2.0f, 3.0f, 4.0f]); + v4.y = 4.0f; + v4.y += 1; + v4.y -= 1; + assert(v4.vector == [3.0f, 4.0f, 3.0f, 4.0f]); + v4.z = 5.0f; + v4.z += 1; + v4.z -= 1; + assert(v4.vector == [3.0f, 4.0f, 5.0f, 4.0f]); + v4.w = 6.0f; + v4.w += 1; + v4.w -= 1; + assert(v4.vector == [3.0f, 4.0f, 5.0f, 6.0f]); + assert((v4.x == 3.0f) && (v4.x == v4.s) && (v4.x == v4.r)); + assert((v4.y == 4.0f) && (v4.y == v4.t) && (v4.y == v4.g)); + assert((v4.z == 5.0f) && (v4.z == v4.p) && (v4.z == v4.b)); + assert((v4.w == 6.0f) && (v4.w == v4.q) && (v4.w == v4.a)); + v4.set(0.0f, 1.0f, 2.0f, 3.0f); + assert(v4.vector == [0.0f, 1.0f, 2.0f, 3.0f]); + v4.update(vec4(3.0f, 4.0f, 5.0f, 6.0f)); + assert(v4.vector == [3.0f, 4.0f, 5.0f, 6.0f]); + } + + private void dispatchImpl(int i, string s, int size)(ref vt[size] result) const { + static if(s.length > 0) { + result[i] = vector[coord_to_index!(s[0])]; + dispatchImpl!(i + 1, s[1..$])(result); + } + } + + /// Implements dynamic swizzling. + /// Returns: a Vector + @property Vector!(vt, s.length) opDispatch(string s)() const { + vt[s.length] ret; + dispatchImpl!(0, s)(ret); + Vector!(vt, s.length) ret_vec; + ret_vec.vector = ret; + return ret_vec; + } + + unittest { + vec2 v2 = vec2(1.0f, 2.0f); + assert(v2.xytsy == [1.0f, 2.0f, 2.0f, 1.0f, 2.0f]); + + assert(vec3(1.0f, 2.0f, 3.0f).xybzyr == [1.0f, 2.0f, 3.0f, 3.0f, 2.0f, 1.0f]); + assert(vec4(v2, 3.0f, 4.0f).xyzwrgbastpq == [1.0f, 2.0f, 3.0f, 4.0f, + 1.0f, 2.0f, 3.0f, 4.0f, + 1.0f, 2.0f, 3.0f, 4.0f]); + assert(vec4(v2, 3.0f, 4.0f).wgyzax == [4.0f, 2.0f, 2.0f, 3.0f, 4.0f, 1.0f]); + assert(vec4(v2.xyst).vector == [1.0f, 2.0f, 1.0f, 2.0f]); + } + + /// Returns the squared magnitude of the vector. + @property real magnitude_squared() const { + real temp = 0; + + foreach(index; TupleRange!(0, dimension)) { + temp += vector[index]^^2; + } + + return temp; + } + + /// Returns the magnitude of the vector. + @property real magnitude() const { + return sqrt(magnitude_squared); + } + + alias magnitude_squared length_squared; /// ditto + alias magnitude length; /// ditto + + /// Normalizes the vector. + void normalize() { + real len = length; + + if(len != 0) { + foreach(index; TupleRange!(0, dimension)) { + vector[index] = cast(type)(vector[index]/len); + } + } + } + + /// Returns a normalized copy of the current vector. + @property Vector normalized() const { + Vector ret; + ret.update(this); + ret.normalize(); + return ret; + } + + Vector opUnary(string op : "-")() const { + Vector ret; + + foreach(index; TupleRange!(0, dimension)) { + ret.vector[index] = -vector[index]; + } + + return ret; + } + + unittest { + assert(vec2(1.0f, 1.0f) == -vec2(-1.0f, -1.0f)); + assert(vec2(-1.0f, 1.0f) == -vec2(1.0f, -1.0f)); + + assert(-vec3(1.0f, 1.0f, 1.0f) == vec3(-1.0f, -1.0f, -1.0f)); + assert(-vec3(-1.0f, 1.0f, -1.0f) == vec3(1.0f, -1.0f, 1.0f)); + + assert(vec4(1.0f, 1.0f, 1.0f, 1.0f) == -vec4(-1.0f, -1.0f, -1.0f, -1.0f)); + assert(vec4(-1.0f, 1.0f, -1.0f, 1.0f) == -vec4(1.0f, -1.0f, 1.0f, -1.0f)); + } + + // let the math begin! + Vector opBinary(string op : "*")(vt r) const { + Vector ret; + + foreach(index; TupleRange!(0, dimension)) { + ret.vector[index] = vector[index] * r; + } + + return ret; + } + + Vector opBinary(string op : "/")(vt r) const { + Vector ret; + + foreach(index; TupleRange!(0, dimension)) { + ret.vector[index] = vector[index] / r; + } + + return ret; + } + + Vector opBinary(string op)(Vector r) const if((op == "+") || (op == "-")) { + Vector ret; + + foreach(index; TupleRange!(0, dimension)) { + ret.vector[index] = mixin("vector[index]" ~ op ~ "r.vector[index]"); + } + + return ret; + } + + vt opBinary(string op : "*")(Vector r) const { + return dot(this, r); + } + + // vector * matrix (for matrix * vector -> struct Matrix) + Vector!(vt, T.cols) opBinary(string op : "*", T)(T inp) const if(isCompatibleMatrix!T && (T.rows == dimension)) { + Vector!(vt, T.cols) ret; + ret.clear(0); + + foreach(c; TupleRange!(0, T.cols)) { + foreach(r; TupleRange!(0, T.rows)) { + ret.vector[c] += vector[r] * inp.matrix[r][c]; + } + } + + return ret; + } + + auto opBinaryRight(string op, T)(T inp) const if(!is_vector!T && !is_matrix!T && !is_quaternion!T) { + return this.opBinary!(op)(inp); + } + + unittest { + import gl3n.linalg.matrix : mat2, mat3; + + vec2 v2 = vec2(1.0f, 3.0f); + auto v2times2 = 2 * v2; + assert((v2*2.5f).vector == [2.5f, 7.5f]); + assert((v2+vec2(3.0f, 1.0f)).vector == [4.0f, 4.0f]); + assert((v2-vec2(1.0f, 3.0f)).vector == [0.0f, 0.0f]); + assert((v2*vec2(2.0f, 2.0f)) == 8.0f); + + vec3 v3 = vec3(1.0f, 3.0f, 5.0f); + assert((v3*2.5f).vector == [2.5f, 7.5f, 12.5f]); + assert((v3+vec3(3.0f, 1.0f, -1.0f)).vector == [4.0f, 4.0f, 4.0f]); + assert((v3-vec3(1.0f, 3.0f, 5.0f)).vector == [0.0f, 0.0f, 0.0f]); + assert((v3*vec3(2.0f, 2.0f, 2.0f)) == 18.0f); + + vec4 v4 = vec4(1.0f, 3.0f, 5.0f, 7.0f); + assert((v4*2.5f).vector == [2.5f, 7.5f, 12.5f, 17.5]); + assert((v4+vec4(3.0f, 1.0f, -1.0f, -3.0f)).vector == [4.0f, 4.0f, 4.0f, 4.0f]); + assert((v4-vec4(1.0f, 3.0f, 5.0f, 7.0f)).vector == [0.0f, 0.0f, 0.0f, 0.0f]); + assert((v4*vec4(2.0f, 2.0f, 2.0f, 2.0f)) == 32.0f); + + mat2 m2 = mat2(1.0f, 2.0f, 3.0f, 4.0f); + vec2 v2_2 = vec2(2.0f, 2.0f); + assert((v2_2*m2).vector == [8.0f, 12.0f]); + + mat3 m3 = mat3(1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f); + vec3 v3_2 = vec3(2.0f, 2.0f, 2.0f); + assert((v3_2*m3).vector == [24.0f, 30.0f, 36.0f]); + } + + void opOpAssign(string op : "*")(vt r) { + foreach(index; TupleRange!(0, dimension)) { + vector[index] *= r; + } + } + + void opOpAssign(string op : "/")(vt r) { + foreach(index; TupleRange!(0, dimension)) { + vector[index] /= r; + } + } + + void opOpAssign(string op)(Vector r) if((op == "+") || (op == "-")) { + foreach(index; TupleRange!(0, dimension)) { + mixin("vector[index]" ~ op ~ "= r.vector[index];"); + } + } + + unittest { + vec2 v2 = vec2(1.0f, 3.0f); + v2 *= 2.5f; + assert(v2.vector == [2.5f, 7.5f]); + v2 -= vec2(2.5f, 7.5f); + assert(v2.vector == [0.0f, 0.0f]); + v2 += vec2(1.0f, 3.0f); + assert(v2.vector == [1.0f, 3.0f]); + assert(almost_equal(v2.length, sqrt(10.0f))); + assert(v2.length_squared == 10.0f); + assert((v2.magnitude == v2.length) && (v2.magnitude_squared == v2.length_squared)); + v2 /= 2.0f; + assert(v2.vector == [0.5f, 1.5f]); + assert(almost_equal(v2.normalized, vec2(1.0f/sqrt(10.0f), 3.0f/sqrt(10.0f)))); + + vec3 v3 = vec3(1.0f, 3.0f, 5.0f); + v3 *= 2.5f; + assert(v3.vector == [2.5f, 7.5f, 12.5f]); + v3 -= vec3(2.5f, 7.5f, 12.5f); + assert(v3.vector == [0.0f, 0.0f, 0.0f]); + v3 += vec3(1.0f, 3.0f, 5.0f); + assert(v3.vector == [1.0f, 3.0f, 5.0f]); + assert(almost_equal(v3.length, sqrt(35.0f))); + assert(v3.length_squared == 35.0f); + assert((v3.magnitude == v3.length) && (v3.magnitude_squared == v3.length_squared)); + v3 /= 2.0f; + assert(v3.vector == [0.5f, 1.5f, 2.5f]); + assert(almost_equal(v3.normalized, vec3(1.0f/sqrt(35.0f), 3.0f/sqrt(35.0f), 5.0f/sqrt(35.0f)))); + + vec4 v4 = vec4(1.0f, 3.0f, 5.0f, 7.0f); + v4 *= 2.5f; + assert(v4.vector == [2.5f, 7.5f, 12.5f, 17.5]); + v4 -= vec4(2.5f, 7.5f, 12.5f, 17.5f); + assert(v4.vector == [0.0f, 0.0f, 0.0f, 0.0f]); + v4 += vec4(1.0f, 3.0f, 5.0f, 7.0f); + assert(v4.vector == [1.0f, 3.0f, 5.0f, 7.0f]); + assert(almost_equal(v4.length, sqrt(84.0f))); + assert(v4.length_squared == 84.0f); + assert((v4.magnitude == v4.length) && (v4.magnitude_squared == v4.length_squared)); + v4 /= 2.0f; + assert(v4.vector == [0.5f, 1.5f, 2.5f, 3.5f]); + assert(almost_equal(v4.normalized, vec4(1.0f/sqrt(84.0f), 3.0f/sqrt(84.0f), 5.0f/sqrt(84.0f), 7.0f/sqrt(84.0f)))); + } + + int opCmp(ref const Vector vec) const { + foreach(i, a; vector) { + if(a < vec.vector[i]) { + return -1; + } else if(a > vec.vector[i]) { + return 1; + } + } + + // Vectors are the same + return 0; + } + + bool opEquals(T)(const T vec) const if(!isArray!T && T.dimension == dimension) { + return vector == vec.vector; + } + + bool opEquals(T)(const(T)[] array) const if(!isArray!T && !is_vector!T) { + if(array.length != dimension) { + return false; + } + + foreach(index; TupleRange!(0, dimension)) { + if(vector[index] != array[index]) { + return false; + } + } + + return true; + } + + bool opCast(T : bool)() const { + return isFinite; + } + + unittest { + assert(vec2(1.0f, 2.0f) == vec2(1.0f, 2.0f)); + assert(vec2(1.0f, 2.0f) != vec2(1.0f, 1.0f)); + assert(vec2(1.0f, 2.0f) == vec2d(1.0, 2.0)); + assert(vec2(1.0f, 2.0f) != vec2d(1.0, 1.0)); + assert(vec2(1.0f, 2.0f) == vec2(1.0f, 2.0f).vector); + assert(vec2(1.0f, 2.0f) != vec2(1.0f, 1.0f).vector); + assert(vec2(1.0f, 2.0f) == vec2d(1.0, 2.0).vector); + assert(vec2(1.0f, 2.0f) != vec2d(1.0, 1.0).vector); + + assert(vec3(1.0f, 2.0f, 3.0f) == vec3(1.0f, 2.0f, 3.0f)); + assert(vec3(1.0f, 2.0f, 3.0f) != vec3(1.0f, 2.0f, 2.0f)); + assert(vec3(1.0f, 2.0f, 3.0f) == vec3d(1.0, 2.0, 3.0)); + assert(vec3(1.0f, 2.0f, 3.0f) != vec3d(1.0, 2.0, 2.0)); + assert(vec3(1.0f, 2.0f, 3.0f) == vec3(1.0f, 2.0f, 3.0f).vector); + assert(vec3(1.0f, 2.0f, 3.0f) != vec3(1.0f, 2.0f, 2.0f).vector); + assert(vec3(1.0f, 2.0f, 3.0f) == vec3d(1.0, 2.0, 3.0).vector); + assert(vec3(1.0f, 2.0f, 3.0f) != vec3d(1.0, 2.0, 2.0).vector); + + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) == vec4(1.0f, 2.0f, 3.0f, 4.0f)); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) != vec4(1.0f, 2.0f, 3.0f, 3.0f)); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) == vec4d(1.0, 2.0, 3.0, 4.0)); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) != vec4d(1.0, 2.0, 3.0, 3.0)); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) == vec4(1.0f, 2.0f, 3.0f, 4.0f).vector); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) != vec4(1.0f, 2.0f, 3.0f, 3.0f).vector); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) == vec4d(1.0, 2.0, 3.0, 4.0).vector); + assert(vec4(1.0f, 2.0f, 3.0f, 4.0f) != vec4d(1.0, 2.0, 3.0, 3.0).vector); + + assert(!(vec4(float.nan))); + if(vec4(1.0f)) { } + else { assert(false); } + } + +} + +/// Calculates the product between two vectors. +T.vt dot(T)(const T veca, const T vecb) @safe pure nothrow if(is_vector!T) { + T.vt temp = 0; + + foreach(index; TupleRange!(0, T.dimension)) { + temp += veca.vector[index] * vecb.vector[index]; + } + + return temp; +} + +/// Calculates the cross product of two 3-dimensional vectors. +T cross(T)(const T veca, const T vecb) @safe pure nothrow if(is_vector!T && (T.dimension == 3)) { + return T(veca.y * vecb.z - vecb.y * veca.z, + veca.z * vecb.x - vecb.z * veca.x, + veca.x * vecb.y - vecb.x * veca.y); +} + +/// Calculates the distance between two vectors. +T.vt distance(T)(const T veca, const T vecb) @safe pure nothrow if(is_vector!T) { + return (veca - vecb).length; +} + +unittest { + // dot is already tested in Vector.opBinary, so no need for testing with more vectors + vec3 v1 = vec3(1.0f, 2.0f, -3.0f); + vec3 v2 = vec3(1.0f, 3.0f, 2.0f); + + assert(dot(v1, v2) == 1.0f); + assert(dot(v1, v2) == (v1 * v2)); + assert(dot(v1, v2) == dot(v2, v1)); + assert((v1 * v2) == (v1 * v2)); + + assert(cross(v1, v2).vector == [13.0f, -5.0f, 1.0f]); + assert(cross(v2, v1).vector == [-13.0f, 5.0f, -1.0f]); + + assert(distance(vec2(0.0f, 0.0f), vec2(0.0f, 10.0f)) == 10.0); +} + +/// reflect a vector using a surface normal +T reflect(T)(const T vec, const T norm) @safe pure nothrow if(is_vector!T) { + return (2 * (vec * norm) * norm) - vec; +} + +unittest +{ + assert(vec2(1,1).reflect(vec2(0,1)) == vec2(-1,1)); + assert(vec2(-1,1).reflect(vec2(0,1)) == vec2(1,1)); + assert(vec2(2,1).reflect(vec2(0,1)) == vec2(-2,1)); + + assert(vec3(1,1,1).reflect(vec3(0,1,0)) == vec3(-1,1,-1)); +} + +/// Pre-defined vector types, the number represents the dimension and the last letter the type (none = float, d = double, i = int). +alias Vector!(float, 2) vec2; +alias Vector!(float, 3) vec3; /// ditto +alias Vector!(float, 4) vec4; /// ditto + +alias Vector!(double, 2) vec2d; /// ditto +alias Vector!(double, 3) vec3d; /// ditto +alias Vector!(double, 4) vec4d; /// ditto + +alias Vector!(int, 2) vec2i; /// ditto +alias Vector!(int, 3) vec3i; /// ditto +alias Vector!(int, 4) vec4i; /// ditto + +/*alias Vector!(ubyte, 2) vec2ub; +alias Vector!(ubyte, 3) vec3ub; +alias Vector!(ubyte, 4) vec4ub;*/ diff --git a/libgl3n.a b/libgl3n.a new file mode 100644 index 0000000000000000000000000000000000000000..0731d895685fd2baddbae03cdee7a8dd3c738237 GIT binary patch literal 11005220 zcmeF)2V7P4|3C1TiW_Z+dn=j)l?#`pI8a1TBnN6DMkpZ2We68VrA)<9;>L{|wPD$? ztz~_+VYIO#5yscnwmZ=R+V4q*_=&vu4)9A$n#(E&NGM zt7@T3U7#qh7UF2mo?2K%iyy0nmuSJkTKJ3ZeXSM-*8_43YhfZS`n(nvQsWO?ju!k; z3#X}DjoRo`pX)cQjYL||yEZmb*TJ=MjGnGr2lbqR?8bF4h`Q~ngDjeNxDFoGe4`G2 z(>zuOH#bmr7lXwl8v1D+d_i4)t%LCm0sm@sai_ROe3%9{sf!Lba5=ZSSWDgd)Wx&n zyW;nBe^^~Kx>4yRP7v>*S+~{2Q{r*)g68zPNWMuq?q+4pM#{Uz9xiISNOW(arkgiq zem2)dGhfe=I5%UxAFPYcH1J4W?4gBk*Tv7Y;CNlsZ_f7ntS-jT zm~WU5>hyD6ET(yXaCz~N__0{M1?#_BJ#-M0#plGjE!F&Rahv$PIFTEQw*HIa4`T1u zDtwjr9yNQ`L;W_uVgGsvq}hS>Fo%YQ*29CEW9s2c>cUP{x2^IPF+@zKZd2-EU_17= 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