feat(geometry): test swept upright cylinders against convex prisms

Author: mrdav30

docs/wiki/bounds-and-geometry.md

@@ -218,6 +218,13 @@ Choose the represented boundary carefully:
 This distinction is why the API exposes named sweep methods instead of treating
 every query as an expanded axis-aligned bound.
 
+`FixedConvexPrismRelations.IntersectsSweptUprightCylinderStrict` answers the
+joint continuous relation between a translated upright cylinder and a rotated
+vertical convex prism. It keeps one exact parameter domain for both footprint
+and height overlap, so planar tangency, vertical tangency, and intervals that
+meet only at one boundary parameter do not become false positive volume
+intersections through independently rounded roots.
+
 ## Triangles and contacts
 
 Triangles preserve vertex order. `FixedTriangle2d` exposes planar barycentric
@@ -277,6 +284,7 @@ physics-response API.
 | Swept sphere versus cylinder or box                        | `FixedSegment`                                                            |
 | Centered shape support, containment, or materialization    | `FixedSegment2d`, `FixedSegment` static helpers                           |
 | Shape support inside a world-Y layer                       | `FixedSlabProjection`                                                     |
+| Swept upright cylinder versus a vertical convex prism      | `FixedConvexPrismRelations`                                               |
 | Triangle contacts or finite-shape relations                | `FixedTriangle`                                                           |
 | Relative witnesses outside ordinary world-coordinate range | `FixedPointAnchor`, `FixedPointAnchor2d`, contact-anchor types            |
 

src/FixedMathSharp/Geometry/Primitives/Relations/FixedConvexPrismRelations.cs

@@ -16,6 +16,59 @@ namespace FixedMathSharp;
 /// </summary>
 public static class FixedConvexPrismRelations
 {
+    /// <summary>
+    /// Determines whether an upright cylinder translated between two
+    /// bottom-center points has strict positive-volume overlap with a rotated
+    /// vertical convex prism at any shared continuous parameter in [0, 1].
+    /// </summary>
+    /// <remarks>
+    /// Planar tangency, vertical tangency, and contact that exists only where
+    /// the planar and vertical strict intervals meet at one boundary parameter
+    /// return <see langword="false"/>. A zero radius requires the swept axis
+    /// point to enter the strict prism footprint. The joint parameter relation
+    /// is evaluated with exact wide intermediates and does not publish rounded
+    /// interval endpoints.
+    /// </remarks>
+    /// <param name="bottomStart">The cylinder bottom center at parameter zero.</param>
+    /// <param name="bottomEnd">The cylinder bottom center at parameter one.</param>
+    /// <param name="radius">The nonnegative cylinder radius.</param>
+    /// <param name="height">The positive full cylinder height.</param>
+    /// <param name="prismOrigin">The center of the vertical convex prism.</param>
+    /// <param name="prismRotation">The prism footprint rotation about world Y.</param>
+    /// <param name="prismLocalOffsets">At least three ordered convex-footprint offsets.</param>
+    /// <param name="prismHalfThickness">The positive prism half-thickness along world Y.</param>
+    /// <exception cref="ArgumentOutOfRangeException">
+    /// <paramref name="radius"/> is negative, <paramref name="height"/> is not
+    /// positive, or <paramref name="prismHalfThickness"/> is not positive.
+    /// </exception>
+    /// <exception cref="ArgumentException">
+    /// Fewer than three ordered prism offsets were supplied.
+    /// </exception>
+    public static bool IntersectsSweptUprightCylinderStrict(
+        Vector3d bottomStart,
+        Vector3d bottomEnd,
+        Fixed64 radius,
+        Fixed64 height,
+        Vector3d prismOrigin,
+        Fixed64 prismRotation,
+        ReadOnlySpan<Vector2d> prismLocalOffsets,
+        Fixed64 prismHalfThickness)
+    {
+        if (height <= Fixed64.Zero)
+            throw new ArgumentOutOfRangeException(nameof(height));
+        ValidatePrism(radius, prismLocalOffsets, prismHalfThickness);
+        return WideConvexPrismRelations
+            .IntersectsSweptUprightCylinderStrict(
+                bottomStart,
+                bottomEnd,
+                radius,
+                height,
+                prismOrigin,
+                prismRotation,
+                prismLocalOffsets,
+                prismHalfThickness);
+    }
+
     /// <summary>
     /// Attempts to construct canonical contact anchors between a rigidly
     /// transformed triangle and a rotated vertical convex prism.

src/FixedMathSharp/Geometry/Wide/Convex/WideConvex2dRelations.ProjectionMath.cs

@@ -468,7 +468,7 @@ private static void GetWorldPoint(
             secondRotatedY);
     }
 
-    private static void GetRotatedOffset(
+    internal static void GetRotatedOffset(
         RotationFrame2d rotation,
         Vector2d localPoint,
         out Signed192 x,

src/FixedMathSharp/Geometry/Wide/Convex/WideConvex2dRelations.cs

@@ -33,7 +33,7 @@ internal WideAxis2d(Signed192 x, Signed192 y)
             new(WideArithmetic.Negate(value.X), WideArithmetic.Negate(value.Y));
     }
 
-    private readonly struct RotationFrame2d
+    internal readonly struct RotationFrame2d
     {
         internal static readonly RotationFrame2d Identity = new(
             Signed192.One,