A C# port of the GJK+EPA collision solver used for convex-convex distance and penetration queries. It wraps GJK and EPA routines to compute witness points, penetration depth/normal, and signed distances between ConvexShape instances while managing temporary pools and transforms.
/* * C# / XNA port of Bullet (c) 2011 Mark Neale <[email protected]> * * Bullet Continuous Collision Detection and Physics Library * Copyright (c) 2003-2008 Erwin Coumans http://www.bulletphysics.com/ * * This software is provided 'as-is', without any express or implied warranty. * In no event will the authors be held liable for any damages arising from * the use of this software. * * Permission is granted to anyone to use this software for any purpose, * including commercial applications, and to alter it and redistribute it * freely, subject to the following restrictions: * * 1. The origin of this software must not be misrepresented; you must not * claim that you wrote the original software. If you use this software * in a product, an acknowledgment in the product documentation would be * appreciated but is not required. * 2. Altered source versions must be plainly marked as such, and must not be * misrepresented as being the original software. * 3. This notice may not be removed or altered from any source distribution. */ // Adapted from BulletXNA 73b2e1b9: namespace isolation, no XNA rendering, one type per file. #nullable disable #pragma warning disable CS1591, CS0168, CS0219, CS0414, CS0660, CS0661, CS0659, CS0693, CS8981, CS0108, CS0114 using System; using System.Collections.Generic; using HumanoidRetargeter.Core.Formats.Mmd.Bullet.LinearMath; using System.Diagnostics; namespace HumanoidRetargeter.Core.Formats.Mmd.Bullet.BulletCollision; internal class GjkEpaSolver2 { static EPA epa = new EPA(); public static void Initialize(ConvexShape shape0, ref IndexedMatrix wtrs0, ConvexShape shape1, ref IndexedMatrix wtrs1, ref GjkEpaSolver2Results results, GjkEpaSolver2MinkowskiDiff shapeR, bool withmargins) { /* Results */ results.witnesses0 = IndexedVector3.Zero; results.witnesses1 = IndexedVector3.Zero; results.status = GjkEpaSolver2Status.Separated; /* Shape */ shapeR.m_shapes[0] = shape0; shapeR.m_shapes[1] = shape1; shapeR.m_toshape1 = wtrs1._basis.TransposeTimes(ref wtrs0._basis); shapeR.m_toshape0 = wtrs0.InverseTimes(ref wtrs1); shapeR.EnableMargin(withmargins); } public static bool Distance(ConvexShape shape0, ref IndexedMatrix wtrs0, ConvexShape shape1, ref IndexedMatrix wtrs1, ref IndexedVector3 guess, ref GjkEpaSolver2Results results) { using (GjkEpaSolver2MinkowskiDiff shape = BulletGlobals.GjkEpaSolver2MinkowskiDiffPool.Get()) using (GJK gjk = BulletGlobals.GJKPool.Get()) { Initialize(shape0, ref wtrs0, shape1, ref wtrs1, ref results, shape, false); gjk.Initialise(); GJKStatus gjk_status = gjk.Evaluate(shape, ref guess); if (gjk_status == GJKStatus.Valid) { IndexedVector3 w0 = IndexedVector3.Zero; IndexedVector3 w1 = IndexedVector3.Zero; for (uint i = 0; i < gjk.m_simplex.rank; ++i) { float p = gjk.m_simplex.p[i]; w0 += shape.Support(ref gjk.m_simplex.c[i].d, 0) * p; IndexedVector3 temp = -gjk.m_simplex.c[i].d; w1 += shape.Support(ref temp, 1) * p; } results.witnesses0 = wtrs0 * w0; results.witnesses1 = wtrs0 * w1; results.normal = w0 - w1; results.distance = results.normal.Length(); results.normal /= results.distance > GJK_MIN_DISTANCE ? results.distance : 1; return (true); } else { //GjkEpaSolver2Status results.status = (gjk_status == GJKStatus.Inside) ? GjkEpaSolver2Status.Penetrating : GjkEpaSolver2Status.GJK_Failed; return (false); } } } public static bool Penetration(ConvexShape shape0, ref IndexedMatrix wtrs0, ConvexShape shape1, ref IndexedMatrix wtrs1, ref IndexedVector3 guess, ref GjkEpaSolver2Results results) { return Penetration(shape0, ref wtrs0, shape1, ref wtrs1, ref guess, ref results, true); } public static bool Penetration(ConvexShape shape0, ref IndexedMatrix wtrs0, ConvexShape shape1, ref IndexedMatrix wtrs1, ref IndexedVector3 guess, ref GjkEpaSolver2Results results, bool usemargins) { using (GjkEpaSolver2MinkowskiDiff shape = BulletGlobals.GjkEpaSolver2MinkowskiDiffPool.Get()) using (GJK gjk = BulletGlobals.GJKPool.Get()) { Initialize(shape0, ref wtrs0, shape1, ref wtrs1, ref results, shape, usemargins); gjk.Initialise(); IndexedVector3 minusGuess = -guess; GJKStatus gjk_status = gjk.Evaluate(shape, ref minusGuess); switch (gjk_status) { case GJKStatus.Inside: { //EPA epa = new EPA(); eStatus epa_status = epa.Evaluate(gjk, ref minusGuess); if (epa_status != eStatus.Failed) { IndexedVector3 w0 = IndexedVector3.Zero; for (uint i = 0; i < epa.m_result.rank; ++i) { // order of results here is 'different' , EPA.evaluate. w0 += shape.Support(ref epa.m_result.c[i].d, 0) * epa.m_result.p[i]; } results.status = GjkEpaSolver2Status.Penetrating; results.witnesses0 = wtrs0 * w0; results.witnesses1 = wtrs0 * (w0 - epa.m_normal * epa.m_depth); results.normal = -epa.m_normal; results.distance = -epa.m_depth; return (true); } else results.status = GjkEpaSolver2Status.EPA_Failed; } break; case GJKStatus.Failed: results.status = GjkEpaSolver2Status.GJK_Failed; break; } } return (false); } // public float SignedDistance(ref IndexedVector3 position, float margin, ConvexShape shape0, ref IndexedMatrix wtrs0, ref GjkEpaSolver2Results results) { using (GjkEpaSolver2MinkowskiDiff shape = BulletGlobals.GjkEpaSolver2MinkowskiDiffPool.Get()) using (GJK gjk = BulletGlobals.GJKPool.Get()) { SphereShape shape1 = BulletGlobals.SphereShapePool.Get(); shape1.Initialize(margin); IndexedMatrix wtrs1 = IndexedMatrix.CreateFromQuaternion(IndexedQuaternion.Identity); wtrs0._origin = position; Initialize(shape0, ref wtrs0, shape1, ref wtrs1, ref results, shape, false); gjk.Initialise(); IndexedVector3 guess = new IndexedVector3(1); GJKStatus gjk_status = gjk.Evaluate(shape, ref guess); if (gjk_status == GJKStatus.Valid) { IndexedVector3 w0 = IndexedVector3.Zero; IndexedVector3 w1 = IndexedVector3.Zero; for (int i = 0; i < gjk.m_simplex.rank; ++i) { float p = gjk.m_simplex.p[i]; w0 += shape.Support(ref gjk.m_simplex.c[i].d, 0) * p; IndexedVector3 temp = -gjk.m_simplex.c[i].d; w1 += shape.Support(ref temp, 1) * p; } results.witnesses0 = wtrs0 * w0; results.witnesses1 = wtrs0 * w1; IndexedVector3 delta = results.witnesses1 - results.witnesses0; float margin2 = shape0.GetMarginNonVirtual() + shape1.GetMarginNonVirtual(); float length = delta.Length(); results.normal = delta / length; results.witnesses0 += results.normal * margin2; return (length - margin2); } else { if (gjk_status == GJKStatus.Inside) { if (Penetration(shape0, ref wtrs0, shape1, ref wtrs1, ref gjk.m_ray, ref results)) { IndexedVector3 delta = results.witnesses0 - results.witnesses1; float length = delta.Length(); if (length >= MathUtil.SIMD_EPSILON) results.normal = delta / length; return (-length); } } } BulletGlobals.SphereShapePool.Free(shape1); } return (MathUtil.SIMD_INFINITY); } // public bool SignedDistance(ConvexShape shape0, ref IndexedMatrix wtrs0, ConvexShape shape1, ref IndexedMatrix wtrs1, ref IndexedVector3 guess, ref GjkEpaSolver2Results results) { if (!Distance(shape0, ref wtrs0, shape1, ref wtrs1, ref guess, ref results)) return (Penetration(shape0, ref wtrs0, shape1, ref wtrs1, ref guess, ref results, false)); else return (true); } /* GJK */ public const int GJK_MAX_ITERATIONS = 128; public const float GJK_ACCURARY = 0.0001f; public const float GJK_MIN_DISTANCE = 0.0001f; public const float GJK_DUPLICATED_EPS = 0.0001f; public const float GJK_SIMPLEX2_EPS = 0f; public const float GJK_SIMPLEX3_EPS = 0f; public const float GJK_SIMPLEX4_EPS = 0f; /* EPA */ public const int EPA_MAX_VERTICES = 64; public const int EPA_MAX_FACES = EPA_MAX_VERTICES * 2; public const int EPA_MAX_ITERATIONS = 255; public const float EPA_ACCURACY = 0.0001f; public const float EPA_FALLBACK = 10 * EPA_ACCURACY; public const float EPA_PLANE_EPS = 0.00001f; public const float EPA_INSIDE_EPS = 0.01f; }