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-rw-r--r--src/BulletCollision/NarrowPhaseCollision/btGjkEpa3.h2126
1 files changed, 1063 insertions, 1063 deletions
diff --git a/src/BulletCollision/NarrowPhaseCollision/btGjkEpa3.h b/src/BulletCollision/NarrowPhaseCollision/btGjkEpa3.h
index 5389d05f5..6fedbbb3e 100644
--- a/src/BulletCollision/NarrowPhaseCollision/btGjkEpa3.h
+++ b/src/BulletCollision/NarrowPhaseCollision/btGjkEpa3.h
@@ -1,1063 +1,1063 @@
-/*
-Bullet Continuous Collision Detection and Physics Library
-Copyright (c) 2003-2014 Erwin Coumans http://continuousphysics.com/Bullet/
-
-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.
-*/
-
-/*
-Initial GJK-EPA collision solver by Nathanael Presson, 2008
-Improvements and refactoring by Erwin Coumans, 2008-2014
-*/
-#ifndef BT_GJK_EPA3_H
-#define BT_GJK_EPA3_H
-
-#include "LinearMath/btTransform.h"
-#include "btGjkCollisionDescription.h"
-
-struct btGjkEpaSolver3
-{
- struct sResults
- {
- enum eStatus
- {
- Separated, /* Shapes doesnt penetrate */
- Penetrating, /* Shapes are penetrating */
- GJK_Failed, /* GJK phase fail, no big issue, shapes are probably just 'touching' */
- EPA_Failed /* EPA phase fail, bigger problem, need to save parameters, and debug */
- } status;
- btVector3 witnesses[2];
- btVector3 normal;
- btScalar distance;
- };
-};
-
-#if defined(DEBUG) || defined(_DEBUG)
-#include <stdio.h> //for debug printf
-#ifdef __SPU__
-#include <spu_printf.h>
-#define printf spu_printf
-#endif //__SPU__
-#endif
-
-// Config
-
-/* GJK */
-#define GJK_MAX_ITERATIONS 128
-#define GJK_ACCURARY ((btScalar)0.0001)
-#define GJK_MIN_DISTANCE ((btScalar)0.0001)
-#define GJK_DUPLICATED_EPS ((btScalar)0.0001)
-#define GJK_SIMPLEX2_EPS ((btScalar)0.0)
-#define GJK_SIMPLEX3_EPS ((btScalar)0.0)
-#define GJK_SIMPLEX4_EPS ((btScalar)0.0)
-
-/* EPA */
-#define EPA_MAX_VERTICES 64
-#define EPA_MAX_FACES (EPA_MAX_VERTICES * 2)
-#define EPA_MAX_ITERATIONS 255
-#define EPA_ACCURACY ((btScalar)0.0001)
-#define EPA_FALLBACK (10 * EPA_ACCURACY)
-#define EPA_PLANE_EPS ((btScalar)0.00001)
-#define EPA_INSIDE_EPS ((btScalar)0.01)
-
-// Shorthands
-typedef unsigned int U;
-typedef unsigned char U1;
-
-// MinkowskiDiff
-template <typename btConvexTemplate>
-struct MinkowskiDiff
-{
- const btConvexTemplate* m_convexAPtr;
- const btConvexTemplate* m_convexBPtr;
-
- btMatrix3x3 m_toshape1;
- btTransform m_toshape0;
-
- bool m_enableMargin;
-
- MinkowskiDiff(const btConvexTemplate& a, const btConvexTemplate& b)
- : m_convexAPtr(&a),
- m_convexBPtr(&b)
- {
- }
-
- void EnableMargin(bool enable)
- {
- m_enableMargin = enable;
- }
- inline btVector3 Support0(const btVector3& d) const
- {
- return m_convexAPtr->getLocalSupportWithMargin(d);
- }
- inline btVector3 Support1(const btVector3& d) const
- {
- return m_toshape0 * m_convexBPtr->getLocalSupportWithMargin(m_toshape1 * d);
- }
-
- inline btVector3 Support(const btVector3& d) const
- {
- return (Support0(d) - Support1(-d));
- }
- btVector3 Support(const btVector3& d, U index) const
- {
- if (index)
- return (Support1(d));
- else
- return (Support0(d));
- }
-};
-
-enum eGjkStatus
-{
- eGjkValid,
- eGjkInside,
- eGjkFailed
-};
-
-// GJK
-template <typename btConvexTemplate>
-struct GJK
-{
- /* Types */
- struct sSV
- {
- btVector3 d, w;
- };
- struct sSimplex
- {
- sSV* c[4];
- btScalar p[4];
- U rank;
- };
-
- /* Fields */
-
- MinkowskiDiff<btConvexTemplate> m_shape;
- btVector3 m_ray;
- btScalar m_distance;
- sSimplex m_simplices[2];
- sSV m_store[4];
- sSV* m_free[4];
- U m_nfree;
- U m_current;
- sSimplex* m_simplex;
- eGjkStatus m_status;
- /* Methods */
-
- GJK(const btConvexTemplate& a, const btConvexTemplate& b)
- : m_shape(a, b)
- {
- Initialize();
- }
- void Initialize()
- {
- m_ray = btVector3(0, 0, 0);
- m_nfree = 0;
- m_status = eGjkFailed;
- m_current = 0;
- m_distance = 0;
- }
- eGjkStatus Evaluate(const MinkowskiDiff<btConvexTemplate>& shapearg, const btVector3& guess)
- {
- U iterations = 0;
- btScalar sqdist = 0;
- btScalar alpha = 0;
- btVector3 lastw[4];
- U clastw = 0;
- /* Initialize solver */
- m_free[0] = &m_store[0];
- m_free[1] = &m_store[1];
- m_free[2] = &m_store[2];
- m_free[3] = &m_store[3];
- m_nfree = 4;
- m_current = 0;
- m_status = eGjkValid;
- m_shape = shapearg;
- m_distance = 0;
- /* Initialize simplex */
- m_simplices[0].rank = 0;
- m_ray = guess;
- const btScalar sqrl = m_ray.length2();
- appendvertice(m_simplices[0], sqrl > 0 ? -m_ray : btVector3(1, 0, 0));
- m_simplices[0].p[0] = 1;
- m_ray = m_simplices[0].c[0]->w;
- sqdist = sqrl;
- lastw[0] =
- lastw[1] =
- lastw[2] =
- lastw[3] = m_ray;
- /* Loop */
- do
- {
- const U next = 1 - m_current;
- sSimplex& cs = m_simplices[m_current];
- sSimplex& ns = m_simplices[next];
- /* Check zero */
- const btScalar rl = m_ray.length();
- if (rl < GJK_MIN_DISTANCE)
- { /* Touching or inside */
- m_status = eGjkInside;
- break;
- }
- /* Append new vertice in -'v' direction */
- appendvertice(cs, -m_ray);
- const btVector3& w = cs.c[cs.rank - 1]->w;
- bool found = false;
- for (U i = 0; i < 4; ++i)
- {
- if ((w - lastw[i]).length2() < GJK_DUPLICATED_EPS)
- {
- found = true;
- break;
- }
- }
- if (found)
- { /* Return old simplex */
- removevertice(m_simplices[m_current]);
- break;
- }
- else
- { /* Update lastw */
- lastw[clastw = (clastw + 1) & 3] = w;
- }
- /* Check for termination */
- const btScalar omega = btDot(m_ray, w) / rl;
- alpha = btMax(omega, alpha);
- if (((rl - alpha) - (GJK_ACCURARY * rl)) <= 0)
- { /* Return old simplex */
- removevertice(m_simplices[m_current]);
- break;
- }
- /* Reduce simplex */
- btScalar weights[4];
- U mask = 0;
- switch (cs.rank)
- {
- case 2:
- sqdist = projectorigin(cs.c[0]->w,
- cs.c[1]->w,
- weights, mask);
- break;
- case 3:
- sqdist = projectorigin(cs.c[0]->w,
- cs.c[1]->w,
- cs.c[2]->w,
- weights, mask);
- break;
- case 4:
- sqdist = projectorigin(cs.c[0]->w,
- cs.c[1]->w,
- cs.c[2]->w,
- cs.c[3]->w,
- weights, mask);
- break;
- }
- if (sqdist >= 0)
- { /* Valid */
- ns.rank = 0;
- m_ray = btVector3(0, 0, 0);
- m_current = next;
- for (U i = 0, ni = cs.rank; i < ni; ++i)
- {
- if (mask & (1 << i))
- {
- ns.c[ns.rank] = cs.c[i];
- ns.p[ns.rank++] = weights[i];
- m_ray += cs.c[i]->w * weights[i];
- }
- else
- {
- m_free[m_nfree++] = cs.c[i];
- }
- }
- if (mask == 15) m_status = eGjkInside;
- }
- else
- { /* Return old simplex */
- removevertice(m_simplices[m_current]);
- break;
- }
- m_status = ((++iterations) < GJK_MAX_ITERATIONS) ? m_status : eGjkFailed;
- } while (m_status == eGjkValid);
- m_simplex = &m_simplices[m_current];
- switch (m_status)
- {
- case eGjkValid:
- m_distance = m_ray.length();
- break;
- case eGjkInside:
- m_distance = 0;
- break;
- default:
- {
- }
- }
- return (m_status);
- }
- bool EncloseOrigin()
- {
- switch (m_simplex->rank)
- {
- case 1:
- {
- for (U i = 0; i < 3; ++i)
- {
- btVector3 axis = btVector3(0, 0, 0);
- axis[i] = 1;
- appendvertice(*m_simplex, axis);
- if (EncloseOrigin()) return (true);
- removevertice(*m_simplex);
- appendvertice(*m_simplex, -axis);
- if (EncloseOrigin()) return (true);
- removevertice(*m_simplex);
- }
- }
- break;
- case 2:
- {
- const btVector3 d = m_simplex->c[1]->w - m_simplex->c[0]->w;
- for (U i = 0; i < 3; ++i)
- {
- btVector3 axis = btVector3(0, 0, 0);
- axis[i] = 1;
- const btVector3 p = btCross(d, axis);
- if (p.length2() > 0)
- {
- appendvertice(*m_simplex, p);
- if (EncloseOrigin()) return (true);
- removevertice(*m_simplex);
- appendvertice(*m_simplex, -p);
- if (EncloseOrigin()) return (true);
- removevertice(*m_simplex);
- }
- }
- }
- break;
- case 3:
- {
- const btVector3 n = btCross(m_simplex->c[1]->w - m_simplex->c[0]->w,
- m_simplex->c[2]->w - m_simplex->c[0]->w);
- if (n.length2() > 0)
- {
- appendvertice(*m_simplex, n);
- if (EncloseOrigin()) return (true);
- removevertice(*m_simplex);
- appendvertice(*m_simplex, -n);
- if (EncloseOrigin()) return (true);
- removevertice(*m_simplex);
- }
- }
- break;
- case 4:
- {
- if (btFabs(det(m_simplex->c[0]->w - m_simplex->c[3]->w,
- m_simplex->c[1]->w - m_simplex->c[3]->w,
- m_simplex->c[2]->w - m_simplex->c[3]->w)) > 0)
- return (true);
- }
- break;
- }
- return (false);
- }
- /* Internals */
- void getsupport(const btVector3& d, sSV& sv) const
- {
- sv.d = d / d.length();
- sv.w = m_shape.Support(sv.d);
- }
- void removevertice(sSimplex& simplex)
- {
- m_free[m_nfree++] = simplex.c[--simplex.rank];
- }
- void appendvertice(sSimplex& simplex, const btVector3& v)
- {
- simplex.p[simplex.rank] = 0;
- simplex.c[simplex.rank] = m_free[--m_nfree];
- getsupport(v, *simplex.c[simplex.rank++]);
- }
- static btScalar det(const btVector3& a, const btVector3& b, const btVector3& c)
- {
- return (a.y() * b.z() * c.x() + a.z() * b.x() * c.y() -
- a.x() * b.z() * c.y() - a.y() * b.x() * c.z() +
- a.x() * b.y() * c.z() - a.z() * b.y() * c.x());
- }
- static btScalar projectorigin(const btVector3& a,
- const btVector3& b,
- btScalar* w, U& m)
- {
- const btVector3 d = b - a;
- const btScalar l = d.length2();
- if (l > GJK_SIMPLEX2_EPS)
- {
- const btScalar t(l > 0 ? -btDot(a, d) / l : 0);
- if (t >= 1)
- {
- w[0] = 0;
- w[1] = 1;
- m = 2;
- return (b.length2());
- }
- else if (t <= 0)
- {
- w[0] = 1;
- w[1] = 0;
- m = 1;
- return (a.length2());
- }
- else
- {
- w[0] = 1 - (w[1] = t);
- m = 3;
- return ((a + d * t).length2());
- }
- }
- return (-1);
- }
- static btScalar projectorigin(const btVector3& a,
- const btVector3& b,
- const btVector3& c,
- btScalar* w, U& m)
- {
- static const U imd3[] = {1, 2, 0};
- const btVector3* vt[] = {&a, &b, &c};
- const btVector3 dl[] = {a - b, b - c, c - a};
- const btVector3 n = btCross(dl[0], dl[1]);
- const btScalar l = n.length2();
- if (l > GJK_SIMPLEX3_EPS)
- {
- btScalar mindist = -1;
- btScalar subw[2] = {0.f, 0.f};
- U subm(0);
- for (U i = 0; i < 3; ++i)
- {
- if (btDot(*vt[i], btCross(dl[i], n)) > 0)
- {
- const U j = imd3[i];
- const btScalar subd(projectorigin(*vt[i], *vt[j], subw, subm));
- if ((mindist < 0) || (subd < mindist))
- {
- mindist = subd;
- m = static_cast<U>(((subm & 1) ? 1 << i : 0) + ((subm & 2) ? 1 << j : 0));
- w[i] = subw[0];
- w[j] = subw[1];
- w[imd3[j]] = 0;
- }
- }
- }
- if (mindist < 0)
- {
- const btScalar d = btDot(a, n);
- const btScalar s = btSqrt(l);
- const btVector3 p = n * (d / l);
- mindist = p.length2();
- m = 7;
- w[0] = (btCross(dl[1], b - p)).length() / s;
- w[1] = (btCross(dl[2], c - p)).length() / s;
- w[2] = 1 - (w[0] + w[1]);
- }
- return (mindist);
- }
- return (-1);
- }
- static btScalar projectorigin(const btVector3& a,
- const btVector3& b,
- const btVector3& c,
- const btVector3& d,
- btScalar* w, U& m)
- {
- static const U imd3[] = {1, 2, 0};
- const btVector3* vt[] = {&a, &b, &c, &d};
- const btVector3 dl[] = {a - d, b - d, c - d};
- const btScalar vl = det(dl[0], dl[1], dl[2]);
- const bool ng = (vl * btDot(a, btCross(b - c, a - b))) <= 0;
- if (ng && (btFabs(vl) > GJK_SIMPLEX4_EPS))
- {
- btScalar mindist = -1;
- btScalar subw[3] = {0.f, 0.f, 0.f};
- U subm(0);
- for (U i = 0; i < 3; ++i)
- {
- const U j = imd3[i];
- const btScalar s = vl * btDot(d, btCross(dl[i], dl[j]));
- if (s > 0)
- {
- const btScalar subd = projectorigin(*vt[i], *vt[j], d, subw, subm);
- if ((mindist < 0) || (subd < mindist))
- {
- mindist = subd;
- m = static_cast<U>((subm & 1 ? 1 << i : 0) +
- (subm & 2 ? 1 << j : 0) +
- (subm & 4 ? 8 : 0));
- w[i] = subw[0];
- w[j] = subw[1];
- w[imd3[j]] = 0;
- w[3] = subw[2];
- }
- }
- }
- if (mindist < 0)
- {
- mindist = 0;
- m = 15;
- w[0] = det(c, b, d) / vl;
- w[1] = det(a, c, d) / vl;
- w[2] = det(b, a, d) / vl;
- w[3] = 1 - (w[0] + w[1] + w[2]);
- }
- return (mindist);
- }
- return (-1);
- }
-};
-
-enum eEpaStatus
-{
- eEpaValid,
- eEpaTouching,
- eEpaDegenerated,
- eEpaNonConvex,
- eEpaInvalidHull,
- eEpaOutOfFaces,
- eEpaOutOfVertices,
- eEpaAccuraryReached,
- eEpaFallBack,
- eEpaFailed
-};
-
-// EPA
-template <typename btConvexTemplate>
-struct EPA
-{
- /* Types */
-
- struct sFace
- {
- btVector3 n;
- btScalar d;
- typename GJK<btConvexTemplate>::sSV* c[3];
- sFace* f[3];
- sFace* l[2];
- U1 e[3];
- U1 pass;
- };
- struct sList
- {
- sFace* root;
- U count;
- sList() : root(0), count(0) {}
- };
- struct sHorizon
- {
- sFace* cf;
- sFace* ff;
- U nf;
- sHorizon() : cf(0), ff(0), nf(0) {}
- };
-
- /* Fields */
- eEpaStatus m_status;
- typename GJK<btConvexTemplate>::sSimplex m_result;
- btVector3 m_normal;
- btScalar m_depth;
- typename GJK<btConvexTemplate>::sSV m_sv_store[EPA_MAX_VERTICES];
- sFace m_fc_store[EPA_MAX_FACES];
- U m_nextsv;
- sList m_hull;
- sList m_stock;
- /* Methods */
- EPA()
- {
- Initialize();
- }
-
- static inline void bind(sFace* fa, U ea, sFace* fb, U eb)
- {
- fa->e[ea] = (U1)eb;
- fa->f[ea] = fb;
- fb->e[eb] = (U1)ea;
- fb->f[eb] = fa;
- }
- static inline void append(sList& list, sFace* face)
- {
- face->l[0] = 0;
- face->l[1] = list.root;
- if (list.root) list.root->l[0] = face;
- list.root = face;
- ++list.count;
- }
- static inline void remove(sList& list, sFace* face)
- {
- if (face->l[1]) face->l[1]->l[0] = face->l[0];
- if (face->l[0]) face->l[0]->l[1] = face->l[1];
- if (face == list.root) list.root = face->l[1];
- --list.count;
- }
-
- void Initialize()
- {
- m_status = eEpaFailed;
- m_normal = btVector3(0, 0, 0);
- m_depth = 0;
- m_nextsv = 0;
- for (U i = 0; i < EPA_MAX_FACES; ++i)
- {
- append(m_stock, &m_fc_store[EPA_MAX_FACES - i - 1]);
- }
- }
- eEpaStatus Evaluate(GJK<btConvexTemplate>& gjk, const btVector3& guess)
- {
- typename GJK<btConvexTemplate>::sSimplex& simplex = *gjk.m_simplex;
- if ((simplex.rank > 1) && gjk.EncloseOrigin())
- {
- /* Clean up */
- while (m_hull.root)
- {
- sFace* f = m_hull.root;
- remove(m_hull, f);
- append(m_stock, f);
- }
- m_status = eEpaValid;
- m_nextsv = 0;
- /* Orient simplex */
- if (gjk.det(simplex.c[0]->w - simplex.c[3]->w,
- simplex.c[1]->w - simplex.c[3]->w,
- simplex.c[2]->w - simplex.c[3]->w) < 0)
- {
- btSwap(simplex.c[0], simplex.c[1]);
- btSwap(simplex.p[0], simplex.p[1]);
- }
- /* Build initial hull */
- sFace* tetra[] = {newface(simplex.c[0], simplex.c[1], simplex.c[2], true),
- newface(simplex.c[1], simplex.c[0], simplex.c[3], true),
- newface(simplex.c[2], simplex.c[1], simplex.c[3], true),
- newface(simplex.c[0], simplex.c[2], simplex.c[3], true)};
- if (m_hull.count == 4)
- {
- sFace* best = findbest();
- sFace outer = *best;
- U pass = 0;
- U iterations = 0;
- bind(tetra[0], 0, tetra[1], 0);
- bind(tetra[0], 1, tetra[2], 0);
- bind(tetra[0], 2, tetra[3], 0);
- bind(tetra[1], 1, tetra[3], 2);
- bind(tetra[1], 2, tetra[2], 1);
- bind(tetra[2], 2, tetra[3], 1);
- m_status = eEpaValid;
- for (; iterations < EPA_MAX_ITERATIONS; ++iterations)
- {
- if (m_nextsv < EPA_MAX_VERTICES)
- {
- sHorizon horizon;
- typename GJK<btConvexTemplate>::sSV* w = &m_sv_store[m_nextsv++];
- bool valid = true;
- best->pass = (U1)(++pass);
- gjk.getsupport(best->n, *w);
- const btScalar wdist = btDot(best->n, w->w) - best->d;
- if (wdist > EPA_ACCURACY)
- {
- for (U j = 0; (j < 3) && valid; ++j)
- {
- valid &= expand(pass, w,
- best->f[j], best->e[j],
- horizon);
- }
- if (valid && (horizon.nf >= 3))
- {
- bind(horizon.cf, 1, horizon.ff, 2);
- remove(m_hull, best);
- append(m_stock, best);
- best = findbest();
- outer = *best;
- }
- else
- {
- m_status = eEpaInvalidHull;
- break;
- }
- }
- else
- {
- m_status = eEpaAccuraryReached;
- break;
- }
- }
- else
- {
- m_status = eEpaOutOfVertices;
- break;
- }
- }
- const btVector3 projection = outer.n * outer.d;
- m_normal = outer.n;
- m_depth = outer.d;
- m_result.rank = 3;
- m_result.c[0] = outer.c[0];
- m_result.c[1] = outer.c[1];
- m_result.c[2] = outer.c[2];
- m_result.p[0] = btCross(outer.c[1]->w - projection,
- outer.c[2]->w - projection)
- .length();
- m_result.p[1] = btCross(outer.c[2]->w - projection,
- outer.c[0]->w - projection)
- .length();
- m_result.p[2] = btCross(outer.c[0]->w - projection,
- outer.c[1]->w - projection)
- .length();
- const btScalar sum = m_result.p[0] + m_result.p[1] + m_result.p[2];
- m_result.p[0] /= sum;
- m_result.p[1] /= sum;
- m_result.p[2] /= sum;
- return (m_status);
- }
- }
- /* Fallback */
- m_status = eEpaFallBack;
- m_normal = -guess;
- const btScalar nl = m_normal.length();
- if (nl > 0)
- m_normal = m_normal / nl;
- else
- m_normal = btVector3(1, 0, 0);
- m_depth = 0;
- m_result.rank = 1;
- m_result.c[0] = simplex.c[0];
- m_result.p[0] = 1;
- return (m_status);
- }
- bool getedgedist(sFace* face, typename GJK<btConvexTemplate>::sSV* a, typename GJK<btConvexTemplate>::sSV* b, btScalar& dist)
- {
- const btVector3 ba = b->w - a->w;
- const btVector3 n_ab = btCross(ba, face->n); // Outward facing edge normal direction, on triangle plane
- const btScalar a_dot_nab = btDot(a->w, n_ab); // Only care about the sign to determine inside/outside, so not normalization required
-
- if (a_dot_nab < 0)
- {
- // Outside of edge a->b
-
- const btScalar ba_l2 = ba.length2();
- const btScalar a_dot_ba = btDot(a->w, ba);
- const btScalar b_dot_ba = btDot(b->w, ba);
-
- if (a_dot_ba > 0)
- {
- // Pick distance vertex a
- dist = a->w.length();
- }
- else if (b_dot_ba < 0)
- {
- // Pick distance vertex b
- dist = b->w.length();
- }
- else
- {
- // Pick distance to edge a->b
- const btScalar a_dot_b = btDot(a->w, b->w);
- dist = btSqrt(btMax((a->w.length2() * b->w.length2() - a_dot_b * a_dot_b) / ba_l2, (btScalar)0));
- }
-
- return true;
- }
-
- return false;
- }
- sFace* newface(typename GJK<btConvexTemplate>::sSV* a, typename GJK<btConvexTemplate>::sSV* b, typename GJK<btConvexTemplate>::sSV* c, bool forced)
- {
- if (m_stock.root)
- {
- sFace* face = m_stock.root;
- remove(m_stock, face);
- append(m_hull, face);
- face->pass = 0;
- face->c[0] = a;
- face->c[1] = b;
- face->c[2] = c;
- face->n = btCross(b->w - a->w, c->w - a->w);
- const btScalar l = face->n.length();
- const bool v = l > EPA_ACCURACY;
-
- if (v)
- {
- if (!(getedgedist(face, a, b, face->d) ||
- getedgedist(face, b, c, face->d) ||
- getedgedist(face, c, a, face->d)))
- {
- // Origin projects to the interior of the triangle
- // Use distance to triangle plane
- face->d = btDot(a->w, face->n) / l;
- }
-
- face->n /= l;
- if (forced || (face->d >= -EPA_PLANE_EPS))
- {
- return face;
- }
- else
- m_status = eEpaNonConvex;
- }
- else
- m_status = eEpaDegenerated;
-
- remove(m_hull, face);
- append(m_stock, face);
- return 0;
- }
- m_status = m_stock.root ? eEpaOutOfVertices : eEpaOutOfFaces;
- return 0;
- }
- sFace* findbest()
- {
- sFace* minf = m_hull.root;
- btScalar mind = minf->d * minf->d;
- for (sFace* f = minf->l[1]; f; f = f->l[1])
- {
- const btScalar sqd = f->d * f->d;
- if (sqd < mind)
- {
- minf = f;
- mind = sqd;
- }
- }
- return (minf);
- }
- bool expand(U pass, typename GJK<btConvexTemplate>::sSV* w, sFace* f, U e, sHorizon& horizon)
- {
- static const U i1m3[] = {1, 2, 0};
- static const U i2m3[] = {2, 0, 1};
- if (f->pass != pass)
- {
- const U e1 = i1m3[e];
- if ((btDot(f->n, w->w) - f->d) < -EPA_PLANE_EPS)
- {
- sFace* nf = newface(f->c[e1], f->c[e], w, false);
- if (nf)
- {
- bind(nf, 0, f, e);
- if (horizon.cf)
- bind(horizon.cf, 1, nf, 2);
- else
- horizon.ff = nf;
- horizon.cf = nf;
- ++horizon.nf;
- return (true);
- }
- }
- else
- {
- const U e2 = i2m3[e];
- f->pass = (U1)pass;
- if (expand(pass, w, f->f[e1], f->e[e1], horizon) &&
- expand(pass, w, f->f[e2], f->e[e2], horizon))
- {
- remove(m_hull, f);
- append(m_stock, f);
- return (true);
- }
- }
- }
- return (false);
- }
-};
-
-template <typename btConvexTemplate>
-static void Initialize(const btConvexTemplate& a, const btConvexTemplate& b,
- btGjkEpaSolver3::sResults& results,
- MinkowskiDiff<btConvexTemplate>& shape)
-{
- /* Results */
- results.witnesses[0] =
- results.witnesses[1] = btVector3(0, 0, 0);
- results.status = btGjkEpaSolver3::sResults::Separated;
- /* Shape */
-
- shape.m_toshape1 = b.getWorldTransform().getBasis().transposeTimes(a.getWorldTransform().getBasis());
- shape.m_toshape0 = a.getWorldTransform().inverseTimes(b.getWorldTransform());
-}
-
-//
-// Api
-//
-
-//
-template <typename btConvexTemplate>
-bool btGjkEpaSolver3_Distance(const btConvexTemplate& a, const btConvexTemplate& b,
- const btVector3& guess,
- btGjkEpaSolver3::sResults& results)
-{
- MinkowskiDiff<btConvexTemplate> shape(a, b);
- Initialize(a, b, results, shape);
- GJK<btConvexTemplate> gjk(a, b);
- eGjkStatus gjk_status = gjk.Evaluate(shape, guess);
- if (gjk_status == eGjkValid)
- {
- btVector3 w0 = btVector3(0, 0, 0);
- btVector3 w1 = btVector3(0, 0, 0);
- for (U i = 0; i < gjk.m_simplex->rank; ++i)
- {
- const btScalar p = gjk.m_simplex->p[i];
- w0 += shape.Support(gjk.m_simplex->c[i]->d, 0) * p;
- w1 += shape.Support(-gjk.m_simplex->c[i]->d, 1) * p;
- }
- results.witnesses[0] = a.getWorldTransform() * w0;
- results.witnesses[1] = a.getWorldTransform() * w1;
- results.normal = w0 - w1;
- results.distance = results.normal.length();
- results.normal /= results.distance > GJK_MIN_DISTANCE ? results.distance : 1;
- return (true);
- }
- else
- {
- results.status = gjk_status == eGjkInside ? btGjkEpaSolver3::sResults::Penetrating : btGjkEpaSolver3::sResults::GJK_Failed;
- return (false);
- }
-}
-
-template <typename btConvexTemplate>
-bool btGjkEpaSolver3_Penetration(const btConvexTemplate& a,
- const btConvexTemplate& b,
- const btVector3& guess,
- btGjkEpaSolver3::sResults& results)
-{
- MinkowskiDiff<btConvexTemplate> shape(a, b);
- Initialize(a, b, results, shape);
- GJK<btConvexTemplate> gjk(a, b);
- eGjkStatus gjk_status = gjk.Evaluate(shape, -guess);
- switch (gjk_status)
- {
- case eGjkInside:
- {
- EPA<btConvexTemplate> epa;
- eEpaStatus epa_status = epa.Evaluate(gjk, -guess);
- if (epa_status != eEpaFailed)
- {
- btVector3 w0 = btVector3(0, 0, 0);
- for (U i = 0; i < epa.m_result.rank; ++i)
- {
- w0 += shape.Support(epa.m_result.c[i]->d, 0) * epa.m_result.p[i];
- }
- results.status = btGjkEpaSolver3::sResults::Penetrating;
- results.witnesses[0] = a.getWorldTransform() * w0;
- results.witnesses[1] = a.getWorldTransform() * (w0 - epa.m_normal * epa.m_depth);
- results.normal = -epa.m_normal;
- results.distance = -epa.m_depth;
- return (true);
- }
- else
- results.status = btGjkEpaSolver3::sResults::EPA_Failed;
- }
- break;
- case eGjkFailed:
- results.status = btGjkEpaSolver3::sResults::GJK_Failed;
- break;
- default:
- {
- }
- }
- return (false);
-}
-
-#if 0
-int btComputeGjkEpaPenetration2(const btCollisionDescription& colDesc, btDistanceInfo* distInfo)
-{
- btGjkEpaSolver3::sResults results;
- btVector3 guess = colDesc.m_firstDir;
-
- bool res = btGjkEpaSolver3::Penetration(colDesc.m_objA,colDesc.m_objB,
- colDesc.m_transformA,colDesc.m_transformB,
- colDesc.m_localSupportFuncA,colDesc.m_localSupportFuncB,
- guess,
- results);
- if (res)
- {
- if ((results.status==btGjkEpaSolver3::sResults::Penetrating) || results.status==GJK::eStatus::Inside)
- {
- //normal could be 'swapped'
-
- distInfo->m_distance = results.distance;
- distInfo->m_normalBtoA = results.normal;
- btVector3 tmpNormalInB = results.witnesses[1]-results.witnesses[0];
- btScalar lenSqr = tmpNormalInB.length2();
- if (lenSqr <= (SIMD_EPSILON*SIMD_EPSILON))
- {
- tmpNormalInB = results.normal;
- lenSqr = results.normal.length2();
- }
-
- if (lenSqr > (SIMD_EPSILON*SIMD_EPSILON))
- {
- tmpNormalInB /= btSqrt(lenSqr);
- btScalar distance2 = -(results.witnesses[0]-results.witnesses[1]).length();
- //only replace valid penetrations when the result is deeper (check)
- //if ((distance2 < results.distance))
- {
- distInfo->m_distance = distance2;
- distInfo->m_pointOnA= results.witnesses[0];
- distInfo->m_pointOnB= results.witnesses[1];
- distInfo->m_normalBtoA= tmpNormalInB;
- return 0;
- }
- }
- }
-
- }
-
- return -1;
-}
-#endif
-
-template <typename btConvexTemplate, typename btDistanceInfoTemplate>
-int btComputeGjkDistance(const btConvexTemplate& a, const btConvexTemplate& b,
- const btGjkCollisionDescription& colDesc, btDistanceInfoTemplate* distInfo)
-{
- btGjkEpaSolver3::sResults results;
- btVector3 guess = colDesc.m_firstDir;
-
- bool isSeparated = btGjkEpaSolver3_Distance(a, b,
- guess,
- results);
- if (isSeparated)
- {
- distInfo->m_distance = results.distance;
- distInfo->m_pointOnA = results.witnesses[0];
- distInfo->m_pointOnB = results.witnesses[1];
- distInfo->m_normalBtoA = results.normal;
- return 0;
- }
-
- return -1;
-}
-
-/* Symbols cleanup */
-
-#undef GJK_MAX_ITERATIONS
-#undef GJK_ACCURARY
-#undef GJK_MIN_DISTANCE
-#undef GJK_DUPLICATED_EPS
-#undef GJK_SIMPLEX2_EPS
-#undef GJK_SIMPLEX3_EPS
-#undef GJK_SIMPLEX4_EPS
-
-#undef EPA_MAX_VERTICES
-#undef EPA_MAX_FACES
-#undef EPA_MAX_ITERATIONS
-#undef EPA_ACCURACY
-#undef EPA_FALLBACK
-#undef EPA_PLANE_EPS
-#undef EPA_INSIDE_EPS
-
-#endif //BT_GJK_EPA3_H
+/*
+Bullet Continuous Collision Detection and Physics Library
+Copyright (c) 2003-2014 Erwin Coumans http://continuousphysics.com/Bullet/
+
+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.
+*/
+
+/*
+Initial GJK-EPA collision solver by Nathanael Presson, 2008
+Improvements and refactoring by Erwin Coumans, 2008-2014
+*/
+#ifndef BT_GJK_EPA3_H
+#define BT_GJK_EPA3_H
+
+#include "LinearMath/btTransform.h"
+#include "btGjkCollisionDescription.h"
+
+struct btGjkEpaSolver3
+{
+ struct sResults
+ {
+ enum eStatus
+ {
+ Separated, /* Shapes doesnt penetrate */
+ Penetrating, /* Shapes are penetrating */
+ GJK_Failed, /* GJK phase fail, no big issue, shapes are probably just 'touching' */
+ EPA_Failed /* EPA phase fail, bigger problem, need to save parameters, and debug */
+ } status;
+ btVector3 witnesses[2];
+ btVector3 normal;
+ btScalar distance;
+ };
+};
+
+#if defined(DEBUG) || defined(_DEBUG)
+#include <stdio.h> //for debug printf
+#ifdef __SPU__
+#include <spu_printf.h>
+#define printf spu_printf
+#endif //__SPU__
+#endif
+
+// Config
+
+/* GJK */
+#define GJK_MAX_ITERATIONS 128
+#define GJK_ACCURARY ((btScalar)0.0001)
+#define GJK_MIN_DISTANCE ((btScalar)0.0001)
+#define GJK_DUPLICATED_EPS ((btScalar)0.0001)
+#define GJK_SIMPLEX2_EPS ((btScalar)0.0)
+#define GJK_SIMPLEX3_EPS ((btScalar)0.0)
+#define GJK_SIMPLEX4_EPS ((btScalar)0.0)
+
+/* EPA */
+#define EPA_MAX_VERTICES 64
+#define EPA_MAX_FACES (EPA_MAX_VERTICES * 2)
+#define EPA_MAX_ITERATIONS 255
+#define EPA_ACCURACY ((btScalar)0.0001)
+#define EPA_FALLBACK (10 * EPA_ACCURACY)
+#define EPA_PLANE_EPS ((btScalar)0.00001)
+#define EPA_INSIDE_EPS ((btScalar)0.01)
+
+// Shorthands
+typedef unsigned int U;
+typedef unsigned char U1;
+
+// MinkowskiDiff
+template <typename btConvexTemplate>
+struct MinkowskiDiff
+{
+ const btConvexTemplate* m_convexAPtr;
+ const btConvexTemplate* m_convexBPtr;
+
+ btMatrix3x3 m_toshape1;
+ btTransform m_toshape0;
+
+ bool m_enableMargin;
+
+ MinkowskiDiff(const btConvexTemplate& a, const btConvexTemplate& b)
+ : m_convexAPtr(&a),
+ m_convexBPtr(&b)
+ {
+ }
+
+ void EnableMargin(bool enable)
+ {
+ m_enableMargin = enable;
+ }
+ inline btVector3 Support0(const btVector3& d) const
+ {
+ return m_convexAPtr->getLocalSupportWithMargin(d);
+ }
+ inline btVector3 Support1(const btVector3& d) const
+ {
+ return m_toshape0 * m_convexBPtr->getLocalSupportWithMargin(m_toshape1 * d);
+ }
+
+ inline btVector3 Support(const btVector3& d) const
+ {
+ return (Support0(d) - Support1(-d));
+ }
+ btVector3 Support(const btVector3& d, U index) const
+ {
+ if (index)
+ return (Support1(d));
+ else
+ return (Support0(d));
+ }
+};
+
+enum eGjkStatus
+{
+ eGjkValid,
+ eGjkInside,
+ eGjkFailed
+};
+
+// GJK
+template <typename btConvexTemplate>
+struct GJK
+{
+ /* Types */
+ struct sSV
+ {
+ btVector3 d, w;
+ };
+ struct sSimplex
+ {
+ sSV* c[4];
+ btScalar p[4];
+ U rank;
+ };
+
+ /* Fields */
+
+ MinkowskiDiff<btConvexTemplate> m_shape;
+ btVector3 m_ray;
+ btScalar m_distance;
+ sSimplex m_simplices[2];
+ sSV m_store[4];
+ sSV* m_free[4];
+ U m_nfree;
+ U m_current;
+ sSimplex* m_simplex;
+ eGjkStatus m_status;
+ /* Methods */
+
+ GJK(const btConvexTemplate& a, const btConvexTemplate& b)
+ : m_shape(a, b)
+ {
+ Initialize();
+ }
+ void Initialize()
+ {
+ m_ray = btVector3(0, 0, 0);
+ m_nfree = 0;
+ m_status = eGjkFailed;
+ m_current = 0;
+ m_distance = 0;
+ }
+ eGjkStatus Evaluate(const MinkowskiDiff<btConvexTemplate>& shapearg, const btVector3& guess)
+ {
+ U iterations = 0;
+ btScalar sqdist = 0;
+ btScalar alpha = 0;
+ btVector3 lastw[4];
+ U clastw = 0;
+ /* Initialize solver */
+ m_free[0] = &m_store[0];
+ m_free[1] = &m_store[1];
+ m_free[2] = &m_store[2];
+ m_free[3] = &m_store[3];
+ m_nfree = 4;
+ m_current = 0;
+ m_status = eGjkValid;
+ m_shape = shapearg;
+ m_distance = 0;
+ /* Initialize simplex */
+ m_simplices[0].rank = 0;
+ m_ray = guess;
+ const btScalar sqrl = m_ray.length2();
+ appendvertice(m_simplices[0], sqrl > 0 ? -m_ray : btVector3(1, 0, 0));
+ m_simplices[0].p[0] = 1;
+ m_ray = m_simplices[0].c[0]->w;
+ sqdist = sqrl;
+ lastw[0] =
+ lastw[1] =
+ lastw[2] =
+ lastw[3] = m_ray;
+ /* Loop */
+ do
+ {
+ const U next = 1 - m_current;
+ sSimplex& cs = m_simplices[m_current];
+ sSimplex& ns = m_simplices[next];
+ /* Check zero */
+ const btScalar rl = m_ray.length();
+ if (rl < GJK_MIN_DISTANCE)
+ { /* Touching or inside */
+ m_status = eGjkInside;
+ break;
+ }
+ /* Append new vertice in -'v' direction */
+ appendvertice(cs, -m_ray);
+ const btVector3& w = cs.c[cs.rank - 1]->w;
+ bool found = false;
+ for (U i = 0; i < 4; ++i)
+ {
+ if ((w - lastw[i]).length2() < GJK_DUPLICATED_EPS)
+ {
+ found = true;
+ break;
+ }
+ }
+ if (found)
+ { /* Return old simplex */
+ removevertice(m_simplices[m_current]);
+ break;
+ }
+ else
+ { /* Update lastw */
+ lastw[clastw = (clastw + 1) & 3] = w;
+ }
+ /* Check for termination */
+ const btScalar omega = btDot(m_ray, w) / rl;
+ alpha = btMax(omega, alpha);
+ if (((rl - alpha) - (GJK_ACCURARY * rl)) <= 0)
+ { /* Return old simplex */
+ removevertice(m_simplices[m_current]);
+ break;
+ }
+ /* Reduce simplex */
+ btScalar weights[4];
+ U mask = 0;
+ switch (cs.rank)
+ {
+ case 2:
+ sqdist = projectorigin(cs.c[0]->w,
+ cs.c[1]->w,
+ weights, mask);
+ break;
+ case 3:
+ sqdist = projectorigin(cs.c[0]->w,
+ cs.c[1]->w,
+ cs.c[2]->w,
+ weights, mask);
+ break;
+ case 4:
+ sqdist = projectorigin(cs.c[0]->w,
+ cs.c[1]->w,
+ cs.c[2]->w,
+ cs.c[3]->w,
+ weights, mask);
+ break;
+ }
+ if (sqdist >= 0)
+ { /* Valid */
+ ns.rank = 0;
+ m_ray = btVector3(0, 0, 0);
+ m_current = next;
+ for (U i = 0, ni = cs.rank; i < ni; ++i)
+ {
+ if (mask & (1 << i))
+ {
+ ns.c[ns.rank] = cs.c[i];
+ ns.p[ns.rank++] = weights[i];
+ m_ray += cs.c[i]->w * weights[i];
+ }
+ else
+ {
+ m_free[m_nfree++] = cs.c[i];
+ }
+ }
+ if (mask == 15) m_status = eGjkInside;
+ }
+ else
+ { /* Return old simplex */
+ removevertice(m_simplices[m_current]);
+ break;
+ }
+ m_status = ((++iterations) < GJK_MAX_ITERATIONS) ? m_status : eGjkFailed;
+ } while (m_status == eGjkValid);
+ m_simplex = &m_simplices[m_current];
+ switch (m_status)
+ {
+ case eGjkValid:
+ m_distance = m_ray.length();
+ break;
+ case eGjkInside:
+ m_distance = 0;
+ break;
+ default:
+ {
+ }
+ }
+ return (m_status);
+ }
+ bool EncloseOrigin()
+ {
+ switch (m_simplex->rank)
+ {
+ case 1:
+ {
+ for (U i = 0; i < 3; ++i)
+ {
+ btVector3 axis = btVector3(0, 0, 0);
+ axis[i] = 1;
+ appendvertice(*m_simplex, axis);
+ if (EncloseOrigin()) return (true);
+ removevertice(*m_simplex);
+ appendvertice(*m_simplex, -axis);
+ if (EncloseOrigin()) return (true);
+ removevertice(*m_simplex);
+ }
+ }
+ break;
+ case 2:
+ {
+ const btVector3 d = m_simplex->c[1]->w - m_simplex->c[0]->w;
+ for (U i = 0; i < 3; ++i)
+ {
+ btVector3 axis = btVector3(0, 0, 0);
+ axis[i] = 1;
+ const btVector3 p = btCross(d, axis);
+ if (p.length2() > 0)
+ {
+ appendvertice(*m_simplex, p);
+ if (EncloseOrigin()) return (true);
+ removevertice(*m_simplex);
+ appendvertice(*m_simplex, -p);
+ if (EncloseOrigin()) return (true);
+ removevertice(*m_simplex);
+ }
+ }
+ }
+ break;
+ case 3:
+ {
+ const btVector3 n = btCross(m_simplex->c[1]->w - m_simplex->c[0]->w,
+ m_simplex->c[2]->w - m_simplex->c[0]->w);
+ if (n.length2() > 0)
+ {
+ appendvertice(*m_simplex, n);
+ if (EncloseOrigin()) return (true);
+ removevertice(*m_simplex);
+ appendvertice(*m_simplex, -n);
+ if (EncloseOrigin()) return (true);
+ removevertice(*m_simplex);
+ }
+ }
+ break;
+ case 4:
+ {
+ if (btFabs(det(m_simplex->c[0]->w - m_simplex->c[3]->w,
+ m_simplex->c[1]->w - m_simplex->c[3]->w,
+ m_simplex->c[2]->w - m_simplex->c[3]->w)) > 0)
+ return (true);
+ }
+ break;
+ }
+ return (false);
+ }
+ /* Internals */
+ void getsupport(const btVector3& d, sSV& sv) const
+ {
+ sv.d = d / d.length();
+ sv.w = m_shape.Support(sv.d);
+ }
+ void removevertice(sSimplex& simplex)
+ {
+ m_free[m_nfree++] = simplex.c[--simplex.rank];
+ }
+ void appendvertice(sSimplex& simplex, const btVector3& v)
+ {
+ simplex.p[simplex.rank] = 0;
+ simplex.c[simplex.rank] = m_free[--m_nfree];
+ getsupport(v, *simplex.c[simplex.rank++]);
+ }
+ static btScalar det(const btVector3& a, const btVector3& b, const btVector3& c)
+ {
+ return (a.y() * b.z() * c.x() + a.z() * b.x() * c.y() -
+ a.x() * b.z() * c.y() - a.y() * b.x() * c.z() +
+ a.x() * b.y() * c.z() - a.z() * b.y() * c.x());
+ }
+ static btScalar projectorigin(const btVector3& a,
+ const btVector3& b,
+ btScalar* w, U& m)
+ {
+ const btVector3 d = b - a;
+ const btScalar l = d.length2();
+ if (l > GJK_SIMPLEX2_EPS)
+ {
+ const btScalar t(l > 0 ? -btDot(a, d) / l : 0);
+ if (t >= 1)
+ {
+ w[0] = 0;
+ w[1] = 1;
+ m = 2;
+ return (b.length2());
+ }
+ else if (t <= 0)
+ {
+ w[0] = 1;
+ w[1] = 0;
+ m = 1;
+ return (a.length2());
+ }
+ else
+ {
+ w[0] = 1 - (w[1] = t);
+ m = 3;
+ return ((a + d * t).length2());
+ }
+ }
+ return (-1);
+ }
+ static btScalar projectorigin(const btVector3& a,
+ const btVector3& b,
+ const btVector3& c,
+ btScalar* w, U& m)
+ {
+ static const U imd3[] = {1, 2, 0};
+ const btVector3* vt[] = {&a, &b, &c};
+ const btVector3 dl[] = {a - b, b - c, c - a};
+ const btVector3 n = btCross(dl[0], dl[1]);
+ const btScalar l = n.length2();
+ if (l > GJK_SIMPLEX3_EPS)
+ {
+ btScalar mindist = -1;
+ btScalar subw[2] = {0.f, 0.f};
+ U subm(0);
+ for (U i = 0; i < 3; ++i)
+ {
+ if (btDot(*vt[i], btCross(dl[i], n)) > 0)
+ {
+ const U j = imd3[i];
+ const btScalar subd(projectorigin(*vt[i], *vt[j], subw, subm));
+ if ((mindist < 0) || (subd < mindist))
+ {
+ mindist = subd;
+ m = static_cast<U>(((subm & 1) ? 1 << i : 0) + ((subm & 2) ? 1 << j : 0));
+ w[i] = subw[0];
+ w[j] = subw[1];
+ w[imd3[j]] = 0;
+ }
+ }
+ }
+ if (mindist < 0)
+ {
+ const btScalar d = btDot(a, n);
+ const btScalar s = btSqrt(l);
+ const btVector3 p = n * (d / l);
+ mindist = p.length2();
+ m = 7;
+ w[0] = (btCross(dl[1], b - p)).length() / s;
+ w[1] = (btCross(dl[2], c - p)).length() / s;
+ w[2] = 1 - (w[0] + w[1]);
+ }
+ return (mindist);
+ }
+ return (-1);
+ }
+ static btScalar projectorigin(const btVector3& a,
+ const btVector3& b,
+ const btVector3& c,
+ const btVector3& d,
+ btScalar* w, U& m)
+ {
+ static const U imd3[] = {1, 2, 0};
+ const btVector3* vt[] = {&a, &b, &c, &d};
+ const btVector3 dl[] = {a - d, b - d, c - d};
+ const btScalar vl = det(dl[0], dl[1], dl[2]);
+ const bool ng = (vl * btDot(a, btCross(b - c, a - b))) <= 0;
+ if (ng && (btFabs(vl) > GJK_SIMPLEX4_EPS))
+ {
+ btScalar mindist = -1;
+ btScalar subw[3] = {0.f, 0.f, 0.f};
+ U subm(0);
+ for (U i = 0; i < 3; ++i)
+ {
+ const U j = imd3[i];
+ const btScalar s = vl * btDot(d, btCross(dl[i], dl[j]));
+ if (s > 0)
+ {
+ const btScalar subd = projectorigin(*vt[i], *vt[j], d, subw, subm);
+ if ((mindist < 0) || (subd < mindist))
+ {
+ mindist = subd;
+ m = static_cast<U>((subm & 1 ? 1 << i : 0) +
+ (subm & 2 ? 1 << j : 0) +
+ (subm & 4 ? 8 : 0));
+ w[i] = subw[0];
+ w[j] = subw[1];
+ w[imd3[j]] = 0;
+ w[3] = subw[2];
+ }
+ }
+ }
+ if (mindist < 0)
+ {
+ mindist = 0;
+ m = 15;
+ w[0] = det(c, b, d) / vl;
+ w[1] = det(a, c, d) / vl;
+ w[2] = det(b, a, d) / vl;
+ w[3] = 1 - (w[0] + w[1] + w[2]);
+ }
+ return (mindist);
+ }
+ return (-1);
+ }
+};
+
+enum eEpaStatus
+{
+ eEpaValid,
+ eEpaTouching,
+ eEpaDegenerated,
+ eEpaNonConvex,
+ eEpaInvalidHull,
+ eEpaOutOfFaces,
+ eEpaOutOfVertices,
+ eEpaAccuraryReached,
+ eEpaFallBack,
+ eEpaFailed
+};
+
+// EPA
+template <typename btConvexTemplate>
+struct EPA
+{
+ /* Types */
+
+ struct sFace
+ {
+ btVector3 n;
+ btScalar d;
+ typename GJK<btConvexTemplate>::sSV* c[3];
+ sFace* f[3];
+ sFace* l[2];
+ U1 e[3];
+ U1 pass;
+ };
+ struct sList
+ {
+ sFace* root;
+ U count;
+ sList() : root(0), count(0) {}
+ };
+ struct sHorizon
+ {
+ sFace* cf;
+ sFace* ff;
+ U nf;
+ sHorizon() : cf(0), ff(0), nf(0) {}
+ };
+
+ /* Fields */
+ eEpaStatus m_status;
+ typename GJK<btConvexTemplate>::sSimplex m_result;
+ btVector3 m_normal;
+ btScalar m_depth;
+ typename GJK<btConvexTemplate>::sSV m_sv_store[EPA_MAX_VERTICES];
+ sFace m_fc_store[EPA_MAX_FACES];
+ U m_nextsv;
+ sList m_hull;
+ sList m_stock;
+ /* Methods */
+ EPA()
+ {
+ Initialize();
+ }
+
+ static inline void bind(sFace* fa, U ea, sFace* fb, U eb)
+ {
+ fa->e[ea] = (U1)eb;
+ fa->f[ea] = fb;
+ fb->e[eb] = (U1)ea;
+ fb->f[eb] = fa;
+ }
+ static inline void append(sList& list, sFace* face)
+ {
+ face->l[0] = 0;
+ face->l[1] = list.root;
+ if (list.root) list.root->l[0] = face;
+ list.root = face;
+ ++list.count;
+ }
+ static inline void remove(sList& list, sFace* face)
+ {
+ if (face->l[1]) face->l[1]->l[0] = face->l[0];
+ if (face->l[0]) face->l[0]->l[1] = face->l[1];
+ if (face == list.root) list.root = face->l[1];
+ --list.count;
+ }
+
+ void Initialize()
+ {
+ m_status = eEpaFailed;
+ m_normal = btVector3(0, 0, 0);
+ m_depth = 0;
+ m_nextsv = 0;
+ for (U i = 0; i < EPA_MAX_FACES; ++i)
+ {
+ append(m_stock, &m_fc_store[EPA_MAX_FACES - i - 1]);
+ }
+ }
+ eEpaStatus Evaluate(GJK<btConvexTemplate>& gjk, const btVector3& guess)
+ {
+ typename GJK<btConvexTemplate>::sSimplex& simplex = *gjk.m_simplex;
+ if ((simplex.rank > 1) && gjk.EncloseOrigin())
+ {
+ /* Clean up */
+ while (m_hull.root)
+ {
+ sFace* f = m_hull.root;
+ remove(m_hull, f);
+ append(m_stock, f);
+ }
+ m_status = eEpaValid;
+ m_nextsv = 0;
+ /* Orient simplex */
+ if (gjk.det(simplex.c[0]->w - simplex.c[3]->w,
+ simplex.c[1]->w - simplex.c[3]->w,
+ simplex.c[2]->w - simplex.c[3]->w) < 0)
+ {
+ btSwap(simplex.c[0], simplex.c[1]);
+ btSwap(simplex.p[0], simplex.p[1]);
+ }
+ /* Build initial hull */
+ sFace* tetra[] = {newface(simplex.c[0], simplex.c[1], simplex.c[2], true),
+ newface(simplex.c[1], simplex.c[0], simplex.c[3], true),
+ newface(simplex.c[2], simplex.c[1], simplex.c[3], true),
+ newface(simplex.c[0], simplex.c[2], simplex.c[3], true)};
+ if (m_hull.count == 4)
+ {
+ sFace* best = findbest();
+ sFace outer = *best;
+ U pass = 0;
+ U iterations = 0;
+ bind(tetra[0], 0, tetra[1], 0);
+ bind(tetra[0], 1, tetra[2], 0);
+ bind(tetra[0], 2, tetra[3], 0);
+ bind(tetra[1], 1, tetra[3], 2);
+ bind(tetra[1], 2, tetra[2], 1);
+ bind(tetra[2], 2, tetra[3], 1);
+ m_status = eEpaValid;
+ for (; iterations < EPA_MAX_ITERATIONS; ++iterations)
+ {
+ if (m_nextsv < EPA_MAX_VERTICES)
+ {
+ sHorizon horizon;
+ typename GJK<btConvexTemplate>::sSV* w = &m_sv_store[m_nextsv++];
+ bool valid = true;
+ best->pass = (U1)(++pass);
+ gjk.getsupport(best->n, *w);
+ const btScalar wdist = btDot(best->n, w->w) - best->d;
+ if (wdist > EPA_ACCURACY)
+ {
+ for (U j = 0; (j < 3) && valid; ++j)
+ {
+ valid &= expand(pass, w,
+ best->f[j], best->e[j],
+ horizon);
+ }
+ if (valid && (horizon.nf >= 3))
+ {
+ bind(horizon.cf, 1, horizon.ff, 2);
+ remove(m_hull, best);
+ append(m_stock, best);
+ best = findbest();
+ outer = *best;
+ }
+ else
+ {
+ m_status = eEpaInvalidHull;
+ break;
+ }
+ }
+ else
+ {
+ m_status = eEpaAccuraryReached;
+ break;
+ }
+ }
+ else
+ {
+ m_status = eEpaOutOfVertices;
+ break;
+ }
+ }
+ const btVector3 projection = outer.n * outer.d;
+ m_normal = outer.n;
+ m_depth = outer.d;
+ m_result.rank = 3;
+ m_result.c[0] = outer.c[0];
+ m_result.c[1] = outer.c[1];
+ m_result.c[2] = outer.c[2];
+ m_result.p[0] = btCross(outer.c[1]->w - projection,
+ outer.c[2]->w - projection)
+ .length();
+ m_result.p[1] = btCross(outer.c[2]->w - projection,
+ outer.c[0]->w - projection)
+ .length();
+ m_result.p[2] = btCross(outer.c[0]->w - projection,
+ outer.c[1]->w - projection)
+ .length();
+ const btScalar sum = m_result.p[0] + m_result.p[1] + m_result.p[2];
+ m_result.p[0] /= sum;
+ m_result.p[1] /= sum;
+ m_result.p[2] /= sum;
+ return (m_status);
+ }
+ }
+ /* Fallback */
+ m_status = eEpaFallBack;
+ m_normal = -guess;
+ const btScalar nl = m_normal.length();
+ if (nl > 0)
+ m_normal = m_normal / nl;
+ else
+ m_normal = btVector3(1, 0, 0);
+ m_depth = 0;
+ m_result.rank = 1;
+ m_result.c[0] = simplex.c[0];
+ m_result.p[0] = 1;
+ return (m_status);
+ }
+ bool getedgedist(sFace* face, typename GJK<btConvexTemplate>::sSV* a, typename GJK<btConvexTemplate>::sSV* b, btScalar& dist)
+ {
+ const btVector3 ba = b->w - a->w;
+ const btVector3 n_ab = btCross(ba, face->n); // Outward facing edge normal direction, on triangle plane
+ const btScalar a_dot_nab = btDot(a->w, n_ab); // Only care about the sign to determine inside/outside, so not normalization required
+
+ if (a_dot_nab < 0)
+ {
+ // Outside of edge a->b
+
+ const btScalar ba_l2 = ba.length2();
+ const btScalar a_dot_ba = btDot(a->w, ba);
+ const btScalar b_dot_ba = btDot(b->w, ba);
+
+ if (a_dot_ba > 0)
+ {
+ // Pick distance vertex a
+ dist = a->w.length();
+ }
+ else if (b_dot_ba < 0)
+ {
+ // Pick distance vertex b
+ dist = b->w.length();
+ }
+ else
+ {
+ // Pick distance to edge a->b
+ const btScalar a_dot_b = btDot(a->w, b->w);
+ dist = btSqrt(btMax((a->w.length2() * b->w.length2() - a_dot_b * a_dot_b) / ba_l2, (btScalar)0));
+ }
+
+ return true;
+ }
+
+ return false;
+ }
+ sFace* newface(typename GJK<btConvexTemplate>::sSV* a, typename GJK<btConvexTemplate>::sSV* b, typename GJK<btConvexTemplate>::sSV* c, bool forced)
+ {
+ if (m_stock.root)
+ {
+ sFace* face = m_stock.root;
+ remove(m_stock, face);
+ append(m_hull, face);
+ face->pass = 0;
+ face->c[0] = a;
+ face->c[1] = b;
+ face->c[2] = c;
+ face->n = btCross(b->w - a->w, c->w - a->w);
+ const btScalar l = face->n.length();
+ const bool v = l > EPA_ACCURACY;
+
+ if (v)
+ {
+ if (!(getedgedist(face, a, b, face->d) ||
+ getedgedist(face, b, c, face->d) ||
+ getedgedist(face, c, a, face->d)))
+ {
+ // Origin projects to the interior of the triangle
+ // Use distance to triangle plane
+ face->d = btDot(a->w, face->n) / l;
+ }
+
+ face->n /= l;
+ if (forced || (face->d >= -EPA_PLANE_EPS))
+ {
+ return face;
+ }
+ else
+ m_status = eEpaNonConvex;
+ }
+ else
+ m_status = eEpaDegenerated;
+
+ remove(m_hull, face);
+ append(m_stock, face);
+ return 0;
+ }
+ m_status = m_stock.root ? eEpaOutOfVertices : eEpaOutOfFaces;
+ return 0;
+ }
+ sFace* findbest()
+ {
+ sFace* minf = m_hull.root;
+ btScalar mind = minf->d * minf->d;
+ for (sFace* f = minf->l[1]; f; f = f->l[1])
+ {
+ const btScalar sqd = f->d * f->d;
+ if (sqd < mind)
+ {
+ minf = f;
+ mind = sqd;
+ }
+ }
+ return (minf);
+ }
+ bool expand(U pass, typename GJK<btConvexTemplate>::sSV* w, sFace* f, U e, sHorizon& horizon)
+ {
+ static const U i1m3[] = {1, 2, 0};
+ static const U i2m3[] = {2, 0, 1};
+ if (f->pass != pass)
+ {
+ const U e1 = i1m3[e];
+ if ((btDot(f->n, w->w) - f->d) < -EPA_PLANE_EPS)
+ {
+ sFace* nf = newface(f->c[e1], f->c[e], w, false);
+ if (nf)
+ {
+ bind(nf, 0, f, e);
+ if (horizon.cf)
+ bind(horizon.cf, 1, nf, 2);
+ else
+ horizon.ff = nf;
+ horizon.cf = nf;
+ ++horizon.nf;
+ return (true);
+ }
+ }
+ else
+ {
+ const U e2 = i2m3[e];
+ f->pass = (U1)pass;
+ if (expand(pass, w, f->f[e1], f->e[e1], horizon) &&
+ expand(pass, w, f->f[e2], f->e[e2], horizon))
+ {
+ remove(m_hull, f);
+ append(m_stock, f);
+ return (true);
+ }
+ }
+ }
+ return (false);
+ }
+};
+
+template <typename btConvexTemplate>
+static void Initialize(const btConvexTemplate& a, const btConvexTemplate& b,
+ btGjkEpaSolver3::sResults& results,
+ MinkowskiDiff<btConvexTemplate>& shape)
+{
+ /* Results */
+ results.witnesses[0] =
+ results.witnesses[1] = btVector3(0, 0, 0);
+ results.status = btGjkEpaSolver3::sResults::Separated;
+ /* Shape */
+
+ shape.m_toshape1 = b.getWorldTransform().getBasis().transposeTimes(a.getWorldTransform().getBasis());
+ shape.m_toshape0 = a.getWorldTransform().inverseTimes(b.getWorldTransform());
+}
+
+//
+// Api
+//
+
+//
+template <typename btConvexTemplate>
+bool btGjkEpaSolver3_Distance(const btConvexTemplate& a, const btConvexTemplate& b,
+ const btVector3& guess,
+ btGjkEpaSolver3::sResults& results)
+{
+ MinkowskiDiff<btConvexTemplate> shape(a, b);
+ Initialize(a, b, results, shape);
+ GJK<btConvexTemplate> gjk(a, b);
+ eGjkStatus gjk_status = gjk.Evaluate(shape, guess);
+ if (gjk_status == eGjkValid)
+ {
+ btVector3 w0 = btVector3(0, 0, 0);
+ btVector3 w1 = btVector3(0, 0, 0);
+ for (U i = 0; i < gjk.m_simplex->rank; ++i)
+ {
+ const btScalar p = gjk.m_simplex->p[i];
+ w0 += shape.Support(gjk.m_simplex->c[i]->d, 0) * p;
+ w1 += shape.Support(-gjk.m_simplex->c[i]->d, 1) * p;
+ }
+ results.witnesses[0] = a.getWorldTransform() * w0;
+ results.witnesses[1] = a.getWorldTransform() * w1;
+ results.normal = w0 - w1;
+ results.distance = results.normal.length();
+ results.normal /= results.distance > GJK_MIN_DISTANCE ? results.distance : 1;
+ return (true);
+ }
+ else
+ {
+ results.status = gjk_status == eGjkInside ? btGjkEpaSolver3::sResults::Penetrating : btGjkEpaSolver3::sResults::GJK_Failed;
+ return (false);
+ }
+}
+
+template <typename btConvexTemplate>
+bool btGjkEpaSolver3_Penetration(const btConvexTemplate& a,
+ const btConvexTemplate& b,
+ const btVector3& guess,
+ btGjkEpaSolver3::sResults& results)
+{
+ MinkowskiDiff<btConvexTemplate> shape(a, b);
+ Initialize(a, b, results, shape);
+ GJK<btConvexTemplate> gjk(a, b);
+ eGjkStatus gjk_status = gjk.Evaluate(shape, -guess);
+ switch (gjk_status)
+ {
+ case eGjkInside:
+ {
+ EPA<btConvexTemplate> epa;
+ eEpaStatus epa_status = epa.Evaluate(gjk, -guess);
+ if (epa_status != eEpaFailed)
+ {
+ btVector3 w0 = btVector3(0, 0, 0);
+ for (U i = 0; i < epa.m_result.rank; ++i)
+ {
+ w0 += shape.Support(epa.m_result.c[i]->d, 0) * epa.m_result.p[i];
+ }
+ results.status = btGjkEpaSolver3::sResults::Penetrating;
+ results.witnesses[0] = a.getWorldTransform() * w0;
+ results.witnesses[1] = a.getWorldTransform() * (w0 - epa.m_normal * epa.m_depth);
+ results.normal = -epa.m_normal;
+ results.distance = -epa.m_depth;
+ return (true);
+ }
+ else
+ results.status = btGjkEpaSolver3::sResults::EPA_Failed;
+ }
+ break;
+ case eGjkFailed:
+ results.status = btGjkEpaSolver3::sResults::GJK_Failed;
+ break;
+ default:
+ {
+ }
+ }
+ return (false);
+}
+
+#if 0
+int btComputeGjkEpaPenetration2(const btCollisionDescription& colDesc, btDistanceInfo* distInfo)
+{
+ btGjkEpaSolver3::sResults results;
+ btVector3 guess = colDesc.m_firstDir;
+
+ bool res = btGjkEpaSolver3::Penetration(colDesc.m_objA,colDesc.m_objB,
+ colDesc.m_transformA,colDesc.m_transformB,
+ colDesc.m_localSupportFuncA,colDesc.m_localSupportFuncB,
+ guess,
+ results);
+ if (res)
+ {
+ if ((results.status==btGjkEpaSolver3::sResults::Penetrating) || results.status==GJK::eStatus::Inside)
+ {
+ //normal could be 'swapped'
+
+ distInfo->m_distance = results.distance;
+ distInfo->m_normalBtoA = results.normal;
+ btVector3 tmpNormalInB = results.witnesses[1]-results.witnesses[0];
+ btScalar lenSqr = tmpNormalInB.length2();
+ if (lenSqr <= (SIMD_EPSILON*SIMD_EPSILON))
+ {
+ tmpNormalInB = results.normal;
+ lenSqr = results.normal.length2();
+ }
+
+ if (lenSqr > (SIMD_EPSILON*SIMD_EPSILON))
+ {
+ tmpNormalInB /= btSqrt(lenSqr);
+ btScalar distance2 = -(results.witnesses[0]-results.witnesses[1]).length();
+ //only replace valid penetrations when the result is deeper (check)
+ //if ((distance2 < results.distance))
+ {
+ distInfo->m_distance = distance2;
+ distInfo->m_pointOnA= results.witnesses[0];
+ distInfo->m_pointOnB= results.witnesses[1];
+ distInfo->m_normalBtoA= tmpNormalInB;
+ return 0;
+ }
+ }
+ }
+
+ }
+
+ return -1;
+}
+#endif
+
+template <typename btConvexTemplate, typename btDistanceInfoTemplate>
+int btComputeGjkDistance(const btConvexTemplate& a, const btConvexTemplate& b,
+ const btGjkCollisionDescription& colDesc, btDistanceInfoTemplate* distInfo)
+{
+ btGjkEpaSolver3::sResults results;
+ btVector3 guess = colDesc.m_firstDir;
+
+ bool isSeparated = btGjkEpaSolver3_Distance(a, b,
+ guess,
+ results);
+ if (isSeparated)
+ {
+ distInfo->m_distance = results.distance;
+ distInfo->m_pointOnA = results.witnesses[0];
+ distInfo->m_pointOnB = results.witnesses[1];
+ distInfo->m_normalBtoA = results.normal;
+ return 0;
+ }
+
+ return -1;
+}
+
+/* Symbols cleanup */
+
+#undef GJK_MAX_ITERATIONS
+#undef GJK_ACCURARY
+#undef GJK_MIN_DISTANCE
+#undef GJK_DUPLICATED_EPS
+#undef GJK_SIMPLEX2_EPS
+#undef GJK_SIMPLEX3_EPS
+#undef GJK_SIMPLEX4_EPS
+
+#undef EPA_MAX_VERTICES
+#undef EPA_MAX_FACES
+#undef EPA_MAX_ITERATIONS
+#undef EPA_ACCURACY
+#undef EPA_FALLBACK
+#undef EPA_PLANE_EPS
+#undef EPA_INSIDE_EPS
+
+#endif //BT_GJK_EPA3_H
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