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+/*
+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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