path: root/extern/bullet2/src/BulletCollision/NarrowPhaseCollision/btGjkEpa3.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