godot/servers/physics/gjk_epa.cpp

/*************************************************************************/
/*  gjk_epa.cpp                                                          */
/*************************************************************************/
/*                       This file is part of:                           */
/*                           GODOT ENGINE                                */
/*                    http://www.godotengine.org                         */
/*************************************************************************/
/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
/*                                                                       */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the       */
/* "Software"), to deal in the Software without restriction, including   */
/* without limitation the rights to use, copy, modify, merge, publish,   */
/* distribute, sublicense, and/or sell copies of the Software, and to    */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions:                                             */
/*                                                                       */
/* The above copyright notice and this permission notice shall be        */
/* included in all copies or substantial portions of the Software.       */
/*                                                                       */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
/*************************************************************************/
#include "gjk_epa.h"

/*************** Bullet's GJK-EPA2 IMPLEMENTATION *******************/

	// Config

/* GJK	*/
#define GJK_MAX_ITERATIONS	128
#define GJK_ACCURARY		((real_t)0.0001)
#define GJK_MIN_DISTANCE	((real_t)0.0001)
#define GJK_DUPLICATED_EPS	((real_t)0.0001)
#define GJK_SIMPLEX2_EPS	((real_t)0.0)
#define GJK_SIMPLEX3_EPS	((real_t)0.0)
#define GJK_SIMPLEX4_EPS	((real_t)0.0)

/* EPA	*/
#define EPA_MAX_VERTICES	64
#define EPA_MAX_FACES		(EPA_MAX_VERTICES*2)
#define EPA_MAX_ITERATIONS	255
#define EPA_ACCURACY		((real_t)0.0001)
#define EPA_FALLBACK		(10*EPA_ACCURACY)
#define EPA_PLANE_EPS		((real_t)0.00001)
#define EPA_INSIDE_EPS		((real_t)0.01)

namespace GjkEpa2 {


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;

	Vector3	witnesses[2];
	Vector3	normal;
	real_t	distance;
};

// Shorthands
typedef unsigned int	U;
typedef unsigned char	U1;

// MinkowskiDiff
struct	MinkowskiDiff {

	const ShapeSW* m_shapes[2];

	Transform transform_A;
	Transform transform_B;

	// i wonder how this could be sped up... if it can
	_FORCE_INLINE_ Vector3 Support0 ( const Vector3& d ) const {
		return transform_A.xform( m_shapes[0]->get_support( transform_A.basis.xform_inv(d).normalized() ) );
	}

	_FORCE_INLINE_ Vector3 Support1 ( const Vector3& d ) const {
		return transform_B.xform( m_shapes[1]->get_support( transform_B.basis.xform_inv(d).normalized() ) );
	}

	_FORCE_INLINE_ Vector3 Support ( const Vector3& d ) const {
		return ( Support0 ( d )-Support1 ( -d ) );
	}

	_FORCE_INLINE_ Vector3	Support ( const Vector3& d,U index ) const
	{
		if ( index )
			return ( Support1 ( d ) );
		else
			return ( Support0 ( d ) );
	}
};

typedef	MinkowskiDiff tShape;


// GJK
struct	GJK
{
	/* Types		*/
	struct	sSV
	{
		Vector3	d,w;
	};
	struct	sSimplex
	{
		sSV*		c[4];
		real_t	p[4];
		U			rank;
	};
	struct	eStatus	{ enum _ {
		Valid,
		Inside,
		Failed		};};
		/* Fields		*/
		tShape			m_shape;
		Vector3		m_ray;
		real_t		m_distance;
		sSimplex		m_simplices[2];
		sSV				m_store[4];
		sSV*			m_free[4];
		U				m_nfree;
		U				m_current;
		sSimplex*		m_simplex;
		eStatus::_		m_status;
		/* Methods		*/
		GJK()
		{
			Initialize();
		}
		void				Initialize()
		{
			m_ray		=	Vector3(0,0,0);
			m_nfree		=	0;
			m_status	=	eStatus::Failed;
			m_current	=	0;
			m_distance	=	0;
		}
		eStatus::_			Evaluate(const tShape& shapearg,const Vector3& guess)
		{
			U			iterations=0;
			real_t	sqdist=0;
			real_t	alpha=0;
			Vector3	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			=	eStatus::Valid;
			m_shape				=	shapearg;
			m_distance			=	0;
			/* Initialize simplex		*/
			m_simplices[0].rank	=	0;
			m_ray				=	guess;
			const real_t	sqrl=	m_ray.length_squared();
			appendvertice(m_simplices[0],sqrl>0?-m_ray:Vector3(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 real_t	rl=m_ray.length();
				if(rl<GJK_MIN_DISTANCE)
				{/* Touching or inside				*/
					m_status=eStatus::Inside;
					break;
				}
				/* Append new vertice in -'v' direction	*/
				appendvertice(cs,-m_ray);
				const Vector3&	w=cs.c[cs.rank-1]->w;
				bool				found=false;
				for(U i=0;i<4;++i)
				{
					if((w-lastw[i]).length_squared()<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 real_t	omega=vec3_dot(m_ray,w)/rl;
				alpha=MAX(omega,alpha);
				if(((rl-alpha)-(GJK_ACCURARY*rl))<=0)
				{/* Return old simplex				*/
					removevertice(m_simplices[m_current]);
					break;
				}
				/* Reduce simplex						*/
				real_t	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		=	Vector3(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=eStatus::Inside;
				}
				else
				{/* Return old simplex				*/
					removevertice(m_simplices[m_current]);
					break;
				}
				m_status=((++iterations)<GJK_MAX_ITERATIONS)?m_status:eStatus::Failed;
			} while(m_status==eStatus::Valid);
			m_simplex=&m_simplices[m_current];
			switch(m_status)
			{
			case	eStatus::Valid:		m_distance=m_ray.length();break;
			case	eStatus::Inside:	m_distance=0;break;
			default: {}
			}
			return(m_status);
		}
		bool					EncloseOrigin()
		{
			switch(m_simplex->rank)
			{
			case	1:
				{
					for(U i=0;i<3;++i)
					{
						Vector3		axis=Vector3(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 Vector3	d=m_simplex->c[1]->w-m_simplex->c[0]->w;
					for(U i=0;i<3;++i)
					{
						Vector3		axis=Vector3(0,0,0);
						axis[i]=1;
						const Vector3	p=vec3_cross(d,axis);
						if(p.length_squared()>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 Vector3	n=vec3_cross(m_simplex->c[1]->w-m_simplex->c[0]->w,
						m_simplex->c[2]->w-m_simplex->c[0]->w);
					if(n.length_squared()>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(Math::abs(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 Vector3& 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 Vector3& v)
		{
			simplex.p[simplex.rank]=0;
			simplex.c[simplex.rank]=m_free[--m_nfree];
			getsupport(v,*simplex.c[simplex.rank++]);
		}
		static real_t		det(const Vector3& a,const Vector3& b,const Vector3& 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 real_t		projectorigin(	const Vector3& a,
			const Vector3& b,
			real_t* w,U& m)
		{
			const Vector3	d=b-a;
			const real_t	l=d.length_squared();
			if(l>GJK_SIMPLEX2_EPS)
			{
				const real_t	t(l>0?-vec3_dot(a,d)/l:0);
				if(t>=1)		{ w[0]=0;w[1]=1;m=2;return(b.length_squared()); }
				else if(t<=0)	{ w[0]=1;w[1]=0;m=1;return(a.length_squared()); }
				else			{ w[0]=1-(w[1]=t);m=3;return((a+d*t).length_squared()); }
			}
			return(-1);
		}
		static real_t		projectorigin(	const Vector3& a,
			const Vector3& b,
			const Vector3& c,
			real_t* w,U& m)
		{
			static const U		imd3[]={1,2,0};
			const Vector3*	vt[]={&a,&b,&c};
			const Vector3		dl[]={a-b,b-c,c-a};
			const Vector3		n=vec3_cross(dl[0],dl[1]);
			const real_t		l=n.length_squared();
			if(l>GJK_SIMPLEX3_EPS)
			{
				real_t	mindist=-1;
				real_t	subw[2];
				U			subm;
				for(U i=0;i<3;++i)
				{
					if(vec3_dot(*vt[i],vec3_cross(dl[i],n))>0)
					{
						const U			j=imd3[i];
						const real_t	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 real_t	d=vec3_dot(a,n);
					const real_t	s=Math::sqrt(l);
					const Vector3	p=n*(d/l);
					mindist	=	p.length_squared();
					m		=	7;
					w[0]	=	(vec3_cross(dl[1],b-p)).length()/s;
					w[1]	=	(vec3_cross(dl[2],c-p)).length()/s;
					w[2]	=	1-(w[0]+w[1]);
				}
				return(mindist);
			}
			return(-1);
		}
		static real_t		projectorigin(	const Vector3& a,
			const Vector3& b,
			const Vector3& c,
			const Vector3& d,
			real_t* w,U& m)
		{
			static const U		imd3[]={1,2,0};
			const Vector3*	vt[]={&a,&b,&c,&d};
			const Vector3		dl[]={a-d,b-d,c-d};
			const real_t		vl=det(dl[0],dl[1],dl[2]);
			const bool			ng=(vl*vec3_dot(a,vec3_cross(b-c,a-b)))<=0;
			if(ng&&(Math::abs(vl)>GJK_SIMPLEX4_EPS))
			{
				real_t	mindist=-1;
				real_t	subw[3];
				U			subm;
				for(U i=0;i<3;++i)
				{
					const U			j=imd3[i];
					const real_t	s=vl*vec3_dot(d,vec3_cross(dl[i],dl[j]));
					if(s>0)
					{
						const real_t	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);
		}
};

	// EPA
	struct	EPA
	{
		/* Types		*/
		typedef	GJK::sSV	sSV;
		struct	sFace
		{
			Vector3	n;
			real_t	d;
			real_t	p;
			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)	{}
		};
		struct	eStatus { enum _ {
			Valid,
			Touching,
			Degenerated,
			NonConvex,
			InvalidHull,
			OutOfFaces,
			OutOfVertices,
			AccuraryReached,
			FallBack,
			Failed		};};
			/* Fields		*/
			eStatus::_		m_status;
			GJK::sSimplex	m_result;
			Vector3		m_normal;
			real_t		m_depth;
			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	=	eStatus::Failed;
				m_normal	=	Vector3(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]);
				}
			}
			eStatus::_			Evaluate(GJK& gjk,const Vector3& guess)
			{
				GJK::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	=	eStatus::Valid;
					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)
					{
						SWAP(simplex.c[0],simplex.c[1]);
						SWAP(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=eStatus::Valid;
						for(;iterations<EPA_MAX_ITERATIONS;++iterations)
						{
							if(m_nextsv<EPA_MAX_VERTICES)
							{
								sHorizon		horizon;
								sSV*			w=&m_sv_store[m_nextsv++];
								bool			valid=true;
								best->pass	=	(U1)(++pass);
								gjk.getsupport(best->n,*w);
								const real_t	wdist=vec3_dot(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();
										if(best->p>=outer.p) outer=*best;
									} else { m_status=eStatus::InvalidHull;break; }
								} else { m_status=eStatus::AccuraryReached;break; }
							} else { m_status=eStatus::OutOfVertices;break; }
						}
						const Vector3	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]	=	vec3_cross(	outer.c[1]->w-projection,
							outer.c[2]->w-projection).length();
						m_result.p[1]	=	vec3_cross(	outer.c[2]->w-projection,
							outer.c[0]->w-projection).length();
						m_result.p[2]	=	vec3_cross(	outer.c[0]->w-projection,
							outer.c[1]->w-projection).length();
						const real_t	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	=	eStatus::FallBack;
				m_normal	=	-guess;
				const real_t	nl=m_normal.length();
				if(nl>0)
					m_normal	=	m_normal/nl;
				else
					m_normal	=	Vector3(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);
			}
			sFace*				newface(sSV* a,sSV* b,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		=	vec3_cross(b->w-a->w,c->w-a->w);
					const real_t	l=face->n.length();
					const bool		v=l>EPA_ACCURACY;
					face->p		=	MIN(MIN(
						vec3_dot(a->w,vec3_cross(face->n,a->w-b->w)),
						vec3_dot(b->w,vec3_cross(face->n,b->w-c->w))),
						vec3_dot(c->w,vec3_cross(face->n,c->w-a->w)))	/
						(v?l:1);
					face->p		=	face->p>=-EPA_INSIDE_EPS?0:face->p;
					if(v)
					{
						face->d		=	vec3_dot(a->w,face->n)/l;
						face->n		/=	l;
						if(forced||(face->d>=-EPA_PLANE_EPS))
						{
							return(face);
						} else m_status=eStatus::NonConvex;
					} else m_status=eStatus::Degenerated;
					remove(m_hull,face);
					append(m_stock,face);
					return(0);
				}
				m_status=m_stock.root?eStatus::OutOfVertices:eStatus::OutOfFaces;
				return(0);
			}
			sFace*				findbest()
			{
				sFace*		minf=m_hull.root;
				real_t	mind=minf->d*minf->d;
				real_t	maxp=minf->p;
				for(sFace* f=minf->l[1];f;f=f->l[1])
				{
					const real_t	sqd=f->d*f->d;
					if((f->p>=maxp)&&(sqd<mind))
					{
						minf=f;
						mind=sqd;
						maxp=f->p;
					}
				}
				return(minf);
			}
			bool				expand(U pass,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((vec3_dot(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);
			}

	};

	//
	static void	Initialize(	const ShapeSW* shape0,const Transform& wtrs0,
		const ShapeSW* shape1,const Transform& wtrs1,
		sResults& results,
		tShape& shape,
		bool withmargins)
	{
		/* Results		*/
		results.witnesses[0]	=
			results.witnesses[1]	=	Vector3(0,0,0);
		results.status			=	sResults::Separated;
		/* Shape		*/
		shape.m_shapes[0]		=	shape0;
		shape.m_shapes[1]		=	shape1;
		shape.transform_A		=	wtrs0;
		shape.transform_B		=	wtrs1;

	}



//
// Api
//

//

//
bool Distance(	const ShapeSW*	shape0,
									  const Transform&		wtrs0,
									  const ShapeSW*	shape1,
									  const Transform&		wtrs1,
									  const Vector3&		guess,
									  sResults&				results)
{
	tShape			shape;
	Initialize(shape0,wtrs0,shape1,wtrs1,results,shape,false);
	GJK				gjk;
	GJK::eStatus::_	gjk_status=gjk.Evaluate(shape,guess);
	if(gjk_status==GJK::eStatus::Valid)
	{
		Vector3	w0=Vector3(0,0,0);
		Vector3	w1=Vector3(0,0,0);
		for(U i=0;i<gjk.m_simplex->rank;++i)
		{
			const real_t	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]	=	w0;
		results.witnesses[1]	=	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==GJK::eStatus::Inside?
			sResults::Penetrating	:
		sResults::GJK_Failed	;
		return(false);
	}
}

//
bool Penetration(	const ShapeSW*	shape0,
									 const Transform&		wtrs0,
									 const ShapeSW*	shape1,
									 const Transform&		wtrs1,
									 const Vector3&		guess,
									 sResults&				results
									)
{
	tShape			shape;
	Initialize(shape0,wtrs0,shape1,wtrs1,results,shape,false);
	GJK				gjk;
	GJK::eStatus::_	gjk_status=gjk.Evaluate(shape,-guess);
	switch(gjk_status)
	{
	case	GJK::eStatus::Inside:
		{
			EPA				epa;
			EPA::eStatus::_	epa_status=epa.Evaluate(gjk,-guess);
			if(epa_status!=EPA::eStatus::Failed)
			{
				Vector3	w0=Vector3(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			=	sResults::Penetrating;
				results.witnesses[0]	=	w0;
				results.witnesses[1]	=	w0-epa.m_normal*epa.m_depth;
				results.normal			=	-epa.m_normal;
				results.distance		=	-epa.m_depth;
				return(true);
			} else results.status=sResults::EPA_Failed;
		}
		break;
	case	GJK::eStatus::Failed:
		results.status=sResults::GJK_Failed;
		break;
	default: {}
	}
	return(false);
}


/* 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


} // end of namespace





bool gjk_epa_calculate_distance(const ShapeSW *p_shape_A, const Transform& p_transform_A, const ShapeSW *p_shape_B, const Transform& p_transform_B, Vector3& r_result_A, Vector3& r_result_B) {


	GjkEpa2::sResults res;

	if (GjkEpa2::Distance(p_shape_A,p_transform_A,p_shape_B,p_transform_B,p_transform_B.origin-p_transform_A.origin,res)) {

		r_result_A=res.witnesses[0];
		r_result_B=res.witnesses[1];
		return true;
	}

	return false;

}

bool gjk_epa_calculate_penetration(const ShapeSW *p_shape_A, const Transform& p_transform_A, const ShapeSW *p_shape_B, const Transform& p_transform_B, CollisionSolverSW::CallbackResult p_result_callback,void *p_userdata, bool p_swap ) {

	GjkEpa2::sResults res;

	if (GjkEpa2::Penetration(p_shape_A,p_transform_A,p_shape_B,p_transform_B,p_transform_B.origin-p_transform_A.origin,res)) {
		if (p_result_callback) {
			if (p_swap)
				p_result_callback(res.witnesses[1],res.witnesses[0],p_userdata);
			else
				p_result_callback(res.witnesses[0],res.witnesses[1],p_userdata);
		}
		return true;
	}

	return false;
}