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|
/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
/****************************************************************************
History
$Log: not supported by cvs2svn $
Revision 1.2 2005/10/24 09:19:33 ponchio
Added newline at end of file (tired of stupid warnings...)
Revision 1.1 2004/04/26 12:33:59 ganovelli
first version
****************************************************************************/
#ifndef __VCGLIB_INTERSECTIONTRITRI3
#define __VCGLIB_INTERSECTIONTRITRI3
#include <vcg/space/point3.h>
#include <math.h>
namespace vcg {
/** \addtogroup space */
/*@{*/
/**
Triangle/triangle intersection ,based on the algorithm presented in "A Fast Triangle-Triangle Intersection Test",
Journal of Graphics Tools, 2(2), 1997
*/
#ifndef FABS
#define FABS(x) (T(fabs(x)))
#endif
#define USE_EPSILON_TEST
#define TRI_TRI_INT_EPSILON 0.000001
#define CROSS(dest,v1,v2){ \
dest[0]=v1[1]*v2[2]-v1[2]*v2[1]; \
dest[1]=v1[2]*v2[0]-v1[0]*v2[2]; \
dest[2]=v1[0]*v2[1]-v1[1]*v2[0];}
#define DOT(v1,v2) (v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2])
#define SUB(dest,v1,v2){ \
dest[0]=v1[0]-v2[0]; \
dest[1]=v1[1]-v2[1]; \
dest[2]=v1[2]-v2[2];}
#define SORT(a,b) \
if(a>b) \
{ \
T c; \
c=a; \
a=b; \
b=c; \
}
#define EDGE_EDGE_TEST(V0,U0,U1) \
Bx=U0[i0]-U1[i0]; \
By=U0[i1]-U1[i1]; \
Cx=V0[i0]-U0[i0]; \
Cy=V0[i1]-U0[i1]; \
f=Ay*Bx-Ax*By; \
d=By*Cx-Bx*Cy; \
if((f>0 && d>=0 && d<=f) || (f<0 && d<=0 && d>=f)) \
{ \
e=Ax*Cy-Ay*Cx; \
if(f>0) \
{ \
if(e>=0 && e<=f) return 1; \
} \
else \
{ \
if(e<=0 && e>=f) return 1; \
} \
}
#define EDGE_AGAINST_TRI_EDGES(V0,V1,U0,U1,U2) \
{ \
T Ax,Ay,Bx,By,Cx,Cy,e,d,f; \
Ax=V1[i0]-V0[i0]; \
Ay=V1[i1]-V0[i1]; \
/* test edge U0,U1 against V0,V1 */ \
EDGE_EDGE_TEST(V0,U0,U1); \
/* test edge U1,U2 against V0,V1 */ \
EDGE_EDGE_TEST(V0,U1,U2); \
/* test edge U2,U1 against V0,V1 */ \
EDGE_EDGE_TEST(V0,U2,U0); \
}
#define POINT_IN_TRI(V0,U0,U1,U2) \
{ \
T a,b,c,d0,d1,d2; \
/* is T1 completly inside T2? */ \
/* check if V0 is inside tri(U0,U1,U2) */ \
a=U1[i1]-U0[i1]; \
b=-(U1[i0]-U0[i0]); \
c=-a*U0[i0]-b*U0[i1]; \
d0=a*V0[i0]+b*V0[i1]+c; \
\
a=U2[i1]-U1[i1]; \
b=-(U2[i0]-U1[i0]); \
c=-a*U1[i0]-b*U1[i1]; \
d1=a*V0[i0]+b*V0[i1]+c; \
\
a=U0[i1]-U2[i1]; \
b=-(U0[i0]-U2[i0]); \
c=-a*U2[i0]-b*U2[i1]; \
d2=a*V0[i0]+b*V0[i1]+c; \
if(d0*d1>0.0) \
{ \
if(d0*d2>0.0) return 1; \
} \
}
template<class T>
/** CHeck two triangles for coplanarity
@param N
@param V0 A vertex of the first triangle
@param V1 A vertex of the first triangle
@param V2 A vertex of the first triangle
@param U0 A vertex of the second triangle
@param U1 A vertex of the second triangle
@param U2 A vertex of the second triangle
@return true se due triangoli sono cooplanari, false altrimenti
*/
bool coplanar_tri_tri(const Point3<T> N, const Point3<T> V0, const Point3<T> V1,const Point3<T> V2,
const Point3<T> U0, const Point3<T> U1,const Point3<T> U2)
{
T A[3];
short i0,i1;
/* first project onto an axis-aligned plane, that maximizes the area */
/* of the triangles, compute indices: i0,i1. */
A[0]=FABS(N[0]);
A[1]=FABS(N[1]);
A[2]=FABS(N[2]);
if(A[0]>A[1])
{
if(A[0]>A[2])
{
i0=1; /* A[0] is greatest */
i1=2;
}
else
{
i0=0; /* A[2] is greatest */
i1=1;
}
}
else /* A[0]<=A[1] */
{
if(A[2]>A[1])
{
i0=0; /* A[2] is greatest */
i1=1;
}
else
{
i0=0; /* A[1] is greatest */
i1=2;
}
}
/* test all edges of triangle 1 against the edges of triangle 2 */
EDGE_AGAINST_TRI_EDGES(V0,V1,U0,U1,U2);
EDGE_AGAINST_TRI_EDGES(V1,V2,U0,U1,U2);
EDGE_AGAINST_TRI_EDGES(V2,V0,U0,U1,U2);
/* finally, test if tri1 is totally contained in tri2 or vice versa */
POINT_IN_TRI(V0,U0,U1,U2);
POINT_IN_TRI(U0,V0,V1,V2);
return 0;
}
#define NEWCOMPUTE_INTERVALS(VV0,VV1,VV2,D0,D1,D2,D0D1,D0D2,A,B,C,X0,X1) \
{ \
if(D0D1>0.0f) \
{ \
/* here we know that D0D2<=0.0 */ \
/* that is D0, D1 are on the same side, D2 on the other or on the plane */ \
A=VV2; B=(VV0-VV2)*D2; C=(VV1-VV2)*D2; X0=D2-D0; X1=D2-D1; \
} \
else if(D0D2>0.0f)\
{ \
/* here we know that d0d1<=0.0 */ \
A=VV1; B=(VV0-VV1)*D1; C=(VV2-VV1)*D1; X0=D1-D0; X1=D1-D2; \
} \
else if(D1*D2>0.0f || D0!=0.0f) \
{ \
/* here we know that d0d1<=0.0 or that D0!=0.0 */ \
A=VV0; B=(VV1-VV0)*D0; C=(VV2-VV0)*D0; X0=D0-D1; X1=D0-D2; \
} \
else if(D1!=0.0f) \
{ \
A=VV1; B=(VV0-VV1)*D1; C=(VV2-VV1)*D1; X0=D1-D0; X1=D1-D2; \
} \
else if(D2!=0.0f) \
{ \
A=VV2; B=(VV0-VV2)*D2; C=(VV1-VV2)*D2; X0=D2-D0; X1=D2-D1; \
} \
else \
{ \
/* triangles are coplanar */ \
return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2); \
} \
}
template<class T>
/*
@param V0 A vertex of the first triangle
@param V1 A vertex of the first triangle
@param V2 A vertex of the first triangle
@param U0 A vertex of the second triangle
@param U1 A vertex of the second triangle
@param U2 A vertex of the second triangle
@return true if the two triangles interesect
*/
bool NoDivTriTriIsect(const Point3<T> V0,const Point3<T> V1,const Point3<T> V2,
const Point3<T> U0,const Point3<T> U1,const Point3<T> U2)
{
Point3<T> E1,E2;
Point3<T> N1,N2;
T d1,d2;
T du0,du1,du2,dv0,dv1,dv2;
Point3<T> D;
T isect1[2], isect2[2];
T du0du1,du0du2,dv0dv1,dv0dv2;
short index;
T vp0,vp1,vp2;
T up0,up1,up2;
T bb,cc,max;
/* compute plane equation of triangle(V0,V1,V2) */
SUB(E1,V1,V0);
SUB(E2,V2,V0);
CROSS(N1,E1,E2);
N1.Normalize(); // aggiunto rispetto al codice orig.
d1=-DOT(N1,V0);
/* plane equation 1: N1.X+d1=0 */
/* put U0,U1,U2 into plane equation 1 to compute signed distances to the plane*/
du0=DOT(N1,U0)+d1;
du1=DOT(N1,U1)+d1;
du2=DOT(N1,U2)+d1;
/* coplanarity robustness check */
#ifdef USE_TRI_TRI_INT_EPSILON_TEST
if(FABS(du0)<TRI_TRI_INT_EPSILON) du0=0.0;
if(FABS(du1)<TRI_TRI_INT_EPSILON) du1=0.0;
if(FABS(du2)<TRI_TRI_INT_EPSILON) du2=0.0;
#endif
du0du1=du0*du1;
du0du2=du0*du2;
if(du0du1>0.0f && du0du2>0.0f) /* same sign on all of them + not equal 0 ? */
return 0; /* no intersection occurs */
/* compute plane of triangle (U0,U1,U2) */
SUB(E1,U1,U0);
SUB(E2,U2,U0);
CROSS(N2,E1,E2);
d2=-DOT(N2,U0);
/* plane equation 2: N2.X+d2=0 */
/* put V0,V1,V2 into plane equation 2 */
dv0=DOT(N2,V0)+d2;
dv1=DOT(N2,V1)+d2;
dv2=DOT(N2,V2)+d2;
#ifdef USE_TRI_TRI_INT_EPSILON_TEST
if(FABS(dv0)<TRI_TRI_INT_EPSILON) dv0=0.0;
if(FABS(dv1)<TRI_TRI_INT_EPSILON) dv1=0.0;
if(FABS(dv2)<TRI_TRI_INT_EPSILON) dv2=0.0;
#endif
dv0dv1=dv0*dv1;
dv0dv2=dv0*dv2;
if(dv0dv1>0.0f && dv0dv2>0.0f) /* same sign on all of them + not equal 0 ? */
return 0; /* no intersection occurs */
/* compute direction of intersection line */
CROSS(D,N1,N2);
/* compute and index to the largest component of D */
max=(T)FABS(D[0]);
index=0;
bb=(T)FABS(D[1]);
cc=(T)FABS(D[2]);
if(bb>max) max=bb,index=1;
if(cc>max) max=cc,index=2;
/* this is the simplified projection onto L*/
vp0=V0[index];
vp1=V1[index];
vp2=V2[index];
up0=U0[index];
up1=U1[index];
up2=U2[index];
/* compute interval for triangle 1 */
T a,b,c,x0,x1;
NEWCOMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,a,b,c,x0,x1);
/* compute interval for triangle 2 */
T d,e,f,y0,y1;
NEWCOMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,d,e,f,y0,y1);
T xx,yy,xxyy,tmp;
xx=x0*x1;
yy=y0*y1;
xxyy=xx*yy;
tmp=a*xxyy;
isect1[0]=tmp+b*x1*yy;
isect1[1]=tmp+c*x0*yy;
tmp=d*xxyy;
isect2[0]=tmp+e*xx*y1;
isect2[1]=tmp+f*xx*y0;
SORT(isect1[0],isect1[1]);
SORT(isect2[0],isect2[1]);
if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return 0;
return 1;
}
#define DOT(v1,v2) (v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2])
#define ADD(dest,v1,v2) dest[0]=v1[0]+v2[0]; dest[1]=v1[1]+v2[1]; dest[2]=v1[2]+v2[2];
#define MULT(dest,v,factor) dest[0]=factor*v[0]; dest[1]=factor*v[1]; dest[2]=factor*v[2];
#define SET(dest,src) dest[0]=src[0]; dest[1]=src[1]; dest[2]=src[2];
/* sort so that a<=b */
#define SORT2(a,b,smallest) \
if(a>b) \
{ \
float c; \
c=a; \
a=b; \
b=c; \
smallest=1; \
} \
else smallest=0;
template <class T>
inline void isect2(Point3<T> VTX0,Point3<T> VTX1,Point3<T> VTX2,float VV0,float VV1,float VV2,
float D0,float D1,float D2,float *isect0,float *isect1,Point3<T> &isectpoint0,Point3<T> &isectpoint1)
{
float tmp=D0/(D0-D1);
float diff[3];
*isect0=VV0+(VV1-VV0)*tmp;
SUB(diff,VTX1,VTX0);
MULT(diff,diff,tmp);
ADD(isectpoint0,diff,VTX0);
tmp=D0/(D0-D2);
*isect1=VV0+(VV2-VV0)*tmp;
SUB(diff,VTX2,VTX0);
MULT(diff,diff,tmp);
ADD(isectpoint1,VTX0,diff);
}
template <class T>
inline int compute_intervals_isectline(Point3<T> VERT0,Point3<T> VERT1,Point3<T> VERT2,
float VV0,float VV1,float VV2,float D0,float D1,float D2,
float D0D1,float D0D2,float *isect0,float *isect1,
Point3<T> & isectpoint0, Point3<T> & isectpoint1)
{
if(D0D1>0.0f)
{
/* here we know that D0D2<=0.0 */
/* that is D0, D1 are on the same side, D2 on the other or on the plane */
isect2(VERT2,VERT0,VERT1,VV2,VV0,VV1,D2,D0,D1,isect0,isect1,isectpoint0,isectpoint1);
}
else if(D0D2>0.0f)
{
/* here we know that d0d1<=0.0 */
isect2(VERT1,VERT0,VERT2,VV1,VV0,VV2,D1,D0,D2,isect0,isect1,isectpoint0,isectpoint1);
}
else if(D1*D2>0.0f || D0!=0.0f)
{
/* here we know that d0d1<=0.0 or that D0!=0.0 */
isect2(VERT0,VERT1,VERT2,VV0,VV1,VV2,D0,D1,D2,isect0,isect1,isectpoint0,isectpoint1);
}
else if(D1!=0.0f)
{
isect2(VERT1,VERT0,VERT2,VV1,VV0,VV2,D1,D0,D2,isect0,isect1,isectpoint0,isectpoint1);
}
else if(D2!=0.0f)
{
isect2(VERT2,VERT0,VERT1,VV2,VV0,VV1,D2,D0,D1,isect0,isect1,isectpoint0,isectpoint1);
}
else
{
/* triangles are coplanar */
return 1;
}
return 0;
}
#define COMPUTE_INTERVALS_ISECTLINE(VERT0,VERT1,VERT2,VV0,VV1,VV2,D0,D1,D2,D0D1,D0D2,isect0,isect1,isectpoint0,isectpoint1) \
if(D0D1>0.0f) \
{ \
/* here we know that D0D2<=0.0 */ \
/* that is D0, D1 are on the same side, D2 on the other or on the plane */ \
isect2(VERT2,VERT0,VERT1,VV2,VV0,VV1,D2,D0,D1,&isect0,&isect1,isectpoint0,isectpoint1); \
}
#if 0
else if(D0D2>0.0f) \
{ \
/* here we know that d0d1<=0.0 */ \
isect2(VERT1,VERT0,VERT2,VV1,VV0,VV2,D1,D0,D2,&isect0,&isect1,isectpoint0,isectpoint1); \
} \
else if(D1*D2>0.0f || D0!=0.0f) \
{ \
/* here we know that d0d1<=0.0 or that D0!=0.0 */ \
isect2(VERT0,VERT1,VERT2,VV0,VV1,VV2,D0,D1,D2,&isect0,&isect1,isectpoint0,isectpoint1); \
} \
else if(D1!=0.0f) \
{ \
isect2(VERT1,VERT0,VERT2,VV1,VV0,VV2,D1,D0,D2,&isect0,&isect1,isectpoint0,isectpoint1); \
} \
else if(D2!=0.0f) \
{ \
isect2(VERT2,VERT0,VERT1,VV2,VV0,VV1,D2,D0,D1,&isect0,&isect1,isectpoint0,isectpoint1); \
} \
else \
{ \
/* triangles are coplanar */ \
coplanar=1; \
return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2); \
}
#endif
template <class T>
bool tri_tri_intersect_with_isectline( Point3<T> V0,Point3<T> V1,Point3<T> V2,
Point3<T> U0,Point3<T> U1,Point3<T> U2,bool &coplanar,
Point3<T> &isectpt1,Point3<T> &isectpt2)
{
Point3<T> E1,E2;
Point3<T> N1,N2;
T d1,d2;
float du0,du1,du2,dv0,dv1,dv2;
Point3<T> D;
float isect1[2], isect2[2];
Point3<T> isectpointA1,isectpointA2;
Point3<T> isectpointB1,isectpointB2;
float du0du1,du0du2,dv0dv1,dv0dv2;
short index;
float vp0,vp1,vp2;
float up0,up1,up2;
float b,c,max;
Point3<T> diff;
int smallest1,smallest2;
/* compute plane equation of triangle(V0,V1,V2) */
SUB(E1,V1,V0);
SUB(E2,V2,V0);
CROSS(N1,E1,E2);
d1=-DOT(N1,V0);
/* plane equation 1: N1.X+d1=0 */
/* put U0,U1,U2 into plane equation 1 to compute signed distances to the plane*/
du0=DOT(N1,U0)+d1;
du1=DOT(N1,U1)+d1;
du2=DOT(N1,U2)+d1;
/* coplanarity robustness check */
#ifdef USE_EPSILON_TEST
if(fabs(du0)<TRI_TRI_INT_EPSILON) du0=0.0;
if(fabs(du1)<TRI_TRI_INT_EPSILON) du1=0.0;
if(fabs(du2)<TRI_TRI_INT_EPSILON) du2=0.0;
#endif
du0du1=du0*du1;
du0du2=du0*du2;
if(du0du1>0.0f && du0du2>0.0f) /* same sign on all of them + not equal 0 ? */
return 0; /* no intersection occurs */
/* compute plane of triangle (U0,U1,U2) */
SUB(E1,U1,U0);
SUB(E2,U2,U0);
CROSS(N2,E1,E2);
d2=-DOT(N2,U0);
/* plane equation 2: N2.X+d2=0 */
/* put V0,V1,V2 into plane equation 2 */
dv0=DOT(N2,V0)+d2;
dv1=DOT(N2,V1)+d2;
dv2=DOT(N2,V2)+d2;
#ifdef USE_EPSILON_TEST
if(fabs(dv0)<TRI_TRI_INT_EPSILON) dv0=0.0;
if(fabs(dv1)<TRI_TRI_INT_EPSILON) dv1=0.0;
if(fabs(dv2)<TRI_TRI_INT_EPSILON) dv2=0.0;
#endif
dv0dv1=dv0*dv1;
dv0dv2=dv0*dv2;
if(dv0dv1>0.0f && dv0dv2>0.0f) /* same sign on all of them + not equal 0 ? */
return 0; /* no intersection occurs */
/* compute direction of intersection line */
CROSS(D,N1,N2);
/* compute and index to the largest component of D */
max=fabs(D[0]);
index=0;
b=fabs(D[1]);
c=fabs(D[2]);
if(b>max) max=b,index=1;
if(c>max) max=c,index=2;
/* this is the simplified projection onto L*/
vp0=V0[index];
vp1=V1[index];
vp2=V2[index];
up0=U0[index];
up1=U1[index];
up2=U2[index];
/* compute interval for triangle 1 */
coplanar=compute_intervals_isectline(V0,V1,V2,vp0,vp1,vp2,dv0,dv1,dv2,
dv0dv1,dv0dv2,&isect1[0],&isect1[1],isectpointA1,isectpointA2);
if(coplanar) return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2);
/* compute interval for triangle 2 */
compute_intervals_isectline(U0,U1,U2,up0,up1,up2,du0,du1,du2,
du0du1,du0du2,&isect2[0],&isect2[1],isectpointB1,isectpointB2);
SORT2(isect1[0],isect1[1],smallest1);
SORT2(isect2[0],isect2[1],smallest2);
if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return 0;
/* at this point, we know that the triangles intersect */
if(isect2[0]<isect1[0])
{
if(smallest1==0) { SET(isectpt1,isectpointA1); }
else { SET(isectpt1,isectpointA2); }
if(isect2[1]<isect1[1])
{
if(smallest2==0) { SET(isectpt2,isectpointB2); }
else { SET(isectpt2,isectpointB1); }
}
else
{
if(smallest1==0) { SET(isectpt2,isectpointA2); }
else { SET(isectpt2,isectpointA1); }
}
}
else
{
if(smallest2==0) { SET(isectpt1,isectpointB1); }
else { SET(isectpt1,isectpointB2); }
if(isect2[1]>isect1[1])
{
if(smallest1==0) { SET(isectpt2,isectpointA2); }
else { SET(isectpt2,isectpointA1); }
}
else
{
if(smallest2==0) { SET(isectpt2,isectpointB2); }
else { SET(isectpt2,isectpointB1); }
}
}
return 1;
}
} // end namespace
#undef FABS
#undef USE_EPSILON_TEST
#undef TRI_TRI_INT_EPSILON
#undef CROSS
#undef DOT
#undef SUB
#undef SORT
#undef SORT2
#undef ADD
#undef MULT
#undef SET
#undef EDGE_EDGE_TEST
#undef EDGE_AGAINST_TRI_EDGE
#undef POINT_IN_TRI
#undef COMPUTE_INTERVALS_ISECTLINE
#undef NEWCOMPUTE_INTERVALS
#endif
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