Пересечение в пространстве: Два треугольника

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Пересечение в пространстве: Два треугольника - Программирование от RIN.RU

Пересечение в пространстве: Два треугольника

Алгоритм описан в статье Tomas"а Moller"а A Fast Triangle-Triangle Intersection Test.

Линия пересечения находится третьей функцией из данных ниже. В статье не дается алгоритм ее получения, но он понятен из исходника.

/* Triangle/triangle intersection test routine,
* by Tomas Moller, 1997.
* See article "A Fast Triangle-Triangle Intersection Test",
* Journal of Graphics Tools, 2(2), 1997
* updated: 2001-06-20 (added line of intersection)
*
* int tri_tri_intersect(float V0[3],float V1[3],float V2[3],
* float U0[3],float U1[3],float U2[3])
*
* parameters: vertices of triangle 1: V0,V1,V2
* vertices of triangle 2: U0,U1,U2
* result : returns 1 if the triangles intersect, otherwise 0
*
* Here is a version withouts divisions (a little faster)
* int NoDivTriTriIsect(float V0[3],float V1[3],float V2[3],
* float U0[3],float U1[3],float U2[3]);
*
* This version computes the line of intersection as well (if they are not coplanar):
* int tri_tri_intersect_with_isectline(float V0[3],float V1[3],float V2[3],
* float U0[3],float U1[3],float U2[3],int *coplanar,
* float isectpt1[3],float isectpt2[3]);
* coplanar returns whether the tris are coplanar
* isectpt1, isectpt2 are the endpoints of the line of intersection
*/

#include <math.h>

#define FABS(x) ((float)fabs(x)) /* implement as is fastest on your machine */

/* if USE_EPSILON_TEST is true then we do a check:
if |dv|<EPSILON then dv=0.0;
else no check is done (which is less robust)
*/
#define USE_EPSILON_TEST TRUE
#define EPSILON 0.000001

/* some macros */
#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 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 SORT(a,b) \
if(a>b) \
{ \
float c; \
c=a; \
a=b; \
b=c; \
}

#define ISECT(VV0,VV1,VV2,D0,D1,D2,isect0,isect1) \
isect0=VV0+(VV1-VV0)*D0/(D0-D1); \
isect1=VV0+(VV2-VV0)*D0/(D0-D2);

#define COMPUTE_INTERVALS(VV0,VV1,VV2,D0,D1,D2,D0D1,D0D2,isect0,isect1) \
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 */ \
ISECT(VV2,VV0,VV1,D2,D0,D1,isect0,isect1); \
} \
else if(D0D2>0.0f) \
{ \
/* here we know that d0d1<=0.0 */ \
ISECT(VV1,VV0,VV2,D1,D0,D2,isect0,isect1); \
} \
else if(D1*D2>0.0f || D0!=0.0f) \
{ \
/* here we know that d0d1<=0.0 or that D0!=0.0 */ \
ISECT(VV0,VV1,VV2,D0,D1,D2,isect0,isect1); \
} \
else if(D1!=0.0f) \
{ \
ISECT(VV1,VV0,VV2,D1,D0,D2,isect0,isect1); \
} \
else if(D2!=0.0f) \
{ \
ISECT(VV2,VV0,VV1,D2,D0,D1,isect0,isect1); \
} \
else \
{ \
/* triangles are coplanar */ \
return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2); \
}

/* this edge to edge test is based on Franlin Antonio's gem:
"Faster Line Segment Intersection", in Graphics Gems III,
pp. 199-202 */
#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) \
{ \
float 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) \
{ \
float 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; \
} \
}

int coplanar_tri_tri(float N[3],float V0[3],float V1[3],float V2[3],
float U0[3],float U1[3],float U2[3])
{
float 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;
}

int tri_tri_intersect(float V0[3],float V1[3],float V2[3],
float U0[3],float U1[3],float U2[3])
{
float E1[3],E2[3];
float N1[3],N2[3],d1,d2;
float du0,du1,du2,dv0,dv1,dv2;
float D[3];
float isect1[2], isect2[2];
float du0du1,du0du2,dv0dv1,dv0dv2;
short index;
float vp0,vp1,vp2;
float up0,up1,up2;
float b,c,max;

/* 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 */
#if USE_EPSILON_TEST==TRUE
if(fabs(du0)<EPSILON) du0=0.0;
if(fabs(du1)<EPSILON) du1=0.0;
if(fabs(du2)<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;

#if USE_EPSILON_TEST==TRUE
if(fabs(dv0)<EPSILON) dv0=0.0;
if(fabs(dv1)<EPSILON) dv1=0.0;
if(fabs(dv2)<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 */
COMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,isect1[0],isect1[1]);

* compute interval for triangle 2 */
COMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,isect2[0],isect2[1]);

SORT(isect1[0],isect1[1]);
SORT(isect2[0],isect2[1]);

if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return 0;
return 1;
}

#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); \
} \
}

int NoDivTriTriIsect(float V0[3],float V1[3],float V2[3],
float U0[3],float U1[3],float U2[3])
{
float E1[3],E2[3];
float N1[3],N2[3],d1,d2;
float du0,du1,du2,dv0,dv1,dv2;
float D[3];
float isect1[2], isect2[2];
float du0du1,du0du2,dv0dv1,dv0dv2;
short index;
float vp0,vp1,vp2;
float up0,up1,up2;
float bb,cc,max;
float a,b,c,x0,x1;
float d,e,f,y0,y1;
float xx,yy,xxyy,tmp;

/* 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 */
#if USE_EPSILON_TEST==TRUE
if(FABS(du0)<EPSILON) du0=0.0;
if(FABS(du1)<EPSILON) du1=0.0;
if(FABS(du2)<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;

#if USE_EPSILON_TEST==TRUE
if(FABS(dv0)<EPSILON) dv0=0.0;
if(FABS(dv1)<EPSILON) dv1=0.0;
if(FABS(dv2)<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=(float)FABS(D[0]);
index=0;
bb=(float)FABS(D[1]);
cc=(float)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 */
NEWCOMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,a,b,c,x0,x1);

/* compute interval for triangle 2 */
NEWCOMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,d,e,f,y0,y1);

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;
}

/* 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;

inline void
isect2(float VTX0[3],float VTX1[3],float VTX2[3],float VV0,float VV1,float VV2,
float D0,float D1,float D2,float *isect0,float *isect1,float isectpoint0[3],
float isectpoint1[3])
{
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);
}

#if 0
#define ISECT2(VTX0,VTX1,VTX2,VV0,VV1,VV2,D0,D1,D2,isect0,isect1,isectpoint0,isectpoint1)\
tmp=D0/(D0-D1); \
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); */
#endif

inline int compute_intervals_isectline(float VERT0[3],float VERT1[3],float VERT2[3],
float VV0,float VV1,float VV2,float D0,float D1,float D2,
float D0D1,float D0D2,float *isect0,float *isect1,
float isectpoint0[3],float isectpoint1[3])
{
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

int tri_tri_intersect_with_isectline(float V0[3],float V1[3],float V2[3],
float U0[3],float U1[3],float U2[3],int *coplanar,
float isectpt1[3],float isectpt2[3])
{
float E1[3],E2[3];
float N1[3],N2[3],d1,d2;
float du0,du1,du2,dv0,dv1,dv2;
float D[3];
float isect1[2], isect2[2];
float isectpointA1[3],isectpointA2[3];
float isectpointB1[3],isectpointB2[3];
float du0du1,du0du2,dv0dv1,dv0dv2;
short index;
float vp0,vp1,vp2;
float up0,up1,up2;
float b,c,max;
float tmp,diff[3];
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 */
#if USE_EPSILON_TEST==TRUE
if(fabs(du0)<EPSILON) du0=0.0;
if(fabs(du1)<EPSILON) du1=0.0;
if(fabs(du2)<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;

#if USE_EPSILON_TEST==TRUE
if(fabs(dv0)<EPSILON) dv0=0.0;
if(fabs(dv1)<EPSILON) dv1=0.0;
if(fabs(dv2)<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;
}

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