/* Triangle/triangle intersection test routine,
* by Tomas Moller, 1997.
* See article "A Fast Triangle-Triangle Intersection Test",
* Journal of Graphics Tools, 2(2), 1997
*
*
* Copyright (C) 1997 Tomas Möller
* Copyright (C) 2000-2013 Raven Software, Inc.
* Copyright (C) 2001-2013 Activision, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2 as
* published by the Free Software Foundation.
*
* 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 for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, see <http://www.gnu.org/licenses/>.
*
*
* 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
*
*/
#include "tri_coll_test.h"
/* 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 1
#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];
/* 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 qtrue; \
} \
else \
{ \
if(e<=0 && e>=f) return qtrue; \
} \
}
#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 qtrue; \
} \
}
qboolean coplanar_tri_tri(vec3_t N,vec3_t V0,vec3_t V1,vec3_t V2,
vec3_t U0,vec3_t U1,vec3_t U2)
{
vec3_t A;
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 qfalse;
}
qboolean tri_tri_intersect(vec3_t V0,vec3_t V1,vec3_t V2,
vec3_t U0,vec3_t U1,vec3_t U2)
{
vec3_t E1,E2;
vec3_t N1,N2;
float d1,d2;
float du0,du1,du2,dv0,dv1,dv2;
vec3_t D;
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
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 qfalse; /* 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
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 qfalse; /* 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 qtrue;
return qfalse;
}
float LineSegmentDistance( vec3_t a, vec3_t b, vec3_t c, vec3_t d )
{
vec3_t v1, v2, v3, cross;
//FIXME: what if parallel or intersect?
//FIXME: this doesn't take into account the endpoints...
//get the two lines
VectorSubtract( b, a, v1 );
VectorSubtract( c, d, v2 );
//get their normalized cross product
CrossProduct( v1, v2, cross );
/*
float crossLength = VectorLength( cross );
if ( crossLength == 0 )
{//intersect! Or... parallel?
return 0;
}
VectorScale( cross, 1/crossLength, cross );
*/
VectorNormalize( cross );
//now get a vector from v1 to v2
VectorSubtract( d, a, v3 );
//distance is dot product of that new vector and the normalized cross product
float dist = fabs( DotProduct( v3, cross ) );
return dist;
}
extern qboolean G_FindClosestPointOnLineSegment( const vec3_t start, const vec3_t end, const vec3_t from, vec3_t result );
float ShortestLineSegBewteen2LineSegs( vec3_t start1, vec3_t end1, vec3_t start2, vec3_t end2, vec3_t close_pnt1, vec3_t close_pnt2 )
{
float current_dist, new_dist;
vec3_t new_pnt;
//start1, end1 : the first segment
//start2, end2 : the second segment
//output, one point on each segment, the closest two points on the segments.
//compute some temporaries:
//vec start_dif = start2 - start1
vec3_t start_dif;
VectorSubtract( start2, start1, start_dif );
//vec v1 = end1 - start1
vec3_t v1;
VectorSubtract( end1, start1, v1 );
//vec v2 = end2 - start2
vec3_t v2;
VectorSubtract( end2, start2, v2 );
//
float v1v1 = DotProduct( v1, v1 );
float v2v2 = DotProduct( v2, v2 );
float v1v2 = DotProduct( v1, v2 );
//the main computation
float denom = (v1v2 * v1v2) - (v1v1 * v2v2);
//if denom is small, then skip all this and jump to the section marked below
if ( fabs(denom) > 0.001f )
{
float s = -( (v2v2*DotProduct( v1, start_dif )) - (v1v2*DotProduct( v2, start_dif )) ) / denom;
float t = ( (v1v1*DotProduct( v2, start_dif )) - (v1v2*DotProduct( v1, start_dif )) ) / denom;
qboolean done = qtrue;
if ( s < 0 )
{
done = qfalse;
s = 0;// and see note below
}
if ( s > 1 )
{
done = qfalse;
s = 1;// and see note below
}
if ( t < 0 )
{
done = qfalse;
t = 0;// and see note below
}
if ( t > 1 )
{
done = qfalse;
t = 1;// and see note below
}
//vec close_pnt1 = start1 + s * v1
VectorMA( start1, s, v1, close_pnt1 );
//vec close_pnt2 = start2 + t * v2
VectorMA( start2, t, v2, close_pnt2 );
current_dist = Distance( close_pnt1, close_pnt2 );
//now, if none of those if's fired, you are done.
if ( done )
{
return current_dist;
}
//If they did fire, then we need to do some additional tests.
//What we are gonna do is see if we can find a shorter distance than the above
//involving the endpoints.
}
else
{
//******start here for paralell lines with current_dist = infinity****
current_dist = Q3_INFINITE;
}
//test 2 close_pnts first
/*
G_FindClosestPointOnLineSegment( start1, end1, close_pnt2, new_pnt );
new_dist = Distance( close_pnt2, new_pnt );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( new_pnt, close_pnt1 );
VectorCopy( close_pnt2, close_pnt2 );
current_dist = new_dist;
}
G_FindClosestPointOnLineSegment( start2, end2, close_pnt1, new_pnt );
new_dist = Distance( close_pnt1, new_pnt );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( close_pnt1, close_pnt1 );
VectorCopy( new_pnt, close_pnt2 );
current_dist = new_dist;
}
*/
//test all the endpoints
new_dist = Distance( start1, start2 );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( start1, close_pnt1 );
VectorCopy( start2, close_pnt2 );
current_dist = new_dist;
}
new_dist = Distance( start1, end2 );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( start1, close_pnt1 );
VectorCopy( end2, close_pnt2 );
current_dist = new_dist;
}
new_dist = Distance( end1, start2 );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( end1, close_pnt1 );
VectorCopy( start2, close_pnt2 );
current_dist = new_dist;
}
new_dist = Distance( end1, end2 );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( end1, close_pnt1 );
VectorCopy( end2, close_pnt2 );
current_dist = new_dist;
}
//Then we have 4 more point / segment tests
G_FindClosestPointOnLineSegment( start2, end2, start1, new_pnt );
new_dist = Distance( start1, new_pnt );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( start1, close_pnt1 );
VectorCopy( new_pnt, close_pnt2 );
current_dist = new_dist;
}
G_FindClosestPointOnLineSegment( start2, end2, end1, new_pnt );
new_dist = Distance( end1, new_pnt );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( end1, close_pnt1 );
VectorCopy( new_pnt, close_pnt2 );
current_dist = new_dist;
}
G_FindClosestPointOnLineSegment( start1, end1, start2, new_pnt );
new_dist = Distance( start2, new_pnt );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( new_pnt, close_pnt1 );
VectorCopy( start2, close_pnt2 );
current_dist = new_dist;
}
G_FindClosestPointOnLineSegment( start1, end1, end2, new_pnt );
new_dist = Distance( end2, new_pnt );
if ( new_dist < current_dist )
{//then update close_pnt1 close_pnt2 and current_dist
VectorCopy( new_pnt, close_pnt1 );
VectorCopy( end2, close_pnt2 );
current_dist = new_dist;
}
return current_dist;
}