292 lines
9.4 KiB
C
292 lines
9.4 KiB
C
/* Triangle/triangle intersection test routine,
|
|
* by Tomas Moller, 1997.
|
|
* See article "A Fast Triangle-Triangle Intersection Test",
|
|
* Journal of Graphics Tools, 2(2), 1997
|
|
*
|
|
* 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 <math.h>
|
|
#include "../game/q_shared.h"
|
|
#include "../game/g_local.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 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; \
|
|
} \
|
|
}
|
|
|
|
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 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
|
|
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 qtrue;
|
|
return qfalse;
|
|
} |