/* 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 #include "../game/q_shared.h" #include "../game/g_local.h" /* if USE_EPSILON_TEST is true then we do a check: if |dv|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)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)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]