/* 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 June 1999: removed the divisions -- a little faster now! * Updated October 1999: added {} to CROSS and SUB macros * * int NoDivTriTriIsect(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 #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|b) \ { \ float c; \ c=a; \ a=b; \ b=c; \ } /* 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; } #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; /* 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)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)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 */ float 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 */ float d,e,f,y0,y1; NEWCOMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,d,e,f,y0,y1); float 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]