/********************************************************/ /* AABB-triangle overlap test code */ /* by Tomas Akenine-Möller */ /* Function: int triBoxOverlap(float boxcenter[3], */ /* float boxhalfsize[3],float triverts[3][3]); */ /* History: */ /* 2001-03-05: released the code in its first version */ /* 2001-06-18: changed the order of the tests, faster */ /* */ /* Acknowledgement: Many thanks to Pierre Terdiman for */ /* suggestions and discussions on how to optimize code. */ /* Thanks to David Hunt for finding a ">="-bug! */ /********************************************************/ #include #include #define X 0 #define Y 1 #define Z 2 #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 FINDMINMAX(x0,x1,x2,min,max) \ min = max = x0; \ if(x1max) max=x1;\ if(x2max) max=x2; int planeBoxOverlap(float normal[3],float d, float maxbox[3]) { int q; float vmin[3],vmax[3]; for(q=X;q<=Z;q++) { if(normal[q]>0.0f) { vmin[q]=-maxbox[q]; vmax[q]=maxbox[q]; } else { vmin[q]=maxbox[q]; vmax[q]=-maxbox[q]; } } if(DOT(normal,vmin)+d>0.0f) return 0; if(DOT(normal,vmax)+d>=0.0f) return 1; return 0; } /*======================== X-tests ========================*/ #define AXISTEST_X01(a, b, fa, fb) \ p0 = a*v0[Y] - b*v0[Z]; \ p2 = a*v2[Y] - b*v2[Z]; \ if(p0rad || max<-rad) return 0; #define AXISTEST_X2(a, b, fa, fb) \ p0 = a*v0[Y] - b*v0[Z]; \ p1 = a*v1[Y] - b*v1[Z]; \ if(p0rad || max<-rad) return 0; /*======================== Y-tests ========================*/ #define AXISTEST_Y02(a, b, fa, fb) \ p0 = -a*v0[X] + b*v0[Z]; \ p2 = -a*v2[X] + b*v2[Z]; \ if(p0rad || max<-rad) return 0; #define AXISTEST_Y1(a, b, fa, fb) \ p0 = -a*v0[X] + b*v0[Z]; \ p1 = -a*v1[X] + b*v1[Z]; \ if(p0rad || max<-rad) return 0; /*======================== Z-tests ========================*/ #define AXISTEST_Z12(a, b, fa, fb) \ p1 = a*v1[X] - b*v1[Y]; \ p2 = a*v2[X] - b*v2[Y]; \ if(p2rad || max<-rad) return 0; #define AXISTEST_Z0(a, b, fa, fb) \ p0 = a*v0[X] - b*v0[Y]; \ p1 = a*v1[X] - b*v1[Y]; \ if(p0rad || max<-rad) return 0; int triBoxOverlap(float boxcenter[3],float boxhalfsize[3],float triverts[3][3]) { /* use separating axis theorem to test overlap between triangle and box */ /* need to test for overlap in these directions: */ /* 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle */ /* we do not even need to test these) */ /* 2) normal of the triangle */ /* 3) crossproduct(edge from tri, {x,y,z}-directin) */ /* this gives 3x3=9 more tests */ float v0[3],v1[3],v2[3]; float min,max,d,p0,p1,p2,rad,fex,fey,fez; float normal[3],e0[3],e1[3],e2[3]; /* This is the fastest branch on Sun */ /* move everything so that the boxcenter is in (0,0,0) */ SUB(v0,triverts[0],boxcenter); SUB(v1,triverts[1],boxcenter); SUB(v2,triverts[2],boxcenter); /* compute triangle edges */ SUB(e0,v1,v0); /* tri edge 0 */ SUB(e1,v2,v1); /* tri edge 1 */ SUB(e2,v0,v2); /* tri edge 2 */ /* Bullet 3: */ /* test the 9 tests first (this was faster) */ fex = fabs(e0[X]); fey = fabs(e0[Y]); fez = fabs(e0[Z]); AXISTEST_X01(e0[Z], e0[Y], fez, fey); AXISTEST_Y02(e0[Z], e0[X], fez, fex); AXISTEST_Z12(e0[Y], e0[X], fey, fex); fex = fabs(e1[X]); fey = fabs(e1[Y]); fez = fabs(e1[Z]); AXISTEST_X01(e1[Z], e1[Y], fez, fey); AXISTEST_Y02(e1[Z], e1[X], fez, fex); AXISTEST_Z0(e1[Y], e1[X], fey, fex); fex = fabs(e2[X]); fey = fabs(e2[Y]); fez = fabs(e2[Z]); AXISTEST_X2(e2[Z], e2[Y], fez, fey); AXISTEST_Y1(e2[Z], e2[X], fez, fex); AXISTEST_Z12(e2[Y], e2[X], fey, fex); /* Bullet 1: */ /* first test overlap in the {x,y,z}-directions */ /* find min, max of the triangle each direction, and test for overlap in */ /* that direction -- this is equivalent to testing a minimal AABB around */ /* the triangle against the AABB */ /* test in X-direction */ FINDMINMAX(v0[X],v1[X],v2[X],min,max); if(min>boxhalfsize[X] || max<-boxhalfsize[X]) return 0; /* test in Y-direction */ FINDMINMAX(v0[Y],v1[Y],v2[Y],min,max); if(min>boxhalfsize[Y] || max<-boxhalfsize[Y]) return 0; /* test in Z-direction */ FINDMINMAX(v0[Z],v1[Z],v2[Z],min,max); if(min>boxhalfsize[Z] || max<-boxhalfsize[Z]) return 0; /* Bullet 2: */ /* test if the box intersects the plane of the triangle */ /* compute plane equation of triangle: normal*x+d=0 */ CROSS(normal,e0,e1); d=-DOT(normal,v0); /* plane eq: normal.x+d=0 */ if(!planeBoxOverlap(normal,d,boxhalfsize)) return 0; return 1; /* box and triangle overlaps */ }