void LaserScanVisualizer::update( float dt ) { cloud_message_.lock(); D_float::iterator it = point_times_.begin(); D_float::iterator end = point_times_.end(); for ( ; it != end; ++it ) { *it += dt; } cullPoints(); cloud_message_.unlock(); }
EXPORT_C int dBoxBox (const dVector3 p1, const dMatrix3 R1, const dVector3 side1, const dVector3 p2, const dMatrix3 R2, const dVector3 side2, dVector3 normal, dReal *depth, int *return_code, int maxc, dContactGeom *contact, int skip) { const dReal fudge_factor = REAL(1.05); dVector3 p,pp,normalC; const dReal *normalR = 0; dReal A[3],B[3],R11,R12,R13,R21,R22,R23,R31,R32,R33, Q11,Q12,Q13,Q21,Q22,Q23,Q31,Q32,Q33,s,s2,l; int i,j,invert_normal,code; // get vector from centers of box 1 to box 2, relative to box 1 p[0] = p2[0] - p1[0]; p[1] = p2[1] - p1[1]; p[2] = p2[2] - p1[2]; dMULTIPLY1_331 (pp,R1,p); // get pp = p relative to body 1 // get side lengths / 2 A[0] = dMUL(side1[0],REAL(0.5)); A[1] = dMUL(side1[1],REAL(0.5)); A[2] = dMUL(side1[2],REAL(0.5)); B[0] = dMUL(side2[0],REAL(0.5)); B[1] = dMUL(side2[1],REAL(0.5)); B[2] = dMUL(side2[2],REAL(0.5)); // Rij is R1'*R2, i.e. the relative rotation between R1 and R2 R11 = dDOT44(R1+0,R2+0); R12 = dDOT44(R1+0,R2+1); R13 = dDOT44(R1+0,R2+2); R21 = dDOT44(R1+1,R2+0); R22 = dDOT44(R1+1,R2+1); R23 = dDOT44(R1+1,R2+2); R31 = dDOT44(R1+2,R2+0); R32 = dDOT44(R1+2,R2+1); R33 = dDOT44(R1+2,R2+2); Q11 = dFabs(R11); Q12 = dFabs(R12); Q13 = dFabs(R13); Q21 = dFabs(R21); Q22 = dFabs(R22); Q23 = dFabs(R23); Q31 = dFabs(R31); Q32 = dFabs(R32); Q33 = dFabs(R33); // for all 15 possible separating axes: // * see if the axis separates the boxes. if so, return 0. // * find the depth of the penetration along the separating axis (s2) // * if this is the largest depth so far, record it. // the normal vector will be set to the separating axis with the smallest // depth. note: normalR is set to point to a column of R1 or R2 if that is // the smallest depth normal so far. otherwise normalR is 0 and normalC is // set to a vector relative to body 1. invert_normal is 1 if the sign of // the normal should be flipped. #define TST(expr1,expr2,norm,cc) \ s2 = dFabs(expr1) - (expr2); \ if (s2 > 0) return 0; \ if (s2 > s) { \ s = s2; \ normalR = norm; \ invert_normal = ((expr1) < 0); \ code = (cc); \ } s = -dInfinity; invert_normal = 0; code = 0; // separating axis = u1,u2,u3 TST (pp[0],(A[0] + dMUL(B[0],Q11) + dMUL(B[1],Q12) + dMUL(B[2],Q13)),R1+0,1); TST (pp[1],(A[1] + dMUL(B[0],Q21) + dMUL(B[1],Q22) + dMUL(B[2],Q23)),R1+1,2); TST (pp[2],(A[2] + dMUL(B[0],Q31) + dMUL(B[1],Q32) + dMUL(B[2],Q33)),R1+2,3); // separating axis = v1,v2,v3 TST (dDOT41(R2+0,p),(dMUL(A[0],Q11) + dMUL(A[1],Q21) + dMUL(A[2],Q31) + B[0]),R2+0,4); TST (dDOT41(R2+1,p),(dMUL(A[0],Q12) + dMUL(A[1],Q22) + dMUL(A[2],Q32) + B[1]),R2+1,5); TST (dDOT41(R2+2,p),(dMUL(A[0],Q13) + dMUL(A[1],Q23) + dMUL(A[2],Q33) + B[2]),R2+2,6); // note: cross product axes need to be scaled when s is computed. // normal (n1,n2,n3) is relative to box 1. #undef TST #define TST(expr1,expr2,n1,n2,n3,cc) \ s2 = dFabs(expr1) - (expr2); \ if (s2 > 0) return 0; \ l = dSqrt (dMUL((n1),(n1)) + dMUL((n2),(n2)) + dMUL((n3),(n3))); \ if (l > 0) { \ s2 = dDIV(s2,l); \ if (dMUL(s2,fudge_factor) > s) { \ s = s2; \ normalR = 0; \ normalC[0] = dDIV((n1),l); normalC[1] = dDIV((n2),l); normalC[2] = dDIV((n3),l); \ invert_normal = ((expr1) < 0); \ code = (cc); \ } \ } // separating axis = u1 x (v1,v2,v3) TST((dMUL(pp[2],R21)-dMUL(pp[1],R31)),(dMUL(A[1],Q31)+dMUL(A[2],Q21)+dMUL(B[1],Q13)+dMUL(B[2],Q12)),0,-R31,R21,7); TST((dMUL(pp[2],R22)-dMUL(pp[1],R32)),(dMUL(A[1],Q32)+dMUL(A[2],Q22)+dMUL(B[0],Q13)+dMUL(B[2],Q11)),0,-R32,R22,8); TST((dMUL(pp[2],R23)-dMUL(pp[1],R33)),(dMUL(A[1],Q33)+dMUL(A[2],Q23)+dMUL(B[0],Q12)+dMUL(B[1],Q11)),0,-R33,R23,9); // separating axis = u2 x (v1,v2,v3) TST((dMUL(pp[0],R31)-dMUL(pp[2],R11)),(dMUL(A[0],Q31)+dMUL(A[2],Q11)+dMUL(B[1],Q23)+dMUL(B[2],Q22)),R31,0,-R11,10); TST((dMUL(pp[0],R32)-dMUL(pp[2],R12)),(dMUL(A[0],Q32)+dMUL(A[2],Q12)+dMUL(B[0],Q23)+dMUL(B[2],Q21)),R32,0,-R12,11); TST((dMUL(pp[0],R33)-dMUL(pp[2],R13)),(dMUL(A[0],Q33)+dMUL(A[2],Q13)+dMUL(B[0],Q22)+dMUL(B[1],Q21)),R33,0,-R13,12); // separating axis = u3 x (v1,v2,v3) TST((dMUL(pp[1],R11)-dMUL(pp[0],R21)),(dMUL(A[0],Q21)+dMUL(A[1],Q11)+dMUL(B[1],Q33)+dMUL(B[2],Q32)),-R21,R11,0,13); TST((dMUL(pp[1],R12)-dMUL(pp[0],R22)),(dMUL(A[0],Q22)+dMUL(A[1],Q12)+dMUL(B[0],Q33)+dMUL(B[2],Q31)),-R22,R12,0,14); TST((dMUL(pp[1],R13)-dMUL(pp[0],R23)),(dMUL(A[0],Q23)+dMUL(A[1],Q13)+dMUL(B[0],Q32)+dMUL(B[1],Q31)),-R23,R13,0,15); #undef TST if (!code) return 0; // if we get to this point, the boxes interpenetrate. compute the normal // in global coordinates. if (normalR) { normal[0] = normalR[0]; normal[1] = normalR[4]; normal[2] = normalR[8]; } else { dMULTIPLY0_331 (normal,R1,normalC); } if (invert_normal) { normal[0] = -normal[0]; normal[1] = -normal[1]; normal[2] = -normal[2]; } *depth = -s; // compute contact point(s) if (code > 6) { // an edge from box 1 touches an edge from box 2. // find a point pa on the intersecting edge of box 1 dVector3 pa; dReal sign; for (i=0; i<3; i++) pa[i] = p1[i]; for (j=0; j<3; j++) { sign = (dDOT14(normal,R1+j) > 0) ? REAL(1.0) : REAL(-1.0); for (i=0; i<3; i++) pa[i] += dMUL(sign,dMUL(A[j],R1[i*4+j])); } // find a point pb on the intersecting edge of box 2 dVector3 pb; for (i=0; i<3; i++) pb[i] = p2[i]; for (j=0; j<3; j++) { sign = (dDOT14(normal,R2+j) > 0) ? REAL(-1.0) : REAL(1.0); for (i=0; i<3; i++) pb[i] += dMUL(sign,dMUL(B[j],R2[i*4+j])); } dReal alpha,beta; dVector3 ua,ub; for (i=0; i<3; i++) ua[i] = R1[((code)-7)/3 + i*4]; for (i=0; i<3; i++) ub[i] = R2[((code)-7)%3 + i*4]; dLineClosestApproach (pa,ua,pb,ub,&alpha,&beta); for (i=0; i<3; i++) pa[i] += dMUL(ua[i],alpha); for (i=0; i<3; i++) pb[i] += dMUL(ub[i],beta); for (i=0; i<3; i++) contact[0].pos[i] = dMUL(REAL(0.5),(pa[i]+pb[i])); contact[0].depth = *depth; *return_code = code; return 1; } // okay, we have a face-something intersection (because the separating // axis is perpendicular to a face). define face 'a' to be the reference // face (i.e. the normal vector is perpendicular to this) and face 'b' to be // the incident face (the closest face of the other box). const dReal *Ra,*Rb,*pa,*pb,*Sa,*Sb; if (code <= 3) { Ra = R1; Rb = R2; pa = p1; pb = p2; Sa = A; Sb = B; } else { Ra = R2; Rb = R1; pa = p2; pb = p1; Sa = B; Sb = A; } // nr = normal vector of reference face dotted with axes of incident box. // anr = absolute values of nr. dVector3 normal2,nr,anr; if (code <= 3) { normal2[0] = normal[0]; normal2[1] = normal[1]; normal2[2] = normal[2]; } else { normal2[0] = -normal[0]; normal2[1] = -normal[1]; normal2[2] = -normal[2]; } dMULTIPLY1_331 (nr,Rb,normal2); anr[0] = dFabs (nr[0]); anr[1] = dFabs (nr[1]); anr[2] = dFabs (nr[2]); // find the largest compontent of anr: this corresponds to the normal // for the indident face. the other axis numbers of the indicent face // are stored in a1,a2. int lanr,a1,a2; if (anr[1] > anr[0]) { if (anr[1] > anr[2]) { a1 = 0; lanr = 1; a2 = 2; } else { a1 = 0; a2 = 1; lanr = 2; } } else { if (anr[0] > anr[2]) { lanr = 0; a1 = 1; a2 = 2; } else { a1 = 0; a2 = 1; lanr = 2; } } // compute center point of incident face, in reference-face coordinates dVector3 center; if (nr[lanr] < 0) { for (i=0; i<3; i++) center[i] = pb[i] - pa[i] + dMUL(Sb[lanr],Rb[i*4+lanr]); } else { for (i=0; i<3; i++) center[i] = pb[i] - pa[i] - dMUL(Sb[lanr],Rb[i*4+lanr]); } // find the normal and non-normal axis numbers of the reference box int codeN,code1,code2; if (code <= 3) codeN = code-1; else codeN = code-4; if (codeN==0) { code1 = 1; code2 = 2; } else if (codeN==1) { code1 = 0; code2 = 2; } else { code1 = 0; code2 = 1; } // find the four corners of the incident face, in reference-face coordinates dReal quad[8]; // 2D coordinate of incident face (x,y pairs) dReal c1,c2,m11,m12,m21,m22; c1 = dDOT14 (center,Ra+code1); c2 = dDOT14 (center,Ra+code2); // optimize this? - we have already computed this data above, but it is not // stored in an easy-to-index format. for now it's quicker just to recompute // the four dot products. m11 = dDOT44 (Ra+code1,Rb+a1); m12 = dDOT44 (Ra+code1,Rb+a2); m21 = dDOT44 (Ra+code2,Rb+a1); m22 = dDOT44 (Ra+code2,Rb+a2); { dReal k1 = dMUL(m11,Sb[a1]); dReal k2 = dMUL(m21,Sb[a1]); dReal k3 = dMUL(m12,Sb[a2]); dReal k4 = dMUL(m22,Sb[a2]); quad[0] = c1 - k1 - k3; quad[1] = c2 - k2 - k4; quad[2] = c1 - k1 + k3; quad[3] = c2 - k2 + k4; quad[4] = c1 + k1 + k3; quad[5] = c2 + k2 + k4; quad[6] = c1 + k1 - k3; quad[7] = c2 + k2 - k4; } // find the size of the reference face dReal rect[2]; rect[0] = Sa[code1]; rect[1] = Sa[code2]; // intersect the incident and reference faces dReal ret[16]; int n = intersectRectQuad (rect,quad,ret); if (n < 1) return 0; // this should never happen // convert the intersection points into reference-face coordinates, // and compute the contact position and depth for each point. only keep // those points that have a positive (penetrating) depth. delete points in // the 'ret' array as necessary so that 'point' and 'ret' correspond. dReal point[3*8]; // penetrating contact points dReal dep[8]; // depths for those points dReal det1 = dRecip(dMUL(m11,m22) - dMUL(m12,m21)); m11 = dMUL(m11,det1); m12 = dMUL(m12,det1); m21 = dMUL(m21,det1); m22 = dMUL(m22,det1); int cnum = 0; // number of penetrating contact points found for (j=0; j < n; j++) { dReal k1 = dMUL(m22,(ret[j*2]-c1)) - dMUL(m12,(ret[j*2+1]-c2)); dReal k2 = -dMUL(m21,(ret[j*2]-c1)) + dMUL(m11,(ret[j*2+1]-c2)); for (i=0; i<3; i++) point[cnum*3+i] = center[i] + dMUL(k1,Rb[i*4+a1]) + dMUL(k2,Rb[i*4+a2]); dep[cnum] = Sa[codeN] - dDOT(normal2,point+cnum*3); if (dep[cnum] >= 0) { ret[cnum*2] = ret[j*2]; ret[cnum*2+1] = ret[j*2+1]; cnum++; } } if (cnum < 1) return 0; // this should never happen // we can't generate more contacts than we actually have if (maxc > cnum) maxc = cnum; if (maxc < 1) maxc = 1; if (cnum <= maxc) { // we have less contacts than we need, so we use them all for (j=0; j < cnum; j++) { dContactGeom *con = CONTACT(contact,skip*j); for (i=0; i<3; i++) con->pos[i] = point[j*3+i] + pa[i]; con->depth = dep[j]; } } else { // we have more contacts than are wanted, some of them must be culled. // find the deepest point, it is always the first contact. int i1 = 0; dReal maxdepth = dep[0]; for (i=1; i<cnum; i++) { if (dep[i] > maxdepth) { maxdepth = dep[i]; i1 = i; } } int iret[8]; cullPoints (cnum,ret,maxc,i1,iret); for (j=0; j < maxc; j++) { dContactGeom *con = CONTACT(contact,skip*j); for (i=0; i<3; i++) con->pos[i] = point[iret[j]*3+i] + pa[i]; con->depth = dep[iret[j]]; } cnum = maxc; } *return_code = code; return cnum; }
// given two boxes (p1,R1,side1) and (p2,R2,side2), collide them together and // generate contact points. this returns 0 if there is no contact otherwise // it returns the number of contacts generated. // `normal' returns the contact normal. // `depth' returns the maximum penetration depth along that normal. // `return_code' returns a number indicating the type of contact that was // detected: // 1,2,3 = box 2 intersects with a face of box 1 // 4,5,6 = box 1 intersects with a face of box 2 // 7..15 = edge-edge contact // `maxc' is the maximum number of contacts allowed to be generated, i.e. // the size of the `contact' array. // `contact' and `skip' are the contact array information provided to the // collision functions. this function only fills in the position and depth // fields. int dBoxBox(const dVector3 p1, const dMatrix3 R1, const dVector3 side1, const dVector3 p2, const dMatrix3 R2, const dVector3 side2, std::vector<Contact>& result) { const double fudge_factor = 1.05; dVector3 p,pp,normalC = {0.0, 0.0, 0.0, 0.0}; const double *normalR = 0; double A[3],B[3],R11,R12,R13,R21,R22,R23,R31,R32,R33,Q11,Q12,Q13,Q21,Q22,Q23,Q31,Q32,Q33,s,s2,l; int i,j,invert_normal,code; // get vector from centers of box 1 to box 2, relative to box 1 p[0] = p2[0] - p1[0]; p[1] = p2[1] - p1[1]; p[2] = p2[2] - p1[2]; dMULTIPLY1_331 (pp,R1,p); // get pp = p relative to body 1 // get side lengths / 2 A[0] = side1[0]; A[1] = side1[1]; A[2] = side1[2]; B[0] = side2[0]; B[1] = side2[1]; B[2] = side2[2]; // Rij is R1'*R2, i.e. the relative rotation between R1 and R2 R11 = Inner44(R1+0,R2+0); R12 = Inner44(R1+0,R2+1); R13 = Inner44(R1+0,R2+2); R21 = Inner44(R1+1,R2+0); R22 = Inner44(R1+1,R2+1); R23 = Inner44(R1+1,R2+2); R31 = Inner44(R1+2,R2+0); R32 = Inner44(R1+2,R2+1); R33 = Inner44(R1+2,R2+2); Q11 = std::abs(R11); Q12 = std::abs(R12); Q13 = std::abs(R13); Q21 = std::abs(R21); Q22 = std::abs(R22); Q23 = std::abs(R23); Q31 = std::abs(R31); Q32 = std::abs(R32); Q33 = std::abs(R33); // for all 15 possible separating axes: // * see if the axis separates the boxes. if so, return 0. // * find the depth of the penetration along the separating axis (s2) // * if this is the largest depth so far, record it. // the normal vector will be set to the separating axis with the smallest // depth. note: normalR is set to point to a column of R1 or R2 if that is // the smallest depth normal so far. otherwise normalR is 0 and normalC is // set to a vector relative to body 1. invert_normal is 1 if the sign of // the normal should be flipped. #define TST(expr1,expr2,norm,cc) \ s2 = std::abs(expr1) - (expr2); \ if (s2 > s) { \ s = s2; \ normalR = norm; \ invert_normal = ((expr1) < 0); \ code = (cc); \ } s = -1E12; invert_normal = 0; code = 0; // separating axis = u1,u2,u3 TST (pp[0],(A[0] + B[0]*Q11 + B[1]*Q12 + B[2]*Q13),R1+0,1); TST (pp[1],(A[1] + B[0]*Q21 + B[1]*Q22 + B[2]*Q23),R1+1,2); TST (pp[2],(A[2] + B[0]*Q31 + B[1]*Q32 + B[2]*Q33),R1+2,3); // separating axis = v1,v2,v3 TST (Inner41(R2+0,p),(A[0]*Q11 + A[1]*Q21 + A[2]*Q31 + B[0]),R2+0,4); TST (Inner41(R2+1,p),(A[0]*Q12 + A[1]*Q22 + A[2]*Q32 + B[1]),R2+1,5); TST (Inner41(R2+2,p),(A[0]*Q13 + A[1]*Q23 + A[2]*Q33 + B[2]),R2+2,6); // note: cross product axes need to be scaled when s is computed. // normal (n1,n2,n3) is relative to box 1. #undef TST #define TST(expr1,expr2,n1,n2,n3,cc) \ s2 = std::abs(expr1) - (expr2); \ l = sqrt ((n1)*(n1) + (n2)*(n2) + (n3)*(n3)); \ if (l > 0) { \ s2 /= l; \ if (s2*fudge_factor > s) { \ s = s2; \ normalR = 0; \ normalC[0] = (n1)/l; normalC[1] = (n2)/l; normalC[2] = (n3)/l; \ invert_normal = ((expr1) < 0); \ code = (cc); \ } \ } // separating axis = u1 x (v1,v2,v3) TST(pp[2]*R21-pp[1]*R31,(A[1]*Q31+A[2]*Q21+B[1]*Q13+B[2]*Q12),0,-R31,R21,7); TST(pp[2]*R22-pp[1]*R32,(A[1]*Q32+A[2]*Q22+B[0]*Q13+B[2]*Q11),0,-R32,R22,8); TST(pp[2]*R23-pp[1]*R33,(A[1]*Q33+A[2]*Q23+B[0]*Q12+B[1]*Q11),0,-R33,R23,9); // separating axis = u2 x (v1,v2,v3) TST(pp[0]*R31-pp[2]*R11,(A[0]*Q31+A[2]*Q11+B[1]*Q23+B[2]*Q22),R31,0,-R11,10); TST(pp[0]*R32-pp[2]*R12,(A[0]*Q32+A[2]*Q12+B[0]*Q23+B[2]*Q21),R32,0,-R12,11); TST(pp[0]*R33-pp[2]*R13,(A[0]*Q33+A[2]*Q13+B[0]*Q22+B[1]*Q21),R33,0,-R13,12); // separating axis = u3 x (v1,v2,v3) TST(pp[1]*R11-pp[0]*R21,(A[0]*Q21+A[1]*Q11+B[1]*Q33+B[2]*Q32),-R21,R11,0,13); TST(pp[1]*R12-pp[0]*R22,(A[0]*Q22+A[1]*Q12+B[0]*Q33+B[2]*Q31),-R22,R12,0,14); TST(pp[1]*R13-pp[0]*R23,(A[0]*Q23+A[1]*Q13+B[0]*Q32+B[1]*Q31),-R23,R13,0,15); #undef TST if (!code) return 0; if (s > 0.0) return 0; // if we get to this point, the boxes interpenetrate. compute the normal // in global coordinates. Eigen::Vector3d normal; Eigen::Vector3d point_vec; double penetration; if (normalR) { normal << normalR[0],normalR[4],normalR[8]; } else { normal << Inner((R1),(normalC)), Inner((R1+4),(normalC)), Inner((R1+8),(normalC)); //dMULTIPLY0_331 (normal,R1,normalC); } if (invert_normal) { normal *= -1.0; } // compute contact point(s) // single point if (code > 6) { // an edge from box 1 touches an edge from box 2. // find a point pa on the intersecting edge of box 1 dVector3 pa; double sign; for (i=0; i<3; i++) pa[i] = p1[i]; for (j=0; j<3; j++) { #define TEMP_INNER14(a,b) (a[0]*(b)[0] + a[1]*(b)[4] + a[2]*(b)[8]) sign = (TEMP_INNER14(normal,R1+j) > 0) ? 1.0 : -1.0; //sign = (Inner14(normal,R1+j) > 0) ? 1.0 : -1.0; for (i=0; i<3; i++) pa[i] += sign * A[j] * R1[i*4+j]; } // find a point pb on the intersecting edge of box 2 dVector3 pb; for (i=0; i<3; i++) pb[i] = p2[i]; for (j=0; j<3; j++) { sign = (TEMP_INNER14(normal,R2+j) > 0) ? -1.0 : 1.0; #undef TEMP_INNER14 for (i=0; i<3; i++) pb[i] += sign * B[j] * R2[i*4+j]; } double alpha,beta; dVector3 ua,ub; for (i=0; i<3; i++) ua[i] = R1[((code)-7)/3 + i*4]; for (i=0; i<3; i++) ub[i] = R2[((code)-7)%3 + i*4]; dLineClosestApproach (pa,ua,pb,ub,&alpha,&beta); for (i=0; i<3; i++) pa[i] += ua[i]*alpha; for (i=0; i<3; i++) pb[i] += ub[i]*beta; { point_vec << 0.5*(pa[0]+pb[0]), 0.5*(pa[1]+pb[1]), 0.5*(pa[2]+pb[2]); penetration = -s; Contact contact; contact.point = point_vec; contact.normal = normal; contact.penetrationDepth = penetration; result.push_back(contact); } return 1; } // okay, we have a face-something intersection (because the separating // axis is perpendicular to a face). define face 'a' to be the reference // face (i.e. the normal vector is perpendicular to this) and face 'b' to be // the incident face (the closest face of the other box). const double *Ra,*Rb,*pa,*pb,*Sa,*Sb; if (code <= 3) { Ra = R1; Rb = R2; pa = p1; pb = p2; Sa = A; Sb = B; } else { Ra = R2; Rb = R1; pa = p2; pb = p1; Sa = B; Sb = A; } // nr = normal vector of reference face dotted with axes of incident box. // anr = absolute values of nr. dVector3 normal2,nr,anr; if (code <= 3) { normal2[0] = normal[0]; normal2[1] = normal[1]; normal2[2] = normal[2]; } else { normal2[0] = -normal[0]; normal2[1] = -normal[1]; normal2[2] = -normal[2]; } dMULTIPLY1_331 (nr,Rb,normal2); anr[0] = fabs (nr[0]); anr[1] = fabs (nr[1]); anr[2] = fabs (nr[2]); // find the largest compontent of anr: this corresponds to the normal // for the indident face. the other axis numbers of the indicent face // are stored in a1,a2. int lanr,a1,a2; if (anr[1] > anr[0]) { if (anr[1] > anr[2]) { a1 = 0; lanr = 1; a2 = 2; } else { a1 = 0; a2 = 1; lanr = 2; } } else { if (anr[0] > anr[2]) { lanr = 0; a1 = 1; a2 = 2; } else { a1 = 0; a2 = 1; lanr = 2; } } // compute center point of incident face, in reference-face coordinates dVector3 center; if (nr[lanr] < 0) { for (i=0; i<3; i++) center[i] = pb[i] - pa[i] + Sb[lanr] * Rb[i*4+lanr]; } else { for (i=0; i<3; i++) center[i] = pb[i] - pa[i] - Sb[lanr] * Rb[i*4+lanr]; } // find the normal and non-normal axis numbers of the reference box int codeN,code1,code2; if (code <= 3) codeN = code-1; else codeN = code-4; if (codeN==0) { code1 = 1; code2 = 2; } else if (codeN==1) { code1 = 0; code2 = 2; } else { code1 = 0; code2 = 1; } // find the four corners of the incident face, in reference-face coordinates double quad[8]; // 2D coordinate of incident face (x,y pairs) double c1,c2,m11,m12,m21,m22; c1 = Inner14 (center,Ra+code1); c2 = Inner14 (center,Ra+code2); // optimize this? - we have already computed this data above, but it is not // stored in an easy-to-index format. for now it's quicker just to recompute // the four dot products. m11 = Inner44 (Ra+code1,Rb+a1); m12 = Inner44 (Ra+code1,Rb+a2); m21 = Inner44 (Ra+code2,Rb+a1); m22 = Inner44 (Ra+code2,Rb+a2); { double k1 = m11*Sb[a1]; double k2 = m21*Sb[a1]; double k3 = m12*Sb[a2]; double k4 = m22*Sb[a2]; quad[0] = c1 - k1 - k3; quad[1] = c2 - k2 - k4; quad[2] = c1 - k1 + k3; quad[3] = c2 - k2 + k4; quad[4] = c1 + k1 + k3; quad[5] = c2 + k2 + k4; quad[6] = c1 + k1 - k3; quad[7] = c2 + k2 - k4; } // find the size of the reference face double rect[2]; rect[0] = Sa[code1]; rect[1] = Sa[code2]; // intersect the incident and reference faces double ret[16]; int n = intersectRectQuad (rect,quad,ret); if (n < 1) return 0; // this should never happen // convert the intersection points into reference-face coordinates, // and compute the contact position and depth for each point. only keep // those points that have a positive (penetrating) depth. delete points in // the 'ret' array as necessary so that 'point' and 'ret' correspond. //real point[3*8]; // penetrating contact points double point[24]; // penetrating contact points double dep[8]; // depths for those points double det1 = dRecip(m11*m22 - m12*m21); m11 *= det1; m12 *= det1; m21 *= det1; m22 *= det1; int cnum = 0; // number of penetrating contact points found for (j=0; j < n; j++) { double k1 = m22*(ret[j*2]-c1) - m12*(ret[j*2+1]-c2); double k2 = -m21*(ret[j*2]-c1) + m11*(ret[j*2+1]-c2); for (i=0; i<3; i++) { point[cnum*3+i] = center[i] + k1*Rb[i*4+a1] + k2*Rb[i*4+a2]; } dep[cnum] = Sa[codeN] - Inner(normal2,point+cnum*3); if (dep[cnum] >= 0) { ret[cnum*2] = ret[j*2]; ret[cnum*2+1] = ret[j*2+1]; cnum++; } } if (cnum < 1) return 0; // this should never happen // we can't generate more contacts than we actually have int maxc = 4; if (maxc > cnum) maxc = cnum; //if (maxc < 1) maxc = 1; if (cnum <= maxc) { // we have less contacts than we need, so we use them all for (j=0; j < cnum; j++) { point_vec << point[j*3+0] + pa[0], point[j*3+1] + pa[1], point[j*3+2] + pa[2]; Contact contact; contact.point = point_vec; contact.normal = normal; contact.penetrationDepth = dep[j]; result.push_back(contact); } } else { // we have more contacts than are wanted, some of them must be culled. // find the deepest point, it is always the first contact. int i1 = 0; double maxdepth = dep[0]; for (i=1; i<cnum; i++) { if (dep[i] > maxdepth) { maxdepth = dep[i]; i1 = i; } } int iret[8]; cullPoints (cnum,ret,maxc,i1,iret); cnum = maxc; for (j=0; j < cnum; j++) { point_vec << point[iret[j]*3+0] + pa[0], point[iret[j]*3+1] + pa[1], point[iret[j]*3+2] + pa[2]; Contact contact; contact.point = point_vec; contact.normal = normal; contact.penetrationDepth = dep[iret[j]]; result.push_back(contact); } } return cnum; }
int dBoxBox (const dVector3 p1, const dMatrix3 R1, const dVector3 side1, const dVector3 p2, const dMatrix3 R2, const dVector3 side2, dVector3 normal, dReal *depth, int *return_code, int flags, dContactGeom *contact, int skip) { const dReal fudge_factor = REAL(1.05); dVector3 p,pp,normalC={0,0,0}; const dReal *normalR = 0; dReal A[3],B[3],R11,R12,R13,R21,R22,R23,R31,R32,R33, Q11,Q12,Q13,Q21,Q22,Q23,Q31,Q32,Q33,s,s2,l,expr1_val; int i,j,invert_normal,code; // get vector from centers of box 1 to box 2, relative to box 1 p[0] = p2[0] - p1[0]; p[1] = p2[1] - p1[1]; p[2] = p2[2] - p1[2]; dMultiply1_331 (pp,R1,p); // get pp = p relative to body 1 // get side lengths / 2 A[0] = side1[0]*REAL(0.5); A[1] = side1[1]*REAL(0.5); A[2] = side1[2]*REAL(0.5); B[0] = side2[0]*REAL(0.5); B[1] = side2[1]*REAL(0.5); B[2] = side2[2]*REAL(0.5); // Rij is R1'*R2, i.e. the relative rotation between R1 and R2 R11 = dCalcVectorDot3_44(R1+0,R2+0); R12 = dCalcVectorDot3_44(R1+0,R2+1); R13 = dCalcVectorDot3_44(R1+0,R2+2); R21 = dCalcVectorDot3_44(R1+1,R2+0); R22 = dCalcVectorDot3_44(R1+1,R2+1); R23 = dCalcVectorDot3_44(R1+1,R2+2); R31 = dCalcVectorDot3_44(R1+2,R2+0); R32 = dCalcVectorDot3_44(R1+2,R2+1); R33 = dCalcVectorDot3_44(R1+2,R2+2); Q11 = dFabs(R11); Q12 = dFabs(R12); Q13 = dFabs(R13); Q21 = dFabs(R21); Q22 = dFabs(R22); Q23 = dFabs(R23); Q31 = dFabs(R31); Q32 = dFabs(R32); Q33 = dFabs(R33); // for all 15 possible separating axes: // * see if the axis separates the boxes. if so, return 0. // * find the depth of the penetration along the separating axis (s2) // * if this is the largest depth so far, record it. // the normal vector will be set to the separating axis with the smallest // depth. note: normalR is set to point to a column of R1 or R2 if that is // the smallest depth normal so far. otherwise normalR is 0 and normalC is // set to a vector relative to body 1. invert_normal is 1 if the sign of // the normal should be flipped. do { #define TST(expr1,expr2,norm,cc) \ expr1_val = (expr1); /* Avoid duplicate evaluation of expr1 */ \ s2 = dFabs(expr1_val) - (expr2); \ if (s2 > 0) return 0; \ if (s2 > s) { \ s = s2; \ normalR = norm; \ invert_normal = ((expr1_val) < 0); \ code = (cc); \ if (flags & CONTACTS_UNIMPORTANT) break; \ } s = -dInfinity; invert_normal = 0; code = 0; // separating axis = u1,u2,u3 TST (pp[0],(A[0] + B[0]*Q11 + B[1]*Q12 + B[2]*Q13),R1+0,1); TST (pp[1],(A[1] + B[0]*Q21 + B[1]*Q22 + B[2]*Q23),R1+1,2); TST (pp[2],(A[2] + B[0]*Q31 + B[1]*Q32 + B[2]*Q33),R1+2,3); // separating axis = v1,v2,v3 TST (dCalcVectorDot3_41(R2+0,p),(A[0]*Q11 + A[1]*Q21 + A[2]*Q31 + B[0]),R2+0,4); TST (dCalcVectorDot3_41(R2+1,p),(A[0]*Q12 + A[1]*Q22 + A[2]*Q32 + B[1]),R2+1,5); TST (dCalcVectorDot3_41(R2+2,p),(A[0]*Q13 + A[1]*Q23 + A[2]*Q33 + B[2]),R2+2,6); // note: cross product axes need to be scaled when s is computed. // normal (n1,n2,n3) is relative to box 1. #undef TST #define TST(expr1,expr2,n1,n2,n3,cc) \ expr1_val = (expr1); /* Avoid duplicate evaluation of expr1 */ \ s2 = dFabs(expr1_val) - (expr2); \ if (s2 > 0) return 0; \ l = dSqrt ((n1)*(n1) + (n2)*(n2) + (n3)*(n3)); \ if (l > 0) { \ s2 /= l; \ if (s2*fudge_factor > s) { \ s = s2; \ normalR = 0; \ normalC[0] = (n1)/l; normalC[1] = (n2)/l; normalC[2] = (n3)/l; \ invert_normal = ((expr1_val) < 0); \ code = (cc); \ if (flags & CONTACTS_UNIMPORTANT) break; \ } \ } // We only need to check 3 edges per box // since parallel edges are equivalent. // separating axis = u1 x (v1,v2,v3) TST(pp[2]*R21-pp[1]*R31,(A[1]*Q31+A[2]*Q21+B[1]*Q13+B[2]*Q12),0,-R31,R21,7); TST(pp[2]*R22-pp[1]*R32,(A[1]*Q32+A[2]*Q22+B[0]*Q13+B[2]*Q11),0,-R32,R22,8); TST(pp[2]*R23-pp[1]*R33,(A[1]*Q33+A[2]*Q23+B[0]*Q12+B[1]*Q11),0,-R33,R23,9); // separating axis = u2 x (v1,v2,v3) TST(pp[0]*R31-pp[2]*R11,(A[0]*Q31+A[2]*Q11+B[1]*Q23+B[2]*Q22),R31,0,-R11,10); TST(pp[0]*R32-pp[2]*R12,(A[0]*Q32+A[2]*Q12+B[0]*Q23+B[2]*Q21),R32,0,-R12,11); TST(pp[0]*R33-pp[2]*R13,(A[0]*Q33+A[2]*Q13+B[0]*Q22+B[1]*Q21),R33,0,-R13,12); // separating axis = u3 x (v1,v2,v3) TST(pp[1]*R11-pp[0]*R21,(A[0]*Q21+A[1]*Q11+B[1]*Q33+B[2]*Q32),-R21,R11,0,13); TST(pp[1]*R12-pp[0]*R22,(A[0]*Q22+A[1]*Q12+B[0]*Q33+B[2]*Q31),-R22,R12,0,14); TST(pp[1]*R13-pp[0]*R23,(A[0]*Q23+A[1]*Q13+B[0]*Q32+B[1]*Q31),-R23,R13,0,15); #undef TST } while (0); if (!code) return 0; // if we get to this point, the boxes interpenetrate. compute the normal // in global coordinates. if (normalR) { normal[0] = normalR[0]; normal[1] = normalR[4]; normal[2] = normalR[8]; } else { dMultiply0_331 (normal,R1,normalC); } if (invert_normal) { normal[0] = -normal[0]; normal[1] = -normal[1]; normal[2] = -normal[2]; } *depth = -s; // compute contact point(s) if (code > 6) { // An edge from box 1 touches an edge from box 2. // find a point pa on the intersecting edge of box 1 dVector3 pa; dReal sign; // Copy p1 into pa for (i=0; i<3; i++) pa[i] = p1[i]; // why no memcpy? // Get world position of p2 into pa for (j=0; j<3; j++) { sign = (dCalcVectorDot3_14(normal,R1+j) > 0) ? REAL(1.0) : REAL(-1.0); for (i=0; i<3; i++) pa[i] += sign * A[j] * R1[i*4+j]; } // find a point pb on the intersecting edge of box 2 dVector3 pb; // Copy p2 into pb for (i=0; i<3; i++) pb[i] = p2[i]; // why no memcpy? // Get world position of p2 into pb for (j=0; j<3; j++) { sign = (dCalcVectorDot3_14(normal,R2+j) > 0) ? REAL(-1.0) : REAL(1.0); for (i=0; i<3; i++) pb[i] += sign * B[j] * R2[i*4+j]; } dReal alpha,beta; dVector3 ua,ub; // Get direction of first edge for (i=0; i<3; i++) ua[i] = R1[((code)-7)/3 + i*4]; // Get direction of second edge for (i=0; i<3; i++) ub[i] = R2[((code)-7)%3 + i*4]; // Get closest points between edges (one at each) dLineClosestApproach (pa,ua,pb,ub,&alpha,&beta); for (i=0; i<3; i++) pa[i] += ua[i]*alpha; for (i=0; i<3; i++) pb[i] += ub[i]*beta; // Set the contact point as halfway between the 2 closest points for (i=0; i<3; i++) contact[0].pos[i] = REAL(0.5)*(pa[i]+pb[i]); contact[0].depth = *depth; *return_code = code; return 1; } // okay, we have a face-something intersection (because the separating // axis is perpendicular to a face). define face 'a' to be the reference // face (i.e. the normal vector is perpendicular to this) and face 'b' to be // the incident face (the closest face of the other box). // Note: Unmodified parameter values are being used here const dReal *Ra,*Rb,*pa,*pb,*Sa,*Sb; if (code <= 3) { // One of the faces of box 1 is the reference face Ra = R1; // Rotation of 'a' Rb = R2; // Rotation of 'b' pa = p1; // Center (location) of 'a' pb = p2; // Center (location) of 'b' Sa = A; // Side Lenght of 'a' Sb = B; // Side Lenght of 'b' } else { // One of the faces of box 2 is the reference face Ra = R2; // Rotation of 'a' Rb = R1; // Rotation of 'b' pa = p2; // Center (location) of 'a' pb = p1; // Center (location) of 'b' Sa = B; // Side Lenght of 'a' Sb = A; // Side Lenght of 'b' } // nr = normal vector of reference face dotted with axes of incident box. // anr = absolute values of nr. /* The normal is flipped if necessary so it always points outward from box 'a', box 'b' is thus always the incident box */ dVector3 normal2,nr,anr; if (code <= 3) { normal2[0] = normal[0]; normal2[1] = normal[1]; normal2[2] = normal[2]; } else { normal2[0] = -normal[0]; normal2[1] = -normal[1]; normal2[2] = -normal[2]; } // Rotate normal2 in incident box opposite direction dMultiply1_331 (nr,Rb,normal2); anr[0] = dFabs (nr[0]); anr[1] = dFabs (nr[1]); anr[2] = dFabs (nr[2]); // find the largest compontent of anr: this corresponds to the normal // for the incident face. the other axis numbers of the incident face // are stored in a1,a2. int lanr,a1,a2; if (anr[1] > anr[0]) { if (anr[1] > anr[2]) { a1 = 0; lanr = 1; a2 = 2; } else { a1 = 0; a2 = 1; lanr = 2; } } else { if (anr[0] > anr[2]) { lanr = 0; a1 = 1; a2 = 2; } else { a1 = 0; a2 = 1; lanr = 2; } } // compute center point of incident face, in reference-face coordinates dVector3 center; if (nr[lanr] < 0) { for (i=0; i<3; i++) center[i] = pb[i] - pa[i] + Sb[lanr] * Rb[i*4+lanr]; } else { for (i=0; i<3; i++) center[i] = pb[i] - pa[i] - Sb[lanr] * Rb[i*4+lanr]; } // find the normal and non-normal axis numbers of the reference box int codeN,code1,code2; if (code <= 3) codeN = code-1; else codeN = code-4; if (codeN==0) { code1 = 1; code2 = 2; } else if (codeN==1) { code1 = 0; code2 = 2; } else { code1 = 0; code2 = 1; } // find the four corners of the incident face, in reference-face coordinates dReal quad[8]; // 2D coordinate of incident face (x,y pairs) dReal c1,c2,m11,m12,m21,m22; c1 = dCalcVectorDot3_14 (center,Ra+code1); c2 = dCalcVectorDot3_14 (center,Ra+code2); // optimize this? - we have already computed this data above, but it is not // stored in an easy-to-index format. for now it's quicker just to recompute // the four dot products. m11 = dCalcVectorDot3_44 (Ra+code1,Rb+a1); m12 = dCalcVectorDot3_44 (Ra+code1,Rb+a2); m21 = dCalcVectorDot3_44 (Ra+code2,Rb+a1); m22 = dCalcVectorDot3_44 (Ra+code2,Rb+a2); { dReal k1 = m11*Sb[a1]; dReal k2 = m21*Sb[a1]; dReal k3 = m12*Sb[a2]; dReal k4 = m22*Sb[a2]; quad[0] = c1 - k1 - k3; quad[1] = c2 - k2 - k4; quad[2] = c1 - k1 + k3; quad[3] = c2 - k2 + k4; quad[4] = c1 + k1 + k3; quad[5] = c2 + k2 + k4; quad[6] = c1 + k1 - k3; quad[7] = c2 + k2 - k4; } // find the size of the reference face dReal rect[2]; rect[0] = Sa[code1]; rect[1] = Sa[code2]; // intersect the incident and reference faces dReal ret[16]; int n = intersectRectQuad (rect,quad,ret); if (n < 1) return 0; // this should never happen // convert the intersection points into reference-face coordinates, // and compute the contact position and depth for each point. only keep // those points that have a positive (penetrating) depth. delete points in // the 'ret' array as necessary so that 'point' and 'ret' correspond. dReal point[3*8]; // penetrating contact points dReal dep[8]; // depths for those points dReal det1 = dRecip(m11*m22 - m12*m21); m11 *= det1; m12 *= det1; m21 *= det1; m22 *= det1; int cnum = 0; // number of penetrating contact points found for (j=0; j < n; j++) { dReal k1 = m22*(ret[j*2]-c1) - m12*(ret[j*2+1]-c2); dReal k2 = -m21*(ret[j*2]-c1) + m11*(ret[j*2+1]-c2); for (i=0; i<3; i++) point[cnum*3+i] = center[i] + k1*Rb[i*4+a1] + k2*Rb[i*4+a2]; dep[cnum] = Sa[codeN] - dCalcVectorDot3(normal2,point+cnum*3); if (dep[cnum] >= 0) { ret[cnum*2] = ret[j*2]; ret[cnum*2+1] = ret[j*2+1]; cnum++; if ((cnum | CONTACTS_UNIMPORTANT) == (flags & (NUMC_MASK | CONTACTS_UNIMPORTANT))) { break; } } } if (cnum < 1) { return 0; // this should not happen, yet does at times (demo_plane2d single precision). } // we can't generate more contacts than we actually have int maxc = flags & NUMC_MASK; if (maxc > cnum) maxc = cnum; if (maxc < 1) maxc = 1; // Even though max count must not be zero this check is kept for backward compatibility as this is a public function if (cnum <= maxc) { // we have less contacts than we need, so we use them all for (j=0; j < cnum; j++) { dContactGeom *con = CONTACT(contact,skip*j); for (i=0; i<3; i++) con->pos[i] = point[j*3+i] + pa[i]; con->depth = dep[j]; } } else { dIASSERT(!(flags & CONTACTS_UNIMPORTANT)); // cnum should be generated not greater than maxc so that "then" clause is executed // we have more contacts than are wanted, some of them must be culled. // find the deepest point, it is always the first contact. int i1 = 0; dReal maxdepth = dep[0]; for (i=1; i<cnum; i++) { if (dep[i] > maxdepth) { maxdepth = dep[i]; i1 = i; } } int iret[8]; cullPoints (cnum,ret,maxc,i1,iret); for (j=0; j < maxc; j++) { dContactGeom *con = CONTACT(contact,skip*j); for (i=0; i<3; i++) con->pos[i] = point[iret[j]*3+i] + pa[i]; con->depth = dep[iret[j]]; } cnum = maxc; } *return_code = code; return cnum; }