/************************************************************************* * * * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. * * All rights reserved. Email: russ@q12.org Web: www.q12.org * * * * This library is free software; you can redistribute it and/or * * modify it under the terms of EITHER: * * (1) The GNU Lesser bteral Public License as published by the Free * * Software Foundation; either version 2.1 of the License, or (at * * your option) any later version. The text of the GNU Lesser * * bteral Public License is included with this library in the * * file LICENSE.TXT. * * (2) The BSD-style license that is included with this library in * * the file LICENSE-BSD.TXT. * * * * This library is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files * * LICENSE.TXT and LICENSE-BSD.TXT for more details. * * * *************************************************************************/ #include "BoxBoxDetector.h" #include "BulletCollision/CollisionShapes/btBoxShape.h" #include BoxBoxDetector::BoxBoxDetector(btBoxShape* box1,btBoxShape* box2) : m_box1(box1), m_box2(box2) { } // 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. struct dContactGeom; #define dDOTpq(a,b,p,q) ((a)[0]*(b)[0] + (a)[p]*(b)[q] + (a)[2*(p)]*(b)[2*(q)]) #define dInfinity FLT_MAX /*PURE_INLINE btScalar dDOT (const btScalar *a, const btScalar *b) { return dDOTpq(a,b,1,1); } PURE_INLINE btScalar dDOT13 (const btScalar *a, const btScalar *b) { return dDOTpq(a,b,1,3); } PURE_INLINE btScalar dDOT31 (const btScalar *a, const btScalar *b) { return dDOTpq(a,b,3,1); } PURE_INLINE btScalar dDOT33 (const btScalar *a, const btScalar *b) { return dDOTpq(a,b,3,3); } */ static btScalar dDOT (const btScalar *a, const btScalar *b) { return dDOTpq(a,b,1,1); } static btScalar dDOT44 (const btScalar *a, const btScalar *b) { return dDOTpq(a,b,4,4); } static btScalar dDOT41 (const btScalar *a, const btScalar *b) { return dDOTpq(a,b,4,1); } static btScalar dDOT14 (const btScalar *a, const btScalar *b) { return dDOTpq(a,b,1,4); } #define dMULTIPLYOP1_331(A,op,B,C) \ do { \ (A)[0] op dDOT41((B),(C)); \ (A)[1] op dDOT41((B+1),(C)); \ (A)[2] op dDOT41((B+2),(C)); \ } while(0) #define dMULTIPLYOP0_331(A,op,B,C) \ do { \ (A)[0] op dDOT((B),(C)); \ (A)[1] op dDOT((B+4),(C)); \ (A)[2] op dDOT((B+8),(C)); \ } while(0) #define dMULTIPLY1_331(A,B,C) dMULTIPLYOP1_331(A,=,B,C) #define dMULTIPLY0_331(A,B,C) dMULTIPLYOP0_331(A,=,B,C) typedef btScalar dMatrix3[4*3]; void dLineClosestApproach (const btVector3 pa, const btVector3 ua, const btVector3 pb, const btVector3 ub, btScalar *alpha, btScalar *beta) { btVector3 p; p[0] = pb[0] - pa[0]; p[1] = pb[1] - pa[1]; p[2] = pb[2] - pa[2]; btScalar uaub = dDOT(ua,ub); btScalar q1 = dDOT(ua,p); btScalar q2 = -dDOT(ub,p); btScalar d = 1-uaub*uaub; if (d <= btScalar(0.0001f)) { // @@@ this needs to be made more robust *alpha = 0; *beta = 0; } else { d = 1.f/d; *alpha = (q1 + uaub*q2)*d; *beta = (uaub*q1 + q2)*d; } } // find all the intersection points between the 2D rectangle with vertices // at (+/-h[0],+/-h[1]) and the 2D quadrilateral with vertices (p[0],p[1]), // (p[2],p[3]),(p[4],p[5]),(p[6],p[7]). // // the intersection points are returned as x,y pairs in the 'ret' array. // the number of intersection points is returned by the function (this will // be in the range 0 to 8). static int intersectRectQuad2 (btScalar h[2], btScalar p[8], btScalar ret[16]) { // q (and r) contain nq (and nr) coordinate points for the current (and // chopped) polygons int nq=4,nr; btScalar buffer[16]; btScalar *q = p; btScalar *r = ret; for (int dir=0; dir <= 1; dir++) { // direction notation: xy[0] = x axis, xy[1] = y axis for (int sign=-1; sign <= 1; sign += 2) { // chop q along the line xy[dir] = sign*h[dir] btScalar *pq = q; btScalar *pr = r; nr = 0; for (int i=nq; i > 0; i--) { // go through all points in q and all lines between adjacent points if (sign*pq[dir] < h[dir]) { // this point is inside the chopping line pr[0] = pq[0]; pr[1] = pq[1]; pr += 2; nr++; if (nr & 8) { q = r; goto done; } } btScalar *nextq = (i > 1) ? pq+2 : q; if ((sign*pq[dir] < h[dir]) ^ (sign*nextq[dir] < h[dir])) { // this line crosses the chopping line pr[1-dir] = pq[1-dir] + (nextq[1-dir]-pq[1-dir]) / (nextq[dir]-pq[dir]) * (sign*h[dir]-pq[dir]); pr[dir] = sign*h[dir]; pr += 2; nr++; if (nr & 8) { q = r; goto done; } } pq += 2; } q = r; r = (q==ret) ? buffer : ret; nq = nr; } } done: if (q != ret) memcpy (ret,q,nr*2*sizeof(btScalar)); return nr; } #define dAtan2(y,x) ((float)atan2f((y),(x))) /* arc tangent with 2 args */ #define M__PI 3.14159265f // given n points in the plane (array p, of size 2*n), generate m points that // best represent the whole set. the definition of 'best' here is not // predetermined - the idea is to select points that give good box-box // collision detection behavior. the chosen point indexes are returned in the // array iret (of size m). 'i0' is always the first entry in the array. // n must be in the range [1..8]. m must be in the range [1..n]. i0 must be // in the range [0..n-1]. void cullPoints2 (int n, btScalar p[], int m, int i0, int iret[]) { // compute the centroid of the polygon in cx,cy int i,j; btScalar a,cx,cy,q; if (n==1) { cx = p[0]; cy = p[1]; } else if (n==2) { cx = btScalar(0.5)*(p[0] + p[2]); cy = btScalar(0.5)*(p[1] + p[3]); } else { a = 0; cx = 0; cy = 0; for (i=0; i<(n-1); i++) { q = p[i*2]*p[i*2+3] - p[i*2+2]*p[i*2+1]; a += q; cx += q*(p[i*2]+p[i*2+2]); cy += q*(p[i*2+1]+p[i*2+3]); } q = p[n*2-2]*p[1] - p[0]*p[n*2-1]; a = 1.f/(btScalar(3.0)*(a+q)); cx = a*(cx + q*(p[n*2-2]+p[0])); cy = a*(cy + q*(p[n*2-1]+p[1])); } // compute the angle of each point w.r.t. the centroid btScalar A[8]; for (i=0; i M__PI) a -= 2*M__PI; btScalar maxdiff=1e9,diff; #ifndef dNODEBUG *iret = i0; // iret is not allowed to keep this value #endif for (i=0; i M__PI) diff = 2*M__PI - diff; if (diff < maxdiff) { maxdiff = diff; *iret = i; } } } #ifndef dNODEBUG btAssert (*iret != i0); // ensure iret got set #endif avail[*iret] = 0; iret++; } } int dBoxBox2 (const btVector3 p1, const dMatrix3 R1, const btVector3 side1, const btVector3 p2, const dMatrix3 R2, const btVector3 side2, btVector3& normal, btScalar *depth, int *return_code, int maxc, dContactGeom *contact, int skip,btDiscreteCollisionDetectorInterface::Result& output) { const btScalar fudge_factor = btScalar(1.05); btVector3 p,pp,normalC; const btScalar *normalR = 0; btScalar 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]*btScalar(0.5); A[1] = side1[1]*btScalar(0.5); A[2] = side1[2]*btScalar(0.5); B[0] = side2[0]*btScalar(0.5); B[1] = side2[1]*btScalar(0.5); B[2] = side2[2]*btScalar(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 = fabsf(R11); Q12 = fabsf(R12); Q13 = fabsf(R13); Q21 = fabsf(R21); Q22 = fabsf(R22); Q23 = fabsf(R23); Q31 = fabsf(R31); Q32 = fabsf(R32); Q33 = fabsf(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 = fabsf(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] + 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 (dDOT41(R2+0,p),(A[0]*Q11 + A[1]*Q21 + A[2]*Q31 + B[0]),R2+0,4); TST (dDOT41(R2+1,p),(A[0]*Q12 + A[1]*Q22 + A[2]*Q32 + B[1]),R2+1,5); TST (dDOT41(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 = fabsf(expr1) - (expr2); \ if (s2 > 0) return 0; \ l = sqrtf((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 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 btVector3 pa; btScalar sign; for (i=0; i<3; i++) pa[i] = p1[i]; for (j=0; j<3; j++) { sign = (dDOT14(normal,R1+j) > 0) ? btScalar(1.0) : btScalar(-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 btVector3 pb; for (i=0; i<3; i++) pb[i] = p2[i]; for (j=0; j<3; j++) { sign = (dDOT14(normal,R2+j) > 0) ? btScalar(-1.0) : btScalar(1.0); for (i=0; i<3; i++) pb[i] += sign * B[j] * R2[i*4+j]; } btScalar alpha,beta; btVector3 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; { //contact[0].pos[i] = btScalar(0.5)*(pa[i]+pb[i]); //contact[0].depth = *depth; btVector3 pointInWorld; for (i=0; i<3; i++) pointInWorld[i] = (pa[i]+pb[i])*btScalar(0.5); output.addContactPoint(-normal,pointInWorld,-*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 btScalar *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. btVector3 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] = fabsf (nr[0]); anr[1] = fabsf (nr[1]); anr[2] = fabsf (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 btVector3 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 btScalar quad[8]; // 2D coordinate of incident face (x,y pairs) btScalar 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); { btScalar k1 = m11*Sb[a1]; btScalar k2 = m21*Sb[a1]; btScalar k3 = m12*Sb[a2]; btScalar 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 btScalar rect[2]; rect[0] = Sa[code1]; rect[1] = Sa[code2]; // intersect the incident and reference faces btScalar ret[16]; int n = intersectRectQuad2 (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. btScalar point[3*8]; // penetrating contact points btScalar dep[8]; // depths for those points btScalar det1 = 1.f/(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++) { btScalar k1 = m22*(ret[j*2]-c1) - m12*(ret[j*2+1]-c2); btScalar 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] - 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++) { //AddContactPoint... //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]; btVector3 pointInWorld; for (i=0; i<3; i++) pointInWorld[i] = point[j*3+i] + pa[i]; output.addContactPoint(-normal,pointInWorld,-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; btScalar maxdepth = dep[0]; for (i=1; i maxdepth) { maxdepth = dep[i]; i1 = i; } } int iret[8]; cullPoints2 (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]]; btVector3 posInWorld; for (i=0; i<3; i++) posInWorld[i] = point[iret[j]*3+i] + pa[i]; output.addContactPoint(-normal,posInWorld,-dep[iret[j]]); } cnum = maxc; } *return_code = code; return cnum; } void BoxBoxDetector::getClosestPoints(const ClosestPointInput& input,Result& output,class btIDebugDraw* debugDraw) { const btTransform& transformA = input.m_transformA; const btTransform& transformB = input.m_transformB; int skip = 0; dContactGeom *contact = 0; dMatrix3 R1; dMatrix3 R2; for (int i=0;i<3;i++) { for (int j=0;j<3;j++) { R1[i+4*j] = transformA.getBasis()[j][i]; R2[i+4*j] = transformB.getBasis()[j][i]; } } btVector3 normal; btScalar depth; int return_code; int maxc = 10; dBoxBox2 (transformA.getOrigin(), R1, 2.f*m_box1->getHalfExtents(), transformB.getOrigin(), R2, 2.f*m_box2->getHalfExtents(), normal, &depth, &return_code, maxc, contact, skip, output ); }