/************************************************************************* * * * 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 General 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 * * General 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. * * * *************************************************************************/ /* some useful collision utility stuff. this includes some API utility functions that are defined in the public header files. */ #include #include #include #include "collision_util.h" //**************************************************************************** int dCollideSpheres (dVector3 p1, dReal r1, dVector3 p2, dReal r2, dContactGeom *c) { // printf ("d=%.2f (%.2f %.2f %.2f) (%.2f %.2f %.2f) r1=%.2f r2=%.2f\n", // d,p1[0],p1[1],p1[2],p2[0],p2[1],p2[2],r1,r2); dReal d = dDISTANCE (p1,p2); if (d > (r1 + r2)) return 0; if (d <= 0) { c->pos[0] = p1[0]; c->pos[1] = p1[1]; c->pos[2] = p1[2]; c->normal[0] = 1; c->normal[1] = 0; c->normal[2] = 0; c->depth = r1 + r2; } else { dReal d1 = dRecip (d); c->normal[0] = (p1[0]-p2[0])*d1; c->normal[1] = (p1[1]-p2[1])*d1; c->normal[2] = (p1[2]-p2[2])*d1; dReal k = REAL(0.5) * (r2 - r1 - d); c->pos[0] = p1[0] + c->normal[0]*k; c->pos[1] = p1[1] + c->normal[1]*k; c->pos[2] = p1[2] + c->normal[2]*k; c->depth = r1 + r2 - d; } return 1; } void dLineClosestApproach (const dVector3 pa, const dVector3 ua, const dVector3 pb, const dVector3 ub, dReal *alpha, dReal *beta) { dVector3 p; p[0] = pb[0] - pa[0]; p[1] = pb[1] - pa[1]; p[2] = pb[2] - pa[2]; dReal uaub = dDOT(ua,ub); dReal q1 = dDOT(ua,p); dReal q2 = -dDOT(ub,p); dReal d = 1-uaub*uaub; if (d <= REAL(0.0001)) { // @@@ this needs to be made more robust *alpha = 0; *beta = 0; } else { d = dRecip(d); *alpha = (q1 + uaub*q2)*d; *beta = (uaub*q1 + q2)*d; } } // given two line segments A and B with endpoints a1-a2 and b1-b2, return the // points on A and B that are closest to each other (in cp1 and cp2). // in the case of parallel lines where there are multiple solutions, a // solution involving the endpoint of at least one line will be returned. // this will work correctly for zero length lines, e.g. if a1==a2 and/or // b1==b2. // // the algorithm works by applying the voronoi clipping rule to the features // of the line segments. the three features of each line segment are the two // endpoints and the line between them. the voronoi clipping rule states that, // for feature X on line A and feature Y on line B, the closest points PA and // PB between X and Y are globally the closest points if PA is in V(Y) and // PB is in V(X), where V(X) is the voronoi region of X. void dClosestLineSegmentPoints (const dVector3 a1, const dVector3 a2, const dVector3 b1, const dVector3 b2, dVector3 cp1, dVector3 cp2) { dVector3 a1a2,b1b2,a1b1,a1b2,a2b1,a2b2,n; dReal la,lb,k,da1,da2,da3,da4,db1,db2,db3,db4,det; #define SET2(a,b) a[0]=b[0]; a[1]=b[1]; a[2]=b[2]; #define SET3(a,b,op,c) a[0]=b[0] op c[0]; a[1]=b[1] op c[1]; a[2]=b[2] op c[2]; // check vertex-vertex features SET3 (a1a2,a2,-,a1); SET3 (b1b2,b2,-,b1); SET3 (a1b1,b1,-,a1); da1 = dDOT(a1a2,a1b1); db1 = dDOT(b1b2,a1b1); if (da1 <= 0 && db1 >= 0) { SET2 (cp1,a1); SET2 (cp2,b1); return; } SET3 (a1b2,b2,-,a1); da2 = dDOT(a1a2,a1b2); db2 = dDOT(b1b2,a1b2); if (da2 <= 0 && db2 <= 0) { SET2 (cp1,a1); SET2 (cp2,b2); return; } SET3 (a2b1,b1,-,a2); da3 = dDOT(a1a2,a2b1); db3 = dDOT(b1b2,a2b1); if (da3 >= 0 && db3 >= 0) { SET2 (cp1,a2); SET2 (cp2,b1); return; } SET3 (a2b2,b2,-,a2); da4 = dDOT(a1a2,a2b2); db4 = dDOT(b1b2,a2b2); if (da4 >= 0 && db4 <= 0) { SET2 (cp1,a2); SET2 (cp2,b2); return; } // check edge-vertex features. // if one or both of the lines has zero length, we will never get to here, // so we do not have to worry about the following divisions by zero. la = dDOT(a1a2,a1a2); if (da1 >= 0 && da3 <= 0) { k = da1 / la; SET3 (n,a1b1,-,k*a1a2); if (dDOT(b1b2,n) >= 0) { SET3 (cp1,a1,+,k*a1a2); SET2 (cp2,b1); return; } } if (da2 >= 0 && da4 <= 0) { k = da2 / la; SET3 (n,a1b2,-,k*a1a2); if (dDOT(b1b2,n) <= 0) { SET3 (cp1,a1,+,k*a1a2); SET2 (cp2,b2); return; } } lb = dDOT(b1b2,b1b2); if (db1 <= 0 && db2 >= 0) { k = -db1 / lb; SET3 (n,-a1b1,-,k*b1b2); if (dDOT(a1a2,n) >= 0) { SET2 (cp1,a1); SET3 (cp2,b1,+,k*b1b2); return; } } if (db3 <= 0 && db4 >= 0) { k = -db3 / lb; SET3 (n,-a2b1,-,k*b1b2); if (dDOT(a1a2,n) <= 0) { SET2 (cp1,a2); SET3 (cp2,b1,+,k*b1b2); return; } } // it must be edge-edge k = dDOT(a1a2,b1b2); det = la*lb - k*k; if (det <= 0) { // this should never happen, but just in case... SET2(cp1,a1); SET2(cp2,b1); return; } det = dRecip (det); dReal alpha = (lb*da1 - k*db1) * det; dReal beta = ( k*da1 - la*db1) * det; SET3 (cp1,a1,+,alpha*a1a2); SET3 (cp2,b1,+,beta*b1b2); # undef SET2 # undef SET3 } // a simple root finding algorithm is used to find the value of 't' that // satisfies: // d|D(t)|^2/dt = 0 // where: // |D(t)| = |p(t)-b(t)| // where p(t) is a point on the line parameterized by t: // p(t) = p1 + t*(p2-p1) // and b(t) is that same point clipped to the boundary of the box. in box- // relative coordinates d|D(t)|^2/dt is the sum of three x,y,z components // each of which looks like this: // // t_lo / // ______/ -->t // / t_hi // / // // t_lo and t_hi are the t values where the line passes through the planes // corresponding to the sides of the box. the algorithm computes d|D(t)|^2/dt // in a piecewise fashion from t=0 to t=1, stopping at the point where // d|D(t)|^2/dt crosses from negative to positive. void dClosestLineBoxPoints (const dVector3 p1, const dVector3 p2, const dVector3 c, const dMatrix3 R, const dVector3 side, dVector3 lret, dVector3 bret) { int i; // compute the start and delta of the line p1-p2 relative to the box. // we will do all subsequent computations in this box-relative coordinate // system. we have to do a translation and rotation for each point. dVector3 tmp,s,v; tmp[0] = p1[0] - c[0]; tmp[1] = p1[1] - c[1]; tmp[2] = p1[2] - c[2]; dMULTIPLY1_331 (s,R,tmp); tmp[0] = p2[0] - p1[0]; tmp[1] = p2[1] - p1[1]; tmp[2] = p2[2] - p1[2]; dMULTIPLY1_331 (v,R,tmp); // mirror the line so that v has all components >= 0 dVector3 sign; for (i=0; i<3; i++) { if (v[i] < 0) { s[i] = -s[i]; v[i] = -v[i]; sign[i] = -1; } else sign[i] = 1; } // compute v^2 dVector3 v2; v2[0] = v[0]*v[0]; v2[1] = v[1]*v[1]; v2[2] = v[2]*v[2]; // compute the half-sides of the box dReal h[3]; h[0] = REAL(0.5) * side[0]; h[1] = REAL(0.5) * side[1]; h[2] = REAL(0.5) * side[2]; // region is -1,0,+1 depending on which side of the box planes each // coordinate is on. tanchor is the next t value at which there is a // transition, or the last one if there are no more. int region[3]; dReal tanchor[3]; // Denormals are a problem, because we divide by v[i], and then // multiply that by 0. Alas, infinity times 0 is infinity (!) // We also use v2[i], which is v[i] squared. Here's how the epsilons // are chosen: // float epsilon = 1.175494e-038 (smallest non-denormal number) // double epsilon = 2.225074e-308 (smallest non-denormal number) // For single precision, choose an epsilon such that v[i] squared is // not a denormal; this is for performance. // For double precision, choose an epsilon such that v[i] is not a // denormal; this is for correctness. (Jon Watte on mailinglist) #if defined( dSINGLE ) const dReal tanchor_eps = 1e-19; #else const dReal tanchor_eps = 1e-307; #endif // find the region and tanchor values for p1 for (i=0; i<3; i++) { if (v[i] > tanchor_eps) { if (s[i] < -h[i]) { region[i] = -1; tanchor[i] = (-h[i]-s[i])/v[i]; } else { region[i] = (s[i] > h[i]); tanchor[i] = (h[i]-s[i])/v[i]; } } else { region[i] = 0; tanchor[i] = 2; // this will never be a valid tanchor } } // compute d|d|^2/dt for t=0. if it's >= 0 then p1 is the closest point dReal t=0; dReal dd2dt = 0; for (i=0; i<3; i++) dd2dt -= (region[i] ? v2[i] : 0) * tanchor[i]; if (dd2dt >= 0) goto got_answer; do { // find the point on the line that is at the next clip plane boundary dReal next_t = 1; for (i=0; i<3; i++) { if (tanchor[i] > t && tanchor[i] < 1 && tanchor[i] < next_t) next_t = tanchor[i]; } // compute d|d|^2/dt for the next t dReal next_dd2dt = 0; for (i=0; i<3; i++) { next_dd2dt += (region[i] ? v2[i] : 0) * (next_t - tanchor[i]); } // if the sign of d|d|^2/dt has changed, solution = the crossover point if (next_dd2dt >= 0) { dReal m = (next_dd2dt-dd2dt)/(next_t - t); t -= dd2dt/m; goto got_answer; } // advance to the next anchor point / region for (i=0; i<3; i++) { if (tanchor[i] == next_t) { tanchor[i] = (h[i]-s[i])/v[i]; region[i]++; } } t = next_t; dd2dt = next_dd2dt; } while (t < 1); t = 1; got_answer: // compute closest point on the line for (i=0; i<3; i++) lret[i] = p1[i] + t*tmp[i]; // note: tmp=p2-p1 // compute closest point on the box for (i=0; i<3; i++) { tmp[i] = sign[i] * (s[i] + t*v[i]); if (tmp[i] < -h[i]) tmp[i] = -h[i]; else if (tmp[i] > h[i]) tmp[i] = h[i]; } dMULTIPLY0_331 (s,R,tmp); for (i=0; i<3; i++) bret[i] = s[i] + c[i]; } // given boxes (p1,R1,side1) and (p1,R1,side1), return 1 if they intersect // or 0 if not. int dBoxTouchesBox (const dVector3 p1, const dMatrix3 R1, const dVector3 side1, const dVector3 p2, const dMatrix3 R2, const dVector3 side2) { // two boxes are disjoint if (and only if) there is a separating axis // perpendicular to a face from one box or perpendicular to an edge from // either box. the following tests are derived from: // "OBB Tree: A Hierarchical Structure for Rapid Interference Detection", // S.Gottschalk, M.C.Lin, D.Manocha., Proc of ACM Siggraph 1996. // Rij is R1'*R2, i.e. the relative rotation between R1 and R2. // Qij is abs(Rij) dVector3 p,pp; dReal A1,A2,A3,B1,B2,B3,R11,R12,R13,R21,R22,R23,R31,R32,R33, Q11,Q12,Q13,Q21,Q22,Q23,Q31,Q32,Q33; // 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 A1 = side1[0]*REAL(0.5); A2 = side1[1]*REAL(0.5); A3 = side1[2]*REAL(0.5); B1 = side2[0]*REAL(0.5); B2 = side2[1]*REAL(0.5); B3 = side2[2]*REAL(0.5); // for the following tests, excluding computation of Rij, in the worst case, // 15 compares, 60 adds, 81 multiplies, and 24 absolutes. // notation: R1=[u1 u2 u3], R2=[v1 v2 v3] // separating axis = u1,u2,u3 R11 = dDOT44(R1+0,R2+0); R12 = dDOT44(R1+0,R2+1); R13 = dDOT44(R1+0,R2+2); Q11 = dFabs(R11); Q12 = dFabs(R12); Q13 = dFabs(R13); if (dFabs(pp[0]) > (A1 + B1*Q11 + B2*Q12 + B3*Q13)) return 0; R21 = dDOT44(R1+1,R2+0); R22 = dDOT44(R1+1,R2+1); R23 = dDOT44(R1+1,R2+2); Q21 = dFabs(R21); Q22 = dFabs(R22); Q23 = dFabs(R23); if (dFabs(pp[1]) > (A2 + B1*Q21 + B2*Q22 + B3*Q23)) return 0; R31 = dDOT44(R1+2,R2+0); R32 = dDOT44(R1+2,R2+1); R33 = dDOT44(R1+2,R2+2); Q31 = dFabs(R31); Q32 = dFabs(R32); Q33 = dFabs(R33); if (dFabs(pp[2]) > (A3 + B1*Q31 + B2*Q32 + B3*Q33)) return 0; // separating axis = v1,v2,v3 if (dFabs(dDOT41(R2+0,p)) > (A1*Q11 + A2*Q21 + A3*Q31 + B1)) return 0; if (dFabs(dDOT41(R2+1,p)) > (A1*Q12 + A2*Q22 + A3*Q32 + B2)) return 0; if (dFabs(dDOT41(R2+2,p)) > (A1*Q13 + A2*Q23 + A3*Q33 + B3)) return 0; // separating axis = u1 x (v1,v2,v3) if (dFabs(pp[2]*R21-pp[1]*R31) > A2*Q31 + A3*Q21 + B2*Q13 + B3*Q12) return 0; if (dFabs(pp[2]*R22-pp[1]*R32) > A2*Q32 + A3*Q22 + B1*Q13 + B3*Q11) return 0; if (dFabs(pp[2]*R23-pp[1]*R33) > A2*Q33 + A3*Q23 + B1*Q12 + B2*Q11) return 0; // separating axis = u2 x (v1,v2,v3) if (dFabs(pp[0]*R31-pp[2]*R11) > A1*Q31 + A3*Q11 + B2*Q23 + B3*Q22) return 0; if (dFabs(pp[0]*R32-pp[2]*R12) > A1*Q32 + A3*Q12 + B1*Q23 + B3*Q21) return 0; if (dFabs(pp[0]*R33-pp[2]*R13) > A1*Q33 + A3*Q13 + B1*Q22 + B2*Q21) return 0; // separating axis = u3 x (v1,v2,v3) if (dFabs(pp[1]*R11-pp[0]*R21) > A1*Q21 + A2*Q11 + B2*Q33 + B3*Q32) return 0; if (dFabs(pp[1]*R12-pp[0]*R22) > A1*Q22 + A2*Q12 + B1*Q33 + B3*Q31) return 0; if (dFabs(pp[1]*R13-pp[0]*R23) > A1*Q23 + A2*Q13 + B1*Q32 + B2*Q31) return 0; return 1; } //**************************************************************************** // other utility functions void dInfiniteAABB (dxGeom *geom, dReal aabb[6]) { aabb[0] = -dInfinity; aabb[1] = dInfinity; aabb[2] = -dInfinity; aabb[3] = dInfinity; aabb[4] = -dInfinity; aabb[5] = dInfinity; } //**************************************************************************** // Helpers for Croteam's collider - by Nguyen Binh int dClipEdgeToPlane( dVector3 &vEpnt0, dVector3 &vEpnt1, const dVector4& plPlane) { // calculate distance of edge points to plane dReal fDistance0 = dPointPlaneDistance( vEpnt0 ,plPlane ); dReal fDistance1 = dPointPlaneDistance( vEpnt1 ,plPlane ); // if both points are behind the plane if ( fDistance0 < 0 && fDistance1 < 0 ) { // do nothing return 0; // if both points in front of the plane } else if ( fDistance0 > 0 && fDistance1 > 0 ) { // accept them return 1; // if we have edge/plane intersection } else if ((fDistance0 > 0 && fDistance1 < 0) || ( fDistance0 < 0 && fDistance1 > 0)) { // find intersection point of edge and plane dVector3 vIntersectionPoint; vIntersectionPoint[0]= vEpnt0[0]-(vEpnt0[0]-vEpnt1[0])*fDistance0/(fDistance0-fDistance1); vIntersectionPoint[1]= vEpnt0[1]-(vEpnt0[1]-vEpnt1[1])*fDistance0/(fDistance0-fDistance1); vIntersectionPoint[2]= vEpnt0[2]-(vEpnt0[2]-vEpnt1[2])*fDistance0/(fDistance0-fDistance1); // clamp correct edge to intersection point if ( fDistance0 < 0 ) { dVector3Copy(vIntersectionPoint,vEpnt0); } else { dVector3Copy(vIntersectionPoint,vEpnt1); } return 1; } return 1; } // clip polygon with plane and generate new polygon points void dClipPolyToPlane( const dVector3 avArrayIn[], const int ctIn, dVector3 avArrayOut[], int &ctOut, const dVector4 &plPlane ) { // start with no output points ctOut = 0; int i0 = ctIn-1; // for each edge in input polygon for (int i1=0; i1= 0 ) { // emit point avArrayOut[ctOut][0] = avArrayIn[i0][0]; avArrayOut[ctOut][1] = avArrayIn[i0][1]; avArrayOut[ctOut][2] = avArrayIn[i0][2]; ctOut++; } // if points are on different sides if( (fDistance0 > 0 && fDistance1 < 0) || ( fDistance0 < 0 && fDistance1 > 0) ) { // find intersection point of edge and plane dVector3 vIntersectionPoint; vIntersectionPoint[0]= avArrayIn[i0][0] - (avArrayIn[i0][0]-avArrayIn[i1][0])*fDistance0/(fDistance0-fDistance1); vIntersectionPoint[1]= avArrayIn[i0][1] - (avArrayIn[i0][1]-avArrayIn[i1][1])*fDistance0/(fDistance0-fDistance1); vIntersectionPoint[2]= avArrayIn[i0][2] - (avArrayIn[i0][2]-avArrayIn[i1][2])*fDistance0/(fDistance0-fDistance1); // emit intersection point avArrayOut[ctOut][0] = vIntersectionPoint[0]; avArrayOut[ctOut][1] = vIntersectionPoint[1]; avArrayOut[ctOut][2] = vIntersectionPoint[2]; ctOut++; } } } void dClipPolyToCircle(const dVector3 avArrayIn[], const int ctIn, dVector3 avArrayOut[], int &ctOut, const dVector4 &plPlane ,dReal fRadius) { // start with no output points ctOut = 0; int i0 = ctIn-1; // for each edge in input polygon for (int i1=0; i1= 0 ) { // emit point if (dVector3Length2(avArrayIn[i0]) <= fRadius*fRadius) { avArrayOut[ctOut][0] = avArrayIn[i0][0]; avArrayOut[ctOut][1] = avArrayIn[i0][1]; avArrayOut[ctOut][2] = avArrayIn[i0][2]; ctOut++; } } // if points are on different sides if( (fDistance0 > 0 && fDistance1 < 0) || ( fDistance0 < 0 && fDistance1 > 0) ) { // find intersection point of edge and plane dVector3 vIntersectionPoint; vIntersectionPoint[0]= avArrayIn[i0][0] - (avArrayIn[i0][0]-avArrayIn[i1][0])*fDistance0/(fDistance0-fDistance1); vIntersectionPoint[1]= avArrayIn[i0][1] - (avArrayIn[i0][1]-avArrayIn[i1][1])*fDistance0/(fDistance0-fDistance1); vIntersectionPoint[2]= avArrayIn[i0][2] - (avArrayIn[i0][2]-avArrayIn[i1][2])*fDistance0/(fDistance0-fDistance1); // emit intersection point if (dVector3Length2(avArrayIn[i0]) <= fRadius*fRadius) { avArrayOut[ctOut][0] = vIntersectionPoint[0]; avArrayOut[ctOut][1] = vIntersectionPoint[1]; avArrayOut[ctOut][2] = vIntersectionPoint[2]; ctOut++; } } } }