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Defines | Typedefs | Functions
btBoxBoxDetector.cpp File Reference
#include "btBoxBoxDetector.h"
#include "BulletCollision/CollisionShapes/btBoxShape.h"
#include <float.h>
#include <string.h>

Go to the source code of this file.

Defines

#define dDOTpq(a, b, p, q)   ((a)[0]*(b)[0] + (a)[p]*(b)[q] + (a)[2*(p)]*(b)[2*(q)])
#define dInfinity   FLT_MAX
#define dMULTIPLYOP1_331(A, op, B, C)
#define dMULTIPLYOP0_331(A, op, B, C)
#define dMULTIPLY1_331(A, B, C)   dMULTIPLYOP1_331(A,=,B,C)
#define dMULTIPLY0_331(A, B, C)   dMULTIPLYOP0_331(A,=,B,C)
#define dAtan2(y, x)   ((float)atan2f((y),(x))) /* arc tangent with 2 args */
#define M__PI   3.14159265f
#define TST(expr1, expr2, norm, cc)
#define TST(expr1, expr2, n1, n2, n3, cc)

Typedefs

typedef btScalar dMatrix3 [4 *3]

Functions

static btScalar dDOT (const btScalar *a, const btScalar *b)
static btScalar dDOT44 (const btScalar *a, const btScalar *b)
static btScalar dDOT41 (const btScalar *a, const btScalar *b)
static btScalar dDOT14 (const btScalar *a, const btScalar *b)
void dLineClosestApproach (const btVector3 &pa, const btVector3 &ua, const btVector3 &pb, const btVector3 &ub, btScalar *alpha, btScalar *beta)
static int intersectRectQuad2 (btScalar h[2], btScalar p[8], btScalar ret[16])
void cullPoints2 (int n, btScalar p[], int m, int i0, int 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)

Define Documentation

#define dAtan2 (   y,
 
)    ((float)atan2f((y),(x))) /* arc tangent with 2 args */

Definition at line 170 of file btBoxBoxDetector.cpp.

#define dDOTpq (   a,
  b,
  p,
 
)    ((a)[0]*(b)[0] + (a)[p]*(b)[q] + (a)[2*(p)]*(b)[2*(q)])

Definition at line 52 of file btBoxBoxDetector.cpp.

#define dInfinity   FLT_MAX

Definition at line 53 of file btBoxBoxDetector.cpp.

#define dMULTIPLY0_331 (   A,
  B,
 
)    dMULTIPLYOP0_331(A,=,B,C)

Definition at line 79 of file btBoxBoxDetector.cpp.

#define dMULTIPLY1_331 (   A,
  B,
 
)    dMULTIPLYOP1_331(A,=,B,C)

Definition at line 78 of file btBoxBoxDetector.cpp.

#define dMULTIPLYOP0_331 (   A,
  op,
  B,
 
)
Value:
do { \
  (A)[0] op dDOT((B),(C)); \
  (A)[1] op dDOT((B+4),(C)); \
  (A)[2] op dDOT((B+8),(C)); \
} while(0)

Definition at line 71 of file btBoxBoxDetector.cpp.

#define dMULTIPLYOP1_331 (   A,
  op,
  B,
 
)
Value:
do { \
  (A)[0] op dDOT41((B),(C)); \
  (A)[1] op dDOT41((B+1),(C)); \
  (A)[2] op dDOT41((B+2),(C)); \
} while(0)

Definition at line 65 of file btBoxBoxDetector.cpp.

#define M__PI   3.14159265f

Definition at line 171 of file btBoxBoxDetector.cpp.

#define TST (   expr1,
  expr2,
  norm,
  cc 
)
Value:
s2 = fabsf(expr1) - (expr2); \
  if (s2 > 0) return 0; \
  if (s2 > s) { \
    s = s2; \
    normalR = norm; \
    invert_normal = ((expr1) < 0); \
    code = (cc); \
  }
#define TST (   expr1,
  expr2,
  n1,
  n2,
  n3,
  cc 
)
Value:
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); \
    } \
  }

Typedef Documentation

typedef btScalar dMatrix3[4 *3]

Definition at line 81 of file btBoxBoxDetector.cpp.


Function Documentation

void cullPoints2 ( int  n,
btScalar  p[],
int  m,
int  i0,
int  iret[] 
)

Definition at line 181 of file btBoxBoxDetector.cpp.

{
  // 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<n; i++) A[i] = dAtan2(p[i*2+1]-cy,p[i*2]-cx);

  // search for points that have angles closest to A[i0] + i*(2*pi/m).
  int avail[8];
  for (i=0; i<n; i++) avail[i] = 1;
  avail[i0] = 0;
  iret[0] = i0;
  iret++;
  for (j=1; j<m; j++) {
    a = btScalar(j)*(2*M__PI/m) + A[i0];
    if (a > 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<n; i++) {
      if (avail[i]) {
       diff = fabsf (A[i]-a);
       if (diff > 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++;
  }
}

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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 
)

Definition at line 248 of file btBoxBoxDetector.cpp.

{
  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 = p2 - p1;
  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;

#ifdef USE_CENTER_POINT
           for (i=0; i<3; i++) 
                     pointInWorld[i] = (pa[i]+pb[i])*btScalar(0.5);
              output.addContactPoint(-normal,pointInWorld,-*depth);
#else
              output.addContactPoint(-normal,pb,-*depth);
#endif //
              *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<cnum; i++) {
      if (dep[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;
}

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static btScalar dDOT ( const btScalar a,
const btScalar b 
) [static]

Definition at line 61 of file btBoxBoxDetector.cpp.

{ return dDOTpq(a,b,1,1); }

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static btScalar dDOT14 ( const btScalar a,
const btScalar b 
) [static]

Definition at line 64 of file btBoxBoxDetector.cpp.

{ return dDOTpq(a,b,1,4); }

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static btScalar dDOT41 ( const btScalar a,
const btScalar b 
) [static]

Definition at line 63 of file btBoxBoxDetector.cpp.

{ return dDOTpq(a,b,4,1); }

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static btScalar dDOT44 ( const btScalar a,
const btScalar b 
) [static]

Definition at line 62 of file btBoxBoxDetector.cpp.

{ return dDOTpq(a,b,4,4); }

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void dLineClosestApproach ( const btVector3 pa,
const btVector3 ua,
const btVector3 pb,
const btVector3 ub,
btScalar alpha,
btScalar beta 
)

Definition at line 83 of file btBoxBoxDetector.cpp.

{
  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;
  }
}

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static int intersectRectQuad2 ( btScalar  h[2],
btScalar  p[8],
btScalar  ret[16] 
) [static]

Definition at line 117 of file btBoxBoxDetector.cpp.

{
  // 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;
}

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