NvidiaWarp-GarmentCode/warp/native/intersect_tri.h

/* Triangle/triangle intersection test routine,
 * by Tomas Moller, 1997.
 * See article "A Fast Triangle-Triangle Intersection Test",
 * Journal of Graphics Tools, 2(2), 1997
 *
 * Updated June 1999: removed the divisions -- a little faster now!
 * Updated October 1999: added {} to CROSS and SUB macros
 *
 * int NoDivTriTriIsect(float V0[3],float V1[3],float V2[3],
 *                      float U0[3],float U1[3],float U2[3])
 *
 * parameters: vertices of triangle 1: V0,V1,V2
 *             vertices of triangle 2: U0,U1,U2
 * result    : returns 1 if the triangles intersect, otherwise 0
 *
 */

 /*
 Copyright 2020 Tomas Akenine-Möller

 Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
 documentation files (the "Software"), to deal in the Software without restriction, including without limitation
 the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and
 to permit persons to whom the Software is furnished to do so, subject to the following conditions:

 The above copyright notice and this permission notice shall be included in all copies or substantial
 portions of the Software.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
 WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS
 OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT
 OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */

/* if USE_EPSILON_TEST is true then we do a check:
         if |dv|<EPSILON then dv=0.0;
   else no check is done (which is less robust)
*/
#define USE_EPSILON_TEST TRUE
#define EPSILON 0.000001


/* some macros */
#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];}

/* sort so that a<=b */
#define SORT(a,b)       \
             if(a>b)    \
             {          \
               float c; \
               c=a;     \
               a=b;     \
               b=c;     \
             }


/* this edge to edge test is based on Franlin Antonio's gem:
   "Faster Line Segment Intersection", in Graphics Gems III,
   pp. 199-202 */
#define EDGE_EDGE_TEST(V0,U0,U1)                      \
  Bx=U0[i0]-U1[i0];                                   \
  By=U0[i1]-U1[i1];                                   \
  Cx=V0[i0]-U0[i0];                                   \
  Cy=V0[i1]-U0[i1];                                   \
  f=Ay*Bx-Ax*By;                                      \
  d=By*Cx-Bx*Cy;                                      \
  if((f>0 && d>=0 && d<=f) || (f<0 && d<=0 && d>=f))  \
  {                                                   \
    e=Ax*Cy-Ay*Cx;                                    \
    if(f>0)                                           \
    {                                                 \
      if(e>=0 && e<=f) return 1;                      \
    }                                                 \
    else                                              \
    {                                                 \
      if(e<=0 && e>=f) return 1;                      \
    }                                                 \
  }

#define EDGE_AGAINST_TRI_EDGES(V0,V1,U0,U1,U2) \
{                                              \
  float Ax,Ay,Bx,By,Cx,Cy,e,d,f;               \
  Ax=V1[i0]-V0[i0];                            \
  Ay=V1[i1]-V0[i1];                            \
  /* test edge U0,U1 against V0,V1 */          \
  EDGE_EDGE_TEST(V0,U0,U1);                    \
  /* test edge U1,U2 against V0,V1 */          \
  EDGE_EDGE_TEST(V0,U1,U2);                    \
  /* test edge U2,U1 against V0,V1 */          \
  EDGE_EDGE_TEST(V0,U2,U0);                    \
}

#define POINT_IN_TRI(V0,U0,U1,U2)           \
{                                           \
  float a,b,c,d0,d1,d2;                     \
  /* is T1 completly inside T2? */          \
  /* check if V0 is inside tri(U0,U1,U2) */ \
  a=U1[i1]-U0[i1];                          \
  b=-(U1[i0]-U0[i0]);                       \
  c=-a*U0[i0]-b*U0[i1];                     \
  d0=a*V0[i0]+b*V0[i1]+c;                   \
                                            \
  a=U2[i1]-U1[i1];                          \
  b=-(U2[i0]-U1[i0]);                       \
  c=-a*U1[i0]-b*U1[i1];                     \
  d1=a*V0[i0]+b*V0[i1]+c;                   \
                                            \
  a=U0[i1]-U2[i1];                          \
  b=-(U0[i0]-U2[i0]);                       \
  c=-a*U2[i0]-b*U2[i1];                     \
  d2=a*V0[i0]+b*V0[i1]+c;                   \
  if(d0*d1>0.0)                             \
  {                                         \
    if(d0*d2>0.0) return 1;                 \
  }                                         \
}

CUDA_CALLABLE inline int coplanar_tri_tri(float N[3],float V0[3],float V1[3],float V2[3],
                     float U0[3],float U1[3],float U2[3])
{
   float A[3];
   short i0,i1;
   /* first project onto an axis-aligned plane, that maximizes the area */
   /* of the triangles, compute indices: i0,i1. */
   A[0]=fabsf(N[0]);
   A[1]=fabsf(N[1]);
   A[2]=fabsf(N[2]);
   if(A[0]>A[1])
   {
      if(A[0]>A[2])
      {
          i0=1;      /* A[0] is greatest */
          i1=2;
      }
      else
      {
          i0=0;      /* A[2] is greatest */
          i1=1;
      }
   }
   else   /* A[0]<=A[1] */
   {
      if(A[2]>A[1])
      {
          i0=0;      /* A[2] is greatest */
          i1=1;
      }
      else
      {
          i0=0;      /* A[1] is greatest */
          i1=2;
      }
    }

    /* test all edges of triangle 1 against the edges of triangle 2 */
    EDGE_AGAINST_TRI_EDGES(V0,V1,U0,U1,U2);
    EDGE_AGAINST_TRI_EDGES(V1,V2,U0,U1,U2);
    EDGE_AGAINST_TRI_EDGES(V2,V0,U0,U1,U2);

    /* finally, test if tri1 is totally contained in tri2 or vice versa */
    POINT_IN_TRI(V0,U0,U1,U2);
    POINT_IN_TRI(U0,V0,V1,V2);

    return 0;
}



#define NEWCOMPUTE_INTERVALS(VV0,VV1,VV2,D0,D1,D2,D0D1,D0D2,A,B,C,X0,X1) \
{ \
        if(D0D1>0.0f) \
        { \
                /* here we know that D0D2<=0.0 */ \
            /* that is D0, D1 are on the same side, D2 on the other or on the plane */ \
                A=VV2; B=(VV0-VV2)*D2; C=(VV1-VV2)*D2; X0=D2-D0; X1=D2-D1; \
        } \
        else if(D0D2>0.0f)\
        { \
                /* here we know that d0d1<=0.0 */ \
            A=VV1; B=(VV0-VV1)*D1; C=(VV2-VV1)*D1; X0=D1-D0; X1=D1-D2; \
        } \
        else if(D1*D2>0.0f || D0!=0.0f) \
        { \
                /* here we know that d0d1<=0.0 or that D0!=0.0 */ \
                A=VV0; B=(VV1-VV0)*D0; C=(VV2-VV0)*D0; X0=D0-D1; X1=D0-D2; \
        } \
        else if(D1!=0.0f) \
        { \
                A=VV1; B=(VV0-VV1)*D1; C=(VV2-VV1)*D1; X0=D1-D0; X1=D1-D2; \
        } \
        else if(D2!=0.0f) \
        { \
                A=VV2; B=(VV0-VV2)*D2; C=(VV1-VV2)*D2; X0=D2-D0; X1=D2-D1; \
        } \
        else \
        { \
                /* triangles are coplanar */ \
                return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2); \
        } \
}



CUDA_CALLABLE inline int NoDivTriTriIsect(float V0[3],float V1[3],float V2[3],
                     float U0[3],float U1[3],float U2[3])
{
  float E1[3],E2[3];
  float N1[3],N2[3],d1,d2;
  float du0,du1,du2,dv0,dv1,dv2;
  float D[3];
  float isect1[2], isect2[2];
  float du0du1,du0du2,dv0dv1,dv0dv2;
  short index;
  float vp0,vp1,vp2;
  float up0,up1,up2;
  float bb,cc,max;

  /* compute plane equation of triangle(V0,V1,V2) */
  SUB(E1,V1,V0);
  SUB(E2,V2,V0);
  CROSS(N1,E1,E2);
  d1=-DOT(N1,V0);
  /* plane equation 1: N1.X+d1=0 */

  /* put U0,U1,U2 into plane equation 1 to compute signed distances to the plane*/
  du0=DOT(N1,U0)+d1;
  du1=DOT(N1,U1)+d1;
  du2=DOT(N1,U2)+d1;

  /* coplanarity robustness check */
#if USE_EPSILON_TEST==TRUE
  if(fabsf(du0)<EPSILON) du0=0.0;
  if(fabsf(du1)<EPSILON) du1=0.0;
  if(fabsf(du2)<EPSILON) du2=0.0;
#endif
  du0du1=du0*du1;
  du0du2=du0*du2;

  if(du0du1>0.0f && du0du2>0.0f) /* same sign on all of them + not equal 0 ? */
    return 0;                    /* no intersection occurs */

  /* compute plane of triangle (U0,U1,U2) */
  SUB(E1,U1,U0);
  SUB(E2,U2,U0);
  CROSS(N2,E1,E2);
  d2=-DOT(N2,U0);
  /* plane equation 2: N2.X+d2=0 */

  /* put V0,V1,V2 into plane equation 2 */
  dv0=DOT(N2,V0)+d2;
  dv1=DOT(N2,V1)+d2;
  dv2=DOT(N2,V2)+d2;

#if USE_EPSILON_TEST==TRUE
  if(fabsf(dv0)<EPSILON) dv0=0.0;
  if(fabsf(dv1)<EPSILON) dv1=0.0;
  if(fabsf(dv2)<EPSILON) dv2=0.0;
#endif

  dv0dv1=dv0*dv1;
  dv0dv2=dv0*dv2;

  if(dv0dv1>0.0f && dv0dv2>0.0f) /* same sign on all of them + not equal 0 ? */
    return 0;                    /* no intersection occurs */

  /* compute direction of intersection line */
  CROSS(D,N1,N2);

  /* compute and index to the largest component of D */
  max=fabsf(D[0]);
  index=0;
  bb=fabsf(D[1]);
  cc=fabsf(D[2]);
  if(bb>max) max=bb,index=1;
  if(cc>max) max=cc,index=2;

  /* this is the simplified projection onto L*/
  vp0=V0[index];
  vp1=V1[index];
  vp2=V2[index];

  up0=U0[index];
  up1=U1[index];
  up2=U2[index];

  /* compute interval for triangle 1 */
  float a,b,c,x0,x1;
  NEWCOMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,a,b,c,x0,x1);

  /* compute interval for triangle 2 */
  float d,e,f,y0,y1;
  NEWCOMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,d,e,f,y0,y1);

  float xx,yy,xxyy,tmp;
  xx=x0*x1;
  yy=y0*y1;
  xxyy=xx*yy;

  tmp=a*xxyy;
  isect1[0]=tmp+b*x1*yy;
  isect1[1]=tmp+c*x0*yy;

  tmp=d*xxyy;
  isect2[0]=tmp+e*xx*y1;
  isect2[1]=tmp+f*xx*y0;

  SORT(isect1[0],isect1[1]);
  SORT(isect2[0],isect2[1]);

  if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return 0;
  return 1;
}