jedi-academy/code/qcommon/tri_coll_test.cpp

/* Triangle/triangle intersection test routine,
 * by Tomas Moller, 1997.
 * See article "A Fast Triangle-Triangle Intersection Test",
 * Journal of Graphics Tools, 2(2), 1997
 *
 * int tri_tri_intersect(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
 *
 */

// leave this at the top for PCH reasons...
#include "../game/common_headers.h"




#include <math.h>
#include "../game/q_shared.h"
#include "../game/g_local.h"

/* 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 1
#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;     \
             }

#define ISECT(VV0,VV1,VV2,D0,D1,D2,isect0,isect1) \
              isect0=VV0+(VV1-VV0)*D0/(D0-D1);    \
              isect1=VV0+(VV2-VV0)*D0/(D0-D2);


#define COMPUTE_INTERVALS(VV0,VV1,VV2,D0,D1,D2,D0D1,D0D2,isect0,isect1) \
  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 */ \
    ISECT(VV2,VV0,VV1,D2,D0,D1,isect0,isect1);          \
  }                                                     \
  else if(D0D2>0.0f)                                    \
  {                                                     \
    /* here we know that d0d1<=0.0 */                   \
    ISECT(VV1,VV0,VV2,D1,D0,D2,isect0,isect1);          \
  }                                                     \
  else if(D1*D2>0.0f || D0!=0.0f)                       \
  {                                                     \
    /* here we know that d0d1<=0.0 or that D0!=0.0 */   \
    ISECT(VV0,VV1,VV2,D0,D1,D2,isect0,isect1);          \
  }                                                     \
  else if(D1!=0.0f)                                     \
  {                                                     \
    ISECT(VV1,VV0,VV2,D1,D0,D2,isect0,isect1);          \
  }                                                     \
  else if(D2!=0.0f)                                     \
  {                                                     \
    ISECT(VV2,VV0,VV1,D2,D0,D1,isect0,isect1);          \
  }                                                     \
  else                                                  \
  {                                                     \
    /* triangles are coplanar */                        \
    return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2);      \
  }



/* 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;                 \
  }                                         \
}

qboolean coplanar_tri_tri(vec3_t N,vec3_t V0,vec3_t V1,vec3_t V2,
                     vec3_t U0,vec3_t U1,vec3_t U2)
{
   vec3_t A;
   short i0,i1;
   /* first project onto an axis-aligned plane, that maximizes the area */
   /* of the triangles, compute indices: i0,i1. */
   A[0]=fabs(N[0]);
   A[1]=fabs(N[1]);
   A[2]=fabs(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 qfalse;
}

qboolean tri_tri_intersect(vec3_t V0,vec3_t V1,vec3_t V2,
                      vec3_t U0,vec3_t U1,vec3_t U2)
{
  vec3_t E1,E2;
  vec3_t N1,N2;
  float	d1,d2;
  float du0,du1,du2,dv0,dv1,dv2;
  vec3_t D;
  float isect1[2], isect2[2];
  float du0du1,du0du2,dv0dv1,dv0dv2;
  short index;
  float vp0,vp1,vp2;
  float up0,up1,up2;
  float b,c,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
  if(fabs(du0)<EPSILON) du0=0.0;
  if(fabs(du1)<EPSILON) du1=0.0;
  if(fabs(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
  if(fabs(dv0)<EPSILON) dv0=0.0;
  if(fabs(dv1)<EPSILON) dv1=0.0;
  if(fabs(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=fabs(D[0]);
  index=0;
  b=fabs(D[1]);
  c=fabs(D[2]);
  if(b>max) max=b,index=1;
  if(c>max) max=c,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 */
  COMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,isect1[0],isect1[1]);

  /* compute interval for triangle 2 */
  COMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,isect2[0],isect2[1]);

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

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


float LineSegmentDistance( vec3_t a, vec3_t b, vec3_t c, vec3_t d )
{
	vec3_t	v1, v2, v3, cross;
	//FIXME: what if parallel or intersect?
	//FIXME: this doesn't take into account the endpoints...

	//get the two lines
	VectorSubtract( b, a, v1 );
	VectorSubtract( c, d, v2 );

	//get their normalized cross product
	CrossProduct( v1, v2, cross );
	/*
	float crossLength = VectorLength( cross );
	if ( crossLength == 0 )
	{//intersect!  Or... parallel?
		return 0;
	}
	VectorScale( cross, 1/crossLength, cross );
	*/
	VectorNormalize( cross );

	//now get a vector from v1 to v2
	VectorSubtract( d, a, v3 );

	//distance is dot product of that new vector and the normalized cross product
	float dist = fabs( DotProduct( v3, cross ) );

	return dist;
}

extern qboolean G_FindClosestPointOnLineSegment( const vec3_t start, const vec3_t end, const vec3_t from, vec3_t result );
float ShortestLineSegBewteen2LineSegs( vec3_t start1, vec3_t end1, vec3_t start2, vec3_t end2, vec3_t close_pnt1, vec3_t close_pnt2 )
{
	float	current_dist, new_dist;
	vec3_t	new_pnt;
	//start1, end1 : the first segment
	//start2, end2 : the second segment

	//output, one point on each segment, the closest two points on the segments.

	//compute some temporaries:
	//vec start_dif = start2 - start1
	vec3_t	start_dif;
	VectorSubtract( start2, start1, start_dif );
	//vec v1 = end1 - start1
	vec3_t	v1;
	VectorSubtract( end1, start1, v1 );
	//vec v2 = end2 - start2
	vec3_t	v2;
	VectorSubtract( end2, start2, v2 );
	//
	float v1v1 = DotProduct( v1, v1 );
	float v2v2 = DotProduct( v2, v2 );
	float v1v2 = DotProduct( v1, v2 );

	//the main computation

	float denom = (v1v2 * v1v2) - (v1v1 * v2v2);

	//if denom is small, then skip all this and jump to the section marked below
	if ( fabs(denom) > 0.001f )
	{
		float s = -( (v2v2*DotProduct( v1, start_dif )) - (v1v2*DotProduct( v2, start_dif )) ) / denom;
		float t = ( (v1v1*DotProduct( v2, start_dif )) - (v1v2*DotProduct( v1, start_dif )) ) / denom;
		qboolean done = qtrue;

		if ( s < 0 )
		{
			done = qfalse;
			s = 0;// and see note below
		}

		if ( s > 1 ) 
		{
			done = qfalse;
			s = 1;// and see note below
		}

		if ( t < 0 ) 
		{
			done = qfalse;
			t = 0;// and see note below
		}

		if ( t > 1 ) 
		{
			done = qfalse;
			t = 1;// and see note below
		}

		//vec close_pnt1 = start1 + s * v1
		VectorMA( start1, s, v1, close_pnt1 );
		//vec close_pnt2 = start2 + t * v2
		VectorMA( start2, t, v2, close_pnt2 );

		current_dist = Distance( close_pnt1, close_pnt2 );
		//now, if none of those if's fired, you are done. 
		if ( done )
		{
			return current_dist;
		}
		//If they did fire, then we need to do some additional tests.

		//What we are gonna do is see if we can find a shorter distance than the above
		//involving the endpoints.
	}
	else
	{
		//******start here for paralell lines with current_dist = infinity****
		current_dist = Q3_INFINITE;
	}

	//test 2 close_pnts first
	/*
	G_FindClosestPointOnLineSegment( start1, end1, close_pnt2, new_pnt );
	new_dist = Distance( close_pnt2, new_pnt );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( new_pnt, close_pnt1 );
		VectorCopy( close_pnt2, close_pnt2 );
		current_dist = new_dist;
	}

	G_FindClosestPointOnLineSegment( start2, end2, close_pnt1, new_pnt );
	new_dist = Distance( close_pnt1, new_pnt );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( close_pnt1, close_pnt1 );
		VectorCopy( new_pnt, close_pnt2 );
		current_dist = new_dist;
	}
	*/
	//test all the endpoints
	new_dist = Distance( start1, start2 );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( start1, close_pnt1 );
		VectorCopy( start2, close_pnt2 );
		current_dist = new_dist;
	}

	new_dist = Distance( start1, end2 );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( start1, close_pnt1 );
		VectorCopy( end2, close_pnt2 );
		current_dist = new_dist;
	}

	new_dist = Distance( end1, start2 );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( end1, close_pnt1 );
		VectorCopy( start2, close_pnt2 );
		current_dist = new_dist;
	}

	new_dist = Distance( end1, end2 );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( end1, close_pnt1 );
		VectorCopy( end2, close_pnt2 );
		current_dist = new_dist;
	}

	//Then we have 4 more point / segment tests

	G_FindClosestPointOnLineSegment( start2, end2, start1, new_pnt );
	new_dist = Distance( start1, new_pnt );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( start1, close_pnt1 );
		VectorCopy( new_pnt, close_pnt2 );
		current_dist = new_dist;
	}

	G_FindClosestPointOnLineSegment( start2, end2, end1, new_pnt );
	new_dist = Distance( end1, new_pnt );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( end1, close_pnt1 );
		VectorCopy( new_pnt, close_pnt2 );
		current_dist = new_dist;
	}

	G_FindClosestPointOnLineSegment( start1, end1, start2, new_pnt );
	new_dist = Distance( start2, new_pnt );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( new_pnt, close_pnt1 );
		VectorCopy( start2, close_pnt2 );
		current_dist = new_dist;
	}

	G_FindClosestPointOnLineSegment( start1, end1, end2, new_pnt );
	new_dist = Distance( end2, new_pnt );
	if ( new_dist < current_dist )
	{//then update close_pnt1 close_pnt2 and current_dist
		VectorCopy( new_pnt, close_pnt1 );
		VectorCopy( end2, close_pnt2 );
		current_dist = new_dist;
	}

	return current_dist;
}