long t_c_intersection(Triangle3 t)
{
long v1_test,v2_test,v3_test;
float d,denom;
Point3 vect12,vect13,norm;
Point3 hitpp,hitpn,hitnp,hitnn;
/* First compare all three vertexes with all six face-planes */
/* If any vertex is inside the cube, return immediately! */
if ((v1_test = face_plane(t.v1)) == INSIDE) return(INSIDE);
if ((v2_test = face_plane(t.v2)) == INSIDE) return(INSIDE);
if ((v3_test = face_plane(t.v3)) == INSIDE) return(INSIDE);
/* If all three vertexes were outside of one or more face-planes, */
/* return immediately with a trivial rejection! */
if ((v1_test & v2_test & v3_test) != 0) return(OUTSIDE);
/* Now do the same trivial rejection test for the 12 edge planes */
v1_test |= bevel_2d(t.v1) << 8;
v2_test |= bevel_2d(t.v2) << 8;
v3_test |= bevel_2d(t.v3) << 8;
if ((v1_test & v2_test & v3_test) != 0) return(OUTSIDE);
/* Now do the same trivial rejection test for the 8 corner planes */
v1_test |= bevel_3d(t.v1) << 24;
v2_test |= bevel_3d(t.v2) << 24;
v3_test |= bevel_3d(t.v3) << 24;
if ((v1_test & v2_test & v3_test) != 0) return(OUTSIDE);
/* If vertex 1 and 2, as a pair, cannot be trivially rejected */
/* by the above tests, then see if the v1-->v2 triangle edge */
/* intersects the cube. Do the same for v1-->v3 and v2-->v3. */
/* Pass to the intersection algorithm the "OR" of the outcode */
/* bits, so that only those cube faces which are spanned by */
/* each triangle edge need be tested. */
if ((v1_test & v2_test) == 0)
if (check_line(t.v1,t.v2,v1_test|v2_test) == INSIDE) return(INSIDE);
if ((v1_test & v3_test) == 0)
if (check_line(t.v1,t.v3,v1_test|v3_test) == INSIDE) return(INSIDE);
if ((v2_test & v3_test) == 0)
if (check_line(t.v2,t.v3,v2_test|v3_test) == INSIDE) return(INSIDE);
/* By now, we know that the triangle is not off to any side, */
/* and that its sides do not penetrate the cube. We must now */
/* test for the cube intersecting the interior of the triangle. */
/* We do this by looking for intersections between the cube */
/* diagonals and the triangle...first finding the intersection */
/* of the four diagonals with the plane of the triangle, and */
/* then if that intersection is inside the cube, pursuing */
/* whether the intersection point is inside the triangle itself. */
/* To find plane of the triangle, first perform crossproduct on */
/* two triangle side vectors to compute the normal vector. */
SUB(t.v1,t.v2,vect12);
SUB(t.v1,t.v3,vect13);
CROSS(vect12,vect13,norm)
/* The normal vector "norm" X,Y,Z components are the coefficients */
/* of the triangles AX + BY + CZ + D = 0 plane equation. If we */
/* solve the plane equation for X=Y=Z (a diagonal), we get */
/* -D/(A+B+C) as a metric of the distance from cube center to the */
/* diagonal/plane intersection. If this is between -0.5 and 0.5, */
/* the intersection is inside the cube. If so, we continue by */
/* doing a point/triangle intersection. */
/* Do this for all four diagonals. */
d = norm.x * t.v1.x + norm.y * t.v1.y + norm.z * t.v1.z;
/* if one of the diagonals is parallel to the plane, the other will intersect the plane */
if(fabs(denom=(norm.x + norm.y + norm.z))>EPS)
/* skip parallel diagonals to the plane; division by 0 can occur */
{
hitpp.x = hitpp.y = hitpp.z = d / denom;
if (fabs(hitpp.x) <= 0.5)
if (point_triangle_intersection(hitpp,t) == INSIDE) return(INSIDE);
}
if(fabs(denom=(norm.x + norm.y - norm.z))>EPS)
{
hitpn.z = -(hitpn.x = hitpn.y = d / denom);
if (fabs(hitpn.x) <= 0.5)
if (point_triangle_intersection(hitpn,t) == INSIDE) return(INSIDE);
}
if(fabs(denom=(norm.x - norm.y + norm.z))>EPS)
{
hitnp.y = -(hitnp.x = hitnp.z = d / denom);
if (fabs(hitnp.x) <= 0.5)
if (point_triangle_intersection(hitnp,t) == INSIDE) return(INSIDE);
}
if(fabs(denom=(norm.x - norm.y - norm.z))>EPS)
{
hitnn.y = hitnn.z = -(hitnn.x = d / denom);
if (fabs(hitnn.x) <= 0.5)
if (point_triangle_intersection(hitnn,t) == INSIDE) return(INSIDE);
}
/* No edge touched the cube; no cube diagonal touched the triangle. */
/* We're done...there was no intersection. */
return(OUTSIDE);
}
extern int
trivial_vertex_tests(int nverts, const real verts[][3],
int already_know_verts_are_outside_cube)
{
/*register*/ unsigned long cum_and; /* cumulative logical ANDs */
/*register*/ int i;
/*
* Compare the vertices with all six face-planes.
* If it's known that no vertices are inside the unit cube
* we can exit the loop early if we run out of bounding
* planes that all vertices might be outside of. That simply means
* that this test failed and we can go on to the next one.
* If we must test for vertices within the cube, the loop is slightly
* different in that we can trivially accept if we ever do find a
* vertex within the cube, but we can't break the loop early if we run
* out of planes to reject against because subsequent vertices might
* still be within the cube.
*/
cum_and = ~0L; /* Set to all "1" bits */
if(already_know_verts_are_outside_cube)
{
for(i=0; i<nverts; i++)
if(0L == (cum_and = face_plane(verts[i], cum_and)))
break; /* No planes left to trivially reject */
}
else
{
for(i=0; i<nverts; i++)
{
/* Note the ~0L mask below to always test all planes */
unsigned long face_bits = face_plane(verts[i], ~0L);
if(0L == face_bits) /* vertex is inside the cube */
return 1; /* trivial accept */
cum_and &= face_bits;
}
}
if(cum_and != 0L) /* All vertices outside some face plane. */
return 0; /* Trivial reject */
/*
* Now do the just the trivial reject test against the 12 edge planes.
*/
cum_and = ~0L; /* Set to all "1" bits */
for(i=0; i<nverts; i++)
if(0L == (cum_and = bevel_2d(verts[i], cum_and)))
break; /* No planes left that might trivially reject */
if(cum_and != 0L) /* All vertices outside some edge plane. */
return 0; /* Trivial reject */
/*
* Now do the trivial reject test against the 8 corner planes.
*/
cum_and = ~0L; /* Set to all "1" bits */
for(i=0; i<nverts; i++)
if(0L == (cum_and = bevel_3d(verts[i], cum_and)))
break; /* No planes left that might trivially reject */
if(cum_and != 0L) /* All vertices outside some corner plane. */
return 0; /* Trivial reject */
/*
* By now we know that the polygon is not to the outside of any of the
* test planes and can't be trivially accepted *or* rejected.
*/
return -1;
}
