验证体积/ 3D空间中的点

Question

I've been working on development of a mesh library.I want to add a feature such that it will detect if a point is located inside of a 3D mesh or not.

I've tried something like ray casting algo.

But the problem is., In my algo., to test the possibility,I project the point onto plane along Z axis.If projected point is within the quad/tri and z value of projected point is greater that that of original point's Z value, I'll count the face.If not I wont.If the total count is ODD then that means the point is inside the 3D volume.

ispointinside3Dspace(point,facelist)
{
for faces in the object:
{
  project the point onto the face along Z axis;
  if( projected point is within the face):
  {
        if( projectedpoint->z > point->z ):
        {
           face_hit++;
        }
   }
}
if(face_hit%2==1)
{
   return(1);
}
else
{
   return(0);
}
}

If the projected point in this algo is equal to vertex on that face., it will be counted more than once as same vertex will be shared by 4 quads/many tris.Is there any better algo. How should I avoid this overcounting???If I skip the possibility of projected point being a vertex on a face.,I wont get proper results.

Answer 1

The usual approach for this kind of situations is to apply a small tranformation to the whole system (either a rotation or a shear transform). In some cases (at least in 2d) you don't even need to know the exact amount of your transformation but you can do this symbolically and adjust the algorithm accordingly.

In your case, I would probably first check, if your ray hits a vertex (or an edge, which poses the same problem since this hit would be counted at least twice). If so, I'd modify the direction of your projection by a small amount and do the test again. Since changing the projection direction would probably require major changes in your algorithm, you can do this alternatively by applying a small rotation (using a precalculated rotation matrix) to all points of your system.