I have a triangle that is extended in space and each edge is refracted differently, creating a 5 sided polytope. The initial and final triangles are the view radii segments of a frustum. We need to get the u and v along the triangle and the w depth in between the triangles of a point inside the polytope.
I think I can do this using trilinear interpolation and treating two vertices on each side as merged and using my own volume calculations. I just need to interpolate some values given by the three points and a z. http://bmia.bmt.tue.nl/People/BRomeny/Courses/8C080/Interpolation.pdf