Want some sort of hierarchy. Want to get things like positions of corners, normals and area of surface, etc. Position and normal from mesh elt. Two main ways of representing a mesh for a polygon. You end up storing 3-D data in your mesh, so it can't be shared.
Advantage is that the mesh-space is simple.
Disadvantage is that you need to map both ways. Need to talk about how the program should work. Got a MC RTer. Gonna get a model in, create some fixed-sized mesh. For each elt, Ei, you're going to find the projection of the radiance f'n onto that elt by integrating against the dual.