You need only give the multiplicity of *real* roots.
The idea behind this problems is that one can use a Z-buffer algorithm to act like a ray caster. An advantage is that the Z-buffer algorithm
does fast incremental calculations and can usually outperform a ray caster when resolving visibility over a grid of pixels. For most of
this problem, however, you are asked to count rays cast, and for that you can simply think of the Z-buffer algorithm as a ray caster (since
both algorithms resolve resolve visibility along each line of sight, albeit in a different manner).You may neglect shadow rays when computing the number of rays cast. In other words, just count the number of primary rays from the viewer and the number of reflected and refracted rays, as needed for each sub-problem.
Problem 3b states that the new image plane is "again of size m x m". This is a little confusing, since the previous image plane was n x n, with m x m supersampling per pixel. It should simply state that the image plane in 3b is of size m x m. I've consciously equated the pixel and reflection supersampling rates, both being m x m (though I could have just as easily chosen to make them different). The homework was modified to reflect this clarification on 11/12/06.