Transforming Rays and Spheres
A unit sphere fixed at the origin is (at best) barely useful. You certainly couldn’t have more than one, which makes it hard to make any kind of scene out of them. What you want is to be able to transform this sphere—scale it larger or smaller, move it around, and maybe (if one side were textured differently) rotate it a bit.
If you allow moving the sphere, though, your beautiful ray-sphere intersection algorithm has to change, because it assumes the sphere is always at the origin and always has a radius of 1. It would be lovely if you could keep that assumption, while still allowing spheres to be resized and repositioned. It would make your implementation so much cleaner and simpler.
Well, let’s consider this. ...
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