This chapter continues my discussion about how to render a single arbitrarily transformed sphere. In Chapter 1, I tantalized you by describing what the inner loop is going to look like. Then I listed a whole bunch of vector/matrix algebra operations and the geometric constructions they represent. Now I'll start out to derive the inner loop of the rendering algorithm, and you will see all the matrix algebra in action. Most of our time, however, will be spent picking the correct coordinate system to make the inner loop fast and accurate. Even if you never have occasion to write ...
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