How to draw a sphere. 1

I have written a special-purpose program that is highly optimized for drawing spheres. This program involves quite a variety of interesting tricks, but when I started to write about them, I realized that lot of matrix mathematics background is necessary to understand the sphere-rendering algorithm. I consider the matrix mathematics necessary to manipulate (and ultimately render) second-order surfaces. I wanted an algorithm that drew a texture-mapped sphere arbitrarily scaled, translated, and placed into perspective. It had to work for any view of the sphere and needed to be fast