How to draw a sphere.2. Coordinate systems

For pt. 1 see ibid., 1995. The author continues his discussion about how to render a single arbitrarily transformed sphere. In part 1 he described what the inner loop is going to look like and he listed a whole bunch of vector matrix algebra operations and the geometric constructions they represent. He now starts to derive the inner loop of the rendering algorithm in order to see all the matrix algebra in action. Most of the time, however, will be spent picking the correct coordinate system to make the inner loop fast and accurate. Even if you aren´t going to write special purpose sphere rendering programs, this will clearly illustrate the workings of the homogeneous perspective transform and the geometric interpretations of transformation matrices