In response to a broad expression of customer interest, Rogers and Clarke Manufacturing Company has recently developed its first-generation CNC spherical generator. This paper presents some theoretical aspects of the design, and some of the obstacles we had to ad-dress. The fundamentals of manual generator setups are well known. The only mathematics involved was to solve a simple equation for the generator head angle, given the rough cutting diameter of the cup wheel, and the work radius to be achieved. Subsequent "cut and try" refinement of the setup is normally an "art" unsullied by mathematical analysis. But the computer requires more precise instruction. Our theoretical considerations, mathematical models, and applications experience are discussed. With the factor of diamond wheel radius wear, it is not possible to finish every lens with computer control. Therefore, the operator of a Rogers and Clarke CNC Spherical Generator has the availability of manual controls for individual machine functions. CNC Spherical Generators are designed specifically for the shop with numerous short runs and perhaps a low diamond wheel inventory. The computer controls system permits much faster setup times, particularly for less experienced operators.