Local discretization without tolerance in the CAD/CAM and NC programming of a sculptured surface

In CAD/CAM and NC programming of a sculptured surface, one is confronted with non-identity between the parametric and the Cartesian coordinate systems. The conventional way to unify the non-identity is to convert the parametric representation into the Cartesian representation through discretization of the surface with a specified tolerance by means of a recursive segmentation. A new algorithm-local discretization of a sculptured surface without tolerance-is presented in this article in order to be able to evaluate a non-spherical cutter path in the CAD/CAM and NC programming of a sculptured surface. With the new algorithm the discrete data total is lesser, the data structure is simpler, the data is easily manipulated and maintained, and the computational precision of the cutter location is independent of tolerances specified in the conventional way.