Surface slicing algorithm based on topology transition

摘要

Presented in this paper is an algorithm to compute the intersections of a parametric regular surface with a set of parallel planes. Rather than using an ordinary surface-plane intersection algorithm repeatedly, we pre-process a surface to identify points, called topology transition points (TTP's), on the surface where the topologies of intersection curves change. It turns out that such points can be computed efficiently, exactly and robustly employing a normal surface, and they are categorized into seven distinct groups. Analyzing the properties of such characteristic points on the surface, the starting points to trace intersection curves can be found rather efficiently and robustly. Such intersection contours can be used in various applications including rapid prototyping, solid freeform fabrication, process planning, NC tool path generation for surfaces, etc.