Topological Classification and Determination of Non-Degenerate Intersections of Two Dupin Cyclides

Abstract

The surface-surface intersection is a fundamental task in CAD/CAM. We present the classification and a full enumeration of the topology of all non-degenerate intersections of two Dupin cyclides. Inversion geometry is first used to transform the intersection of two Dupin cyclides to that of a cyclide and a torus. Then the topology of the intersection curve is reduced to the arrangements of the main circle of the torus and another pair of circles, which can be characterized by a simple algebraic sequence. Based on the classification and enumeration results, an efficient determination algorithm for the topology of two Dupin cyclides is also provided. • A classification of the non-degenerate intersections of two Dupin cyclides is given by a simple algebraic sequence. • A full enumeration of all non-degenerate intersections of two Dupin cyclides based on a simple algebraic sequence is provided. • An efficient and robust algorithm of determining the inter- section topology of two Dupin cyclides is provided.