Topological Classification and Determination of Non-Degenerate Intersections of Two Dupin Cyclides. (December 2022)

• Record Type: Journal Article
• Authors: Yao, Shanshan; Jia, Xiaohong
• Is Part Of: Computer aided design. Volume 153(2022)
• Publication Date: 2022-12
• Subjects: Torus -- Dupin cyclide -- Intersection -- Topology -- Inversion; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2022.103406
• Languages: English
• ISSNs: 0010-4485

Abstract

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. Highlights: For non-degenerate intersections of two Dupin cyclides we provide: 1. A classification and a full enumeration based on a simple algeberaic sequence;2. An efficient and robust algorithm of determining the intersection topology.