Conversion of biquadratic rational Bézier surfaces into patches of particular Dupin cyclides: the torus and the double sphere

Abstract

Toruses and double spheres are particular cases of Dupin cyclides. In this paper, we study the conversion of rational biquadratic B´ezier surfaces into Dupin cyclide patches. We give the conditions that the B´ezier surface should satisfy to be convertible, and present a new conversion algorithm to construct the torus or double sphere patch corresponding to a given Bézier surface, some conversion examples are illustrated and commented.