Applications of a Fruitful Relation between a Dupin Cyclide and a Right Circular Cone

摘要

A powerful way of handling a Dupin cyclide is presented. It is based on the concept of inversion, which yields a fruitful relation between the symmetric Dupin horn cyclide, from which all other Dupin cyclides may be obtained by offsetting, and a right circular cone. This relation has two Important applications. First, it is used for constructing rational rectangular and triangular Bezier Patches on the cyclide. Second, it allows to establish an approximative isometry between cyclide and Cone patches, a useful result e.g. for scattered data interpolation techniques on Dupin cyclides.