Geometric Modelling

A powerful way of handling a Dupin cyc1ide is presented. It is based on the concept of inversion, which yields a fruitful relation between the symmetric Dupin horn cyc1ide, from which all other Dupin cyc1ides 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 cyc1ide. Second, it allows to establish an approximative isometry between cyc1ide and cone patches, a useful result e.g. for scattered data interpolation techniques on Dupin cyc1ides.