Construction of Bézier rectangles and triangles on the symmetric Dupin horn cyclide by means of inversion

Abstract

Dupin cyclides may be obtained as offsets of a special Dupin cyclide, the so-called symmetric Dupin horn cyclide. A novel approach based on the concept of inversion is presented for generating rational Bézier patches on the symmetric Dupin horn cyclide. This leads to a new formulation for rational rectangular biquadratic cyclide Bézier patches, and to a rational Bézier representation of triangular patches of degree 4 on the symmetric Dupin horn cyclide.