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

摘要

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 Beszier patches on the symmetric Dupin horn cyclide. This leads to a new formulation for rational rectangular biquadratic cyclide Bezier patches, and to a rational Bezier representation of triangular patches of degree 4 on the symmetric Dupin horn cyclide.