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Construction of Bézier rectangles and triangles on the symmetric Dupin horn cyclide by means of inversion. (English) Zbl 0906.68169

Summary: 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.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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