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Geometry and Computing
We consider Bézier-like formulas with weights in quaternion and geometric (Clifford) algebra for parametrizing rational curves and surfaces. The simplest non-trivial quaternionic case of bilinear formulas for surface patches is studied in detail. Such formulas reproduce well known biquadratic parametrizations of principal Dupin cyclide patches, and are characterized in general as special Darboux cyclide patches. We also survey the most general case of geometric algebra generated bydoi:10.1007/978-3-319-08635-4_8 fatcat:ijaix3n5prbzze4de2gf4miady