Bézier-like Parametrizations of Spheres and Cyclides Using Geometric Algebra

  title={B{\'e}zier-like Parametrizations of Spheres and Cyclides Using Geometric Algebra},
  author={Rimvydas Krasauskas and Severinas Zube},
We introduce new Bézier-like formulas with quaternionic weights for rational curves and surfaces in Euclidean 3-space. They are useful for representation of Möbius invariant geometric objects. Any Bézier curves and surfaces on 2-spheres can be converted to the quaternionic Bézier (QB) form of twice lower degree. Our focus is on bilinear QB-surfaces: we derive their implicitization formula and show that in general they are patches on special quartic surfaces usually called Darboux cyclides. In… CONTINUE READING


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