On quadratic two-parameter families of spheres and their envelopes
M. Peternell, B. Odehnal, M. L. Sampoli.

Comput. Aided Geom. Design 25, 342-355, (2008).


In the present paper we investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean R³. The four dimensional cyclographic model of the set of spheres in R³ is an appropriate framework to show that a quadratic triangular Bézier patch in R4 corresponds to a two-parameter family of spheres with rational envelope surface. The construction shows also that the envelope has rational o sets. Further we outline how to generalize the construction to obtain a much larger class of surfaces with similar properties.



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