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 offsets. Further we outline how to generalize the construction to obtain a much larger class of surfaces with similar properties.
Peternell, M., Odehnal, B., Sampoli, M.L. (2008). On quadratic two-parameter families of spheres and their envelopes. COMPUTER AIDED GEOMETRIC DESIGN, 25(4-5), 342-355 [10.1016/j.cagd.2007.10.007].
On quadratic two-parameter families of spheres and their envelopes
SAMPOLI, MARIA LUCIA
2008-01-01
Abstract
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 offsets. Further we outline how to generalize the construction to obtain a much larger class of surfaces with similar properties.
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https://hdl.handle.net/11365/10284
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