On quadratic two-parameter families of spheres and their envelopes

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 osets. Further we outline how to generalize the construction to obtain a much larger class of surfaces with similar properties.

Bibtex:

@article{peternell-2008-qufamsph,
   author = {Martin Peternell and Boris Odehnal and Maria L. Sampoli },
   title = " {O}n quadratic two-parameter families of spheres
   and their envelopes",
   journal = {Comput. Aided Geom. Design},
   year = {2008},
   volume={25},
   pages = "342-355",
   url = "http://www.geometrie.tuwien.ac.at/peternell/twoparsphereenv.pdf"

}