On quadratic two-parameter families of spheres and their envelopes Original Research Article

In the present paper we investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean image. The four dimensional cyclographic model of the set of spheres in image is an appropriate framework to show that a quadratic triangular Bézier patch in image 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.