Sphere-geometric aspects of bisector surfaces

Abstract:

The bisector surface B of two smooth input objects P and Q is the locus of centers of spheres which are tangent to P and Q, respectively. This definition already indicates that methods from sphere geometry, in particular Lie-sphere geometry apply nicely to the construction of these surfaces. The computation of bisector surfaces of general input surfaces results in the solution of a system of nonlinear equations. We show that if both surfaces are canal surfaces or if one surface is a Lie-sphere, the construction is elementary.

Bibtex:

@inproceedings{peternell-2006-bs,
	author = {Martin Peternell},
	title = "Sphere-Geometric Aspects of Bisector Surfaces",
	booktitle = "Algebraic Geometry and Geometric Modeling",
	year = {2006},
	pages = "107-112",
	note = "{P}roceedings of the conference in Barcelona, 
		September 4-7",

}