Technical Report CIS9908

TR#:CIS9908
Class:CIS
Title: A Computational Model for the Surface--Surface and Surface--Curve Bisector Surfaces
Authors: Gershon Elber and Myung Soo Kim
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Abstract: The bisector of two rational surfaces in R^3 is nonrational, in general. Moreover, in R^3, the bisector of a rational curve and a rational surface is also nonrational. Thus, the bisector surfaces in these two special cases must be approximated numerically. Unfortunately, these bisector surfaces are algebraic surfaces of very high degree; thus the numerical approximation is a non-trivial task. This paper suggests a new computational model for constructing the curve-surface and surface-surface bisectors. The curve-surface bisector problem is reformulated as a trivariate zero-set finding problem, whereas the surface-surface bisector problem is reduced to that of finding the common zero-set of two four-variate functions.
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