Technical Report CIS9908

Title: A Computational Model for the Surface--Surface and Surface--Curve Bisector Surfaces
Authors: Gershon Elber and Myung Soo Kim
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.
CopyrightThe above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information

Remark: Any link to this technical report should be to this page (, rather than to the URL of the PDF files directly. The latter URLs may change without notice.

To the list of the CIS technical reports of 1999
To the main CS technical reports page

Computer science department, Technion