Technical Report CIS9904

Title: Rational Bisectors of CSG Primitives
Authors: Gershon Elber and Myung-Soo Kim
Abstract: The bisector surface of two rational surfaces in $\Reals^3$ is non-rational, in general. However, in some special cases, the bisector surfaces can have rational parameterization. This paper classifies some of these special cases that are related to constructive solid geometry (CSG). We consider the bisector surfaces between points, lines, planes, spheres, cylinders, cones, and tori. Many cases are shown to yield rational bisector surfaces, while several other cases are still left as open questions.
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