Rational bisectors of CSG primitives
Gershon Elber, Myung-Soo Kim · 1999
The bisector surface of two rational surfaces in IR 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.