Computing the Voronoi cells of planes, spheres and cylinders in R3
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
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The bisector of two rational surfaces in R^3 is, in general, nonrational; and so is the bisector of a rational curve and a rational surface. Thus, bisector surfaces in these two cases must be approximated numerically. Unfortunately, they are algebraic surfaces of very high degree and numerical approximation is non-trivial.This paper suggests a new computational model for constructing curve-surface and surface-surface bisectors in R3. The curve-surface bisector problem is reformulated as the search for a trivariate zero-set; and the surface-surface bisector problem is reduced to that of finding the common zero-set of two four-variate functions.