Voronoi diagram computations for planar NURBS curves

We present robust and efficient algorithms for computing Voronoi diagrams of planar freeform curves. Boundaries of the Voronoi diagram consist of portions of the bisector curves between pairs of planar curves. Our scheme is based on computing critical structures of the Voronoi diagrams, such as self-intersections and junction points of bisector curves. Since the geometric objects we consider in this paper are represented as freeform NURBS curves, we were able to reformulate the solution to the problem of computing those critical structures into the zero-set solutions of a system of nonlinear piecewise rational equations in parameter space. We present a new algorithm for computing error-bounded bisector curves using a distance surface constructed from error-bounded offset approximations of planar curves. This error-bounded algorithm is fast and produces bisector curves that are correct both in the topology and the geometry. Once bisectors are computed, both local and global self-inters...

• Type: Journal
• Year: 2008
• Where: SMA
• Authors: Joon-Kyung Seong, Elaine Cohen, Gershon Elber
• Keywords: Junction Points, Piecewise Rational Equations, SMA 2008, Solid Modeling, Voronoi Diagram