The Voronoi diagram of three arbitrary lines in R3

Hazel Everett 1 Christian Gillot 1 Daniel Lazard 2 Sylvain Lazard 1 Marc Pouget 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 SALSA - Solvers for Algebraic Systems and Applications
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : In this paper we study the Voronoi diagram of lines in R3 . The Voronoi diagram of three lines in general position was studied in [8]. In this paper we complete this work by presenting a complete characterization of the Voronoi diagram of three arbitrary lines in R3 . As in the general case, we prove that the arcs of trisectors are always monotonic in some direction and we show how to separate the connected components and to sort points along each arc of a trisector using only rational linear semi-algebraic tests. These results are important for the robust computation of the Voronoi diagram of polyhedra.
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Hazel Everett, Christian Gillot, Daniel Lazard, Sylvain Lazard, Marc Pouget. The Voronoi diagram of three arbitrary lines in R3. 25th European Workshop on Computational Geometry - EuroCG'09, Mar 2009, Bruxelles, Belgium. pp.297-300. ⟨inria-00425378⟩

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