The Voronoi diagram of three arbitrary lines in R

In this paper we study the Voronoi diagram of lines in R. The Voronoi diagram of three lines in general position was studied in [14]. In this paper we complete this work by presenting a complete characterization of the Voronoi diagram of three arbitrary lines in R. 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. †LORIA INRIA Lorraine University Nancy 2, [email protected] ‡LIP6 INRIA Rocquencourt University Pierre et Marie Curie, [email protected]