The Voronoi diagram of three arbitrary lines in R3
نویسندگان
چکیده
In this paper we study the Voronoi diagram of lines in R. 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 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 semialgebraic tests. These results are important for the robust computation of the Voronoi diagram of polyhedra.
منابع مشابه
The Voronoi diagram of three lines in R3
We give a complete description of the Voronoi diagram of three lines in R3. In particular, we show that the topology of the Voronoi diagram is invariant for three lines in general position, that is, that are pairwise skew and not all parallel to a common plane. The trisector consists of four unbounded branches of either a non-singular quartic or of a cubic and line that do not intersect in real...
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