Abstract
We introduce a new, efficient, and complete algorithm, and its exact implementation, to compute the Voronoi diagram of lines in space. This is a major milestone towards the robust construction of the Voronoi diagram of polyhedra. As we follow the exact geometric-computation paradigm, it is guaranteed that we always compute the mathematically correct result. The algorithm is complete in the sense that it can handle all configurations, in particular all degenerate ones. The algorithm requires O(n 3 + ε) time and space, where n is the number of lines. The Voronoi diagram is represented by a data structure that permits answering point-location queries in O(log2 n) expected time. The implementation employs the Cgal packages for constructing arrangements and lower envelopes together with advanced algebraic tools.
This work has been supported in part by the Israel Science Foundation (grant no. 236/06), by the German-Israeli Foundation (grant no. 969/07), and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University.
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Hemmer, M., Setter, O., Halperin, D. (2010). Constructing the Exact Voronoi Diagram of Arbitrary Lines in Three-Dimensional Space. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_34
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