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Divide-and-Conquer for Voronoi Diagrams Revisited6 Oswin Aichholzer,a
 

Summary: Divide-and-Conquer for Voronoi Diagrams Revisited6
Oswin Aichholzer,a
, Wolfgang Aignera
, Franz Aurenhammerb
, Thomas Hackla
, Bert J¨uttlerc
,
Elisabeth Pilgerstorferc
, Margot Rablc
aInstitute for Software Technology, Graz University of Technology, Austria
b
Institute for Theoretical Computer Science, Graz University of Technology, Austria
cInstitute of Applied Geometry, Johannes Kepler University Linz, Austria
Abstract
We show how to divide the edge graph of a Voronoi diagram into a tree that corresponds to the medial axis of an
(augmented) planar domain. Division into base cases is then possible, which, in the bottom-up phase, can be merged
by trivial concatenation. The resulting construction algorithm--similar to Delaunay triangulation methods--is not
bisector-based and merely computes dual links between the sites, its atomic steps being inclusion tests for sites in
circles. This guarantees computational simplicity and numerical stability. Moreover, no part of the Voronoi diagram,
once constructed, has to be discarded again. The algorithm works for polygonal and curved objects as sites and, in

  

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz
Jüttler, Bert - Institut für Angewandte Geometrie, Johannes Kepler Universität Linz

 

Collections: Computer Technologies and Information Sciences; Mathematics