Preprocessing Imprecise Points for Delaunay Triangulation: Simplified and Extended

Authors:
Kevin Buchin;Maarten Löffler;Pat Morin;Wolfgang Mulzer
Affiliations:
TU Eindhoven, Dept. of Mathematics and Computer Science, Eindhoven, The Netherlands;University of California, Computer Science Department, 92697, Irvine, CA, USA;Carleton University, School of Computer Science, Ottawa, Canada;Princeton University, Department of Computer Science, 08540, Princeton, NJ, USA
Venue:
Algorithmica
Year:
2011

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Abstract

Suppose we want to compute the Delaunay triangulation of a set P whose points are restricted to a collection ℛ of input regions known in advance. Building on recent work by Löffler and Snoeyink, we show how to leverage our knowledge of ℛ for faster Delaunay computation. Our approach needs no fancy machinery and optimally handles a wide variety of inputs, e.g., overlapping disks of different sizes and fat regions.