An empirical comparison of techniques for updating Delaunay triangulations

The computation of Delaunay triangulations from static point sets has been extensively studied in computational geometry. When the points move with known trajectories, kinetic data structures can be used to maintain the triangulation. However, there has been little work so far on how to maintain the triangulation when the points move without explicit motion plans, as in the case of a physical simulation. In this paper we examine how to update Delaunay triangulations after small displacements of the defining points, as might be provided by a physics-based integrator. We have implemented a variety of update algorithms, many new, toward this purpose. We ran these algorithms on a corpus of data sets to provide running time comparisons and determined that updating Delaunay can be significantly faster than recomputing. Categories and Subject Descriptors: F.2.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity—Nonnumerical Algorithms and Problems; I.6.m [Computing Me...

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Leonidas J. Guibas, Daniel Russel
• Keywords: COMPGEOM 2004, Delaunay Triangulations, Kinetic Data Structures, Static Point Sets