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Voronoi-Delaunay duality and Delaunay meshes

Abstract

We define a Delaunay mesh to be a manifold triangle mesh whose edges form an intrinsic Delaunay triangulation or iDT of its vertices, where the triangulated domain is the piecewise flat mesh surface. We show that meshes constructed from a smooth surface by taking an iDT or a restricted Delaunay triangulation, do not in general yield a Delaunay mesh. We establish a precise dual relationship between the iDT and the Voronoi tessellation of the vertices of a piecewise flat (pwf) surface and exploit this duality to demonstrate criteria which ensure the existence of a proper Delaunay triangulation.

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Supplemental Material
Citation
Category
Paper in Conference Proceedings or in Workshop Proceedings (Full Paper in Proceedings)
Event Title
ACM symposium on Solid and physical modeling 2007
Divisions
Visualization and Data Analysis
Subjects
Computergraphik
Event Location
Beijing
Event Type
Conference
Event Dates
June 4-6
Date
June 2007
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