Fast Delaunay Triangulation and Voronoi Diagram Generation on the Sphere

We describe a fast surface reconstruction approach that takes random points distributed near the surface of a sphere as input, and generates as output a Delaunay surface mesh and its dual Voronoi diagram of the sphere. The method starts from dividing the sphere surface into several initial triangles...

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Bibliographic Details
Published in2010 Second World Congress on Software Engineering Vol. 1; pp. 187 - 190
Main Authors Yingdong Ma, Qian Chen
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2010
Subjects
Algorithm design and analysis
Delaunay triangulation
Equations
History
Indexes
Mathematical model
randomized incremental algorithm
Surface reconstruction
Three dimensional displays
Voronoi diagram
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Summary:We describe a fast surface reconstruction approach that takes random points distributed near the surface of a sphere as input, and generates as output a Delaunay surface mesh and its dual Voronoi diagram of the sphere. The method starts from dividing the sphere surface into several initial triangles and introduces a concept of index sites in order to employ the randomized incremental algorithm to get the Delaunay triangulation. We develop a heuristic point search method which can locate a random point within the current triangle efficiently. This method is very efficient because no additional storage is needed to record the flip history and a new random point insertion algorithm is used. We test the performance on a collection of point sample sets and demonstrate a 30% performance improvement compared to existing O(n log n) 3D randomized incremental algorithms.
ISBN:9781424492879
1424492874
DOI:10.1109/WCSE.2010.136