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JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A 2009, Vol. 35 Issue (8) :962-967    DOI:
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Delaunay triangulation and Voronoi diagrams for Riemannian manifolds
Cheng Dan1, Yang Qin2, Cai Qiang2, Jin Maozhong3*
1. School of Computer Science and Technology, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. College of Computer Science and Engineering, Beijing Technology & Business University, Beijing 100037, China;
3. School of Computer Science and Technology, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

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Abstract Delaunay triangulation and Voronoi diagrams in Riemannian space were studied. Firstly, the existence and generation algorithm of Delaunay triangulation and Voronoi diagrams were discussed. Then on the basis of analysing the existed research achievements, some properties of Delaunay triangulation and Voronoi diagrams for Riemannian were given and proved. The necessities of describing object by Riemannian manifolds and advantages of researching Riemannian manifolds by charts were presented. Finally, taking 2-manifold as an example, the algorithm of getting Riemannian manifolds according to initial data of models was described, which included creating charts, defining functions of manifolds, and so on. The algorithm of creating Delaunay triangulation and Voronoi diagrams of models based on charts was presented, and some examples were provided.
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Cheng Dan
Yang Qin
Cai Qiang
Jin Maozhong
KeywordsRiemannian manifolds   Delaunay triangulation   Voronoi diagrams   existence   generation algorithm     
Received 2008-12-22;
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Cheng Dan, Yang Qin, Cai Qiang,Jin Maozhong.Delaunay triangulation and Voronoi diagrams for Riemannian manifolds[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2009,V35(8): 962-967
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http://bhxb.buaa.edu.cn//EN/     or     http://bhxb.buaa.edu.cn//EN/Y2009/V35/I8/962
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