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Voronoi Diagram and Delaunay Triangulation
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Voronoi: Russian Delaunay: French
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Applications 「資料分群與樣式辨認（Data Clustering and Pattern Recognition）」
應用Voronoi Diagram於臺北盆地地下水模式參數最佳化之研究 採用二維Voronoi網路(Voronoi diagram)模型, 從微觀角度分析氧化鋅非線性電阻片中的電流、溫度和熱應力的分布 Simulation of polycrystalline structure with Voronoi diagram
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Properties #1 The Voronoi diagram has the property that for each site every point in the region around that site is closer to that site than to any of the other sites
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Properties #2 The Delaunay triangulation is the geometric dual of the Voronoi diagram. Alternately, it can be defined as a triangulation of the sites with the additional property that for each triangle of the triangulation, the circumcircle of that triangle is empty of all other sites. There is a line segment connecting Pi and Pj in a Delaunay triangulation if and only if the Voronoi Diagram Regions of Pi and Pj share the same edge.
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Euler's formula For planar graph G=(V,E), |E| <= 3 |V| - 6 F=E-V+2
In a Delaunay triangulation, V = n, E 3n – 6 F = E - V + 2 3n n + 2 = 2n - 4.
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