Can someone help me to understand the purpose of delaunay triangulation? what is it use for? Also I got to know that delaunay triangulation is the dual graph of voronoi diagram but not really fully understand it. Thanks so much
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The Delaunay triangulation is a "good" triangulation in that it finds triangles that are not too skewed. It is unique and guarantees that the circumcircle of any triangle is empty. It is relatively fast to build, requiring no more than O(N Log(N)) operations.
It is used where triangulations are used, for instance for interpolation on irregular 2D point sets.
It is said to be the dual of the Voronoi diagram because vertexes (sites) are in one-to-one correspondence with the faces (regions) and vice versa. And when two Voronoi regions share an edge, the corresponding sites are linked by a triangle side.
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The MST was mentioned by @Phpdna. Does a good answer deserve a downvote ? – Nov 12 '14 at 15:33
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The question is about triangulation: 2D. – Nov 12 '14 at 15:54