Systematic triangulations

Efficient and objective interpretation of spatial data depends upon the evaluation of local variation in the adjacency relationships of the data set. For scattered data, this in turn relies upon the systematic triangulation of the locational information. The Optimal, Greedy, and Delaunay triangulations are discussed and some differences illustrated by a simple example which also displays the “most equiangular” property of the Delaunay triangulation. This property makes the Delaunay triangulation the most appropriate for triangle based interpolation because it is a result of nearest neighbor spatial ordering of the data. Of the three approaches, only the Delaunay triangulation has efficient published algorithms.

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