Minimal roughness property of the Delaunay triangulation (Q751165)
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scientific article; zbMATH DE number 4176318
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimal roughness property of the Delaunay triangulation |
scientific article; zbMATH DE number 4176318 |
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Minimal roughness property of the Delaunay triangulation (English)
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1990
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A set of scattered data in the plane consists of function values measured on a set of data points in \({\mathbb{R}}^ 2\). A surface model is obtained by triangulating the set of data points and constructing the piecewise linear interpolating surface (PLIS) to the given function values. The roughness measure of a PLIS is the \(L^ 2\) norm squared of the gradient of the surface, integrated over the triangulated region. The author proves that the Delaunay triangulation of the data points minimizes the roughness measure of a PLIS, for any fixed set of values of the function.
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scattered data
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piecewise linear interpolating surface
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roughness measure
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Delaunay triangulation
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