Surface interpolation based on new local coordinates

Abstract Sibson found a “local coordinate property” associated with the Voronoi diagram, and applied it to the surface interpolation from given heights at arbitrarily located sites. This article presents another local coordinate property that is also based on the Voronoi diagram. Our new property is simpler in that the coordinates can be computed from the Voronoi diagram directly while Sibson’s coordinates require the second-order Voronoi diagram. Moreover, our formula is flexible in the sense that it is valid even if the structure of the Voronoi diagram is incorrectly recognized. On the basis of this formula, a new interpolation scheme is constructed.

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