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Interpolation[funcvaluelist, Method→"Voronoi", (options)][x], where funcvaluelist is a list of scattered control points together with the function values in these points, returns the function value of the nearest control point to x. The function is thus constant in regions. If two control points are at the same minimum distance, the function value of the first is returned. 
DistanceFunction  Automatic  distance function to use in calculation of the distance matrix and the calculation of the distance from the interpolation point to the control points. Note, that the function here is expected to return the square of the distance 
If the same interpolation should be used in many different points, the function can be precompiled without specifying in which point it will be used. Not very much time is gained by this, in this case.
