Range queries ask "what's inside this box?" But sometimes the question is "what's nearest to this location?" This is the nearest neighbor problem, and you don't know how big your search radius should be. The nearest point might be right next to you or far away.
Implementing natural neighbour interpolation implies the construction of a geometric Voronoi diagram, however this is not strictly the case. Since the Delaunay triangulation is the dual graph of the Voronoi diagram, all the information needed to perform natural neighbour interpolation is already implicit within the triangulation itself. Algorithms to determine natural neighbours from the Delaunay triangulation can be found in several papers within the literature[4][5]. Unfortunately the relative complexity of natural neighbour interpolation means that it is slower than barycentric interpolation by a considerable margin.
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