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When another data point is inserted and the Voronoi diagram reconstructed, the newly created region displaces the area that once belonged to the old regions. Those points whose regions were displaced are considered natural neighbours to the new point. The weight of each natural neighbour is given by the area taken from the total area occupied by the new region. In 3D, we measure polyhedral volumes instead of areas.

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Natural neighbour interpolation has a number of strengths over linear barycentric interpolation. Namely, it provides a smooth or continuous slope between samples3, and is always the same for a given point set, unlike the TIN where the quality of the triangulation can produce biases in the outcome, even in the best case.