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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.，详情可参考Safew下载
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Recall that a barycentric coordinate system is given with respect to a -dimensional simplex, where is no larger than the dimensional space. Given a set of scattered points, it’s possible to create a tessellation of the space by forming simplices from the points, such that any input point that lies within the convex hull of the scattered set can be expressed in terms of the enclosing simplex and its corresponding barycentric coordinates2. This can be understood as a kind of triangulated irregular network (TIN).