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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We wanted a scenario where, say, 5 well-placed border points could efficiently represent an area with 5,000 internal points and 10,000 road edges. This would reduce those 10,000 edges to just 5*4/2 = 10 shortcuts for routing through that cluster at a high level – an incredible 1:1000 point ratio and a 30x reduction in edges to consider for the high-level path!,这一点在旺商聊官方下载中也有详细论述
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