Occlusion hyperplanes (shown in gray) due to neighbors in dimensions 1, 2, and 3 (A–C, respectively); compare with Figure 10. Every additional dimension adds a new coordinate axis along which the previous constraints are duplicated, roughly doubling the average number of directions available from which neighbors can connect. Once Gabriel balls are “attached” to , the remaining space is greatly reduced, and so is the probability of drawing a sample point from inside the region enclosed by the hyperplanes.
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