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I'm a master's student in Computer Science with a relatively weak background with mathematics, so please Forgive me for using a lot of the wrong terms here. This problem was related to a research topic I'm currently doing.

Given a set of points in a bounded 3d space, it there a way to select a subset of points, so that-

  1. strictly uniformly spread out in the space, or
  2. not strictly, but relatively spread out so that the points aren't crowded in a single area?

Here's some poorly drawn figures that could hopefully better explain my question:

Original set: Original set

Ideal subset: Ideal Subset

Poor subset: Poor Subset

Asaf Karagila
  • 393,674
Felis
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  • You're stuck with selecting a subset of already-specified points? Or can you generate new ones? – A rural reader Jan 19 '23 at 22:26
  • @Aruralreader the set of points are already defined if that helps. – Felis Jan 19 '23 at 23:29
  • You might need to construct some kind of objective function characterizing how 'uniform' any specific subset of points is, for example, the variance of the distance to the nearest neighbor. From there you might do random subsampling, though I imagine there are cleverer ways than that. – A rural reader Jan 20 '23 at 00:45

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