Uniformly selecting a subset of points (sampling?) in a bounded 3d space

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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