Generate uniformly distributed points in n-dimensional sphere

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I have an n-dimensional space and I am trying to dynamically allocate points in the space as I need them.

Every time I search for radius nearest neighbours for point X, I locate the points inside the n sphere of center X and radius R. if the number of neighbours is less than N I want to generate points so that the new points and the existing points inside the sphere of center X are all uniformly distributed.

In other words I want a measure of density of regions of the n sphere and allocate new points in the regions that are less dense.

Any help on this? Thanks