Let $x_i$ be points in $R^D$ space, $i = 0\ ..\ N-1$, where $N$ is fixed.
The problem is to distribute the $N$ points in the space so that their density is equal to given probability density $p(x)$, but at the same time keep them as far as possible from each other.
Here 'equispaced' means something similar to optimal ball packing problems.
Example (the density changes in a radial-symmetric way, but locally the points are densely packed):
I understand the formulation is not exact, so I ask about the formulation too.
I tried to move points iteratively with the forces of attraction to the desired density and repulsion from each other, but I don't know how to derive the forces to get a desired density, for example, densely packed 3D Gaussian distribution.