If you start from N-dimensional Gaussian-distributed vectors and normalize them, you wind up with uniformly distributed vectors on an (N-1)-dimensional hypersph

If you start from N-dimensional Gaussian-distributed vectors and normalize them, you wind up with uniformly distributed vectors on an (N-1)-dimensional hypersphere. Of course, sphere-packing on the surface of a hyperspehere is its own fun problem, and if your data is not actually Gaussian may still not be exactly what you want, but coding the vector magnitude separately from the vector direction is probably a good start.