I have a point, P on an n-sphere (n=300) and I want to sample from a uniform distribution of points a given distance, d, from P. This distance is not critical. For example, if my sphere was the globe and my point was the north pole, then I want to create a uniform distribution of points along one of the lines of latitude - but for an n-sphere
Creating a uniform distribution of points on the n-sphere is straightforward using this method: https://mathoverflow.net/questions/24688/efficiently-sampling-points-uniformly-from-the-surface-of-an-n-sphere or How to generate uniformly distributed points on the surface of the 3-d unit sphere? - and I had considered just sampling a large number of points and rejecting anything that is not ~d from P - however I suspect this will be woefully inefficient.
Any suggestions welcome