hypersphere_distance

hypersphere_distance, an Octave code which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the unit hypersphere in M dimensions.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

hypersphere_distance is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

hypersphere_distance_test

octavedistance, an Octave code which estimates the typical distance between a pair of points randomly selected from the surface or interior of a geometric object such as a circle, disk, sphere, cube.

Reference:

• Panagiotis Siridopoulos,
  The N-Sphere Chord Length Distribution,
  ARXIV,
  https://arxiv.org/pdf/1411.5639.pdf

Source Code:

• hypersphere_distance_histogram.m, displays a histogram from N samples of pairwise distances.
• hypersphere_distance_pdf.m, displays a plot of the exact PDF of the pairwise distances.
• hypersphere_distance_stats.m, estimates the mean and variance of the pairwise distance, using sampling.
• hypersphere_unit_sample.m, returns a random point on the unit hypersphere;