HYPERSPHERE_DISTANCE
Distance Between Random Points on the Unit Hypersphere

HYPERSPHERE_DISTANCE, a MATLAB library 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 GNU LGPL license.

Languages:

HYPERSPHERE_DISTANCE is available in a MATLAB version.

Related Data and Programs:

BALL_DISTANCE, a MATLAB library which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit ball.

CIRCLE_DISTANCE, a MATLAB library which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the unit circle.

DISK_DISTANCE, a MATLAB library which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit disk.

HYPERBALL_DISTANCE, a MATLAB library which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit hyperball in M dimensions.

hypersphere_distance_test

line_distance, a MATLAB library which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit line segment.

RANDOM_DATA, a MATLAB library which uses a random number generator (RNG) to sample points corresponding to various probability density functions (PDF's), spatial dimensions, and geometries, including the M-dimensional cube, ellipsoid, simplex and sphere.

SPHERE_DISTANCE, a MATLAB library which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the unit sphere.

square_distance, a MATLAB library which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit square.

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;
• timestamp.m, prints the YMDHMS date as a timestamp.