BALL_DISTANCE
Distance Between Random Points in the Unit Ball

BALL_DISTANCE is 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 in 3D.

Licensing:

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

Languages:

BALL_DISTANCE is available in a MATLAB version.

Related Data and Programs:

ball_distance_test

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, 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.

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:

• John Hammersley,
  The distribution of distance in a hypersphere,
  The Annals of Mathematical Statistics,
  Volume 21, Number 3, pages 447-452, 1950.

Source Code:

• ball_distance_histogram.m, displays a histogram from N samples of pairwise distances.
• ball_distance_pdf.m, displays a plot of the exact PDF of the pairwise distances.
• ball_distance_stats.m, estimates the mean and variance of the pairwise distance, using sampling.
• ball_unit_sample.m, returns a random point in the unit ball.
• timestamp.m, prints the YMDHMS date as a timestamp.

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