sphere_positive_distance

sphere_positive_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 surface of the unit positive sphere in 3D.

Licensing:

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

Languages:

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

Related Data and Programs:

sphere_positive_distance_test

octave_distance, 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:

• John D Cook,
  Random points in a high-dimensional orthant,
  Posted 9 August 2023,
  https://www.johndcook.com/blog/2023/08/09/random-points-hypersphere-orthant/

Source Code:

• sphere_positive_distance_histogram.m, displays a histogram from N samples of pairwise distances.
• sphere_positive_distance_stats.m, estimates the mean and variance of the pairwise distance, using sampling.
• sphere_positive_sample.m, returns a random point on the unit positive sphere;
• histogram_pdf.m, creates a histogram plot of data, normalized to estimate the PDF;