box_distance

box_distance, a MATLAB code which estimates the distribution and expected value of the distance between two points picked uniformly at random within a 3D box.

The box has sides a <= b <= c.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

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

Related Data and Programs:

box_distance_test

matlab_distance, a MATLAB 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:

• Cleve Moler,
  How Far Apart Are Two Random Points in a Hypercube?,
  https://blogs.mathworks.com/cleve/2017/09/27/how-far-apart-are-two-random-points-in-a-hypercube/
  Posted 27 September 2017.
• Johan Philip,
  The probability distribution of the distance between two random points in a box,
  https://people.kth.se/~johanph/habc.pdf

Source Code:

• box_distance_histogram.m, displays a histogram from N samples of pairwise distances.
• box_distance_mean.m, computes the exact expected value of the pairwise distance.
• box_distance_stats.m, estimates the mean and variance of the pairwise distance, using sampling.
• box_unit_sample.m, returns a random point in the box.