triangle_distance

triangle_distance, an Octave code which estimates the expected value of the distance between a pair of points randomly selected in a triangle in 2D.

This problem is notably more complicated than when the sampling region is a square. In particular, the probability density function for the distance seems to be known only for special cases, such as a right triangle or equilateral triangle.

Licensing:

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

Languages:

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

Related Data and Programs:

triangle_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:

• Uwe Baesel,
  Random chords and point distances in regular polygons,
  Acta Mathematica Universitatis Comenianae,
  Volume LXXXII, Number 1, pages 1-18, 2014.
• Uwe Baesel,
  The distribution function of the distance between two random points in a right-angled triangle,
  arXiv:1208.6228v2 17 September 2012.

Source Code:

• triangle_distance_histogram.m, displays a histogram from N samples of pairwise distances.
• triangle_distance_stats.m, estimates the mean and variance of the pairwise distance, using sampling.
• triangle_equilateral_distance_pdf.m, displays a plot of the exact PDF of the pairwise distances in an equilateral triangle.
• triangle_print.m, prints a triangle.
• triangle_right_distance_pdf.m, displays a plot of the exact PDF of the pairwise distances in an equilateral triangle.
• triangle_right_error.m, determines how close a triangle is to a right triangle.
• triangle_sample.m, returns a random point in a triangle.
• triangle_sides.m, computes the lengths of the sides of a triangle and returns them in increasing order.