triangle_distance

triangle_distance, a MATLAB 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 a Python version.

Related Data and Programs:

ball_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected in the unit ball in 3D.

circle_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the circumference of the unit circle in 2D.

cube_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected in the unit cube in 3D.

cube_surface_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the surface of the unit cube.

disk_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected in the unit disk in 2D.

ellipse_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected on the circumference of the ellipse (x/a)^2+(y/b)^2=1 in 2D.

hyperball_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected in the unit hyperball in M dimensions.

hypercube_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected in the M-dimensional unit hypercube.

hypercube_surface_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the surface of the unit hypercube in D dimensions.

hypersphere_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the unit hypersphere in M dimensions.

line_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected in the unit line segment in 1D.

normal01_multivariate_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected from an isotropic standard normal distribution in M dimensions.

polygon_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected from a polygon in 2D.

sphere_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the surface of the unit sphere in 3D.

square_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected in the unit square in 2D.

square_surface_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the surface of the unit square.

subset_distance, a MATLAB code which estimates the expected value of the Hamming distance between a pair of randomly selected subsets of an M set.

triangle_distance_test

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.