triangle_distance

triangle_distance, a MATLAB library which considers the problem of describing the typical value of the distance between a pair of points randomly selected in a triangle.

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 GNU LGPL license.

Languages:

triangle_distance is available in a MATLAB version.

Related Data and Programs:

BALL_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 ball.

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.

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:

• timestamp.m, prints the YMDHMS date as a timestamp.
• 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. (NOT FINISHED YET.)
• 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.