A library to compute the density of the distance between a point and a random variable uniformly distributed in some sets

TL;DR

This paper introduces a new algorithm for computing the density of the distance from a point to a uniformly distributed random variable in a polygon, matching the complexity of previous methods but based on triangulation.

Contribution

It presents an alternative triangulation-based algorithm for the same problem, implemented in an open source library, expanding computational options for this geometric probability task.

Findings

Algorithm has complexity nlog(n)

Provides an open source implementation

Offers an alternative to Green's theorem-based method

Abstract

In [3], algorithms to compute the density of the distance to a random variable uniformly distributed in (a) a ball, (b) a disk, (c) a line segment, or (d) a polygone were introduced. For case (d), the algorithm, based on Green's theorem, has complexity nlog(n) where n is the number of vertices of the polygone. In this paper, we present for case (d) another algorithm with the same complexity, based on a triangulation of the polygone. We also describe an open source library providing this algorithm as well as the algorithms from [3]. [3] V. Guigues, Computation of the cumulative distribution function of the Euclidean distance between a point and a random variable uniformly distributed in disks, balls, or polyhedrons and application to Probabilistic Seismic Hazard Analysis, arXiv, available at arXiv:1809.02007, 2015.