Related papers: Distance Distributions in Regular Polygons
Distance distributions are a key building block in stochastic geometry modelling of wireless networks and in many other fields in mathematics and science. In this paper, we propose a novel framework for analytically computing the closed…
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
In this report, the explicit probability density functions of the random Euclidean distances associated with equilateral triangles are given, when the two endpoints of a link are randomly distributed in 1) the same triangle, 2) two adjacent…
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,…
We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th neighbour among random points distributed with uniform density in a $D$-dimensional Euclidean space. First we present a heuristic…
It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…
In this paper we obtain the chord length distribution function for any regular polygon. From this function we conclude the density function and the distribution function of the distance between two uniformly and independently distributed…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
In this paper we obtain the density function and the distribution function of the distance between two uniformly and independently distributed random points in any right-angled triangle. The density function is derived from the chord length…
We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
This paper presents a new method to obtain the distance distribution between the mobile node and any reference node in a regular hexagon. The existing distance distribution research mainly focuses on static network deployment and ignores…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
We first review the derivation of the exact expression for the average distance $<r_n>$ of the n-th neighbour of a reference point among a set of N random points distributed uniformly in a unit volume of a D-dimensional geometric space.…
In this paper, we derive formulas for the analytical calculation of the moments of the distance between two uniformly and independently distributed random points in an $n$-sided regular polygon. A number of closed form expressions is…
This letter derives closed-form expressions for the probability density function of the distance between two nodes located in heterogeneous concentric geometries, namely a disk or sphere and a surrounding annulus or spherical shell. Two…
This paper is concerned with the study of a circular random distribution called geodesic Normal distribution recently proposed for general manifolds. This distribution, parameterized by two real numbers associated to some specific location…
We consider $N$ circles of equal radii, $r$, having their centers randomly placed within a square domain $\mathcal{D}$ of size $L \times L$ with periodic boundary conditions ($\mathcal{D} \in \mathbb{R}^2$). When two or more circles…
We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to certain distance of other, with each of these two having a nearest neighbor to a…