Computation of the multi-chord distribution of convex and concave polygons

Garcia-Pelayo Novo, Ricardo Angel (2015). Computation of the multi-chord distribution of convex and concave polygons. "Applied Mathematical Sciences", v. 9 (n. 94); pp. 4669-4708. ISSN 1312-885X. https://doi.org/10.12988/ams.2015.54364.

Description

Title: Computation of the multi-chord distribution of convex and concave polygons
Author/s:
  • Garcia-Pelayo Novo, Ricardo Angel
Item Type: Article
Título de Revista/Publicación: Applied Mathematical Sciences
Date: July 2015
ISSN: 1312-885X
Volume: 9
Subjects:
Freetext Keywords: chord lenght distribution function, polygons, diagonal pentagon, correlation function
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Física Aplicada a las Ingenierías Aeronáutica y Naval
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Analytical expressions for the distribution of the length of chords corre- sponding to the a?ne invariant measure on the set of chords are given for convex polygons. These analytical expressions are a computational improve- ment over other expressions published in 2009 and 2011. The correlation function of convex polygons can be computed from the results obtained in this work, because it is determined by the distribution of chords. An analytical expression for the multi-chord distribution of the length of chords corresponding to the a?ne invariant measure on the set of chords is found for non convex polygons. In addition we give an algorithm to ?nd this multi-chord distribution which, for many concave polygons, is computation- ally more e?cient than the said analytical expression. The results also apply to non simply connected polygons.

More information

Item ID: 44786
DC Identifier: http://oa.upm.es/44786/
OAI Identifier: oai:oa.upm.es:44786
DOI: 10.12988/ams.2015.54364
Official URL: http://www.m-hikari.com/ams/ams-2015/ams-93-96-2015/54364.html
Deposited by: Memoria Investigacion
Deposited on: 26 Apr 2017 11:57
Last Modified: 26 Apr 2017 11:57
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