Study on the Average Size of the Longest-Edge Propagation Path for Triangulations

Oliver-Amadeo Vilca, María-Cecilia Rivara

Abstract

For a triangle t in a triangulation τ, the “longest edge propagating path” Lepp(t), is a finite sequence of neighbor triangles with increasing longest edges. In this paper we study mathematical properties of the LEPP construct. We prove that the average LEPP size over triangulations of random points sets, is between 2 and 4 with standard deviation less than or equal to √6. Then by using analysis of variance and regression analysis we study the statistical behavior of the average LEPP size for triangulations of random point sets obtained with uniform, normal, normal bivariate and exponential distributions. We provide experimental results for verifying that the average LEPP size is in agreement with the analytically derived one.

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Paper Citation


in Harvard Style

Vilca O. and Rivara M. (2020). Study on the Average Size of the Longest-Edge Propagation Path for Triangulations.In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, ISBN 978-989-758-402-2, pages 368-375. DOI: 10.5220/0009162703680375


in Bibtex Style

@conference{grapp20,
author={Oliver-Amadeo Vilca and María-Cecilia Rivara},
title={Study on the Average Size of the Longest-Edge Propagation Path for Triangulations},
booktitle={Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,},
year={2020},
pages={368-375},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009162703680375},
isbn={978-989-758-402-2},
}


in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,
TI - Study on the Average Size of the Longest-Edge Propagation Path for Triangulations
SN - 978-989-758-402-2
AU - Vilca O.
AU - Rivara M.
PY - 2020
SP - 368
EP - 375
DO - 10.5220/0009162703680375