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

Oliver-Amadeo Vilca Huayta; María-Cecilia Rivara

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Paper

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

Topics: Fundamental Methods and Algorithms; Geometric Computing; Modeling and Algorithms; Surface Modeling

In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 0VISIGRAPP, 368-375, 2020 , Valletta, Malta

Authors: Oliver-Amadeo Vilca Huayta ¹ and María-Cecilia Rivara ²

Affiliations: ¹ Departamento de Ingeniería de Sistemas, Universidad Nacional del Altiplano, Avenida Floral N. 1153, Puno, Peru ; ² Departamento de Ciencias de la Computación, Universidad de Chile, Santiago, Chile

Keyword(s): Average LEPP Size, Longest-Edge Propagating Path (LEPP), Triangulation Refinement.

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 several formats:

Huayta, 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 (VISIGRAPP 2020) - GRAPP; ISBN 978-989-758-402-2; ISSN 2184-4321, SciTePress, pages 368-375. DOI: 10.5220/0009162703680375

@conference{grapp20,
author={Oliver{-}Amadeo Vilca Huayta 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 (VISIGRAPP 2020) - GRAPP},
year={2020},
pages={368-375},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009162703680375},
isbn={978-989-758-402-2},
issn={2184-4321},
}

TY - CONF

JO - Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - GRAPP
TI - Study on the Average Size of the Longest-Edge Propagation Path for Triangulations
SN - 978-989-758-402-2
IS - 2184-4321
AU - Huayta, O.
AU - Rivara, M.
PY - 2020
SP - 368
EP - 375
DO - 10.5220/0009162703680375
PB - SciTePress