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

### Oliver-Amadeo Vilca, MarÃa-Cecilia Rivara

#### Abstract

For a triangle t in a triangulation Ï„, the â€œlongest edge propagating pathâ€ 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 âˆš6. 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.

Download#### 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 MarÃa-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