Study on the average size of the longest-edge propagation path for triangulations

Vilca Huayta O.A.; Rivara M.-C. · VISIGRAPP 2020 - Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (2020) · DOI: 10.5220/0009162703680375

Resumen

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. Copyright

Instituciones: Universidad Nacional del Altiplano