Playing with intrinsic triangulations

Details

Supervisors

Remacle, Jean-François

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en informatique, à finalité spécialisée

Abstract

The discrete Laplace-Beltrami operator plays an important role in the Digital Geometry Processing field. It has different applications such as denoizing, parametrization, editing and physical simulations. The problem with this operator is that it uses the cotangents of angles in its calculations which can lead to numerical problems when dealing with too low angles. It would therefore be interesting to compute this operator on a mesh that has better properties. This is where the IDt (Intrinsic Delaunay triangulation) comes into consideration. This type of triangulation produces a better mesh that satisfies preconditions of well-established algorithms. One can then retriangulate their mesh in order to obtain the so-called IDt and make the computations on this new mesh rather than the original one. Some important properties of this triangulations are that it is isogeometric (it does not change the geometry of the object) and that it can be used as a black box so that the final user won't have to understand what's going on under the hood in order to use this feature. The purpose of this work is to implement an algorithm that computes the Intrinsic Delaunay triangulation for triangular meshes using a Halfedge datastructure and to compare it to already existing algorithms.