Topological Data Structure: The Fast Marching Example

This article lies in the field of front propagation algorithms on a surface represented by triangle meshes. An implementation of the fast marching algorithm using a topological structure, the generalized maps or g-maps, as the data structure of the mesh is presented. G-maps have the advantage of allowing to store and retrieve information related to the neighborhood of a cell. In this article, the necessary knowledge about generalized maps and the fast marching method are reviewed in order to facilitate the understanding of the proposed implementation and the benefits brought by g-maps as underlying data structure. Then some various applications of this implementation are presented.