Section: New Results

Non-Euclidean Computational Geometry

Participants : Vincent Despré, Iordan Iordanov, Monique Teillaud.

Implementing Delaunay Triangulations of the Bolza Surface

The Cgal library offers software packages to compute Delaunay triangulations of the (flat) torus of genus one in two and three dimensions. To the best of our knowledge, there is no available software for the simplest possible extension, i.e., the Bolza surface, a hyperbolic manifold homeomorphic to a torus of genus two. We present an implementation based on the theoretical results and the incremental algorithm proposed recently. We describe the representation of the triangulation, we detail the different steps of the algorithm, we study predicates, and report experimental results [5]. The implementation is publicly available in the development branch of Cgal on github (https://members.loria.fr/Monique.Teillaud/DT_Bolza_SoCG17/) and will soon be submitted for integration in the library.