Implementing Delaunay Triangulations of the Bolza Surface

Iordan Iordanov (1) , Monique Teillaud (1)

1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm

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. In this paper, 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

Mots clés: hyperbolic surface; Fuchsian group; arithmetic issues; Dehn's algorithm; CGAL

Domaines: Géométrie algorithmique [cs.CG]

Iordan Iordanov, Monique Teillaud. Implementing Delaunay Triangulations of the Bolza Surface. 33rd International Symposium on Computational Geometry (SoCG 2017), Jul 2017, Brisbane, Australia. pp.44:1 -- 44:15, ⟨10.4230/LIPIcs.SoCG.2017.44⟩. ⟨hal-01568002⟩