Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces

Abstract : We give experimental evidence that the only known upper bound on the diameter of the flip graph of a hyperbolic surface recently proven by Despré, Schlenker, and Teillaud (SoCG'20), is largely overestimated. To this aim, we develop an experimental framework for the storage of triangulations of hyperbolic surfaces and modifications through twists. We show that the computations with algebraic numbers can be overcome, and we propose ways to generate surfaces that are meaningful for the experiments.