Delaunay triangulations of generalized Bolza surfaces

03/10/2021 ∙ by Matthijs Ebbens, et al. ∙ 0

The Bolza surface can be seen as the quotient of the hyperbolic plane, represented by the Poincaré disk model, under the action of the group generated by the hyperbolic isometries identifying opposite sides of a regular octagon centered at the origin. We consider generalized Bolza surfaces 𝕄_g, where the octagon is replaced by a regular 4g-gon, leading to a genus g surface. We propose an extension of Bowyer's algorithm to these surfaces. In particular, we compute the value of the systole of 𝕄_g. We also propose algorithms computing small sets of points on 𝕄_g that are used to initialize Bowyer's algorithm.

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