The Bolza surface can be seen as the quotient of the hyperbolic plane, represented by the Poincar\'e 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 $\mathbb{M}_g$, 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 $\mathbb{M}_g$. We also propose algorithms computing small sets of points on $\mathbb{M}_g$ that are used to initialize Bowyer's algorithm.
翻译:Bolza表面可以被视为超偏平面的商数, 以Poincar\'e磁盘模型为代表, 由超偏异异位数生成的组的动作代表, 以正八角为源。 我们认为波尔萨表面普遍化 $\ mathbb{M ⁇ g$, 八角被普通的 4g$-gon 取代, 导致以g$为单位的表面。 我们提议将鲍耶的算法扩展至这些表面 。 特别是, 我们计算了 $\ mathb{M ⁇ g$的质数值 。 我们还提出了用于初始化 Bowyer 算法的小点数计算算法 $\ mathb{M ⁇ g$ 。