We show that in the Klein projective ball model of hyperbolic space, the hyperbolic Voronoi diagram is affine and amounts to clip a corresponding power diagram, requiring however algebraic arithmetic. By considering the lesser-known Beltrami hemisphere model of hyperbolic geometry, we overcome the arithmetic limitations of Klein construction. Finally, we characterize the bisectors and geodesics in the other Poincar\' e upper half-space, the Poincar\'e ball, and the Lorentz hyperboloid models, and discusses on degenerate cases for which the dual hyperbolic Delaunay complex is not a triangulation.
翻译：我们显示,在双曲空间的克莱因投影球模型中,双曲Voronoi图是直角图,相当于剪切一个相应的电动图,需要多少代数算法。我们通过考虑不那么知名的贝尔特拉米半球超曲几何模型,克服了克莱因构造的算术限制。最后,我们在另一个Poincar' e上半空、Poincar'e球和Lorentz超代谢模型中描述两极双双曲德劳纳综合体不是三角模型的两极化案例。
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