The hyperbolic Voronoi diagram in arbitrary dimension
نویسندگان
چکیده
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 Poincaré upper half-space, the Poincaré ball, and the Lorentz hyperboloid models, and discusses on degenerate cases for which the dual hyperbolic Delaunay complex is not a triangulation.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1210.8234 شماره
صفحات -
تاریخ انتشار 2012