Delaunay Cells for Arrangements of Flats in Hyperbolic Space
نویسنده
چکیده
For n + 1 disjoint flats of dimension k in H, we produce a Delaunay cell which is a generalization of the Delaunay simplex associated to n + 1 points in H. Combinatorially, these Delaunay cells resemble truncated n-dimensional simplices. For certain classes of arrangements of flats in H, we prove that these Delaunay cells can be glued together to form a Delaunay complex, with the result that almost every point of H is in a total of one Delaunay cell, counting with multiplicities and orientations.
منابع مشابه
The hyperbolic Voronoi diagram in arbitrary dimension
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...
متن کامل12 Discrete Aspects of Stochastic Geometry
Stochastic geometry studies randomly generated geometric objects. The present chapter deals with some discrete aspects of stochastic geometry. We describe work that has been done on familiar objects of discrete geometry, like finite point sets, their convex hulls, discrete point sets, arrangements of flats, tessellations of space, under various assumptions of randomness. Most of the results to ...
متن کاملAn Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach
The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. In [1], Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the Lorentz group and its underlying hyperbolic geometry. They defined the Chen addition and then Chen model of hyperbolic geomet...
متن کاملUniversal Approximator Property of the Space of Hyperbolic Tangent Functions
In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.
متن کاملExplicit Parametrization of Delaunay Surfaces in Space Forms via Loop Group Methods
We compute explicit conformal parametrizations of Delaunay surfaces in each of the three space forms Euclidean 3-space , spherical 3-space 3 and hyperbolic 3-space 3 by using the generalized Weierstrass type representation for constant mean curvature (CMC) surfaces established by J. Dorfmeister, F. Pedit and H. Wu.
متن کامل