Centroidal Voronoi tessellations and optimal Delaunay triangulations can be approximated efficiently by non-linear optimisation algorithms. This paper demonstrates that the point distribution used to initialise the optimisation algorithms is important. Compared to conventional random initialisation, certain low-discrepancy point distributions help convergence towards more spatially regular resu...

Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs Xl,m associated to regular tessellations of hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick [FP94]) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs a...

In this paper, shortest paths on two regular tessellations, on the hexagonal and on the triangular grids, are investigated. The shortest paths (built by steps to neighbor pixels) between any two points (cells, pixels) are described as traces and generalized traces on these grids, respectively. In the hexagonal grid, there is only one type of usual neighborhood and at most two directions of the ...

Extending the analogous result of Cannon andWagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs Xl,m associated to regular tessellations of the hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick (Floyd and Plotnick, 1994)) are reciprocal Salem polynomials. As a consequence, the growth ...

In this paper, we try to give the appropriate class of languages to which belong various objects associated with tessellations in the hyperbolic plane.

We consider stationary Poisson line processes in the Euclidean plane and analyze properties of Voronoi tessellations induced by Poisson point processes on these lines. In particular, we describe and test an algorithm for the simulation of typical cells of this class of Cox–Voronoi tessellations. Using random testing, we validate our algorithm by comparing theoretical values of functionals of th...

Abstract. The large development of wireless services and the scarcity of the usable frequencies require an efficient use of the radio spectrum which guarantees interference avoidance. The Channel Assignment (CA) problem achieves this goal by partitioning the radio spectrum into disjoint channels, and assigning channels to the network base stations so as to avoid interference. On a flat region w...

We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in R d. This result generalizes an earlier one proved by Paroux [Adv. for intersection points of motion-invariant Poisson line processes in R 2. Our proof is based on Hoeffd-ing's decomposition of U-statistics which seems to be more efficient and adequate to tackle...

For positive integers p and q with 1/p+1/q < 1/2, a tessellation of type {p, q} is a tessellation of the hyperbolic plane by regular p-gons with q p-gons meeting at each vertex. In this paper, a necessary and sufficient condition on the integers p and q is established to determine when a tessellation of type {p, q} can be realized as a tessellation of the hyperbolic plane by fundamental domains...