515 research outputs found
Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction
General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed
as extensions of Ord's process, are considered. The interaction may occur on
each cell of the tessellation and between neighbour cells. The tessellation may
also be subjected to a geometric hardcore interaction, forcing the cells not to
be too large, too small, or too flat. This setting, natural for applications,
introduces some theoretical difficulties since the interaction is not
necessarily hereditary. Mathematical results available for studying these
models are reviewed and further outcomes are provided. They concern the
existence, the simulation and the estimation of such tessellations. Based on
these results, tools to handle these objects in practice are presented: how to
simulate them, estimate their parameters and validate the fitted model. Some
examples of simulated tessellations are studied in details
HetHetNets: Heterogeneous Traffic Distribution in Heterogeneous Wireless Cellular Networks
A recent approach in modeling and analysis of the supply and demand in
heterogeneous wireless cellular networks has been the use of two independent
Poisson point processes (PPPs) for the locations of base stations (BSs) and
user equipments (UEs). This popular approach has two major shortcomings. First,
although the PPP model may be a fitting one for the BS locations, it is less
adequate for the UE locations mainly due to the fact that the model is not
adjustable (tunable) to represent the severity of the heterogeneity
(non-uniformity) in the UE locations. Besides, the independence assumption
between the two PPPs does not capture the often-observed correlation between
the UE and BS locations.
This paper presents a novel heterogeneous spatial traffic modeling which
allows statistical adjustment. Simple and non-parameterized, yet sufficiently
accurate, measures for capturing the traffic characteristics in space are
introduced. Only two statistical parameters related to the UE distribution,
namely, the coefficient of variation (the normalized second-moment), of an
appropriately defined inter-UE distance measure, and correlation coefficient
(the normalized cross-moment) between UE and BS locations, are adjusted to
control the degree of heterogeneity and the bias towards the BS locations,
respectively. This model is used in heterogeneous wireless cellular networks
(HetNets) to demonstrate the impact of heterogeneous and BS-correlated traffic
on the network performance. This network is called HetHetNet since it has two
types of heterogeneity: heterogeneity in the infrastructure (supply), and
heterogeneity in the spatial traffic distribution (demand).Comment: JSA
From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons
We bridge the properties of the regular triangular, square, and hexagonal honeycomb
Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in
a common framework symmetry breaking processes and the approach to uniform random
distributions of tessellation-generating points. We resort to ensemble simulations of tessellations
generated by points whose regular positions are perturbed through a Gaussian noise,
whose variance is given by the parameter α2 times the square of the inverse of the average
density of points. We analyze the number of sides, the area, and the perimeter of the
Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and
2-parameter gamma distributions provide an efficient description of the statistical properties
of the analyzed geometrical characteristics. The introduction of noise destroys the triangular
and square tessellations, which are structurally unstable, as their topological properties are
discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically
stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise
withα <0.12. For all tessellations and for small values of α, we observe a linear dependence
on α of the ensemble mean of the standard deviation of the area and perimeter of the cells.
Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial
unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations
are indistinguishable. When α >2, results converge to those of Poisson-Voronoi
tessellations. The geometrical properties of n-sided cells change with α until the Poisson-
Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to
be not valid and a square root dependence on n is established. This law allows for an easy
link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1,
the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree
remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond
their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D
Voronoi tessellations
Shape Animation with Combined Captured and Simulated Dynamics
We present a novel volumetric animation generation framework to create new
types of animations from raw 3D surface or point cloud sequence of captured
real performances. The framework considers as input time incoherent 3D
observations of a moving shape, and is thus particularly suitable for the
output of performance capture platforms. In our system, a suitable virtual
representation of the actor is built from real captures that allows seamless
combination and simulation with virtual external forces and objects, in which
the original captured actor can be reshaped, disassembled or reassembled from
user-specified virtual physics. Instead of using the dominant surface-based
geometric representation of the capture, which is less suitable for volumetric
effects, our pipeline exploits Centroidal Voronoi tessellation decompositions
as unified volumetric representation of the real captured actor, which we show
can be used seamlessly as a building block for all processing stages, from
capture and tracking to virtual physic simulation. The representation makes no
human specific assumption and can be used to capture and re-simulate the actor
with props or other moving scenery elements. We demonstrate the potential of
this pipeline for virtual reanimation of a real captured event with various
unprecedented volumetric visual effects, such as volumetric distortion,
erosion, morphing, gravity pull, or collisions
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