In this article, we study a particular example of general random tessellation, the dead leaves model. This model, first studied by the Mathematical Morphology school, is defined as a sequential superimposition of random closed sets, and provides the natural tool to study the occlusion phenomenon, essential ingredient in the formation of visual images. We generalize results from G. Matheron, and...

Reducing the required memory bandwidth is a main issue in 3D computer graphics. PN triangle solves the memory bandwidth problem by using curved surface representation and tessellation. It reconstructs a smooth and detailed 3D model from blocky one on graphics hardware and then reduces bandwidth consumption. To implement a simple dedicated hardware executing complex operations of tessellation, w...

We characterize the conditions under which completing a Delaunay tessellation produces a connguration that is a nondegenerate Delaunay triangulation of an arbitrarily small perturbation of the original sites. One consequence of this result is a simple postpro-cessing step for resolving degeneracies in Delaunay triangulations that does not require symbolic perturbation of the data. We also give ...

Virtual interactive examination of the quality of car body surfaces is an important issue in the development process of a car. The method is based on simulating reflection lines using striped environment maps and strong specular highlights. For this purpose high quality meshes are created from the NURBS surfaces. However, the meshes have a fixed resolution, hence a closer examination requires a...

Robust and time-efficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape’s boundary points, i.e., by removal of noise-sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents . Each component of the VD is attribut...

The voids between galaxies are identified with the volumes of the Poisson Voronoi tessellation. Two new survival functions for the apparent radii of voids are derived. The sectional normalized area of the Poisson Voronoi tessellation is modelled by the Kiang function and by the exponential function. Two new survival functions with equivalent sectional radius are therefore derived; they represen...

In this paper, we study the problem of multi-robot coverage when the evolution of the robots’ positions is uncertain. More precisely, we use the popular Voronoi coverage control approach [1], which is based on the iterative construction of a centroidal Voronoi tessellation, and ask what happens to the control law and the Voronoi tessellation under actuation and measurement noise. We present a f...

The design of a four-dimensional toric code is explored with the goal finding lattice capable implementing logical $\mathsf{CCCZ}$ gate transversally. established octaplex tessellation, which regular tessellation Euclidean space whose underlying 4-cell octaplex, or hyper-diamond. This differs from conventional 4D lattice, based on hypercubic symmetric respect to $X$ and $Z$ only allows for impl...