The $\beta$-Delaunay tessellation in $\mathbb{R}^{d-1}$ is a generalization of the classical Poisson-Delaunay tessellation. As first result this paper we show that shape weighted typical cell tessellation, conditioned on having large volume, close to regular simplex $\mathbb{R}^{d-1}$. This generalizes earlier results Hug and Schneider about (non-weighted) simplex. Second, asymptotic behaviour ...

We describe several challenging issues related to virtual globe manipulations for GIS that highlight the important interplay between geometric modeling and scientific visualization. We begin by motivating and describing a globe tessellation algorithm designed to avoid singularities at the poles, then discuss other uses of the tessellation that enable certain types of shape modeling on the surfa...

When implementing Delaunay tessellation in 3D, a number of engineering decisions must be made about update and location algorithms, arithmetics, perturbations, and representations. We compare five codes for computing 3D Delaunay tessellation: qhull, hull, CGAL, pyramid, and our own tess3, and explore experimentally how these decisions affect the correctness and speed of computation, particularl...

For each positive integer n, we present a tessellation of CP2 that can be lifted, through the branched covering, to a symmetric tessellation of the Fermat surface (a 4-manifold) of degree n inCP3. The process is systematic and symbolically algebraic. Each fourcell in the tessellation is bounded by four pentahedrons, and each pentahedron has four triangular faces and one quadrilateral face. Grap...

The description of distributions related to grain microstructure helps physicists understand the processes in materials and their properties. This paper presents a general statistical methodology for analysis crystallographic orientations grains 3D Laguerre tessellation dataset which represents polycrystalline material. We introduce complex stochastic models may substitute expensive laboratory ...

Models used in real-time graphics are commonly rendered using triangular boundary representations. Triangulation approximates flat surfaces very well, but requires many fine triangles to accurately represent curved surfaces. This project implements two methods for smoothing coarse input meshes using GPU tessellation shaders to obtain smooth surfaces.