Home About us Contact
|
Home About us Contact | ||
|
|
||
Voronoi Cells (voronoi + cell)
Selected AbstractsIsotropic Remeshing with Fast and Exact Computation of Restricted Voronoi DiagramCOMPUTER GRAPHICS FORUM, Issue 5 2009Dong-Ming Yan Abstract We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation-based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd -tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O(mlog n), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi-Newton method, which proved much faster than Lloyd's iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state-of-art approaches. [source] The distribution of Voronoi cells generated by Southern California earthquake epicentersENVIRONMETRICS, Issue 2 2009Frederic Paik Schoenberg Abstract The cells of Voronoi diagrams generated by epicentral locations of Southern California earthquakes are inspected. The tapered Pareto distribution is shown to fit quite well to the distribution of cell areas and perimeters. This same distribution, which has been used to model the distribution of seismic moments, is also a close approximation to the empirical distributions of times and distances between successive earthquakes for the same catalog of Southern California events. Verification is performed using a variety of different windows and sub-sampling procedures in order to confirm that the results are not an artifact of the particular parameters of the selected earthquake catalog. Copyright © 2008 John Wiley & Sons, Ltd. [source] Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003N. SukumarArticle first published online: 11 MAR 200 Abstract Voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids. Natural neighbours are based on the Voronoi diagram, which partitions space into closest-point regions. The Sibson and the Laplace (non-Sibsonian) interpolants which are based on natural neighbours have shown promise within a Galerkin framework for the solution of partial differential equations. In this paper, we focus on the Laplace interpolant with a two-fold objective: first, to unify the previous developments related to the Laplace interpolant and to indicate its ties to some well-known numerical methods; and secondly to propose a Voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids. A conservation law in integral form is discretized on Voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids. The proposed scheme can also be viewed as a point collocation technique. A detailed study on consistency is conducted, and the satisfaction of the discrete maximum principle (stability) is established. Owing to symmetry of the Laplace weight, a symmetric positive-definite stiffness matrix is realized which permits the use of efficient linear solvers. On a regular (rectangular or hexagonal) grid, the difference scheme reduces to the classical finite difference method. Numerical examples for the Poisson equation with Dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme. Copyright © 2003 John Wiley & Sons, Ltd. [source] The natural volume method (NVM): Presentation and application to shallow water inviscid flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2009R. Ata Abstract In this paper a fully Lagrangian formulation is used to simulate 2D shallow water inviscid flows. The natural element method (NEM), which has been used successfully with several solid and fluid mechanics applications, is used to approximate the fluxes over Voronoi cells. This particle-based method has shown huge potential in terms of handling problems involving large deformations. Its main advantage lies in the interpolant character of its shape function and consequently the ease it allows with respect to the imposition of Dirichlet boundary conditions. In this paper, we use the NEM collocationally, and in a Lagrangian kinematic description, in order to simulate shallow water flows that are boundary moving problems. This formulation is ultimately shown to constitute a finite-volume methodology requiring a flux computation on Voronoi cells rather than the standard elements, in a triangular or quadrilateral mesh. St Venant equations are used as the mathematical model. These equations have discontinuous solutions that physically represent the existence of shock waves, meaning that stabilization issues have thus been considered. An artificial viscosity deduced from an analogy with Riemann solvers is introduced to upwind the scheme and therefore stabilize the method. Some inviscid bidimensional flows were used as preliminary benchmark tests, which produced decent results, leading to well-founded hopes for the future of this method in real applications. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||