Delaunay triangulation

About: Delaunay triangulation is a research topic. Over the lifetime, 5816 publications have been published within this topic receiving 126615 citations. The topic is also known as: Delone triangulation.

Query Pre-processing of Topological Constraints: Comparing a Composition-Based with Neighborhood-Based Approach

Abstract: This paper derives and compares two strategies for minimizing topological constraints in a query expressed by a visual example: (1) elimination of topological relations that are implied uniquely by composition and (2) restriction to topological relations that relate near-neighbor objects, as determined by a Delaunay triangulation. In both cases, the query processing approach is to solve a constraint satisfaction problem over a graph of binary topological relations. Individuals and the combination of the composition- and neighborhood-based strategies were implemented and compared with respect to their ability to reduce topological constraints, and with respect to the quality of the results obtained by a similarity-based searching that uses these pre-processing strategies. The main conclusion of this work is that similarity queries that are formulated in a visual language should exploit the metric characteristics of the configuration, even if only topological constraints are considered for making matches.

A three-dimensional adaptive analysis using the meshfree node-based smoothed point interpolation method (NS-PIM)

Abstract: In this paper, a three-dimensional (3-D) adaptive analysis procedure is proposed using the meshfree node-based smoothed point interpolation method (NS-PIM) Previous study has shown that the NS-PIM works well with the simplest four-node tetrahedral mesh, which is easy to be implemented for complicated geometry In contrast to the displacement-based FEM providing lower bound solutions, the NS-PIM possesses the attractive property of providing upper bound solutions in strain energy norm In the present adaptive procedure, a novel error indicator is devised for NS-PIM settings, which evaluates the maximum difference of strain energy values among four nodes in each of the tetrahedral cells A simple h-type local refinement scheme is adopted and coupled with 3-D mesh automatic generator based on Delaunay technology Numerical results indicate that the adaptive refinement procedure can effectively capture the stress concentration and solution singularities, and carry out local refinement automatically The present adaptive procedure achieves much higher convergence in strain energy solution compared to the uniform refinement, and obtains upper bound solution in strain energy efficiently for force driven problems

Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

Abstract: A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle. The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix. Numerical results are presented to verify the theoretical findings.