Book ChapterDOI
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
Jonathan Richard Shewchuk
- pp 203-222
TLDR
Triangle as discussed by the authors is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunayer refinement algorithm for quality mesh generation, and it is shown that the problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is impossible for some PSLGs.Abstract:
Triangle is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunay refinement algorithm for quality mesh generation. Several implementation issues are discussed, including the choice of triangulation algorithms and data structures, the effect of several variants of the Delaunay refinement algorithm on mesh quality, and the use of adaptive exact arithmetic to ensure robustness with minimal sacrifice of speed. The problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is shown to be impossible for some PSLGs, contradicting the claim that a variant of the Delaunay refinement algorithm solves this problem.read more
Citations
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Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
TL;DR: Gmsh as mentioned in this paper is an open-source 3D finite element grid generator with a build-in CAD engine and post-processor that provides a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities.
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The quickhull algorithm for convex hulls
TL;DR: This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm, and provides empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory.
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A simple mesh generator in MATLAB
Per-Olof Persson,Gilbert Strang +1 more
TL;DR: Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics, and an unstructured simplex mesh requires a choice of meshpoints (vertex nodes) to be chosen.
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TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator
TL;DR: The essential algorithms and techniques used to develop TetGen are presented, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations, and filtered exact geometric predicates, which can robustly handle arbitrary complex 3D geometries and is fast in practice.
Book
Computational Fluid Dynamics: Principles and Applications Ed. 3
TL;DR: This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and code parallelization.
References
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Journal ArticleDOI
Two algorithms for constructing a Delaunay triangulation
Der-Tsai Lee,Bruce Schachter +1 more
TL;DR: This paper provides a unified discussion of the Delaunay triangulation and two algorithms are presented for constructing the triangulations over a planar set ofN points.
Journal ArticleDOI
Self-adjusting binary search trees
TL;DR: The splay tree, a self-adjusting form of binary search tree, is developed and analyzed and is found to be as efficient as balanced trees when total running time is the measure of interest.
Journal ArticleDOI
A sweepline algorithm for Voronoi diagrams
TL;DR: A geometric transformation is introduced that allows Voronoi diagrams to be computed using a sweepline technique and is used to obtain simple algorithms for computing the Vor onoi diagram of point sites, of line segment sites, and of weighted point sites.
Journal ArticleDOI
Primitives for the manipulation of general subdivisions and the computation of Voronoi
Leonidas J. Guibas,Jorge Stolfi +1 more
TL;DR: The following problem is discussed: given n points in the plane (the sites) and an arbitrary query point q, find the site that is closest to q, which can be solved by constructing the Voronoi diagram of the griven sites and then locating the query point in one of its regions.
Journal ArticleDOI
A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation
TL;DR: Compared with previous quadtree-based algorithms for quality mesh generation, the Delaunay refinement approach is much simpler and generally produces meshes with fewer triangles.
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