A time-optimal delaunay refinement algorithm in two dimensions
Sariel Har-Peled,Alper Üngör +1 more
- pp 228-236
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TLDR
In this paper, a new refinement algorithm was proposed to generate size-optimal quality-guaranteed Delaunay triangulations in the plane in O(n log n + m) time.Abstract:
We propose a new refinement algorithm to generate size-optimal quality-guaranteed Delaunay triangulations in the plane. The algorithm takes O(n log n + m) time, where n is the input size and m is the output size. This is the first time-optimal Delaunay refinement algorithm.read more
Citations
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Book
Geometric Approximation Algorithms
TL;DR: This book is the first to cover geometric approximation algorithms in detail, and topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings.
Book ChapterDOI
A Practical Delaunay Meshing Algorithm for aLarge Class of Domains
TL;DR: A Delaunay refinement algorithm has been proposed that can mesh domains as general as piecewise smooth complexes and has a provable guarantee about topology, but certain steps are too expensive to make it practical.
Book ChapterDOI
Sparse Voronoi Refinement
TL;DR: A new algorithm is presented, Sparse Voronoi Refinement, that produces a conformal Delaunay mesh in arbitrary dimension with guaranteed mesh size and quality with full proofs at IMR 2006.
Journal ArticleDOI
Off-centers: A new type of Steiner points for computing size-optimal quality-guaranteed Delaunay triangulations
TL;DR: In this paper, a new type of Steiner points, called off-centers, is introduced to improve the quality of Delaunay triangulations in two dimensions, and a new algorithm based on iterative insertion of offcenters is proposed.
Journal ArticleDOI
Efficient and good Delaunay meshes from random points
Mohamed S. Ebeida,Scott A. Mitchell,Andrew A. Davidson,Anjul Patney,Patrick M. Knupp,John D. Owens +5 more
TL;DR: A Conforming Delaunay Triangulation (CDT) algorithm based on maximal Poisson disk sampling that works well in practice, and has the blue-noise property, and is also fast and uses little memory.
References
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Journal ArticleDOI
Constrained delaunay triangulations
TL;DR: It is shown that the constrained Delaunay triangulation (CDT) can be built in optimalO(n logn) time using a divide-and-conquer technique and has a number of properties that make them useful for the finite-element method.
Book
Geometry and Topology for Mesh Generation
TL;DR: 1. Delaunay triangulations 2. Triangle meshes 3. Combinatorial topology 4. Surface simplification 5.Delaunay tetrahedrizations 6. Tetrahedron meshes 7. Open problems.
Journal ArticleDOI
Provably good mesh generation
TL;DR: It is shown how to triangulate a planar point set or a polygonally bounded domain with triangles of bounded aspect ratio, and how to produce a linear-size Delaunay triangulation of a multidimensional point set by adding a linear number of extra points.
Delaunay refinement mesh generation
TL;DR: This thesis aims to further this progress by cementing the foundations of two-dimensional Delaunay refinement, and by extending the technique and its analysis to three dimensions.