A comparison of sequential Delaunay triangulation algorithms
Peter Su,Robert L. Scot Drysdale +1 more
- pp 61-70
TLDR
An experimental comparison of a number of different algorithms for computing the Deluanay triangulation and analyzes the major high-level primitives that algorithms use and does an experimental analysis of how often implementations of these algorithms perform each operation.Abstract:
This paper presents an experimental comparison of a number of different algorithms for computing the Deluanay triangulation. The algorithms examined are: Dwyer’s divide and conquer algorithm, Fortune’s sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri, and Murota, a new bucketing-based algorithm described in this paper, and Devillers’s version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber’s convex hull based algorithm. Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distibutions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.read more
Citations
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Book ChapterDOI
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
TL;DR: 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.
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.
Book ChapterDOI
Chapter 5 – Voronoi Diagrams*
TL;DR: In this article, the authors proposed a method to solve the problem of unstructured data in the context of the Deutsche Forschungsgemeinschaft (DFG).
Journal ArticleDOI
DeWall: A fast divide and conquer Delaunay triangulation algorithm in Ed
TL;DR: The paper deals with Delaunay Triangulations (DT) in Ed space and proposes a new solution, based on an original interpretation of the well-known Divide and Conquer paradigm, which can be simply extended to triangulate point sets in any dimension.
Journal ArticleDOI
High resolution image formation from low resolution frames using Delaunay triangulation
TL;DR: An algorithm based on spatial tessellation and approximation of each triangle patch in the Delaunay triangulation by a bivariate polynomial is advanced to construct a high resolution (HR) high quality image from a set of low resolution (LR) frames.
References
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Book
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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.
Proceedings ArticleDOI
Applications of random sampling in computational geometry, II
TL;DR: Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are given.
Proceedings ArticleDOI
Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams
Leonidas J. Guibas,Jorge Stolfi +1 more
TL;DR: Two algorithms are given, one that constructs the Voronoi diagram of the given sites, and another that inserts a new site in O(n) time, based on the use of the Vor onoi dual, the Delaunay triangulation, and are simple enough to be of practical value.