Journal ArticleDOI
Two algorithms for constructing a Delaunay triangulation
Der-Tsai Lee,Bruce Schachter +1 more
TLDR
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.Abstract:
This paper provides a unified discussion of the Delaunay triangulation. Its geometric properties are reviewed and several applications are discussed. Two algorithms are presented for constructing the triangulation over a planar set ofN points. The first algorithm uses a divide-and-conquer approach. It runs inO(N logN) time, which is asymptotically optimal. The second algorithm is iterative and requiresO(N
2) time in the worst case. However, its average case performance is comparable to that of the first algorithm.read more
Citations
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Journal ArticleDOI
Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Journal ArticleDOI
The Quadtree and Related Hierarchical Data Structures
TL;DR: L'accentuation est mise sur la representation de donnees dans les applications de traitement d'images, d'infographie, les systemes d'informations geographiques and the robotique.
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.
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.
References
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Journal ArticleDOI
Convex hulls of finite sets of points in two and three dimensions
Franco P. Preparata,S. J. Hong +1 more
TL;DR: The presented algorithms use the “divide and conquer” technique and recursively apply a merge procedure for two nonintersecting convex hulls to ensure optimal time complexity within a multiplicative constant.
Journal ArticleDOI
Computing Dirichlet Tessellations in the Plane
Peter H.R. Green,Robin Sibson +1 more
TL;DR: A recursive algorithm for computing the Dirichlet tessellation in a highly efficient way is described, and the problems which arise in its implementation are discussed.
Journal ArticleDOI
Packing and covering
TL;DR: The existence of reasonably dense lattice coverings and reasonably economical lattice covers has been studied in this article, where the authors show that simplices cannot be very dense and coverings with spheres cannot have very economical coverings.
Journal ArticleDOI
Piecewise Quadratic Approximations on Triangles
M. J. D. Powell,M. A. Sabin +1 more
TL;DR: Two methods of constructing piecewise quadratic approximations are described which have the property that, if they are applied on each triangle of a triangulation, then ~(x, y) and its first derivatives are continuous everywhere.
Journal ArticleDOI
Packing and Covering. By C. A. Rogers. Pp. viii, 111. 30s. 1964. (Cambridge)
TL;DR: The existence of reasonably dense lattice coverings and reasonably economical lattice covers has been studied in this paper, where the authors show that simplices cannot be very dense and coverings with spheres cannot have very economical coverings.