Journal ArticleDOI
Efficient VLSI parallel algorithm for Delaunay triangulation on orthogonal tree network in two and three dimensions
TLDR
An algorithm with worst case time complexity O(log/sup 2/N) in two dimensions and O(m/sup 1/2/log N) in three dimensions with N input points and m as the number of tetrahedra in triangulation is given.Abstract:
An algorithm with worst case time complexity O(log/sup 2/N) in two dimensions and O(m/sup 1/2/log N) in three dimensions with N input points and m as the number of tetrahedra in triangulation is given. Its AT/sup 2/ VLSI complexity on Thompson's logarithmic delay model, (1983) is O(N/sup 2/log/sup 6/N) in two dimensions and O(m/sup 2/Nlog/sup 4/ N) in three dimensions. >read more
Citations
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Journal ArticleDOI
Parallel terrain triangulation
TL;DR: A parallel algorithm is presented that builds a TIN based on Delaunay triangulation, by selecting a sparse subset of points from a dense regular grid of sampled data.
Journal ArticleDOI
Managing the complexity of digital terrain models
Florian Schröder,Patrick Roßbach +1 more
TL;DR: The necessary steps for reducing regularly sampled height grids or given triangular meshes to meet specified quality or quantity criteria are described.
Proceedings ArticleDOI
A data-parallel algorithm for three-dimensional Delaunay triangulation and its implementation
TL;DR: A parallel algorithm for constructing the Delaunay triangulation of a set of vertices in three-dimensional space is presented, which achieves a fast running time and good scalability over a wide range of problem sizes and machine sizes.
Journal ArticleDOI
An improved parallel algorithm for delaunay triangulation on distributed memory parallel computers
TL;DR: An improved parallel algorithm for Delaunay triangulation is proposed, which partitions the bounding convex region of the input points set into a number of regions by usingDelaunay edges and generates Delaunays triangles in each region by applying an incremental construction approach.
Journal ArticleDOI
Many-dimensional potential surfaces: What they imply and how to think about them
TL;DR: In this paper, the authors explore the topology of a polyatomic system to find its stationary points and topology, and test the physical plausibility of potential surfaces, e.g., to determine whether a surface developed to describe spectra is valid enough globally to be used for scattering studies.
References
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Computational geometry. an introduction
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Book
Computational Geometry: An Introduction
TL;DR: In this article, the authors present a coherent treatment of computational geometry in the plane, at the graduate textbook level, and point out the way to the solution of the more challenging problems in dimensions higher than two.
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Algorithms in Combinatorial Geometry
TL;DR: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.
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
Geometric structures for three-dimensional shape representation
TL;DR: It is shown that minimal representations (i.e., polyhedra) can be provided by a surface- based method using nearest neighbors structures or by a volume-based method using the Delaunay triangulation.