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Dense Point Sets Have Sparse Delaunay Triangulations
"... Delaunay triangulations and Voronoi diagrams are one of the most thoroughly studies objects in computational geometry, with numerous applications including nearest-neighbor searching, clustering, finite-element mesh generation, deformable surface modeling, and surface reconstruction. Many algorithms ..."
Abstract
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Cited by 29 (2 self)
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Delaunay triangulations and Voronoi diagrams are one of the most thoroughly studies objects in computational geometry, with numerous applications including nearest-neighbor searching, clustering, finite-element mesh generation, deformable surface modeling, and surface reconstruction. Many
Dense Point Sets Have Sparse Delaunay Triangulations ∗ �� � ���� � �� � ��� � �� � ������ � ��������� or “... But Not Too Nasty”
, 2001
"... ..."
Dense Point Sets Have Sparse Delaunay Triangulations or "... But Not Too Nasty"
, 2003
"... The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R³ with spread \Delta has complexity O(\Delta 3). This bound is tight in the worst case for all \Delta = O(pn). In particular, t ..."
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The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R³ with spread \Delta has complexity O(\Delta 3). This bound is tight in the worst case for all \Delta = O(pn). In particular
The Quickhull algorithm for convex hulls
- ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algo ..."
Abstract
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Cited by 713 (0 self)
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algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
- ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
Abstract
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Cited by 534 (11 self)
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are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed
Constrained Delaunay triangulations
- Algorithmica
, 1989
"... Given a set of n vertices in the plane together with a set of noncrossing edges, the constrained Delaunay triangulation (CDT) is the triangulation of the vertices with the following properties: (1) the prespecified edges are included in the triangulation, and (2) it is as close as possible to the De ..."
Abstract
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Cited by 207 (4 self)
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Given a set of n vertices in the plane together with a set of noncrossing edges, the constrained Delaunay triangulation (CDT) is the triangulation of the vertices with the following properties: (1) the prespecified edges are included in the triangulation, and (2) it is as close as possible
Application-layer multicast with Delaunay triangulations
- IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2002
"... Application-layer multicast supports group applications without the need for a network-layer multicast protocol. Here, applications arrange themselves in a logical overlay network and transfer data within the overlay. In this paper, we present an application-layer multicast solution that uses a Del ..."
Abstract
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Cited by 179 (4 self)
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Delaunay triangulation as an overlay network topology. An advantage of using a Delaunay triangulation is that it allows each application to locally derive next-hop routing information without requiring a routing protocol in the overlay. A disadvantage of using a Delaunay triangulation is that the mapping
Laplacian Smoothing and Delaunay Triangulations
- Communications in Applied Numerical Methods
, 1988
"... In contrast to most triangulation algorithms which implicitly assume that triangulation point locations are fixed, 'Laplacian ' smoothing focuses on moving point locations to improve triangulation. Laplacian smoothing is attractive for its simplicity but it does require an existing triangu ..."
Abstract
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Cited by 140 (0 self)
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triangulation. In this paper the effect of Laplacian smoothing on Delaunay triangulations is explored. It will become clear that constraining Laplacian smoothing to maintain a Delaunay triangulation measurably improves Laplacian smoothing. An early reference to the use of Laplacian smoothing is to be found in a
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