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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 ..."
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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
The Stability of Delaunay Triangulations
, 2013
"... We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δgeneric point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex p ..."
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Cited by 7 (5 self)
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We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δgeneric point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex
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 ..."
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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
ON THE AVERAGE LENGTH OF DELAUNAY TRIANGULATIONS
, 1984
"... We shall show that on the average, the total length of a Delaunay triangulation is of the same order as that of a minimum triangulation, u der the assumption that our points are drawn from a homogeneous planar Poisson point distribution. ..."
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Cited by 8 (0 self)
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We shall show that on the average, the total length of a Delaunay triangulation is of the same order as that of a minimum triangulation, u der the assumption that our points are drawn from a homogeneous planar Poisson point distribution.
The Delaunay Triangulation and Function Learning
, 1990
"... In this report we consider the use of the Delaunay triangulation for learning smooth nonlinear functions with bounded second derivatives from sets of random input output pairs. We show that if interpolation is implemented by piecewiselinear approximation over a triangulation of the input sampl ..."
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Cited by 15 (0 self)
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In this report we consider the use of the Delaunay triangulation for learning smooth nonlinear functions with bounded second derivatives from sets of random input output pairs. We show that if interpolation is implemented by piecewiselinear approximation over a triangulation of the input
Structural tolerance and Delaunay triangulation
, 1999
"... In this paper we consider the tolerance of a geometric or combinatorial structure associated to a set of points as a measure of how much the set of points can be perturbed while leaving the (topological or combinatorial) structure essentially unchanged. We concentrate on studying the Delaunay triang ..."
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Cited by 11 (1 self)
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that the tolerance of all the edges can be computed in O(n log n) time. Finally, we extend our study to some subgraphs of the Delaunay triangulation.
Computing Delaunay Triangulation with Imprecise . . .
, 2003
"... The key step in the construction of the Delaunay triangulation of a finite set of planar points is to establish correctly whether a given point of this set is inside oroutside the circle determined by any other three points. We address the problem of formulating the incircle testwhen the coordinate ..."
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Cited by 12 (2 self)
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The key step in the construction of the Delaunay triangulation of a finite set of planar points is to establish correctly whether a given point of this set is inside oroutside the circle determined by any other three points. We address the problem of formulating the incircle testwhen
Outerplanar graphs and Delaunay triangulations
, 2011
"... Over 20 years ago, Dillencourt [1] showed that all outerplanar graphs can be realized as Delaunay triangulations of points in convex position. His proof is elementary, constructive and leads to a simple algorithm for obtaining a concrete Delaunay realization. In this note, we provide two new, altern ..."
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Over 20 years ago, Dillencourt [1] showed that all outerplanar graphs can be realized as Delaunay triangulations of points in convex position. His proof is elementary, constructive and leads to a simple algorithm for obtaining a concrete Delaunay realization. In this note, we provide two new
Applicationlayer multicast with Delaunay triangulations
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2002
"... Applicationlayer multicast supports group applications without the need for a networklayer multicast protocol. Here, applications arrange themselves in a logical overlay network and transfer data within the overlay. In this paper, we present an applicationlayer multicast solution that uses a Del ..."
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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 nexthop routing information without requiring a routing protocol in the overlay. A disadvantage of using a Delaunay triangulation is that the mapping
Results 1  10
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1,283