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» On the Geometric Dilation of Finite Point Sets
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CCCG
2009
15 years 24 days ago
On the Dilation of Delaunay Triangulations of Points in Convex Position
Let S be a finite set of points in the Euclidean plane, and let E be the complete graph whose point-set is S. Chew, in 1986, proved a lower bound of /2 on the stretch factor of th...
Shiliang Cui, Iyad A. Kanj, Ge Xia
94
Voted
GD
2006
Springer
15 years 3 months ago
The Number of Triangulations on Planar Point Sets
We give a brief account of results concerning the number of triangulations on finite point sets in the plane, both for arbitrary sets and for specific sets such as the n
Emo Welzl
82
Voted
CCCG
2010
15 years 1 months ago
Coloring geometric hypergraph defined by an arrangement of half-planes
We prove that any finite set of half-planes can be colored by two colors so that every point of the plane, which belongs to at least three half-planes in the set, is covered by ha...
Radoslav Fulek
CORR
2008
Springer
151views Education» more  CORR 2008»
14 years 11 months ago
Geometric Set Cover and Hitting Sets for Polytopes in $R^3$
Suppose we are given a finite set of points P in R3 and a collection of polytopes T that are all translates of the same polytope T. We consider two problems in this paper. The firs...
Sören Laue
CG
2004
Springer
14 years 11 months ago
Surface processing methods for point sets using finite elements
We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based process...
Ulrich Clarenz, Martin Rumpf, Alexandru Telea