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» Distinct distances in three and higher dimensions
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STOC
2003
ACM
117views Algorithms» more  STOC 2003»
10 years 7 months ago
Distinct distances in three and higher dimensions
Improving an old result of Clarkson et al., we show that the number of distinct distances determined by a set P of n points in three-dimensional space is (n77/141) = (n0.546 ), fo...
Boris Aronov, János Pach, Micha Sharir, G&a...
COMPGEOM
2010
ACM
10 years 2 days ago
Incidences in three dimensions and distinct distances in the plane
d Abstract] György Elekes Eötvös University Micha Sharir Tel Aviv University and New York University We first describe a reduction from the problem of lower-bounding the numbe...
György Elekes, Micha Sharir
CCCG
2008
9 years 8 months ago
On distinct distances among points in general position and other related problems
A set of points in the plane is said to be in general position if no three of them are collinear and no four of them are cocircular. If a point set determines only distinct vector...
Adrian Dumitrescu
AUTOMATICA
2007
88views more  AUTOMATICA 2007»
9 years 7 months ago
Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence
In this paper, we generalize the notion of persistence, which has been originally introduced for two-dimensional formations, to Rd for d 3, seeking to provide a theoretical framew...
Changbin Yu, Julien M. Hendrickx, Baris Fidan, Bri...
SMA
2006
ACM
101views Solid Modeling» more  SMA 2006»
10 years 28 days ago
A higher dimensional formulation for robust and interactive distance queries
We present an efficient and robust algorithm for computing the minimum distance between a point and freeform curve or surface by lifting the problem into a higher dimension. This...
Joon-Kyung Seong, David E. Johnson, Elaine Cohen
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