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CCCG
2009
13 years 6 months ago
Every Large Point Set contains Many Collinear Points or an Empty Pentagon
We prove the following generalised empty pentagon theorem: for every integer 2, every sufficiently large set of points in the plane contains collinear points or an empty pentagon...
Zachary Abel, Brad Ballinger, Prosenjit Bose, S&ea...
3DPVT
2006
IEEE
189views Visualization» more  3DPVT 2006»
13 years 11 months ago
Fast Safe Spline Surrogates for Large Point Clouds
To support real-time computation with large, possibly evolving point clouds and range data, we fit a trimmed uniform tensor-product spline function from one direction. The graph ...
Ashish Myles, Jörg Peters
MLDM
2005
Springer
13 years 10 months ago
Clustering Large Dynamic Datasets Using Exemplar Points
In this paper we present a method to cluster large datasets that change over time using incremental learning techniques. The approach is based on the dynamic representation of clus...
William Sia, Mihai M. Lazarescu
COMPGEOM
2010
ACM
13 years 10 months ago
Points with large quadrant-depth
We characterize the set of all pairs (a, b) such that for every set P of n points in general position in R2 there always exists a point p ∈ P and two opposite quadrants determin...
Roel Apfelbaum, Itay Ben-Dan, Stefan Felsner, Rom ...
SIAMDM
2010
123views more  SIAMDM 2010»
13 years 3 months ago
Large Bichromatic Point Sets Admit Empty Monochromatic 4-Gons
We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES (k) such that any set S of at least fES (k) points in general posit...
Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Fe...