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...
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 ...
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...
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 ...
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...