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