STABBING SIMPLICES OF POINT SETS WITH k-FLATS
نویسندگان
چکیده
منابع مشابه
Stabbing Simplices of Point Sets with k-flats
Let S be a set of n points in Rd in general position. A set H of k-flats is called an mk-stabber of S if the relative interior of any m-simplex with vertices in S is intersected by at least one element of H. In this paper we give lower and upper bounds on the size of minimum mk-stabbers of point sets in Rd and in general position. We study mainly mk-stabbers in the plane and in R3.
متن کاملStabbing simplices by points and flats
The following result was proved by Bárány in 1982: For every d ≥ 1 there exists cd > 0 such that for every n-point set S in R d there is a point p ∈ R contained in at least cdn d+1 −O(n) of the d-dimensional simplices spanned by S. We investigate the largest possible value of cd. It was known that cd ≤ 1/(2(d+ 1)!) (this estimate actually holds for every point set S). We construct sets showing ...
متن کاملLarge simplices determined by finite point sets
Given a set P of n points in R, let d1 > d2 > . . . denote all distinct inter-point distances generated by point pairs in P . It was shown by Schur, Martini, Perles, and Kupitz that there is at most one d-dimensional regular simplex of edge length d1 whose every vertex belongs to P . We extend this result by showing that for any k the number of d-dimensional regular simplices of edge length dk ...
متن کاملPoint Location in Zones of K-flats in Arrangements
Let A( H) be the arrangement of a set H of n hyperplanes in d-space. A k-flat is defined to be a k-dimensional affine subspace of d-space. The zone of a k-flat 1 with respect to H is the closure of all cells in A(H) that intersect I. In this paper we study some problems on zones of k-flats. Our most important result is a data structure for point location in the zone of a k-flat. This structure ...
متن کاملOn k-convex point sets
We extend the (recently introduced) notion of k-convexity of a two-dimensional subset of the Euclidean plane to finite point sets. A set of n points is ∗Corresponding author. Email addresses: [email protected] (Oswin Aichholzer), [email protected] (Franz Aurenhammer), [email protected] (Thomas Hackl), [email protected] (Ferran Hurtado), [email protected] (Alexander Pilz), pedro.ramos@uah...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Computational Geometry & Applications
سال: 2014
ISSN: 0218-1959,1793-6357
DOI: 10.1142/s021819591460005x