Some Discrete Properties of the Space of Line Transversals to Disjoint Balls
From MaRDI portal
Publication:5188768
DOI10.1007/978-1-4419-0999-2_3zbMath1208.52006OpenAlexW1524788995MaRDI QIDQ5188768
Publication date: 5 March 2010
Published in: Nonlinear Computational Geometry (Search for Journal in Brave)
Full work available at URL: https://hal.inria.fr/inria-00335946/file/Survey-Transversals-to-Balls.pdf
spherelineHelly's theoremgeometric permutationconvexity structuregeometric transversalcone of directionsseparation setpinning configuration
Related Items (3)
Pinning a line by balls or ovaloids in \(\mathbb R^{3}\) ⋮ Helly’s theorem: New variations and applications ⋮ Lower bounds to Helly numbers of line transversals to disjoint congruent balls
Cites Work
- No Helly theorem for stabbing translates by lines in \(\mathbb{R}^3\)
- A generalization of Hadwiger's transversal theorem to intersecting sets
- Upper bounds on geometric permutations for convex sets
- The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n-2
- Über ein Problem aus der kombinatorischen Geometrie
- On common transversals
- Geometric permutations and common transversals
- Geometric permutations of disjoint translates of convex sets
- Small-dimensional linear programming and convex hulls made easy
- The different ways of stabbing disjoint convex sets
- Proof of Grünbaum's conjecture on common transversals for translates
- Line transversals of balls and smallest enclosing cylinders in three dimensions
- Helly-type theorems and generalized linear programming
- A Helly-type theorem for unions of convex sets
- Geometric permutations of balls with bounded size disparity.
- On neighbors in geometric permutations.
- A constant bound for geometric permutations of disjoint unit balls
- A Helly-type theorem for line transversals to disjoint unit balls
- Multivariate regression depth
- Geometric permutations of disjoint unit spheres
- Polyhedral line transversals in space
- Efficient algorithm for transversal of disjoint convex polygons.
- Geometric permutations of higher dimensional spheres
- Bounding the piercing number
- A short proof of an interesting Helly-type theorem
- Sharp bounds on geometric permutations of pairwise disjoint balls in \(\mathbb{R}^d\)
- Line transversals to disjoint balls
- Helly-type theorems for line transversals to disjoint unit balls
- The envelope of lines meeting a fixed line and tangent to two spheres
- Forbidden families of geometric permutations in \(\mathbb R^{d}\)
- The maximal number of geometric permutations for \(n\) disjoint translates of a convex set in \(\mathbb R\) is \(\Omega(n)\)
- A Helly-type transversal theorem for \(n\)-dimensional unit balls
- Geometric permutations induced by line transversals through a fixed point
- On the complexity of some geometric problems in unbounded dimension
- COMPUTING SHORTEST TRANSVERSALS OF SETS
- Common Transversals for Families of Sets†
- On Components in Some Families of Sets
- An on-line algorithm for fitting straight lines between data ranges
- Regression Depth
- The Partition Technique for Overlays of Envelopes
- Foundations of a theory of convexity on affine Grassmann manifolds
- A combinatorial bound for linear programming and related problems
- New results on shortest paths in three dimensions
- Hadwiger and Helly-type theorems for disjoint unit spheres in R 3
- Cremona convexity, frame convexity and a theorem of Santaló
- Helly Type Theorems Derived From Basic Singular Homology
- Spherical Theorems of Helly Type and Congruence Indices of Spherical Caps
- Algorithms - ESA 2003
- Computational line geometry
- The triples of geometric permutations for families of disjoint translates
- A tight bound on the number of geometric permutations of convex fat objects in \(\mathbb{R}^d\)
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Some Discrete Properties of the Space of Line Transversals to Disjoint Balls
