Treffer: Line transversals to disjoint balls
Title:
Line transversals to disjoint balls
Authors:
Contributors:
Departement of mathematics, RIDER UNIVERSITY, Effective Geometric Algorithms for Surfaces and Visibility (VEGAS), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)
Source:
23rd Annual ACM Symposium on Computational Geometry 2007 - SoCG'07. :245-254
Publisher Information:
CCSD; ACM Press, 2007.
Publication Year:
2007
Collection:
collection:CNRS
collection:INRIA
collection:INPL
collection:INRIA-LORRAINE
collection:LORIA2
collection:INRIA-NANCY-GRAND-EST
collection:TESTALAIN1
collection:UNIV-LORRAINE
collection:INRIA2
collection:LORIA
collection:INRIA-ETATSUNIS
collection:AM2I-UL
collection:INRIA
collection:INPL
collection:INRIA-LORRAINE
collection:LORIA2
collection:INRIA-NANCY-GRAND-EST
collection:TESTALAIN1
collection:UNIV-LORRAINE
collection:INRIA2
collection:LORIA
collection:INRIA-ETATSUNIS
collection:AM2I-UL
Subject Terms:
lines, geometric transversal theory, disjoint balls, convexity, Hessian, Helly-type theorem, Hadwiger-type theorem, ACM: F.: Theory of Computation, F.2: ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, F.2.2: Nonnumerical Algorithms and Problems, F.2.2.2: Geometrical problems and computations, [INFO.INFO-CG]Computer Science [cs], Computational Geometry [cs.CG]
Subject Geographic:
Original Identifier:
HAL:
Document Type:
Konferenz
conferenceObject<br />Conference papers
Language:
English
Relation:
info:eu-repo/semantics/altIdentifier/doi/10.1145/1247069.1247115
DOI:
10.1145/1247069.1247115
Access URL:
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.inria.00176201v1
Database:
HAL
Weitere Informationen
SESSION: Session 8A
We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$ disjoint balls in $\mathbb{R}^d$. As a consequence, we can improve upon several old and new results on line transversals to disjoint balls in arbitrary dimension, such as bounds on the number of connected components and Helly-type theorems.