Intersections of translates of convex bodies
نویسندگان
چکیده
منابع مشابه
Pairs of Convex Bodies with Centrally Symmetric Intersections of Translates
For a pair of convex bodies K and K ′ in Ed , the d-dimensional intersections K ∩ (x + K ′), x ∈ Ed , are centrally symmetric if and only if K and K ′ are represented as direct sums K = R ⊕ P and K ′ = R′ ⊕ P ′ such that: (i) R is a compact convex set of some dimension m, 0 ≤ m ≤ d, and R′ = z − R for a suitable vector z ∈ Ed , (ii) P and P ′ are isothetic parallelotopes, both of dimension d − m.
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We show that the visibility graph of a set of non-intersecting translates of the same compact convex object in R always contains a Hamiltonian path. Furthermore, we show that every other edge in the Hamiltonian path can be used to obtain a perfect matching that is realized by a set of non-intersecting lines of sight. ? 2001 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1956
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10456