Huck, Christian
(2009).
Uniqueness in discrete tomography of Delone sets with long-range order.
Discrete and Computational Geometry, 42(4),
pp. 740–758.
Abstract
We address the problem of determining finite subsets of Delone sets Λ⊂ℝd with long-range order by X-rays in prescribed Λ-directions, i.e., directions parallel to nonzero interpoint vectors of Λ. Here, an X-ray in direction u of a finite set gives the number of points in the set on each line parallel to u. For our main result, we introduce the notion of algebraic Delone sets Λ⊂ℝ2 and derive a sufficient condition for the determination of the convex subsets of these sets by X-rays in four prescribed Λ-directions.
| Item Type: |
Journal Article
|
| Copyright Holders: |
2009 Springer Science+Business Media, LLC |
| ISSN: |
1432-0444 |
| Funders: |
Engineering and Physical Sciences Research Council [grant number EP/D058465/1] |
| Keywords: |
discrete tomography; discrete parallel X-ray; U-polygon; algebraic Delone set; p-adic valuation; cyclotomic model set |
| Academic Unit/Department: |
Mathematics, Computing and Technology > Mathematics and Statistics |
| Item ID: |
23206 |
| Depositing User: |
Uwe Grimm
|
| Date Deposited: |
21 Sep 2010 13:11 |
| Last Modified: |
23 Oct 2012 14:35 |
| URI: |
http://oro.open.ac.uk/id/eprint/23206 |
Actions (login may be required)
