Discrete & Computational Geometry

, 42:740

Uniqueness in Discrete Tomography of Delone Sets with Long-Range Order

Article

DOI: 10.1007/s00454-009-9213-z

Cite this article as:
Huck, C. Discrete Comput Geom (2009) 42: 740. doi:10.1007/s00454-009-9213-z

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.

Keywords

Discrete tomographyDiscrete parallel X-rayU-polygonAlgebraic Delone setp-adic valuationCyclotomic model set

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Fakultät für Mathematik, Universität BielefeldBielefeldGermany
  2. 2.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUK