Discrete tomography of planar model sets
Michael Baake1, Peter Gritzmann, Christian Huck
1Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany. mbaake@math.uni-bielefeld.de
Acta Crystallographica. Section A, Foundations of Crystallography
|October 24, 2006
Summary
Researchers developed an efficient discrete tomography approach for mathematical quasicrystals. This method introduces cyclotomic model sets, addressing key problems in their reconstruction and uniqueness.
Area of Science:
- Mathematical Physics
- Crystallography
- Discrete Geometry
Background:
- Discrete tomography is established for periodic systems.
- Investigating finite point sets requires specialized methods.
- Quasicrystals present unique structural challenges.
Purpose of the Study:
- To develop an efficient discrete tomography approach for mathematical quasicrystals.
- Introduce and analyze cyclotomic model sets.
- Address consistency, reconstruction, and uniqueness problems.
Main Methods:
- Introduction of the cyclotomic model set class.
- Analysis of consistency conditions for these sets.
- Development of reconstruction and uniqueness algorithms.
Main Results:
- A novel framework for discrete tomography of quasicrystals.
- Defined properties of cyclotomic model sets.
- Established conditions for unique reconstruction.
Conclusions:
- The proposed method offers an efficient approach for quasicrystal analysis.
- Cyclotomic model sets provide a tractable model for discrete tomography.
- This work lays the foundation for further research in quasicrystal structure determination.
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