Discrete tomography of planar model sets

Acta Crystallographica Section A: Foundations of Crystallography

Volumn 62, Issue 6, 2006, Pages 419-433

  Baake, Michael ^a   Gritzmann, Peter ^b   Huck, Christian ^a   Langfeld, Barbara ^b   Lord, Katja ^b  

^a BIELEFELD UNIVERSITY   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Planar model sets; Tomography

Indexed keywords

EID: 33750372852     PISSN: 01087673     EISSN: 16005724     Source Type: Journal    
DOI: 10.1107/S0108767306030091     Document Type: Article

References (40)

1. Agarwal, P. K. & Sharir, M. (2000). Handbook of Computational Geometry, edited by J.-R. Sack & J. Urrutia, pp. 49-119. Amsterdam: North-Holland.
2. Alpers, A. & Gritzmann, P. (2006). SIAM J. Discrete Math. 20, 227-239.
3. Alpers, A., Gritzmann, P. & Thorens, L. (2001). Digital and Image Geometry, edited by G. Bertrand, A. Imiya & R. Klette, pp. 175-186. Lecture Notes in Computer Science, Vol. 2243. Berlin: Springer.
4. Ammann, R., Grünbaum, B. & Shephard, G. C. (1992). Discrete Comput. Geom. 8, 1-25.
5. Baake, M. (2002). Quasicrystals. An Introduction to Structure, Physical Properties, and Applications, edited by J.-B. Suck, M. Schreiber & P. Häussler, pp. 17-48. Berlin: Springer. http:// www.arxiv.org/math-ph/ 9901014.
6. Baake, M. & Grimm, U. (2004). Z. Kristallogr. 219, 72-80. http:// www.arxiv.org/math.CO/0301021.
7. Baake, M., Grimm, U. & Moody, R. V. (2002). Preprint. http:// www.arxiv.org/math.HO/0203252.
8. Baake, M. & Joseph, D. (1990). Phys. Rev. B, 42, 8091-8102.
9. Baake, M., Kramer, P., Schlottmann, M. & Zeidler, D. (1990a). Mod. Phys. Lett. B4, 249-258.
10. Baake, M., Kramer, P., Schlottmann, M. & Zeidler, D. (1990b). Int. J. Mod. Phys. B4, 2217-2268.
11. Baake, M. & Moody, R. V. (2000). Editors. Directions in Mathematical Quasicrystals. CRM Monograph Series, Vol. 13. Providence, RI: American Mathematical Society.
12. Basu, S., Pollack, R. & Roy, M.-F. (1996). J. ACM, 43, 1002-1045.
13. Basu, S., Pollack, R. & Roy, M.-F. (1997). J. Complexity, 13, 28-37.
14. Borevich, Z. I. & Shafarevich, I. R. (1966). Number Theory. New York: Academic Press.
15. Buchberger, B., Collins, G. E. & Loos, R. (1982). Editors. Computing Supplementum. Wien: Springer.
16. Cowley, J. M. (1995). Diffraction Physics. Amsterdam: North-Holland.
17. Edelsbrunner, H. (1987). Algorithms in Combinatorial Geometry. EATCS Monographs on Theoretical Computer Science, Vol. 10. Berlin: Springer.
18. Edelsbrunner, H., O'Rourke, J. & Seidel, R. (1986). SIAM J. Comput. 15, 341-363.
19. Fewster, P. F. (2003). X-ray Scattering from Semiconductors, 2nd ed. London: Imperial College Press.
20. Gähler, F. (1993). J. Non-Cryst. Solids, 153-154, 160-164.
21. Gardner, R. J. & Gritzmann, P. (1997). Trans. Am. Math. Soc. 349, 2271-2295.
22. Gardner, R. J., Gritzmann, P. & Prangenberg, D. (1999). Discrete Math. 202, 45-71.
23. Gritzmann, P. (1997). Lecture Notes in Computer Science, edited by E. Ahronovitz & C. Fiorio, pp. 19-32. London: Springer.
24. Gritzmann, P., Prangenberg, D., de Vries, S. & Wiegelmann, M. (1998). Int. J. Imaging Syst. Technol. 9, 101-109.
25. Gritzmann, P., de Vries, S. & Wiegelmann, M. (2000). SIAM J. Optim. 11, 522-546.
26. Guinier, A. (1994). X-ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies. New York: Dover.
27. Halperin, D. (2004). Handbook of Discrete and Computational Geometry, 2nd ed., edited by J. Goodman & J. O'Rourke, pp. 529-562. Boca Raton, FL: Chapman and Hall/CRC.
28. Herman, G. T. & Kuba, A. (1999). Editors. Discrete Tomography: Foundations, Algorithms, and Applications. Boston: Birkhäuser.
29. Huck, C. (2006). Preprint. Uniqueness in discrete tomography of planar model sets.
30. Kisielowski, C., Schwander, P., Baumann, F. H., Seibt, M., Kim, Y. & Ourmazd, A. (1995). Ultramicroscopy, 58, 131-155.
31. Lang, S. (1993). Algebra, 3rd ed. Reading, MA: Addison-Wesley.
32. Moody, R. V. (2000). From Quasicrystals to More Complex Systems, edited by F. Axel, F. Dénoyer & J.-P. Gazeau, pp. 145-166. Les Ulis: EDP Sciences; Berlin: Springer. http://www.arxiv.org/math.MG/0002020.
33. Pleasants, P. A. B. (2000). Directions in Mathematical Quasicrystals, edited by M. Baake & R. V. Moody, pp. 95-141. CRM Monograph Series, Vol. 13. Providence, RI: American Mathematical Society.
34. Preparata, F. P. & Shamos, M. I. (1985). Computational Geometry: An Introduction. New York: Springer.
35. Schlottmann, M. (1998). Quasicrystals and Discrete Geometry, edited by J. Patera, pp. 247-264. Fields Institute Monographs, Vol. 10. Providence, RI: American Mathematical Society.
36. Schlottmann, M. (2000). Directions in Mathematical Quasicrystals, edited by M. Baake & R. V. Moody, pp. 143-159. CRM Monograph Series, Vol. 13. Providence, RI: American Mathematical Society.
37. Schwander, P., Kisielowski, C., Seibt, M., Baumann, F. H., Kim, Y. & Ourmazd, A. (1993). Phys. Rev. Lett. 71, 4150-4153.
38. Slump, C. H. & Gerbrands, J. J. (1982). Comput. Graphics Image Process. 18, 18-36.
39. Steurer, W. (2004). Z. Kristallogr. 219, 391-446.
40. Washington, L. C. (1997). Introduction to Cyclotomic Fields, 2nd ed. New York: Springer.