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Reliable and Efficient Geometric Computing

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

Abstract

Computing with geometric objects (points, curves, and surfaces) is central for many engineering disciplines and lies at the heart of computer aided design systems. Implementing geometric algorithms is notoriously difficult and most actual implementations are incomplete: they are known to crash or deliver the wrong result on some instances.

In the introductory part of the talk, we illustrate the pitfalls of geometric computing [5] and explain for one algorithm in detail where the problem lies and what goes wrong.

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References

  1. CGAL (Computational Geometry Algorithms Library), http://www.cgal.org

  2. EXACUS (EXAct computation with CUrves and Surfaces) (2003), www.mpi-sb.mpg.de/projects/EXACUS

  3. Fortune, S., van Wyk, C.: Efficient exact integer arithmetic for computational geometry. In: 7th ACM Conference on Computational Geometry, pp. 163–172 (1993)

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  4. Halperin, D., Shelton, C.: A perturbation scheme for spherical arrangements with application to molecular modeling. CGTA: Computational Geometry: Theory and Applications, 10 (1998)

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  5. Kettner, L., Mehlhorn, K., Pion, S., Schirra, S., Yap, C.: Classroom examples of robustness problems in geometric computations. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 702–713. Springer, Heidelberg (2004), www.mpi-sb.mpg.de/~mehlhorn/ftp/ClassRoomExample.ps

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  6. LEDA (Library of Efficient Data Types and Algorithms), http://www.mpi-sb.mpg.de/LEDA/leda.html

  7. Mehlhorn, K., Näher, S.: The LEDA Platform for Combinatorial and Geometric Computing, p. 1018. Cambridge University Press, Cambridge (1999)

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  8. Mehlhorn, K., Osbild, R., Sagraloff, M.: Reliable and Efficient Computational Geometry via Controlled Perturbation. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052. Springer, Heidelberg (2006)

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  9. Yap, C.: Towards exact geometric computation. CGTA: Computational Geometry: Theory and Applications, 7 (1997)

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© 2006 Springer-Verlag Berlin Heidelberg

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Mehlhorn, K. (2006). Reliable and Efficient Geometric Computing. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_2

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  • DOI: https://doi.org/10.1007/11841036_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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