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Generalized Maps in Geological Modeling: Object-Oriented Design of Topological Kernels

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Advances in Software Tools for Scientific Computing

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 10))

Abstract

A boundary based topological representation technique known as generalized maps is presented and applied to modeling the topology of complex geological structures. Extensions of this concept for capturing geologists’ needs for specifying topological relationship information between topological cells are suggested. Object-oriented design of topological kernels based on generalized maps is given and issues of implementation in C++ are discussed. Examples of applications are presented for modeling the topology of surface triangulations and geological fault networks.

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References

  1. E. Arge. Siscat triangulation, ideas for new design. Technical report, Numerical Objects AS, 1997.

    Google Scholar 

  2. B. Baumgart. A polyhedron representation for computer vision. In AFIPS National Conference 44, pages 589–596, 1975.

    Google Scholar 

  3. Y. Bertrand and J.-F. Dufourd. Algebraic specification of a 3d-modeller based on hypermaps. Graphical Models and Image Processing, 56(1):29–60, 1994.

    Article  Google Scholar 

  4. The CAS.CADE web site. World Wide Web document at http://www.matra-datavision.com/gb/products/cascade/

  5. J.-F. Dufourd. Formal specification of topological subdivisions using hyper-maps. Computer Aided Design, 23(2):99–116, 1991.

    Article  MATH  Google Scholar 

  6. M. S. Floater, Y. Halbwachs, ø.Hjelle, and M. Reimers. OMEGA: A CAD-based approach to geological modelling. In COCAD ENSG Conference, 3D Modeling of Natural Objects: A Challenge for the 2000’s, E.N.S. Géologie, Nancy, France, 1998.

    Google Scholar 

  7. The Gocad Web Site. World Wide Web document at http://www.ensg.u-nancy.fr/COCAD/gocad.html.

    Google Scholar 

  8. Y. Halbwachs, G. Courrioux, X. Renaud, and P. Repusseau. Topological and geometric characterization of fault networks using 3-dimensional generalized maps. Mathematical Geology, 28(5):625–656, 1996.

    Article  Google Scholar 

  9. .ø.Hjelle. Data structures in siscat. Report STF42 A96007, SINTEF Applied Mathematics, 1996.

    Google Scholar 

  10. P. Lienhardt. Subdivision of n-dimensional spaces and n-dimensional generalized maps. In 5th ACM Symposium on Computational Geometry, pages 228236, Saarbrucken, Germany, 1989.

    Google Scholar 

  11. P. Lienhardt. Topological models for boundary representation: A comparison with n-dinensional generalized maps. Computer-Aided Design, 23(1):59–82, 1991.

    Article  MATH  Google Scholar 

  12. P. Lienhardt. N-dimensional generalized maps and cellular quasi-manifolds. Intern. Jour. Computational Geometry and Applications, 4(3):275–324, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. A. Mchugh. Algorithmic Graph Theory.Prentice-Hall Inc., 1990.

    Google Scholar 

  14. The Siscat Home Page. World Wide Web document at http://www.oslo.sintef.no/siscat

  15. B. L. Stephane Contreaux and J.-L. Mallet. A celluar topological model based on generalized maps: The GOCAD approach. In GOCAD ENSG Conference. 3D Modelling of Natural Objects: A Challenge for the 2000’s, Nancy, 1998.

    Google Scholar 

  16. W. T. Tutte. Graph Theory, volume 21 of Encyclopedia of Mathematics and its Applications.Addison-Wesley, Reading, MA., 1984.

    Google Scholar 

  17. K. Weiler. Edge based data structures for solid modeling in curved-surface environments. IEEE Computer Graphics and Applications, 5(1):21–40, 1985.

    Article  Google Scholar 

  18. K. Weiler. Topological Structures for Geometric Modeling.PhD thesis, Rensselaer Polytechnic Institute, 1986.

    Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Halbwachs, Y., Hjelle, Ø. (2000). Generalized Maps in Geological Modeling: Object-Oriented Design of Topological Kernels. In: Langtangen, H.P., Bruaset, A.M., Quak, E. (eds) Advances in Software Tools for Scientific Computing. Lecture Notes in Computational Science and Engineering, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57172-5_11

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  • DOI: https://doi.org/10.1007/978-3-642-57172-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66557-1

  • Online ISBN: 978-3-642-57172-5

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