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A Polyhedral Approach to Surface Reconstruction from Planar Contours

  • Ernst Althaus
  • Christian Fink
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2337)

Abstract

We investigate the problem of reconstruction a surface given its contours on parallel slices. We present a branch-and-cut algorithm which computes the surface with the minimal area. This surface is assumed to be the best reconstruction since a long time. Nevertheless there were no algorithms to compute this surface. Our experiments show that the running time of our algorithm is very reasonable and that the computed surfaces are highly similar to the original surfaces.

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References

  1. 1.
  2. 2.
    Dr. Gill Barequet’s home page. http://www.cs.technion.ac.il/barequet/.
  3. 3.
    CGAL-Computational Geometry Algorithms Library. http://www.cgal.org.
  4. 4.
    Siu-Wing Cheng and Tamal K. Dey. Improved constructions of delaunay based contour surfaces. In Proceedings of the ACM Symposium on Solid Modeling and Applications, pages 322–323, 1999.Google Scholar
  5. 5.
  6. 6.
    C. Fink. Oberflächenrekonstruktion von planaren Konturen. Master’s thesis, Universität des Saarlandes, 2001.Google Scholar
  7. 7.
    H. Fuchs, Z. M. Kedem, and S. P. Uselton. Optimal surface reconstruction from planar contours. Graphics and Image Processing, 20(10):693–702, 1977.MathSciNetzbMATHGoogle Scholar
  8. 8.
    M. Hong, T.W. Sederberg, K.S. Klimaszewski, and K. Kaneda. Triangulation of branching contours using area minimization. International Journal of Computational Geometry & Applications, 8(4):389–406, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    V. Kann. Maximum bounded 3-dimensional matching is MAXSNP-complete. Information Processing Letters, 37:27–35, 1991.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    E. Keppel. Approximating complex surfaces by triangulation of contour lines. IBM J. of Research and Development, 19:2–11, 1975.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    LEDA (Library of Efficient Data Types and Algorithms). http://www.mpi-sb.mpg.de/LEDA/leda.html.
  12. 12.
    SCIL-Symbolic Constraints for Integer Linear programming. http://www.mpi-sb.mpg.de/SCIL.
  13. 13.
  14. 14.
    Laurence A. Wolsey. Integer programming. Wiley-interscience series in discrete mathematics and optimization. Wiley & Sons, New York, 1998.zbMATHGoogle Scholar
  15. 15.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ernst Althaus
    • 1
  • Christian Fink
    • 2
  1. 1.International Computer Science InstituteBerkeleyUSA
  2. 2.Max-Planck-Institute für InformatikSaarbrücken

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