Skip to main content
SpringerLink
Log in

A Polyhedral Approach to Surface Reconstruction from Planar Contours

  • Conference paper
  • First Online:
Book cover Integer Programming and Combinatorial Optimization (IPCO 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2337))

  • 1451 Accesses

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.

Research partially supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ABACUS-A Branch And CUt System. http://www.informatik.uni-koeln.de/ls_juenger/projects/abacus.html.

  2. Dr. Gill Barequet’s home page. http://www.cs.technion.ac.il/barequet/.

  3. CGAL-Computational Geometry Algorithms Library. http://www.cgal.org.

  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. CPLEX. http://www.cplex.com.

  6. C. Fink. Oberflächenrekonstruktion von planaren Konturen. Master’s thesis, Universität des Saarlandes, 2001.

    Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  9. V. Kann. Maximum bounded 3-dimensional matching is MAXSNP-complete. Information Processing Letters, 37:27–35, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Keppel. Approximating complex surfaces by triangulation of contour lines. IBM J. of Research and Development, 19:2–11, 1975.

    Article  MathSciNet  MATH  Google Scholar 

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

  12. SCIL-Symbolic Constraints for Integer Linear programming. http://www.mpi-sb.mpg.de/SCIL.

  13. SoPlex. http://www.zib.de/Optimization/Software/Soplex.

  14. Laurence A. Wolsey. Integer programming. Wiley-interscience series in discrete mathematics and optimization. Wiley & Sons, New York, 1998.

    MATH  Google Scholar 

  15. XPRESS. http://www.dash.co.uk/.

Download references

Author information

Authors and Affiliations

  1. International Computer Science Institute, 1947 Center St., Suite 600, Berkeley, CA, 94704-1198, USA

    Ernst Althaus

  2. Max-Planck-Institute für Informatik, Im Stadtwald, 66123, Saarbrücken

    Christian Fink

Authors
  1. Ernst Althaus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Fink
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Program in Applied and Computational Mathematics, University of Princeton, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    William J. Cook

  2. Sloan School of Management, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Andreas S. Schulz

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Althaus, E., Fink, C. (2002). A Polyhedral Approach to Surface Reconstruction from Planar Contours. In: Cook, W.J., Schulz, A.S. (eds) Integer Programming and Combinatorial Optimization. IPCO 2002. Lecture Notes in Computer Science, vol 2337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47867-1_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-47867-1_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43676-8

  • Online ISBN: 978-3-540-47867-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation