Skip to main content

Automatic Extraction of Quadrilateral Patches from Triangulated Surfaces Using Morse Theory

  • Conference paper
Proceedings of the 16th International Meshing Roundtable

Summary

A method for decompose the triangulated surface into quadrilateral patches using Morse theory and Spectral mesh analysis is proposed. The quadrilateral regions extracted are then regularized by means of geodesic curves and fitted using a B-splines creating a new grid on which NURBS surfaces can be fitted.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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. C. Bajaj and D. Schikore. Topology preserving data simplification with error bounds. Computers and Graphics, 22(1):3–12, 1998.

    Article  Google Scholar 

  2. M. Bertram, X. Tricoche, and H. Hagen. Adaptive smooth scattered-data approximation for large-scale terrain visualization. EUROGRAPHICS IEEE TCVG Symposium on Visualization, 2003.

    Google Scholar 

  3. P. Boulanger. Triangulating trimmed nurbs surfaces. Curve and Surface Design, 2000.

    Google Scholar 

  4. P. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci. A topological hierarchy for functions on triangulated surfaces. TVCG 10, 4, 385396, 2004.

    Google Scholar 

  5. S. Dong, P. Bremer, M. Garland, V. Pascucci, and J. Hart. Quadrangulating a mesh using laplacian eigenvectors. Technical Report UIUCDCS-R-2005-2583, 2005.

    Google Scholar 

  6. M. Eck and H. Hoppe. Automatic reconstruction of b-spline surface of arbitrary topological type. ACM-0-89791-747-4, 8, 1996.

    Google Scholar 

  7. H. Edelsbrunner, J. Harer, and A. Zomorodians. Hierarchical morse-smale complexes for piecewise linear 2-manifolds. Discrete Comput. Geom, 30:87–107, 2003.

    MATH  MathSciNet  Google Scholar 

  8. B. Gregorski, B. Hamann, and D. Joy. Reconstruction of b-spline surfaces from scattered data points. Proceedings of Computer Graphics International, 2000.

    Google Scholar 

  9. V. Krishnamurthy and M. Levoy. Fitting smooth surfaces to dense polygon meshes. In SIGGRAPH 96 Conference Proceedings, ACM SIGGRAPH, Addison Wesley, 1996.

    Google Scholar 

  10. C. Loop. Smooth spline surfaces over irregular meshes. Apple Computer Inc., 1994.

    Google Scholar 

  11. X. Ni, M. Garland, and J. Hart. Simplification and repair of polygonal models using volumetric techniques. Proc. SIGGRAPH, TOG 23,3,613-622, 2004.

    Article  Google Scholar 

  12. I. Park, S. Lee, and I. Yun. Constructing nurbs surface model from scattered and unorganized range data. 3dim, 00:0312, 1999.

    Google Scholar 

  13. G. Weber, G. Scheuermann, H. Hagen, and B. Hamann. Exploring scalar fields using critical isovalues. 2002.

    Google Scholar 

  14. A. Yvart, S. Hahmann, and G. Bonneau. Smooth adaptive fitting of 3d models using hierarchical triangular splines. Shape Modelling International, 2005.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Branch, J.W., Prieto, F., Boulanger, P. (2008). Automatic Extraction of Quadrilateral Patches from Triangulated Surfaces Using Morse Theory. In: Brewer, M.L., Marcum, D. (eds) Proceedings of the 16th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75103-8_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75103-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75102-1

  • Online ISBN: 978-3-540-75103-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics