Skip to main content

A Hole-filling Algorithm Using Non-uniform Rational B-splines

  • Conference paper
Proceedings of the 16th International Meshing Roundtable

Abstract

A three-dimensional (3D) geometric model obtained from a 3D device or other approaches is not necessarily watertight due to the presence of geometric deficiencies. These inadequacies must be repaired to create a valid surface mesh on the model as a pre-process of computational engineering analyses. This procedure has been a tedious and labor-intensive step, as there are many kinds of deficiencies that can make the geometry to be nonwatertight, such as gaps and holes. It is still challenging to repair discrete surface models based on available geometric information. The focus of this paper is to develop a new automated method for patching holes on the surface models in order to achieve watertightness. It describes a numerical algorithm utilizing Non-Uniform Rational B-Splines (NURBS) surfaces to generate smooth triangulated surface patches for topologically simple holes on discrete surface models. The Delaunay criterion for point insertion and edge swapping is used in this algorithm to improve the outcome. Surface patches are generated based on existing points surrounding the holes without altering them. The watertight geometry produced can be used in a wide range of engineering applications in the field of computational engineering simulation studies.

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. Barequet, G. and Sharir M., “Filling Gaps in the Boundary of a Polyhedron,” Computer Aided Geometric Design, Vol. 12, 1995, pp. 207-229.

    Article  MATH  MathSciNet  Google Scholar 

  2. Barequet, G. and Kumar, S., “Repairing CAD Models,” Proceedings of IEEE Visualization 1997, 1997, pp. 363-370.

    Google Scholar 

  3. Lee, Y. K., Lim, C. K., Ghazialam, H., Vardhan, H. and Eklund, E., “Surface Mesh Generation for Dirty Geometries by Shrink Wrapping using Cartesian Grid Approach,” Proceedings of the 15th International Meshing Roundtable, Springer, 2006, pp. 393-410.

    Google Scholar 

  4. Jun, Y., “A Piecewise Hole Filling Algorithm in Reverse Engineering,” Computer-Aided Design, Vol. 37, 2005, pp. 263-270.

    Article  Google Scholar 

  5. Davis, J., Marschner, S. R., Garr, M. and Levoy, M., “Filling Holes in Complex Surfaces using Volumetric Diffusion,” Proceedings of First International Symposium on 3D Data Processing, Visualization, Transmission, 2002, pp. 428-861.

    Google Scholar 

  6. Curless, B. and Levoy M., “A Volumetric Method for Building Complex Models from Range Images,” Computer Graphics, Vol. 30, 1996, pp. 303-312.

    Google Scholar 

  7. Ju, T., “Robust Repair of Polygonal Models,” Proceedings of ACM SIGGRAPH, 2004 ACM Transactions on Graphics, Vol. 23, pp. 888-895.

    Google Scholar 

  8. Liepa, P., “Filling Holes in Meshes,” Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry processing, Eurographics Association, 2003, pp. 200-205.

    Google Scholar 

  9. Kobbelt, L. P., Vorsatz, J., Ulf, L. and Seidel, H.-P., “A Shrink Wrapping Approach to Remeshing Polygonal Surfaces,” Computer Graphics Forum (Eurographics 99), Vol. 18, 1999, pp. 119-130.

    Article  Google Scholar 

  10. Bruno, L., “Dual Domain Extrapolation,” ACM Transactions on Graphics (SIGGRAPH), Vol. 22, 2003, pp. 364-369.

    Article  Google Scholar 

  11. Branch, J., Prieto, F. and Boulanger, P., “A Hole-Filling Algorithm for Triangular Meshes using Local Radial Basis Function,” Proceedings of the 15th International Meshing Roundtable, Springer, 2006, pp. 411-431.

    Google Scholar 

  12. Kumar, A., “Hole Patching in 3D Unstructured Surface Mesh,” Masters Thesis, University of Alabama at Birmingham, Birmingham, AL, May 2007.

    Google Scholar 

  13. Piegel, L. A. and Tiller, W., The NURBS Book, 2nd ed., Springer, Berlin, 1996.

    Google Scholar 

  14. Lorenson, W. E. and Cline, H. E., “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics, Vol. 21, 1987, pp. 163-169.

    Article  Google Scholar 

  15. Visualization ToolKit (VTK), http://www.vtk.org/.

    Google Scholar 

  16. Ito, Y., Shum, P. C., Shih, A. M., Soni, B. K. and Nakahashi, K., “Robust Generation of High-Quality Unstructured Meshes on Realistic Biomedical Geometry,” International Journal for Numerical Methods in Engineering, Vol. 65, Issue 6, 2006, pp. 943-973.

    Google Scholar 

  17. Yoo, T. S., Insight into Images. Principles and Practice for Segmentation, Registration, and Image Analysis, A K Peters, Wellesley, MA, 2004.

    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

Kumar, A., Shih, A., Ito, Y., Ross, D., Soni, B. (2008). A Hole-filling Algorithm Using Non-uniform Rational B-splines. 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_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75103-8_10

  • 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