Skip to main content

Multiresolution Approximation of Polyhedral Solids

  • Chapter
  • 147 Accesses

Abstracts

Multiresolution models with different levels of detail are a basic tool for handling very large and complex systems in computer aided design applications such as ship design. In this work, we discuss several automatic simplification algorithms that generate a multiresolution family of solid models that approximate with different levels of detail the boundary representation of a given polyhedral solid. Methods based on the simplification of triangular meshes are discussed together with octree based algorithms. Comparison criteria include the possibility of geometry and topology simplification, the availability of approximation bounds and feature preservation.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Ayala, C. Andújar, and P. Brunet. Automatic simplification of orthogonal polyhedra. In D.W. Fellner, editor, Modelling Virtual Worlds Distributed Graphics, pages 137–147.Internationalen Workshop MVD’95, Infix, 1995.

    Google Scholar 

  2. C. Andújar, D. Ayala, P. Brunet, R. Joan-Arinyo, and J. Solé. Automatic generation of multiresolution boundary representations. Computer Graphics Forum, 1996. To appear.

    Google Scholar 

  3. P. Brunet, I. Navazo, and A. Vinacua. A modelling scheme for the approximate representation of closed surfaces. Computing, 8:75–90, 1993.

    Google Scholar 

  4. J. H. Clark. Hierarchical geometric models for visible surface algorithms. Communications of the ACM, 19(10):547–554, 1976.

    Article  MATH  Google Scholar 

  5. M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle. Multiresolution analysis of arbitrary meshes. In R. Cook, editor, Computer Graphics ACM SIGGRAPH 95, pages 173–182, Los Angeles, August 1995.

    Google Scholar 

  6. T. A. Funkhouser and C.H. Sequin. Adaptive display algorithm for interactive frame rates during visualization of complex virtual environments. In Computer Graphics ACM SIGGRAPH 93, pages 247–254, 1993.

    Google Scholar 

  7. M.H. Gross, R. Gatti, and O. Staad. Fast multiresolution surface meshing. In GM. Nielson and D. Silver, editors, Visualization’s, pages 135–142. Atlanta, GA, October 29–November 3 1995.

    Google Scholar 

  8. B. Hamann. Curvature approximation for triangulated surfaces. In G Farin, H. Hagen, H. Noltemeier, and W. Knödel, editors, Geometric Modelling, pages 139–153. Springer, 1993.

    Google Scholar 

  9. B. Hamann. A data reduction scheme for triangulated surfaces. Computer Aided Geometric Design, 11:197–214, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  10. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle. Mesh optimization. In SIGGRAPH’93, Computer Graphics Proceedings, Annual Conference Series, pages 19–26, 1993.

    Google Scholar 

  11. RS. Heckbert and M. Garland. Multiresolution modeling for fast rendering. In Graphics Interfacef94, pages 43–50, 1994.

    Google Scholar 

  12. T. He, L. Hong, A. Kaufman, A. Varshney, and S. Wang. Voxel based object simplification. In GM. Nielson and D. Silver, editors, Visualization’95, pages 296–303, Atlanta, GA, October 29–November 3 1995.

    Google Scholar 

  13. R. Juan–Arinyo and J. Solé. Constructing face octrees from voxel–based volume representations. Computer–Aided Design, 27(10):783–791, 1995.

    Google Scholar 

  14. A.D. Kalvin and R.H. Taylor. Superfaces: Polyhedral approximation with bounded error. In Yongmin Kim, editor, Medical Imaging 1994: Image Capture, Formatting, and Display, pages 12–13, Newport Beach, CA, 1994. Proceedings SPIE 2164.

    Google Scholar 

  15. J.V. Miller, D.E. Breen, W.E. Lorensen, R.M. O’Bara, and M.J.Wozny. Geometrically deformed models: A method for extracting closed geometric models from volume data. Computer Graphics, 25, 4:217–226, 1991.

    Google Scholar 

  16. I. Navazo and S. Vila. Handling very complex environments using a discrete visibility graph. This issue, 1996.

    Google Scholar 

  17. J. Rossignac and P. Borrel. Multiresolution 3D aproximations for rendering complex scenes. In B. Falcidieno and TL. Kunii, editors, Modeling in Computer Graphics, pages 455–465. Springer-Verlag, 1993.

    Google Scholar 

  18. W. J. Schroeder, J. A. Zarge, and W. E. Lorensen. Decimation of triangle meshes. Computer graphics, 26(2):65–70, 1992.

    Google Scholar 

  19. S. Teller and P. Hanrahan. Global visibility algorithms for illumination computations. Computer Graphics Annual Conference Series, pages 239–246, 1993.

    Google Scholar 

  20. G. Turk. Re-tiling polygonal surfaces. Computer Graphics, 26(2):55–64, 1992.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ayala, D., Brunet, P., Joan-Arinyo, R., Navazo, I. (1997). Multiresolution Approximation of Polyhedral Solids. In: Roller, D., Brunet, P. (eds) CAD Systems Development. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60718-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-60718-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64523-5

  • Online ISBN: 978-3-642-60718-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics