Skip to main content

Generalization of Modified Octrees for Geometric Modeling

  • Chapter
Geometric Modeling: Theory and Practice

Part of the book series: Focus on Computer Graphics ((FOCUS COMPUTER))

Abstract

This paper discusses several aspects of modified octrees that can be generalized in order to obtain solid representations using less primitive elements than the traditional modified octree. The aspects under study include the use of elements of different type as internal nodes, a general refinement approach and cuboids, pyramids, prisms and tetrahedra as final elements. These concepts can be applied to the generation of mixed elements meshes for different applications. In particular, the new ideas are presented here for the generation of mixed element meshes that satisfy Delaunay condition. Examples are given to compare a new implementation with previous approaches.

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 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. M. A. Yerry and S. Shephard, ā€œAutomatic Three-dimensional Mesh Generation by the Modified-Octree Techniqueā€, Int. J. Numer. Methods Eng., vol. 20, pp. 1965ā€“1990, 1984.

    ArticleĀ  MATHĀ  Google ScholarĀ 

  2. M. S. Shephard and M. K. Georges, ā€œAutomatic Three Dimesional Generation by the Finite Octree Techniqueā€, in International Journal for Numerical Methods in Engineering, vol. 32, pp. 709ā€“749, 1991.

    ArticleĀ  MATHĀ  Google ScholarĀ 

  3. R. E. Bank, D. J. Rose, and W. Fichtner, ā€œNumerical methods for semiconductor device simulationā€, IEEE Trans. on El. Dev., vol. ED-30, no. 9, pp. 1031ā€“1041, 1983.

    Google ScholarĀ 

  4. N. Hitschfeld and W. Fichtner, ā€œ3-D Grid Generator for Semiconductor Devices using a fully flexible Refinement Approachā€, in Int. Conf. on Semiconductor Devices and Processes, pub. in Simulation of Semiconductor Devices and Processes, vol. 5, pp. 413ā€“416, Springer-Verlag, 1993.

    Google ScholarĀ 

  5. N. Hitschfeld and R. Farias, ā€œ1-irregular element tessellation in mixed element meshes for the control volume discretization methodā€, in Proceedings of the 5th International Meshing Roundtable, pp. 195ā€“204, Pittsburgh, Pennsylvania, U.S.A., October 10ā€“11, 1996.

    Google ScholarĀ 

  6. N. Hitschfeld, S. MĆ¼ller, and W. Fichtner, ā€œGeneration of 3-d Delaunay Meshes for Complex Geometries using Iterative Refinementā€, Ifip Transactions. Algorithms, Software, Architecture. Information Processing 92., vol. I, pp. 388ā€“394, 1992.

    Google ScholarĀ 

  7. N. Hitschfeld, ā€œAlgorithms and data structures for handling a very flexible refinement approachā€, in Proceedings of the 4th International Meshing Roundtable, pp. 265ā€“276, Sandia National laboratories. Albuquerque, October 1995.

    Google ScholarĀ 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

Ā© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hitschfeld, N. (1997). Generalization of Modified Octrees for Geometric Modeling. In: Strasser, W., Klein, R., Rau, R. (eds) Geometric Modeling: Theory and Practice. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60607-6_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-60607-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61883-6

  • Online ISBN: 978-3-642-60607-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics