Skip to main content
SpringerLink
Log in

Compact Combinatorial Maps in 3D

  • Conference paper
Book cover Computational Visual Media (CVM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7633))

Included in the following conference series:

Abstract

We propose a compact data structure for volumetric meshes of arbitrary topology and bounded valence, which offers cell-face, face-edge, and edge-vertex incidence queries in constant time. Our structure is simple to implement, easy to use, and allows for arbitrary, user-defined volume cells, while remaining very efficient in memory usage compared to previous work.

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 72.00
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. Alumbaugh, T.J., Jiao, X.: Compact Array-Based Mesh Data Structures. In: Hanks, B.W. (ed.) Engineering, IMR 2005, pp. 485–503. Springer, Heidelberg (2005)

    Google Scholar 

  2. Sieger, D., Botsch, M.: Design, Implementation, and Evaluation of the Surface Mesh Data Structure. In: Quadros, W.R. (ed.) Proceedings of the 20th International Meshing Roundtable, vol. 90, pp. 533–550. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Serna, S.P., Stork, A., Fellner, D.W.: Considerations toward a Dynamic Mesh Data Structure. In: SIGRAD Conference, pp. 83–90 (2011)

    Google Scholar 

  4. Tautges, T.J., Blacker, T., Mitchell, S.A.: The Whisker Weaving Algorithm: a Connectivity-Based Method for Constructing All-Hexahedral Finite Element Meshes. Int. J. for Numer. Methods in Eng. 39(19), 3327–3349 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Murdoch, P.: The spatial twist continuum: A connectivity based method for representing all-hexahedral finite element meshes. Finite Elements in Analysis and Design 28(2), 137–149 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Guibas, L., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of voronoi. ACM Trans. Graph. 4(2), 74–123 (1985)

    Article  MATH  Google Scholar 

  7. Brisson, E.: Representing geometric structures in d dimensions: topology and order. In: Proceedings of the Fifth Annual Symposium on Computational Geometry, SCG 1989, vol. 9, pp. 218–227. ACM Press (1989)

    Google Scholar 

  8. Edmonds, J.R.: A combinatorial representation for polyhedral surfaces. Notices Amer. Math. Soc. 7, 646 (1960)

    Google Scholar 

  9. Beall, M.W., Shephard, M.S.: A general topology-based mesh data structure. Int. J. for Numer. Methods in Eng. 40(9), 1573–1596 (1997)

    Article  MathSciNet  Google Scholar 

  10. Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design 23(1), 59–82 (1991)

    Article  MATH  Google Scholar 

  11. Prat, S., Gioia, P., Bertrand, Y.: Connectivity compression in an arbitrary dimension. The Visual Computer 21(8-10), 876–885 (2005)

    Article  Google Scholar 

  12. Blandford, D.K., Blelloch, G.E., Cardoze, D.E., Kadow, C.: Compact Representations of Simplicial Meshes in Two and Three Dimensions. International Journal of Computational Geometry and Applications 15(1), 3–24 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Celes, W., Paulino, G.H., Espinha, R.: A compact adjacency-based topological data structure for finite element mesh representation. International Journal for Numerical Methods in Engineering 64(11), 1529–1556 (2005)

    Article  MATH  Google Scholar 

  14. Damiand, G.: Combinatorial maps. In: CGAL User and Reference Manual, 4.0 edn., CGAL Editorial Board (2012)

    Google Scholar 

  15. OVM: OpenVolumeMesh - A Generic and Versatile Index-Based Data Structure for Polytopal Meshes (2012), http://www.openvolumemesh.org/

  16. Botsch, M., Steinberg, S., Bischoff, S., Kobbelt, L.: OpenMesh - a generic and efficient polygon mesh data structure. Structure (2002)

    Google Scholar 

  17. Kirk, B.S., Peterson, J.W., Stogner, R.H., Carey, G.F.: libmesh: a c++ library for parallel adaptive mesh refinement/coarsening simulations. Eng. with Comput. 22(3), 237–254 (2006)

    Article  Google Scholar 

  18. CGoGN: Combinatorial and Geometric modeling with Generic N-dimensional Maps (2012), http://cgogn.u-strasbg.fr/Wiki/index.php/CGoGN

  19. Dobkin, D.P., Laszlo, M.J.: Primitives for the manipulation of three-dimensional subdivisions. In: Proceedings of the third annual Symposium on Computational Geometry, SCG 1987, pp. 86–99. ACM, New York (1987)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Michigan State University, USA

    Xin Feng, Yuanzhen Wang & Yiying Tong

  2. Zhejiang University, China

    Yanlin Weng

Authors
  1. Xin Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanzhen Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanlin Weng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yiying Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Zhongguancun East Street #1, 100084, Beijing, China

    Shi-Min Hu

  2. School of Computer Science and Informatics, Cardiff University, 5 The Parade, Roath, CF24 3AA, Cardiff, UK

    Ralph R. Martin

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Feng, X., Wang, Y., Weng, Y., Tong, Y. (2012). Compact Combinatorial Maps in 3D. In: Hu, SM., Martin, R.R. (eds) Computational Visual Media. CVM 2012. Lecture Notes in Computer Science, vol 7633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34263-9_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34263-9_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34262-2

  • Online ISBN: 978-3-642-34263-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation