Skip to main content

Advertisement

Springer Nature Link
Log in

Polygonization of implicit surfaces with sharp features by edge-spinning

  • original article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

This paper presents an adaptive approach for polygonization of implicit surfaces. The algorithm generates a well-shaped triangular mesh with respect to a given approximation error. The error is proportional to a local surface curvature estimation. Polygonization of surfaces of high curvature, as well as surfaces with sharp features, is possible using a simple technique combined with a particle system approach. The algorithm is based on a surface tracking scheme, and it is compared with other algorithms based on a similar principle, such as the marching cube and the marching triangle algorithms.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Akkouche S, Galin E (2001) Adaptive implicit surface polygonization using marching triangles. Comput Graph Forum 20(2):67–80

    Article  Google Scholar 

  2. Allgower EL, Gnutzmann S (1987) An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces. SIAM J Numer Anal 24:452–469

    Article  MathSciNet  Google Scholar 

  3. Alliez P, Cohen-Steiner D, Devillers O, Lévy B, Desbrun M (2003) Anisotropic polygonal remeshing. In: SIGGRAPH 2003, ACM TOG 22(3):485–493

  4. Baumgart B-G (1975) Winged-Edge Polyhedron Representation for Computer Vision. National Computer Conference, Stanford University, Stanford, California, AFIPS Proc 1975, 44:589–596

  5. Bloomenthal J (1994) Graphics gems IV. Academic Press, New York

  6. Bloomenthal J (1995) Skeletal design of natural forms. Dissertation, University of Calgary, Canada

  7. Bloomenthal J, Bajaj Ch, Blinn J, Cani-Gascuel M-P, Rockwood A, Wyvill B, Wyvill G (1997) Introduction to implicit surfaces. Kaufmann, San Francisco

  8. Bloomenthal J (1988) Polygonization of implicit surfaces. Comput-Aided Geom Des 5(4):341–355

    Google Scholar 

  9. Čermák M, Skala V (2004) Adaptive edge spinning algorithm for polygonization of implicit surfaces. In: Proceedings of Computer Graphics International, CGI 2004, pp 36–43, Crete, Greece

  10. Čermák M, Skala V (2002) Polygonization by the edge spinning. In: Proceedings of the International Conference Algoritmy 2002, pp 245–252, Slovakia

  11. Čermák M, Skala V (2002) Accelerated edge spinning algorithm for implicit surfaces. In: Proceedings of the International Conference ICCVG 2002, pp 174–179, Zakopane, Poland

  12. Čermák M, Skala V (2002) Space subdivision for fast polygonization of implicit surfaces. In: Proceedings of the International Conference ECI 2002, pp 302–307, Slovakia

  13. Figueiredo LH (1992) Computational morphology of implicit curves. Dissertation, Istituto de Matematica Purea Aplicada

  14. Figueiredo LH, Gomes JM, Terzopoulos D, Velho L (1992) Physically-based methods for polygonization of implicit surfaces. In: Proceedings of Graphics Interface 92:250–257

  15. Hartmann E (1998) A marching method for the triangulation of surfaces. Vis Comput 14:95–108

    Article  Google Scholar 

  16. Hilton A, Stoddart AJ, Illingworth J, Windeatt T (1996) Marching triangles: range image fusion for complex object modelling. In: Proceedings of the International Conference on Image Processing 2:381–384

  17. “Hyperfun: language for F-Rep geometric modeling,” http://cis.k.hosei.ac.jp/∼F-rep/

  18. Ju T, Losasso F, Schaefer S, Warren J (2002) Dual contouring of Hermite data. In: SIGGRAPH 2002, pp 339–346

  19. Karkanis T, Stewart AJ (2001) Curvature-dependent triangulation of implicit surfaces. IEEE Comput Graph Appl 21(2):60–69

    Article  Google Scholar 

  20. Kobbelt LP, Botsch M, Schwanecke U, Seidel H-P (2001) Feature sensitive surface extraction from volume data. In: SIGGRAPH 2001 proceedings, pp 57–66

  21. MVE – modular visualization environment project, http://herakles.zcu.cz/research, 2001

  22. Ohtake Y, Belyaev A, Pasko A (2003) Dynamic mesh optimization for polygonized implicit surfaces with sharp features, Vis Comput 19:115–126

    Google Scholar 

  23. Ohtake Y, Belyaev AG (2002) Dual/primal mesh optimization for polygonized implicit surfaces. In: Proceedings of the ACM Solid Modeling Symposium, Saarbrucken, Germany, pp 171–178

  24. Pasko A, Adzhiev V, Karakov M, Savchenko V (2000) Hybrid system architecture for volume modeling. Comput Graph 24:67–68

    Article  Google Scholar 

  25. Rvachov AM, Definition of R-functions, http://www.mit.edu/∼maratr/rvachev/p1.htm

  26. Schmidt MFW (1993) Cutting cubes – visualizing implicit surfaces by adaptive polygonization. Vis Comput 10(2):10–115

    Article  Google Scholar 

  27. Shapiro V, Tsukanov I (1999) Implicit functions with guaranteed differential properties. In: Proceedings of the Fifth Annual Symposium on Solid Modeling and Applications, Ann Arbor, Michigan, pp 258–269

  28. Taubin G (1994) Distance approximations for rasterizing implicit curves. ACM Trans Graph 13:3–42

    Article  Google Scholar 

  29. Triquet F, Meseure F, Chaillou C (2001) Fast polygonization of implicit surfaces. In: Proceedings of the International Conference WSCG, pp 283–290

  30. Uhlir K, Skala V (2003) The implicit function modelling system – comparison of C++ and C# solutions. In: Proceedings of C# and NET Technologies’ 2003, pp 87–91, University of West Bohemia, Czech Republic

  31. Velho L (1996) Simple and efficient polygonization of implicit surfaces. J Graph Tools 1(2):5–24

    Article  Google Scholar 

  32. Velho L, Figueiredo L, Gomes J (1999) A unified approach for hierarchical adaptive tessellation of surfaces. ACM Trans Graph 18(4):329–360

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of West Bohemia in Pilsen, Czech Republic

    Martin Čermák & Václav Skala

Authors
  1. Martin Čermák
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Václav Skala
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Martin Čermák.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Čermák, M., Skala, V. Polygonization of implicit surfaces with sharp features by edge-spinning. Vis Comput 21, 252–264 (2005). https://doi.org/10.1007/s00371-005-0286-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-005-0286-2

Keywords