Skip to main content
Springer Nature Link
Log in

Making Doo-Sabin surface interpolation always work over irregular meshes

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

Abstract

This paper presents a reliable method for constructing a control mesh whose Doo-Sabin subdivision surface interpolates the vertices of a given mesh with arbitrary topology. The method improves on existing techniques in two respects: (1) it is guaranteed to always work for meshes of arbitrary topological type; (2) there is no need to solve a system of linear equations to obtain the control points. Extensions to include normal vector interpolation and/or shape adjustment are also discussed.

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, news and stories from top researchers in related subjects.

References

  1. Brunet P (1988) Including shape handles in recursive subdivisionsurfaces. Comput Aided Geom Des 5(1):41–50

    Article  MathSciNet  Google Scholar 

  2. Catmull E, Clark J (1978) Recursively generated B-spline surfaces on arbitrary topological meshes. Comput Aided Des 10:350–355

    Article  Google Scholar 

  3. Doo D (1978) A subdivision algorithm for smoothing down irregularly shaped polyhedrons. In: Proceedings of the Interactive Techniques in Computer Aided Design, Bologna, IEEE Computer Society, pp 157–165

  4. Doo D, Sabin M (1978) Behaviour of recursive division surfaces near extraordinary points. Comput Aided Des 10:356–360

    Article  Google Scholar 

  5. Foley J, Dam, A, Feiner S, Hughes J (1997) Computer graphics: principles and practice, 2nd edn. Addison-Wesley, Boston

    Google Scholar 

  6. Golub G, van Loan C (1989) Matrix computations, 2nd edn. John Hopkins University Press, Baltimore

  7. Halstead M, Kass M, DeRose T (1993) Efficient, fair interpolation using Catmull-Clark surfaces. In: Computer Graphics, Proceedings of SIGGRAPH 93 27:35–44

  8. Nasri A (1987) Polyhedral subdivision methods for free-form surfaces. ACM Trans Graph 6(1):29–73

    Article  Google Scholar 

  9. Nasri A (1991) Surface interpolation on irregular networks with normal conditions. Comput Aided Geom Des 8(1):89–96

    Article  MathSciNet  Google Scholar 

  10. Sabin M (1991) Cubic recursive division with bounded curvature. In: Laurent PJ, Le Méhauté A, Schumaker LL (eds) Curves and surfaces. Academic Press, Boston, pp 411–414

  11. Shilane P, Min P, Kazhdan M, Funkhouser T (2004) The Princeton shape benchmark. In: Proceedings of Shape Modeling International, Genove, Italy, pp 167–178

  12. Stam, J (1998) Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values. In: Computer Graphics Proceedings, SIGGRAPH 98, pp 395–404

  13. Zorin D, Schröder P (2000) Subdivision for modeling and animation. In: Course Notes of SIGGRAPH 2000. ACM, Boston

  14. Zorin D, Schröder P, Sweldens W (1996) Interpolating subdivision for meshes with arbitrary topology. In: Computer Graphics, SIGGRAPH 96 Proceedings 30:189–192

Download references

Author information

Authors and Affiliations

  1. School of Computer Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798

    Jianmin Zheng

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798

    Yiyu Cai

Authors
  1. Jianmin Zheng
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yiyu Cai
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jianmin Zheng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng, J., Cai, Y. Making Doo-Sabin surface interpolation always work over irregular meshes. Vis Comput 21, 242–251 (2005). https://doi.org/10.1007/s00371-005-0285-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-005-0285-3

Keywords