An Interpolatory Subdivision Scheme for Triangular Meshes and Progressive Transmission

  • Ruotian Ling
  • Xiaonan Luo
  • Ren Chen
  • Guifeng Zheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4270)


This paper proposes a new interpolatory subdivision scheme for triangular meshes that produces C 1 continuous limit surfaces for both regular and irregular settings. The limit surfaces also have bounded curvature, which leads to improved quality surfaces. The eigen-structure analysis demonstrates the smoothness of the limit surfaces. According to the new scheme, the approach for progressive transmission of meshes is presented. Finally, results of refined models with the new scheme are shown. In most cases, the new scheme generates more pleasure surfaces than the traditional modified butterfly scheme, especially near the irregular settings.


Subdivision Scheme Subdivision Surface Progressive Transmission Progressive Mesh Subdivision Rule 
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  1. 1.
    Dyn, N., Levin, D., Gregory, J.A.: A butterfly subdivision scheme for surface interpolatory with tension control. ACM Transactions on Graphics 9, 160–169 (1990)MATHCrossRefGoogle Scholar
  2. 2.
    Zorin, D., Schröder, P., Sweldens, W.: Interpolating subdivision for meshes with arbitrary topology. In: Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, pp. 189–192 (1996)Google Scholar
  3. 3.
    Zheng, G.: Progressive meshes transmission over wireless network. Journal of Computational Information Systems 1, 67–71 (2005)Google Scholar
  4. 4.
    Hoppe, H.: Progressive meshes. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp. 99–108 (1996)Google Scholar
  5. 5.
    Li, G., Ma, W., Bao, H.: A new interpolatory subdivision for quadrilateral meshes. Computer Graphics forum 24, 3–16 (2005)CrossRefGoogle Scholar
  6. 6.
    Reif, U.: An unified approach to subdivision algorithms near extraordinary vertices. Computer Aided Geometric Design 12, 153–174 (1995)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Labsik, U., Greiner, G.: Interpolatory \(\sqrt{3}\) subdivision. Computer Graphics Forum 19, 131–138 (2000)CrossRefGoogle Scholar
  8. 8.
    Dyn, N., Gregory, J.A., Levin, D.: A 4-point interpolatory subdivision scheme for curves design. Computer Aided Design 4, 257–268 (1987)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Zorin, D.: Stationary subdivision and multiresolution surface representation. Ph.D. Thesis, California Institute of Technology, Pasadena, California (1998)Google Scholar
  10. 10.
    Zorin, D.: A Method for Analysis of C 1-continuity of subdivision Surfaces. SIAM Journal of Numerical Analysis 37, 1677–1708 (2000)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Loop, C.: Smooth ternary subdivision of triangle meshes. In: Cohen, A., Schumaker, L.L. (eds.) Curve and Surface Fitting, St Malo. Nashboro Press, Brentwood (2002)Google Scholar
  12. 12.
    Loop, C.: Bounded curvature triangle mesh subdivision with the convex hull property. The Visual Computer 18, 316–325 (2002)CrossRefGoogle Scholar
  13. 13.
    Stam, J., Loop, C.: Quad/triangle subdivision. Computer Graphics Forum 22, 1–7 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ruotian Ling
    • 1
  • Xiaonan Luo
    • 1
  • Ren Chen
    • 1
  • Guifeng Zheng
    • 1
  1. 1.Computer Application InstituteSun Yat-sen UniversityGuangzhouChina

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