Bounding the Distance between a Loop Subdivision Surface and Its Limit Mesh

  • Zhangjin Huang
  • Guoping Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4975)


Given a control mesh of a Loop subdivision surface, by pushing the control vertices to their limit positions, a limit mesh of the Loop surface is obtained. Compared with the control mesh, the limit mesh is a tighter linear approximation in general, which inscribes the limit surface. We derive an upper bound on the distance between a Loop subdivision surface patch and its limit triangle in terms of the maximum norm of the mixed second differences of the initial control vertices and a constant that depends only on the valence of the patch’s extraordinary vertex. A subdivision depth estimation formula for the limit mesh approximation is also proposed.


Loop subdivision surfaces Limit mesh Error bound Subdivision depth 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Zhangjin Huang
    • 1
  • Guoping Wang
    • 1
  1. 1.School of Electronic Engineering and Computer SciencePeking UniversityBeijingChina

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