C2 Continuous Spline Surfaces over Catmull-Clark Meshes

  • Jin Jin Zheng
  • Jian J. Zhang
  • Hong Jun Zhou
  • L. G. Shen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3482)


An efficient method for generating a C 2 continuous spline surface over a Catmull-Clark mesh is presented in this paper. The spline surface is the same as the Catmull-Clark limit surface except in the immediate neighborhood of the irregular mesh points. The construction process presented in this paper consists of three steps: subdividing the initial mesh at most twice using the Catmull-Clark subdivision rules; generating a bi-cubic Bézier patch for each regular face of the resultant mesh; generating a C 2 Gregory patch around each irregular vertex of the mesh. The union of all patches forms a C 2 spline surface. Differing from the previous methods proposed by Loop, DeRose and Peters, this method achieves an overall C 2 smoothness rather than only a C 1 continuity.


Open Mesh Subdivision Surface Mesh Vertex Spline Surface Irregular Mesh 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jin Jin Zheng
    • 1
  • Jian J. Zhang
    • 2
  • Hong Jun Zhou
    • 3
  • L. G. Shen
    • 1
  1. 1.Department of PMPIUniversity of Science and Technology of ChinaHefeiP R China
  2. 2.NCCABournemouth UniversityPoole, DorsetUK
  3. 3.NSRLUniversity of Science and Technology of ChinaHefeiP R China

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