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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)

Abstract

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.

Keywords

Open Mesh Subdivision Surface Mesh Vertex Spline Surface Irregular Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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