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.
This work is supported by “Hundred Talents project” of CAS and NSF of China(60473133).
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Zheng, J.J., Zhang, J.J., Zhou, H.J., Shen, L.G. (2005). C 2 Continuous Spline Surfaces over Catmull-Clark Meshes. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424857_108
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DOI: https://doi.org/10.1007/11424857_108
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