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A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Computer Aided Geometric Design
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Computer Aided Geometric Design
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Computer Aided Geometric Design
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Second order smoothness over extraordinary vertices
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Modified subdivision surfaces with continuous curvature
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Constructing curvature-continuous surfaces by blending
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Tuning subdivision algorithms using constrained energy optimization
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Guided C2 spline surfaces with V-shaped tessellation
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
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C2 splines covering polar configurations
Computer-Aided Design
An introduction to guided and polar surfacing
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
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Computer Aided Geometric Design
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Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
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Computer-Aided Design
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We present a second order smooth filling of an n-valent Catmull-Clark spline ring with n biseptic patches. While an underdetermined biseptic solution to this problem has appeared previously, we make several advances in this paper. Most notably, we cast the problem as a constrained minimization and introduce a novel quadratic energy functional whose absolute minimum of zero is achieved for bicubic polynomials. This means that for the regular 4-valent case, we reproduce the bicubic B-splines. In other cases, the resulting surfaces are aesthetically well behaved. We extend our constrained minimization framework to handle the case of input mesh with boundary.