Polyhedral subdivision methods for free-form surfaces
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design
Generalized B-spline surfaces of arbitrary topology
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
A G1 triangular spline surface of arbitrary topological type
Computer Aided Geometric Design
Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Control point surfaces over non-four-sided areas
Computer Aided Geometric Design
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Modelings surfaces from meshes of arbitrary topology
Computer Aided Geometric Design
The n-sided control point surfaces without twist constraints
Computer Aided Geometric Design
Interactive Deformation of Irregular Surface Models
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
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An efficient method for generating a C2 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 C2 Gregory patch around each irregular vertex of the mesh. The union of all patches forms a C2 spline surface. Differing from the previous methods proposed by Loop, DeRose and Peters, this method achieves an overall C2 smoothness rather than only a C1 continuity.