Cubic recursive division with bounded curvature
Curves and surfaces
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
A variational approach to subdivision
Computer Aided Geometric Design
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Gaussian and Mean Curvature of Subdivision Surfaces
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Subdivision scheme tuning around extraordinary vertices
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Analyzing a generalized Loop subdivision scheme
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Loop subdivision with curvature control
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Local energy-optimizing subdivision algorithms
Computer Aided Geometric Design
G2 tensor product splines over extraordinary vertices
SGP '08 Proceedings of the Symposium on Geometry Processing
Subdivision surfaces integrated in a CAD system
Computer-Aided Design
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In this paper a method is presented to fair the limit surface of a subdivision algorithm around an extraordinary point. The eigenvalues and eigenvectors of the subdivision matrix determine the continuity and shape of the limit surface. The dominant, subdominant and subsub-dominant eigenvalues should satisfy linear and quadratic equality- and inequality-constraints to guarantee continuous normal and bounded curvature globally. The remaining eigenvalues need only satisfy linear inequality-constraints. In general, except for the dominant eigenvalue, all eigenvalues can be used to optimize the shape of the limit surface with our method.