Conditions for tangent plane continuity over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
An investigation of curvature variations over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
Cubic recursive division with bounded curvature
Curves and surfaces
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Gaussian and Mean Curvature of Subdivision Surfaces
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Analysis and tuning of subdivision algorithms
Proceedings of the 21st spring conference on Computer graphics
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Parametrizations for triangular Gk spline surfaces of low degree
ACM Transactions on Graphics (TOG)
Concentric tessellation maps and curvature continuous guided surfaces
Computer Aided Geometric Design
Ternary subdivision for quadrilateral meshes
Computer Aided Geometric Design
Loop subdivision with curvature control
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
ACM Transactions on Graphics (TOG)
On the curvature of guided surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
Local energy-optimizing subdivision algorithms
Computer Aided Geometric Design
ACM SIGGRAPH Asia 2008 papers
Pairs of bi-cubic surface constructions supporting polar connectivity
Computer Aided Geometric Design
Computer Aided Geometric Design
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
Efficient substitutes for subdivision surfaces
ACM SIGGRAPH 2009 Courses
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
An appropriate geometric invariant for the C2-analysis of subdivision surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Dinus: Double insertion, nonuniform, stationary subdivision surfaces
ACM Transactions on Graphics (TOG)
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
An introduction to guided and polar surfacing
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Tuned ternary quad subdivision
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
Subdivision surfaces integrated in a CAD system
Computer-Aided Design
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For subdivision surfaces, it is important to characterize local shape near flat spots and points where the surface is not twice continuously differentiable. Applying general principles derived in [Computer Aided Geometric Design, doi:10.1016/j.cagd.2004.04.006, in press], this paper characterizes shape near such points for the subdivision schemes devised by Catmull and Clark and by Loop. For generic input data, both schemes fail to converge to the hyperbolic or elliptic limit shape suggested by the geometry of the input mesh: the limit shape is a function of the valence of the extraordinary point rather than the mesh geometry. We characterize the meshes for which the schemes behave as expected and indicate modifications of the schemes that prevent convergence to the wrong shape. We also introduce a type of chart that, for a specific scheme, can help a designer to detect early when a mesh will lead to undesirable curvature behavior.