Cubic recursive division with bounded curvature
Curves and surfaces
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Curvature continuous spline surfaces over irregular meshes
Computer Aided Geometric Design
Computer Aided Geometric Design
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
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Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Modelings surfaces from meshes of arbitrary topology
Computer Aided Geometric Design
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
C2 free-form surfaces of degree (3,5)
Computer Aided Geometric Design
Geometric Modelling, Dagstuhl, Germany, 1996
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
Subdivision scheme tuning around extraordinary vertices
Computer Aided Geometric Design
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Computer Aided Geometric Design
Second order smoothness over extraordinary vertices
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
C2 subdivision over triangulations with one extraordinary point
Computer Aided Geometric Design
Constructing curvature-continuous surfaces by blending
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
ACM SIGGRAPH Asia 2008 papers
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Computer Aided Geometric Design
Computer Aided Geometric Design
An Iterative Method for Fast Mesh Denoising
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
ACM SIGGRAPH 2009 papers
Mesh Smoothing for Parameterized Body Model with Loop Subdivision Algorithm
AST '09 Proceedings of the 2009 International e-Conference on Advanced Science and Technology
G2 tensor product splines over extraordinary vertices
SGP '08 Proceedings of the Symposium on Geometry Processing
Guided C2 spline surfaces with V-shaped tessellation
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Locally adjustable interpolation for meshes of arbitrary topology
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
Manifold-based surfaces with boundaries
Computer Aided Geometric Design
Modeling smooth shape using subdivision on differential coordinates
Computer-Aided Design
C2 splines covering polar configurations
Computer-Aided Design
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
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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We present a modification to subdivision surfaces, which guarantees second-order smoothness everywhere in the surface, including extraordinary points. The idea is to blend the limit surface with a low degree polynomial defined over the characteristic map, in the vicinity of each extraordinary point. We demonstrate our method on Catmull-Clark surfaces, but a similar modification can be applied to other schemes as well. The proposed modification to Catmull-Clark is simple to implement and can be applied to quad meshes of arbitrary topological type, even when extraordinary vertices share edges.