Conditions for tangent plane continuity over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
Cubic recursive division with bounded curvature
Curves and surfaces
Proceedings of the 27th 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
Geometric Modelling, Dagstuhl, Germany, 1996
Improved Triangular Subdivision Schemes
CGI '98 Proceedings of the Computer Graphics International 1998
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Subdivision scheme tuning around extraordinary vertices
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Lofting curve networks using subdivision surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Analysis and tuning of subdivision algorithms
Proceedings of the 21st spring conference on Computer graphics
On the curvature of guided surfaces
Computer Aided Geometric Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
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For a stationary, affine invariant, symmetric, linear and local subdivision scheme that is C^2 apart from the extraordinary point the curvature is bounded if the square of the subdominant eigenvalue equals the subsubdominant eigenvalue. This paper gives a technique for quickly establishing an interval to which the curvature is confined at the extraordinary point. The approach factors the work into precomputed intervals that depend only on the scheme and a mesh-specific component. When the intervals are tight enough they can be used as a test of shape-faithfulness of the given subdivision scheme; i.e., if the limit surface in the neighborhood of the extraordinary point of the subdivision scheme is consistent with the geometry implied by the input mesh.