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
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
Gaussian and Mean Curvature of Subdivision Surfaces
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Computing curvature bounds for bounded curvature subdivision
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
Analysis and tuning of subdivision algorithms
Proceedings of the 21st spring conference on Computer graphics
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Parametrizations for triangular Gk spline surfaces of low degree
ACM Transactions on Graphics (TOG)
Loop subdivision with curvature control
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
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
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Tuning subdivision algorithms using constrained energy optimization
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
Bounded curvature subdivision without eigenanalysis
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
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
Uniform interpolation curves and surfaces based on a family of symmetric splines
Computer Aided Geometric Design
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We provide asymptotic expansions for the fundamental forms, the Weingarten map, the principal curvatures, and the principal directions of surfaces generated by linear stationary subdivision schemes. Further, we define the central surface. The central surface is a spline ring that captures basic shape properties of the surface in the vicinity of an extraordinary vertex. Relating the shape properties to the spectrum of the subdivision matrix via the discrete Fourier transform yields conditions for the construction of high-quality subdivision schemes. In particular, the subsub-dominant eigenvalue should be triple and correspond to the Fourier blocks with indices 0, 2 and n - 2 of the subdivision matrix.