A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
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A subdivision algorithm for trigonometric spline curves
Computer Aided Geometric Design
Subdivision Methods for Geometric Design: A Constructive Approach
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A Method for Analysis of C1-Continuity of Subdivision Surfaces
SIAM Journal on Numerical Analysis
Uniform hyperbolic polynomial B-spline curves
Computer Aided Geometric Design
ACM SIGGRAPH 2003 Papers
Some Non-Stationary Subdivision Schemes
GMAI '07 Proceedings of the Geometric Modelling and Imaging
Composite 2 subdivision surfaces
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
An approximating C2 non-stationary subdivision scheme
Computer Aided Geometric Design
C-curves: An extension of cubic curves
Computer Aided Geometric Design
Unifying C-curves and H-curves by extending the calculation to complex numbers
Computer Aided Geometric Design
Subdivision surfaces for CAD-an overview
Computer-Aided Design
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Introduction to the Mathematics of Subdivision Surfaces
Introduction to the Mathematics of Subdivision Surfaces
A generalized curve subdivision scheme of arbitrary order with a tension parameter
Computer Aided Geometric Design
Analyzing midpoint subdivision
Computer Aided Geometric Design
Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction
Journal of Computational and Applied Mathematics
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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This article presents a generalized B-spline surface subdivision scheme of arbitrary order with a tension parameter. We first propose a tensor-product subdivision scheme that produces k"uxk"v order generalized B-spline limit surfaces. Generalized B-spline surface is the unified and extended form of B-splines, trigonometric B-splines and hyperbolic B-splines (Fang et al. 2010). The tensor product subdivision scheme can be used to generate various surfaces of revolution, including those generated by classical analytic curves that can be exactly represented by generalized B-spline curves. By extending a bi-order (say k) tensor-product scheme to meshes of arbitrary topology, we further propose a generalized surface subdivision scheme with a tension parameter. Several well-known subdivision schemes, including Doo-Sabin subdivision, Catmull-Clark subdivision, and two other subdivision schemes proposed by Morin et al. (2001) and Stam (2001), become special cases of the generalized subdivision scheme. The tension parameter can be used to adjust the shape of subdivision surfaces. The scheme produces higher order C^k^-^2 continuous limit surfaces except at extraordinary points where the continuity is C^1. Convenient and hierarchical methods are also presented for embedding sharp features and semi-sharp features on the resulting limit surfaces.