Two-scale difference equations II. local regularity, infinite products of matrices and fractals
SIAM Journal on Mathematical Analysis
Convexity preservation of the four-point interpolatory subdivision scheme
Computer Aided Geometric Design
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Rational quadratic circles are parametrized by chord length
Computer Aided Geometric Design
A family of subdivision schemes with cubic precision
Computer Aided Geometric Design
Convergence and C1 analysis of subdivision schemes on manifolds by proximity
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Artifacts in box-spline surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graphical Models
Curvature of approximating curve subdivision schemes
Proceedings of the 7th international conference on Curves and Surfaces
Curvature-sensitive splines and design with basic curves
Computer-Aided Design
Non-uniform interpolatory subdivision via splines
Journal of Computational and Applied Mathematics
Interproximate curve subdivision
Journal of Computational and Applied Mathematics
Non-uniform non-tensor product local interpolatory subdivision surfaces
Computer Aided Geometric Design
A smoothness criterion for monotonicity-preserving subdivision
Advances in Computational Mathematics
A new four-point shape-preserving C3 subdivision scheme
Computer Aided Geometric Design
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A step of subdivision can be considered to be a sequence of simple, highly local stages. By manipulating the stages of a subdivision step we can create families of schemes, each designed to meet different requirements. We postulate that such modification can lead to improved behaviour. We demonstrate this using the four-point scheme as an example. We explain how it can be broken into stages and how these stages can be manipulated in various ways. Six variants that all improve on the quality of the limit curve are presented and analysed. We present schemes which perfectly preserve circles, schemes which improve the Holder continuity, and schemes which relax the interpolating property to achieve higher smoothness.