Mathematics of Computation
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision
Computer Aided Geometric Design
Extended subdivision surfaces: Building a bridge between NURBS and Catmull-Clark surfaces
ACM Transactions on Graphics (TOG)
A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics
Computer Aided Geometric Design
Four-point curve subdivision based on iterated chordal and centripetal parameterizations
Computer Aided Geometric Design
Selective knot insertion for symmetric, non-uniform refine and smooth B-spline subdivision
Computer Aided Geometric Design
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
The importance of polynomial reproduction in piecewise-uniform subdivision
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Non-uniform interpolatory subdivision via splines
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
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Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing curve of a non-uniform refinement with the advantages of a shape-controlled interpolation method and an arbitrary point insertion rule. The result is a non-uniform interpolatory 4-point scheme that is unique in combining a number of distinctive properties. In fact it generates visually-pleasing limit curves where special features ranging from cusps and flat edges to point/edge tension effects may be included without creating undesired undulations. Moreover such a scheme is capable of inserting new points at any positions of existing intervals, so that the most convenient parameter values may be chosen as well as the intervals for insertion. Such a fully flexible curve scheme is a fundamental step towards the construction of high-quality interpolatory subdivision surfaces with features control.