A symmetric, non-uniform, refine and smooth subdivision algorithm for general degree B-splines

DOI10.1016/j.cagd.2007.12.001zbMath1205.65045OpenAlexW2001198123WikidataQ59751103 ScholiaQ59751103MaRDI QIDQ625161

Malcolm A. Sabin, Thomas J. Cashman, Neil A. Dodgson

Publication date: 15 February 2011

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cagd.2007.12.001

zbMATH Keywords

smoothingsubdivisionNURBSknot insertionnon-uniformlane-riesenfeld

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Rate of convergence, degree of approximation (41A25)

Related Items (11)

Elementary factorisation of box spline subdivision ⋮ Conversion of trimmed NURBS surfaces to Catmull-Clark subdivision surfaces ⋮ Seamless integration of design and Kirchhoff-Love shell analysis using analysis-suitable unstructured T-splines ⋮ Selective knot insertion for symmetric, non-uniform refine and smooth B-spline subdivision ⋮ Adjustable speed surface subdivision ⋮ L-system specification of knot-insertion rules for non-uniform B-spline subdivision ⋮ Repeated local operations and associated interpolation properties of dual \(2n\)-point subdivision schemes ⋮ Non-uniform interpolatory curve subdivision with edge parameters built upon compactly supported fundamental splines ⋮ Nonstationary interpolatory subdivision schemes reproducing high-order exponential polynomials ⋮ Dyadic T-mesh subdivision ⋮ Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: geometric design and isogeometric analysis considerations

Cites Work

• Non-uniform subdivision for B-splines of arbitrary degree
• Two blossoming proofs of the Lane-Riesenfeld algorithm
• Blossoms are polar forms
• Smoothness of subdivision surfaces at extraordinary points
• A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
• Non-uniform B-Spline Subdivision Using Refine and Smooth
• On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
• A unified framework for primal/dual quadrilateral subdivision schemes
• A subdivision scheme for surfaces of revolution

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