The distance of a subdivision surface to its control polyhedron

DOI10.1016/j.jat.2008.10.012zbMath1185.41009OpenAlexW2060155980MaRDI QIDQ1048973

Jörg Peters, Xiaobin Wu

Publication date: 8 January 2010

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2008.10.012

zbMATH Keywords

convergencedistancelower boundbox-splinesubdivision surfacecontrol polyhedroncharacteristic spline

Mathematics Subject Classification ID

Spline approximation (41A15)

Related Items (3)

A formula for estimating the deviation of a binary interpolatory subdivision curve from its data polygon ⋮ Subdivision depth computation for tensor product \(n\)-ary volumetric models ⋮ Error bounds for Loop subdivision surfaces

Uses Software

• SubLiME

Cites Work

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• A unified approach to subdivision algorithms near extraordinary vertices
• Surface algorithms using bounds on derivatives
• Box splines
• Best bounds on the approximation of polynomials and splines by their control structure
• Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon
• Convergence of subdivision and degree elevation
• Subdivision surfaces
• Deformable surface modeling base on dual subdivision
• Computational formula of depth for Catmull-Clark subdivision surfaces
• Matrix Based Subdivision Depth Computation for Extra-Ordinary Catmull-Clark Subdivision Surface Patches
• Tight linear envelopes for splines

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