Curvature of singular Bézier curves and surfaces

DOI10.1016/j.cagd.2011.03.004zbMath1227.65021OpenAlexW2074608392MaRDI QIDQ551493

Thomas W. Sederberg, Xin Li, Hong-Wei Lin

Publication date: 20 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2011.03.004

zbMATH Keywords

singular pointscurvaturerational Bézier curvescontrol pointscontrol polygonosculating parabolaosculating paraboloidsrational Bézier surface

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (4)

Derivatives of isogeometric functions on \(n\)-dimensional rational patches in \(\mathbb R^d\) ⋮ Surface patches with rounded corners ⋮ Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: geometric design and isogeometric analysis considerations ⋮ Convergence analysis on a second order algorithm for orthogonal projection onto curves

Cites Work

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• A note on degenerate triangular Bézier patches
• Curvature computations for degenerate surface patches
• Degenerate polynomial patches of degree 11 for almost \(GC^ 2\) interpolation over triangles
• On degenerate surface patches
• Degenerate polynomial patches of degree 4 and 5 used for geometrically smooth interpolation in \(\mathbb{R}^ 3\)
• \(G^{2}\) interpolation of free form curve networks by biquintic Gregory patches
• TURBS - topologically unrestricted rational B-splines
• Degenerate Bézier patches with continuous curvature
• Gaussian and mean curvatures of rational Bézier patches
• Curvature formulas for implicit curves and surfaces

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