Arc length estimation and the convergence of polynomial curve interpolation

DOI10.1007/s10543-005-0031-2zbMath1095.65011OpenAlexW1975308552MaRDI QIDQ2490361

Michael S. Floater

Publication date: 2 May 2006

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-005-0031-2

zbMATH Keywords

Lagrange interpolationcurve fittingapproximation orderHermite interpolationcurve lengthcurve parameterization

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Numerical interpolation (65D05)

Related Items (9)

Rapid blending of closed curves based on curvature flow ⋮ Extrapolation methods for approximating arc length and surface area ⋮ A chain rule for multivariate divided differences ⋮ The approximation order of four-point interpolatory curve subdivision ⋮ Numerical curve length calculation using polynomial interpolation ⋮ Geometric constraints on quadratic Bézier curves using minimal length and energy ⋮ Point-based methods for estimating the length of a parametric curve ⋮ On the deviation of a parametric cubic spline interpolant from its data polygon ⋮ Two chain rules for divided differences and Faà di Bruno’s formula

Cites Work

• Geometric Hermite interpolation
• High accurate rational approximation of parametric curves
• Good approximation of circles by curvature-continuous Bézier curves
• High accuracy geometric Hermite interpolation
• Choosing nodes in parametric curve interpolation
• An \(O(h^{2n})\) Hermite approximation for conic sections
• A divided difference formula for the error in Hermite interpolation
• On the Influence of Parametrization in Parametric Interpolation
• The Curious History of Faa di Bruno's Formula
• A general framework for high-accuracy parametric interpolation
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