On geometric interpolation by planar parametric polynomial curves

DOI10.1090/S0025-5718-07-01988-6zbMath1201.41001OpenAlexW2012627344MaRDI QIDQ3592687

Marjeta Krajnc, Jernej Kozak, Gašper Jaklič, Emil Žagar

Publication date: 13 September 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01988-6

zbMATH Keywords

asymptotic analysisapproximation orderGeometric interpolation

Mathematics Subject Classification ID

Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

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Interpolation of planar \(G^1\) data by Pythagorean-hodograph cubic biarcs with prescribed arc lengths ⋮ Interpolation scheme for planar cubic \(G^2\) spline curves ⋮ A fast solver for boundary integral equations of the modified Helmholtz equation ⋮ Planar cubic \(G^{1}\) interpolatory splines with small strain energy ⋮ Curvature variation minimizing cubic Hermite interpolants ⋮ Necklaces count polynomial parametric osculants ⋮ Highly accurate Lagrangian flux calculation via algebraic quadratures on spline-approximated donating regions ⋮ CLOSED FORM FORMULA FOR THE NUMBER OF RESTRICTED COMPOSITIONS ⋮ Point data reconstruction and smoothing using cubic splines and clusterization ⋮ Parameterization for polynomial curve approximation via residual deep neural networks ⋮ Geometric interpolation by planar cubic polynomial curves ⋮ On geometric interpolation of circle-like curves ⋮ Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves ⋮ Geometric Hermite interpolation by cubic \(G^1\) splines ⋮ Shape preserving interpolation by cubic \(G^{1}\) splines in \({\mathbb{R}^3}\) ⋮ On planar polynomial geometric interpolation

Cites Work

• Geometric Hermite interpolation with maximal order and smoothness
• High order approximation method for curves
• High accuracy geometric Hermite interpolation
• Interpolation with piecewise quadratic visually \(C^ 2\) Bézier polynomials
• Advanced determinant calculus: a complement
• On Geometric Interpolation by Polynomial Curves
• A general framework for high-accuracy parametric interpolation
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