On interpolation by Planar cubic $G^2$ pythagorean-hodograph spline curves

DOI10.1090/S0025-5718-09-02298-4zbMath1200.41003OpenAlexW2075461425WikidataQ114093877 ScholiaQ114093877MaRDI QIDQ3584778

Marjeta Krajnc, Vito Vitrih, Emil Žagar, Jernej Kozak, Gašper Jaklič

Publication date: 30 August 2010

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-09-02298-4

zbMATH Keywords

interpolation by spline curvesPythagorean-hodograph splines

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical smoothing, curve fitting (65D10) Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15) Computer-aided design (modeling of curves and surfaces) (65D17) Approximation by other special function classes (41A30)

Related Items (17)

Construction of \(G^2\) planar Hermite interpolants with prescribed arc lengths ⋮ \(C^2\) Hermite interpolation by Pythagorean-hodograph quintic triarcs ⋮ Sparse Pythagorean hodograph curves ⋮ Interpolation of \(G^1\) Hermite data by \(C^1\) cubic-like sparse Pythagorean hodograph splines ⋮ Unnamed Item ⋮ On the construction of polynomial minimal surfaces with Pythagorean normals ⋮ Classification of planar Pythagorean hodograph curves ⋮ Hermite \(G^1\) rational spline motion of degree six ⋮ Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints ⋮ \(G^{1}\) Hermite interpolation by PH cubics revisited ⋮ Quasi-elastic cubic splines in \(\mathbb{R}^d\) ⋮ \( G^2 \slash C^1\) Hermite interpolation by planar PH B-spline curves with shape parameter ⋮ \(C^1\) Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs ⋮ An approach to geometric interpolation by Pythagorean-hodograph curves ⋮ The planning of the trajectory of UAV group with the performance of Pythagorean Hodograph and Bernstein-Bezier composite curves in the plane ⋮ Planar projections of spatial Pythagorean-hodograph curves ⋮ A new method to design cubic Pythagorean-hodograph spline curves with control polygon

Cites Work

• A control polygon scheme for design of planar \(C^2\) PH quintic spline curves
• Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• The conformal map \(z\to z^ 2\) of the hodograph plane
• On \(G^ 2\) continuous cubic spline interpolation
• Geometric Hermite interpolation with Tschirnhausen cubics
• Hermite interpolation with Tschirnhausen cubic spirals
• Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method
• Euclidean and Minkowski Pythagorean hodograph curves over planar cubics
• Hermite interpolation by Pythagorean hodograph curves of degree seven
• Shape-preserving interpolation by G1 and G2 PH quintic splines
• Hermite Interpolation by Pythagorean Hodograph Quintics
• Efficient solution of the complex quadratic tridiagonal system for \(C^2\) PH quintic splines
• A practical guide to splines.

This page was built for publication: On interpolation by Planar cubic $G^2$ pythagorean-hodograph spline curves