\(G^1\) interpolation of \(v\)-asymmetric data with arc-length constraints by Pythagorean-hodograph cubic splines

DOI10.1016/j.cagd.2023.102188OpenAlexW4360841418MaRDI QIDQ6046142

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Publication date: 15 May 2023

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2023.102188

zbMATH Keywords

arc-length constraintrectifying control polygon\(v\)-asymmetric Hermite interpolationPH cubic spline

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx)

Cites Work

• The conformal map \(z\to z^ 2\) of the hodograph plane
• Construction of \(G^1\) planar Hermite interpolants with prescribed arc lengths
• \(C^1\) Hermite interpolation with PH curves by boundary data modification
• Existence of Pythagorean-hodograph quintic interpolants to spatial \(G^1\) Hermite data with prescribed arc lengths
• Shape analysis of planar PH curves with the Gauss-Legendre control polygons
• Construction of \(G^2\) planar Hermite interpolants with prescribed arc lengths
• Interpolation of planar \(G^1\) data by Pythagorean-hodograph cubic biarcs with prescribed arc lengths
• Controlling extremal Pythagorean hodograph curves by Gauss-Legendre polygons
• Approximation of monotone clothoid segments by degree 7 Pythagorean-hodograph curves
• Rectifying control polygon for planar Pythagorean hodograph curves
• Hermite Interpolation by Pythagorean Hodograph Quintics
• Interpolation by $G^2$ Quintic Pythagorean-Hodograph Curves

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