New algebraic and geometric characterizations of planar quintic Pythagorean-hodograph curves

DOI10.1016/j.cagd.2023.102256OpenAlexW4389365783MaRDI QIDQ6153622

Alberto Viscardi, Lucia Romani, Kai Hormann

Publication date: 14 February 2024

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2023.102256

zbMATH Keywords

Pythagorean-hodographBézier control polygonplanar quintic curves

Mathematics Subject Classification ID

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

Cites Work

• On control polygons of quartic Pythagorean-hodograph curves
• Offset-rational parametric plane curves
• Topological criterion for selection of quintic pythagorean-hodograph Hermite interpolants
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• The conformal map \(z\to z^ 2\) of the hodograph plane
• Geometric characteristics of planar quintic Pythagorean-hodograph curves
• Singular cases of planar and spatial \(C^1\) Hermite interpolation problems based on quintic Pythagorean-hodograph curves
• Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets
• Identification and ``reverse engineering of Pythagorean-hodograph curves
• Hermite Interpolation by Pythagorean Hodograph Quintics
• Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves
• Pythagorean Triples in Uniquef Factorization Domains
• Construction and shape analysis of PH quintic Hermite interpolants
• Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints

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