Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3

DOI10.1016/j.cam.2012.04.002zbMath1244.14023OpenAlexW2016025665WikidataQ114202149 ScholiaQ114202149MaRDI QIDQ442722

Takis Sakkalis, Rida T. Farouki

Publication date: 3 August 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2012.04.002

zbMATH Keywords

quaternionsPythagorean-hodograph curvesoctonionscomplex numbersHopf mapparameterization of \(n\)-tuples

Mathematics Subject Classification ID

Plane and space curves (14H50) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (10)

Construction of PH splines based on H-Bézier curves ⋮ On polynomial general helices in \(n\)-dimensional Euclidean space \(\mathbb {R}^{n}\) ⋮ Classification of polynomial minimal surfaces ⋮ \(C^2\) Hermite interpolation by Pythagorean-hodograph quintic triarcs ⋮ Algebraic and geometric characterizations of a class of algebraic-hyperbolic Pythagorean-hodograph curves ⋮ Geometric characteristics of planar quintic Pythagorean-hodograph curves ⋮ Unnamed Item ⋮ Geometry of the ringed surfaces in \(\mathbb{R}^4\) that generate spatial Pythagorean hodographs ⋮ Identification of two classes of planar septic Pythagorean hodograph curves ⋮ A new approach to generate all Pythagorean triples

Cites Work

• Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• A characterization of helical polynomial curves of any degree
• The conformal map \(z\to z^ 2\) of the hodograph plane
• Clifford algebra, spin representation, and rational parameterization of curves and surfaces
• Minkowski Pythagorean hodographs
• Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves
• Helical polynomial curves and double Pythagorean hodographs. I: Quaternion and Hopf map representations
• Wronskians and Linear Independence
• POLYNOMIAL PARAMETRIZATION OF PYTHAGOREAN TUPLES
• Cross Products of Vectors in Higher Dimensional Euclidean Spaces
• Hermite Interpolation by Pythagorean Hodograph Quintics
• Efficient solution of the complex quadratic tridiagonal system for \(C^2\) PH quintic splines

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