Existence of Pythagorean-hodograph quintic interpolants to spatial \(G^1\) Hermite data with prescribed arc lengths

DOI10.1016/j.jsc.2019.02.008zbMath1432.65024OpenAlexW2917363923WikidataQ114154469 ScholiaQ114154469MaRDI QIDQ2000275

Rida T. Farouki

Publication date: 28 June 2019

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2019.02.008

zbMATH Keywords

shape optimizationPythagorean-hodograph curvespolynomial rootsexistence conditionsgeometric Hermite interpolationarc length constraints

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (17)

A new method to construct polynomial minimal surfaces ⋮ 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 ⋮ Interpolation of \(G^1\) Hermite data by \(C^1\) cubic-like sparse Pythagorean hodograph splines ⋮ Controlling extremal Pythagorean hodograph curves by Gauss-Legendre polygons ⋮ \(G^1\) interpolation of \(v\)-asymmetric data with arc-length constraints by Pythagorean-hodograph cubic splines ⋮ Partition of the space of planar quintic Pythagorean-hodograph curves ⋮ On \(G^1\) and \(G^2\) Hermite interpolation by spatial algebraic-trigonometric Pythagorean hodograph curves with polynomial parametric speed ⋮ Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints ⋮ Construction of \(G^2\) spatial interpolants with prescribed arc lengths ⋮ Rational minimal-twist motions on curves with rotation-minimizing Euler-Rodrigues frames ⋮ Gauss-Lobatto polygon of Pythagorean hodograph curves ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Geometric interpolation of ER frames with \(G^2\) Pythagorean-hodograph curves of degree 7 ⋮ Construction of periodic adapted orthonormal frames on closed space curves ⋮ Planar projections of spatial Pythagorean-hodograph curves

Uses Software

• BRENT

Cites Work

• Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• Clifford algebra, spin representation, and rational parameterization of curves and surfaces
• Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves
• Construction of \(G^1\) planar Hermite interpolants with prescribed arc lengths
• Interpolation with spatial rational Pythagorean-hodograph curves of class 4
• Euler-Rodrigues frames on spatial Pythagorean-hodograph curves.
• Helical polynomial curves and double Pythagorean hodographs. I: Quaternion and Hopf map representations
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• Unnamed Item
• Unnamed Item

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