A complete classification of quintic space curves with rational rotation-minimizing frames

DOI10.1016/j.jsc.2011.09.012zbMath1232.53004OpenAlexW2015682863MaRDI QIDQ655571

Takis Sakkalis, Rida T. Farouki

Publication date: 4 January 2012

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2011.09.012

zbMATH Keywords

quaternionspolynomial identitiesPythagorean-hodograph curvescomplex numbersHopf maprotation-minimizing frames

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Computational aspects in algebraic geometry (14Q99) Numerical approximation and computational geometry (primarily algorithms) (65D99)

Related Items (19)

A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames ⋮ Rational frames of minimal twist along space curves under specified boundary conditions ⋮ Mapping rational rotation-minimizing frames from polynomial curves on to rational curves ⋮ Spatial Pythagorean-hodograph B-spline curves and 3D point data interpolation ⋮ Parametric curves with Pythagorean binormal ⋮ On new types of rational rotation-minimizing frame space curves ⋮ Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves ⋮ Corrigendum to ``Rational rotation-minimizing frames on polynomial space curves of arbitrary degree ⋮ Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants ⋮ Rotation-minimizing osculating frames ⋮ Rational minimal-twist motions on curves with rotation-minimizing Euler-Rodrigues frames ⋮ Geometry of the ringed surfaces in \(\mathbb{R}^4\) that generate spatial Pythagorean hodographs ⋮ Rational rotation-minimizing frames -- recent advances and open problems ⋮ \(C^{1}\) and \(C^{2}\) interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames ⋮ Geometric interpolation of ER frames with \(G^2\) Pythagorean-hodograph curves of degree 7 ⋮ Construction of periodic adapted orthonormal frames on closed space curves ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Sweeping surfaces according to type-2 Bishop frame in Euclidean 3-space

Cites Work

• Unnamed Item
• Unnamed Item
• Quintic space curves with rational rotation-minimizing frames
• Equivalence of distinct characterizations for rational rotation-minimizing frames on quintic space curves
• Offset-rational parametric plane curves
• Nonexistence of rational rotation-minimizing frames on cubic curves
• Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• Two moving coordinate frames for sweeping along a 3D trajectory
• Parametric generalized offsets to hypersurfaces
• Clifford algebra, spin representation, and rational parameterization of curves and surfaces
• Euler-Rodrigues frames on spatial Pythagorean-hodograph curves.
• Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves
• Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
• Construction of Rational Curves with Rational Rotation-Minimizing Frames via Möbius Transformations
• Design of rational rotation–minimizing rigid body motions by Hermite interpolation
• Mathematics of Surfaces XI

This page was built for publication: A complete classification of quintic space curves with rational rotation-minimizing frames