On new types of rational rotation-minimizing frame space curves

DOI10.1016/j.jsc.2015.08.005zbMath1332.53016OpenAlexW1614440331MaRDI QIDQ898269

Charles Ching-An Cheng, Takis Sakkalis

Publication date: 8 December 2015

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2015.08.005

zbMATH Keywords

Pythagorean hodograph curverotation-minimizing framequaternion polynomial

Mathematics Subject Classification ID

Computer science aspects of computer-aided design (68U07) Differential geometric aspects in kinematics (53A17) Curves in Euclidean and related spaces (53A04)

Related Items (8)

A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames ⋮ Mapping rational rotation-minimizing frames from polynomial curves on to rational curves ⋮ Factorization of quaternionic polynomials of bi-degree \((n,1)\) ⋮ Kempe's universality theorem for rational space curves ⋮ Factorization of motion polynomials ⋮ Geometric interpolation of ER frames with \(G^2\) Pythagorean-hodograph curves of degree 7 ⋮ Rational motions with generic trajectories of low degree ⋮ Rational framing motions and spatial rational Pythagorean hodograph curves

Cites Work

• Quintic space curves with rational rotation-minimizing frames
• A complete classification of quintic space curves with rational rotation-minimizing frames
• Nonexistence of rational rotation-minimizing frames on cubic curves
• On roots of quaternion polynomials.
• Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• On the multiplicity of zeroes of polynomials with quaternionic coefficients
• Two moving coordinate frames for sweeping along a 3D trajectory
• Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves
• Corrigendum to ``Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
• On the Zeros of Polynomials over Division Rings

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