Rational minimal-twist motions on curves with rotation-minimizing Euler-Rodrigues frames
From MaRDI portal
Publication:1736369
DOI10.1016/j.cam.2018.12.012zbMath1410.53002OpenAlexW2905101756WikidataQ128733381 ScholiaQ128733381MaRDI QIDQ1736369
Alessandra Sestini, Rida T. Farouki, Carlotta Giannelli
Publication date: 26 March 2019
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://escholarship.org/uc/item/8v87c9m8
Pythagorean-hodograph curvesrotation-minimizing frameEuler-Rodrigues framespatial motion planningrigid body motionsminimal twist frame
Kinematics of a rigid body (70B10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Curves in Euclidean and related spaces (53A04)
Related Items
Construction of \(G^2\) spatial interpolants with prescribed arc lengths ⋮ Geometric interpolation of ER frames with \(G^2\) Pythagorean-hodograph curves of degree 7 ⋮ Construction of periodic adapted orthonormal frames on closed space curves
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quintic space curves with rational rotation-minimizing frames
- A complete classification of quintic space curves with rational rotation-minimizing frames
- Rational rotation-minimizing frames -- recent advances and open problems
- \(G^{1}\) motion interpolation using cubic PH biarcs with prescribed length
- 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
- Cubic Pythagorean hodograph spline curves and applications to sweep surface modeling.
- Clifford algebra, spin representation, and rational parameterization of curves and surfaces
- Construction of \(G^1\) planar Hermite interpolants with prescribed arc lengths
- Rational frames of minimal twist along space curves under specified boundary conditions
- Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
- 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
- Existence of Pythagorean-hodograph quintic interpolants to spatial \(G^1\) Hermite data with prescribed arc lengths
- A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames
- Helical polynomial curves and double Pythagorean hodographs. I: Quaternion and Hopf map representations
- Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
- Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants
- There is More than One Way to Frame a Curve
- 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
