Rational rotation-minimizing frames -- recent advances and open problems
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Publication:668341
DOI10.1016/j.amc.2015.04.122zbMath1410.53001OpenAlexW329706346MaRDI QIDQ668341
Publication date: 19 March 2019
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2015.04.122
angular velocityquaternionsHopf mapPythagorean-hodograph curverotation-minimizing framespatial motion design
Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Curves in Euclidean and related spaces (53A04) Computer-aided design (modeling of curves and surfaces) (65D17)
Related Items (14)
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 ⋮ Helical polynomial curves interpolating \(G^{1}\) data with prescribed axes and pitch angles ⋮ Spatial Pythagorean-hodograph B-spline curves and 3D point data interpolation ⋮ Variational principles for nonlinear Kirchhoff rods ⋮ Construction of \(G^2\) spatial interpolants with prescribed arc lengths ⋮ Generalized Bishop frames of regular curves in \(\mathbb{E}^4 \) ⋮ Rational minimal-twist motions on curves with rotation-minimizing Euler-Rodrigues frames ⋮ \(C^{1}\) and \(C^{2}\) interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames ⋮ \(G^{1}\) motion interpolation using cubic PH biarcs with prescribed length ⋮ The rotating rigid body model based on a non-twisting frame ⋮ Geometric interpolation of ER frames with \(G^2\) Pythagorean-hodograph curves of degree 7 ⋮ Construction of periodic adapted orthonormal frames on closed space curves
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