Two moving coordinate frames for sweeping along a 3D trajectory
Computer Aided Geometric Design
Computing frames along a trajectory
Computer Aided Geometric Design
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
Computer Aided Geometric Design
Characterization and construction of helical polynomial space curves
Journal of Computational and Applied Mathematics
A characterization of quintic helices
Journal of Computational and Applied Mathematics
Computation of rotation minimizing frames
ACM Transactions on Graphics (TOG)
Constrained design of polynomial surfaces from geodesic curves
Computer-Aided Design
Cubic polynomial patches through geodesics
Computer-Aided Design
Nonexistence of rational rotation-minimizing frames on cubic curves
Computer Aided Geometric Design
Journal of Symbolic Computation
Quintic space curves with rational rotation-minimizing frames
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Construction of Bézier surface patches with Bézier curves as geodesic boundaries
Computer-Aided Design
Construction of rational surface patches bounded by lines of curvature
Computer Aided Geometric Design
Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
Journal of Symbolic Computation
Advances in Computational Mathematics
Parametric representation of a surface pencil with a common line of curvature
Computer-Aided Design
A complete classification of quintic space curves with rational rotation-minimizing frames
Journal of Symbolic Computation
Construction of rational curves with rational rotation-minimizing frames via möbius transformations
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Parametric representation of a surface pencil with a common asymptotic curve
Computer-Aided Design
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An orthonormal frame (f"1,f"2,f"3) is rotation-minimizing with respect to f"i if its angular velocity @w satisfies @w@?f"i=0 - or, equivalently, the derivatives of f"j and f"k are both parallel to f"i. The Frenet frame (t,p,b) along a space curve is rotation-minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation-minimizing with respect to the tangent t have attracted much interest. This study is concerned with rotation-minimizing osculating frames (f,g,b) incorporating the binormal b, and osculating-plane vectors f, g that have no rotation about b. These frame vectors may be defined through a rotation of t, p by an angle equal to minus the integral of curvature with respect to arc length. In aeronautical terms, the rotation-minimizing osculating frame (RMOF) specifies yaw-free rigid-body motion along a curved path. For polynomial space curves possessing rational Frenet frames, the existence of rational RMOFs is investigated, and it is found that they must be of degree 7 at least. The RMOF is also employed to construct a novel type of ruled surface, with the property that its tangent planes coincide with the osculating planes of a given space curve, and its rulings exhibit the least possible rate of rotation consistent with this constraint.