Computing frames along a trajectory

DOI10.1016/0167-8396(89)90008-3zbMath0664.65017OpenAlexW2024715780MaRDI QIDQ1115090

Heinrich Guggenheimer

Publication date: 1989

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-8396(89)90008-3

zbMATH Keywords

torsioncurvatureFrenet frameframesdifferential invariants

Mathematics Subject Classification ID

Algorithms for approximation of functions (65D15) Curves in Euclidean and related spaces (53A04)

Related Items (18)

Characterization of curves that Lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere ⋮ NURBS approximation of surface / surface intersection curves ⋮ Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves ⋮ Almost rotation-minimizing rational parametrization of canal surfaces ⋮ Quintic space curves with rational rotation-minimizing frames ⋮ Construction of rational surface patches bounded by lines of curvature ⋮ Characterization of spherical and plane curves using rotation minimizing frames ⋮ Characterization and construction of helical polynomial space curves. ⋮ Inverse kinematics for optimal tool orientation control in 5-axis CNC machining ⋮ Rotation-minimizing osculating frames ⋮ Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves ⋮ Geometry of the ringed surfaces in \(\mathbb{R}^4\) that generate spatial Pythagorean hodographs ⋮ Rational rotation-minimizing frames -- recent advances and open problems ⋮ Rational rotation-minimizing frames on polynomial space curves of arbitrary degree ⋮ Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics ⋮ Geometric Design Using Space Curves with Rational Rotation-Minimizing Frames ⋮ Construction of periodic adapted orthonormal frames on closed space curves ⋮ Euler-Rodrigues frames on spatial Pythagorean-hodograph curves.

Cites Work

• Two moving coordinate frames for sweeping along a 3D trajectory
• There is More than One Way to Frame a Curve
• Distribution of Zeros and Limit Behavior of Solutions of Differential Equations

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