Illustration from Scientific Research

The computation of the torsion τ n and the 3D curvature к n from the Frenet–Serret frame with a binormal vector b (red), normal vector n (green) and tangent vector t (blue) at subsequent arc-length positions (black filled circles) enumerated by n along the 3D centre line (black line), using the rotation angle of the local bending plane ω τ and the in-plane rotation angle ψ of the tangent. Additionally, we measure ω 3D as the orientation of the normal vector with respect to the x–y plane of the laboratory frame.

DOI