Calculates the straightness index of a 3-dimensional trajectory, \(D / L\),
where D is the beeline distance between the first and last points in
the trajectory,and L is the path length travelled (Batschelet, 1981).
Benhamou (2004) considers the straightness index to be a reliable measure of
the efficiency of a directed walk, but inapplicable to random trajectories.
The straightness index of a random walk tends towards zero as the number of
steps increases, hence should only be used to compare the tortuosity of
random walks consisting of a similar number of steps.
Traj3DStraightness(trj3d)The straightness index of trj, which is a value between 0
(infinitely tortuous) to 1 (a straight line).
3-dimensional trajectory to calculate straightness of.
The straightness index is also known as the net-to-gross displacement ratio.
According to Batschelet (1981), this value (termed d) is an
approximation of r, which is the length of the mean vector of turning
angles of a constant step-length trajectory (see
TrajMeanVectorOfTurningAngles and
TrajRediscretize for creating a constant step-length
trajectory).
Batschelet, E. (1981). Circular statistics in biology. ACADEMIC PRESS, 111 FIFTH AVE., NEW YORK, NY 10003, 1981, 388.
Benhamou, S. (2004). How to reliably estimate the tortuosity of an animal's path. Journal of Theoretical Biology, 229(2), 209-220. doi:10.1016/j.jtbi.2004.03.016
Traj3DFromCoords, Traj3DDistance for
trajectory distance (or displacement), and Traj3DLength for
trajectory path length, Traj3DStraightness for the
straightness of a 2D trajectory.