The sinuosity index of Benhamou (2004), a turning-angle-based measure of path tortuosity that — unlike the displacement-based [path_straightness()] / [path_tortuosity()] — does not rely on net start-to-end displacement, so it is well-behaved for convoluted or random-search paths: $$S = 2 \left[ p\,\frac{1+c}{1-c} + b^2 \right]^{-1/2}$$ where \(p\) is the mean step length, \(c\) the mean cosine of the interior turning angles, and \(b\) the coefficient of variation of step length. A perfectly straight path gives `0`; more winding paths give larger values.
Value
A single sinuosity value `>= 0`, or `NA_real_` when fewer than three finite points are available or all steps have zero length.
Details
Unlike the straightness index, sinuosity is **not** scale-invariant: it has units of \(1/\sqrt{\mathrm{length}}\). For the most reliable comparison across trajectories the path should be resampled to a common step length (rediscretisation); the \(b\) term mitigates variable step length but does not fully replace it.
References
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
Examples
path_sinuosity(x = 0:5, y = rep(0, 6)) # straight -> 0
#> [1] 0