l_g#

ktch.coiling.l_g(s, e_g, r0=1.0)[source]#

Arc length of the growth trajectory at growth stage s.

Maps the growth stage \(s\) to the trajectory arc length \(l_G\) ([Noshita_2014]):

\[l_G(s) = \frac{r_0}{E_G}\left(e^{E_G s} - 1\right),\]

with the limit \(l_G(s) = r_0 s\) as \(E_G \to 0\). Because \(|dp/ds| = r(s)\), the arc length depends only on the expansion rate e_g (and r0), not on c_g/t_g. s may be array-like.

Parameters:

sarray-like: Growth stage \(s\).
e_gfloat: Expansion rate \(E_G\) (the logarithm of Okamoto’s original \(E\)).
r0float, default = 1.0: Initial tube radius (arc length scales with r0).

Returns:

l_gfloat or ndarray: Trajectory arc length at s.