s_g

ktch.coiling.s_g(l_g, e_g, r0=1.0)

Growth stage of the growth trajectory at arc length l_g.

Inverse of l_g() ([Noshita_2014]):

\[s(l_G) = \frac{1}{E_G}\,\ln\!\left(1 + \frac{E_G\, l_G}{r_0}\right),\]

with the limit \(s = l_G / r_0\) as \(E_G \to 0\). l_g may be array-like.

Parameters:

l_garray-like

Trajectory arc length.

e_gfloat

Expansion rate \(E_G\).

r0float, default = 1.0

Initial tube radius.

Returns:

sfloat or ndarray

Growth stage \(s\).

See also

l_g

Inverse function (growth stage to arc length).

References

[Noshita_2014]

Noshita, K., 2014. Quantification and geometric analysis of coiling patterns in gastropod shells based on 3D and 2D image data. Journal of Theoretical Biology 363, 93–104.