theta_r

ktch.coiling.theta_r(l_r, w_r, t_r, d_r, r0=1.0)

Coiling angle of growth trajectory at arc length l_r.

Inverse of l_r() (analytic, since the arc length is affine in \(W_R^{\theta/2\pi}\)):

\[\theta(l_R) = \frac{2\pi}{\ln W_R}\, \ln\!\left(1 + \frac{l_R\,(1 - D_R)\,\ln W_R}{r_0\,\sqrt{\Lambda}}\right).\]

Parameters:

l_rarray-like

Trajectory arc length.

w_r, t_r, d_rfloat

Raup parameters (w_r > 1, -1 < d_r < 1).

r0float, default = 1.0

Initial tube radius.

Returns:

thetafloat or ndarray

Coiling angle \(\theta\) (radians).

See also

l_r

Inverse function (coiling angle 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.