Cyclic Gaussian

Cyclic gaussian dispersion for orientation.

$w(\theta) = e^{-\frac{\sin^2 \theta}{2 \sigma^2}}$

This provides a close match to the gaussian distribution for low angles, but the tails are limited to $\pm 90^\circ$. For $\sigma$ large the distribution is approximately uniform. The usual polar coordinate projection applies, with $\theta$ weights scaled by $\cos \theta$ and $\phi$ weights unscaled.

This is eqivalent to a Maier-Saupe distribution with order parameter $a = 1/(2 \sigma^2)$, with $\sigma$ in radians.

Distribution coded by P Kienzle.