Closed lgrcia closed 5 months ago
Faster rotations of the spherical harmonics. This is described in the technical paper but the idea is to go from 6 rotations
to 4
In the previous implementation I merged all rotations, which ends up not being optimal (because of the rotation around y).
The combined rotation to orient the star in the plane of the sky is defined by the axis
\begin{equation} v = \frac{1}{\sqrt{1 - \cos^2{\left(\frac{inc}{2} \right)} \cos^2{\left(\frac{obl}{2}\right)}}} \begin{pmatrix} \sin{\left(\frac{inc}{2} \right)} \cos{\left(\frac{obl}{2}\right)}\\ \sin{\left(\frac{inc}{2} \right)} \sin{\left(\frac{obl}{2}\right)}\\ - \cos{\left(\frac{inc}{2} \right)} \sin{\left(\frac{obl}{2}\right)}\\ \end{pmatrix}, \end{equation}
and angle $\omega = 2 \cos^{-1}{\left(\cos{\left(\frac{inc}{2} \right)} \cos{\left(\frac{obl}{2}\right)} \right)}.$
Faster rotations of the spherical harmonics. This is described in the technical paper but the idea is to go from 6 rotations
to 4
In the previous implementation I merged all rotations, which ends up not being optimal (because of the rotation around y).
The combined rotation to orient the star in the plane of the sky is defined by the axis
and angle $\omega = 2 \cos^{-1}{\left(\cos{\left(\frac{inc}{2} \right)} \cos{\left(\frac{obl}{2}\right)} \right)}.$