I need to perform two sequential rotations, about different points, by different angles.
Call the initial point $A$, and the final solution after the two rotations $A'$.
Call the two centers of rotation $C_1$ and $C_2$.
Call the two angles $\theta_1$ and $\theta_2$.
Is there a way to calculate a new center of rotation $C_3$ and angle $\theta_3$ that will rotate $A$ to $A'$ in one operation?
I know I can perform the operations sequentially using translation and rotation matrices, but I have to perform these calculations many, many times, using the same $C_1$, $C_2$, $\theta_1$ and $\theta_2$, so it would roughly cut my time in half if I could find $C_3$ and $\theta_3$ first.
I've just realized that $C_3$ and $\theta_3$ will be dependent on the specific starting point, thus I'd have to re-calculate $C_3$ and $\theta_3$ for every point I want to do the rotations on, and the extra calculations may mean that there is no benefit to doing this over just doing the sequential matrix calculations... Anyway, if anyone knows any shortcuts, given my question above, please let me know. Thanks.