I have three points that represent a rigid body. The rigid body undergoes a planar transformation in $\Bbb R^3$ due to rotation and translation. I am working with angular velocity with nonzero $\vec i$, $\vec j$, and $\vec k$ components, and what I am trying to accomplish cannot be done easily in $\Bbb R^3$. How can I map my points to $\Bbb R^2$, perform operations (rotations), and then map back to $\Bbb R^3$?
Robjohn provided a solution here, 3D to 2D rotation matrix , but I'd like to understand the math behind his solution. Thank you