For a robotic camera I'm using, in its default position its Euler angles (roll, pitch, yaw) are 0. In that case, when I am trying to detect planes I look for planes with the normal vector $v = [0, 0, 1]$
However, lets say the camera has moved and now has some given roll, pitch and yaw.
The world is still the same and so I need to find the same planes, what is the equivalent normal vector I should look for in this new position?
Thanks
You could write it as the product of three rotations
$$R = R_r R_pR_y$$
$$R = \begin{bmatrix}1 & 0 & 0 \\0 &\cos \alpha & \sin \alpha \\ 0 & -\sin\alpha & \cos\alpha\end{bmatrix} \begin{bmatrix}\cos \beta & 0 & \sin \beta \\0 &1 & 0 \\ -\sin\beta & 0 & \cos\beta\end{bmatrix} \begin{bmatrix}\cos \gamma & \sin \gamma & 0 \\-\sin \gamma &\cos \gamma & 0 \\ 0 & 0 & 1\end{bmatrix}$$
So this would be your rotation matrix to reach from your initial position to your final position if $\alpha, \beta , \gamma$ are roll, pitch and yaw
Can you use this to see what happens to $(0,0,1)$