Transform exercise
- We want to translate and rotate the 2D point \( \mathbf{p} = [2\ \ 0]^\top \) The translation vector is \( [-2\ \ 0]^\top \). The rotation is by \( 90^\circ \). What are the approximate coordinates of the point after the transform?
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✱Does the order in which the rotation and translation are applied matter?
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The matrix \( \mathbf{M_2} \) rotates a 2D point by 45 degrees.
$$ \mathbf{M_2} = \left[ \begin{array}{cc} \cos{45^\circ} & -\sin{45^\circ} \\ \sin{45^\circ} & \cos{45^\circ} \\ \end{array} \right] $$
✱What is the rotation that will rotate a 3D point by 45 degrees around the z-axis?