In Figure $10,$ coordinate frames are attached to the base of robot arm, table corner, workpiece, and camera with positions and orientations as shown. The workpiece is a cube object with size $20$x$20$x$20$ cm$,$ and $\{2\}$ is attached at the cube centre. The camera is mounted directly on top of the cube at height $2$ meters.

From Figure $10,$ suppose the block on the table is rotated $90$ degree about z$2$ and moved so that its center has coordinate $[00\mathrm{.}80\mathrm{.}1]^$T relative to the frame $\{1\}.$ Compute the homogeneous transformation relating the block frame to the camera frame, and the block frame to the base frame.