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===== Homework 04 - Rigid motion as a coordinate transformation =====

=== Task ===

You can find the description of the task [[https://cw.fel.cvut.cz/wiki/_media/courses/pkr/labs/hw4_rigid_motion.pdf|here]].

For task 1:

  # approximate rotation
  R = np.array([[0.8047,   -0.5059,   -0.3106],
                [0.3106,    0.8047,   -0.5059],
                [0.5059,    0.3106,    0.8047]])

  # less approximate rotation
  u, s, vh = np.linalg.svd(R)
  R = u.dot(vh)

  # translation t, or OO' in beta
  o_o_pr_beta = np.array([[-1], [0.5], [1]])

For task 2:

Create a function ''compute_rot_t(R_1, t_1, R_2, t_2, R_3, t_3)'' which takes as inputs three transformations as mentioned in the task description and outputs object pose after the motion.


Input/Output specifications for ''compute_rot_t'':
  - ''R_1, R_2, R_3'' : rotation matrices (3x3 matrix of type ''np.ndarray'')
  - ''t_1, t_2, t_3'' : translation (3x1 matrix of type ''np.ndarray'')
  - **Return value** : dictionary with 2 keys ''"r"'' and ''"t"'', whose values are the rotation (3x3 matrix of type ''np.ndarray'') and the translation (3x1 matrix of type ''np.ndarray'') of the object after the motion expressed in the world frame.

Implement the solution in a single file ''hw04.py''. The file must contain the ''compute_rot_t'' function, such that it can be imported (by the automatic evaluation) as

<code>
import hw04
res = hw04.compute_rot_t(*args)
</code>

=== Upload ===

Upload a zip archive ''hw04.zip'' (via the [[https://cw.felk.cvut.cz/upload/|course ware]]) containing:
  - ''hw04.json'' - json file containing the solution of Task 1
  - ''hw04.py'' - python script containing the implemented function ''compute_rot_t''

<note>
All the files must be contained in the root of ''hw04.zip''.
</note>

**Creating** ''hw04.json'':

Create an empty dictionary in Python:

<code>
solution = {}
</code>

The key for this dictionary will be ''"x_pr_beta"'', translation, a list of three float values. 

<code>
import json
with open("hw04.json", "w") as outfile:
    json.dump(solution, outfile)
</code>