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===== Homework 05 - Motion Axis =====

=== Task ===
The goal of this task is to [[https://cw.fel.cvut.cz/wiki/_media/courses/pkr/labs/hw05.pdf|estimate joint axes of a robot from 3D point measurements]].

As the task description explains, we will estimate the robot motion axes by moving joints one by one and measuring the coordinates of three points fixed to the end effector of the mechanism.
Two sets of variables are required to solve the task: point coordinates before the motion that are stored in [[https://cw.fel.cvut.cz/wiki/_media/courses/pkr/labs/x_measurements.txt|x_measurements]], and point coordinates after the motion stored in [[https://cw.fel.cvut.cz/wiki/_media/courses/pkr/labs/y_measurements.txt|y_measurements]].

''x_measurements'' and ''y_measurements'' are 4 x 3 x 3 numpy matrices saved to text files. The first dimension corresponds to the number of joints.
The second dimension is 3 as we measure coordinates of vectors in $\mathbb{R}^3$. The third dimension corresponds to the number of points measured.
So x_measurements[0, :, 0] represents the coordinates of $\vec{x_1}$ before moving the first joint. 

To load the files, use 
  np.loadtxt(filename).reshape((4, 3, 3))

Create a function ''get_axis_from_point_measurement(x_measurements, y_measurements)'' which takes as inputs coordinates of three points before and after moving one revolute joint and outputs the axis of motion of that joint.


Input/Output specifications for ''get_axis_from_point_measurement'':
  - ''x_measurements'' : coordinates of points before motion (3x3 matrix of type ''np.ndarray'')
  - ''y_measurements'' : coordinates of points after motion (3x3 matrix of type ''np.ndarray'')
  - **Return value** : dictionary with 2 keys ''"a_dir"'' and ''"a_point"'', whose values are the direction vector (3x1 matrix of type ''np.ndarray'') and the point (3x1 matrix of type ''np.ndarray'') that describe the axis of motion.

   
Visualize found axis of motion as lines in 3D. Please use this viewpoint to make it easier for the assessment
  ax.view_init(azim=50, elev=20) 
  
=== Upload ===

Upload a zip archive ''hw05.zip'' (via the [[https://cw.felk.cvut.cz/upload/|course ware]]) containing:
  - ''hw05.py'' - python script containing the implemented function ''get_axis_from_point_measurement''
  - ''hw05.pdf'' - report file containing visualization of the axes of motion

<note>
All the files must be contained in the root of ''hw05.zip''.
</note>