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===== Homework 06 - Rotation parameterization by quaternions =====
=== Task ===

In Maple:

   - Verify that formula (7.74) in [[http://cmp.felk.cvut.cz/cmp/courses/PRO/2012/Lecture/PRO-2012-Lecture-12.pdf|PRO-2012-Lecture-12.pdf]] for quaternion composition holds true.
   - Verify that formula (7.76) in [[http://cmp.felk.cvut.cz/cmp/courses/PRO/2012/Lecture/PRO-2012-Lecture-12.pdf|PRO-2012-Lecture-12.pdf]] for quaternion composition holds true.
     - Find the quaternion representation r1 and matrix representation R1 of the rotation by Pi/2 around x-axis.
     - Find the quaternion representations quaternion representation r2 and matrix representation R2 of the rotation by Pi/2 around y-axis.
     - Construct the quaternion representations r21 of the rotation r21 = r2 o r1 using the composition 'o' of quaternions.
     - Find the rotation matrix R21 = R2.R1 by matrix multiplication '.'.
     - Construct the rotation matrix from r21 and compare it to R21.
     - Construct the quaternion from the rotation matrix R21 and compare it to r21. (Hint: R->axis & angle->quaternion). 


=== Upload ===

Upload via the [[https://cw.felk.cvut.cz/upload/|course ware]] the zip archive ''hw06.zip'' containing 
  - hw06.mws Maple script (functions) solving the assignment. 
  - hw06.pdf description of the solution (algorithms, results, comments).