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===== Homework 02 - Rigid motion as a coordinate transformation =====

=== Task ===

Use MATLAB to solve the following problems related to rigid motion. Use different colors to display your results.

  - Simulate the rigid motion with matrix R and translation o_{\beta'} prescribed by Equation 4.4 in {{http://cmp.felk.cvut.cz/cmp/courses/PRO/2014/Lecture/PRO-2014-Lecture.pdf|PRO-2014-Lecture.pdf}}. Basis \beta equals the standard basis. 

  % approximate rotation
  R = [0.8047   -0.5059   -0.3106
       0.3106    0.8047   -0.5059
       0.5059    0.3106    0.8047];

  % less approximate rotation
  [U,D,V] = svd(R);
  R = U*V';

  % translation o_{\beta'}
  o = [1;1;1];

  - Find the coordinates of vectors of \beta' in \beta and vice versa.
  - Plot vectors of \beta and \beta' in the standard basis, list the numeric values.
  - Plot coordinate systems (O=0,\beta) and (O',\beta'). i.e. plot the basic vectors as bound vectors originating from points O and  O', respectively, list the numeric values.
  - Plot the position vector of point X represented in (O=0,\beta) by vector X_\beta = [1;2;3], list the numeric values.
  - Plot the position vector of point Y represented in (0',\beta') by vector Y_{\beta'} = [1;2;3], list the numeric values.
  - Plot the position vector of the point Z where point X moves w.r.t. (O=0,\beta), list the numeric values.
=== Upload ===

Upload  via the [[https://cw.felk.cvut.cz/upload/|course ware]] the zip archive ''hw02.zip'' containing 
  - hw02.pdf report file describing your solution with all figures 
  - hw02.m MATLAB source code, which generates the results and figures for the report
  - all your additional MATLAB files required by hw02.m