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
PRO-2014-Lecture.pdf. Basis \beta equals the standard basis \sigma.
% 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 bound vector X_\beta = [1;2;3] representing point X in (0,\sigma), list the numeric values.
Plot the position vector in (O',\beta') of point Y represented in (O',\beta') by vector Y_{\beta'} = [1;2;3], list the numeric values.
Consider point Z, where X moves by the motion given above. Plot the bound vector representing the point Z w.r.t. (O=0,\beta), list the numeric values.