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.
% 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.