Converting differences of Euler Angles

Hi, I have a series of data points collected with the position (X, Y, Z) and orientation (RotZ, RotY, RotX). Just as I will be using the 3d distance formula to look at overall position differences between points, I'm looking to describe the overall orientation differences. How do I convert my Euler angle representation of orientation differences into overall rotational differences. (My coordinate axes are arbitrary, so I would prefer not to describe orientation changes as rotation about those axes.) Any help or suggestions for useful functions would be appreciated. Thanks in advance! - MG

Answer 1

[Matt J]

You could convert your Euler angles to a rotation matrix R and then find the overall axis about which R rotates. This is given by the eigenvector of R with eigenvalue 1, e.g.,

    >> R=Rz(45)*Rx(30)*Rz(20)   %A rotation matrix based on z-x-z Euler angles

    R =

        0.4550   -0.8173    0.3536
        0.8739    0.3336   -0.3536
        0.1710    0.4698    0.8660

    >> [V,D]=eig(R);

    >> d=diag(D); [~,idx]=min(abs(d-1)); rotaxis = V(:,idx)

    rotaxis =

        0.4357
        0.0966
        0.8949

[Matt J]

You can then also get the overall angle of rotation about rotaxis as follows

>> anglesep=@(a,b) atan2(norm(cross(a,b)),dot(a,b))*180/pi;
>> N=null(rotaxis'); 
>> rotangle = anglesep(R*N(:,1),N(:,1))

rotangle =

     70.8938