How to calculate 3 rotation angles and scaling factor from 3 by 3 affine parameters matrix

My apologies if my question is too simple, but I can't seem to find an answer. I need to calculate 3 rotation angles: Rx, Ry, Rz and a scaling factor from a matrix of 3 by 3 affine parameters which I get from Helmert 3D affine function which exist in Geodesic Transformation Toolbox (<http://www.mathworks.com/matlabcentral/fileexchange/9696-geodetic-transformations-toolbox)>. As part of calculated transformation model I get 3 translation parameters followed by 9 affine parameters, and I'm not sure how I can calculate rotation angles and scaling factor for the transformation.

Any points are greatly appreciated.

Answer 1

[Matt J]

The determinant of the matrix should give the scale factor (cubed), so you can obtain the pure rotational part as

 scale=det(A)^(1/3);

 R=A/scale;

There are many ways to factor a rotation matrix R into 3 separate rotations Rx, Ry, Rz. Choose one that suits you from here

http://en.wikipedia.org/wiki/Euler_angles

[Pim van Ooij]

Hi Matt,

Don't you mean R=A/scale? This would produce the best results for me. Do you have a reference for this problem? I would like to read more about it. Thanks, Pim

[Matt J]

Thanks, Pim. I fixed it. Hartley and Zisserman, Multiple View Geometry is a pretty good reference.

[Anna Horna]

@Matt J can you please check that? https://www.mathworks.com/matlabcentral/answers/789509-help-for-do-a-script-helmert-transformation-geodesy?s_tid=srchtitle