How to get the sequential rotational angles needed around x, y, and z axis according to the cosine direction changes?

Hello,

Now I have a question below:

I have a vector of coordinate (x0,y0,z0) and direction cosine (alpha_0, beta_0, gamar_0). I want to move it to (x1, y1, z1) and it has cosine direction of (alpha_1, beta_1, gamar_1).

How to get the sequential translational quanity along x, y, and z axis, and the sequential rotational angle around x, y and z axis?

Thank you very much !

Ruik

[Matt J]

There is no unique choice for the rotation if you only have only one moving point (x0,y0,z0). Allowing both translation and rotation makes it even more trivial: you can always bring a single start point (x0,y0,z0) to a new point (x1, y1, z1) by applying a simple translation t=(x1-x0,y1-y0,z1-z0) without doing any rotation at all.

Answer 1

[Matt J]

If you have multiple start and target points, then you can find the roto-translation optimally consistent with all of them by using this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/26186-absolute-orientation-horn-s-method