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

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ruik zhang 2023-4-13

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https://ww2.mathworks.cn/matlabcentral/answers/1946718-how-to-get-the-sequential-rotational-angles-needed-around-x-y-and-z-axis-according-to-the-cosine

编辑： Matt J 2023-4-13

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

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Matt J 2023-4-13

编辑：Matt J 2023-4-13

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.

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Answer 1

Matt J 2023-4-13

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https://ww2.mathworks.cn/matlabcentral/answers/1946718-how-to-get-the-sequential-rotational-angles-needed-around-x-y-and-z-axis-according-to-the-cosine#answer_1215458

编辑：Matt J 2023-4-13

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