Decomposing a Transformation Matrix

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Kash Costello
Kash Costello 2018-11-28
编辑： Matt J 2018-11-28
Hi!
I have been trying to look for a function that will "undo" a transformation matrix.
I saw in Matlab that there's a function "makehgtform" to create a transformation matrix. Now, I'm looking for something that is the exact opposite of this.
Example:
M = makehgtform('xrotate',30*pi/180);
It would result to a 4x4 matrix. But I want to actually extract the X, Y, Z translation and X,Y,Z rotation.
Can anyone help me or just give me an idea? I would really appreciate it! :(
Thanks in advance!

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Matt J
Matt J 2018-11-28
编辑：Matt J 2018-11-28
Here's an example that makes use of the attached file for rotation matrix decomposition.
>> M = makehgtform('translate',[1,2,3],'xrotate',30*pi/180)
M =
1.0000 0 0 1.0000
0 0.8660 -0.5000 2.0000
0 0.5000 0.8660 3.0000
0 0 0 1.0000
>> translation=M(1:3,end)
translation =
1
2
3
>> rotation=rot2taitbryan(M(1:3,1:3),'xyz'), %see attached file
rotation =
30.0000 0 0
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Kash Costello
Kash Costello 2018-11-28
Ok I'm being an idiot but I'm still confused even after reading that document. I guess I don't fully grasp what atan2 is and still, it didn't explain why the sequence is like that. My question still remains... :(
Matt J
Matt J 2018-11-28
编辑：Matt J 2018-11-28
I guess I don't fully grasp what atan2 is
Even after googling? https://en.wikipedia.org/wiki/Atan2

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Bruno Luong
Bruno Luong 2018-11-28
Translation vector is T(1:3,4);
Rotation matrix is T(1:3,1:3).
If you want to decompose in rotation on axis, there are many conventions (intrinsic, extrinsic, Euler's angle, Tait–Bryan angles, etc...) see https://en.wikipedia.org/wiki/Euler_angles and pick your choice.

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