Decomposing a Transformation Matrix

2018 11 28
2 个回答
回答已采纳
更新时间：2018 11 28
3 次查看（30 天）

0 个投票

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!

请先登录，再回答此问题。

 采纳的回答

Matt J
Matt J 2018-11-28
编辑：Matt J 2018-11-28

2 个投票

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

9 个评论
显示 7更早的评论 隐藏 7更早的评论

Kash Costello
Kash Costello 2018-11-28
Hi omg you are a life saver! Yes, I know that the translation is the last column and the rotation matrix is the first 3x3 but I didn't think of actually... processing them separately. -facepalm- Anyway, I saw the matlab function! Is it possible to NOT use the function you created? Like, just use any built-in commands in matlab?
I tried to use this:
M = makehgtform('translate',[1,2,3],'xrotate',30*pi/180);
M2 = M(1:3,1:3);
translation = M(1:3,end);
eul = rotm2eul(M2,'ZYX');
eul1 = eul.*(180/pi);
eul2 = fliplr(eul1);
It gave me --> 30.0000,0,0 just like what I want. But when I tried to put
'yrotate',30*pi/180
It's giving me --> 33.6901,25.6589,33.6901
Do you have any idea what happened on this one? Thanks a lot!!
Matt J
Matt J 2018-11-28
You can extract the lines of code from rot2taitbryan.m that are relevant to you, if you wish. I do not know what conventions rotm2eul uses and cannot play around with it, since I do not have the Robotics System Toolbox.
Kash Costello
Kash Costello 2018-11-28
Okay, that's fine. Thanks so so so much! I really appreciate your help and the code you shared. It helped me a lot!!
Kash Costello
Kash Costello 2018-11-28
Oh uh by the way... if it's not too much to ask, could you explain (perhaps with an example?) why you wrote the function that way? I'm watching videos but I'm still kind of confused. If it's not okay, I totally understand. Thanks again! Have a good day!
Matt J
Matt J 2018-11-28
It's not mine. I downloaded it from somewhere.
Kash Costello
Kash Costello 2018-11-28
Oh. Okay, but do you at least know why the sequence is like this?
case 'XYZ'
ang(1) = atan2d(-R(2,3),R(3,3));
ang(2) = asind(R(1,3));
ang(3) = atan2d(-R(1,2),R(1,1));
I understand why it's R(2,3), R(3,3) and such. But I am confused why it's -R(2,3) first and why not R(3,3).
Bruno Luong
Bruno Luong 2018-11-28
编辑：Bruno Luong 2018-11-28
Oh. Okay, but do you at least know why the sequence is like this?
See this document section 2.1
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

请先登录，再进行评论。

更多回答（1 个）

Bruno Luong
Bruno Luong 2018-11-28

0 个投票

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.

类别

在 帮助中心 和 File Exchange 中查找有关 Coordinate Transformations 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by