Rotate 1 by N vector

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Peter Popoola
Peter Popoola 2018-3-8
评论： Jan 2018-3-10
Hello, everyone. Is there a way (function) in Matlab to rotate a row vector of N dimensions by a given angle? I've only been able to use the matrix multiplication for 2D and 3D cases.
Thanks!
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Peter Popoola
Peter Popoola 2018-3-10
Thanks for the comment, Guillaume. I didn't know that. I guess I'll have to find a way around it.
Jan
Jan 2018-3-10
I consider this as not complicated:
R = eye(numel(u)) + ...
(v * u.' - u * v.') * sin(a) + ...
(u * u.' + v * v.') * (cos(a) - 1);
Here u and v are two orthogonal unit vectors to describe the n-dimensional hyperplane to rotate in. Remember, that in 3D one vector is sufficient to define a plane to rotate in, but in 4D (and N-D), this is not unique anymore. a is the angle in radians to rotate, and the direction is from u to v.
I publish this in the FileExchange currently.

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回答（2 个）

Rik
Rik 2018-3-8
You mean something like this?
v=1:10;
v2=imrotate(v,45);
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Rik
Rik 2018-3-10
File a bug report with GNU. There are often minor differences between Octave and Matlab, especially in edge cases like this. Apparently Octave assumes both dimensions are larger than 1.
Peter Popoola
Peter Popoola 2018-3-10
Okay, Rik. Thank you!

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Jan
Jan 2018-3-8
编辑：Jan 2018-3-10
See WikiPedia: Rotation_matrix_from_axis_and_angle
Here the axis of rotation u, the cross-product matrix []_x and the tensor cross-product (x) are not limited to 3D, but work for n dimensions also. So you can create the n-D rotation matrix in a straight-forward way and multiply your vector with.
[EDITED] See FEX: Rotation Matrix
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Peter Popoola
Peter Popoola 2018-3-9
Thanks once again, Jan. I take it there's no Matlab function that does this? Because I haven't really been able to wrap my head around the formulation given here, and how it can be extended to the N-dimensional case. Thank you for your help!

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