MATLAB Answers

John deGrassie

Vectorized Solution to Rotate Multiple Points each at a Different Angle

Asked by John deGrassie
on 7 Mar 2013

I want to rotate a matrix of points, i.e. column vectors. However, I want to rotate each vector in the matrix by a different angle. For example:

pointMatrix  = [v1,v2,v3,v4]; %vi is a column vector
rotateAngles = [10,20,30,40]; %degrees

Say I want to rotate these points around the z-axis. Therefore, for one point I could do something like the following:

Rz = [[cos(rotateAngles(1)) -sin(rotateAngles(1)) 0];...
      [sin(rotateAngles(1))  cos(rotateAngles(1)) 0];...
      [       0                      0            1]];
v1Rotated = Rz*v1;

Is there a non-loop way to rotate all the vectors in my pointMatrix by each one's unique rotation angle? Something like this...

   allRotatedPoints = superRotationMatrix*pointMatrix;

where the superRotationMatrix "magically" rotates each column by the corresponding angle.




2 Answers

Answer by Teja Muppirala
on 8 Mar 2013
Edited by Teja Muppirala
on 8 Mar 2013
 Accepted answer

This vectorized solution uses complex exponentials and works about 2 orders of magnitude faster for large vectors.

M = exp(rotateAngles*1i) .* ([1 1i 0]*pointMatrix);
allRotatedPoints = [real(M); imag(M); pointMatrix(3,:)];


Matt J
Answer by Matt J
on 7 Mar 2013
Edited by Matt J
on 7 Mar 2013

You can use MTIMESX on the file exchange

If your superRotationMatrix is 3x3xN and you reshape your pointMatrix to be 3x1xN, then


will give you the rotated vectors in a 3x1xN output.


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