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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.
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,:)];
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.