this is a mathematical question, probably very easy for some people, but I want to make sure my solution is correct.
I have a matrix of points P with three columns (for x, y and z coordinates) and tons of rows, let's say one thousand ,but the number really doesn't matter.
I have to flip this matrix P and rotate it with given flipping (let's call it F) and rotation (let's call it R) matrices. A flip of the x-coordinates wo be a matrix as in [-1 0 0; 0 1 0; 0 0 1], for example. The roation matrix is also a 3x3 matrix, but not so simple as that (but it's given).
I would like to unite these two matrices in one for future calculations and I'm not sure if the multiplication of the two would be correct, as in:
I'm aware that when rotating the order of rotations is important. It's not the same to rotate first in x and then in y as the other way around. Does this matter here?
I'll add an example:
P = [ 1 1 0]
F = [-1 0 0; 0 1 0; 0 0 1]
T = [0.9999,-0.0097,-0.001;0.0095,0.9998,-0.0160;0.0101,0.01593,0.9998]
First comes the flipping, then the rotation:
Flipping = F * transpose(P)
Rotation = ]The result is [-1.009600000000000;0.990300000000000;0.005830000000000]