3D Rotation Matrix

Hi all, I'm new here and am trying to obtain a 3D rotation matrix.

Currently, I have a set of points (x,y,z) from which I have designated one particular point as the origin, and obtained an x'- and y'- vector, based on some features. This also means I can obtain the z'-vector by taking cross product of x' and y'.

I would like to rotate all these points, such that the x'-, y'- and z'- are in line with the x-, y- and z- axes respectively.

An example of the vectors to be mapped would be say:

x': [-0.2831 -0.9246 0.2548]'

y': [0.9242 -0.1919 0.3303]'

How do I obtain a rotation matrix to be applied to all my points? Thank you for your help!

[Walter Roberson]

Duplicated by later https://www.mathworks.com/matlabcentral/answers/349969-3d-rotation-matrix which appears to have been updated.

Answer 1

[KSSV]

If t is the angle by which you want to rotate your coordinates, the following are the rotation matrices.

Along X:

Rx = [1 0 0; 0 cos(t) -sin(t) ; 0 sin(t) cos(t)] ;

Along Y:

    Ry = [cos(t) 0 sin(t) ; 0 1 0 ; -sin(t) 0  cos(t)] ;

Along Z axes:

      Rz = [cos(t) -sin(t) 0 ; sin(t) cos(t) 0 ; 0 0 1] ;