How to rotate points on 3D coordinate systems

I have some points on a 3D Cartesian coordinate system. I want to transfer it form 3D coordinate system to another system which is generated from the first one by a rotation around the x, y or z-axis by (alpha) degrees counterclockwise and clockwise and calculate the position vector in the new coordinate system after the rotation. What is the best solution?

[Cedric]

Google 3D rotation matrices (or just Wikipedia), and/or look at my "scary alternative" here.

Answer 1

[Sean de Wolski]

https://www.mathworks.com/help/releases/R2017b/vision/ref/pctransform.html

[Sterling Baird]

Tough luck if you don't have the computer vision toolbox.