How to rotate about an axis parallel to x axis?

I'm trying to rotate a vector around one axis parallel to x axis.

To my understanding, the rotation around x axis in 3d space is by applying:

a = 1;

xcord = [0 a]; ycord = [0 0]; zcord = [0 0];

pos = [xcord; ycord; zcord];

theta = 30;

Rot = [1, 0, 0; 0, cosd(theta), -sind(theta); 0, sind(theta), cosd(theta)];

pos_new = Rot*pos;

This follows the axis-angle representation of rotating about x axis. But what if I want to rotate about an axis parallel to x axis?

Thanks in advance.

Answer 1

[John D'Errico]

Simple. Effectively, you transform the problem to a rotation around the x axis, then after the rotation, you tranform back.

For example, suppose you want to rotate around an "axis" that lives along the coordinates [x 1 2]? This is parallel to the x axis. Think of the x axis as the set of points [x 0 0].

Given your points in pos, you would then do:

axisvec = [0 1 2]';
rotatedpos = axisvec + Rot*(pos - axisvec)

This does exactly as I said. It translates the points so that the new origin is the point [0 1 2]. Then it perform the rotation. Then it translates the coordinates system back to the original domain.

[yunya liu]

Really helpful. That's what I'm looking for. I previously only did rotation about origin point not around specific axis. Thanks very much.