How to rotate about an axis parallel to x axis?

14 views (last 30 days)
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.

Accepted Answer

John D'Errico
John D'Errico on 28 Apr 2022
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.
  1 Comment
yunya liu
yunya liu on 28 Apr 2022
Really helpful. That's what I'm looking for. I previously only did rotation about origin point not around specific axis. Thanks very much.

Sign in to comment.

More Answers (0)


Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!