# Rotate a 3D data cloud to align with one axis

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Nima Mirzaeian on 13 Jan 2020
Edited: Image Analyst on 15 Jan 2020
Hello! I have a cloud of data points in form of a spindle. How can I rotate the entire set so that the spindle long axis align with x axis? Thank you!

Looky on 14 Jan 2020
I'm not sure if any built in functions exist for this purpose.
However, one mathematical way would be the following:
1. Determine long axis of the spindle(how to do this depends on how you create your spindle). Save as vector r and normalize it: r=r/norm(r);
2. Determine angle between r and the x-axis, use dot product between r and (1, 0, 0) => angle=acosd(dot(r,[1, 0, 0]))
3. Determine rotation-vector u by crossing x-axis and r: u=cross([1,0,0],r);u=u/norm(u);
4. Implement rotation matrix, see here: Wiki RotMat
5. Multiply the vector representation of every single point with the rotation matrix
Example implementation of the rotation matrix(angle in degree):
u=u/norm(u);
rotMat=eye(3)*cosd(angle(1))+sind(angle(1))*[0,-u(3), u(2);u(3),0,-u(1);-u(2),u(1) 0]+(1-cosd(angle(1)))* [u(1)^2, u(1)*u(2), u(1)*u(3); u(1)*u(2), u(2)^2, u(2)*u(3); u(1)*u(3), u(2)*u(3), u(3)^2 ];
vector=vector*rotMat;
vector=vector/norm(vector);

#### 1 Comment

Nima Mirzaeian on 15 Jan 2020
Thanks!! It worked!

Image Analyst on 15 Jan 2020
Edited: Image Analyst on 15 Jan 2020
You might be looking for the view() function, if you want to rotate the whole coordinate system (data plus axes) so that you're looking at it "straight on" or from a certain angle/viewpoint.