# How to rotate entire 3d data with x,y,z values along a particular axis (say x axis)?

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Sagar on 30 Mar 2014
Edited: Visa Suomi on 26 Sep 2017
I need to rotate my 3d dataset defined by x,y,z coordinate along x axis at a specified angle (say 45 degree). This kinds of rotations are often needed when processing scanner and LIDAR data. MATLAB can do exactly what I want to do, but in graphic objects only i.e. using rotate(h,direction,alpha). However, this doesn't change the source data. I need to get the new rotated data, how can I retrieve the new rotated x,y,z data? Or, could you please suggest how to calculate in MATLAB?
Thank you,

Roger Stafford on 30 Mar 2014
Let X,Y,Z be arrays of the rotated points in the dataset. For rotation along the x-axis:
X = x;
Y = y*cos(p)-z*sin(p);
Z = y*sin(p)+z*cos(p);
For rotation p radians in the direction from the y-axis toward the z-axis, that is, in accordance with the "right-hand rule" about the positive x-axis.

Sagar on 31 Mar 2014
Thanks, exactly what I was looking for. It would be great, if you can provide similar formula for rotating around y and z axis as well.
Visa Suomi on 26 Sep 2017
Here are the transformations for all three axes.
Around X-axis:
X = x;
Y = y*cos(theta) - z*sin(theta);
Z = y*sin(theta) + z*cos(theta);
Around Y-axis:
X = x*cos(theta) + z*sin(theta);
Y = y;
Z = z*cos(theta) - x*sin(theta);
Around Z-axis:
X = x*cos(theta) - y*sin(theta);
Y = x*sin(theta) + y*cos(theta);
Z = z;

Matt J on 30 Mar 2014

Matt J on 31 Mar 2014
If you attach your VarName1,2,3 data in a .mat file, I'll take a look at it.
Matt J on 31 Mar 2014
Sorry, never mind. The syntax needs to be
XYZnew = AxelRot(XYZ, angle, [1 0 0],[]);
Sagar on 31 Mar 2014
That works. Thanks,
-Sagar