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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.

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;

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