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

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,

Answer 1

[Roger Stafford]

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]

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]

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;

Answer 2

[Matt J]

See Syntax 3 of this FEX file

http://www.mathworks.com/matlabcentral/fileexchange/30864-3d-rotation-about-shifted-axis

[Matt J]

It would be great, if you can provide similar formula for rotating around y and z axis as well.

    XYZ=[X(:),Y(:),Z(:)].';

 XYZnew = AxelRot(XYZ, angle, [0 1 0]); %rotation in y
 XYZnew = AxelRot(XYZ, angle, [0 0 1]); %rotation in z

[Sagar]

Hi Matt, thank you very much for this, but I get the following error when I run this,

 XYZ=[VarName1(:),VarName2(:),VarName3(:)];
 XYZnew = AxelRot(XYZ, angle, [1 0 0]); %rotation in x.

I didn't transpose as you had done, because VarName1, VarName2, and VarName3 are already column vectors (of size N*1) in my case.

error:
Error using  - 
Matrix dimensions must agree.

Error in AxelRot (line 85)
    AxisShift=x0-(x0.'*u).*u;

What could be the error?

[Matt J]

XYZ is expected to be 3xN. Without the transpose, it will be Nx3.

[Sagar]

Hi Matt, apparently, that is not the issue. I transposed the matrix but still get the same error:

XYZ=[VarName1,VarName2,VarName3].'; XYZnew = AxelRot(XYZ, angle, [1 0 0]); %rotation in x.

Error using - Matrix dimensions must agree.

Error in AxelRot (line 85) AxisShift=x0-(x0.'*u).*u;

[Matt J]

If you attach your VarName1,2,3 data in a .mat file, I'll take a look at it.

[Matt J]

Sorry, never mind. The syntax needs to be

 XYZnew = AxelRot(XYZ, angle, [1 0 0],[]);

[Sagar]

That works. Thanks,

-Sagar