MATLAB: Rotate surface X Y Z around Y axis

rotate xyz surface

Hi I have three arrays with cooridnates X Y Z. This is surface with part of sphere. I want to rotate this surface around Y axis of an angle BETA tan(BETA)=0.5 . I have tried rotate this by scrpit:
N=numel(Z); ang=atan(0.5); for i=1:1:N X(i)=(X(i).*cos(ang))-(Z(i).*sin(ang)); Z(i)=(X(i).*sin(ang))+(Z(i).*sin(ang)); i=i+1; end
but it change shape of part of sphere.
I want to have a shape like this:
h=surf(X,Y,Z); zdir = [0 1 0]; ang=atan(0.5); rotate(h,zdir,-rad2deg(ang)); axis equal
I will be very appreciated for any help with make script to rotate matrix. Thanks for help.

Best Answer

There is a mistake in your code, the Z coordinate should be computed as
Z(i) = X(i)*sin(ang) + Z(i)*cos(ang)
Though, the main problem is that in the loop, you first compute the rotated X(i) and then use this new value for computing Z(i), although the old one should be used. Use either the function rotate or the rotation matrix
[cos(ang) 0 sin(ang); ...
 0 1 0; ...
 -sin(ang) 0 cos(ang)]
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