# Rotate surface X Y Z around Y axis

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Andrew on 20 Feb 2014
Answered: Andrew on 20 Feb 2014
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.

jandas on 20 Feb 2014
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)]

Iain on 20 Feb 2014
The obvious issue is that you're updating X, then using the updated X to calculate a new Z.
Store the old X, or the new one, in a temporary variable before updating Z.
Or, you could use a matrix form, eg.
Xnew = |cos(a) -sin(a) | * X
Ynew |sin(a) cos(a) | Y
Or, more generally,
Xaxis2 = T * Xaxis1;

Andrew on 20 Feb 2014
Thanks a lot!