Antenna pattern rotation

Can anybody tell me what do we mean by rotation of an antenna by some angle.? I have drawn 3D radiation pattern of an antenna and lets suppose I want to rotate it by some angle around any x,y,z axis. What I think of is to first convert the spherical coordinates to cartesian and then multiplying the with some rotation matrix. But I am confused what is the use of doing this as rotating antenna pattern with some rotating matrix will not change the pattern shape (or does it ?) just it will tilt to a new angle around some axis.

Also do I need to convert back to spherical coordinates after rotating the pattern in cartesian coordinate ? Because in order to plot it again I again need to come back to rectangular coordinate system.

If antenna has rotational symmetric pattern is space then nothing will change by rotating antenna physically or multiplying it with rotational matrix mathematically. But if it is not symmetric then for sure rotation will rotate the field pattern in space. About conversion to spherical coordinate is for mathematical and computational ease you can do the same by remaining in the Cartesian space but that may make the computation little complex.
converting back to Cartesian space is totally dependent on what you want to plot

@nomigoraya I understad your first point but regarding the second point
" conversion to spherical coordinate is for mathematical and computational ease you can do the same by remaining in the Cartesian space but that may make the computation little complex". I am not sure I fully understand it. Can you please elaborate little bit. Thank you.

Look any point in the space can be represented in Cartesian, Cylindrical or Spherical co_ordinate system. The point in space remains the same only the variables defining it changes as in Cartesian system there lengths will define the point while same point will be defined by two lengths and one angle in cylindrical system that is radius, height and angle and so on with spherical where one length radius and two angles define the same point. Important consideration to be noted is that point is same so if it is defined in Cartesian system you just need to multiply it with some conversion formula to go to cylindrical and spherical system.
Now next point why it is done? Reason is very simple and bit clear from names and come from symmetry of objects for example just think about cylinder any point on cylinder can be defined far easily with giving radius, height and angle. Now try to define the same point in Cartesian obviously you can define it but it would be far more difficult to visualize and then manipulate mathematically but for sure you can define it in Cartesian and Spherical System.