Make a texture a clickable Button
In games and other 3D scenes, generally when the user clicks the mouse, a ray is cast into the scene in the direction the camera is facing, and a check is done to see what geometry in the scene it intersects. If it intersects nothing, it is ignored. If it intersects a single object, then the application processes a click on that object (at the location of the intersection). If more than one object is intersected, then usually the front-most object is assumed to be the on the user wanted to click on, so that is processed.

In general, geometry is stored using x,y,z coordinates rather than spherical coordinates, as the GPU hardware works in cartesian coordinates.