Convert relative to global

What do you mean by "three flags"? You give the position, (10, 20, 30) of one point. But knowing the coordinates of a single point and your position relative to that point is sufficient. Your x, y, z coordinates, taking that one point as origin are x= [itex]\rho cos(\theta) sin(\phi)[/itex], y= [itex]\rho sin(\theta) sin(\phi)[/itex] and z= [itex]\rho cos(\phi)[/itex]. Your x, y, z "global" coordinates, relative to the same coordinate system in which your point is (10, 20, 30) are x= [itex]\rho cos(\theta) sin(\phi)+ 10[/itex], y= [itex]\rho sin(\theta) sin(\phi)+ 20[/itex] and z= [itex]\rho cos(\phi)+ 30[/itex], a simple translation.

I am assuming here that your "[itex]\theta[/itex]" and "[itex]\phi[/itex] are relative to the "global" coordinate system. If not, you might need three points and would need to specify how [itex]\theta[/itex] and [itex]\phi[/itex] are measured.