A mathematical description of the absolute out-of-plane height distribution in 3D shape measurement with an arbitrarily arranged fringe projection profilometry system is presented, and a corresponding algorithm is proposed to determine the parameters required for accurate 3D shape determination in practical applications. The proposed technique requires neither a specific and precise experimental setup nor a manual measurement of geometric parameters, and it yields high measurement accuracies while allowing the system components to be arbitrarily set and positioned. Computer simulations and a real experiment have been conducted to verify the validity of the technique.