A new programmable prediction method is developed to refine the occultation band by taking into consideration the triaxiality of an occulting body, as well as two more factors, namely, the barycenter offset of an occulting planet from the relevant planetary satellite system and the gravitational deflection of light rays due to an occulting planet. Although these factors can be neglected in most cases, it is shown that there are cases when these factors can cause a variation ranging from several tens to thousands of kilometers in the boundaries of occultation bands. Knowledge of analytic geometry simplifies the process of derivation and computation. This method is applied to long-term predictions of Jovian and Saturnian events.