Do you have more information on the Rational Function Coefficients used by Orthoengine?
Rational Functions (RF) is commonly used in a lot of imagery. It is a way to give out the ortho transformation coefficients without giving out the sensor information. It is an approximation of a rigorous model. NIMA uses it for their NITF format. Space Imaging uses it for their IKONOS data. Hence, it is quite powerful. RF is better than standard polynomial because it supports elevation as well. Thin Plate Spline (TPS) requires a lot more GCPs than RF. For example, 20 coefficients require only 40 GCPs for RF. TPS is like an exact fit and it works well if you have a lot of GCPs. It is difficult to tell which order is best for RF.