General Fifth Order Polynomial

The General Fifth Order Parametric method provides an interface to define a simple fifth order polynomial transformation between two CoordSys objects. The "A" parameters provide terms for the shift in the Easting, and the "B" parameters provide terms for the shift in the Northing.  The basic formula for computing the difference takes the following form:

dx = A0 + (Au1v0 * u) + (Au0v1 * v) + (Au2v0 * u^2) + (Auv * uv) + (Au0v2 * v^2) +
            (Au3v0 * u^3) + (Au2v1 * u^2v) + (Au1v2 * uv^2) +  (Au0v3 * v^3) +
            (Au4v0 * u^4) + (Au3v1 * u^3v) + (Au2v2 * u^2v^2) + (Au1v3 * uv^3) + (Au0v4 * v^4)+ 
            (Au5v0 * u^5) + (Au4v1 * u^4v) + (Au3v2 * u^3v^2) + (Au2v3 * u^2v^3) + (Au1v4 * uv^4) + (Au0v5 * v^5)

dy = B0 + (Bu1v0 * u) + (Bu0v1 * v) + (Bu2v0 * u^2) + (Buv * uv) + (Bu0v2 * v^2) + 
            (Bu3v0 * u^3) + (Bu2v1 * u^2v) + (Bu1v2 * uv^2) + (Bu0v3 * v^3) + 
            (Bu4v0 * u^4) + (Bu3v1 * u^3v) + (Bu2v2 * u^2v^2) + (Bu1v3 * uv^3) + (Bu0v4 * v^4) + 
            (Bu5v0 * u^5) + (Bu4v1 * u^4v) + (Bu3v2 * u^3v^2) + (Bu2v3 * u^2v^3) + (Bu1v4 * uv^4) + (Bu0v5 * v^5)
  

The "General Fifth Order Parametric" ParametricTransform has the following Parameters:

*Note : a polynomial shift is generally defined for a small area.  Using the method to shift data outside of the pre-defined bounds can lead to undesirable results.