General Sixth Order Parametric

The General Sixth Order Parametric method provides an interface to define a simple sixth order polynomial transformation between two HorizontalCoordSys objects. The "A" parameters provide terms for the transform in the Easting, and the "B" parameters provide terms for the transform 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) +
            (Au6v0 * u^6) + (Au5v1 * u^5v) + (Au4v2 * u^4v^2) + (Au3v3 * u^3v^3) + (Au2v4 * u^2v^4) + (Au1v5 * uv^5) +      (Au0v6 * v^6)

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) +
            (Bu6v0 * u^6) + (Bu5v1 * u^5v) + (Bu4v2 * u^4v^2) + (Bu3v3 * u^3v^3) + (Bu2v4 * u^2v^4) + (Bu1v5 * uv^5) +       (Bu0v6 * v^6)
  

The "General Sixth 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.