General Sixth Order Polynomial

The General Sixth Order Polynomial Datum Shift method provides an interface to define a simple sixth order polynomial transformation between two Horizontal Datums.   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) +
            (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 Polynomial" DatumShift 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.