General Fourth Order Polynomial

The General Fourth Order Polynomial Datum Shift method provides an interface to define a simple fourth 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)

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)

The "General Fourth 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.

Parameter Name

Type
A0 Double
Au1v0 Double
Au0v1 Double
Au2v0 Double
Au1v1 Double
Au0v2 Double
B0 Double
Bu1v0 Double
Bu0v1 Double
Bu2v0 Double
Bu1v1 Double
Bu0v2 Double
Au3v0 Double
Au2v1 Double
Au1v2 Double
Au0v3 Double
Bu3v0 Double
Bu2v1 Double
Bu1v2 Double
Bu0v3 Double
Au4v0 Double
Au3v1 Double
Au2v2 Double
Au1v3 Double
Au0v4 Double
Bu4v0 Double
Bu3v1 Double
Bu2v2 Double
Bu1v3 Double
Bu0v4 Double