General Fourth Order Parametric – Global Mapper

The General Fourth Order Parametric method provides an interface to define a simple fourth 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)

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 Parametric" ParametricTransform has the following Parameters:

A polynomial transform is generally defined for a small area. Using the method to transform 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