Fourth Order Polynomial Transform – Global Mapper

Given a set of Control points and their subsequent Observed points, the corresponding Fourth OrderPolynomial Transform is generated. Once the MathTransform IsSolved, other points can be sent through, via Transform, and will be modified as follows:

x_in, y_in : input point coordinates
x_out, y_out : output point coordinates

x = (x_in + Xshift_in) * scale_in
y = (y_in + Yshift_in) * scale_in

x' = (Xx * x) + (Xy * y) + X1 + (Xxy * x * y) + (Xx2 * x * x) + (Xy2 * y * y) + (Xx3 * x * x * x) + (Xx2y * x * x * y) + (Xxy2 * x * y * y) + (Xy3 * y * y * y) + (Xx4 * x * x * x * x) + (Xx3y * x * x * x * y) + (Xx2y2 * x * x * y * y) + (Xxy3 * x * y * y * y) + (Xy4 * y * y * y * y)
y' = (Yx * x) + (Yy * y) + Y1 + (Yxy * x * y) + (Yx2 * x * x) + (Yy2 * y * y) + (Yx3 * x * x * x) + (Yx2y * x * x * y) + (Yxy2 * x * y * y) + (Yy3 * y * y * y) + (Yx4 * x * x * x * x) + (Yx3y * x * x * x * y) + (Yx2y2 * x * x * y * y) + (Yxy3 * x * y * y * y) + (Yy4 * y * y * y * y)

x_out = (x' * scale_out) + Xshift_out
y_out = (y' * scale_out) + Yshift_out

The "FourthOrderPolynomial" MathTransform has the following Parameters:

Parameter Name	Parameter String	Units
input point scale	scale_in	double
input x-coordinate shift	Xshift_in	double
input y-coordinate shift	Yshift_in	double
output point scale	scale_out	double
output x-coordinate shift	Xshift_out	double
output y-coordinate shift	Yshift_out	double
x' x coefficient	Xx	double
x' y coefficient	Xy	double
x' delta	X1	double
x' (x * y) coefficient	Xxy	double
x' x² coefficient	Xx2	double
x' y² coefficient	Xy2	double
x' x³ coefficient	Xx3	double
x' (x² * y) coefficient	Xx2y	double
x' (x * y²) coefficient	Xxy2	double
x' y³ coefficient	Xy3	double
x' x⁴ coefficient	Xx4	double
x' (x³ * y) coefficient	Xx3y	double
x' (x² * y²) coefficient	Xx2y2	double
x' (x * y³) coefficient	Xxy3	double
x' y⁴ coefficient	Xy4	double
y' x coefficient	Yx	double
y' y coefficient	Yy	double
y' delta	Y1	double
y' (x * y) coefficient	Yxy	double
y' x² coefficient	Yx2	double
y' y² coefficient	Yy2	double
y' x³ coefficient	Yx3	double
y' (x² * y) coefficient	Yx2y	double
y' (x * y²) coefficient	Yxy2	double
y' y³ coefficient	Yy3	double
y' x⁴ coefficient	Yx4	double
y' (x³ * y) coefficient	Yx3y	double
y' (x² * y²) coefficient	Yx2y2	double
y' (x * y³) coefficient	Yxy3	double
y' y⁴ coefficient	Yy4	double

There are no Settings parameters for this MathTransform.