By selecting this section the coordinate operation will perform a polynomial transformation. This transformation can be made for geographic coordinates (φ, λ) as well as for plane coordinates (N, E) marked with (Y, X).

Polynomial transformation method

It selects from the list one of the following polynomial transformation method:
• General polynomial;
• Reversible polynomial;
• Complex polynomial;
• Madrid to ED50 polynomial.

For the methods General polynomial and Reversible polynomial the degree of the polynomial can be: 2, 3, 4, 6 or 13 and for the method Complex polynomial the degree of the polynomial can be 3 or 4.

Button Load coefficients from the EPSG database

It opens The window of loading parameters from the EPSG database. The data taken from an operation of type Polynomial transformation is: source and destination system parameters, the direction of the transformation and the coefficients of the polynomial transformation.

Transformation direction

It selects the direction in which the transformation will be applied: forward or inverse. The inverse direction is possible only for the Reversible polynomial method.

Coordinates of evaluation point in source CRS / Coordinates of evaluation point

Xso (φ.so)

Xso (φ.so) – represents the 1^st ordinate of the evaluation point in the source system (the X-east coordinate or φ latitude).

Introduce the value in decimal degrees or in the measurement unit for lengths.

Yso (λ.so)

Yso (λ.so) – represents the 2^nd ordinate of the evaluation point in the source system (the Y-north coordinate or λ longitude).

Introduce the value in decimal degrees or in the measurement unit for lengths.

Coordinates of evaluation point in target CRS

Xto (φ.to)

Xto (φ.to) – represents the 1^st ordinate of the evaluation point in the target system (the X-east coordinate or φ longitude).

Introduce the value in decimal degrees or in the measurement unit for lengths.

Yto (λ.to)

Yto (λ.to) – represents the 2^nd ordinate of the evaluation point in the target system (the Y-north coordinate or λ longitude).

Introduce the value in decimal degrees or in the measurement unit for lengths.

Scaling factors for source and target CRS coordinate differences / Scaling factor for coordinate differences

S(s)

S(s) – represents the scale factor for the source coordinate system.

Introduce the scale factor as a relative value to the unit.

S(t)

S(t) – represents the scale factor for the target coordinate system.

Introduce the scale factor as a relative value to the unit.

Coefficients

Introduce in the table the values of the polynomial transformation coefficients.

The manual introduction of the coefficients must be made observing the powers of U and V (X and Y normalized coordinates). For example, for the General polynomial and Reversible polynomial method the coefficient U³×V¹ must be introduced at the 11^th index in the table. For the Madrid to ED50 method the polynomial coefficients must be introduced observing the index of the A and B coefficients.