A PolyMap is a form of Mapping which performs a general polynomial transformation. Each output coordinate is a polynomial function of all the input coordinates. The coefficients are specified separately for each output coordinate. The forward and inverse transformations are defined independantly by separate sets of coefficients. If no inverse transformation is supplied, an iterative method can be used to evaluate the inverse based only on the forward transformation.
For instance, if the PolyMap has 3 inputs and 2 outputs, each group consisting of 5 elements, A groups such as "(1.2, 2.0, 1.0, 3.0, 0.0)" describes a coefficient with value 1.2 which is used within the definition of output 2. The output value is incremented by the product of the coefficient value, the value of input coordinate 1 raised to the power 1, and the value of input coordinate 2 raised to the power 3. Input coordinate 3 is not used since its power is specified as zero. As another example, the group "(-1.0, 1.0, 0.0, 0.0, 0.0 )" describes adds a constant value -1.0 onto output 1 (it is a constant value since the power for every input axis is given as zero).
Each final output coordinate value is the sum of the "ncoeff_f" terms described by the "ncoeff_f" groups within the supplied array.
AST A Library for Handling World Coordinate Systems in Astronomy