The forward transformation of a UnitNormMap subtracts the specified centre and then transforms the resulting vector to a unit vector and the vector norm. The output contains one more coordinate than the input: the initial Nin outputs are in the same order as the input; the final output is the norm. If the norm is 0, then the output of the forward transformation is AST__BAD for each component of the unit vector and 0 for the norm (the final value).
The inverse transformation of a UnitNormMap multiplies each component of the provided vector by the provided norm and adds the specified centre. The output contains one fewer coordinate than the input: the initial Nin inputs are in the same order as the output; the final input is the norm. If the provided norm is 0 then the other input values are ignored, and the output vector is the centre.
Example: if centre = [1, -1] then [5, 2] transforms to [4, 3] after subtracting the centre; the norm is 5, so the output is [0.8, 0.6, 5].
UnitNormMap enables radially symmetric transformations, as follows:
apply a UnitNormMap to produce a unit vector and norm (radius)
apply a one-dimensional mapping to the norm (radius), while passing the unit vector unchanged
apply the same UnitNormMap in the inverse direction to produce the result
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A null Object pointer (AST__NULL) will be returned if this function is invoked with the AST error status set, or if it should fail for any reason.