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