This function creates a new UnitNormMap and optionally initialises its attributes.

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

RESULT = AST_UNITNORMMAP( NCOORD, CENTRE, OPTIONS, STATUS )

NCOORD = INTEGER (Given)

CENTRE( NCOORD ) = DOUBLE PRECISION (Given)

OPTIONS = CHARACTER $\ast$ ( $\ast$ ) (Given)

STATUS = INTEGER (Given and Returned)

AST_UNITNORMMAP = INTEGER

• A null Object pointer (AST__NULL) will be returned if this function is invoked with STATUS set to an error value, or if it should fail for any reason.

The protected interface to this function includes an extra parameter at the end of the parameter list descirbed above. This parameter is a pointer to the integer inherited status variable: " int $\ast$status" .