Variables and data coordinates.

Variables are used in transformation functions to represent the coordinates of data points which will be transformed. Their names may be chosen freely to make the definition as comprehensible as possible; they may be of any length and may contain any alphanumeric character (including underscore) although they must start with an alphabetic character.

A variable becomes defined when it appears on the left hand side of a transformation function and the name of each variable must appear on the left hand side of one (and only one) such function. Variables which appear on the left hand side of forward transformation functions are termed output variables, while those appearing on the left hand side of inverse transformation functions are termed input variables.

Variables act only as ``dummy arguments'' and their names have no significance outside the transformation being defined. The correspondence between variables and the coordinates of external data points is established by the order in which the variables are defined. In the following, for instance, the first coordinate of an input data point would correspond with the variable `ALPHA' and the second coordinate with `OMEGA', while the two coordinates of an output data point would correspond with the variables `p' and `q' respectively:

Forward $\left\{ \mbox{ \begin{tabular}{l} \lq \texttt{p = ALPHA + 2}' \\ \lq \texttt{q = 44 - 2 * OMEGA}' \\ \end{tabular}}\right.$

Inverse $\left\{ \mbox{ \begin{tabular}{l} \lq \texttt{ALPHA = p - 2}' \\ \lq \texttt{OMEGA = ( 44 - q ) / 2}' \end{tabular}}\right.$

Note that expressions appearing on the right hand side of forward transformation functions may only refer to input variables, while those appearing on the right hand side of inverse transformation functions may only refer to output variables.