Formulating a Transformation

The first stage in creating a transformation is to formulate a description of it in a form which may be used in a program. In future, there may be a number of ways of formulating such a description and of creating a corresponding transformation from it. At present, however, only one method is supported, based on the explicit use of transformation functions.

For instance, suppose you wished to create the [ $(x,y) \leftrightarrow (r,\theta)$] transformation relating a two-dimensional Cartesian coordinate system $(x,y)$ to a Polar system $(r,\theta)$. In this case, the transformation's two mappings might be defined in terms of the following transformation functions:

$$\begin{array}{cc} \mbox{Forward } \left\{ \begin{array}{lll}... ...a ) \\ y & = & r \sin( \theta ) \end{array}\right. \end{array}$$ (3)

This description of the transformation could now be used in a program by converting it directly into character data, as follows: