Mappings

The most important part of any transformation is a pair of ``numerical recipes'' which provide a description of the precise numerical steps which must be carried out in order to perform coordinate conversion in each direction. These ``recipes'' are termed the forward and inverse mappings.²It will frequently be possible to define both of these, so that coordinate conversion may be performed in either direction. However, this may not always be possible (or desirable), so a transformation may also exist even if only one of its two possible mappings is defined. In this case, coordinate conversion will only be possible in one direction.

As will be seen later, it is often convenient to extract the mappings from a transformation and to process them as separate entities.