Classifying Transformations

As well as holding mapping information describing how to convert from one coordinate system to another, a transformation may also carry information about the character of its mappings. When plotting a graph, for instance, it may be important to know whether the mapping being used is linear, because a more complex (and costly) algorithm may be required if it is not. Indeed, in many circumstances, the absence of a vital property such as linearity could actually make it impossible for an application to proceed, in which case it must issue an appropriate error message and abort.

There are a number of mapping characteristics, in addition to linearity, which can influence or simplify the coding of applications in this way. However, it is often difficult to determine by indirect means (such as transforming test points) whether the necessary special properties are present. Provision has therefore been made for handling this type of information explicitly.