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#### Classification properties.

Usually, information about any special characteristics which are present is directly available only to the application which creates a transformation. Consequently, this application should be responsible for declaring that such properties are present, so that other applications may subsequently enquire about them. This process is termed classification and the basic classification properties which may be declared are indicated in Table , where each is briefly described. These properties are defined more precisely (and mathematically) in Appendix .

Table: The basic classification properties which may be declared for a transformation and the symbolic constants associated with each. The constants are defined in the include file TRN_PAR.

 Property Brief Description Symbolic Constant LINEAR Preserves straight lines. TRN__LIN INDEPENDENT Preserves the independence of the axes. TRN__INDEP DIAGONAL Preserves the axes themselves. TRN__DIAG ISOTROPIC Preserves angles and shapes (e.g. circles). TRN__ISOT POSITIVE_DET A component of reflection is absent. TRN__POSDT NEGATIVE_DET A component of reflection is present. TRN__NEGDT CONSTANT_DET The area (or volume) scale factor is constant. TRN__CONDT UNIT_DET Areas (or volumes) are preserved. TRN__UNIDT

In most situations, a transformations's mappings are not adequately described by any one of the basic properties alone, but require a composite classification comprising a set of several of these properties. For instance, the combination:

LINEAR and ISOTROPIC and POSITIVE_DET and UNIT_DET

would indicate that a mapping represents a rigid rotation about an axis (or a point in two dimensions). Facts such as this may not be obvious without some thought, however, so those classifications which apply to a number of the most common types of mapping are set out in Table  in Appendix .

Classification information is conveniently processed in the form of a 1-dimensional logical classification array, each of whose elements indicates the presence or absence of one particular property. Each basic property therefore has an integer symbolic constant associated with it (see Table ) which identifies the array element to be used (the precise mechanism is illustrated below). Not all possible combinations of the basic properties are permitted (see Appendix ) but the number of different classifications possible is nevertheless still quite large.

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TRANSFORM Coordinate Transformation Facility