The ability to simplify compound Mappings is provided by the astSimplify function. This function encapsulates a number of heuristics for converting Mappings, or combinations of Mappings within a CmpMap, into simpler, equivalent ones. When applied to a CmpMap, astSimplify tries to reduce the number of individual Mappings within it by merging neighbouring component Mappings together. It will do this with both series and parallel combinations of Mappings, or both, and will handle CmpMaps nested to any depth ().
To illustrate how astSimplify works, consider the combination of Mappings shown in the Figure below.
If this were contained in a CmpMap, it could be simplified as follows:
AstMapping *simpler; ... simpler = astSimplify( cmpmap );
In this case, the result would be a simple 3-dimensional UnitMap (the identity Mapping). To reach this conclusion, astSimplify will have made a number of deductions, roughly as follows:
This example is a little contrived, but illustrates how astSimplify can deal with even quite complicated compound Mappings through a series of incremental simplifications. Where possible, this will result in either a simpler compound Mapping or, if feasible, an atomic (non-compound) Mapping, as here. If no simplification is possible, astSimplify will just return a pointer to the original Mapping.
Although astSimplify cannot identify every simplification that is theoretically possible, sufficient rules are included to deal with the most common and important cases.
AST A Library for Handling World Coordinate Systems in Astronomy