The following predicates are provided in order to be able to determine whether or not a transformation has a particular characteristic.
transformation-equal[Generic Function]
Arguments: transformation1 transformation2
Summary: Returns t if the two transformations have equivalent effects (that is, are mathematically equal); otherwise, it returns nil .
identity-transformation-p[Generic Function]
Summary: Returns t if transformation is equal (in the sense of transformation-equal ) to the identity transformation; otherwise, it returns nil .
translation-transformation-p[Generic Function]
Summary: Returns t if transformation is a pure translation, that is, a transformation that moves every point by the same distance in x and the same distance in y . Otherwise, it returns nil .
invertible-transformation-p[Generic Function]
Summary: Returns t if transformation has an inverse; otherwise, it returns nil .
reflection-transformation-p[Generic Function]
Summary: Returns t if transformation inverts the "handedness" of the coordinate system; otherwise, it returns nil . Note that this is a very inclusive category--transformations are considered reflections even if they distort, scale, or skew the coordinate system, as long as they invert the handedness.
rigid-transformation-p[Generic Function]
Summary: Returns t if transformation transforms the coordinate system as a rigid object, that is, as a combination of translations, rotations, and pure reflections. Otherwise, it returns nil .
Rigid transformations are the most general category of transformations that preserve magnitudes of all lengths and angles.
even-scaling-transformation-p[Generic Function]
Summary: Returns t if transformation multiplies all x -lengths and y -lengths by the same magnitude; otherwise, it returns nil . This includes pure reflections through vertical and horizontal lines.
scaling-transformation-p[Generic Function]
Summary: Returns t if transformation multiplies all x -lengths by one magnitude and all y -lengths by another magnitude; otherwise, it returns nil . This category includes even scalings as a subset.
rectilinear-transformation-p[Generic Function]
Summary: Returns t if transformation will always transform any axis-aligned rectangle into another axis-aligned rectangle; otherwise, it returns nil . This category includes scalings as a subset, and also includes 90 degree rotations.
Rectilinear transformations are the most general category of transformations for which the bounding rectangle of a transformed object can be found by transforming the bounding rectangle of the original object.
Common Lisp Interface Manager 2.0 User's Guide - 7 Aug 2017