Transformations To change the current user space coordinate system, you define a transformation which defines how to transform coordinates from the new user space coordinate system into the previous coordinate system. Mathematically, the transformation is represented by a transformation matrix which maps coordinates in the new user space coordinate system into the previous coordinate system. Transformation matrices define the mathematical mapping from one coordinate space into another. Whenever a new transformation is provided, a new CTM is calculated by the following formula. Transformations alter coordinate systems, not objects.
All objects defined outside the scope of a transformation are unchanged by the transformation.
All objects defined within the scope of a transformation will be drawn in the transformed coordinate system. All coordinates used within the scope the transformation are specified in the transformed coordinate system. Matrix operations are not commutative - the order in which transformations are specified is significant. Mathematically, all transformations can be expressed as matrices. This scales the coordinates so that one unit in the x and y directions of the new coordinate system is the same as sx and sy units in the previous coordinate system, respectively.