The transformation matrix shown above can be set equal to an entity as complex as:
M*I*S*V*D
where * symbolizes matrix multiplication. As mentioned earlier, all the transformation types might not have a distinct value at all times. One, or all, could simply be the identity transformation.
These intermediate space and step-wise transformations are not actually how the operating system performs transformations. The reason for this relates to the way the PM stores transformation information. The transformation matrix data structure MATRIXLF, undergoes continuous modification during the drawing process, and it can be influenced by more than one transformation function from the application responding, for example, to what a user wants the drawing to look like.
For example, after creating the model of a building from drawing primitives, the user might want to see two identical buildings side-by-side. The application has already applied a series of transformations to the two segments in world coordinate space to create the model of the building. If the application, rather than the PM, had to perform the entire transformation over again from start to finish, it would have to keep track of much more detail. The PM enables applications to process a smaller portion of the MATRIXLF structure, in this example the "V" or "V and D" component, to enable the user to see two buildings side-by-side.