AMT Datasouth PAL - Manual (Page 15)

PAL Fundamentals 9
transformation matrix also includes three additional constant values. However, since the extra
values do not change, PAL does not need to keep the values as part of the matrix.
The following diagram shows the mathematical representation of a transformation matrix.
A B 0
C D 0
E F 1
Special mathematical rules exist for changing the values A through F in response to scaling, ro-
tating, and relocating the origin (translating) of a coordinate system. However, once PAL has
updated the six values to reflect any changes to the user's coordinate system, PAL simply uses
these values in the following formulas to convert the user's coordinates to actual dot positions on a
printed page.
X' = AX + CY + E
Y' = BX + DY + F
X and Y represent a coordinate in the user's coordinate system. X' and Y' represent the same co-
ordinate on a printer page.
PAL uses the term current transformation matrix to indicate the transformation matrix currently in
use by PAL. PAL automatically initializes the current transformation matrix to the values
necessary to convert the PAL default coordinate system (points) to the physical page coordinate
system (dots).
The discussions within this manual of the various PAL operators which affect the current
transformation matrix describe the various ways in which the programmer may alter the matrix.