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There are 4 levels to the coordinate systems used in this library. The levels are labeled with symbols, U, V, R, and W, in descending order, and are referred to as the "U-coordinate", "V-coordinate", "R-coordinate", and "W-coordinate ", respectively. (See Fig.1.3) The letters U, V, R, and W are derived from the names of the systems below, and terms such as "U-coordinate" will be used as abbreviations. (These terms may further be shortened to "UC".)
| U | User coordinate |
| V | Virtual rectangular coordinate |
| R | Normalized rectangular coordinate |
| W | Workstation coordinate |
In the explanation of arguments in the reference manual, the coordinates for the U-coordinate
is written as (UX,UY),
with characters representing the coordinate system.
(The normalized rectangular coordinate is called an R-coordinate instead of the N-coordinate
based on the rules of FORTRAN concerning floating-point variables.
The highest-level U-coordinate includes many systems from the normal X-Y coordinate
to map projection coordinates.
In the V-coordinate, one level below the UC, a rectangular coordinate is defined, one for 2-D and 3-D each,
and the various UC systems are transformed to these 2 types.
This transformation is called "the normalization transformation".
On the other hand, the W-coordinate, which is the lowest-level system, is a device-specific coordinate,
and is different according to device.
To unify these coordinate systems, the R-coordinate is defined one level above the WC.
All coordinates are transformed to WC via the RC.
This transformation is called the "workstation transformation".
The RC is a 2-D rectangular coordinate, and the defined range for both the x- and y-axes are [0,1].
The transformation that connects the higher two and lower two levels of coordinate systems,
or one from the VC to RC, is called the "perspective transformation".
The perspective transformation is, true to its name, a transformation using the perspective representation,
and is basically a transformation from the 3-D VC to the 2-D RC.
The 2-D VC is first allocated to a 3-D VC before perspective transformation.
This 2-D VC can be allotted to an arbitrary plane that is perpendicular to the x-, y-, or the z-axis in the 3-D system.
Through this, a 2-D plot may be drawn from an oblique viewpoint.
In the initial state, the perspective transformation from the 2-D VC is an identical transformation,
so no special attention is needed in perspective transformation as long as the 2-D coordinate system is treated normally.
However, there may be a need to use the perspective transformation later on,
so the user is advised to distinguish between the VC and the RC.
In other words, "information accompanying the plot" such as axes, should be transformed along with the plot in the perspective transformation,
so it should be drawn in the VC.
"Information accompanying the page" such as page numbers and values of parameters drawn by SLPACK
should be drawn in the RC.
The normalization transformation of map coordinate systems are carried out in two steps:
"rotation" and "projection".
The intermediate coordinate system (the rotated UC) is called the T-coordinate
(Terrestrial coordinate).
In the TC, the defined ranges of the x-axis and y-axis are
[-180, 180] and [-90, 90], respectively.
All maps are transformed according to the definitions for various map projections from this coordinate system.
To select an arbitrary longitude as the central longitude, or to make projections on the transverse aspect or the oblique aspect,
the coordinate system must be rotated before the projection.
Since the TC is a temporary work coordinate system during the normalization transformation, the user normally does not need be aware of it. However, since clipping of the map coordinates is performed in the TC and not in the UC, one needs to take the TC into consideration during clipping.