## Coordinate Systems

Each IML graph is associated with two independent
cartesian coordinate systems, a *world coordinate
system* and a *normalized coordinate system*.

*Understanding World Coordinates*

The *world coordinate system* is the
coordinate system defined by your data.
Because these coordinates help define objects
in the data's two-dimensional world, these
are referred to as *world coordinates*.
For example, suppose that you have a data set containing heights and
weights and that you are interested in plotting height versus weight.
Your data induces a world coordinate system in which each point
(*x*,*y*) represents a pair of data values (*height,weight*).
The world could be defined by the observed ranges of
heights and weights, or it could be enlarged to include a
range of all reasonable values for heights and weights.
Now consider a more realistic example of
the stock price data for ACME Corporation.
Suppose that the stock price data were
actually the year end prices of ACME stock for
the years 1971 through 1986, as shown below:

YEAR PRICE
71 123.75
72 128.00
73 139.75
74 155.50
75 139.75
76 151.50
77 150.375
78 149.125
79 159.50
80 152.375
81 147.00
82 134.125
83 138.75
84 123.625
85 127.125
86 125.500

The actual range of YEAR is from 71 to 86, and
the range of PRICE is from $123.625 to $159.50.
These are the ranges in world coordinate space for the stock data.
Of course, you could say that the range for PRICE
could start at $0 and range upwards to, for example, $200.
Or, if you were interested only in prices during the 80s, you
could say the range for PRICE is from $123.625 to $152.375.
As you see, it all depends on how you want to define your world.
Figure 12.2 shows a graph of the stock data
with the world defined as the actual data given.
The corners of the rectangle give
the actual boundaries for this data.

**Figure 12.2:** World Coordinates

*Understanding Normalized Coordinates*

The *normalized coordinate system* is defined relative
to your display device, usually a monitor or plotter.
It is always defined with points varying between (0,0)
and (100,100), where (0,0) refers to the lower left
corner and (100,100) refers to the upper right corner.
In summary,

- the world coordinate system is
defined relative to your data
- the normalized coordinate system is
defined relative to the display device

Figure 12.3 shows the ACME stock
data in terms of normalized coordinates.
There is a natural mathematical relationship between
each point in world and normalized coordinates.
The normalized device coordinate system is mapped to the device
display area so that (0,0), the lower left corner, corresponds
to (71, 123.625) in world coordinates, and (100,100), the upper
right corner, corresponds to (86,159.5) in world coordinates.

**Figure 12.3:** Normalized Coordinates

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.