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Notes On a typical computer generated graphics raster, there are several hundred pixel points available
in both the horizontal and vertical directions, and they are much closer together than suggested
in figure 11.2 below. The standard grid could simply be modified to take this into account, but
only points with whole number coordinates can be properly depicted. The point (¼, 1) would
have to be depicted as (3, 1) unless some form of scaling were used. Indeed, since the individual
pixels are rather close together on the screen, it might be better to magnify this and use, say,
ten points for a unit, marking (31, 10) on the raster to represent this point.

Figure 11.2: Continuous and Discrete Grids

Continuous Grid Discrete Grid
11.3.2 Where is the Origin?

When the Macintosh, the first popular graphics-oriented computer was developed but at the
top left corner. The positive horizontal direction was still to the right, but the positive vertical
direction goes down, rather than up. There are still four quadrants, as points can have negative
coordinates, but three of the quadrants are off the screen. As with many other parts of the
interface, this arrangement was subsequently copied into other graphics user systems, including
the various versions of Windows. The standard mathematical system and the Mac/Windows
screen are illustrated in Figure 11.3.

A graphing module used on either of these systems will need to have the option of using the
native system directly, or passing conventional mathematical coordinates and then translating
to the native screen.
Figure 11.3: The Standard Mathematical System and the Mac/Windows Screen

+
+
(0, 0)

– (0, 0) +

IV
– +
Conventional Axes Macintosh/Windows Axes

11.3.3 Measuring Angles
Yet another option needed for graphing is created by the fact that when the focus is on polar
coordinates that is, the angle and distance from the origin are given rather than on rectangular
coordinates, there are two common systems for measuring angles. In the standard system used

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