6 DUIM-Graphics Library

6.3 Drawing is approximate

Note that although the drawing plane contains an infinite number of mathematical points, and drawing can be described as an infinite number of color and opacity computations, the drawing plane cannot be viewed directly and has no material existence: it is only an abstraction. What can be viewed directly is the result of rendering portions of the drawing plane onto a medium. No infinite computations or objects of infinite size are required to implement DUIM, because the results of rendering have finite size and finite resolution.

A drawing plane is described as having infinitely fine spatial, color, and opacity resolution, and as allowing coordinates of unbounded positive or negative magnitude. A viewport into a drawing plane, on the other hand, views only a finite region (usually rectangular) of the drawing plane. Furthermore, a viewport has limited spatial resolution and can only produce a limited number of colors. These limitations are imposed by the display hardware on which the viewport is displayed. A viewport also has limited opacity resolution, determined by the finite arithmetic used in the drawing engine.

Coordinates are real numbers in implementation-defined units. Often these units equal the spatial resolution of a viewport, so that a line of thickness 1 is equivalent to the thinnest visible line. However, this equivalence is not required and should not be assumed by application programs.

DUIM can be quite restrictive in the size and resolution of its viewports. For example, the spatial resolution might be only a few dozen points per inch, the maximum size might be only a few hundred points on a side, and there could be as few as two displayable colors (usually black and white). Fully transparent and fully opaque opacity levels are supported, but a DUIM implementation might support only a few opacity levels in between (or possibly even none). A DUIM implementation might implement color blending and unsaturated colors by stippling, although it is preferred, when possible, for a viewport to display a uniform color as a uniform color rather than as a perceptible stipple.

However, there are no such limitations when DUIM records the output to a sheet, since DUIM just remembers the drawing operations that were performed, not the results of rendering.

The application programmer uses the DUIM graphic drawing model as an interface to describe the intended visual appearance. DUIM then approximates that ideal appearance in a viewport, within its limitations of spatial resolution, color resolution, number of simultaneously displayable colors, and drawing speed.

Naturally, doing this usually requires trade-offs, for example between speed and accuracy, and these trade-offs depend on the hardware and software environment and the user concerns in any given situation. For example:

If the device only supports a limited number of colors, the desired color may be approximated using techniques such as dithering or stippling.
If the device cannot draw curves precisely, they may be approximated, with or without anti-aliasing.
If the device has limited opacity resolution, color blending may be approximate. A viewport might display colors that do not appear in the drawing plane, both because of color and opacity approximation and because of anti-aliasing at the edges of drawn shapes.

Drawing computations are always carried out "in color", even if the viewport is only capable of displaying black and white. In other words, the DUIM drawing model is always the fully general model, even if an implementation's color resolution is limited enough that full use of the model is not possible. Of course an application that fundamentally depends on color will not work well on a viewport that cannot display color. Other applications will degrade gracefully.

Whether the implementation uses raster graphics or some other display technique is invisible at this interface. DUIM does not specify the existence of pixels nor the exact details of scan conversion, which will vary from one drawing engine to the next.