Because even high-resolution computer monitors have a relatively small number of pixels, when graphics or text display distinguish between individual pixels. The result is that purportedly smooth curves are often rendered with jagged edges. This "jagged-edge" effect is called aliasing, and removing it is thus called antialiasing. For example, consider the approximation to a circle illustrated above, which is magnified three times. As can be seen, the sides of the circle are not smooth, but jagged and ugly.
The simplest, and most common, way to antialias an image is to render the graphic at a higher resolution, and then decrease its size to the original with a scaling filter. This emulates a higher-resolution display by using more than two colors in the graphic (there will be shades of gray on the edges as well). The additional colors smooth the edges to a great extent. A close-up of an antialiased edge is illustrated as well.
The graphics above show a comparison of figures at varying levels of anti-aliasing. The annuli were rendered at 1, 2, 4, and 8 times the resolution of the original, respectively. Note that this method of antialiasing causes an exponential increase in computational time (e.g., the last figure took 64 times as long to render as the first).
Antialiasing of three-dimensional graphics can also be performed in exactly the same fashion, as shown above. The figure above compares the magnified edges of the cubic structure.
