Note that since vector-graphics displays, capable of drawing nearly perfect
lines, predated raster-graphics displays. Thus, the expectations for line quality
were set very high. The nature of raster-graphics display, however, only allows
us to display a discrete approximation of a line, since we are restricted to
only turn on discrete points, or pixels. In order to discuss, line drawing we
must first consider the mathematically ideal line (or line segment).
From geometry we know that a line, or line segment, can be uniquely specified
by two points. From algebra we also know that a line can be specified by a slope,
usually given the name m and a y-axis intercept called b. Generally in computer
graphics, a line will be specified by two endpoints. But the slope and y-intercept
are often calculated as intermediate results for use by most line-drawing algorithms.
The goal of any line drawing algorithm is to construct the best possible approximation
of an ideal line given the inherent limitations of a raster display.