Quest for the Ideal Line

The best we can do is a discrete approximation of an ideal line.
Plot of a discrete line overlaid with an ideal line

      Important line qualities:
      • Continuous appearence
      • Uniform thickness and brightness
      • Turn on the pixels nearest the ideal line
      • How fast is the line generated
Lecture 5 Slide 3 6.837 Fall '98


Quest for the Ideal Line

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). Plot of a discrete line overlaid with an ideal line

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. Following is a list of some of line qualities that are often considered.