Line-Drawing Algorithms Our first adventure into scan conversion. Scan-conversion or rasterization Due to the scanning nature of raster displays Algorithms are fundamental to both 2-D and 3-D computer graphics Transforming the continuous into this discrete (sampling) Line drawing was easy for vector displays Most incremental line-drawing algorithms were first developed for pen-plotters Most of the early scan-conversion algorithms developed for plotters can be attributed to one man, Jack Bresenham.
	Lecture 5		Slide 2		6.837 Fall '98

Line drawing is our first adventure into the area of scan conversion. The need for scan conversion, or rasterization, techniques is a direct result of scanning nature of raster displays (thus the names).

Vector displays are particularly well suited for the display of lines. All that is needed on a vector display to generate a line is to supply the appropriate control voltages to the x and y deflection circuitry, and the electron beam would traverse the line illuminating the desired segment. The only inaccuracies in the lines drawn a vector display resulted from various non-linearities, such as quantization and amplifier saturation, and the various noise sources in the display circuitry.

When raster displays came along the process of drawing lines became more difficult. Luckily, raster display pioneers could benefit from previous work done in the area of digital plotter algorithms. A pen-plotter is a hardcopy device used primarily to display engineering line drawings. Digital plotters, like raster displays, are discretely addressable devices, where position of the pen on a plotter is controlled by special motors called stepper motors that are connected to mechanical linkages that translates the motor's rotation into a linear translation. Stepper motors can precisely turn a fraction of a rotation (for example 2 degrees) when the proper controlling voltages are applied. A typical flat-bed plotter uses two of these motors, one for the x-axis and a second for the y-axis, to control the position of a pen over a sheet of paper. A solenoid is used to raise and lower the actual pen when drawing and positioning.

The bottom line is that most of the popular line-drawing algorithms used to on computer screens (and laser and ink-jet printers for that matter) were originally developed for use on pen-plotters. Furthermore, most of this work is attributed by a single man, Jack Bresenham, who was an IBM employee. He is currently a professor at Winthrop University.

In this lecture I will gradually evolve from the basics of algebra to the famous Bresenham line-drawing algorithms (along the same lines as a famous paper by Bob Sproull), and then I'll discuss some developments that have happened since then.