Line drawing algorithm
This article may be expanded with text translated from the corresponding article in German. (December 2009) Click [show] for important translation instructions.

A line drawing algorithm is a graphical algorithm for approximating a line segment on discrete graphical media. On discrete media, such as pixelbased displays and printers, line drawing requires such an approximation (in nontrivial cases). Basic algorithms rasterize lines in one color. A better representation with multiple color gradations requires an advanced process, spatial antialiasing.
On continuous media, by contrast, no algorithm is necessary to draw a line. For example, oscilloscopes use natural phenomena to draw lines and curves.
The Cartesian slopeintercept equation for a straight line is With m representing the slope of the line and b as the y intercept. Given that the two endpoints of the line segment are specified at positions and . we can determine values for the slope m and y intercept b with the following calculations, so, .
A naive linedrawing algorithm
The simplest method of screening is the direct drawing of the equation defining the line.
dx = x2  x1 dy = y2  y1 for x from x1 to x2 { y = y1 + dy * (x  x1) / dx plot(x, y) }
It is here that the points have already been ordered so that . This algorithm works just fine when (i.e., slope is less than or equal to 1), but if (i.e., slope greater than 1), the line becomes quite sparse with lots of gaps, and in the limiting case of , only a single point is plotted.
The naïve line drawing algorithm is inefficient and thus, slow on a digital computer. Its inefficiency stems from the number of operations and the use of floatingpoint calculations. Line drawing algorithms such as Bresenham's or Wu's are preferred instead.
List of line drawing algorithms
The following is a partial list of line drawing algorithms:
 Digital Differential Analyzer (graphics algorithm) — Similar to the naive linedrawing algorithm, with minor variations.
 Bresenham's line algorithm — optimized to use only additions (i.e. no divisions or multiplications); it also avoids floatingpoint computations.
 Xiaolin Wu's line algorithm — can perform spatial antialiasing, appears "ropey" from brightness varying along the length of the line
 GuptaSproull algorithm
References
Fundamentals of Computer Graphics, 2nd Edition, A.K. Peters by Peter Shirley