Line drawing algorithm

A line drawing algorithm is a graphical algorithm for approximating a line segment on discrete graphical media. On discrete media, such as pixel-based displays and printers, line drawing requires such an approximation (in nontrivial cases).

On continuous media, by contrast, no algorithm is necessary to draw a line. For example, oscilloscopes use natural phenomena to draw lines and curves.

A naïve line-drawing algorithm

dx = x2 - x1
dy = y2 - y1
for x from x1 to x2 {
	y = y1 + (dy) * (x - x1)/(dx)
	plot(x, y)
}

It is assumed here that the points have already been ordered so that $x_2 > x_1$ . This algorithm works just fine when $dx >= dy$ (i.e., slope is less than or equal to 1), but if $dx < dy$ (i.e., slope greater than 1), the line becomes quite sparse with lots of gaps, and in the limiting case of $dx = 0$ , 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 floating-point 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 line-drawing algorithm, with minor variations.
Bresenham's line algorithm — optimized to use only additions (i.e. no divisions or multiplications); it also avoids floating-point computations.
Xiaolin Wu's line algorithm — can perform anti-aliasing

References

Fundamentals of Computer Graphics, 2nd Edition, A.K. Peters by Peter Shirley