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# 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 na&iuml;ve 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 $dx >= dy$, but it is quite slow on a digital computer, as it requires floating-point calculations. If $dx < dy$, the line becomes quite sparse, and in the limiting case of $dx = 0$, only a single point is plotted!

List of line drawing algorithms

The following is a partial list of line drawing algorithms:
*Bresenham's line algorithm &mdash; optimized to use only additions (i.e. no divisions or multiplications); it also avoids floating-point computations.
*Xiaolin Wu's line algorithm &mdash; can perform anti-aliasing
* [http://www.edepot.com/algorithm.html EFLA line algorithm] &mdash; A very fast implementation.
* [http://gatopeichs.pbwiki.com/gatopeich%27s-Graphic-Algorithms#LineDrawingbyIntegerOperations gatopeich's line algorithm] &mdash; Fast, simple, aesthetic. Based on pure integer operations.

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