line drawing

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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 x₂ > x₁. 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:

• 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