Line drawing algorithm

In computer graphics, a line drawing algorithm is an algorithm for approximating a line segment on discrete graphical media, such as pixel-based displays and printers. On such media, line drawing requires an approximation (in nontrivial cases). Basic algorithms rasterize lines in one color. A better representation with multiple color gradations requires an advanced process, spatial anti-aliasing.

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

List of line drawing algorithms

The following is a partial list of line drawing algorithms:
* Naive algorithm
* 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 division Multiplications); it also avoids floating-point computations.
* Xiaolin Wu's line algorithm — can perform spatial anti-aliasing, appears "ropey" from brightness varying along the length of the line, though this effect may be greatly reduced by pre-compensating the pixel values for the target display's gamma curve, e.g. out = in ^ (1/2.4).
* Gupta-Sproull algorithm

A naive line-drawing 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 do
y = y1 + dy × (x − x1) / dx
plot(x, y)

It is here that the points have already been ordered so that $x_2 > x_1$.
This algorithm works just fine when $dx \geq dy$ (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 many gaps, and in the limiting case of $dx = 0$, a division by zero exception will occur.

The naive 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. Algorithms such as Bresenham's line algorithm or Xiaolin Wu's line algorithm are preferred instead.

Gupta and Sproll algorithm

The Gupta-Sproll algorithm is based on Bresenham's line algorithm but adds antialiasing.

An optimized variant of the Gupta-Sproull algorithm can be written in pseudocode as follows:

DrawLine(x1, x2, y1, y2)

The IntensifyPixel(x,y,r) function takes a radial line transformation and sets the intensity of the pixel (x,y) with the value of a cubic polynomial that depends on the pixel's distance r from the line.

References

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

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Computer graphics algorithms