# Line drawing algorithm

Two rasterized lines. The colored pixels are shown as circles. Above: monochrome screening; below: Gupta-Sproull anti-aliasing; the ideal line is considered here as a surface.

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

Lines using Xiaolin Wu's algorithm, showing "ropey" appearance.

The following is a partial list of line drawing algorithms:

### 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 ${\displaystyle x_{2}>x_{1}}$. This algorithm works just fine when ${\displaystyle dx\geq dy}$ (i.e., slope is less than or equal to 1), but if ${\displaystyle dx (i.e., slope greater than 1), the line becomes quite sparse with many gaps, and in the limiting case of ${\displaystyle dx=0}$, 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. Line drawing algorithms such as Bresenham's or Wu's are preferred instead.

## References

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