# Xiaolin Wu's line algorithm

Antialiased line drawn with Xiaolin Wu's algorithm

Xiaolin Wu's line algorithm is an algorithm for line antialiasing, which was presented in the article An Efficient Antialiasing Technique in the July 1991 issue of Computer Graphics, as well as in the article Fast Antialiasing in the June 1992 issue of Dr. Dobb's Journal.

Bresenham's algorithm draws lines extremely quickly, but it does not perform anti-aliasing. In addition, it cannot handle the case where the line endpoints do not lie exactly on integer points of the pixel grid. A naïve approach to anti-aliasing the line would take an extremely long time, but Wu's algorithm is quite fast (it is still slower than Bresenham's, though). The basis of the algorithm is to draw pairs of pixels straddling the line, coloured according to proximity. Pixels at the line ends are handled separately. Lines less than one pixel long should be handled as a special case.

An extension to the algorithm for circle drawing was presented by Xiaolin Wu in the book Graphics Gems II. Just like the line drawing algorithm is a replacement for Bresenham's line drawing algorithm, the circle drawing algorithm is a replacement for Bresenham's circle drawing algorithm.

## Pseudocode implementation

Here is pseudocode for the nearly-horizontal case (Δx > Δy). To extend the algorithm to work for all lines, swap the x and y coordinates when near-vertical lines appear (for reference, see Bresenham's line algorithm). This implementation is only valid for x, y ≥ 0.

``````function plot(x, y, c) is
plot the pixel at (x, y) with brightness c (where 0 ≤ c ≤ 1)

function ipart(x) is
return integer part of x

function round(x) is
return ipart(x + 0.5)

function fpart(x) is
return fractional part of x

function rfpart(x) is
return 1 - fpart(x)

function drawLine(x1,y1,x2,y2) is

dx = x2 - x1
dy = y2 - y1

if abs(dx) > abs(dy) then
//handle "horizontal" lines
if x2 < x1
swap x1, x2
swap y1, y2
end if

// handle first endpoint
xend = round(x1)
yend = y1 + gradient * (xend - x1)
xgap = rfpart(x1 + 0.5)
xpxl1 = xend  // this will be used in the main loop
ypxl1 = ipart(yend)
plot(xpxl1, ypxl1, rfpart(yend) * xgap)
plot(xpxl1, ypxl1 + 1, fpart(yend) * xgap)
intery = yend + gradient // first y-intersection for the main loop

// handle second endpoint
xend = round(x2)
yend = y2 + gradient * (xend - x2)
xgap = fpart(x2 + 0.5)
xpxl2 = xend  // this will be used in the main loop
ypxl2 = ipart(yend)
plot(xpxl2, ypxl2, rfpart(yend) * xgap)
plot(xpxl2, ypxl2 + 1, fpart(yend) * xgap)

// main loop
for x from xpxl1 + 1 to xpxl2 - 1 do
plot(x, ipart(intery), rfpart(intery))
plot(x, ipart(intery) + 1, fpart(intery))
repeat
else
//handle "vertical" lines  same code as above but X takes the role of Y
end function
```
```