# Xiaolin Wu's line algorithm

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**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.

## [edit] Pseudocode implementation

Here is pseudocode for the nearly-horizontal case (Δ*x* > Δ*y*). 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**
gradient = dy / dx
*// 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))
intery = intery + gradient
**repeat**
**else**
*//handle "vertical" lines same code as above but X takes the role of Y*
**end function**

## [edit] References

- Abrash, Michael (June 1992). "Fast Antialiasing (Column)".
*Dr. Dobb's Journal***17**(6): 139(7). http://www.gamedev.net/reference/articles/article382.asp. - Wu, Xiaolin (July 1991). "An efficient antialiasing technique".
*Computer Graphics***25**(4): 143–152. doi: . ISBN 0-89791-436-8. http://portal.acm.org/citation.cfm?id=122734. - Wu, Xiaolin (1991). "Fast Anti-Aliased Circle Generation". in James Arvo (Ed.).
*Graphics Gems II*. San Francisco: Morgan Kaufmann. pp. 446–?. ISBN 0-12-064480-0.