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 cannot 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.
Here is pseudocode for the nearly-horizontal case (Failed to parse (syntax error): {\displaystyle δx > δy} ). The extension to cover
nearly-vertical lines is trivial, and left as an exercise for the reader.
Template:Wikicode
function plot(x, y, c) {
plot the pixel at (x,y) with brightness c // where
}
function ipart(x) {
return integer part of x
}
function round(x) {
return ipart(x + 0.5)
}
function fpart(x) {
return fractional part of x
}
function rfpart(x) {
return 1 - fpart(x)
}
// check that x1 < x2
if x2 < x1
swap x1, x2
dx = x2 - x1
dy = y2 - y1
gradient = dy / dx
// handle first endpoint
xend = round(x1)
yend = y1 + gradient * (xend - x1)
xgap = rfpart(x1 + 0.5)
xpxl1 = xend
ypxl1 = ipart(yend)
brightness1 = rfpart(yend) * xgap
brightness2 = fpart(yend) * xgap
plot(xpxl1, ypxl1, brightness1)
plot(xpxl1, ypxl1+1, brightness2)
intery = yend + gradient // first y-intersection for later
// handle second endpoint
xend = round(x2)
yend = y2 + gradient * (xend - x2)
xgap = rfpart(x2 - 0.5)
xpxl2 = xend
ypxl2 = ipart(yend)
brightness1 = rfpart(yend) * xgap
brightness2 = fpart(yend) * xgap
plot(xpxl2, ypxl2, brightness1)
plot(xpxl2, ypxl2+1, brightness2)
for x from xpxl1+1 to xpxl2-1 {
brightness1 = rfpart(intery)
brightness2 = fpart(intery)
plot(x, ipart(intery), brightness1)
plot(x, ipart(intery)+1, brightness2)
intery = intery + gradient
}
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 an replacement for of Bresenham's line algorithm, the circle drawing algorithm is a replacement
for Bresenham's circle drawing algorithm.
References
0-89791-436-8.
- Wu, Xiaolin (1991). Fast Anti-Aliased Circle Generation. In James Arvo (Ed.),
thm%26ie%3DUTF-8%26id%3DKw3YPvf8A-AC&sig=xFsWaJHNOOlbog9Rgk-3hbCvJws Graphics Gems II]. pp. 446--?. San Francisco: Morgan
Kaufmann. ISBN 0-12-064480-0.
External links
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