Xiaolin Wu's line 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 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 (<math>\Delta x > \Delta y<math>). The extension to cover nearly-vertical lines is trivial, and left as an exercise for the reader.

function plot(x, y, c)
	plot the pixel at (x, y) with brightness c // where 0 ≤ c ≤ 1
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  // 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 = rfpart(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 {
	plot(x, ipart(intery), rfpart(intery))
	plot(x, ipart(intery) + 1, fpart(intery))
	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.


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