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.
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(x0,y0,x1,y1) is boolean steep := abs(y1 - y0) > abs(x1 - x0) if steep then swap(x0, y0) swap(x1, y1) end if if x0 > x1 then swap(x0, x1) swap(y0, y1) end if dx := x1 - x0 dy := y1 - y0 gradient := dy / dx // handle first endpoint xend := round(x0) yend := y0 + gradient * (xend - x0) xgap := rfpart(x0 + 0.5) xpxl1 := xend // this will be used in the main loop ypxl1 := ipart(yend) if steep then plot(ypxl1, xpxl1, rfpart(yend) * xgap) plot(ypxl1+1, xpxl1, fpart(yend) * xgap) else plot(xpxl1, ypxl1, rfpart(yend) * xgap) plot(xpxl1, ypxl1+1, fpart(yend) * xgap) end if intery := yend + gradient //first y-intersection for the main loop //handle second endpoint xend := round(x1) yend := y1 + gradient * (xend - x1) xgap := fpart(x1 + 0.5) xpxl2 := xend //this will be used in the main loop ypxl2 := ipart(yend) if steep then plot(ypxl2, xpxl2, rfpart(yend) * xgap) plot(ypxl2+1, xpxl2, fpart(yend) * xgap) else plot(xpxl2, ypxl2, rfpart(yend) * xgap) plot(xpxl2, ypxl2+1, fpart(yend) * xgap) end if // main loop for x from xpxl1 + 1 to xpxl2 - 1 do if steep then plot(ipart(intery), x, rfpart(intery)) plot(ipart(intery)+1, x, fpart(intery)) else plot(x, ipart (intery), rfpart(intery)) plot(x, ipart (intery)+1, fpart(intery)) end if intery = intery + gradient
end function
Note: If at the beginning of the routine abs(dx) < abs(dy) is true, then all plotting should be done with x and y reversed.
Famous quotes containing the word line:
“Where were you when I laid the foundation of the earth? Tell me, if you have understanding. Who determined its measurements—surely you know! Or who stretched the line upon it? On what were its bases sunk, or who laid its cornerstone when the morning stars sang together and all the heavenly beings shouted for joy?”
—Bible: Hebrew, Job 38:4 -7.
God, to Job.