Xiaolin Wu's line algorithm

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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 any cases where the line endpoints do not lie exactly on integer points of the pixel grid. A naive approach to anti-aliasing the line would take an extremely long time. Wu's algorithm is comparatively fast, but is still slower than Bresenham's algorithm. The algorithm consists of drawing pairs of pixels straddling the line, each coloured according to its distance from the line. Pixels at the line ends are handled separately. Lines less than one pixel long are 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

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