Xiaolin Wu's line algorithm

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 the case 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, 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.

References

Abrash, Michael (1992). "Fast Antialiasing (Column)". Dr. Dobb's Journal. 17 (6): 139(7). {{cite journal}}: Unknown parameter |month= ignored (help)
Wu, Xiaolin (1991). "An efficient antialiasing technique". Computer Graphics. 25 (4): 143–152. doi:10.1145/127719.122734. ISBN 0-89791-436-8. {{cite journal}}: Unknown parameter |month= ignored (help)
Wu, Xiaolin (1991). "Fast Anti-Aliased Circle Generation". In James Arvo (Ed.) (ed.). Graphics Gems II. San Francisco: Morgan Kaufmann. pp. 446–450. ISBN 0-12-064480-0.

External links