Xiaolin Wu's line algorithm

Xiaolin Wu's line algorithm is an algorithm for line antialiasing.

Antialiasing technique

Xiaolin Wu's line algorithm 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 as 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.

Algorithm

<syntaxhighlight lang="pascal" line="1"> function plot(x, y, c) is

   plot the pixel at (x, y) with brightness c (where 0 ≤ c ≤ 1)

// integer part of x function ipart(x) is

   return floor(x)

function round(x) is

   return ipart(x + 0.5)

// fractional part of x function fpart(x) is

   return x - ipart(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

   if dx == 0.0 then
       gradient := 1.0
   else
       gradient := dy / dx
   end if

   // 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
   if steep then
       for x from xpxl1 + 1 to xpxl2 - 1 do
          begin
               plot(ipart(intery)  , x, rfpart(intery))
               plot(ipart(intery)+1, x,  fpart(intery))
               intery := intery + gradient
          end
   else
       for x from xpxl1 + 1 to xpxl2 - 1 do
          begin
               plot(x, ipart(intery),  rfpart(intery))
               plot(x, ipart(intery)+1, fpart(intery))
               intery := intery + gradient
          end
   end if

end function </syntaxhighlight>

References

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

External links