Xiaolin Wu's line algorithm

Demonstration of Xiaolin Wu's algorithm

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

Anti-Aliased Lines (blue) generated with Xiaolin Wu's line algorithm alongside standard lines (red) generated with Bresenham's line algorithm

Antialiasing technique

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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

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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 

References

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  • 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.
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