Xiaolin Wu's line 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.

Antialiased line drawn with Xiaolin Wu's algorithm

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.

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.

Xiaolin Wu's line algorithm

References

External links