Xiaolin Wu's line algorithm: Difference between revisions

Revision as of 14:55, 15 June 2005

Revision as of 15:05, 15 June 2005

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[[Bresenham's line algorithm|Bresenham's algorithm]] draws lines extremely quickly, but it cannot 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 line algorithm|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.

Here is [[pseudocode]] for the nearly-horizontal case (<math>\deltaDelta x > \deltaDelta y</math>). The extension to cover nearly-vertical lines is trivial, and left as an exercise for the reader.

{{wikicode}}

<code>

'''function''' plot(x, y, c) {

plot the pixel at (x, y) with brightness c ''// where <math>0<= &le; c<= &le; 1</math>''

'''function''' ipart(x) {

}

'''function''' ipart(x) {

'''return''' ''integer part of x''

'''function''' round(x) {

}

'''function''' round(x) {

'''return''' ipart(x + 0.5)

'''function''' fpart(x) {

}

'''function''' fpart(x) {

'''return''' ''fractional part of x''

'''function''' rfpart(x) {

}

'''function''' rfpart(x) {

'''return''' 1 - fpart(x)

''// check that x₁x1 < x₂x2''

}

'''if x2 < x1

''// check that x₁ < x₂''

swap x1, x2

'''if x₂ < x₁

dx = x2 - x1

swap x₁, x₂

dy = y2 - y1

dx = x₂ - x₁

dy = y₂ - y₁

gradient = dy / dx

''// handle first endpoint''

xend = round(x₁x1)

yend = y₁y1 + gradient * (xend - x₁x1)

xgap = rfpart(x₁x1 + 0.5)

xpxl1 = xend '' // this will be used in the main loop''

ypxl1 = ipart(yend)

brightness1plot(xpxl1, =ypxl1, rfpart(yend) * xgap)

brightness2plot(xpxl1, =ypxl1 + 1, fpart(yend) * xgap)

intery = yend + gradient ''// first y-intersection for laterthe main loop''

plot(xpxl1, ypxl1, brightness1)

plot(xpxl1, ypxl1+1, brightness2)

intery = yend + gradient ''// first y-intersection for later''

''// handle second endpoint''

xend = round(x₂x2)

yend = y₂y2 + gradient * (xend - x₂x2)

xgap = rfpart(x₂x2 - 0.5)

xpxl2 = xend '' // this will be used in the main loop''

ypxl2 = ipart(yend)

brightness1plot(xpxl2, =ypxl2, rfpart(yend) * xgap)

brightness2plot(xpxl2, =ypxl2 + 1, fpart(yend) * xgap)

plot(xpxl2, ypxl2, brightness1)

''// main loop''

plot(xpxl2, ypxl2+1, brightness2)

'''for''' x '''from''' xpxl1 + 1 '''to''' xpxl2 - 1 {

brightness1plot(x, =ipart(intery), rfpart(intery))

brightness2plot(x, ipart(intery) + =1, fpart(intery))

plot(x, ipart(intery), brightness1)

plot(x, ipart(intery)+1, brightness2)

intery = intery + gradient

}

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==External links==

* [http://www.ece.mcmaster.ca/~xwu/ Xiaolin Wu's homepage]

{{comp-stub}}

[[Category:Geometric algorithms]]