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{{Short description|Line algorithm with antialiasing}}
{{multiple|
{{third-party|date=April 2018}}
{{no footnotes|date=January 2013}}
{{Cleanup|reason=Implementation does not provide explanation|date=November 2023}}
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[[File:LineXiaolinWu.gif|thumb|336px|Demonstration of Xiaolin Wu's algorithm]]
'''Xiaolin Wu's line algorithm''' is an [[algorithm]] for line [[spatial anti-aliasing|antialiasing]].
[[File:Xiaolin anti-aliased line comparison.png|thumb|Anti-Aliased Lines (blue) generated with Xiaolin Wu's line algorithm alongside standard lines (red) generated with Bresenham's line algorithm]]
==Antialiasing technique==
Xiaolin Wu's line algorithm was presented in the article "An Efficient Antialiasing Technique" in the July 1991 issue of ''[[Computer Graphics (newsletter)|Computer Graphics]]'', as well as in the article "Fast Antialiasing" in the June 1992 issue of ''[[Dr. Dobb's Journal]]''.
[[Bresenham's line algorithm|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
An extension to the algorithm for circle drawing was presented by Xiaolin Wu in the book ''
==Algorithm==
Like [[Bresenham's line algorithm|Bresenham’s line algorithm]], this method steps
along one axis and considers the two nearest pixels to the ideal line. Instead of
choosing the nearest, it draws both, with intensities proportional to their vertical
distance from the true line. This produces smoother, anti-aliased lines.
[[File:Wu-line-animation.gif|thumb|Animation showing symmetry of Wu's line algorithm ]]
The pseudocode below assumes a line where <math>x_0 < x_1</math>, <math>y_0 < y_1</math>,
and the slope <math>k = \frac{dy}{dx}</math> satisfies <math>0 \le k \le 1</math>. This
is a standard simplification — the algorithm can be extended to all directions using symmetry.
The algorithm is well-suited to older CPUs and microcontrollers because:
* It avoids floating point arithmetic in the main loop (only used to initialize d)
* It renders symmetrically from both ends, halving the number of iterations
* The main loop uses only addition and bit shifts — no multiplication or division
<syntaxhighlight lang="python" line="1">
function draw_line(x0, y0, x1, y1)
N := 8 # brightness resolution (bits)
M := 15 # fixed-point fractional bits
I := maximum brightness value
# Compute gradient and convert to fixed-point step
k := float(y1 - y0) / (x1 - x0)
d := floor((k << M) + 0.5)
# Start with fully covered pixels at each end
img[x0, y0] := img[x1, y1] := I
D := 0 # Fixed-point accumulator
while true:
x0 := x0 + 1
x1 := x1 - 1
if x0 > x1:
break
D := D + d
if D overflows:
y0 := y0 + 1
y1 := y1 - 1
# Brightness = upper N bits of fractional part of D
v := D >> (M - N)
img[x0, y0] := img[x1, y1] := I - v
img[x0, y0 + 1] := img[x1, y1 -1] := v
</syntaxhighlight>
===Floating Point Implementation===
<syntaxhighlight lang="pascal" line="1">
function plot(x, y, c) is
// fractional part of x
function fpart(x) is
function rfpart(x) is
function drawLine(x0,y0,x1,y1) is
swap(x0, x1)
swap(y0, y1)
if dx == 0.0 then
gradient :=
else
gradient := dy / dx
end
// handle first endpoint
xend := floor(x0)
yend := y0 + gradient * (xend - x0)
xgap := 1 - (x0 - xend)
xpxl1 := xend // this will be used in the main loop
ypxl1 := floor(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 := ceil(x1)
yend := y1 + gradient * (xend - x1)
xgap := 1 - (xend - x1)
xpxl2 := xend //this will be used in the main loop
ypxl2 := floor(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(floor(intery) , x, rfpart(intery))
plot(floor(intery)+1, x, fpart(intery))
intery := intery + gradient
end
else
for x from xpxl1 + 1 to xpxl2 - 1 do
begin
plot(x, floor(intery), rfpart(intery))
plot(x, floor(intery)+1, fpart(intery))
intery := intery + gradient
end
end if
end function
</syntaxhighlight>
==References==
Line 91 ⟶ 157:
| title = Fast Antialiasing (Column)
| journal=[[Dr. Dobb's Journal]]
|
}}
* {{cite journal
Line 97 ⟶ 163:
| url = http://portal.acm.org/citation.cfm?id=122734
| title = An efficient antialiasing technique
| journal=
|
| doi = 10.1145/127719.122734
| isbn=0-89791-436-8
| url-access=subscription
}}
* {{cite book
Line 106 ⟶ 173:
| year = 1991
| chapter = Fast Anti-Aliased Circle Generation
| editor = James Arvo
| title = Graphics Gems II
| pages = 446–450
Line 116 ⟶ 183:
==External links==
* [http://www.ece.mcmaster.ca/~xwu/ Xiaolin Wu's homepage]
* [https://www.eng.mcmaster.ca/ece/faculty/dr-xiaolin-wu Xiaolin Wu's homepage at McMaster University]
{{DEFAULTSORT:Xiaolin Wu's Line Algorithm}}
[[Category:
[[Category:Articles with example pseudocode]]
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