Antialiased Line  Xiaolin Wu’s algorithm
AntiAliased Line Drawing
Below is the image showing line drawn with Bresenham’s line algorithm (left) and Xiaolin Wu’s line algorithm (right) which smooths the line. Which one looks better to you ?
Anti Aliasing concept
Suppose we want to draw a line from point(1 , 1) to point(8 , 4) with rectangular edges . The ideal line would be the one shown in figure A . Since I want to display it on screen I cannot use that . Line needs to go through a process called Rasterization which would determine color of individual pixels . Several algorithms can be used like Bresenham’s Line Algorithm , Digital Differential Analyzer , Xiaolin Wu’s line algorithm , GuptaSproull algorithm . Later two perform antialiasing or line smoothing.
The result produced by first two algorithm is show in figure B.
There are few problems in Line( figure B ).
1. Pixel (4,2) has less coverage than Pixel (3,2), yet they’re both drawn fully black.
2. Pixel (2,2) has almost as much coverage as (4,2), and yet it’s drawn fully white.
To overcome these drawbacks and produce a much smoother looking line we use Xiaolin Wu’s line algorithm
Xiaolin Wu’s line algorithm
Consider the figure shown below which is drawn using Bresenham’s Line Generation Algorithm . Take a segment and its initial coordinate x. By the X in the loop is added 1 towards the end of the segment. At each step, the error is calculated – the distance between the actual ycoordinate at that location and the nearest grid cell. If the error does not exceed half the height of the cell, it is filled. That’s the whole algorithm.
We will modify this algorithm so that it can produce an antialiased line .
Xiaolin Wu’s line algorithm is characterized by the fact that at each step of the calculation is carried out for the two closest to the line of pixels, and they are colored with different intensity, depending on the distance. Current intersection middle pixel intensity gives 100% if the pixel is within 0.9 pixel, the intensity will be 10%. In other words, one hundred percent of the intensity is divided between the pixels which limit vector line on both sides.
In the picture the red and green color shows the distance to the two adjacent pixels. To calculate the error, you can use floating point and take the error value of the fractional part.
NOTE:The following implementation uses SDL library to draw pixels on screen . If you are on debian system like ubuntu just run following command to install SDL library.
sudo aptget install libsdl2dev
To build use
gcc filename.c lSDL2
Note:If the projection of the segment on the xaxis is less than the projection on the yaxis, or the beginning and end of the segment are swapped, then the algorithm will not work. To avoid this, you need to check the direction of the vector and its slope, and then swap the coordinates of the line , ultimately to reduce everything to some one or at least two cases.
Following algorithm assumes that only integer coordinates will be given as inputs since pixel value cannot be floating point.

// C program to implement Xiaolin Wu's line drawing
// algorithm.
// We must install SDL library using above steps
// to run this prorgram
#include<SDL2/SDL.h>
// SDL stuff
SDL_Window* pWindow = 0;
SDL_Renderer* pRenderer = 0;
// swaps two numbers
void
swap(
int
* a ,
int
*b)
{
int
temp = *a;
*a = *b;
*b = temp;
}
// returns absolute value of number
float
absolute(
float
x )
{
if
(x < 0)
return
x;
else
return
x;
}
//returns integer part of a floating point number
int
iPartOfNumber(
float
x)
{
return
(
int
)x;
}
//rounds off a number
int
roundNumber(
float
x)
{
return
iPartOfNumber(x + 0.5) ;
}
//returns fractional part of a number
float
fPartOfNumber(
float
x)
{
if
(x>0)
return
x  iPartOfNumber(x);
else
return
x  (iPartOfNumber(x)+1);
}
//returns 1  fractional part of number
float
rfPartOfNumber(
float
x)
{
return
1  fPartOfNumber(x);
}
// draws a pixel on screen of given brightness
// 0<=brightness<=1. We can use your own library
// to draw on screen
void
drawPixel(
int
x ,
int
y ,
float
brightness)
{
int
c = 255*brightness;
SDL_SetRenderDrawColor(pRenderer, c, c, c, 255);
SDL_RenderDrawPoint(pRenderer, x, y);
}
void
drawAALine(
int
x0 ,
int
y0 ,
int
x1 ,
int
y1)
{
int
steep = absolute(y1  y0) > absolute(x1  x0) ;
// swap the coordinates if slope > 1 or we
// draw backwards
if
(steep)
{
swap(&x0 , &y0);
swap(&x1 , &y1);
}
if
(x0 > x1)
{
swap(&x0 ,&x1);
swap(&y0 ,&y1);
}
//compute the slope
float
dx = x1x0;
float
dy = y1y0;
float
gradient = dy/dx;
if
(dx == 0.0)
gradient = 1;
int
xpxl1 = x0;
int
xpxl2 = x1;
float
intersectY = y0;
// main loop
if
(steep)
{
int
x;
for
(x = xpxl1 ; x <=xpxl2 ; x++)
{
// pixel coverage is determined by fractional
// part of y coordinate
drawPixel(iPartOfNumber(intersectY), x,
rfPartOfNumber(intersectY));
drawPixel(iPartOfNumber(intersectY)1, x,
fPartOfNumber(intersectY));
intersectY += gradient;
}
}
else
{
int
x;
for
(x = xpxl1 ; x <=xpxl2 ; x++)
{
// pixel coverage is determined by fractional
// part of y coordinate
drawPixel(x, iPartOfNumber(intersectY),
rfPartOfNumber(intersectY));
drawPixel(x, iPartOfNumber(intersectY)1,
fPartOfNumber(intersectY));
intersectY += gradient;
}
}
}
// Driver code
int
main(
int
argc,
char
* args[])
{
SDL_Event event;
// initialize SDL
if
(SDL_Init(SDL_INIT_EVERYTHING) >= 0)
{
// if succeeded create our window
pWindow = SDL_CreateWindow(
"AntiAliased Line "
,
SDL_WINDOWPOS_CENTERED, SDL_WINDOWPOS_CENTERED,
640, 480,
SDL_WINDOW_SHOWN);
// if the window creation succeeded create our renderer
if
(pWindow != 0)
pRenderer = SDL_CreateRenderer(pWindow, 1, 0);
}
else
return
1;
// sdl could not initialize
while
(1)
{
if
(SDL_PollEvent(&event) && event.type == SDL_QUIT)
break
;
// Sets background color to white
SDL_SetRenderDrawColor(pRenderer, 255, 255, 255, 255);
SDL_RenderClear(pRenderer);
// draws a black AALine
drawAALine(80 , 200 , 550, 150);
// show the window
SDL_RenderPresent(pRenderer);
}
// clean up SDL
SDL_Quit();
return
0;
}
Output:
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