Bresenham's line algorithm

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The Bresenham line algorithm is an algorithm which determines which order to form a close approximation to a straight line between two given points. It is commonly used to draw lines on a computer screen, as it uses only integer addition, subtraction and bit shifting, all of which are very cheap operations in standard computer architectures.


In the following pseudocode sample plot(x,y) plots a point and abs returns absolute value:

 function line(x0, x1, y0, y1)
     int deltax := x1 - x0
     int deltay := y1 - y0
     real error := 0
     real deltaerr := abs (deltay / deltax)    // Assume deltax != 0 (line is not vertical),
           // note that this division needs to be done in a way that preserves the fractional part
     int y := y0
     for x from x0 to x1
         error := error + deltaerr
         if error ≥ 0.5 then
             y := y + 1
             error := error - 1.0