Bresenham's Line Algorithm

An accurate and efficient raster line-generating algorithm, developed by Bresenham, scan converts lines using only incrementa1 integer calculations that can be further adapted to display circles and other curves.

1. Input the two line endpoints and store the left endpoint in (x₀,y₀)

2. Load (x₀,y₀) into the frame buffer; i.e, plot the first point.

3. Calculate constants Δx, Δy, 2Δy, and 2Δy - 2Δx, and obtain the starting value for the decision parameter as
   p₀ = 2Δy - ΔX
   

4. At each x_k along the line, starting at k = 0, perform the following test:

   If p_k < 0, the next point to plot is (x_k + 1 , y_k and

   p_{k + 1}= p_k + 2Δy

   Otherwise, the next point to plot is (x_k + 1 , y_k + 1) and

   p_{k + 1}= p_k + 2Δy - 2Δx

5. Repeat step 4 Δx times