Bresenham's algorithm

Bresenham's algorithm is a line drawing algorithm used in computer graphics to generate a digital approximation of a straight line between two points. It is an efficient and widely used algorithm that uses only integer arithmetic, making it well-suited for implementation in hardware or software with limited resources.

The algorithm is based on the idea of using an incremental error to determine which pixel to plot next along the line. Starting at one endpoint of the line, the algorithm calculates the error between the ideal position of the next pixel on the line and the actual position of the last plotted pixel. It then selects the pixel with the smallest error as the next pixel to plot.

The steps of Bresenham's algorithm can be summarized as follows:

1. Calculate the differences in x and y between the two endpoints of the line, and store them in dx and dy, respectively.

2. Initialize the error term to zero and the increment for y to 1.

3. For each pixel along the line in the x-direction, plot the current pixel and update the error term as follows:

   a. If the error term is greater than or equal to 0.5, increment the y-coordinate by the increment value and subtract 1 from the error term.

   

   b. Otherwise, leave the y-coordinate unchanged and add the slope (dy/dx) to the error term.

4. Repeat step 3 for each pixel along the line in the y-direction, using the absolute value of the slope (|dy/dx|) to determine whether to increment or decrement the x-coordinate.

Bresenham's algorithm is efficient and produces accurate and smooth lines, making it a popular choice for line drawing in computer graphics. It can also be extended to draw circles, ellipses, and other shapes, and is used in many real-time graphics applications, including video games and computer-aided design (CAD) software.