Midpoint line algorithm

The Midpoint Line Algorithm is a line drawing algorithm used in computer graphics to generate a digital approximation of a straight line between two points. Like Bresenham's algorithm, it 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 the midpoint between two candidate pixels to determine which pixel to plot next along the line. Starting at one endpoint of the line, the algorithm calculates the distance between the midpoint and the ideal position of the next pixel on the line. It then selects the pixel with the smallest distance as the next pixel to plot.

The steps of the Midpoint Line 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. Set the starting point to (x1, y1).

3. Initialize the error term to zero.

4. 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 less than or equal to zero, increment the y-coordinate and add the difference in x to the error term.

   

   b. Otherwise, leave the y-coordinate unchanged and add the sum of the differences in x and y to the error term.

5. Repeat step 4 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.

The Midpoint Line Algorithm is similar to Bresenham's algorithm in terms of efficiency and accuracy, but it may produce slightly different results for lines with very steep slopes or nearly horizontal slopes. However, it can be a useful alternative to Bresenham's algorithm in certain situations, and is also used in other algorithms such as the midpoint circle algorithm for drawing circles.