Midpoint circle algorithm

The Midpoint Circle Algorithm is a circle drawing algorithm used in computer graphics to generate a digital approximation of a circle with a specified radius and center point. It is a variation of the Midpoint Line Algorithm and uses similar principles to determine which pixels to plot along the circumference of the circle.

The algorithm works by plotting points along the eight octants of the circle, starting at the point (0, r) on the positive y-axis, where r is the radius of the circle. For each octant, the algorithm uses the midpoint between two candidate pixels to determine which pixel to plot next along the circumference of the circle.

The steps of the Midpoint Circle Algorithm can be summarized as follows:

1. Set the radius r and center point (xc, yc) of the circle.

2. Initialize the x-coordinate to zero and the y-coordinate to r.

3. Calculate the initial value of the decision parameter as P = 5/4 - r.

4. Plot the eight points of the circle in the first octant (0 to 45 degrees) using the Midpoint Line Algorithm, with the starting point at (0, r) and the end point at (x, y).

5. For each subsequent octant, reflect the points plotted in the previous octant across the x- and/or y-axis as necessary, and use the Midpoint Line Algorithm to plot the remaining points of the circle.

6. Repeat steps 4 and 5 for each octant until all points of the circle have been plotted.

The Midpoint Circle Algorithm is efficient and produces accurate circles with a smooth edge, making it a popular choice for circle drawing in computer graphics. It can also be extended to draw ellipses and other shapes using similar principles.