Midpoint Circle Algorithm
The Midpoint Circle Algorithm is an alternative and efficient method for drawing circles compared to the standard equation r^2 = x^2 + y^2. It's advantageous because it only uses integer arithmetic and can efficiently determine the pixels that lie on the circumference of a circle. Here's a description of how the Midpoint Circle Algorithm works:
Initialization: Given the center coordinates (xc, yc) and the radius r of the circle, initialize the variables x and y as (0, r).
Initial Decision Parameter: Calculate the initial decision parameter as P0 = 5/4 - r.
Plotting Points: Start plotting points on the circumference of the circle using the current position (x, y). Since circles are symmetric, you can plot points in all eight octants simultaneously.
Update the Decision Parameter: At each step, evaluate the decision parameter and determine the next point to plot based on its value:
If Pk < 0, update Pk+1 = Pk + 2x + 1 and increment x.
If Pk ≥ 0, update Pk+1 = Pk + 2x - 2y + 1, increment x, and decrement y.
Iterate: Repeat steps 3 and 4 until x ≤ y.
→ This algorithm efficiently calculates and plots the points lying on the circumference of the circle, making it a popular choice for drawing circles in computer graphics.
