Explain Midpoint algorithm for circle

The Midpoint Circle Drawing Algorithm is a graphics algorithm that determines the points needed for rasterizing a circle. Here's a step-by-step explanation:

1. Initialization: Start from the topmost point on the circle which is (0, r) where r is the radius of the circle. The decision parameter for the algorithm is set to (5/4) - r.

2. Decision Parameter Calculation: The decision parameter at any position (x, y) can be calculated using the formula: P = (Xk+1)^2 + (Yk-1)^2 - r^2. If P < 0, this means we are inside the circle and the next pixel is along the East direction. If P >= 0, this means we are outside or at the circle and the next pixel is in the South East direction.

3. Position Update: Depending on the decision parameter, we update the position of the next point along the circle's circumference. If P < 0, the next point is (Xk+1, Yk). If P >= 0, the next point is (Xk+1, Yk-1).

4. Symmetry Utilization: A circle is symmetric along its diameter. So, we can calculate the positions of the next points by calculating the position of just one point in one octant and then reflecting that point in the other seven octants.

5. Repeat Steps: Repeat steps 2-4 until Xk+1 > Yk. This is because we only calculate points in one octant and then use symmetry to get the points in the other octants.

This algorithm is efficient because it uses only integer addition and subtraction, avoiding the costly operations of multiplication and division.