MidPoint Circle AlgorithmIt is based on the following function for testing the spatial relationship between the arbitrary point (x, y) and a circle of radius r centered at the origin: Now, consider the coordinates of the point halfway between pixel T and pixel S This is called midpoint (xi+1,yi-) and we use it to define a decision parameter: Pi=f (xi+1,yi-) = (xi+1)2+(yi-)2-r2 ...............equation 2 If Pi is -ve ⟹midpoint is inside the circle and we choose pixel T If Pi is+ve ⟹midpoint is outside the circle (or on the circle)and we choose pixel S. The decision parameter for the next step is: Pi+1=(xi+1+1)2+(yi+1-)2- r2............equation 3 Since xi+1=xi+1, we have If pixel T is choosen ⟹Pi<0 We have yi+1=yi If pixel S is choosen ⟹Pi≥0 We have yi+1=yi-1 We can continue to simplify this in n terms of (xi,yi) and get Now, initial value of Pi (0,r)from equation 2 We can put ≅1 Algorithm:Step1: Put x =0, y =r in equation 2 Step2: Repeat steps while x ≤ y Step3: End Program to draw a circle using Midpoint Algorithm:Output: Next TopicScan converting a Ellipse |