Circle Drawing Algorithms
In computer graphics, popular algorithms used to generate circle are
 Mid Point Circle Drawing Algorithm
 Bresenham’s Circle Drawing Algorithm
In this article, we will discuss about Mid Point Circle Drawing Algorithm.
Mid Point Circle Drawing Algorithm
Given the centre point and radius of circle, Mid Point Circle Drawing Algorithm attempts to generate the points of one octant. 
The points for other octacts are generated using the eight symmetry property.
Procedure
Given
 Centre point of Circle = (X_{0}, Y_{0})
 Radius of Circle = R
The points generation using Mid Point Circle Drawing Algorithm involves the following steps
Step01:
Assign the starting point coordinates (X_{0}, Y_{0}) as
 X_{0} = 0
 Y_{0} = R
Step02:
Calculate the value of initial decision parameter P_{0} as
P_{0} = 1 – R
Step03:
Suppose the current point is (X_{k}, Y_{k}) and the next point is (X_{k+1}, Y_{k+1}).
Find the next point of the first octant depending on the value of decision parameter P_{k}.
Follow the below two cases
Step04:
If the given centre point (X_{0}, Y_{0}) is not (0, 0), then do the following and plot the point
 X_{plot} = X_{c} + X_{0}
 Y_{plot} = Y_{c} + Y_{0}
Here, (X_{c}, Y_{c}) denotes the current value of X and Y coordinates.
Step05:
Keep repeating Step03 and Step04 until X_{plot} >= Y_{plot}.
Step06:
Step05 generates all the points for one octant.
To find the points for other seven octants, follow the eight symmetry property of circle.
This is depicted by the following figure
Also ReadLine Drawing Algorithms
PRACTICE PROBLEMS BASED ON MID POINT CIRCLE DRAWING ALGORITHM
Problem01:
Given the centre point coordinates (0, 0) and radius as 10, generate all the points to form a circle.
Solution
Given
 Centre Coordinates of Circle (X_{0}, Y_{0}) = (0, 0)
 Radius of Circle = 10
Step01:
Assign the starting point coordinates (X_{0}, Y_{0}) as
 X_{0} = 0
 Y_{0} = R = 10
Step02:
Calculate the value of initial decision parameter P_{0} as
P_{0} = 1 – R
P_{0} = 1 – 10
P_{0} = 9
Step03:
As P_{initial} < 0, so case01 is satisfied.
Thus,
 X_{k+1} = X_{k} + 1 = 0 + 1 = 1
 Y_{k+1} = Y_{k} = 10
 P_{k+1 }= P_{k} + 2 x X_{k+1} + 1 = 9 + (2 x 1) + 1 = 6
Step04:
This step is not applicable here as the given centre point coordinates is (0, 0).
Step05:
Step03 is executed similarly until X_{k+1} >= Y_{k+1} as follows
P_{k}  P_{k+1}  (X_{k+1}, Y_{k+1}) 
(0, 10)  
9  6  (1, 10) 
6  1  (2, 10) 
1  6  (3, 10) 
6  3  (4, 9) 
3  8  (5, 9) 
8  5  (6, 8) 
Algorithm Terminates These are all points for Octant1. 
Algorithm calculates all the points of octant1 and terminates.
Now, the points of octant2 are obtained using the mirror effect by swapping X and Y coordinates.
Octant1 Points  Octant2 Points 
(0, 10)  (8, 6) 
(1, 10)  (9, 5) 
(2, 10)  (9, 4) 
(3, 10)  (10, 3) 
(4, 9)  (10, 2) 
(5, 9)  (10, 1) 
(6, 8)  (10, 0) 
These are all points for Quadrant1. 
Now, the points for rest of the part are generated by following the signs of other quadrants.
The other points can also be generated by calculating each octant separately.
Here, all the points have been generated with respect to quadrant1
Quadrant1 (X,Y)  Quadrant2 (X,Y)  Quadrant3 (X,Y)  Quadrant4 (X,Y) 
(0, 10)  (0, 10)  (0, 10)  (0, 10) 
(1, 10)  (1, 10)  (1, 10)  (1, 10) 
(2, 10)  (2, 10)  (2, 10)  (2, 10) 
(3, 10)  (3, 10)  (3, 10)  (3, 10) 
(4, 9)  (4, 9)  (4, 9)  (4, 9) 
(5, 9)  (5, 9)  (5, 9)  (5, 9) 
(6, 8)  (6, 8)  (6, 8)  (6, 8) 
(8, 6)  (8, 6)  (8, 6)  (8, 6) 
(9, 5)  (9, 5)  (9, 5)  (9, 5) 
(9, 4)  (9, 4)  (9, 4)  (9, 4) 
(10, 3)  (10, 3)  (10, 3)  (10, 3) 
(10, 2)  (10, 2)  (10, 2)  (10, 2) 
(10, 1)  (10, 1)  (10, 1)  (10, 1) 
(10, 0)  (10, 0)  (10, 0)  (10, 0) 
These are all points of the Circle. 
Problem02:
Given the centre point coordinates (4, 4) and radius as 10, generate all the points to form a circle.
Solution
Given
 Centre Coordinates of Circle (X_{0}, Y_{0}) = (4, 4)
 Radius of Circle = 10
As stated in the algorithm,
 We first calculate the points assuming the centre coordinates is (0, 0).
 At the end, we translate the circle.
Step01, Step02 and Step03 are already completed in Problem01.
Now, we find the values of X_{plot} and Y_{plot} using the formula given in Step04 of the main algorithm.
The following table shows the generation of points for Quadrant1
 X_{plot} = X_{c} + X_{0 }= 4 + X_{0}
 Y_{plot} = Y_{c} + Y_{0} = 4 + Y_{0}
(X_{k+1}, Y_{k+1)}  (X_{plot}, Y_{plot}) 
(0, 10)  (4, 14) 
(1, 10)  (5, 14) 
(2, 10)  (6, 14) 
(3, 10)  (7, 14) 
(4, 9)  (8, 13) 
(5, 9)  (9, 13) 
(6, 8)  (10, 12) 
(8, 6)  (12, 10) 
(9, 5)  (13, 9) 
(9, 4)  (13, 8) 
(10, 3)  (14, 7) 
(10, 2)  (14, 6) 
(10, 1)  (14, 5) 
(10, 0)  (14, 4) 
These are all points for Quadrant1. 
The following table shows the points for all the quadrants
Quadrant1 (X,Y)  Quadrant2 (X,Y)  Quadrant3 (X,Y)  Quadrant4 (X,Y) 
(4, 14)  (4, 14)  (4, 6)  (4, 6) 
(5, 14)  (3, 14)  (3, 6)  (5, 6) 
(6, 14)  (2, 14)  (2, 6)  (6, 6) 
(7, 14)  (1, 14)  (1, 6)  (7, 6) 
(8, 13)  (0, 13)  (0, 5)  (8, 5) 
(9, 13)  (1, 13)  (1, 5)  (9, 5) 
(10, 12)  (2, 12)  (2, 4)  (10, 4) 
(12, 10)  (4, 10)  (4, 2)  (12, 2) 
(13, 9)  (5, 9)  (5, 1)  (13, 1) 
(13, 8)  (5, 8)  (5, 0)  (13, 0) 
(14, 7)  (6, 7)  (6, 1)  (14, 1) 
(14, 6)  (6, 6)  (6, 2)  (14, 2) 
(14, 5)  (6, 5)  (6, 3)  (14, 3) 
(14, 4)  (6, 4)  (6, 4)  (14, 4) 
These are all points of the Circle. 
Advantages of Mid Point Circle Drawing Algorithm
The advantages of Mid Point Circle Drawing Algorithm are
 It is a powerful and efficient algorithm.
 The entire algorithm is based on the simple equation of circle X^{2} + Y^{2} = R^{2}.
 It is easy to implement from the programmer’s perspective.
 This algorithm is used to generate curves on raster displays.
Disadvantages of Mid Point Circle Drawing Algorithm
The disadvantages of Mid Point Circle Drawing Algorithm are
 Accuracy of the generating points is an issue in this algorithm.
 The circle generated by this algorithm is not smooth.
 This algorithm is time consuming.
Important Points

To gain better understanding about Mid Point Circle Drawing Algorithm,
Next ArticleBresenham Circle Drawing Algorithm
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