Bresenham Circle Drawing Algorithm

The Bresenham circle drawing algorithm is a computer graphics algorithm used to draw circles in a 2D space. It is named after its inventor, Jack Bresenham, who also created the Bresenham line drawing algorithm.

The algorithm works by incrementally plotting pixels on the circumference of a circle. It uses integer arithmetic and avoids using expensive floating-point operations, making it more efficient than other circle-drawing algorithms.

The basic idea behind the algorithm is to determine the positions of the pixels that lie closest to the ideal circle, using a decision-making process similar to that used in the Bresenham line drawing algorithm. At each step, the algorithm decides which pixel to plot based on which decision results in a closer approximation of the circle.

The Bresenham circle drawing algorithm can also be extended to draw ellipses by scaling the x and y radii independently. Additionally, the algorithm can be modified to draw arcs or pie slices by limiting the range of angles over which pixels are plotted.

The Bresenham circle drawing algorithm is widely used in computer graphics applications, such as image editing software and video games, and it is also used in scientific and engineering applications for visualization purposes.

Rules of Circle Drawing

Center point of circle (X0, Y0)
Radius of circle = R

Step 1
Starting Point (X0 Y0)
as X0 = 0
   Y0 = R

Step 2
P0 = 1-R

Step 3
Repeat
if Pk<0 then
Xk+1 = Xk+1
Yk+1 = Yk
Pk+1 = Pk+4*Xk+1+6

if Pk>=0 then
Xk+1 = Xk+1
Yk+1 = Yk-1
Pk+1 = Pk+4*(Xk+1 - Yk+1)+10

Step 4
Xplot = Xc + X0
Yplot = Yc + Y0

Keep repeating Step-03 and Step-04 until Xplot => Yplot.

Advantages of Bresenham Circle Drawing Algorithm:

1. Efficiency: The algorithm is more efficient than other circle drawing algorithms because it uses integer arithmetic and avoids using expensive floating-point operations.
2. Accuracy: The algorithm produces accurate and precise results, as it calculates the coordinates of the pixels that should be colored to approximate the circle.
3. Flexibility: The algorithm can be easily adapted to draw ellipses or arcs by scaling the x and y radii independently or limiting the range of angles over which pixels are plotted.
4. Easy to implement: The Bresenham circle drawing algorithm is relatively easy to implement and does not require a large amount of memory or processing power.

Disadvantages of Bresenham Circle Drawing Algorithm:

1. Limited to 2D: The algorithm is limited to two-dimensional (2D) graphics and cannot be used for three-dimensional (3D) graphics or more complex visualizations.
2. Aliasing: The algorithm can produce jagged or stair-stepped circles, especially for larger circles, which can be visually unappealing. However, this can be mitigated by using anti-aliasing techniques.
3. Limited to circles: The algorithm can only draw circles, and cannot be used to draw curved or irregular shapes.
4. Slightly distorted circles: The algorithm can produce slightly distorted circles due to the use of integer arithmetic and the need to make decisions about which pixel to plot. However, the distortions are usually not noticeable for smaller circles.