Bresenham's Circle Drawing Algorithm

Bresenham's Circle

About This Algorithm

It is not easy to display a continuous smooth arc on the computer screen as our computer screen is made of pixels organized in matrix form. So, to draw a circle on a computer screen we should always choose the nearest pixels from a printed pixel so as they could form an arc. One such algorithm that uses this method is Bresenham's Circle Drawing Algorithm. This algorithm uses the key feature of circle that it is highly symmetric. So, for whole 360 degree of circle we will divide it in 8-parts each octant of 45 degree. In order to that we will use Bresenham's Circle Algorithm for calculation of the locations of the pixels in the first octant of 45 degrees. ........

It assumes that the circle is centered on the origin. So for every pixel (x, y) it calculates, we draw a pixel in each of the 8 octants of the circle as shown below :

To achieve the best approximation to the true circle, we have to select those pixels in the raster that fall the least distance from the true circle. It is noticed that if the points are generated from 90^o to 45^o, each new point closest to the true circle can be found by appplying either of the two options :

Increment in positive x direction by one unit i.e. (x+1,y) is the east direction
Increment in positive x direction and negative y direction both by one unit i.e. (x+1,y-1) in the south-east direction

Therefore, a method of selecting between these two choices is all that is necessary to find the points closest to the true circle.

My Try To Implement The Algorithm Using Canvas :

NOTE : Enter The Radius With Which The Circle Will Be Drawn. If You Don't Input Any Radius Or Input Radius Greater Then 75 units Then The Default Radius Taken Is 60 units.
This Code Draws 8 Lines As This Algorithm Uses 8-Point Symmetry. As This Algorithm Works On Rasterized Pixels, So The Calculated Pixel Values We Get Are Not Accurate.

Enter The Radius For The Circle :