Question

How can you generate a circle of center C and radius R using Bresenhem’s algorithm? Also, make flow chart for this algorithm. Write a C/C++ program to implement Bresenhem’s circle algorithm.

Answer 1

The Bresenham's circle drawing algorithm.

the 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 :-

Explanation:

Now, we will see how to calculate the next pixel location from a previously known pixel location (x, y). In Bresenham's algorithm at any point (x, y) we have two option either to choose the next pixel in the east i.e. (x+1, y) or in the south east i.e. (x+1, y-1).

And this can be decided by using the decision parameter d as:

• If d > 0, then (x+1, y-1) is to be chosen as the next pixel as it will be closer to the arc.
• else (x+1, y) is to be chosen as next pixel.

Now to draw the circle for a given radius 'r' and centre (xc, yc) We will start from (0, r) and move in first quadrant till x=y (i.e. 45 degree). We should start from listed initial condition:

d = 3 - (2 * r)
x = 0
y = r

Now for each pixel, we will do the following operations:

1. Set initial values of (xc, yc) and (x, y)
2. Set decision parameter d to d = 3 - (2 * r).
3. call drawCircle(int xc, int yc, int x, int y) function.
4. Repeat steps 5 to 8 until x < = y
5. Increment value of x.
6. If d < 0, set d = d + (4*x) + 6
7. Else, set d = d + 4 * (x - y) + 10 and decrement y by 1.
8. call drawCircle(int xc, int yc, int x, int y) function

Draw circle() function.

// function to draw all other 7 pixels 

// present at symmetric position 

drawCircle(int xc, int yc, int x, int y) 

{ 

    putpixel(xc+x, yc+y, RED); 

    putpixel(xc-x, yc+y, RED); 

    putpixel(xc+x, yc-y, RED); 

    putpixel(xc-x, yc-y, RED); 

    putpixel(xc+y, yc+x, RED); 

    putpixel(xc-y, yc+x, RED); 

    putpixel(xc+y, yc-x, RED); 

    putpixel(xc-y, yc-x, RED); 

} 



Below is C implementation of above approach.



// C-program for circle drawing 

// using Bresenham's Algorithm 

// in computer-graphics 

#include <stdio.h> 

#include <dos.h> 

#include <graphics.h> 

  

// Function to put pixels 

// at subsequence points 

void drawCircle(int xc, int yc, int x, int y) 

{ 

    putpixel(xc+x, yc+y, RED); 

    putpixel(xc-x, yc+y, RED); 

    putpixel(xc+x, yc-y, RED); 

    putpixel(xc-x, yc-y, RED); 

    putpixel(xc+y, yc+x, RED); 

    putpixel(xc-y, yc+x, RED); 

    putpixel(xc+y, yc-x, RED); 

    putpixel(xc-y, yc-x, RED); 

} 

  

// Function for circle-generation 

// using Bresenham's algorithm 

void circleBres(int xc, int yc, int r) 

{ 

    int x = 0, y = r; 

    int d = 3 - 2 * r; 

    drawCircle(xc, yc, x, y); 

    while (y >= x) 

    { 

        // for each pixel we will 

        // draw all eight pixels 

          

        x++; 

  

        // check for decision parameter 

        // and correspondingly  

        // update d, x, y 

        if (d > 0) 

        { 

            y--;  

            d = d + 4 * (x - y) + 10; 

        } 

        else

            d = d + 4 * x + 6; 

        drawCircle(xc, yc, x, y); 

        delay(50); 

    } 

} 

  

  

// driver function 

int main() 

{ 

    int xc = 50, yc = 50, r2 = 30; 

    int gd = DETECT, gm; 

    initgraph(&gd, &gm, "");  // initialize graph 

    circleBres(xc, yc, r);    // function call 

    return 0; 

} 

Output: