The ellipse has a major and minor axis. If a₁ and b₁are major and minor axis respectively. The centre of ellipse is (i, j). The value of x will be incremented from i to a₁and value of y will be calculated using the following formula

Drawback of Polynomial Method:

1. It requires squaring of values. So floating point calculation is required.
2. Routines developed for such calculations are very complex and slow.

Algorithm:

1. Set the initial variables: a = length of major axis; b = length of minor axis; (h, k) = coordinates of ellipse center; x = 0; i = step; x_end = a.

2. Test to determine whether the entire ellipse has been scan-converted. If x>x_end, stop.

Exception Handling in Java - Javatpoint

3. Compute the value of the y coordinate:

4. Plot the four points, found by symmetry, at the current (x, y) coordinates:

          Plot (x + h, y + k)           Plot (-x + h, -y + k)           Plot (-y - h, x + k)           Plot (y + h, -x + k)

5. Increment x; x = x + i.

6. Go to step 2.

Program to draw an Ellipse using Polynomial Method:

1. #include <graphics.h>  
2. #include <stdlib.h>  
3. #include <math.h>  
4. #include <stdio.h>  
5. #include <conio.h>  
6. #include <iostream.h>  
7.   
8. class bresen  
9. {  
10.     float x, y, a, b, r, t, te, xend, h, k, step;  
11.     public:  
12.     void get ();  
13.     void cal ();  
14. };  
15.     void main ()  
16.     {  
17.     bresen b;  
18.     b.get ();  
19.     b.cal ();  
20.     getch ();  
21.    }  
22.     void bresen :: get ()  
23.    {  
24.     cout<<"\n ENTER CENTER OF ELLIPSE";  
25.     cout<<"\n enter (h, k) ";  
26.     cin>>h>>k;  
27.     cout<<"\n ENTER LENGTH OF MAJOR AND MINOR AXIS";  
28.     cin>>a>>b;  
29.     cout<<"\n ENTER Step Size";  
30.     cin>> step;  
31.    }  
32. void bresen ::cal ()  
33. {  
34.     /* request auto detection */  
35.     int gdriver = DETECT,gmode, errorcode;  
36.     int midx, midy, i;  
37.     /* initialize graphics and local variables */  
38.     initgraph (&gdriver, &gmode, " ");  
39.     /* read result of initialization */  
40.     errorcode = graphresult ();  
41.     if (errorcode ! = grOK)    /*an error occurred */  
42.     {  
43.         printf("Graphics error: %s \n", grapherrormsg (errorcode);  
44.         printf ("Press any key to halt:");  
45.         getch ();  
46.         exit (1); /* terminate with an error code */  
47.     }  
48.     x = 0;  
49.     xend=a;  
50.     whilex (x<xend)  
51.     {  
52.         t= (1-((x * x)/ (a * a)));  
53.         if (t<0)  
54.             te=-t;  
55.         else  
56.             te=t;  
57.         y=b * sqrt (te);  
58.         putpixel (h+x, k+y, RED);  
59.         putpixel (h-x, k+y, RED);  
60.         putpixel (h+x, y-y, RED);  
61.         putpixel (h-x, k-y, RED);  
62.         x+=step;  
63.     }  
64.     getch();  
65. }  

Output: