Computer Graphics Polynomial Method

Computer Graphics Polynomial Method with Computer Graphics Tutorial, Line Generation Algorithm, 2D Transformation, 3D Computer Graphics, Types of Curves, Surfaces, Computer Animation, Animation Techniques, Keyframing, Fractals etc.

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Polynomial Method:

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:

It requires squaring of values. So floating point calculation is required.
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.

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:

#include 
#include 
#include 
#include 
#include 
#include 

class bresen
{
	float x, y, a, b, r, t, te, xend, h, k, step;
	public:
	void get ();
	void cal ();
};
	void main ()
    {
	bresen b;
	b.get ();
	b.cal ();
	getch ();
   }
	void bresen :: get ()
   {
	cout<<"\n ENTER CENTER OF ELLIPSE";
	cout<<"\n enter (h, k) ";
	cin>>h>>k;
	cout<<"\n ENTER LENGTH OF MAJOR AND MINOR AXIS";
	cin>>a>>b;
	cout<<"\n ENTER Step Size";
	cin>> step;
   }
void bresen ::cal ()
{
	/* request auto detection */
	int gdriver = DETECT,gmode, errorcode;
	int midx, midy, i;
	/* initialize graphics and local variables */
	initgraph (&gdriver, &gmode, " ");
	/* read result of initialization */
	errorcode = graphresult ();
	if (errorcode ! = grOK)    /*an error occurred */
	{
 		printf("Graphics error: %s \n", grapherrormsg (errorcode);
		printf ("Press any key to halt:");
		getch ();
		exit (1); /* terminate with an error code */
	}
	x = 0;
	xend=a;
	whilex (x

Output:

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