Computer Graphics Polynomial Method

by Online Tutorials Library July 14, 2022

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:

Next TopicTrignometric Method

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Computer Graphics Polynomial Method

Polynomial Method:

Drawback of Polynomial Method:

Algorithm:

Program to draw an Ellipse using Polynomial Method:

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