WRITE A PROGRAM TO DRAW AN ELLIPSE USING C++ BUILDER

 DRAW AN ELLIPSE

The midpoint algorithm is applied to the first quadrant in two parts, region 1 and region 2. We process by taking unit step in x-coordinate direction and finding the closest value for y for each x steps in region 1.

In the first quadrant at region 1 we start at position (0,Ry) and incrementing X and calculating Y closer to the path along clockwise direction. When the slope becomes -1 then shift unit step in X to Y and compute corresponding X closest to ellipse path at region 2 at the same direction.

  

ALGORITHM:

1. Start
2. Input centre co-ordinates of the ellipse
3. Input x-radius and y-radius
4. For region 1, Pk=Ry²(X_k+1)²+Rx²(Y_k-0.5)²-Rx²Ry²
   1. While px<py, increment x and set Px=Px+2Ry²
   2. If Pk<0, set Pk+1=Pk+Ry²+Px
   3. else set y=y-1, Py=Py-2Rx² and P_k+1=P_k+Ry²+Px-Py
5. For region 2, Pk=Ry²(X+0.5)²+Rx²(Y-1)²-Rx²Ry²
   1. While y>0, decrement the value of y and set Py=Py-2Rx²
   2. If p>0, set Pk+1=Pk+Rx²-Py
   3. Else increment Px=Px+2Ry²and set P_k+1=P_k+Rx²+Px-Py
6. Display ellipse
7. Stop
   
   
     
   SOURCE CODE:
   
   
   
   
   //---------------------------------------------------------------------------
   #include <vcl\vcl.h>
   #pragma hdrstop
   
   
   #include "ellipse.h"
   //---------------------------------------------------------------------------
   #pragma resource "*.dfm"
   TForm1 *Form1;
   //---------------------------------------------------------------------------
   __fastcall TForm1::TForm1(TComponent* Owner)
   : TForm(Owner)
   {
   }
   //---------------------------------------------------------------------------
   void __fastcall TForm1::Button1Click(TObject *Sender)
   {
   int Xc=StrToInt(Edit1->Text);
   int Yc=StrToInt(Edit2->Text);
   int rx=StrToInt(Edit3->Text);
   int ry=StrToInt(Edit4->Text);
   int rxSq = rx * rx;
   int rySq = ry * ry;
   int X = 0, Y = ry, p;
   int px = 0, py = 2 * rxSq * Y;
   Canvas->Pixels[Xc+X][Yc+Y]=RGB(0,0,255);
   Canvas->Pixels[Xc-X][Yc+Y]=RGB(0,255,0);
   Canvas->Pixels[Xc+X][Yc-Y]=RGB(255,255,0);
   Canvas->Pixels[Xc-X][Yc-Y]=RGB(255,0,255);
   p = rySq - (rxSq * ry) + (0.25 * rxSq);
   while (px < py)
   {
   X++;
   px = px + 2 * rySq;
   if (p < 0)
   p = p + rySq + px;
   else
   {
   Y--;
   py = py - 2 * rxSq;
   p = p + rySq + px - py;
   }
   Canvas->Pixels[Xc+X][Yc+Y]=RGB(0,0,255);
   Canvas->Pixels[Xc-X][Yc+Y]=RGB(0,255,0);
   Canvas->Pixels[Xc+X][Yc-Y]=RGB(255,255,0);
   Canvas->Pixels[Xc-X][Yc-Y]=RGB(255,0,255);
   }
   p = rySq*(X+0.5)*(X+0.5) + rxSq*(Y-1)*(Y-1) - rxSq*rySq;
   while (Y > 0)
   {
   Y--;
   py = py - 2 * rxSq;
   if (p > 0)
   p = p + rxSq - py;
   else
   {
   X++;
   px = px + 2 * rySq;
   p = p + rxSq - py + px;
   }
   Canvas->Pixels[Xc+X][Yc+Y]=RGB(0,0,255);
   Canvas->Pixels[Xc-X][Yc+Y]=RGB(0,255,0);
   Canvas->Pixels[Xc+X][Yc-Y]=RGB(255,255,0);
   Canvas->Pixels[Xc-X][Yc-Y]=RGB(255,0,255);
   }
   
   
   }
   //---------------------------------------------------------------------------
   
   
   
   
   Ouput: