Bezier Curve for n

//---------------------------------------------------------------------------

#include <vcl.h>
#include <vector>
#include <math.h>
#pragma hdrstop

#include "Unit1.h"
std::vector<POINT> points;

//---------------------------------------------------------------------------
#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;
//---------------------------------------------------------------------------
__fastcall TForm1::TForm1(TComponent* Owner)
        : TForm(Owner)
{
}
//----------------------------GLOBAL-----------------------------------------
//---------------------------------------------------------------------------

        int a[100],b[100]; //points coordinates
        int i=0;
        int m=0;

        double t=0.0001, tk=0.0001;

        float x=0,y=0;
        float BComb=1;

        POINT position;

//-------------------------DrawEllipse---------------------------------------
//---------------------------------------------------------------------------

 void DrawEllipse(int x, int y)
{
        Form1->Image1->Canvas->Pen->Color = clTeal;
        Form1->Image1->Canvas->Ellipse(x -4, y - 4, x + 4, y + 4);
}

//---------------------------Factorial---------------------------------------
//---------------------------------------------------------------------------
int Fact(int i)
{
        return (i<=1)? 1 : i*Fact(i-1);
}
//---------------------------Bernstein---------------------------------------
//---------------------------------------------------------------------------
float  Bernstein(float t, int i)
{
        return (pow(t,i)*pow(1-t,m-i-1))*(Fact(m-1))/((Fact(i)*Fact(m-1-i)));
}
//--------------------------Image1Click--------------------------------------
//---------------------------------------------------------------------------
void __fastcall TForm1::Image1Click(TObject *Sender)
{
        GetCursorPos(&position);

        position.x -= (Form1->Left+10);
        position.y -= (Form1->Top+30);

        points.push_back(position);
        DrawEllipse(position.x, position.y);

         a[i]=position.x;
         b[i]=position.y;

         i++;
         m++;

}
//-----------------------Button1Click---------------------------------------
//---------------------------------------------------------------------------
void __fastcall TForm1::Button1Click(TObject *Sender)
{

        Image1->Canvas->Pen->Style=psDot;
        Form1->Image1->Canvas->Pen->Color = clPurple;
        Form1->Image1->Canvas->MoveTo(a[0], b[0]);

        for(int i = 0; i < m; i++)
        {
                Form1->Image1->Canvas->LineTo(a[i], b[i]);
        }
        Form1->Image1->Canvas->Pen->Style=psSolid;

}
//-----------------------Button2Click---------------------------------------
//---------------------------------------------------------------------------
void __fastcall TForm1::Button2Click(TObject *Sender)
{
       /* if(ColorDialog1->Execute())
          Form1->Canvas->Pen->Color=ColorDialog1->Color;
        */

        Form1->Image1->Canvas->Pen->Style=psSolid;
        Form1->Image1->Canvas->Pen->Color = clSkyBlue;
        Form1->Image1->Canvas->MoveTo(a[0], b[0]);

        for(t=0;t<1;t+=tk)
        {
                 float  x=pow((1-t),3)*a[0] + 3*pow((1-t),2)*t*a[1]
                            +3*(1-t)*pow(t,2)*a[2] + pow(t,3)*a[3];

                 float  y=pow((1-t),3)*b[0] + 3*pow((1-t),2)*t*b[1]
                            +3*(1-t)*pow(t,2)*b[2] + pow(t,3)*b[3];

        Form1->Image1->Canvas->LineTo(x, y);
        }
}
//-----------------------Button3Click---------------------------------------
//---------------------------------------------------------------------------
void __fastcall TForm1::Button3Click(TObject *Sender)
{
        /* if(ColorDialog1->Execute())
          Form1->Canvas->Pen->Color=ColorDialog1->Color;
        */

        x=0;y=0;
         for(t=0.00001;t<1;t+=tk)
         {
                 for(int i=0;i<m;i++)
                 {
                        x+=Bernstein(t,i)*a[i];
                        y+=Bernstein(t,i)*b[i];
                 }

                Form1->Image1->Canvas->Pixels[x][y]=clBlack;
                x=0;y=0;
        }
}