Кривая Безье

static long Fact (int n)  // факториал
{
    long r=1;
    for (int i = 1; i <=n; i++) {
        r*=i;
    }
    return r;
}

float getBasis(int i, float t)
{
 
   return (Fact(n)/(Fact(i)*Fact(n-i)))*pow(t,i)*pow(1-t,n-i);
}

void Bezier ()
{
    float step=0.01;
    int x,y;
    float gb;
    //int **res = new int*[n];
    x=p[0][1];
    y=p[0][2];
   for (int i=0; i < n; i++)
   {
 
    for (float t = 0.01; t < 1; t+=step)
        {
           gb=getBasis(i+1, t);//if (t>1)t=1;
           x+=p[i][1]*gb;
           y+=p[i][2]*gb;
           im->LineTo(x,y);
 
        }
    }
}

void Bezier ()
{
    float step=0.01;
    int x,y;
    for (float t = 0.01; t <= 1; t+=step)
        {
        x=0;
        y=0;
            for (int i=0; i < n; i++)
            {
 
            x+=p[i][1]*getBasis(i, t);
            y+=p[i][2]*getBasis(i, t);
            }
            im->LineTo(x,y);
        }
}

const count = 10;
TPoint point[count];
//---------------------------------------------------------------------------
unsigned __int64 factor(UINT n)
{
  unsigned __int64 result = 1;
  for (UINT i = 1; i <= n; i++)
    result *= i;
  return result;
}
//---------------------------------------------------------------------------
double basis(UINT i, UINT n, double t)
{
  return factor(n-1) / factor(i) / factor(n-1-i) * pow(t, i) * pow(1-t, n-1-i);
}
//---------------------------------------------------------------------------
TPoint bezier(UINT n, double t)
{
  TPoint b = TPoint(0, 0);
  double temp;
  for (UINT i = 0; i < n; i++)
  {
    temp = basis(i, n, t);
    b.x += point[i].x * temp;
    b.y += point[i].y * temp;
  }
  return b;
}
//---------------------------------------------------------------------------
void __fastcall TForm1::ButtonClick(TObject *Sender)
{
  Refresh();
  UINT n = count, delta = 500;
  TPoint a;
  double step = 0.0001;
  randomize();
  for (UINT i = 0; i < n; i++)
    point[i] = TPoint(random(delta), random(delta));
  Canvas->MoveTo(point[0].x, point[0].y);
  for(double t = step; t <= 1; t += step)
  {
    a = bezier(n, t);
    Canvas->LineTo(a.x, a.y);
  }
}

void __fastcall TForm1::ButtonClick(TObject *Sender)
{
  Refresh();
  UINT n = count, offset = 500, r = 3;
  TPoint a;
  TColor color = clRed;
  TColor color2 = clBlack;
  double step = 0.0001;
  randomize();
  for (UINT i = 0; i < n; i++)
    point[i] = TPoint(random(offset), random(offset));
 
  Canvas->Pen->Color = color2;
  Canvas->TextOutW(point[0].x, point[0].y, 1);
  Canvas->Ellipse(point[0].x - r, point[0].y - r, point[0].x + r, point[0].y + r);
  for (UINT i = 1; i < n; i++)
  {
    Canvas->TextOutW(point[i].x, point[i].y, i+1);
    Canvas->MoveTo(point[i-1].x, point[i-1].y);
    Canvas->LineTo(point[i].x, point[i].y);
    Canvas->Ellipse(point[i].x - r, point[i].y - r, point[i].x + r, point[i].y + r);
  }
 
  Canvas->MoveTo(point[0].x, point[0].y);
  Canvas->Pen->Color = color;
  for(double t = step; t <= 1; t += step)
  {
    a = bezier(n, t);
    Canvas->LineTo(a.x, a.y);
  }
 
//  Canvas->MoveTo(point[0].x, point[0].y);
//  Canvas->Pen->Color = clBlue;
//  Canvas->PolyBezier(point, n-1);
}