В-сплайновые кривые - C++ Builder - Ответ 9144578

const count = 7, m = 10;
TPoint point[count];
double tmin = 0, tmax = 1, t[m+1] = {tmin, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, tmax};
int n = count - 1, p = m - count;  // p = m - n - 1;
 
double N(UINT i, UINT j, double T)
{
  if (j == 0)
  {
    if (T >= t[i] && T < t[i+1])  // && t[i+1] > t[i])
      return 1;
    else
      return 0;
  }
  else
  {
    double memb1 = (t[i+j] - t[i]) ? (T - t[i]) / (t[i+j] - t[i]) : 0,
           memb2 = (t[i+j+1] - t[i+1]) ? (t[i+j+1] - T) / (t[i+j+1] - t[i+1]) : 0;
    return memb1 * N(i, j-1, T) + memb2 * N(i+1, j-1, T);
  }
}
//---------------------------------------------------------------------------
TPoint C(UINT p, double T)
{
  TPoint b = TPoint(0, 0);
  double temp;
  for (int i = 0; i <= n; i++)
  {
    temp = N(i, p, T);
    b.x += point[i].x * temp;
    b.y += point[i].y * temp;
  }
  return b;
}
//---------------------------------------------------------------------------
void init()
{
  for (int i = 1; i <= p; i++)
  {
    t[i] = tmin;
    t[m-i] = tmax;
  }
}
//---------------------------------------------------------------------------
void __fastcall TForm1::ButtonClick(TObject *Sender)
{
  Refresh();
  init();
  UINT offset = 25, range = 500 - 2 * offset, r = 3;
  double step = 1e-5;
  TPoint a;
  TColor color = clRed;
  TColor color2 = clGray;
  randomize();
  for (int i = 0; i <= n; i++)
    point[i] = TPoint(offset + random(range), offset + random(range));
 
  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 (int 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);
  }
 
  if (p * 2 <= m - 1)
    for(double T = tmin; T <= tmax; T += step)
    {
      a = C(p, T);
      Canvas->Pixels[a.x][a.y] = color;
    }
  else
    MessageBox(Application->Handle, String("Должно выполняться условие\n\nm-1 >= 2p\n\nПри m=" + String(m) + ", p=" + String(p) + " оно не соблюдается.").c_str(), L"Ошибка", 0);
}