double blend(int k, int t, K_NOT u, double v){  // calculate the blending value
  double value;

  if (t==1){
    if ((u[k]<=v) && (v<u[k+1]))
      value=1;
    else
      value=0;
      
  }else{
    if ((u[k+t-1]==u[k]) && (u[k+t]==u[k+1]))  // check for divide by zero
      value = 0;
    else
    if (u[k+t-1]==u[k]) // if a term's denominator is zero,use just the other
      value = (u[k+t] - v) / (u[k+t] - u[k+1]) * blend(k+1, t-1, u, v);
    else
    if (u[k+t]==u[k+1])
      value = (v - u[k]) / (u[k+t-1] - u[k]) * blend(k, t-1, u, v);
    else
      value = (v - u[k]) / (u[k+t-1] - u[k]) * blend(k, t-1, u, v) +
              (u[k+t] - v) / (u[k+t] - u[k+1]) * blend(k+1, t-1, u, v);
  }
  return value;
}
void BSpline(int quality, const T_PointVector & points, T_PointVector & line_points , const BSplineDescription & bsplinedsc )
{
  line_points.clear();

	int size = (int)points.size();
	if (size<2) return;

	double t=0.0;
	double step=1.0/quality;

	//T_PointVector P(size);
	S_Point P;
	
	for (int p=0; p<=quality; p++, t+=step){
	  P.x=0;
	  P.y=0;
	  if(t>=1) t=0.99999;
	  
		for (int j=0; j<size - 1; j++){
			for (int i=0; i<size-1-j;i++){
				double N = blend(i, bsplinedsc.k, bsplinedsc.U, t);
				P.x=P.x + points[i].x * N;
				P.y=P.y + points[i].y * N;
				
				
			}
		}
		
		line_points.push_back(P);
	}
}