// Function to get all bPoints from the given Control Points. The last entry in
// in the Vector is the Point on the Curve given by the actual u Parameter
// e.g. bPoints = {C^0_0, C^0_1, C^0_2, C^0_3, C^0_4, C^1_(r-n+1),.., C^n_r}
vector<Point2D> getBPoints(float u) {
    vector<Point2D> Result;

    vector<Point2D> RefPoints=cPoints;
    vector<Point2D> NewPoints;
    while(RefPoints.size()>=2)
    {
        for(int i=0; i<RefPoints.size()-1; ++i)
        {
            NewPoints.push_back(RefPoints[i]*(1-u)+RefPoints[i+1]*u);
            Result.push_back(RefPoints[i]*(1-u)+RefPoints[i+1]*u);
        }
        RefPoints=NewPoints;
        NewPoints.clear();
    }

return Result;
}

// plots the Bezier Curve using the plot Function, which plots a line.
// Parameter smooth defines how many lines are used to plot the Curve. The more
// lines are used, the more the Curve looks like a real Curve
void plotBCurve(float smooth) {

    if(cPoints.size()>2)
    {
        vector<Point2D> Points;

        for(int i=0; i<1/smooth; ++i)
        {
            vector<Point2D> Bla=getBPoints(smooth*i);
            Points.push_back(Bla.back());
        }

        //render the points:
        for(int i=0; i<Points.size()-1; ++i)
        {
            plotLine(Points[i], Points[i+1], 0, 1);
        }
    }

}