二次样条差值算法

//注明：a为存储每段二次曲线的系数的二维矩阵
//二次样条差值
void fit_second(Point *p, int n, double y0d, vector<vector<double> > &a)
{
    vector <double> va;
    for (int i=0; i<n-1; i++)
    {
        double x0 = p[i].x;
        double y0 = p[i].y;
        double x1 = p[i+1].x;
        double y1 = p[i+1].y;
        double h0 = x1 - x0;
        //S(x) = (y1-y0-h0*y0')*(x-x0)^2/(h0^2)  +  y0'*(x-x0)  +  y0
        double a2 = (y1-y0-h0*y0d)/(h0*h0);
        double a1 = (-2*x0)*(y1-y0-h0*y0d)/(h0*h0) + y0d;
        double a0 = (x0*x0)*(y1-y0-h0*y0d)/(h0*h0) - y0d*x0 + y0;
        y0d = 2*(y1-y0)/h0 - y0d;
        va.clear();
        va.push_back(a0);
        va.push_back(a1);
        va.push_back(a2);
        a.push_back(va);
    }
}