using System;

namespace Science.Mathematics.VectorCalculus
{
    public class TangentVectorOnSurface
    {
        private Surface s;
        private double[] u;
        public TangentVectorOnSurface(Surface surface, double[] at)
        {
            s = surface;
            u = at;
        }
        public double[] At
        {
            get { return u; }
            set { u = value; }
        }
        private Vector[] res;
        public Vector[] Result
        {
            get { return res; }
        }
        private int kth;
        public void Compute()
        {
            int n = s.Parametrization(u).Length;
            res = new Vector[u.Length];
            for(int i = 0; i < u.Length; i++) res[i] = new Vector(n);
            Function.ToLastType<double[], double> f 
                = new Function.ToLastType<double[], double>(func);
            PartialDerivative obj = new PartialDerivative(f,u);
            for (int k = 0; k < n; k++)
            {
                kth = k;
                for (int j = 0; j < u.Length; j++)
                {
                    obj.WithRespectTo = j;
                    obj.Compute();
                    res[j][kth] = obj.Result;
                }
            }
        }
        private double func(double[] v)
        {
            return s.Parametrization(v)[kth];
        }
    }
}