using System;

namespace Science.Mathematics.VectorCalculus
{
    public class VectorField : Vector 
    {
        private Function.ToLastType<double[], double[]> f;
        public VectorField(Function.ToLastType<double[],double[]> function) : base()
        {
            f = function;
        }
        public void FindComponents(Point at)
        {
            el = f(at.Coordinate); 
        }
        public bool ConservativeQ(Point at0, Point at1, Point at2)
        {
            Curl obj = new Curl(f,at0.Coordinate);
            obj.Compute();
            if(obj.Result.Norm > 0.0000001) return false;
            obj.At = at1.Coordinate;
            obj.Compute();
            if (obj.Result.Norm > 0.0000001) return false;
            obj.At = at2.Coordinate;
            obj.Compute();
            if (obj.Result.Norm > 0.0000001) return false;
            return true;
        }
        private Point xx;
        public double Potential(Point x)
        {
            xx = x;
            Function.ToLastType<double, double[]> pp
                = new Function.ToLastType<double, double[]>(path);
            Path pa = new Path(pp);
            pa.ParameterFrom = 0.0;
            pa.ParameterTo = 3.0;
            LineIntegral obj = new LineIntegral(this, pa);
            obj.Compute();
            return obj.Result;
        }
        private double[] path(double t)
        {
            double[] p = new double[3];
            if (t < 1.0)
            {
                p[0] = t * xx.Coordinate[0];
                p[1] = 0.0;
                p[2] = 0.0;
            }
            else if (t > 1.0 & t < 2.0)
            {
                p[0] = xx.Coordinate[0];
                p[1] = (t - 1.0)*xx.Coordinate[1];
                p[2] = 0.0;
            }
            else
            {
                p[0] = xx.Coordinate[0];
                p[1] = xx.Coordinate[1];
                p[2] = (t - 2.0)*xx.Coordinate[2];
            }
            return p;
        }
    }
}