using MathNet Numerics LinearAlgebra Double using System using System

using MathNet.Numerics.LinearAlgebra.Double;
using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Diagnostics;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;

namespace Exam3
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        private void Form1_Load(object sender, EventArgs e)
        {

        }

        private void Form1_Paint(object sender, PaintEventArgs e)
        {
            var g = e.Graphics;
            var D = new double[,]{{50,100},{100,200},{150,200},{200,100},};

            int k = 3;
            var X = new int[] { 0, 0, 0, 1, 2, 2, 2 };
            var N = new double[D.GetLength(0), 4];
            var T = new double[] { 0, 0.817256, 1.182744, 2 };

            for (var i = 0; i < D.GetLength(0); i++)
            {
                for (var j = 0; j < 4; j++)
                {
                    N[i, j] = GetBasisFunc(j + 1, k, T[i], X);
                }
            }

            var Dmatrix = DenseMatrix.OfArray(D);
            var Nmatrix = DenseMatrix.OfArray(N);
            var NInverse = Nmatrix.Inverse();
            var Bmatrix = NInverse * Dmatrix;
            var B = Bmatrix.ToArray();

            for (var i = 0; i < B.GetLength(0); i++)
            {
                g.DrawEllipse(new Pen(Color.Blue), (float)B[i, 0], (float)B[i, 1], 4f, 4f);
            }

            for (double t = 0; t <= 2; t += 0.001)
            {
                double x = B[0, 0] * GetBasisFunc(1, k, t, X) + B[1, 0] * GetBasisFunc(2, k, t, X) + B[2, 0] * GetBasisFunc(3, k, t, X) + B[3, 0] * GetBasisFunc(4, k, t, X);
                double y = B[0, 1] * GetBasisFunc(1, k, t, X) + B[1, 1] * GetBasisFunc(2, k, t, X) + B[2, 1] * GetBasisFunc(3, k, t, X) + B[3, 1] * GetBasisFunc(4, k, t, X);
                g.DrawEllipse(new Pen(Color.Red), (float)x, (float)y, 2f, 2f);
            }

        }

        private double GetBasisFunc(int i, int k, double t, int[] X)
        {
            double result = 0;
            if (k == 1)
            {
                if ((t >= X[(i) - 1]) && (t <= X[(i + 1) - 1]))
                    result = 1;
                else
                    result = 0;
            }
            else
            {
                if (X[(i + k - 1) - 1] - X[(i) - 1] != 0)
                    result = (t - X[(i) - 1]) * GetBasisFunc(i, k - 1, t, X) / (X[(i + k - 1) - 1] - X[(i) - 1]);
                if (X[(i + k) - 1] - X[(i + 1) - 1] != 0)
                    result += (X[(i + k) - 1] - t) * GetBasisFunc(i + 1, k - 1, t, X) / (X[(i + k) - 1] - X[(i + 1) - 1]);
            }

            return result;
        }

        private void Form1_Paint_1(object sender, PaintEventArgs e)
        {
            var g = e.Graphics;
            var D = new double[,] { { 50, 100 }, { 100, 200 }, { 150, 200 }, { 200, 100 }, };

            int k = 3;
            var X = new int[] { 0, 0, 0, 1, 2, 2, 2 };
            var N = new double[D.GetLength(0), 4];
            var T = new double[] { 0, 0.817256, 1.182744, 2 };

            for (var i = 0; i < D.GetLength(0); i++)
            {
                for (var j = 0; j < 4; j++)
                {
                    N[i, j] = GetBasisFunc(j + 1, k, T[i], X);
                }
            }

            var Dmatrix = DenseMatrix.OfArray(D);
            var Nmatrix = DenseMatrix.OfArray(N);
            var NInverse = Nmatrix.Inverse();
            var Bmatrix = NInverse * Dmatrix;
            var B = Bmatrix.ToArray();

            for (var i = 0; i < B.GetLength(0); i++)
            {
                g.DrawEllipse(new Pen(Color.Blue), (float)B[i, 0], (float)B[i, 1], 4f, 4f);
            }

            for (double t = 0; t <= 2; t += 0.001)
            {
                double x = B[0, 0] * GetBasisFunc(1, k, t, X) + B[1, 0] * GetBasisFunc(2, k, t, X) + B[2, 0] * GetBasisFunc(3, k, t, X) + B[3, 0] * GetBasisFunc(4, k, t, X);
                double y = B[0, 1] * GetBasisFunc(1, k, t, X) + B[1, 1] * GetBasisFunc(2, k, t, X) + B[2, 1] * GetBasisFunc(3, k, t, X) + B[3, 1] * GetBasisFunc(4, k, t, X);
                g.DrawEllipse(new Pen(Color.Red), (float)x, (float)y, 2f, 2f);
            }
        }

    }
}