using System using System Collections Generic using System ComponentMo

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;

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

        private bool isEqualNull(double num)
        {
            return Math.Abs(num) <= 1e-8;
        }

        public int[] knots = { };

        private double getNik(double t, int i, int k)
        {
            double[,] Niks = new double[k, i + k];

            for (int kk = 1; kk <= k; ++kk)
            {
                for (int ii = i; ii < k + i - kk + 1; ++ii)
                {
                    double NikPrev1, NikPrev2;
                    if (kk == 1)
                    {
                        if (isEqualNull(Math.Abs(knots[ii] - t)) || (knots[ii] < t && t < knots[ii + 1]))
                        {
                            NikPrev1 = 1;
                        }
                        else
                        {
                            NikPrev1 = 0;
                        }
                        Niks[kk - 1, ii] = NikPrev1;
                        continue;
                    }
                    else
                    {
                        NikPrev1 = Niks[kk - 2, ii];
                        NikPrev2 = Niks[kk - 2, ii + 1];
                    }

                    double numerator1 = (t - knots[ii]) * NikPrev1,
                           znam1 = knots[ii + kk - 1] - knots[ii];

                    double numerator2 = (knots[ii + kk] - t) * NikPrev2,
                           znam2 = knots[ii + kk] - knots[ii + 1];

                    double proportion1, proportion2;

                    if (isEqualNull(numerator1) || isEqualNull(znam1))
                    {
                        proportion1 = 0;
                    }
                    else
                    {
                        proportion1 = numerator1 / znam1;
                    }

                    if (isEqualNull(numerator2) || isEqualNull(znam2))
                    {
                        proportion2 = 0;
                    }
                    else
                    {
                        proportion2 = numerator2 / znam2;
                    }

                    double curN = proportion1 + proportion2;

                    Niks[kk - 1, ii] = curN;
                }
            }

            return Niks[k - 1, i];
        }

        public int[] getKnots(int n, int k)
        {
            int size = n + k;
            int[] knots = new int[size];
            int temp = 0;
            for (int i = 0; i < size; ++i)
            {
                if (i >= k && size - i >= k)
                {
                    ++temp;
                }
                knots[i] = temp;
            }
            return knots;
        }


        private void pictureBox1_Click(object sender, EventArgs e)
        {
            Graphics g = pictureBox1.CreateGraphics();
            
            int k = 2;
            const int n = 3;
            double t = 0;
            int[,] mea = new int[n, 2] { { 0, 100 }, { 100, -100 }, { 200, 100 } };
            
            knots = getKnots(n, k);

           

            for (int i = 1; i < knots.Length; i++)
            {
                double t_min = knots[i - 1];
                double t_max = knots[i];

                double sum_x = 0;
                double sum_y = 0;
                while (t_min < t_max)
                {
                    t_min += 0.01;
                    double Nik = getNik(t_min, i, k);
                    sum_x += mea[i, 0] * Nik;
                    sum_y += mea[i, 1] * Nik;
                }
                g.DrawEllipse(new Pen(new SolidBrush(Color.Blue), 2), new RectangleF(new PointF((float)(sum_x), (float)(mea[i, 1] * sum_y)), new Size(2, 2)));

            }
        }
    }
}