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 WindowsFormsApplication1
{
    public partial class Form1 : Form
    {
        Graphics g;
        Random rnd1 = new Random(11);

        float[,] ctrlArray;
        double[] knots;
        double t_step = 0.01;
        int n, k;
        PointF startCoordOffset;

        public Form1()
        {
            InitializeComponent();
            g = pictureBox1.CreateGraphics();
            startCoordOffset = new PointF(pictureBox1.Width / 2, pictureBox1.Height / 2);
            g.TranslateTransform(startCoordOffset.X, startCoordOffset.Y);
            t_step = (double)trackBar3.Value / 1000;
        }

        private void exitToolStripMenuItem_Click(object sender, EventArgs e)
        {
            Application.Exit();
        }

        private void buildToolStripMenuItem_Click(object sender, EventArgs e)
        {
            n = trackBar1.Value;
            k = trackBar2.Value;

            generateCtrlArray(n);
            drawBSpline(n, k);
        }

        private void drawBSpline(int n, int k) // n - кол-во точек, k - порядок
        {
            g.Clear(Color.White);
            g.DrawString("n = " + n.ToString() + "; k = " + k.ToString(), new Font("Arial", 14), Brushes.Black,
                -startCoordOffset.X + 10,
                -startCoordOffset.Y + 10
            );

            knots = getKnots(n, k);

            double t, t_max;
            List<Tuple<PointF, int> > pointsList = new List<Tuple<PointF, int> >();
            List<Pen> pensList = new List<Pen>();
            for (int index = 1; index < knots.Length; ++index)
            {
                t = knots[index - 1];
                t_max = knots[index];
                Pen tempPen = new Pen(new SolidBrush(Color.FromArgb(190, rnd1.Next() % 256, rnd1.Next() % 256, rnd1.Next() % 256)), 3);
                bool penAdded = false;
                while (t < t_max) {
                    float x = 0, y = 0;
                    for (int i = 0; i < n; ++i)
                    {
                        float curN = (float)getNik(t, i, k);
                        x += ctrlArray[i, 0] * curN;
                        y += ctrlArray[i, 1] * curN;
                    }
                    if (!penAdded) {
                        pensList.Add(tempPen);
                        penAdded = true;
                    }
                    pointsList.Add(new Tuple<PointF, int>(new PointF(x, y), pensList.Count - 1));
                    t += t_step;
                }
            }

            PointF prevPoint = new PointF();
            foreach (Tuple<PointF, int> point in pointsList) {
                double dist = 0,
                       limit = trackBar3.Value + 1;
                if (prevPoint != null) {
                    dist = Math.Sqrt((prevPoint.X - point.Item1.X) * (prevPoint.X - point.Item1.X)
                        + (prevPoint.Y - point.Item1.Y) * (prevPoint.Y - point.Item1.Y));
                }
                if (dist < limit) {
                    g.DrawEllipse(pensList[point.Item2], point.Item1.X, point.Item1.Y, 2, 2);
                }
                prevPoint = point.Item1;
            }
        }

        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];
        }

        private double getNikRecursion(double t, int i, int k)
        {
            if (k == 1) {
                if (isEqualNull(Math.Abs(knots[i] - t)) || (knots[i] < t && t < knots[i + 1])) {
                    return 1;
                } else {
                    return 0;
                }
            }

            double numerator1 = (t - knots[i]) * getNikRecursion(t, i, k - 1),
                   znam1 = knots[i + k - 1] - knots[i];

            double numerator2 = (knots[i + k] - t) * getNikRecursion(t, i + 1, k - 1),
                   znam2 = knots[i + k] - knots[i + 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;

            return curN;
        }

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

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

        private void generateCtrlArray(int n)
        {
            float layerWidth = pictureBox1.Width,
                  layerHeight = pictureBox1.Height;
            float spaceBetweenPoints = layerWidth / n;
            float x = spaceBetweenPoints / 2 - startCoordOffset.X, y = (checkBox1.Checked ? 1 : -1) * 150;

            ctrlArray = new float[n, 2];
            for (int i = 0; i < n; ++i) {
                ctrlArray[i, 0] = x;
                ctrlArray[i, 1] = y;
                x += spaceBetweenPoints;
                y *= -1;
            }
        }

        private void trackBar1_Scroll(object sender, EventArgs e)
        {
            n = trackBar1.Value;
            k = trackBar2.Value;
            if (k > n) {
                trackBar2.Value = n;
                k = n;
            }
            generateCtrlArray(n);
            drawBSpline(n, k);
        }

        private void trackBar2_Scroll(object sender, EventArgs e)
        {
            n = trackBar1.Value;
            k = trackBar2.Value;
            if (k > n) {
                trackBar2.Value = n;
                k = n;
            }
            generateCtrlArray(n);
            drawBSpline(n, k);
        }

        private void trackBar3_Scroll(object sender, EventArgs e)
        {
            t_step = (double)trackBar3.Value / 1000;
            n = trackBar1.Value;
            k = trackBar2.Value;
            generateCtrlArray(n);
            drawBSpline(n, k);
        }

        private void checkBox1_CheckedChanged(object sender, EventArgs e)
        {
            generateCtrlArray(n);
            drawBSpline(n, k);
        }
    }
}