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 periodBS {
    public partial class Form1 : Form {
        public int n, k;
        public List<float> knot = new List<float>();
        public float tmin = 0.0f,
                     tmax = 0.0f;
        public float[,] ctrlPoint = new float[,] {{50, 100, 150, 200, 250, 300, 350},
                                                    {120, 20, 120, 20, 120, 20, 120}};
        public Pen black = new Pen(Color.Black),
                   yellow = new Pen(Color.Red);
        Graphics view;

        public Form1() {
            InitializeComponent();
        }

        // получение периодического узлового вектора
        public List<float> GetKnot(int n, int k) {
            int nKnots = n + k + 1;
            List<float> retValue = new List<float>(new float[nKnots]);
            for (int i = 0; i < nKnots; ++i) 
                retValue[i] = i;
            return retValue;
        }

        // нерекурсивный расчет базисных функций
        public float GetNormalizedFunction2(int i, int k, float t) {
            float[,] N = new float[k, i + k];

            for (int height = 1; height <= k; ++height) {
                for (int width = i; width <= i + (k - height); ++width) {
                    float downValue = 0.0f,
                          downRightValue = 0.0f;
                    if (height == 1) {
                        if ((t >= knot[width]) && (t < knot[width + 1]))
                            downValue = 1.0f;
                        else
                            downValue = 0.0f;
                        N[height - 1, width] = downValue;
                        continue;
                    }
                    else {
                        downValue = N[height - 2, width];
                        downRightValue = N[height - 2, width + 1];
                    }

                    float fNum = (t - knot[width]) * downValue,
                          fDenum = knot[width + height - 1] - knot[width],
                          sNum = (knot[width + height] - t) * downRightValue,
                          sDenum = knot[width + height] - knot[width + 1],
                          retValue = 0.0f;
                    if (!fDenum.Equals(0.0f))
                        retValue += fNum / fDenum;
                    if (!sDenum.Equals(0.0f))
                        retValue += sNum / sDenum;
                    N[height - 1, width] = retValue;
                }
            }
            return N[k - 1, i];
        }

        private void btn_draw_Click(object sender, EventArgs e) {
            n = int.Parse(tb_n.Text);
            k = int.Parse(tb_k.Text);
            knot = GetKnot(n, k);
            tmin = k - 1;
            tmax = n;
            drawBS();
            drawBasis();
        }

        // отрисовка базисных функций
        public void drawBasis() {
            view = pb_basis.CreateGraphics();
            for (int i = 0; i < ctrlPoint.GetLength(1); ++i) {
                for (float t = tmin; t <= tmax; t += 0.005f) {
                    float basis = GetNormalizedFunction2(i, k, t);
                    view.DrawEllipse(black, t * 100.0f - 400.0f, 200.0f - basis * 200.0f, 1, 1);
                }
            }
        }

        // отрисовка b-сплайна
        public void drawBS() {
            view = pb_bs.CreateGraphics();

            // отрисовка контрольных точек 
            for (int i = 0; i < ctrlPoint.GetLength(1); ++i)
                view.DrawEllipse(yellow, ctrlPoint[0, i], ctrlPoint[1, i], 4, 4);

            // отрисовка кривой
            float x = 0.0f,
                  y = 0.0f,
                  curBasis = 0.0f;
            for (float t = tmin; t <= tmax; t += 0.005f) {
                x = 0.0f;
                y = 0.0f;
                for (int i = 0; i < ctrlPoint.GetLength(1); ++i) {
                    curBasis = GetNormalizedFunction2(i, k, t);
                    x += ctrlPoint[0, i] * curBasis;
                    y += ctrlPoint[1, i] * curBasis;
                }
                view.DrawEllipse(black, x, y, 1, 1);
            }
        }
    }
}