deCasteljau algoritmus

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

namespace deCasteljau
{
    public partial class Form1 : Form
    {
        Graphics g;
        public Form1()
        {
            InitializeComponent();
            g = CreateGraphics();
            MouseUp += new MouseEventHandler(Form1_MouseUp);
            MouseDown +=new MouseEventHandler(Form1_MouseDown);
            MouseMove +=new MouseEventHandler(Form1_MouseMove);
        }

        const int DB = 200;
        static PointF[] kp;
        static List<PointF> pontok = new List<PointF>();
        static int R = 4;
        static bool megvan_ = false;
        static int pontIndex = 0;

        private PointF deCasteljau_iter2(float u)
        {
            int n = kp.Length - 1;
            PointF[] Q = new PointF[n + 1];
            for (int i = 0; i <= n; i++)
                Q[i] = kp[i];
            for (int r = 1; r <= n; r++)
                for (int i = 0; i <= n - r; i++)
                    Q[i] = new PointF((1 - u) * Q[i].X + u * Q[i + 1].X, (1 - u) * Q[i].Y + u * Q[i + 1].Y);

            return Q[0];
        }

        private PointF deCasteljau_rek(int i, int r, float u)
        {
            if (r == 0) { return kp[i]; }
            else
            {
                PointF P1 = deCasteljau_rek(i, r - 1, u);
                PointF P2 = deCasteljau_rek(i + 1, r - 1, u);
                return new PointF(((1 - u) * P1.X + u * P2.X), ((1 - u) * P1.Y + u * P2.Y));
            }
        }

        private void drawDeCasteljau_iter()
        {
            //Invalidate();
            //Update();
            Graphics myG = CreateGraphics();
            int db = DB;
            double A = 0;
            double b = 1;
            double h = Math.Abs(b - A) / db;//h:lépésköz, db:a görbe pontjainak a szama
            double u = A;
            PointF[] pontok = new PointF[db + 1];//a görbe pontjai
            for (int i = 0; i <= db; i++)
            {
                // pontok[i] = deCasteljau(0, kp.Length - 1, (float)u);
                pontok[i] = deCasteljau_iter2((float)u);
                u += h;
            }

            myG.DrawLines(new Pen(Color.Blue), pontok);
        }

        private void drawDeCasteljau()
        {
            //Invalidate();
            //Update();
            Graphics myG = CreateGraphics();
            int db = DB;
            double A = 0;
            double b = 1;
            double h = Math.Abs(b - A) / db;//h:lépésköz, db:a görbe pontjainak a szama
            double u = A;
            PointF[] pontok = new PointF[db + 1];//a görbe pontjai
            for (int i = 0; i <= db; i++)
            {
                // pontok[i] = deCasteljau(0, kp.Length - 1, (float)u);
                pontok[i] = Bezier((float)u);
                u += h;
            }

            myG.DrawLines(new Pen(Color.Blue), pontok);
        }

        private PointF Bezier(float u)
        {
            int n = kp.Length - 1;
            PointF point = new PointF();
            for (int i = 0; i <= n; i++)
            {
                float b = Bernstein((double)i, (double)n, u);
                point.X += kp[i].X * b;
                point.Y += kp[i].Y * b;
            }
            return point;
        }

        private int Fact(double n)
        {
            int x = 1;
            for (int i = 1; i <= n; i++)
                x *= i;
            return x;
        }

        private float Bernstein(double i, double n, float u)
        {
            if (i < 0 || i > n) return 0;

            return (float)(Fact(n) / (Fact(i) * Fact(n - i)) * Math.Pow(u, i) * Math.Pow(1 - u, n - i));
        }

        private void Rajz()
        {
            kp = new PointF[pontok.Count];
            for (int i = 0; i < kp.Length; i++)
                kp[i] = pontok[i];

            g.DrawLines(new Pen(Color.Black), kp);

            drawDeCasteljau();
        }

        private void Form1_MouseUp(object sender, MouseEventArgs e)
        {

            if (!megvan_) { pontok.Add(new PointF(e.X, e.Y)); }
            Invalidate();
            Update();
            foreach (PointF x in pontok)
            {
                g.DrawEllipse(Pens.Red, x.X - R, x.Y - R, 2 * R, 2 * R);
            }

            if (pontok.Count >= 3) Rajz();
            megvan_ = false;
        }



        private void Form1_MouseDown(object sender, MouseEventArgs e)
        {
            for (int i = 0; i < pontok.Count; i++)
            {
                PointF x = pontok[i];
                if (e.X > x.X - R && e.X < x.X + R && e.Y > x.Y - R && e.Y < x.Y + R)
                {
                    pontIndex = i;
                    megvan_ = true;
                    break;
                }
            }

            if (e.Button == System.Windows.Forms.MouseButtons.Right)
            {
                pontok.RemoveAt(pontIndex);
            }
        }


        private void Form1_MouseMove(object sender, MouseEventArgs e)
        {
            if (megvan_)
            {
                pontok[pontIndex] = new PointF(e.X, e.Y);
                Invalidate();
                Update();
                Rajz();
            }
        }
    }
}