てけとーにマウスで引いたギザギザな線を微妙にきれいな曲線で描画したい

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;

using System.Drawing.Drawing2D;

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

        private bool isDragging = false;

        List<Point> bezierPoints = new List<Point>();

        private void Form1_MouseDown(object sender, MouseEventArgs e)
        {
            if (e.Button == MouseButtons.Left)
            {
                isDragging = true;

                bezierPoints.Clear();
                bezierPoints.Add(e.Location);
            }
        }

        private void Form1_MouseMove(object sender, MouseEventArgs e)
        {
            if (isDragging)
            {
                bezierPoints.Add(e.Location);

                using (Pen pen = new Pen(Color.Black, 3.0f))
                using (Bitmap b = new Bitmap(ClientRectangle.Width, ClientRectangle.Height))
                using (Graphics g1 = Graphics.FromImage(b))
                using (Graphics g2 = Graphics.FromHwnd(Handle))
                {
                    g1.FillRectangle(SystemBrushes.Window, ClientRectangle);
                    g1.DrawLines(pen, bezierPoints.ToArray());

                    g2.DrawImage(b, 0, 0);
                }
            }
        }

        private void Form1_MouseUp(object sender, MouseEventArgs e)
        {
            if (isDragging && e.Button == MouseButtons.Left)
            {
                bezierPoints.Add(e.Location);

                using (Graphics g = Graphics.FromHwnd(Handle))
                using (Pen pen = new Pen(Color.Black, 3.0f))
                {
                    g.FillRectangle(SystemBrushes.Window, ClientRectangle);

                    if (bezierPoints.Count <= 0)
                    {
                        /* Do nothing */
                    }
                    else if (bezierPoints.Count <= 3)
                    {
                        g.DrawLines(pen, bezierPoints.ToArray());
                    }
                    else
                    {
                        /* 全体の20%（または20個）まで点を間引く */
                        int LIMIT_OF_POINT_COUNT = Math.Max(20, bezierPoints.Count * 20 / 100);
                        while (bezierPoints.Count > LIMIT_OF_POINT_COUNT)
                        {
                            List<Point> p = new List<Point>();
                            p.Add(bezierPoints[0]); /* 始点を追加 */

                            for (int i = 2; i <= bezierPoints.Count - 2; i += 2)
                            {
                                p.Add(new Point(
                                    (bezierPoints[i - 1].X + bezierPoints[i].X) / 2,
                                    (bezierPoints[i - 1].Y + bezierPoints[i].Y) / 2));
                            }
                            p.Add(bezierPoints[bezierPoints.Count - 1]);

                            bezierPoints = p; /* 終点を追加 */
                        }

                        g.SmoothingMode = SmoothingMode.HighQuality;
                        g.DrawCurve(pen, bezierPoints.ToArray());
                    }
                }

                isDragging = false;
            }
        }
    }
}