アクセスカウンター

Fractal: Dragon Curve (WPF with C#)


Applied rule of recursive drawing

It seems that some of the unmovable points (the green points shown in the left figure) are located at a specific position in each periodic pattern in the drawn curve.
This figure indicates an applied rule of recursive drawing. When the complexity order is increased, additional green points and new red-lined paths are generated in the same manner. Here, two sets of fractional ratios of {cos 25o and sin 25o} or {sin 25o and cos 25o} in length and  turning angles of {25o in left, 90o in right and 65o in left} or {65o in right, 90o in left and 25o in right} are alternately inherited for all the order.



//   DragonCurve_Turtle_WPF_001\MainWindow.xaml.cs
//   Dragon Curve
//    (WPF application with C#
//     on Microsoft Visual Studio Express 2013 for Windows Desktop)
//   Oct. 29, 2014, by Masao Sakuraba
//   (Ref. 1-5 guided me to this program.)
//   * NOTE1: Blue-color parts were automatically generated by Visual Studio.
//   * NOTE2: Red-color parts were newly added.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
using System.Diagnostics;       // Namespace for class "Stopwatch".
using ThinkLib;                 // After adding the file "ThinkLib.dll" as a reference [2].

namespace DragonCurve_Turtle_WPF_001
{
    /// <summary>
    /// MainWindow.xaml の相互作用ロジック
    /// </summary>
    public partial class MainWindow : Window
    {
        Turtle pen1;    // Make a turtle using ThinkLib [3].
        double PI = 3.141592654;

        void PatternGenerator1(Turtle _pen, double _length, int _complexity)
        {
            if (_complexity == 0 | _length < 2.4)
            {
                _pen.Forward(_length);
            }
            else
            {
                _pen.Left(25);
                PatternGenerator1(_pen, _length * Math.Cos(PI / 180 * 25), _complexity - 1);
                _pen.Right(90);                                       // Cross recursion [4].
                PatternGenerator2(_pen, _length * Math.Sin(PI / 180 * 25), _complexity - 1);
                _pen.Left(65);
            }
        }

        void PatternGenerator2(Turtle _pen, double _length, int _complexity)
        {
            if (_complexity == 0 | _length < 2.4)
            {
                _pen.Forward(_length);
            }
            else
            {
                _pen.Right(65);
                PatternGenerator1(_pen, _length * Math.Sin(PI / 180 * 25), _complexity - 1);
                _pen.Left(90);
                PatternGenerator2(_pen, _length * Math.Cos(PI / 180 * 25), _complexity - 1);
                _pen.Right(25);
            }
        }

        public MainWindow()
        {
            InitializeComponent();
            pen1 = new Turtle(playground);  // After making Canvas in MainWindow
                                            // with the Canvas name of "playground" [3].
            pen1.Visible = false;      // When you do not like showning a turtle [5].
        }

        private void Button1_Click(object sender, RoutedEventArgs e)
        {                                      // After making Button for Event Handler.
            double Length = 220.0;
            int Complexity = 30;

            pen1.Clear();
            pen1.LineBrush = Brushes.Blue;
            pen1.BrushWidth = 0.7;
            pen1.WarpTo(Length * 0.8, Length * 0.9);

            Stopwatch TimeMeasure = new Stopwatch();    // Make a stopwatch.
            TimeMeasure.Start();

            PatternGenerator1(pen1, Length, Complexity);

            double Time_in_s = (TimeMeasure.Elapsed).TotalSeconds;
            Label1.Content = ("Drawing Time : " + Time_in_s + " s.");
        }
    }
}


Reference
(1) "Think Sharply with C#" by Prof. Peter Wentworth (Rhodes Univ.),
    http://www.ict.ru.ac.za/resources/ThinkSharply/thinksharply/
(2) "Appendices : Getting Started with ThinkLib",
    http://www.ict.ru.ac.za/Resources/ThinkSharply/ThinkSharply/thinklib_getting_started.html
(3) "Chapter 7 : Hello, little turtles!",
    http://www.ict.ru.ac.za/Resources/ThinkSharply/ThinkSharply/hello_little_turtles.html
(4) "Chapter 21 : Recursion",
    http://www.ict.ru.ac.za/Resources/ThinkSharply/ThinkSharply/recursion.html
(5) "Appendices : ThinkLib.Turtle Documentation",
    http://www.ict.ru.ac.za/Resources/ThinkSharply/ThinkSharply/thinklib_turtle_docs.html



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