How to resolve the algorithm Dragon curve step by step in the C# programming language

Published on 12 May 2024 09:40 PM
#C_Sharp

How to resolve the algorithm Dragon curve step by step in the C# programming language

Table of Contents

Problem Statement

Create and display a dragon curve fractal. (You may either display the curve directly or write it to an image file.)

Here are some brief notes the algorithms used and how they might suit various languages. This always has F at even positions and S at odd. Eg. after 3 levels F_S_F_S_F_S_F_S. The +/- turns in between bend to the left or right the same as the "successive approximation" method above. Read more at for instance Joel Castellanos' L-system page. Variations are possible if you have only a single symbol for line draw, for example the Icon and Unicon and Xfractint code. The angles can also be broken into 45-degree parts to keep the expansion in a single direction rather than the endpoint rotating around. The string rewrites can be done recursively without building the whole string, just follow its instructions at the target level. See for example C by IFS Drawing code. The effect is the same as "recursive with parameter" above but can draw other curves defined by L-systems.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Dragon curve step by step in the C# programming language

Purpose: This C# program demonstrates the creation of the Dragon Curve fractal using a recursive algorithm.

Explanation:

Initialization:

  • The DragonCurve class inherits from Form and represents the user interface window for the application.
  • The constructor initializes the form's size, position, and graphics settings.
  • startingAngle is set to -iter * (π/4) to control the initial angle of the curve.
  • side is calculated based on the number of iterations (iter) and the desired size of the curve.

Generating the Dragon Curve Sequence:

  • The getSequence method generates the sequence of turns that define the shape of the Dragon Curve.
  • It recursively creates a copy of the sequence, reverses it, adds a right turn, and then adds the reversed copy with left turns.

Drawing the Dragon Curve:

  • In the OnPaint method, the curve is drawn using the sequence of turns.
  • The initial coordinates and angle are initialized.
  • A line is drawn from the starting point to the first point on the curve.
  • The loop iterates through the sequence of turns, adjusting the angle and drawing lines accordingly.

Main Method:

  • The Main method creates an instance of the DragonCurve class with an iteration count of 14 and runs the application using Application.Run.

Output: When the program is executed, it displays a window with the Dragon Curve fractal drawn in black. The fractal has 14 iterations, resulting in a complex and intricate pattern.

Source code in the csharp programming language

using System;
using System.Collections.Generic;
using System.Drawing;
using System.Drawing.Drawing2D;
using System.Windows.Forms;

public class DragonCurve : Form
{
    private List<int> turns;
    private double startingAngle, side;

    public DragonCurve(int iter)
    {
        Size = new Size(800, 600);
        StartPosition = FormStartPosition.CenterScreen;
        DoubleBuffered = true;
        BackColor = Color.White;

        startingAngle = -iter * (Math.PI / 4);
        side = 400 / Math.Pow(2, iter / 2.0);

        turns = getSequence(iter);
    }

    private List<int> getSequence(int iter)
    {
        var turnSequence = new List<int>();
        for (int i = 0; i < iter; i++)
        {
            var copy = new List<int>(turnSequence);
            copy.Reverse();
            turnSequence.Add(1);
            foreach (int turn in copy)
            {
                turnSequence.Add(-turn);
            }
        }
        return turnSequence;
    }

    protected override void OnPaint(PaintEventArgs e)
    {
        base.OnPaint(e);
        e.Graphics.SmoothingMode = SmoothingMode.AntiAlias;

        double angle = startingAngle;
        int x1 = 230, y1 = 350;
        int x2 = x1 + (int)(Math.Cos(angle) * side);
        int y2 = y1 + (int)(Math.Sin(angle) * side);
        e.Graphics.DrawLine(Pens.Black, x1, y1, x2, y2);
        x1 = x2;
        y1 = y2;
        foreach (int turn in turns)
        {
            angle += turn * (Math.PI / 2);
            x2 = x1 + (int)(Math.Cos(angle) * side);
            y2 = y1 + (int)(Math.Sin(angle) * side);
            e.Graphics.DrawLine(Pens.Black, x1, y1, x2, y2);
            x1 = x2;
            y1 = y2;
        }
    }

    [STAThread]
    static void Main()
    {
        Application.Run(new DragonCurve(14));
    }
}

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