How to resolve the algorithm Pythagoras tree step by step in the Java programming language

Published on 12 May 2024 09:40 PM
#Java

How to resolve the algorithm Pythagoras tree step by step in the Java programming language

Table of Contents

Problem Statement

The Pythagoras tree is a fractal tree constructed from squares. It is named after Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to represent the Pythagorean theorem.

Construct a Pythagoras tree of order 7 using only vectors (no rotation or trigonometric functions).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Pythagoras tree step by step in the Java programming language

Java Programming Language

Pythagoras Tree

This Java program creates a colorful, recursive representation of a Pythagoras tree. Here's a detailed breakdown:

1. Class Definition: - Inherits from JPanel for displaying the tree.

2. Class Variables: - depthLimit controls the recursion depth of the tree. - hue is used for generating different colors for each branch.

3. Constructor: - Initializes the panel's preferred size and background color.

4. drawTree Method: - Recursive method that draws a single tree branch: - Calculates the points for the square and triangle shapes. - Fills and outlines the shapes using different colors based on the recursion depth. - Recursively calls itself to draw sub-branches.

5. paintComponent Method: - Overridden to initiate the tree drawing process. - Calls drawTree to generate the main branch.

6. main Method:

- SwingUtilities is used to create and display a JFrame containing the PythagorasTree panel.

Program Execution:

  1. The program creates a JFrame with the PythagorasTree panel.
  2. When the panel is painted, it invokes the paintComponent method.
  3. The paintComponent method initiates the recursive drawTree method to draw the tree branches.
  4. The recursion stops when the specified depthLimit is reached.
  5. The result is a colorful, multi-layered Pythagoras tree fractal.

Source code in the java programming language

import java.awt.*;
import java.awt.geom.Path2D;
import javax.swing.*;

public class PythagorasTree extends JPanel {
    final int depthLimit = 7;
    float hue = 0.15f;

    public PythagorasTree() {
        setPreferredSize(new Dimension(640, 640));
        setBackground(Color.white);
    }

    private void drawTree(Graphics2D g, float x1, float y1, float x2, float y2,
            int depth) {

        if (depth == depthLimit)
            return;

        float dx = x2 - x1;
        float dy = y1 - y2;

        float x3 = x2 - dy;
        float y3 = y2 - dx;
        float x4 = x1 - dy;
        float y4 = y1 - dx;
        float x5 = x4 + 0.5F * (dx - dy);
        float y5 = y4 - 0.5F * (dx + dy);

        Path2D square = new Path2D.Float();
        square.moveTo(x1, y1);
        square.lineTo(x2, y2);
        square.lineTo(x3, y3);
        square.lineTo(x4, y4);
        square.closePath();

        g.setColor(Color.getHSBColor(hue + depth * 0.02f, 1, 1));
        g.fill(square);
        g.setColor(Color.lightGray);
        g.draw(square);

        Path2D triangle = new Path2D.Float();
        triangle.moveTo(x3, y3);
        triangle.lineTo(x4, y4);
        triangle.lineTo(x5, y5);
        triangle.closePath();

        g.setColor(Color.getHSBColor(hue + depth * 0.035f, 1, 1));
        g.fill(triangle);
        g.setColor(Color.lightGray);
        g.draw(triangle);

        drawTree(g, x4, y4, x5, y5, depth + 1);
        drawTree(g, x5, y5, x3, y3, depth + 1);
    }

    @Override
    public void paintComponent(Graphics g) {
        super.paintComponent(g);
        drawTree((Graphics2D) g, 275, 500, 375, 500, 0);
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> {
            JFrame f = new JFrame();
            f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            f.setTitle("Pythagoras Tree");
            f.setResizable(false);
            f.add(new PythagorasTree(), BorderLayout.CENTER);
            f.pack();
            f.setLocationRelativeTo(null);
            f.setVisible(true);
        });
    }
}

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