Рисование спирали в Java

Вот то, что вы ищете ... хороший взгляд на объяснение вашему профессору, что вы поняли это самостоятельно, но, как бы то ни было, создание красивого спирального узора было забавным.

import java.awt.Dimension;

import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.geom.GeneralPath;
import java.awt.geom.Point2D;

import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.UIManager;

public class Spiral extends JPanel implements Runnable {

    public static final int WIDTH = 500;

    public static final double PIX_RES = 3;
    public static final double WEIGHT = PIX_RES / WIDTH;

    public static final long SLEEP_TIME = 10;

    private final GeneralPath topRight = new GeneralPath();
    private final GeneralPath topLeft = new GeneralPath();
    private final GeneralPath bottomLeft = new GeneralPath();
    private final GeneralPath bottomRight = new GeneralPath();

    public Spiral(){
        this(WIDTH);
    }

    public Spiral(final int width) {
        super();
        this.setPreferredSize(new Dimension(width, width));
        topRight.moveTo(width, 0);
        topLeft.moveTo(0, 0);
        bottomLeft.moveTo(0, width);
        bottomRight.moveTo(width, width);
    }

    @Override
    public void paintComponent(final Graphics g) {
        final Graphics2D g2 = (Graphics2D) g;
        g2.draw(topLeft);
        g2.draw(topRight);
        g2.draw(bottomLeft);
        g2.draw(bottomRight);
    }

    /**
     * generated by eclipse
     */
    private static final long serialVersionUID = -756842929825603438L;

    @Override
    public void run() {
        while (true) {
            iterate();
            this.repaint();
            try {
                Thread.sleep(SLEEP_TIME);
            } catch (InterruptedException e) {
                e.printStackTrace();
            }
        }
    }

    private void iterate() {
        final double dx = topRight.getCurrentPoint().getX()
                - topLeft.getCurrentPoint().getX();
        final double dy = -topRight.getCurrentPoint().getY()
                + topLeft.getCurrentPoint().getY();
        final Point2D pTR = topRight.getCurrentPoint();
        final Point2D pTL = topLeft.getCurrentPoint();
        final Point2D pBL = bottomLeft.getCurrentPoint();
        final Point2D pBR = bottomRight.getCurrentPoint();

        topRight.lineTo(pTR.getX() - dx * WEIGHT, pTR.getY() + dy * WEIGHT);
        topLeft.lineTo(pTL.getX() + dy * WEIGHT, pTL.getY() + dx * WEIGHT);
        bottomRight.lineTo(pBR.getX() - dy * WEIGHT, pBR.getY() - dx * WEIGHT);
        bottomLeft.lineTo(pBL.getX() + dx * WEIGHT, pBL.getY() - dy * WEIGHT);
    }

    public static void main(String... args) {
        final JFrame frame = new JFrame("spiral");

        try {
            UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());
        } catch (Exception e) {
            // who cares
        }

        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

        final Spiral spiral = new Spiral();

        frame.setContentPane(spiral);
        frame.pack();
        frame.setVisible(true);

        (new Thread(spiral)).start();
    }
}

Этот эффект называется «кривой преследования». Я изменил вашу программу, чтобы продемонстрировать эффект.

import java.awt.Graphics;
import java.awt.Color;
import javax.swing.JPanel;
import javax.swing.JFrame;

public class Slugs extends JPanel {

    private static final long serialVersionUID = 1L;

    // Max length of line segment.
    final double range = 1;

    // Total number of iterations of the algorithm.
    final int num = 2000;

    // current iteration
    public int i = 0;

    // Declare arrays for points.
    final double[][][] points = new double[4][2][];

    public Slugs (final int width, final int height) {

        // initialize arrays for points.
        for (int line = 0; line < points.length; line++)
        {
            for (int axis = 0; axis < points[line].length; axis++)
            {
                points[line][axis] = new double[num];
            }
        }

        // First point placed in center of panel.
        points[0][0][0] = 100;
        points[0][1][0] = 100;

        points[1][0][0] = 100;
        points[1][1][0] = 700;

        points[2][0][0] = 700;
        points[2][1][0] = 700;

        points[3][0][0] = 700;
        points[3][1][0] = 100;

        // Generate a random point.
        for (int i = 1; i < num; i++)
        {
            // for each line
            for (int line = 0; line < points.length; line++) {

                // calculate vector from last point on this line to last point
                // on the line we're chasing
                final double vectX =
                    points[(line + 1) % 4][0][i - 1] - points[line][0][i - 1];
                final double vectY =
                    points[(line + 1) % 4][1][i - 1] - points[line][1][i - 1];

                // find length of the vector
                final double length = hypot(vectX, vectY);

                // adjust vector length to max allowable range
                final double deltaX = vectX / length * range;
                final double deltaY = vectY / length * range;

                // record current point
                points[line][0][i] = points[line][0][i - 1] + deltaX;
                points[line][1][i] = points[line][1][i - 1] + deltaY;
            }
        }
    }

    public void paintComponent(Graphics g) {

        if(i < num - 1) { 

            g.setColor(Color.blue);

            for (int line = 0; line < points.length; line++)
            {
                g.drawLine(
                    (int) points[line][0][i],     (int) points[line][1][i],
                    (int) points[line][0][i + 1], (int) points[line][1][i + 1]);
            }

            i++;
            delay(0);

            // sketchy recursion. If num is too high the program will crash
            repaint();
        }
    }

    public static void main(String[] args) {

        // Generates frame.
        JFrame frame = new JFrame();

        // Sets frame resolution and other frame parameters.
        frame.setSize(800, 800);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        Slugs panel = new Slugs(frame.getWidth(), frame.getHeight());
        frame.getContentPane().add(panel);
        frame.setVisible(true);
        frame.setResizable(false);
    }

    //Defines speed of delay between ticks.
    public static void delay(long milliseconds) {
        try {
            Thread.sleep(milliseconds);
        }
        catch (InterruptedException e) {
            e.printStackTrace();
        }
    }

    // hypotenuse length
    static double hypot(double a, double b)
    {
        return Math.sqrt(a * a + b * b);
    }
}