Ok, so my goal is to draw a rectangular spiral in java. So far, I've created the Spiral Viewer class and the SpiralComponent but I'm not quite sure how I would implement the SpiralGenerator class. Here's what I have:

SpiralViewer:

import javax.swing.JFrame;
/**
   Test driver for Spiral class.
*/
public class SpiralViewer
{
   public static void main(String[] args)
   {
      JFrame frame = new JFrame();
      final int FRAME_WIDTH = 400;
      final int FRAME_HEIGHT = 400;

      frame.setSize(FRAME_WIDTH, FRAME_HEIGHT);
      frame.setTitle("SpiralViewer");
      frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
      SpiralComponent component = new SpiralComponent();
      frame.add(component);
      frame.setVisible(true);
   }
}

SpiralComponent:

import javax.swing.JComponent;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.geom.Point2D;
import java.awt.geom.Line2D;

public class SpiralComponent extends JComponent
{
   public void paintComponent(Graphics g)
   {
      Graphics2D g2 = (Graphics2D) g;
      final int INITIAL_SIZE = 10;

      int size = Math.min(getWidth(), getHeight());
      SpiralGenerator gen = new SpiralGenerator(
         INITIAL_SIZE,
         new Point2D.Double(size / 2, size / 2));

      while (true)
      {
         Line2D.Double segment = gen.nextSegment();
         if (!segment.intersects(getBounds()))
            return;
         g2.draw(segment);
      }
   }
}

Spiral Generator:

import java.awt.geom.Point2D;
import java.awt.geom.Line2D;

public class SpiralGenerator
{
   /**
      Creates a spiral generator.
      @param initialSize the size of the first (shortest) segment
      of the spiral, in pixels
      @param start the starting point of the spiral
   */
   public SpiralGenerator(double initialSize, Point2D.Double start)
   {
	   init = start;
	   size = initialSize;
   }

   /**
      Returns the next segment of the spiral.
      @return the next segment
   */
   public Line2D.Double nextSegment()
   {
	   Line2D.Double test = new Line2D.Double(0.0,0.0,0.0,0.0);

	   return test;
   }

   // private implementation
   private double size;
   private Point2D.Double init;

}

SpiralTester:

import java.awt.geom.Point2D;
import java.awt.geom.Line2D;

public class SpiralTester
{
   public static void main(String[] args)
   {
      SpiralGenerator gen = new SpiralGenerator(10, new Point2D.Double(100, 100));
      Line2D line = gen.nextSegment();
      System.out.println(line.getX1()); 
      System.out.println("Expected: 100");
      System.out.println(line.getY1()); 
      System.out.println("Expected: 100");
      System.out.println(line.getX2()); 
      System.out.println("Expected: 110");
      System.out.println(line.getY2()); 
      System.out.println("Expected: 100");
      line = gen.nextSegment();
      System.out.println(line.getX1()); 
      System.out.println("Expected: 110");
      System.out.println(line.getY1());
      System.out.println("Expected: 100");
      System.out.println(line.getX2());
      System.out.println("Expected: 110");
      System.out.println(line.getY2());
      System.out.println("Expected: 90");
   }
}

There are two different ways you can approach drawing the spiral.
1) Using GeneralPath to define the path from a fixed coordinate system in which you define the coordinates of the segments to be drawn on a fixed x-y plane.
2) Using coordinate transformations (translate, rotate) to alter the coodinate system as you draw each segment. With translation and rotation, drawing the path becomes trivial. You simply draw a line in a fixed direction (which ever way you want to go from your origin, like 0,0 to 0,100, translate to the end of that line, rotate 90 deg left or right, draw a slightly shorter line in the same direction as the first (perhaps 0,0 to 0,90), and continue until you reach the endpoint you want. By moving and rotating your origin as you draw, you only have to draw increasingly shorter line segments in the direction of path traversal.

There are some examples of using coordinate transforms here:
http://www.java2s.com/Code/Java/2D-Graphics-GUI/TransformTranslationandRotation.htm

Hope that helps get you started.

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