public class KochComponent extends JComponent {
 
    List<Point> points = null;
 
    /** create the initial triangle */
    private void createTriangle() {
        points = new ArrayList<Point>();
 
        int length = Math.min(getWidth(), getHeight())*2/3;
 
        int x1 = (getWidth()-length)/2;
        int y1 = length/2;
        points.add(new Point(x1, y1));
 
        int x2 = x1+length;
        int y2 = y1;
        points.add(new Point(x2, y2));
 
        int x3 = x1+(length/2);
        int y3 = y1+length;
        points.add(new Point(x3, y3));
 
    }
 
    public void next() {
        numIterations++;
 
        List<Point> newPoints = new ArrayList<Point>();
        // generate the new points for each line segment
        for(int i = 0; i<points.size(); i++) {
            Point p1 = points.get(i);
            Point p2 = i==points.size()-1 ? 
              points.get(0) : points.get(i+1);
            newPoints.add(p1);
            newPoints.addAll(getKochPoints(p1, p2));
        }
        points = newPoints;
        repaint();
    }
 
    public void paintComponent(Graphics g) {
        // this is just to account for the fact that
        // the component has no initial width or height
        if(points==null) {
            createTriangle();
        }
 
        Graphics2D g2 = (Graphics2D)g;
 
        // Use this code to draw the actual poly
        // Polygon koch = new Polygon();
        // for (Point p : points){
        //   koch.addPoint(p.x, p.y);
        // }
        // g2.draw(koch);
 
        // This just draws unconnected points
        // for demo purposes
        for(Point p : points) {
            g2.drawRect(p.x, p.y, 1, 1);
        }
    }
 
    /** Generate the points to add for each segment
     * for each iteration.
     * I am just putting in the easy ones here.
     * You get to do the trickier one!
     */
    private List<Point> getKochPoints(Point p1, Point p2) {
        List<Point> kochPoints = new ArrayList<Point>();
 
        int dx = p2.x-p1.x;
        int dy = p2.y-p1.y;
 
        Point kp1 = new Point(p1.x+dx/3, p1.y+dy/3);
        kochPoints.add(kp1);
 
        // you have to figure out how to generate 
        // kp2 here (the top of the triangle)
 
        Point kp3 = new Point(p1.x+2*dx/3, p1.y+2*dy/3);
        kochPoints.add(kp3);
 
        return kochPoints;
    }
 
    private int numIterations;
}

import java.awt.Graphics;
import java.awt.Graphics2D;
import javax.swing.JComponent;
import java.awt.geom.Line2D;
import java.util.ArrayList;
import java.awt.geom.GeneralPath;
import java.awt.Polygon;
import java.awt.Point;

public class KochComponent3 extends JComponent {

    ArrayList<Point> points = null;

    /** create the initial triangle */
    private void createTriangle() {
        points = new ArrayList<Point>();

        int length = Math.min(getWidth(), getHeight())*2/3;

        int x1 = (getWidth()-length)/2;
        int y1 = length/2;
        points.add(new Point(x1, y1));

        int x2 = x1+length;
        int y2 = y1;
        points.add(new Point(x2, y2));

        int x3 = x1+(length/2);
        int y3 = y1+length;
        points.add(new Point(x3, y3));

    }

    public void next() {
        numIterations++;

        ArrayList<Point> newPoints = new ArrayList<Point>();
        // generate the new points for each line segment
        for(int i = 0; i<points.size(); i++) {
            Point p1 = points.get(i);
            Point p2 = i==points.size()-1 ? 
              points.get(0) : points.get(i+1);
            newPoints.add(p1);
            newPoints.addAll(getKochPoints(p1, p2));
        }
        points = newPoints;
        repaint();
    }

    public void paintComponent(Graphics g) 
    {
        if(points==null) {
            createTriangle();
        }

        Graphics2D g2 = (Graphics2D)g;
         Polygon koch = new Polygon();
         for (Point p : points){
           koch.addPoint(p.x, p.y);
         }
         g2.draw(koch);

    }

    /** Generate the points to add for each segment
     * for each iteration.
     * I am just putting in the easy ones here.
     * You get to do the trickier one!
     */
    private ArrayList<Point> getKochPoints(Point p1, Point p2) {
        ArrayList<Point> kochPoints = new ArrayList<Point>();

        int dx = p2.x-p1.x;
        int dy = p2.y-p1.y;
        double xtra = dx / 3;
        double use = xtra * xtra;

        int test = (int)(Math.sqrt(use-(use/36)));
        int test2 = p1.y+dy/3-test;        
        
        Point kp1 = new Point(p1.x+dx/3, p1.y+dy/3);
        kochPoints.add(kp1);
        if(p1.y == p2.y)
        {
            Point kp2 = new Point((p1.x+(dx/3)+((dx/3)/2)), ((p1.y+dy/3)-test));
            kochPoints.add(kp2);
        }
        else if(p1.x > p1.y)
        {
            Point kp2 = new Point(p1.x, p1.y+(dy/3)+test+11);
            kochPoints.add(kp2); 

        }
        else
        {
            Point kp2 = new Point(p1.x+(dx), p1.y+(2*dy/3) + test+11);
            kochPoints.add(kp2);
       
  

        }
            
        
        Point kp3 = new Point(p1.x+2*dx/3, p1.y+2*dy/3);
        kochPoints.add(kp3);

        return kochPoints;
    }

    private int numIterations;
}