Zoom relative to mouse position

Hi,

I am trying to figure out how to zoom relative to the mouse pointer
position. Below, please find my sample code.

When I initially position the mouse pointer on one corner of the red
rectangle and use the mouse wheel, I am able to zoom in and out as
expected. As soon as I move the pointer position, let's say to another
corner of the red rectangle, and try to zoom in or out, my position
relative to the rectangle shifts around.

I think I may be missing a transform or two. In another attempt, in the
mouseWheelMoved method, I inverted tx from the previous iteration and
transformed the mouse position p with the inverted transform before
recalculating the new transform; but the behavior got more erratic.

Any help is greatly appreciated. What am I missing here?

Thanks.

Here is my code:

import java.awt.Color;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Point;
import java.awt.event.MouseWheelEvent;
import java.awt.event.MouseWheelListener;
import java.awt.geom.AffineTransform;
import java.awt.geom.Path2D;
import java.awt.geom.Rectangle2D;

import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JScrollPane;

@SuppressWarnings("serial")
public class ZoomDemo extends JPanel {

     AffineTransform tx = new AffineTransform();

     Rectangle2D.Double rect = new Rectangle2D.Double(100, 100, 20, 30);

     public ZoomDemo() {
       this.addMouseWheelListener(new ZoomHandler());
     }

     @Override
     public void paint(Graphics g) {
       super.paint(g);
       Graphics2D g2 = (Graphics2D) g;

       Path2D.Double path;
       g2.setColor(Color.RED);
       path = new Path2D.Double(rect, tx);
       g2.draw(path);
     }

     private class ZoomHandler implements MouseWheelListener {

       Point oldPoint = null;

       double scale = 1.0;

       public void mouseWheelMoved(MouseWheelEvent e) {
         if (e.getScrollType() == MouseWheelEvent.WHEEL_UNIT_SCROLL) {

           scale += (.1 * e.getWheelRotation());
           scale = Math.max(0.1, scale);
           Point p = e.getPoint();

           tx = AffineTransform.getTranslateInstance(p.getX(), p.getY());
           tx.scale(scale, scale);
           tx.translate(-p.getX(), -p.getY());

           ZoomDemo.this.revalidate();
           ZoomDemo.this.repaint();
         }
       }
     }

     public static void main(String[] args) {

       JFrame f = new JFrame("ZoomDemo");
       ZoomDemo zoomDemo = new ZoomDemo();
       JScrollPane sp = new JScrollPane(zoomDemo);
       f.getContentPane().add(sp);
       f.setSize(500, 500);
       f.setLocationRelativeTo(null);
       f.setVisible(true);
     }
}