How do you implement position-sensitive zooming inside a JScrollPane?

I am trying to implement position-sensitive zooming inside a JScrollPane. The JScrollPane contains a component with a customized paint that will draw itself inside whatever space it is allocated - so zooming is as easy as using a MouseWheelListener that resizes the inner component as required.

But I also want zooming into (or out of) a point to keep that point as central as possible within the resulting zoomed-in (or -out) view (this is what I refer to as 'position-sensitive' zooming), similar to how zooming works in google maps. I am sure this has been done many times before - does anybody know the "right" way to do it under Java Swing?. Would it be better to play with Graphic2D's transformations instead of using JScrollPanes?

Sample code follows:

package test;

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

public class FPanel extends javax.swing.JPanel {

private Dimension preferredSize = new Dimension(400, 400);    
private Rectangle2D[] rects = new Rectangle2D[50];

public static void main(String[] args) {        
    JFrame jf = new JFrame("test");
    jf.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    jf.setSize(400, 400);
    jf.add(new JScrollPane(new FPanel()));
    jf.setVisible(true);
}    

public FPanel() {
    // generate rectangles with pseudo-random coords
    for (int i=0; i<rects.length; i++) {
        rects[i] = new Rectangle2D.Double(
                Math.random()*.8, Math.random()*.8, 
                Math.random()*.2, Math.random()*.2);
    }
    // mouse listener to detect scrollwheel events
    addMouseWheelListener(new MouseWheelListener() {
        public void mouseWheelMoved(MouseWheelEvent e) {
            updatePreferredSize(e.getWheelRotation(), e.getPoint());
        }
    });
}

private void updatePreferredSize(int n, Point p) {
    double d = (double) n * 1.08;
    d = (n