import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseWheelEvent;
import java.awt.geom.AffineTransform;
import java.awt.geom.Point2D;
import java.awt.image.BufferedImage;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
import javax.swing.JFrame;
import javax.swing.JPanel;

public class ZoomOperations extends JPanel{
    private boolean repaint;
    private double zoom;
    private List<Point2D.Double> points;
    private AffineTransform at;
    private BufferedImage img;

    public ZoomOperations()   {
            repaint = true;
            zoom = 0.1;
            points = new ArrayList<>();
            at = new AffineTransform();
            img = null;
            Random r = new Random();
            for (int i = 0; i < 100; i++)
                    points.add(new Point2D.Double(5000 * r.nextDouble(), 5000 * r.nextDouble()));

            addMouseWheelListener(new MouseAdapter() {

                    public void mouseWheelMoved(MouseWheelEvent e) {
                            if (e.getPreciseWheelRotation() < 0)
                                    zoom = Math.min(zoom+= 0.02,2);
                            else
                                    zoom = Math.max(zoom-= 0.02,0.01);
                            repaint();
                    }
            });
    }

     protected void paintComponent(Graphics g) {
            super.paintComponent(g);
            Graphics2D g2d = (Graphics2D) g;
            if (img == null)
                    img = (BufferedImage)createImage(5000, 5000);
            at = g2d.getTransform();
            at.translate(0, 0);
            at.scale(zoom, zoom);
            g2d.setTransform(at);
            if (repaint){
                    Graphics2D g2c = img.createGraphics();
                    for (Point2D.Double p:points)
                            g2c.fillOval((int)p.x-50, (int)p.y-50, 50, 50);
                    g2c.dispose();
                    repaint = false;
            }

            g2d.drawImage(img, 0, 0, this);
     }

    public static void main(String[] args) {
            JFrame jf = new JFrame();
            jf.setSize(800, 600);
            jf.add(new ZoomOperations());
            jf.setVisible(true);
    }

}

private boolean repaint;

img = (BufferedImage) createImage(5000, 5000);  // How to set the size ?