Why does drawing of ellipses appear inaccurate?

Question

Below is a very simple applet: it defines two points (px, py) and
(qx, qy), finds the distance (radius) between those two points,
and then plots the point (px, py), along with the circle centered at
(qx, qy) with radius radius.
Mathematically, the circle should pass through the point, so
in the applet I'd expect to see the visible portion of the circle
passing through the plotted point.
Instead, the visible portion of the circle misses the point by
a distance of what looks like around 100 pixels. This is a much
bigger error than would be expected from the floating-point
rounding errors present.
Questions:
(1) Can anybody else reproduce this?
(2) Can anybody explain it?!
(3) How do I fix this?
I'm using javac version 1.5.0_13 to compile the file, on
OS X 10.5.2; this is the version of the Java SDK that comes
with OS X.
Any hints would be very much appreciated!
Mark
// file EllipseBug.java
import javax.swing.JApplet;
import java.awt.Graphics2D;
import java.awt.geom.Ellipse2D;
import java.lang.Math;
public final class EllipseBug extends JApplet {
public void paint(java.awt.Graphics g) {
double px = 304.38061674008816;
double py = 18.38237885462553;
double qx = 562886.1525819342;
double qy = 114549.8147372959;
double radius = Math.sqrt((px-qx)*(px-qx) + (py-qy)*(py-qy));
Graphics2D g2 = (Graphics2D)g;
g2.fill(new Ellipse2D.Double(px-2., py-2., 4., 4.));
g2.draw(new Ellipse2D.Double(qx-radius, qy-radius, 2.*radius, 2.*radius));
}

Answer 1

An animated version of this. It animates quite slowly so you can see the real oddity at ang=0.33, 1.24, 1.9, 2.8 etc.
import java.awt.Color;
import java.awt.Graphics2D;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.geom.Ellipse2D;
import java.awt.geom.Point2D;
import javax.swing.JApplet;
import javax.swing.Timer;
public final class EllipseBug extends JApplet {
    private double RADIUS = 50000.0;
    private Point2D.Double p = new Point2D.Double(100.0, 100.0);
    private Point2D.Double q = new Point2D.Double(100.0, 50100.0);
    private double ang = 0.0;
    @Override
    public void init() {
        Timer timer = new Timer(50, new ActionListener() {
            public void actionPerformed(ActionEvent e) {
                ang += 0.001;
                q.x = 100.0 + RADIUS * Math.sin(ang);
                q.y = 100.0 + RADIUS * Math.cos(ang);
                repaint();
                System.out.printf("ang=%f%n", ang);
        timer.start();
        // draw a circle center Q thru P
    @Override
    public void paint(java.awt.Graphics g) {
        Graphics2D g2 = (Graphics2D)g;
        g2.setColor(Color.WHITE);
        g2.fillRect(0, 0, getWidth(), getHeight());
        g2.setColor(Color.BLUE);
        g2.draw(new Ellipse2D.Double(q.x-RADIUS, q.y-RADIUS, 2*RADIUS, 2*RADIUS));
        g2.setColor(Color.GREEN);
        g2.drawLine((int)p.x, (int)p.y, (int)q.x, (int)q.y);
}You will probably get an explanation of what's going on at the 2D forum:
http://forum.java.sun.com/forum.jspa?forumID=20