public class Point2D implements Comparable<Point2D> {
    public static final Comparator<Point2D> X_ORDER = new XOrder();
    public static final Comparator<Point2D> Y_ORDER = new YOrder();
    public static final Comparator<Point2D> R_ORDER = new ROrder();
    
    public final Comparator<Point2D> POLAR_ORDER = new PolarOrder();
    public final Comparator<Point2D> ATAN2_ORDER = new Atan2Order();
    public final Comparator<Point2D> DISTANCE_TO_ORDER = new DistanceToOrder();

    private final double x;
    private final double y;

    /*Many many methods omitted here*/

    // compare by y-coordinate, breaking ties by x-coordinate
    public int compareTo(Point2D that) {
        if (this.y < that.y) return -1;
        if (this.y > that.y) return +1;
        if (this.x < that.x) return -1;
        if (this.x > that.x) return +1;
        return 0;
    }

    // compare points according to their x-coordinate
    private static class XOrder implements Comparator<Point2D> {
        public int compare(Point2D p, Point2D q) {
            if (p.x < q.x) return -1;
            if (p.x > q.x) return +1;
            return 0;
        }
    }

    // compare points according to their distance to this point
    private class DistanceToOrder implements Comparator<Point2D> {
        public int compare(Point2D p, Point2D q) {
            double dist1 = distanceSquaredTo(p);
            double dist2 = distanceSquaredTo(q);
            if      (dist1 < dist2) return -1;
            else if (dist1 > dist2) return +1;
            else                    return  0;
        }

     }
}