PtsArea

public class Point {
    private final int x;
    private final int y;

    public int getX() {
        return x;
    }

    public int getY() {
        return y;
    }

    public Point(int x, int y) {
        this.x = x;
        this.y = y;
    }

    @Override
    public boolean equals(Object o) {
        if (o == null) {
            return false;
        }
        if (this.getClass() != o.getClass()){
            return false;
        }

        Point that = (Point) o;
        return (this.x == that.x) && (this.y == that.y);
    }

    @Override
    public int hashCode() {
        return 31 * x + 37 * y;
    }

    @Override
    public String toString() {
        return "Point{" + "x=" + x + ", y=" + y + '}';
    }
}

//-------------------------------
public class Area_question {
    public final NavigableSet<Point> xIndex
            = new TreeSet<>(new Comparator<Point>() {
        @Override
        public int compare(Point o1, Point o2) {
            return o1.getX() - o2.getX();
        }
    });
    public final NavigableSet<Point> yIndex
            = new TreeSet<>(new Comparator<Point>() {
        @Override
        public int compare(Point o1, Point o2) {
            return o1.getY() - o2.getY();
        }
    });
    void addPoint(Point point){
        xIndex.add(point);
        yIndex.add(point);
    }

    Collection<Point> selectPoints(
        int leftX, int rightX,
        int bottomY, int topY){
        Point leftEdge = new Point(leftX, 0);
        Point rightEdge = new Point(rightX, 0);
        Point bottomEdge = new Point(0, bottomY);
        Point topEdge = new Point(0, topY);
        Collection<Point> xSelection = xIndex
                .subSet(leftEdge, true, rightEdge, true);
        Collection<Point> ySelection = yIndex
                .subSet(bottomEdge, true, topEdge, true);

        System.out.println("x selection:");
       for (Point p: xSelection)
           System.out.println(p);
        System.out.println("---------");

        xSelection.retainAll(ySelection);

        System.out.println("after y selection:");
        for (Point p: xSelection)
           System.out.println(p);
        System.out.println("---------");

        return xSelection;
    }
}

//-------------------------------
public class Area_test {
    public static void main(String[] args) {
        Area_question area = new Area_question();
        area.addPoint(new Point(100, 101));
        area.addPoint(new Point(902, 103));
        area.addPoint(new Point(104, 905));
        area.addPoint(new Point(906, 907));
        System.out.println("Before");
        for (Point p: area.xIndex)
            System.out.println(p);
        System.out.println("=======");
        System.out.println(area.selectPoints(0,500,1,490));
        System.out.println("=======");
        System.out.println(area.selectPoints(0,500,1,490));
        System.out.println("After");
        for (Point p: area.xIndex)
            System.out.println(p);
    }
}
//-------------------------------
Результаты:

Before
Point{x=100, y=101}
Point{x=104, y=905}
Point{x=902, y=103}
Point{x=906, y=907}
=======
x selection:
Point{x=100, y=101}
Point{x=104, y=905}
---------
after y selection:
Point{x=100, y=101}
---------
[Point{x=100, y=101}]
=======
x selection:
Point{x=100, y=101}
---------
after y selection:
Point{x=100, y=101}
---------
[Point{x=100, y=101}]
After
Point{x=100, y=101}
Point{x=902, y=103}
Point{x=906, y=907}