When a Scene or SubScene has its width or height set to 0, coordinate transformations stop working because the transformation matrix contains NaNs. This is a consequence of divisions by zero in both parallel and perspective projections.

Even though a 0x0 scene is mathematically degenerate, it is still desirable for coordinate transformation APIs to remain numerically well-behaved and return finite results whenever possible, rather than being poisoned by NaN/Infinity.

Here is an application that demonstrates the failing coordinate transformations. Click on the buttons to resize the SubScene and observe the console output:

public class ZeroSizeSubScene extends Application {

    @Override
    public void start(Stage stage) {
        var rect = new Rectangle(50, 50, Color.RED);
        var subScene = new SubScene(new Group(rect), 100, 100);
        subScene.setFill(Color.GRAY);

        // Also try a perspective camera:
        //
        // var camera = new PerspectiveCamera();
        // camera.setRotate(45);
        // camera.setTranslateX(-20);
        // camera.setRotationAxis(new Point3D(0, 1, 0));
        // subScene.setCamera(camera);

        class MyButton extends Button {
            public MyButton(String text, double width, double height) {
                super(text);
                setOnAction(_ -> {
                    var timeline = new Timeline(
                        new KeyFrame(Duration.seconds(1), new KeyValue(subScene.widthProperty(), width)),
                        new KeyFrame(Duration.seconds(1), new KeyValue(subScene.heightProperty(), height)));

                    timeline.setOnFinished(_ -> {
                        Point2D p0 = rect.localToScreen(0, 0);
                        System.out.println("rect.localToScreen(0, 0) = " + p0);
                    });

                    timeline.play();
                });
            }
        }

        VBox.setMargin(subScene, new Insets(0, 0, 20, 0));

        var root = new VBox(5,
            subScene,
            new CheckBox("Rotate SubScene") {{ setOnAction(_ -> subScene.setRotate(isSelected() ? 45 : 0)); }},
            new MyButton("Size: 100x100", 100, 100),
            new MyButton("Size: 10x10", 10, 10),
            new MyButton("Size: 100x0", 100, 0),
            new MyButton("Size: 0x100", 0, 100),
            new MyButton("Size: 0x0", 0, 0)
        );

        Scene scene = new Scene(root, 300, 300);
        stage.setScene(scene);
        stage.show();
    }
}