Animation + resizing leads to OOM error in javafx2, so it's partial backport of 8096749 to javafx2.

test case:

import javafx.animation.Animation;
import javafx.animation.AnimationTimer;
import javafx.animation.FadeTransition;
import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.layout.StackPane;
import javafx.scene.layout.VBox;
import javafx.scene.paint.Color;
import javafx.scene.shape.Rectangle;
import javafx.scene.text.Font;
import javafx.scene.text.Text;
import javafx.stage.Stage;
import javafx.stage.StageStyle;
import javafx.util.Duration;

public class TransparentStage extends Application {

    public static final int MAX_WIDTH = 1920;
    public static final int MAX_HEIGHT = 1080;
    public static final int MIN_WIDTH = 10;
    public static final int MIN_HEIGHT = 10;

    @Override
    public void start(final Stage stage) {
        stage.initStyle(StageStyle.TRANSPARENT);
        Text text = new Text("Transparent!");
        text.setFont(new Font(40));

        VBox box = new VBox();
        box.getChildren().add(text);
        final Scene scene = new Scene(box, MAX_WIDTH, MAX_HEIGHT);
        scene.setFill(null);
        stage.setScene(scene);
        stage.show();

        Rectangle rect = new Rectangle(MAX_WIDTH, MAX_HEIGHT);
        rect.setFill(Color.SALMON);
        rect.setOpacity(0);
        box.getChildren().add(rect);


        AnimationTimer animationTimer = new AnimationTimer() {
            @Override
            public void handle(long now) {
                final double width = stage.getWidth();
                final double height = stage.getHeight();

                final double newWidth = (MIN_WIDTH + width + 10)% MAX_WIDTH;
                final double newHeight = (MIN_HEIGHT + height + 10)% MAX_HEIGHT;
                stage.setWidth(newWidth);
                stage.setHeight(newHeight);
            }
        };
        animationTimer.start();
        FadeTransition ft = new FadeTransition(Duration.seconds(5), rect);
        ft.setToValue(1);
        ft.setCycleCount(100);
        ft.play();
    }

    public static void main(String[] args) {
        launch(args);
    }
}

To reproduce the issue you need to run jvm with the following args: -Xms1000m -Xmx1000m