如何将输出从System.out重定向到JavaFx TextArea

TextArea textArea = new TextArea();

PrintStream printStream = new PrintStream(new TextAreaOutputStream(textArea));

System.setOut(printStream);

import java.io.IOException;
import java.io.OutputStream;

public class TextAreaOutputStream extends OutputStream {
    private TextArea textArea;

    public TextAreaOutputStream(TextArea textArea) {
        this.textArea = textArea;
    }

    @Override
    public void write(int b) throws IOException {
        textArea.appendText(String.valueOf((char) b));
    }
}

import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.TextArea;
import javafx.scene.layout.StackPane;
import javafx.stage.Stage;

import java.io.IOException;
import java.io.OutputStream;
import java.io.PrintStream;

public class RedirectSystemOut extends Application {
    public static void main(String[] args) {
        launch(args);
    }

    @Override
    public void start(Stage primaryStage) {
        TextArea textArea = new TextArea();

        PrintStream printStream = new PrintStream(new TextAreaOutputStream(textArea));
        System.setOut(printStream);

        System.out.println("Hello, World!");

        StackPane root = new StackPane(textArea);
        primaryStage.setScene(new Scene(root, 300, 200));
        primaryStage.show();
    }

    public static class TextAreaOutputStream extends OutputStream {
        private TextArea textArea;

        public TextAreaOutputStream(TextArea textArea) {
            this.textArea = textArea;
        }

        @Override
        public void write(int b) throws IOException {
            textArea.appendText(String.valueOf((char) b));
        }
    }
}