JavaFX provides several classes and APIs for creating animations, such as the AnimationTimer, Timeline, and Transition classes.

AnimationTimer is a class that provides a way to create custom animations. It is designed to be used with a Canvas or a Group of nodes. You create a subclass of AnimationTimer, and then override the handle() method to implement the animation logic. The handle() method is called by the JavaFX runtime on each frame of the animation.

Here's an example of how to use AnimationTimer to create a simple animation that moves a circle across the screen:

import javafx.animation.AnimationTimer;
import javafx.application.Application;
import javafx.scene.Group;
import javafx.scene.Scene;
import javafx.scene.paint.Color;
import javafx.scene.shape.Circle;
import javafx.stage.Stage;

public class MyApplication extends Application {
    @Override
    public void start(Stage primaryStage) {
        Group root = new Group();
        Scene scene = new Scene(root, 400, 400, Color.WHITE);

        Circle circle = new Circle(20, Color.BLUE);
        root.getChildren().add(circle);

        new AnimationTimer() {
            private long lastTime = 0;
            private double x = 0;

            @Override
            public void handle(long now) {
                if (lastTime == 0) {
                    lastTime = now;
                }

                double elapsedSeconds = (now - lastTime) / 1_000_000_000.0;
                double deltaX = elapsedSeconds * 50.0;

                x += deltaX;
                circle.setTranslateX(x);

                lastTime = now;
            }
        }.start();

        primaryStage.setScene(scene);
        primaryStage.show();
    }

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

In this example, we create a Circle object and add it to a Group that is displayed in a Scene. We then create an instance of AnimationTimer and override its handle() method to move the circle across the screen. The handle() method calculates the elapsed time since the last frame and uses it to update the position of the circle. The start() method is called to begin the animation.

Another way to create animations in JavaFX is to use the Timeline class. A Timeline is a series of keyframes that define the values of one or more properties of an object over time. You can use a KeyValue object to specify the value of a property at a specific point in time, and then use a KeyFrame object to specify the duration and timing of the animation.

Here's an example of how to use Timeline to create a simple animation that changes the color of a rectangle:

import javafx.animation.KeyFrame;
import javafx.animation.KeyValue;
import javafx.animation.Timeline;
import javafx.application.Application;
import javafx.scene.Group;
import javafx.scene.Scene;
import javafx.scene.paint.Color;
import javafx.scene.shape.Rectangle;
import javafx.stage.Stage;
import javafx.util.Duration;

public class MyApplication extends Application {
    @Override
    public void start(Stage primaryStage) {
        Group root = new Group();
        Scene scene = new Scene(root, 400, 400, Color.WHITE);

        Rectangle rect = new Rectangle(100, 100, 200, 200);
        rect.setFill(Color.RED);
        root.getChildren().add(rect);

        KeyValue keyValue = new KeyValue(rect.fillProperty(), Color.BLUE);
        KeyFrame keyFrame = new KeyFrame(Duration.seconds(2), keyValue);

        Timeline timeline = new Timeline(keyFrame);
        timeline.setCycleCount(Timeline.INDEFINITE);
        timeline.setAutoReverse(true);
        timeline.play();

        primaryStage.setScene(scene);