SO this is my program of bouncing balls, i want to add a collision detection tha

Question

SO this is my program of bouncing balls, i want to add a collision detection that when the balls collide they do something, like merge or bounce back . Can anyone help me ?

import javafx.animation.KeyFrame;
import javafx.animation.Timeline;
import javafx.application.Application;
import javafx.beans.property.DoubleProperty;
import javafx.geometry.Pos;
import javafx.scene.Node;
import javafx.stage.Stage;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.ScrollBar;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.HBox;
import javafx.scene.layout.Pane;
import javafx.scene.paint.Color;
import javafx.scene.shape.Circle;
import javafx.util.Duration;

public class MultipleBounceBall extends Application {
@Override // Override the start method in the Application class
public void start(Stage primaryStage) {
MultipleBallPane ballPane = new MultipleBallPane();
ballPane.setStyle("-fx-border-color: yellow");

Button btAdd = new Button("+");
Button btSubtract = new Button("-");
HBox hBox = new HBox(10);
hBox.getChildren().addAll(btAdd, btSubtract);
hBox.setAlignment(Pos.CENTER);

// Add or remove a ball
btAdd.setOnAction(e -> ballPane.add());
btSubtract.setOnAction(e -> ballPane.subtract());

// Pause and resume animation
ballPane.setOnMousePressed(e -> ballPane.pause());
ballPane.setOnMouseReleased(e -> ballPane.play());

// Use a scroll bar to control animation speed
ScrollBar sbSpeed = new ScrollBar();
sbSpeed.setMax(20);
sbSpeed.setValue(10);
ballPane.rateProperty().bind(sbSpeed.valueProperty());
  
BorderPane pane = new BorderPane();
pane.setCenter(ballPane);
pane.setTop(sbSpeed);
pane.setBottom(hBox);

// Create a scene and place the pane in the stage
Scene scene = new Scene(pane, 250, 150);
primaryStage.setTitle("MultipleBounceBall"); // Set the stage title
primaryStage.setScene(scene); // Place the scene in the stage
primaryStage.show(); // Display the stage
}

private class MultipleBallPane extends Pane {
private Timeline animation;

public MultipleBallPane() {
// Create an animation for moving the ball
animation = new Timeline(
new KeyFrame(Duration.millis(50), e -> moveBall()));
animation.setCycleCount(Timeline.INDEFINITE);
animation.play(); // Start animation
}

public void add() {
Color color = new Color(Math.random(),
Math.random(), Math.random(), 0.5);
getChildren().add(new Ball(30, 30, 20, color));
}
  
public void subtract() {
if (getChildren().size() > 0) {
getChildren().remove(getChildren().size() - 1);
}
}

public void play() {
animation.play();
}

public void pause() {
animation.pause();
}

public void increaseSpeed() {
animation.setRate(animation.getRate() + 0.1);
}

public void decreaseSpeed() {
animation.setRate(
animation.getRate() > 0 ? animation.getRate() - 0.1 : 0);
}

public DoubleProperty rateProperty() {
return animation.rateProperty();
}

protected void moveBall() {
for (Node node: this.getChildren()) {
Ball ball = (Ball)node;
// Check boundaries
if (ball.getCenterX() < ball.getRadius() ||
ball.getCenterX() > getWidth() - ball.getRadius()) {
ball.dx *= -1; // Change ball move direction
}
if (ball.getCenterY() < ball.getRadius() ||
ball.getCenterY() > getHeight() - ball.getRadius()) {
ball.dy *= -1; // Change ball move direction
}

// Adjust ball position
ball.setCenterX(ball.dx + ball.getCenterX());
ball.setCenterY(ball.dy + ball.getCenterY());
}
}
}

class Ball extends Circle {
private double dx = 1, dy = 1;

Ball(double x, double y, double radius, Color color) {
super(x, y, radius);
setFill(color); // Set ball color
}
}
  
/**
* The main method is only needed for the IDE with limited
* JavaFX support. Not needed for running from the command line.
*/
public static void main(String[] args) {
launch(args);
}
}

Explanation / Answer

public boolean colliding(Ball ball)
{
    float xd = position.getX() - ball.position.getX();
    float yd = position.getY() - ball.position.getY();

    float sumRadius = getRadius() + ball.getRadius();
    float sqrRadius = sumRadius * sumRadius;

    float distSqr = (xd * xd) + (yd * yd);

    if (distSqr <= sqrRadius)
    {
        return true;
    }

    return false;
}

public void resolveCollision(Ball ball)
{
    // get the mtd
    Vector2d delta = (position.subtract(ball.position));
    float d = delta.getLength();
    // minimum translation distance to push balls apart after intersecting
    Vector2d mtd = delta.multiply(((getRadius() + ball.getRadius())-d)/d);


    // resolve intersection --
    // inverse mass quantities
    float im1 = 1 / getMass();
    float im2 = 1 / ball.getMass();

    // push-pull them apart based off their mass
    position = position.add(mtd.multiply(im1 / (im1 + im2)));
    ball.position = ball.position.subtract(mtd.multiply(im2 / (im1 + im2)));

    // impact speed
    Vector2d v = (this.velocity.subtract(ball.velocity));
    float vn = v.dot(mtd.normalize());

    // sphere intersecting but moving away from each other already
    if (vn > 0.0f) return;

    // collision impulse
    float i = (-(1.0f + Constants.restitution) * vn) / (im1 + im2);
    Vector2d impulse = mtd.multiply(i);

    // change in momentum
    this.velocity = this.velocity.add(impulse.multiply(im1));
    ball.velocity = ball.velocity.subtract(impulse.multiply(im2));

}

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