reposition object in circle

Question

As you can see on the image, I have a p1 and p2 objects with (x,y) coordinates which I know the values, and I know radius of all these circle objects.

However, I want to calculate new position x,y which would be p3 center point. Basically, as you can see it's p2 position + radius.

I am doing this for java game which is based on libgdx. I would appreciate any math or java language directions/examples.

Answer 1

See code comments for explanation.

import java.awt.*;
import java.awt.geom.Ellipse2D;
import java.awt.geom.Line2D;
import java.awt.geom.Point2D;
import javax.swing.*;

class CenteredCircle extends Ellipse2D.Double {
    CenteredCircle(Point2D.Double p, double radius) {
        super(p.x - radius, p.y - radius, 2 * radius, 2 * radius);
    }   
}

public class CircleDemo extends JFrame {
    public CircleDemo() {
            int width = 640; int height = 480;
            setSize(new Dimension(width, height));
            setLocationRelativeTo(null);
            setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            setVisible(true);
    
            JPanel p = new JPanel() {
                @Override
                public void paintComponent(Graphics g) {
                    Graphics2D g2d = (Graphics2D) g;
                    // center p1
                    Point2D.Double p1 = new Point2D.Double(getSize().width/2, getSize().height/2);
                    double radius = 130.0;

                    // big circle
                    Shape circle2 = new CenteredCircle(p1, radius);
                    g2d.draw(circle2);                    

                    // 12 small circles
                    for (int angle = 0; angle < 360; angle += 30) {
                        // this is the magic part
                        // a polar co-ordinate has a length and an angle
                        // by changing the angle we rotate
                        // the transformed co-ordinate is the center of the small circle
                        Point2D.Double newCenter = polarToCartesian(radius, angle);
                        // draw line just for visualization
                        Line2D line = new Line2D.Double(p1.x, p1.y, p1.x + newCenter.x, p1.y+ newCenter.y);
                        g2d.draw(line);
                        // draw the small circle
                        Shape circle = new CenteredCircle(
                            new Point2D.Double(p1.x + newCenter.x, p1.y + newCenter.y),
                            radius/4);
                        g2d.draw(circle);  
                    }
                }
            };
            setTitle("Circle Demo");
            getContentPane().add(p);
        }
    public static void main(String arg[]) {
        SwingUtilities.invokeLater(new Runnable() {
            @Override
            public void run() {
                new CircleDemo();
            }
        });
    }    
    static Point2D.Double polarToCartesian(double r, double theta) {
        theta = (theta * Math.PI) / 180.0; // multiply first, then divide to keep error small
        return new Point2D.Double(r * Math.cos(theta), r * Math.sin(theta));
    }
    // not needed, just for completeness
    public static Point2D.Double cartesianToPolar(double x, double y) {
        return new Point2D.Double(Math.sqrt(x * x + y * y), (Math.atan2(y, x) * 180) / Math.PI);
    }    
}