如何生成以Java为中心的随机多边形？

import javafx.application.Application;
import javafx.scene.Group;
import javafx.scene.Scene;
import javafx.scene.paint.Color;
import javafx.scene.shape.Polygon;
import javafx.stage.Stage;

public class RandomPolygonGenerator extends Application {

    private static final int SIDES = 6; // 多边形边数
    private static final double RADIUS = 100; // 多边形半径

    @Override
    public void start(Stage primaryStage) {
        Group root = new Group();
        Scene scene = new Scene(root, 400, 400);

        // 计算顶点坐标
        double centerX = scene.getWidth() / 2;
        double centerY = scene.getHeight() / 2;
        double[] points = calculatePolygonPoints(centerX, centerY, SIDES, RADIUS);

        // 创建多边形对象
        Polygon polygon = new Polygon(points);
        polygon.setFill(Color.TRANSPARENT);
        polygon.setStroke(Color.BLACK);

        root.getChildren().add(polygon);

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

    private double[] calculatePolygonPoints(double centerX, double centerY, int sides, double radius) {
        double[] points = new double[sides * 2];
        for (int i = 0; i < sides; i++) {
            double angle = 2 * Math.PI * i / sides;
            points[i * 2] = centerX + radius * Math.cos(angle);
            points[i * 2 + 1] = centerY + radius * Math.sin(angle);
        }
        return points;
    }

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