Chapter 18 Exercise 27, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

18.27 (Koch snowflake fractal)
The text presented the Sierpinski triangle fractal. In this exercise, you
will write a program to display another fractal, called the Koch snowflake,
named after a famous Swedish mathematician.
A Koch snowflake is created as follows:

1. Begin with an equilateral triangle, which is considered to be the Koch
fractal of order (or level) 0, as shown in Figure 18.14a.
2. Divide each line in the shape into three equal line segments and draw
an out- ward equilateral triangle with the middle line segment as
the base to create a Koch fractal of order 1, as shown in Figure 18.14b.
3. Repeat

import javafx.collections.ObservableList;
import javafx.geometry.Point2D;
import javafx.scene.Node;
import javafx.scene.layout.Pane;
import javafx.scene.paint.Color;
import javafx.scene.shape.Circle;
import javafx.scene.shape.Line;
import javafx.scene.text.Text;

import java.util.ArrayList;

public class PaneCollection {


    public static void drawArrowLine(double x1, double y1, double x2,   double y2, Pane pane) {
        drawArrowLine(x1, y1, x2, y2, pane, 15);
    }

    public static void drawArrowLine(double x1, double y1, double x2,   double y2, Pane pane, int length) {
        drawArrowLine(new Line(x1, y1, x2, y2), pane, length);
    }

    public static void drawArrowLine(Line line, Pane pane) {
        drawArrowLine(line, pane, 15);
    }

    public static void drawArrowLine(Line line, Pane pane, int length) {
        ObservableList<Node> list = pane.getChildren();

        double arctan = Math.atan(slope(line));
        double set45 = (line.getStartX() > line.getEndX()) ? 1.57 / 2 : -1.57 * 1.5;

        list.add(line);
        list.add(new Line(line.getEndX(), line.getEndY(),
                (line.getEndX() + Math.cos(arctan - set45) * length),
                (line.getEndY() + Math.sin(arctan - set45) * length)));
        list.add(new Line(line.getEndX(), line.getEndY(),
                (line.getEndX() + Math.cos(arctan + set45) * length),
                (line.getEndY() + Math.sin(arctan + set45) * length)));
    }

    public static double slope(Line line) {
        return (line.getStartY() - line.getEndY()) / (line.getStartX() - line.getEndX());
    }

    public static double distance(double x1, double y1, double x2, double y2) {

        return Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
    }

    public static double distance(Line line) {
        return distance(line.getStartX(), line.getStartY(), line.getEndX(), line.getEndY());
    }

    public static MyPoint getCenterPoint(Line line) {

        return new MyPoint(
                (line.getStartX() + line.getEndX()) / 2,
                (line.getStartY() + line.getEndY()) / 2);
    }

    public static void drawPointCounter(Pane pane, Point2D[] points) {
        int counter = 1;

        for (Point2D point : points) {
            Circle temp = new Circle(point.getX(), point.getY(), 5, Color.TRANSPARENT);
            Text text = new Text(point.getX(), point.getY(), "" + counter++);
            pane.getChildren().addAll(temp, text);
        }
    }

    public static boolean containsPoint(ArrayList<Point2D> points, double x, double y) {
        for (Point2D p : points) {
            if (p.getX() == x && p.getY() == y) return true;
        }
        return false;
    }

    public static boolean removePoint(ArrayList<Point2D> points, double x, double y) {

        int index = 0;
        for (Point2D p : points) {
            if (p.getX() == x && p.getY() == y) {
                points.remove(index);
                return true;
            }
            index++;
        }
        return false;
    }

    public static Line copyLine(Line l) {
        return new Line(l.getStartX(), l.getStartY(), l.getEndX(), l.getEndY());
    }


}

import javafx.application.Application;
import javafx.collections.ObservableList;
import javafx.geometry.Insets;
import javafx.geometry.Pos;
import javafx.scene.Node;
import javafx.scene.Scene;
import javafx.scene.control.Label;
import javafx.scene.control.TextField;
import javafx.scene.input.KeyCode;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.HBox;
import javafx.scene.layout.Pane;
import javafx.scene.shape.Line;
import javafx.stage.Stage;

public class Exercise_27 extends Application {

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

    @Override
    public void start(Stage primaryStage) throws Exception {


        KochSnowflakePane pane = new KochSnowflakePane();

        Scene scene = new Scene(pane);
        primaryStage.setScene(scene);
        primaryStage.setTitle("Koch Snowflake");
        primaryStage.show();
    }

    private class KochSnowflakePane extends BorderPane {

        Pane pane = new Pane();
        ObservableList<Node> list = pane.getChildren();

        int order;

        KochSnowflakePane() {

            TextField tfOrder = new TextField();
            tfOrder.setAlignment(Pos.BASELINE_RIGHT);
            tfOrder.setPrefColumnCount(4);
            Label lblOrder = new Label("Enter an order: ");

            tfOrder.setOnKeyPressed(e -> {


                if (e.getCode() == KeyCode.ENTER) {
                    try {
                        order = Integer.parseInt(tfOrder.getText());
                    } catch (NumberFormatException ex) {
                        order = 0;
                        tfOrder.setText("0");
                    }
                } else if (e.getCode() == KeyCode.UP) {
                    order = Integer.parseInt(tfOrder.getText()) + 1;
                    tfOrder.setText(order + "");

                } else if (e.getCode() == KeyCode.DOWN) {
                    order = Math.max(Integer.parseInt(tfOrder.getText()) - 1, 0);
                    tfOrder.setText(order + "");

                }
                draw();

            });

            tfOrder.setText("0");
            pane.setPrefSize(400, 400);
            setCenter(pane);
            setMargin(pane, new Insets(100));

            HBox hBox = new HBox(20, lblOrder, tfOrder);
            hBox.setAlignment(Pos.BASELINE_CENTER);
            hBox.setPadding(new Insets(30, 10, 10, 10));
            setBottom(hBox);
            draw();
        }

        private void draw() {
            list.clear();
            double length = 400;

            Line l1 = new Line(200, 0, 200 + length * Math.cos(1 * (Math.PI * 2 / 6)), 0 + length * Math.sin(1 * (Math.PI * 2 / 6)));
            Line l2 = new Line(l1.getEndX(), l1.getEndY(), l1.getEndX() - length, l1.getEndY());
            Line l3 = new Line(l2.getEndX(), l2.getEndY(), l1.getStartX(), l1.getStartY());
            list.addAll(l1, l2, l3);
            draw(order);
        }

        private void draw(int order) {

            if (order == 0)
                return;

            Line[] lines = new Line[list.size()];
            for (int i = 0; i < list.size(); i++) {
                lines[i] = (Line) list.get(i);
            }

            for (Line line : lines) {
                createTriangle(line);
            }
            draw(order - 1);

        }

        private void createTriangle(Line line) {

            double distance = PaneCollection.distance(line) / 3;

            double dy = (line.getStartY() - line.getEndY());
            double dx = (line.getEndX() - line.getStartX());
            double theta = Math.atan2(dy, dx);

            double x1 = line.getStartX() + distance * Math.cos(theta);
            double y1 = line.getStartY() - distance * Math.sin(theta);

            double x2 = line.getEndX() + distance * Math.cos(theta + Math.toRadians(180));
            double y2 = line.getEndY() - distance * Math.sin(theta + Math.toRadians(180));

            double x3 = x2 + distance * Math.cos(theta + Math.toRadians(120));
            double y3 = y2 - distance * Math.sin(theta + Math.toRadians(120));

            Line l1 = new Line(line.getStartX(), line.getStartY(), x1, y1);
            Line l2 = new Line(x2, y2, line.getEndX(), line.getEndY());
            Line l3 = new Line(l1.getEndX(), l1.getEndY(), x3, y3);
            Line l4 = new Line(l3.getEndX(), l3.getEndY(), x2, y2);

            pane.getChildren().remove(line);
            list.addAll(l1, l2, l3, l4);

        }


    }

}