JavaAlgorithms/Others/KochSnowflake.java

package Others;

import java.awt.*;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.ArrayList;
import javax.imageio.ImageIO;

/**
 * The Koch snowflake is a fractal curve and one of the earliest fractals to have been described.
 * The Koch snowflake can be built up iteratively, in a sequence of stages. The first stage is an
 * equilateral triangle, and each successive stage is formed by adding outward bends to each side of
 * the previous stage, making smaller equilateral triangles. This can be achieved through the
 * following steps for each line: 1. divide the line segment into three segments of equal length. 2.
 * draw an equilateral triangle that has the middle segment from step 1 as its base and points
 * outward. 3. remove the line segment that is the base of the triangle from step 2. (description
 * adapted from https://en.wikipedia.org/wiki/Koch_snowflake ) (for a more detailed explanation and
 * an implementation in the Processing language, see
 * https://natureofcode.com/book/chapter-8-fractals/ #84-the-koch-curve-and-the-arraylist-technique
 * ).
 */
public class KochSnowflake {

  public static void main(String[] args) {
    // Test Iterate-method
    ArrayList<Vector2> vectors = new ArrayList<Vector2>();
    vectors.add(new Vector2(0, 0));
    vectors.add(new Vector2(1, 0));
    ArrayList<Vector2> result = Iterate(vectors, 1);

    assert result.get(0).x == 0;
    assert result.get(0).y == 0;

    assert result.get(1).x == 1. / 3;
    assert result.get(1).y == 0;

    assert result.get(2).x == 1. / 2;
    assert result.get(2).y == Math.sin(Math.PI / 3) / 3;

    assert result.get(3).x == 2. / 3;
    assert result.get(3).y == 0;

    assert result.get(4).x == 1;
    assert result.get(4).y == 0;

    // Test GetKochSnowflake-method
    int imageWidth = 600;
    double offsetX = imageWidth / 10.;
    double offsetY = imageWidth / 3.7;
    BufferedImage image = GetKochSnowflake(imageWidth, 5);

    // The background should be white
    assert image.getRGB(0, 0) == new Color(255, 255, 255).getRGB();

    // The snowflake is drawn in black and this is the position of the first vector
    assert image.getRGB((int) offsetX, (int) offsetY) == new Color(0, 0, 0).getRGB();

    // Save image
    try {
      ImageIO.write(image, "png", new File("KochSnowflake.png"));
    } catch (IOException e) {
      e.printStackTrace();
    }
  }

  /**
   * Go through the number of iterations determined by the argument "steps". Be careful with high
   * values (above 5) since the time to calculate increases exponentially.
   *
   * @param initialVectors The vectors composing the shape to which the algorithm is applied.
   * @param steps The number of iterations.
   * @return The transformed vectors after the iteration-steps.
   */
  public static ArrayList<Vector2> Iterate(ArrayList<Vector2> initialVectors, int steps) {
    ArrayList<Vector2> vectors = initialVectors;
    for (int i = 0; i < steps; i++) {
      vectors = IterationStep(vectors);
    }

    return vectors;
  }

  /**
   * Method to render the Koch snowflake to a image.
   *
   * @param imageWidth The width of the rendered image.
   * @param steps The number of iterations.
   * @return The image of the rendered Koch snowflake.
   */
  public static BufferedImage GetKochSnowflake(int imageWidth, int steps) {
    if (imageWidth <= 0) {
      throw new IllegalArgumentException("imageWidth should be greater than zero");
    }

    double offsetX = imageWidth / 10.;
    double offsetY = imageWidth / 3.7;
    Vector2 vector1 = new Vector2(offsetX, offsetY);
    Vector2 vector2 =
        new Vector2(imageWidth / 2, Math.sin(Math.PI / 3) * imageWidth * 0.8 + offsetY);
    Vector2 vector3 = new Vector2(imageWidth - offsetX, offsetY);
    ArrayList<Vector2> initialVectors = new ArrayList<Vector2>();
    initialVectors.add(vector1);
    initialVectors.add(vector2);
    initialVectors.add(vector3);
    initialVectors.add(vector1);
    ArrayList<Vector2> vectors = Iterate(initialVectors, steps);
    return GetImage(vectors, imageWidth, imageWidth);
  }

  /**
   * Loops through each pair of adjacent vectors. Each line between two adjacent vectors is divided
   * into 4 segments by adding 3 additional vectors in-between the original two vectors. The vector
   * in the middle is constructed through a 60 degree rotation so it is bent outwards.
   *
   * @param vectors The vectors composing the shape to which the algorithm is applied.
   * @return The transformed vectors after the iteration-step.
   */
  private static ArrayList<Vector2> IterationStep(ArrayList<Vector2> vectors) {
    ArrayList<Vector2> newVectors = new ArrayList<Vector2>();
    for (int i = 0; i < vectors.size() - 1; i++) {
      Vector2 startVector = vectors.get(i);
      Vector2 endVector = vectors.get(i + 1);
      newVectors.add(startVector);
      Vector2 differenceVector = endVector.subtract(startVector).multiply(1. / 3);
      newVectors.add(startVector.add(differenceVector));
      newVectors.add(startVector.add(differenceVector).add(differenceVector.rotate(60)));
      newVectors.add(startVector.add(differenceVector.multiply(2)));
    }

    newVectors.add(vectors.get(vectors.size() - 1));
    return newVectors;
  }

  /**
   * Utility-method to render the Koch snowflake to an image.
   *
   * @param vectors The vectors defining the edges to be rendered.
   * @param imageWidth The width of the rendered image.
   * @param imageHeight The height of the rendered image.
   * @return The image of the rendered edges.
   */
  private static BufferedImage GetImage(
      ArrayList<Vector2> vectors, int imageWidth, int imageHeight) {
    BufferedImage image = new BufferedImage(imageWidth, imageHeight, BufferedImage.TYPE_INT_RGB);
    Graphics2D g2d = image.createGraphics();

    // Set the background white
    g2d.setBackground(Color.WHITE);
    g2d.fillRect(0, 0, imageWidth, imageHeight);

    // Draw the edges
    g2d.setColor(Color.BLACK);
    BasicStroke bs = new BasicStroke(1);
    g2d.setStroke(bs);
    for (int i = 0; i < vectors.size() - 1; i++) {
      int x1 = (int) vectors.get(i).x;
      int y1 = (int) vectors.get(i).y;
      int x2 = (int) vectors.get(i + 1).x;
      int y2 = (int) vectors.get(i + 1).y;

      g2d.drawLine(x1, y1, x2, y2);
    }

    return image;
  }

  /** Inner class to handle the vector calculations. */
  private static class Vector2 {

    double x, y;

    public Vector2(double x, double y) {
      this.x = x;
      this.y = y;
    }

    @Override
    public String toString() {
      return String.format("[%f, %f]", this.x, this.y);
    }

    /**
     * Vector addition
     *
     * @param vector The vector to be added.
     * @return The sum-vector.
     */
    public Vector2 add(Vector2 vector) {
      double x = this.x + vector.x;
      double y = this.y + vector.y;
      return new Vector2(x, y);
    }

    /**
     * Vector subtraction
     *
     * @param vector The vector to be subtracted.
     * @return The difference-vector.
     */
    public Vector2 subtract(Vector2 vector) {
      double x = this.x - vector.x;
      double y = this.y - vector.y;
      return new Vector2(x, y);
    }

    /**
     * Vector scalar multiplication
     *
     * @param scalar The factor by which to multiply the vector.
     * @return The scaled vector.
     */
    public Vector2 multiply(double scalar) {
      double x = this.x * scalar;
      double y = this.y * scalar;
      return new Vector2(x, y);
    }

    /**
     * Vector rotation (see https://en.wikipedia.org/wiki/Rotation_matrix)
     *
     * @param angleInDegrees The angle by which to rotate the vector.
     * @return The rotated vector.
     */
    public Vector2 rotate(double angleInDegrees) {
      double radians = angleInDegrees * Math.PI / 180;
      double ca = Math.cos(radians);
      double sa = Math.sin(radians);
      double x = ca * this.x - sa * this.y;
      double y = sa * this.x + ca * this.y;
      return new Vector2(x, y);
    }
  }
}