Java Algorithms How to - Convert Plot polar function onto cartesian grid








Question

We would like to know how to convert Plot polar function onto cartesian grid.

Answer

import static java.lang.Math.PI;
import static java.lang.Math.cos;
import static java.lang.Math.log;
import static java.lang.Math.round;
import static java.lang.Math.sin;
import static java.lang.Math.tan;
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import java.awt.Color;
import java.awt.Graphics;
import java.awt.Point;
import java.awt.image.BufferedImage;

import javax.swing.ImageIcon;
import javax.swing.JFrame;
import javax.swing.JLabel;

public class Main {
  public static void main(String[] args) {
    final int width = 512;
    final int height = 512;
    BufferedImage img = new BufferedImage(width, height,
        BufferedImage.TYPE_4BYTE_ABGR);
    Graphics g = img.getGraphics();
    g.setColor(Color.black);
    g.fillRect(0, 0, width, height);
    g.setColor(Color.white);
    final double A = 8;
    final double B = 0.5;
    final double N = 4;
    final double scale = 128;
    final double zoom = 50;
    final double step = 1 / scale;
    Point last = null;
    final Point origin = new Point(width / 2, height / 2);

    for (double t = 0; t <= 2 * PI; t += step) {
      final double r = zoom * polarFunction(t, A, B, N);
      final int x = (int) round(r * cos(t));
      final int y = (int) round(r * sin(t));
      Point next = new Point(x, y);
      if (last != null) {
        g.drawLine(origin.x + last.x, origin.y + last.y, origin.x + next.x,
            origin.y + next.y);
      }
      last = next;
    }

    JFrame frame = new JFrame();
    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.getContentPane().add(new JLabel(new ImageIcon(img)));
    frame.pack();
    frame.setVisible(true);
  }
  public static double polarFunction(double t, double A, double B, double N) {
    return A / log(B * tan(t / (2 * N)));
  }
}