example of how to plot polar functions including a cool formula for describing spiral arms of galaxies

PolarFunctionPlotter.java

import static java.lang.Math.*;

import java.awt.Color;
import java.awt.Graphics;
import java.awt.Image;
import java.awt.Point;
import java.awt.image.BufferedImage;

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


public class PolarFunctionPlotter {
	public static void main(String[] args) {
		PolarFunctionPlotter plotter = new PolarFunctionPlotter(512, 512);
		plotter.setForeground(Color.white);
		plotter.setBackground(Color.black);
		plotter.clear();

		// polar rose
		plotter.setForeground(Color.pink);
		plotter.setZoom(60);
		plotter.setResolution(1024);
		plotter.plot(new PolarFunction() {
			@Override public double compute(double t) {
				return 4 * cos(8 * t + 3);
			}
		});

		// limacon
		plotter.setForeground(Color.yellow);
		plotter.setZoom(40);
		plotter.setResolution(128);
		plotter.plot(new PolarFunction() {
			@Override public double compute(double t) {
				return 2 + 3 * sin(t);
			}
		});

		// spiral arm given by r = A / log(B*tan(t/2*N))
		// props to Harry I. Ringermacher and Lawrence R. Mead
		// http://arxiv.org/pdf/0908.0892 (warning: it's a PDF)
		plotter.setZoom(20);
		plotter.setForeground(Color.red);
		plotter.plot(new PolarFunction() {
			@Override public double compute(double t) {
				return 8 / log(0.5 * tan(t / (2 * 4)));
			}
		});

		final JFrame frame = new JFrame("PolarFunctionPlotterTest");
		frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
		frame.getContentPane().add(new JLabel(new ImageIcon(plotter.getCanvas())));
		frame.pack();
		frame.setLocationRelativeTo(null);
		frame.setVisible(true);
	}

	public static interface PolarFunction {
		public double compute(double t);
	}

	private double zoom;
	private double resolution;
	private int width;
	private int height;
	private Color background;
	private Color foreground;
	private final BufferedImage canvas;
	private final Point origin;

	public PolarFunctionPlotter(int width, int height) {
		zoom = 10;
		resolution = 32;
		foreground = Color.black;
		background = Color.white;
		canvas = new BufferedImage(width, height, BufferedImage.TYPE_4BYTE_ABGR);
		origin = new Point(width / 2, height / 2);
		this.width = width;
		this.height = height;
	}

	public void clear() {
		final Graphics g = canvas.getGraphics();
		g.setColor(background);
		g.fillRect(0, 0, width, height);
	}

	public void plot(PolarFunction fn) {
		final Graphics g = canvas.getGraphics();
		g.setColor(foreground);
		final double step = 1 / resolution;
		Point last = null;
		for (double t = 0; t <= 2 * Math.PI; t+= step) {
			final double r = zoom * fn.compute(t);
			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;
		}
	}

	public double getZoom() {
		return zoom;
	}

	public void setZoom(double zoom) {
		this.zoom = zoom;
	}

	public double getResolution() {
		return resolution;
	}

	public void setResolution(double resolution) {
		this.resolution = resolution;
	}

	public int getWidth() {
		return width;
	}

	public void setWidth(int width) {
		this.width = width;
	}

	public int getHeight() {
		return height;
	}

	public void setHeight(int height) {
		this.height = height;
	}

	public Color getBackground() {
		return background;
	}

	public void setBackground(Color background) {
		this.background = background;
	}

	public Color getForeground() {
		return foreground;
	}

	public void setForeground(Color foreground) {
		this.foreground = foreground;
	}

	public Image getCanvas() {
		return this.canvas;
	}
}