Archimedean spiral

Archimedean spiral is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The Archimedean spiral is a spiral named after the Greek mathematician Archimedes. It can be described by the equation:

$\,r=a+b\theta$

with real numbers a and b.

Draw an Archimedean spiral.

Java

Works with: Java version 8

<lang java>import java.awt.*; import static java.lang.Math.*; import javax.swing.*;

public class ArchimedeanSpiral extends JPanel {

   public ArchimedeanSpiral() {
       setPreferredSize(new Dimension(640, 640));
       setBackground(Color.white);
   }

   void drawGrid(Graphics2D g) {
       g.setColor(new Color(0xEEEEEE));
       g.setStroke(new BasicStroke(2));

       double angle = toRadians(45);

       int w = getWidth();
       int center = w / 2;
       int margin = 10;
       int numRings = 8;

       int spacing = (w - 2 * margin) / (numRings * 2);

       for (int i = 0; i < numRings; i++) {
           int pos = margin + i * spacing;
           int size = w - (2 * margin + i * 2 * spacing);
           g.drawOval(pos, pos, size, size);

           double ia = i * angle;
           int x2 = center + (int) (cos(ia) * (w - 2 * margin) / 2);
           int y2 = center - (int) (sin(ia) * (w - 2 * margin) / 2);

           g.drawLine(center, center, x2, y2);
       }
   }

   void drawSpiral(Graphics2D g) {
       g.setStroke(new BasicStroke(2));
       g.setColor(Color.orange);

       double degrees = toRadians(0.1);
       double center = getWidth() / 2;
       double end = 360 * 2 * 10 * degrees;
       double a = 0;
       double b = 20;
       double c = 1;

       for (double theta = 0; theta < end; theta += degrees) {
           double r = a + b * pow(theta, 1 / c);
           double x = r * cos(theta);
           double y = r * sin(theta);
           plot(g, (int) (center + x), (int) (center - y));
       }
   }

   void plot(Graphics2D g, int x, int y) {
       g.drawOval(x, y, 1, 1);
   }

   @Override
   public void paintComponent(Graphics gg) {
       super.paintComponent(gg);
       Graphics2D g = (Graphics2D) gg;
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
               RenderingHints.VALUE_ANTIALIAS_ON);

       drawGrid(g);
       drawSpiral(g);
   }

   public static void main(String[] args) {
       SwingUtilities.invokeLater(() -> {
           JFrame f = new JFrame();
           f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
           f.setTitle("Archimedean Spiral");
           f.setResizable(false);
           f.add(new ArchimedeanSpiral(), BorderLayout.CENTER);
           f.pack();
           f.setLocationRelativeTo(null);
           f.setVisible(true);
       });
   }

}</lang>