// Spirals
// archimedean:  r=aT
// logarithmic/equiangular: log r=aT
// hyperbolic/reciprocal: rT=a
// parabolic/Fermat: r^2=aT


import java.awt.*;
import javax.swing.*;
import java.text.*;	

public class Spirals extends JApplet {

    double a;
    
    public void init() {
    	String input;
    	
        input = JOptionPane.showInputDialog("a","1.0");
        a = Double.parseDouble(input);
    }
    
    public void paint (Graphics g) {
    	int w = getWidth();
    	int h = getHeight();  
    	double r, x, y;  
	int stopAngle=720;  //??
	int xTranslate, yTranslate;
	xTranslate = w / 2;
	yTranslate = -h / 2;
	
	//Archimedean spiral
	for (int theta=1; theta<stopAngle; theta++) {
	    r = a * theta;
	    x = r * Math.cos(Math.toRadians(theta));
	    y = r * Math.sin(Math.toRadians(theta));
	    g.drawLine((int)x+xTranslate,h-(int)y+yTranslate, 
	    	       (int)x+xTranslate,h-(int)y+yTranslate);
	    //System.out.println(""+x+" "+y);
	}

	//logarithmic/equiangular spiral
	g.setColor(Color.RED);
	for (int theta=1; theta<stopAngle; theta++) {
	    r = Math.exp(a * theta);
	    x = r * Math.cos(Math.toRadians(theta));
	    y = r * Math.sin(Math.toRadians(theta));
	    g.drawLine((int)x+xTranslate,h-(int)y+yTranslate, 
	    	       (int)x+xTranslate,h-(int)y+yTranslate);
	    //System.out.println(""+x+" "+y);
	}	
	
	//hyperbolic/reciprocal spiral
	g.setColor(Color.GREEN);
	for (int theta=1; theta<stopAngle; theta++) {
	    r = a / theta;
	    x = r * Math.cos(Math.toRadians(theta));
	    y = r * Math.sin(Math.toRadians(theta));
	    g.drawLine((int)x+xTranslate,h-(int)y+yTranslate, 
	    	       (int)x+xTranslate,h-(int)y+yTranslate);
	    //System.out.println(""+x+" "+y);
	}

	//parabolic/Fermat spiral
	g.setColor(Color.MAGENTA);
	for (int theta=1; theta<stopAngle; theta++) {
	    r = Math.sqrt(a * theta);
	    x = r * Math.cos(Math.toRadians(theta));
	    y = r * Math.sin(Math.toRadians(theta));
	    g.drawLine((int)x+xTranslate,h-(int)y+yTranslate, 
	    	       (int)x+xTranslate,h-(int)y+yTranslate);
	    //System.out.println(""+x+" "+y);
	}

    }
}