/* the ngon (regular polygon)  is composed of 2n congruent triangles. 
  center angle is 360/2n.
  base is opposite the center angle.
  height is adjacent to center angle.
 */

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

public class PolygonsCircle extends JApplet {

    public void init() {
    	double b_in, h_in, areaT_in, areaNgon_in;
    	double b_circum, h_circum, areaT_circum, areaNgon_circum ;
    	DecimalFormat	d3 = new DecimalFormat ("0.000");
    		
	System.out.println("INscribed and Circumscribed regular polygons of unit circle");
        System.out.println("N   IN:    b    h     At    An   %c"+
        	           "      OUT:  b     h     At    An   %c");

    	for (int ngon=3; ngon<20; ngon++) {
    	    b_in = Math.sin(Math.toRadians(180.0/ngon));
    	    h_in = Math.sqrt(1 - b_in*b_in);
    	    areaT_in = 0.5 * b_in * h_in;
    	    areaNgon_in = areaT_in * 2 * ngon;
 
    	    b_circum = Math.tan(Math.toRadians(180.0/ngon));
    	    h_circum = 1;
    	    areaT_circum = 0.5 * b_circum * h_circum;
    	    areaNgon_circum = areaT_circum * 2 * ngon;   	    
    	    	
    	    System.out.println(""+ngon+"        "+d3.format(b_in)+" "+d3.format(h_in)+" "+
    	    	               d3.format(areaT_in)+" "+d3.format(areaNgon_in)+" "+d3.format((areaNgon_in/Math.PI))+
    	    	                "        "+d3.format(b_circum)+" "+d3.format(h_circum)+" "+
    	    	               d3.format(areaT_circum)+" "+d3.format(areaNgon_circum)+" "+d3.format((areaNgon_circum/Math.PI)));
    	}
    }
    
    public void paint (Graphics g) {
    	int w = getWidth();
    	int h = getHeight();    
    	int r = w<=h ? w/2 : h/2;   //min of width height
    	int x, y, xn, yn;
    	Color [] colors = {Color.WHITE, Color.BLACK, 
    		           Color.DARK_GRAY,Color.GRAY,Color.LIGHT_GRAY,
    		           Color.RED, Color.GREEN, Color.BLUE,
    	                   Color.CYAN, Color.YELLOW, Color.MAGENTA,
    	                   Color.ORANGE, Color.PINK};
    	                   
    	g.drawOval(0,0,2*r,2*r);
    	
    	for (int ngon=12; ngon>=3; ngon--) {
    	    double angle = 360.0/ngon;
    	    Polygon poly = new Polygon();
    	    x = r + r;
    	    y = r;
    	    //Point p = new Point(x,y);
    	    poly.addPoint(x,y);
    	    for (int points=1; points<=ngon; points++) {
    	    	xn = (int)(Math.cos(Math.toRadians(angle*points)) * r + r);
    	    	yn = (int)(Math.sin(Math.toRadians(angle*points)) * r + r);
    	    	//g.drawLine(x,y, xn,yn);
    	    	x = xn;
    	    	y = yn;
    	    	poly.addPoint(x,y);
    	    }
    	    g.setColor(colors[ngon-2]);
    	    g.fillPolygon(poly);
    	}   
    	
    }
}