import java.applet.Applet;
import java.awt.*;
import java.awt.event.*;
import java.applet.*;
import java.awt.geom.*;
import java.math.*;
import java.util.Random;




public class AuxDraw {


    public static GeneralPath getArrow(Complex z1,Complex z2,double d) {
	GeneralPath gp=new GeneralPath();
	gp.moveTo((float)(z1.x),(float)(z1.y));
	gp.lineTo((float)(z2.x),(float)(z2.y));

	gp.moveTo((float)(z2.x),(float)(z2.y));
	Complex w=new Complex();
	w=Complex.minus(z1,z2);
	w=w.unit();
	double c=Math.cos(Math.PI/6);
	double s=Math.sin(Math.PI/6);
	w=Complex.times(w,new Complex(d*c,d*s));
	w=Complex.plus(z2,w);
	gp.lineTo((float)(w.x),(float)(w.y));

	gp.moveTo((float)(z2.x),(float)(z2.y));
	w=new Complex();
	w=Complex.minus(z1,z2);
	w=w.unit();
                  c=Math.cos(11*Math.PI/6);
	s=Math.sin(11*Math.PI/6);
	w=Complex.times(w,new Complex(d*c,d*s));
	w=Complex.plus(z2,w);
	gp.lineTo((float)(w.x),(float)(w.y));

	return(gp);
    }

    public static GeneralPath disk(Complex z,double r, int N) {
	GeneralPath gp=new GeneralPath();
	for(int k=0;k<N;++k) {
	    double t=2.0*Math.PI*k/N;
	    double c=z.x+r*Math.cos(t);
	    double s=z.y+r*Math.sin(t);
	    if(k==0) gp.moveTo((float)(c),(float)(s));
	    if(k!=0) gp.lineTo((float)(c),(float)(s));
	}
	gp.closePath();
	return(gp);
    }

}