import java.awt.*;
import java.awt.event.*;
import java.applet.*;
import java.awt.geom.*;
import java.math.*;

public class Renormalize {

    /**In this file we study the renorm sets defined
       relative to the two parameters s and t=R(s).
       The s-parameter is considered the range and
       the t-parameter is considered the domain.*/


    /**Here is the renormalization map*/

    public static double renormReal(double s) {
	if(s>.5) return(1-s);
	double t=.5/s;
	t=t-Math.floor(t);
	return(t);
    }



    public static PolygonWrapper renormDomain(double s) {
	double t=renormReal(s);
	PolygonWrapper P=new PolygonWrapper();
	if(s>.5) P=renormDomain1(t);
	if(s<.5) P=renormDomain2(t);
	return(P);
    }

    public static PolygonWrapper renormRange(double s) {
	if(s>.5) return(renormRange1(s));
	return(renormRange2(s));
    }

    public static Complex renormMap(double s,Complex z) {
	if(s>.5) return(renormMap1(s,z));
	return(renormMap2(s,z));
    }



    public static Complex renormMap1(double s,Complex z) {
	double t=renormReal(s);
	Complex z0=new Complex(-.5-.5/t,-.5);
	Complex w=Complex.convexAverage(t/s,z0,z);
	w.x=w.x+.5/t-.5/s;
	return(w);
    }

    public static PolygonWrapper renormRange1(double s) {
	double t=renormReal(s);
	PolygonWrapper P=renormDomain1(t);
	for(int i=0;i<P.count;++i) P.z[i]=renormMap(s,P.z[i]);
	return(P);
    }

    public static Complex renormMap2(double s,Complex z) {
	double t=renormReal(s);
	Complex z0=new Complex(-.5/t-.5,-.5);
	Complex w=Complex.primitiveRoot(8);
        Complex Z=Complex.convexAverage(t*Math.sqrt(2),z0,z);
	Z=Complex.minus(Z,z0);
	Z=Complex.times(w,Z.conjugate());
	Z=Complex.plus(Z,z0);
	Z.x=Z.x+.5/t-.5/s;
	return(Z);
    }

    public static PolygonWrapper renormRange2(double s) {
	double t=renormReal(s);
	PolygonWrapper P=renormDomain2(t);
	for(int i=0;i<P.count;++i) P.z[i]=renormMap(s,P.z[i]);
	return(P);
    }


    public static PolygonWrapper renormDomain1(double t) {
	PolygonWrapper P=new PolygonWrapper();
	P.count=4;
	double u=.5/t;
	P.z[0]=new Complex(0,0);
	P.z[1]=new Complex(u,0);
	P.z[2]=new Complex(u,1);
	P.z[3]=new Complex(1,1);
	Complex z=new Complex(-.5/t-.5,-.5);
	for(int i=0;i<P.count;++i) P.z[i]=Complex.plus(P.z[i],z);
	return(P);
    }

    public static PolygonWrapper renormDomain2(double t) {
	PolygonWrapper P=new PolygonWrapper();
	P.count=5;
	P.z[0]=new Complex(0,0);
	P.z[1]=new Complex(1/t,0);
	P.z[2]=new Complex(1/t+.5,.5);
	P.z[3]=new Complex(1/t,1);
	P.z[4]=new Complex(1,1);
	Complex z=new Complex(-.5/t-.5,-.5);
	for(int i=0;i<P.count;++i) P.z[i]=Complex.plus(P.z[i],z);
	return(P);
    }



}