import java.applet.Applet;
import java.awt.*;
import java.awt.event.*;



public class test1 extends Applet {
    PixCanvas P;
    ControlCanvas C;

	      public void init() { 
                  setBackground(Color.white);
		  P=new PixCanvas();
		  P.resize(500,500);
		  P.setBackground(Color.black);
		  C=new ControlCanvas(P);
		  C.resize(305,500);
		  C.setBackground(Color.blue);
		  this.add(C);
		  this.add(P);

	      }
}





class DBCanvas extends Canvas {
    
    public void update(Graphics g) {
        Graphics g2;
        Image offscreen = null;
        offscreen = createImage(size().width, size().height);
        g2 = offscreen.getGraphics();
        paint(g2);
        g.drawImage(offscreen, 0, 0, this);
	offscreen.flush();
    }
}



class PixCanvas extends DBCanvas {
    Tiling T;

    PixCanvas() {
	T=new Tiling(5,2,0);
	T=T.reset();
    }

    public void paint(Graphics g) {
	g.translate(250,250);
	g.setColor(Color.blue);
	g.drawOval(-1,-1,2,2);

	T.render(g);
	
    }






}



class ControlCanvas extends DBCanvas implements MouseListener {
    VSlider[] V=new VSlider[20];
    ListenSquare L[]=new ListenSquare[10];
    int tiles;
    ViewInteger v1,v2,v3;
    PixCanvas P;

    ControlCanvas(PixCanvas P) {     
       this.P=P; 
       addMouseListener(this);
       Color[] C=new Color[5];
       C[1]=Color.black;
       C[2]=Color.green;
       C[3]=Color.yellow;
       C[4]=new Color(0,0,200);
       tiles=5;
       v1=new ViewInteger(0);
       v2=new ViewInteger(0); 
       v3=new ViewInteger(0);


	for(int i=1;i<=10;++i) {
	    V[i]=new VSlider(20*i-15,155,15,320,310,310,C,"");
	}

	L[1]=new ListenSquare(215,170,15,15,Color.green,"-",1);
        L[2]=new ListenSquare(275,170,15,15,Color.green,"+",2); 
        L[3]=new ListenSquare(215,270,15,15,Color.green,"-",3);
        L[4]=new ListenSquare(275,270,15,15,Color.green,"+",4);
        L[5]=new ListenSquare(215,220,15,15,Color.green,"-",5);
        L[6]=new ListenSquare(275,220,15,15,Color.green,"+",6);
        L[7]=new ListenSquare(275,355,15,15,Color.green,"",7);
        L[8]=new ListenSquare(275,315,15,15,Color.green,"",8);
        L[9]=new ListenSquare(275,335,15,15,Color.green,"",9);
    }

    public void paint(Graphics g) {
	g.setColor(Color.white); 
        g.setFont(new Font("TimesRoman",Font.PLAIN,15));
	g.drawString("circles",230,327);
        g.drawString("lines",235,347);
        g.drawString("both",236,367);
        g.drawString("# of layers",223,265);
        g.drawString("# of tiles",226,165);
        g.drawString("# of twists",222,215);
	v1.x=P.T.n;
	v1.render(252,183,Color.yellow,g);
	v2.x=P.T.k;
        v2.render(252,233,Color.yellow,g);
        v3.x=P.T.layers;
        v3.render(252,283,Color.yellow,g);
	g.setColor(Color.yellow);
        g.setFont(new Font("TimesRoman",Font.PLAIN,20));
        g.setColor(Color.black);
        g.fillRect(205,385,93,110);
	g.fillRect(5,5,294,145);
	g.setColor(Color.yellow);
	g.drawRect(205,385,93,110);
        g.drawRect(5,5,294,145);
	g.setColor(Color.white);
	g.drawString("Rich:",212,405);
        g.drawString("Applet 30",212,425);
        g.setFont(new Font("TimesRoman",Font.PLAIN,15));
        g.drawString("Conformal",220,455);
        g.drawString("Rectangle",220,470);
        g.drawString("Tilings",220,485);
	for(int i=1;i<=tiles;++i) V[i].render(g);
	for(int i=1;i<=9;++i) L[i].render(g);
        g.setFont(new Font("TimesRoman",Font.PLAIN,12));
	g.drawString("A conformal rectangle is a quadrilateral with 2 properties:",10,20);
	g.drawString("1. It is inscribed in a circle     2. One of the complex affine",10,35);
	g.drawString("maps which identifies opposite edges is linear.  This linear",10,50);
	g.drawString("map is called the holonomy.  Up to similarity a conformal",10,65);
        g.drawString("rectangle is determined by its holonomy and the cross ratio",10,80);
	g.drawString("of its vertices.  This applets draws conformal rectangle",10,95);
	g.drawString("tilings of the punctured plane.  The sliders let you select",10,110);
	g.drawString("the various cross ratios and the other buttons let you select",10,125);
	g.drawString("the topology.  The holonomy is found by Newton's method.",10,140);



    }


    public void mouseReleased(MouseEvent e) {}
    public void mousePressed(MouseEvent e)  {}
    public void mouseEntered(MouseEvent e)  {}
    public void mouseExited(MouseEvent e)   {}
    public void mouseClicked(MouseEvent e)  {
        e.consume();
	Point p=new Point();
	p.x=e.getX();
	p.y=e.getY();
	int test1=0;
	for(int i=1;i<=tiles;++i) {
	    if(V[i].inside(p)==1) test1=i;
	    if(V[i].inside(p)==2) { 
		P.T.sp[i]=1-P.T.sp[i];P.repaint();
		V[i].mode=1-V[i].mode;
		V[i].redo(this);
	    }
	}





	if(test1>0) {
	    Tiling S=new Tiling(P.T.n,P.T.k,P.T.mode);
	    S.k=P.T.k;
	    S.n=P.T.n;
	    S.layers=P.T.layers;
	    S.l=P.T.l;
	    for(int i=1;i<=P.T.n;++i) {
		S.sp[i]=P.T.sp[i];
		S.m[i]=P.T.m[i];
	    }
            S.m[test1]=(p.y-V[test1].pos2)/50.0;
	    S=S.improve(10);
            Complex z=new Complex();
	    z=S.error();
	    if(z.norm(z)<.0001) {
		P.T=S;
	        V[test1].pos=p.y;
	        V[test1].redo(this);
		P.repaint();
	    }
	}






	int test2=0;
        for(int i=1;i<=9;++i) {
	    if(L[i].inside(p)==1) test2=i;
	}

	if(test2==1) {
	    if(tiles>3) --tiles;
	    P.T.n=tiles;
	    for(int i=1;i<=10;++i) {
              V[i]=V[i].reset();
	      V[i].mode=0;
	    }
	    P.T=new Tiling(tiles,0,P.T.mode);
	    P.T=P.T.reset();
	    P.repaint();
	    repaint(0,150,300,350);
	}

        if(test2==2) {
	    if(tiles<10) ++tiles;   
	    P.T.n=tiles;
            for(int i=1;i<=10;++i) {
              V[i]=V[i].reset();
	      V[i].mode=0;
	    }
            P.T=new Tiling(tiles,0,P.T.mode);
	    P.T=P.T.reset();
	    P.repaint();
	    repaint(0,150,300,350);
	}

	if(test2==3) {
	    if(P.T.layers>0) --P.T.layers;
	    P.repaint();  repaint(150,150,150,350);
	}


	if(test2==4) {
	    if(P.T.layers<35) ++P.T.layers;
	    P.repaint();  repaint(150,150,150,350);
	}

	if(test2==5) {   
            for(int i=1;i<=10;++i) {
              V[i]=V[i].reset();
	      V[i].mode=0;
	      V[i].redo(this);
	    }

	    if(P.T.k>0) --P.T.k;
	    P.T=P.T.reset();
	    P.T.layers=P.T.n;
	    P.repaint();
	    repaint(150,150,150,350);
	}

	if(test2==6) {  
            for(int i=1;i<=10;++i) {
               V[i]=V[i].reset();
	       V[i].mode=0;
               V[i].redo(this);
	    }
	    if(P.T.k<P.T.n) ++P.T.k;
	    P.T=P.T.reset();
	    P.repaint();  
            repaint(150,150,150,350);
	}

	if(test2==7) {
	    P.T.mode=0;
	    P.repaint();
	}

	if(test2==8) {
	    P.T.mode=1;
	    P.repaint();
	}

	if(test2==9) {
	    P.T.mode=2;
	    P.repaint();
	}

    }
}






class Tiling {
    double[] m=new double[20];
    int[] sp=new int[20];
    int n,layers,k;
    Complex l;
    int mode;
    Tiling(int n,int k,int mo) {
	this.n=n;
	this.k=k;
	for(int i=1;i<=n;++i) {m[i]=0.0;sp[i]=0;}
	l=new Complex(0,0);
	layers=n;
	this.mode=mo;
    }



    void render(Graphics g) {
	int i;
	ConformalRectangle[] R=new ConformalRectangle[11];
	for(i=1;i<=n;++i) R[i]=new ConformalRectangle();
	R[1].v=new Complex(.25,0.0);
	for(i=1;i<=n;++i) {
            R[i].l=l;
            R[i].m=m[i];
	    if(i<n)   R[i+1].v=R[i].v.times(R[i].v,R[i].keyVertex());
	}
	if(mode==0) {

	for(i=1;i<=n;++i) {
		if(sp[i]==1)  R[i].lineRender2(g,Color.yellow,layers,1);
	}
	for(i=1;i<=n;++i) R[i].circleRender2(g,Color.blue,layers);
	for(i=1;i<=n;++i) R[i].lineRender2(g,Color.yellow,layers,0);
	}

	if(mode==1) {
            for(i=1;i<=n;++i) R[i].circleRender2(g,Color.blue,layers);
	}

	if(mode==2) {
        for(i=1;i<=n;++i) {
		if(sp[i]==1)  R[i].lineRender2(g,Color.yellow,layers,1);
	}
        for(i=1;i<=n;++i) R[i].lineRender2(g,Color.yellow,layers,0);
	}

    }

    Tiling reset() {
	Tiling S=new Tiling(n,k,mode);
	for(int i=1;i<=n;++i) {S.m[i]=0;sp[i]=0;}
	S.l=new Complex(1.0,0.0);
	S.layers=layers;
	S=S.improve(10);
	return(S);
    }



    Tiling perturb(Complex z) {
	Tiling S=new Tiling(n,k,mode);
	for(int i=1;i<=n;++i) {
           S.m[i]=m[i];
	   S.sp[i]=sp[i];
	}
	S.layers=layers;
	S.l=S.l.plus(l,z);
	return(S);
    }


    Complex error() {
        ConformalRectangle[] R=new ConformalRectangle[11];
        Complex[] Z=new Complex[11];
	for(int i=1;i<=n;++i) {
          R[i]=new ConformalRectangle();
	  R[i].l=l;
	  R[i].m=m[i];
	  R[i].v.x=1.0;
          R[i].v.y=0.0;
	  Z[i]=new Complex();
	  Z[i]=R[i].keyVertex();
	  Z[i]=Z[i].log(Z[i]);
	}

	Complex L=new Complex();
	L=l.log(l);
	Complex total=new Complex();
	for(int j=1;j<=n;++j) total=total.plus(total,Z[j]);
	for(int j=1;j<=k;++j) total=total.minus(total,L);
	total.y=total.y-2.0*Math.PI;
	return(total);
    }

    Complex diffError() {
	Tiling S1=this;
	Complex z=new Complex(.001,0);
	Tiling S2=S1.perturb(z);
	Complex z1=S1.error();
	Complex z2=S2.error();
	Complex z3=new Complex();
	z3=z3.minus(z1,z2);
	z3.x=1000*z3.x;
	z3.y=1000*z3.y;
	return(z3);
    }



    Tiling improve() {
	Tiling S=new Tiling(n,k,mode);
	Complex z1=new Complex();
	Complex z2=new Complex();
	Complex z3=new Complex();
	z1=error();
	z2=diffError();
	z3=z3.divide(z1,z2);
	if(z3.norm(z3)>50.0) z3=new Complex(0,0);
	S=perturb(z3);
	return(S);
    }

    Tiling improve(int w) {
	Tiling S=this;
	for(int i=1;i<=w;++i) S=S.improve();
	return(S);
    }




}














class ConformalRectangle {
    Complex v,l;
    double m;

    ConformalRectangle(Complex v,Complex l,double m) {
	this.v=v;
	this.l=l;
	this.m=m;
    }

    ConformalRectangle() {
	this.v=new Complex();
	this.l=new Complex();
	this.m=0.0;
    }

    Complex keyVertex() {
	Complex w,b,X;
	Complex[] z=new Complex[10];
	for(int i=1;i<=9;++i) z[i]=new Complex();
	b=new Complex();
	X=new Complex();
	X.x=Math.exp(m);
	X.y=0.0;
	z[1].x=-2.0;
	z[1].y=0.0;
	z[2]=z[2].times(z[1],l);
	z[3]=X;
	z[4]=z[4].times(z[2],z[3]);
	z[5]=z[5].times(X,z[5].times(l,l));
	z[6]=z[6].plus(z[2],z[3]);
	z[7]=z[6].plus(z[6],z[4]);
	z[8]=z[8].plus(z[7],z[5]);
	z[9]=z[9].quadraticRoot(l,z[8],l);
	return(z[9]);
    }

    void lineRender(Graphics g,Color C,int n,int special) {
	Complex[] z=new Complex[6];
	for(int i=1;i<=5;++i) z[i]=new Complex();
	z[1]=v;
	z[5]=z[1];
	z[2]=z[2].times(l,v);
	z[4]=z[4].times(v,keyVertex());
	z[3]=z[3].times(l,z[4]);
	for(int k=1;k<=n;++k) {
	    for(int j=1;j<=5;++j) {
		z[j]=l.times(l,z[j]);
	    }
	}
	int x1=0;
	int y1=0;
	int x2=0;
	int y2=0;
	int x3=0;
	int y3=0;
	x3=(int)(.5*z[1].x+.5*z[3].x);
        y3=(int)(.5*z[1].y+.5*z[3].y);
	if(z[1].norm(z[1])<750) {
	 if(special==1) {
         g.setColor(new Color(0,0,100));
	 for(int j=1;j<=4;++j) {
	    x1=(int)(z[j].x);
	    y1=(int)(z[j].y);      
            x2=(int)(z[j+1].x);
	    y2=(int)(z[j+1].y);
            int[] xpoints={x1,x2,x3};
	    int[] ypoints={-y1,-y2,-y3};
	    g.fillPolygon(xpoints,ypoints,3);
	 }}

	 if(special==0) {
         g.setColor(C); 
         for(int j=1;j<=4;++j) {
	    x1=(int)(z[j].x);
	    y1=(int)(z[j].y);      
            x2=(int)(z[j+1].x);
	    y2=(int)(z[j+1].y);
	    g.drawLine(x1,-y1,x2,-y2);
	 }}
	}
    }



    void circleRender(Graphics g,Color C,int n) {
	g.setColor(C);
	Complex[] z=new Complex[6];
	for(int i=1;i<=5;++i) z[i]=new Complex();
	z[1]=v;
	z[2]=z[2].times(l,v);
	z[4]=z[4].times(v,keyVertex());
	z[3]=z[3].times(l,z[4]);
	z[5]=z[5].center(z[1],z[2],z[4]);
        for(int k=1;k<=n;++k) {
	    for(int j=1;j<=5;++j) {
		z[j]=l.times(l,z[j]);
	    }
	}
	double d=z[5].norm(z[5].minus(z[5],z[1]));
	int x1=(int)(z[5].x-d);
	int y1=(int)(z[5].y-d);
	int x2=(int)(2*d);
	int y2=(int)(2*d);
	g.drawOval(x1,-y1-(int)(2*d),x2,y2);
    }

    void lineRender2(Graphics g,Color C,int n,int special) {
	for(int i=0;i<=n;++i) lineRender(g,C,i,special);
    }

    void circleRender2(Graphics g,Color C,int n) {
	for(int i=0;i<=n;++i) circleRender(g,C,i);
    }

}












class Complex {
    double x,y;

    Complex() {
	    this.x=0.0;
	    this.y=0.0;
    }

    Complex(double x,double y) {
	    this.x=x;
	    this.y=y;
    }

    Complex random() {
	Complex z=new Complex();
	z.x=2.0*Math.random()-1.0;
	z.y=2.0*Math.random()-1.0;
	return(z);
    }

    Complex randomUnit() {
	Complex z=new Complex();
	z=z.random();
	z=z.unit(z);
	return(z);
    }


    double norm(Complex z) {
	double d;
	d=z.x*z.x+z.y*z.y;
	d=Math.sqrt(d);
	return(d);
    }

    Complex unit(Complex z) {
	Complex w=new Complex();
	double d;
	d=z.norm(z);
        w.x=z.x/d;
	w.y=z.y/d;
	return(w);
    }


    Complex plus(Complex z1,Complex z2) {
	Complex w= new Complex();
	w.x=z1.x+z2.x;
        w.y=z1.y+z2.y;
	return(w);
    }

    Complex minus(Complex z1,Complex z2) {
	Complex w= new Complex();
	w.x=z1.x-z2.x;
        w.y=z1.y-z2.y;
	return(w);
    }

    Complex times(Complex z1,Complex z2) {
	Complex w= new Complex();
	w.x=z1.x*z2.x-z1.y*z2.y;
        w.y=z1.x*z2.y+z1.y*z2.x;
	return(w);
    }

    Complex inverse(Complex z) {
	Complex w=new Complex();
	double d;
	d=z.x*z.x+z.y*z.y;
	w.x=z.x/d;
	w.y=-z.y/d;
	return(w);
    }


    Complex divide(Complex z1,Complex z2) {
	Complex w= new Complex();
	w=w.times(z1,w.inverse(z2));
	return(w);
    }

    Complex conjugate(Complex z) {
	Complex w=new Complex();
	w.x=x;
	w.y=-y;
	return(w);
    }

    double disc(Complex z) {
	double d1,d2,d3,d4,d5;
	d1=norm(z);d3=d1*d1;
        d1=d1*d1*d1*d1;
	Complex zzz=z.times(z.times(z,z),z);
	d2=zzz.x;
	d3=d1-8.0*d2+18.0*d3-27.0;
	return(d3);
    }


    Complex log(Complex z) {
	Complex w=new Complex();
	double d1=z.norm(z);
        double d2=Math.atan2(z.y,z.x);
	w.x=Math.log(d1);
	w.y=d2;
	return(w);
    }





    Complex squareRoot(Complex z) {
	Complex w=new Complex();
	double d1,d2;
	d1=z.norm(z);
	d1=Math.sqrt(d1);
	d2=Math.atan2(z.y,z.x);
	d2=.5*d2;
	w.x=d1*Math.cos(d2);
	w.y=d1*Math.sin(d2);
	return(w);
    }




    Complex quadraticRoot(Complex a,Complex b,Complex c) {
	Complex z[]=new Complex[20];
	for(int i=1;i<=11;++i) z[i]=new Complex();
	z[3]=z[3].times(b,b);
	z[4]=a.times(a,c);
	z[4].x=4*z[4].x;
	z[4].y=4*z[4].y;
	z[5]=z[4].minus(z[3],z[4]);
	z[6]=z[5].squareRoot(z[5]);
	z[7]=z[6].minus(z[6],b);
	z[8]=z[7].divide(z[7],a.plus(a,a));
        z[9]=z[6].plus(z[6],b);
	z[9].x=-z[9].x;
	z[9].y=-z[9].y;
        z[10]=z[9].divide(z[9],a.plus(a,a));
	z[11]=z[8];
	if(z[8].y<0) z[11]=z[10];
	return(z[11]);
    }


   Complex center(Complex z1,Complex z2,Complex z3) {
   double x1,x2,y1,y2,x3,y3;
   double den;
   Complex z=new Complex(); 
   x1=z1.x;
   y1=z1.y;
   x2=z2.x;
   y2=z2.y;
   x3=z3.x;
   y3=z3.y;
   den=2.0*(x2*y1-x3*y1-x1*y2+x3*y2+x1*y3-x2*y3);
   z.x=(x2*x2*y1-x3*x3*y1-x1*x1*y2+x3*x3*y2 -
   y1*y1*y2+y1*y2*y2+x1*x1*y3-x2*x2*y3 +
   y1*y1*y3-y2*y2*y3-y1*y3*y3+y2*y3*y3)/den;
   z.y=(x1*x1*x2-x1*x2*x2-x1*x1*x3+x2*x2*x3 +
   x1*x3*x3-x2*x3*x3+x2*y1*y1-x3*y1*y1-
   x1*y2*y2+x3*y2*y2+x1*y3*y3-x2*y3*y3)/den;
   return(z);
   }




    void print() {
	System.out.println(x+" + "+y+" I");
    }
}











class ListenSquare {
    int x,y,w,h;
    Color C;
    String S;
    int v;
    ListenSquare(int x,int y,int w,int h,Color C,String S,int v) {
	this.x=x;
	this.y=y;
	this.h=h;
	this.w=w;
	this.C=C;
	this.S=S; 
	this.v=v;
    }

    void render(Graphics g) {
	g.setColor(Color.black);
        g.fillRect(x,y,w,h);
	g.setColor(C);
	g.drawRect(x,y,w,h);
	g.setColor(Color.white);
        g.setFont(new Font("TimesRoman",Font.PLAIN,13));
	g.drawString(S,x+5,y+13);
    }

    int inside(Point p) {
	int test=0;
	if((p.x>x)&&(p.x<x+w)&&(p.y>y)&&(p.y<y+h)) test=1;
	return(test);
    }

}






class VSlider {
    int x,y,w,h;
    int pos,pos2;
    Color[] C;
    String S;
    int mode;
    VSlider(int x,int y,int w,int h,int pos,int pos2,Color[] C,String S) {
	this.x=x;
	this.y=y;
	this.h=h;
	this.w=w;
	this.pos=pos;
	this.pos2=pos2;
	this.C=C;
	this.S=S; 
	mode=0;
    }

    void render(Graphics g) {
	g.setColor(C[1]);
	g.fillRect(x,y,w,h);  
        if(mode==1) g.setColor(C[4]);
	g.fillRect(x,y+h+5,w,w);
	g.setColor(C[2]);
        g.drawRect(x,y,w,h);
        g.drawRect(x,y+h+5,w,w);
	g.setColor(C[3]);
	g.drawRect(x+1,pos-1,w-2,2); 
        g.setColor(C[2]);    
        g.setFont(new Font("TimesRoman",Font.PLAIN,13));
	g.drawString(S,x,y+h+12);
    }

    int inside(Point p) {
	int test=0;
	if((p.x>x)&&(p.x<x+w)&&(p.y>y)&&(p.y<y+h)) test=1;
	if((p.x>x)&&(p.x<x+w)&&(p.y>y+h+5)&&(p.y<y+h+5+w)) {
           test=2;
	}
	return(test);
    }

    void redo(ControlCanvas C) {
	C.repaint(x,y,w,h+w+5);
    }

    VSlider reset() {
	VSlider V=this;
	V.pos=this.pos2;
	return(V);
    }

}




class ViewInteger {
    int x;
    ViewInteger(int x) {
	this.x=x;
    }

    void render(int u, int v, Color C,Graphics g) {
	int y=x;
	int place=0;
	while(y>0) {
	    int z=y-10*(y/10);
	    g.setColor(C);
	    char ch=(char)(z+48);
            Character CH1=new Character(ch);
	    g.drawString(CH1.toString(),u-place,v);
	    place=place+8;
	    y=(y-z)/10;
	}
	if(x==0) g.drawString("0",u,v);
    }
}