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

public class test1 extends Applet {
    DisplayCanvas C;
    GroupSelector G;
    public void init() { 
        C=new DisplayCanvas();   
        G=new GroupSelector(C);
	C=C.add(G);
	C.setSize(300,552);
	C.setBackground(Color.black);
	add(G);
	add(C);
        setBackground(Color.black);
    }
    public void paint(Graphics g) { }
}

 


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




class DisplayCanvas extends DBCanvas implements MouseListener,MouseMotionListener {
    GroupSelector X;
    int init;
    String[] St=new String[200];
    int pos;
    ListenSquare scroll;
    int SCROLL;


    DisplayCanvas() {
	init=0;
	for(int i=1;i<=199;++i) St[i]="";
	pos=0;
	addMouseListener(this);
	addMouseMotionListener(this);
	scroll=new ListenSquare(281,120,19,20);
	SCROLL=0;

	St[0]="(drag the blue square to scroll the text.)";
	St[1]="This applet lets you investigate the complex";
	St[2]="hyperbolic reflection triangle groups.";
	St[3]="Such a group is specified by choosing";
	St[4]="a triple points p1,p2,p3 in CH^2.";
	St[5]="Here CH^2 is the unit ball in C^2,";
	St[6]="Equipped with a certain Riemannian";
	St[7]="metric which is invariant under the group";
	St[8]="of complex projective automorphisms.";
	St[10]="Once these points are chosen, there";
	St[11]="are 3 complex lines C1,C2,C3 such that";
	St[12]="C1 contains p2,p3;";
	St[13]="C2 contains p3,p1;";
	St[14]="C3 contains p1,p2;";
	St[15]="The type of the triangle group is (a1,a2,a3),";
	St[16]="Where the angle between C1 and C2 is Pi/a3";
	St[17]="Where the angle between C2 and C3 is Pi/a1";
	St[18]="Where the angle between C3 and C1 is Pi/a2";
	St[19]="The case of interest is when a1,a2,a3";
	St[20]="are all integers and (1/a1)+(1/a2)+(1/a3)<1";

	St[22]="Using the red,green,blue buttons at the";
	St[23]="bottom of the applet you can select a1,a2,a3";
	St[24]="subject to the constraints that 2<a1,a2,a3<1000.";
	St[25]="Once these values are selected, there is,";
	St[26]="up to isometry a 1-parameter family of";
	St[27]="possible triangles.";

	St[29]="Using the isometries we can normalize so that";
	St[30]="p1=(0,0)";
	St[31]="p2=(a,0), with 0<a<1";
	St[32]="p3=b.v, where b is complex and v=(cos(a1),sin(a1)).";
	St[33]="The big picture give a graphics representation";
	St[34]="these points:";
	St[35]="the horizontal yellow line is (a,0).";
	St[36]="the red dot is the point b";
	St[37]="the red edge is the vector v";
	St[38]="the blue circle is an extra piece of data";
	St[39]="which records some of the structure";
	St[40]="underlying our construction of these";
	St[41]="triangles.";

	St[43]="The purple 'parameter' bar lets you select";
	St[44]="the parameter, as follows:";
	St[45]="The left end of the parameter corresponds";
	St[46]="to the critical parameter-more on this below.";
	St[47]="Somewhere before the right end corresponds";
	St[48]="the totally real parameter-more on this below..";
	St[49]="When you select a parameter that does";
	St[50]="not correspond to an actual triangle";
	St[51]="the word `error' appears.";

	St[53]="Once C1,C2,C3 are selected we have unique";
	St[54]="complex reflections I1,I2,I3.  Here I1 is";
	St[55]="an isometry of CH^2 which fixes C1.";
	St[56]="Likewise for I1 and I2. These maps are unique.";
	St[57]="The group generated by I1,I2,I3 is a complex";
	St[58]="hyperbolic reflection triangle group.";
	St[59]="Two triangles are isometric iff the";
	St[60]="corresponding groups are conjugate.";
	St[61]="Thus the isometry classes of triangles";
	St[62]="are bijective with the conjugacy classes";
	St[63]="triangle groups.  By constructing the";
	St[64]="triangle we construct the triangle group.";

	St[66]="Now we can explain the special parameters.";
	St[67]="The totally real parameter is the parameter";
	St[68]="such that all three points lie in a totally";
	St[69]="real slice of CH^2. This means that the";
	St[70]="corresponding triangle is isometric to";
	St[71]="a triangle which lies in R^2 intersect CH^2.";
	St[72]="The critical parameter is the smallest";
	St[73]="parameter with the following property.";
	St[74]="For all larger parameters, all words of";
	St[75]="length 3 and 4 in the generators";
	St[76]="are hyperbolic elements.";

	St[78]="The applet lets you choose up to 6 words.";
	St[79]="Once you select a word and a triangle";
	St[80]="The applet computes the discriminant of";
	St[81]="the trace of the word.";
	St[82]="The discriminant of the trace of the word";
	St[83]="is positive when the word is hyperbolic,";
	St[84]="and negative when the word is elliptic";
	St[85]="When the discriminant is 0 the word";
	St[86]="could be either parabolic or elliptic.";
	St[87]="The applet displays the discriminant of";
	St[88]="the trace of the word to the right of the word.";

	St[90]="Two things you can check using the applet:";
	St[91]="1. The discriminant of the trace of";
	St[92]="any given word seems to be monotone in";
	St[93]="the parameter, if the angles are held fixed.";
	St[94]="2. For the range of parameters considered,";
	St[95]="every elliptic element is is conjugate to";
	St[96]="a word of length 2.  In other words";
	St[97]="The representation of the triangle group";
	St[98]="carries infinite order words to words which";
	St[99]="are either parabolic or loxodromic.";
	St[100]="I don't know how to prove these to items.";
	St[101]="The second item would establish the main";
	St[102]="discreteness conjectures for the complex";
	St[103]="hyperbolic triangle groups.";

	St[105]="I've given a very sketchy explanation here.";
	St[106]="If this explanation doesn't make much";
	St[107]="sense, or if it does make sense but";
	St[108]="you want more information, you can";
	St[109]="can download my survey article";
	St[110]="entitled `complex hyperbolic triangle groups";
	St[111]="published in the 2002 proceedings of the";
	St[112]="International Congress of Mathematicians.";
	St[113]="You might also want to read";
	St[114]="Anna Pratoussevitch's article entitled";
	St[115]="'Traces in Complex Hyperbolic Triangle Groups'";
	St[116]="published in Geometriae Dedicata.";

	St[117]="This applet is far from perfected, though";
	St[118]="it is an improvement over the previous";
	St[119]="version.  I hope to periodically improve";
	St[120]="the applet until it is user-friendly,";
	St[121]="comprehensive, and actually useful as";
	St[122]="a research tool.";

	St[124]="I would welcome any comments or suggestions.";
    }

    DisplayCanvas add(GroupSelector X) {
	DisplayCanvas D=this;
	D.X=X;
	return(D);
    }

    public void paint(Graphics g) {
        g.setColor(Color.black);
	g.fillRect(0,126,500,500);
	g.setColor(new Color(0,0,100));
	g.fillRect(280,120,20,498);
        g.setColor(Color.yellow);
        g.drawRect(0,120,280,431);


	scroll.render(g,new Color(100,100,255));

	g.setColor(Color.white);
        g.setFont(new Font("TimesRoman",Font.PLAIN,12));
	double ev=0.0;
	g.setColor(Color.yellow);
	g.drawRect(0,0,300,120);
	for(int i=1;i<=6;++i) {
	       g.setColor(Color.blue);
               g.fillRect(5, 20*i-18,300,16);
	       ev=evaluate(i);
	       doubleRender(ev,g,10,20*i-5);
	}
	g.clipRect(0,120,300,500);
	g.translate(0,-pos);
	for(int i=0;i<=199;++i) {
	    g.drawString(St[i],10,15*i+190);
	}
	g.translate(0,pos);


    }

    public void mouseExited(MouseEvent e) {}
    public void mouseEntered(MouseEvent e) {}
    public void mouseClicked(MouseEvent e) {}
    public void mousePressed(MouseEvent e) {
	e.consume();
	Point p=new Point();
	p.x=e.getX();
	p.y=e.getY();
	SCROLL=scroll.inside(p);
    }
    public void mouseReleased(MouseEvent e) {}
    public void mouseMoved(MouseEvent e) {}
    public void mouseDragged(MouseEvent e) {
	e.consume();
	Point p=new Point();
	p.x=e.getX();
	p.y=e.getY();
	if((p.y>=130)&&(SCROLL==1)) {
	    pos=4*(p.y-130);
	    scroll.y=p.y-10;
	    repaint();
	}
    }



    void doubleRender(double d,Graphics g,int x,int y) {
	g.setColor(Color.white);
	if(d>1000000000) g.drawString(">1000000000",x,y);
	if((d>=0)&&(d<=1000000000)) {
	    Integer I=new Integer(0);
	    int big=(int)(d);
	    g.drawString(I.toString(big),x+10,y);
	    double rem=d-big;
	    int small=(int)(rem*100000);
	    g.fillOval(x+135,y,2,2);	    
            g.drawOval(x+135,y,2,2);
            g.drawString(I.toString(small),x+140,y);
	}

	if(d<0) {
            Integer I=new Integer(0);
	    int big=(int)(-d+.000001);
	    g.drawString("-",x,y);
	    g.drawString(I.toString(big),x+10,y);
	}


    }

     double evaluate(int i) {
	    double ev=X.G.evaluate(X.W[i].W);
	    return(ev);
     }

}








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);
    }

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























class Vector {
    Complex x,y,z;
    Vector() {
	this.x=new Complex();
	this.y=new Complex();
	this.z=new Complex();
    }

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


    Vector plus(Vector v1,Vector v2) {
	Vector w=new Vector();
	w.x=w.x.plus(v1.x,v2.x);
        w.y=w.y.plus(v1.y,v2.y);
        w.z=w.z.plus(v1.z,v2.z);
	return(w);
    }

    Vector minus(Vector v1,Vector v2) {
	Vector w=new Vector();
	w.x=w.x.minus(v1.x,v2.x);
        w.y=w.y.minus(v1.y,v2.y);
        w.z=w.z.minus(v1.z,v2.z);
	return(w);
    }


    Complex dot21(Vector v,Vector w) {
	Complex z[]=new Complex[5];
	for(int i=1;i<=4;++i) z[i]=new Complex();
	z[1]=z[1].times(v.x,w.x.conjugate(w.x));
        z[2]=z[2].times(v.y,w.y.conjugate(w.y));
        z[3]=z[3].times(v.z,w.z.conjugate(w.z));
	z[4]=z[4].minus(z[4].plus(z[1],z[2]),z[3]);
	return(z[4]);
    }

    Complex dot30(Vector v,Vector w) {
	Complex z[]=new Complex[5];
	for(int i=1;i<=4;++i) z[i]=new Complex();
	z[1]=z[1].times(v.x,w.x.conjugate(w.x));
        z[2]=z[2].times(v.y,w.y.conjugate(w.y));
        z[3]=z[3].times(v.z,w.z.conjugate(w.z));
	z[4]=z[4].plus(z[4].plus(z[1],z[2]),z[3]);
	return(z[4]);
    }

    Complex dot30real(Vector v,Vector w) {
	Complex z[]=new Complex[5];
	for(int i=1;i<=4;++i) z[i]=new Complex();
	z[1]=z[1].times(v.x,w.x);
        z[2]=z[2].times(v.y,w.y);
        z[3]=z[3].times(v.z,w.z);
	z[4]=z[4].plus(z[4].plus(z[1],z[2]),z[3]);
	return(z[4]);
    }

    Vector random() {
	Vector v=new Vector();
	v.x=v.x.random();
	v.y=v.y.random();
	v.z=v.z.random();
	return(v);
    }


    double norm21(Vector v) {
	Complex z=new Complex();
	z=v.dot21(v,v);
	return(z.x);
    }


    double norm30() {
	Complex z=new Complex();
	z=this.dot30(this,this);
	return(z.x);
    }


    double dist21(Vector v,Vector w) {
        Complex z[]=new Complex[6];
	for(int i=1;i<=5;++i) z[i]=new Complex();
	z[1]=v.dot21(v,w);
	z[2]=v.dot21(w,v);
	z[3]=v.dot21(v,v);
	z[4]=v.dot21(w,w);
	z[5]=z[1].divide(z[1].times(z[1],z[2]),z[3].times(z[3],z[4]));
	return(z[5].x);
    }

    Vector scale(Complex z,Vector v) {
	Vector w=new Vector();
	w.x=z.times(z,v.x);
        w.y=z.times(z,v.y);
        w.z=z.times(z,v.z);
	return(w);
    }

    Vector box(Vector v,Vector w) {
	Vector x=new Vector();
	Complex z1=new Complex();
	Complex z2=new Complex();
	Complex z3=new Complex();
	z1=z1.minus(z1.times(v.z,w.y),z1.times(v.y,w.z));
        z2=z1.minus(z1.times(v.x,w.z),z1.times(v.z,w.x));
        z3=z1.minus(z1.times(v.x,w.y),z1.times(v.y,w.x));
	x.x=z1.conjugate(z1);
	x.y=z2.conjugate(z2);
	x.z=z3.conjugate(z3);
	return(x);
    }

    Vector reflect(Vector w) {
	Vector v1=new Vector();
	Vector v2=new Vector();
	Complex z1=new Complex();
	Complex z2=new Complex();
	Complex z3=new Complex();
        Vector v3=this;
	z1=v3.dot21(w,v3);
	z2=v3.dot21(v3,v3);
	z3=z1.divide(z1,z2);
	z3.x=2.0*z3.x;
	z3.y=2.0*z3.y;
	v1=v1.scale(z3,v3);
	v2=v2.minus(v1,w);
	return(v2);
    }

    Vector e1() {
	Vector v=new Vector();
	v.x.x=1.0;v.x.y=0.0; 
	v.y.x=0.0;v.y.y=0.0;
	v.z.x=0.0;v.z.y=0.0;
	return(v);
    }

    Vector e2() {
	Vector v=new Vector();
	v.x.x=0.0;v.x.y=0.0; 
	v.y.x=1.0;v.y.y=0.0;
	v.z.x=0.0;v.z.y=0.0;
	return(v);
    }

    Vector e3() {
	Vector v=new Vector();
	v.x.x=0.0;v.x.y=0.0; 
	v.y.x=0.0;v.y.y=0.0;
	v.z.x=1.0;v.z.y=0.0;
	return(v);
    }



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


    void realPrint() {
	System.out.println(x.x+" "+y.x+" "+z.x);
    }




}

















class Matrix {
    Vector x,y,z;
    Matrix() {
	this.x=new Vector();
	this.y=new Vector();
	this.z=new Vector();
    }

    Matrix(Vector x,Vector y,Vector z) {
	this.x=x;
	this.y=y;
	this.z=z;
    }

    Matrix identity() {
	Matrix m=new Matrix();
	m.x=m.x.e1();
	m.y=m.y.e2();
	m.z=m.z.e3();
	return(m);
    }


    Matrix transpose(Matrix m) {
	Matrix w=new Matrix();
	w.x.x=m.x.x;
	w.x.y=m.y.x;
	w.x.z=m.z.x;
        w.y.x=m.x.y;
	w.y.y=m.y.y;
	w.y.z=m.z.y;
        w.z.x=m.x.z;
	w.z.y=m.y.z;
	w.z.z=m.z.z;
	return(w);
    }



    Matrix times(Matrix m1,Matrix m2) {
	Matrix w=new Matrix();
	Vector v=new Vector();
	Matrix mm2=m2.transpose(m2);
	w.x.x=v.dot30real(m1.x,mm2.x);
        w.x.y=v.dot30real(m1.x,mm2.y);
        w.x.z=v.dot30real(m1.x,mm2.z);
	w.y.x=v.dot30real(m1.y,mm2.x);
        w.y.y=v.dot30real(m1.y,mm2.y);
        w.y.z=v.dot30real(m1.y,mm2.z);
	w.z.x=v.dot30real(m1.z,mm2.x);
        w.z.y=v.dot30real(m1.z,mm2.y);
        w.z.z=v.dot30real(m1.z,mm2.z);
	return(w);
    }



    Matrix reflect(Vector v) {
	Matrix m=new Matrix();
	m.x=v.reflect(v.e1());
        m.y=v.reflect(v.e2());
        m.z=v.reflect(v.e3());
	m=m.transpose(m);
	return(m);
    }


    Complex trace() {
	Complex z=new Complex();
	Matrix m=this;
	z=z.plus(m.x.x,z.plus(m.y.y,m.z.z));
	return(z);
    }


    double disc() {
	double d;
	Complex z=this.trace();
	d=z.disc(z);
	return(d);
    }

    void print() {
	Matrix m=this;
	m.x.print();
	m.y.print();
	m.z.print();
    }

}



class TriangleGroup {
    Matrix I1,I2,I3;
    Triangle T;
    TriangleGroup() {
	I1=new Matrix();
	I2=new Matrix();
	I3=new Matrix();
    }

   TriangleGroup(Matrix I1,Matrix I2,Matrix I3) {
	this.I1=I1;
        this.I2=I2;
        this.I3=I3;
    }

    TriangleGroup(Triangle T) {
	this.T=T;
	double a=T.a;
	Complex b=T.b;
	double x=T.x;
        Vector v1=new Vector();
	Vector v2=new Vector();
	Vector v3=new Vector();
	v1.z.x=1.0;
	v2.x.x=a;
	v2.z.x=1.0;
	v3.x.x=b.x*Math.cos(Math.PI/x);
        v3.x.y=b.y*Math.cos(Math.PI/x);
        v3.y.x=b.x*Math.sin(Math.PI/x);
        v3.y.y=b.y*Math.sin(Math.PI/x);
	v3.z.x=1.0;
	Vector c1=v1.box(v2,v3);
	Vector c2=v2.box(v3,v1);
	Vector c3=v3.box(v1,v2);
	Matrix i1=new Matrix();
        Matrix i2=new Matrix();
        Matrix i3=new Matrix();
	i1=i1.reflect(c1);
        i2=i2.reflect(c2);
        i3=i3.reflect(c3);
	I1=i1;
	I2=i2;
	I3=i3;
    }

    Vector angle(Vector v1,Vector v2,Vector v3) {
        Vector c1=v1.box(v2,v3);
	Vector c2=v2.box(v3,v1);
	Vector c3=v3.box(v1,v2);
	double d1=c1.dist21(c2,c3);
        double d2=c1.dist21(c3,c1);
        double d3=c1.dist21(c1,c2);
	Vector w=new Vector();
	w.x.x=Math.sqrt(d1);
	w.y.x=Math.sqrt(d2);
	w.z.x=Math.sqrt(d3);
	return(w);
    }


    double evaluate(Word w) {
	Matrix M=new Matrix();
	M=M.identity();
	for(int i=1;i<=w.l;++i)
	    {
	    if(w.n[i]==1) M=M.times(M,I1);
            if(w.n[i]==2) M=M.times(M,I2);
            if(w.n[i]==3) M=M.times(M,I3);
	    }
	double d=M.disc();
	return(d);
    }

    int hypTest() {
	Word[] w= new Word[4];
	for(int i=0;i<=3;++i) {
	    w[i]=new Word();
	}

	w[0].l=3;
	w[0].n[1]=1;
	w[0].n[2]=2;
	w[0].n[3]=3;

	w[1].l=4;
	w[1].n[1]=1;
	w[1].n[2]=2;
	w[1].n[3]=1;
        w[1].n[4]=3;

	w[2].l=4;
	w[2].n[1]=2;
	w[2].n[2]=1;
	w[2].n[3]=2;
        w[2].n[4]=3;

	w[3].l=4;
	w[3].n[1]=3;
	w[3].n[2]=2;
	w[3].n[3]=3;
        w[3].n[4]=1;

	int test=0;
	for(int i=0;i<=3;++i)  {
	    if(evaluate(w[i])<0.0) test=1;
	}
	return(test);
    }




}







class Triangle {
    double x,a;
    double memory;
    Complex b;
    double d;
    double PARABOLIC;
    int a1,a2,a3;

   
    Triangle () {
	this.x=0.0;
	this.a=1.0;
	this.d=0.0;
	this.b=new Complex();
	this.memory=memory;
	a1=1;
	a2=1;
	a3=1;
    }


    Triangle (int aa,int bb,int cc) {
	double C=0.0;
	double B=0.0;
	double aaa=Math.PI/aa;
        double bbb=Math.PI/bb;
	double ccc=Math.PI/cc;
        B=(Math.cos(ccc)*Math.cos(aaa) + Math.cos(bbb));
        B=B/(Math.sin(ccc)*Math.sin(aaa));
	C=(Math.cos(aaa)*Math.cos(bbb) + Math.cos(ccc));
        C=C/(Math.sin(aaa)*Math.sin(bbb));
        B=Math.sqrt(1-1/(B*B));
	C=Math.sqrt(1-1/(C*C));
	this.x=aa;
	this.a=B;
	b=new Complex();
	this.b.x=C;
	this.b.y=0;
	memory=B;
	this.d=(1.0-this.b.x)/4.0;
	a1=aa;
	a2=bb;
	a3=cc;
	PARABOLIC=parabolicParameter();
    }
   
    Vector angle() {
	TriangleGroup G=new TriangleGroup();
	Vector v1=new Vector();
	Vector v2=new Vector();
	Vector v3=new Vector();
	v1.z.x=1.0;
	v2.x.x=a;
	v2.z.x=1.0;
	v3.x.x=b.x*Math.cos(Math.PI/x);
        v3.x.y=b.y*Math.cos(Math.PI/x);
        v3.y.x=b.x*Math.sin(Math.PI/x);
        v3.y.y=b.y*Math.sin(Math.PI/x);
	v3.z.x=1.0;
	return(G.angle(v1,v2,v3));
    }



    Vector angle2() {
	Vector v=this.angle();
	v.x.x=Math.PI/Math.acos(v.x.x);
        v.y.x=Math.PI/Math.acos(v.y.x);
        v.z.x=Math.PI/Math.acos(v.z.x);
	return(v);
    }

    int match() {
	Vector V=angle2();
	Vector W=new Vector();
	W.x.x=a1;
	W.y.x=a2;
	W.z.x=a3;
	Vector X=W.minus(W,V);
	int test=1;
	double d=X.norm30();
	if(d<.000000001) test=0;
	return(test);
    }


    double lowerLimit() {
	double b1,b2,b3;
	b1=a;
	b2=Math.cos(Math.PI/a1);
	b3=Math.sin(Math.PI/a1)*Math.cos(Math.PI/a2)/Math.sin(Math.PI/a2);
	b3=b3*Math.sqrt(1.0-a*a);
	return((b2+b3)/b1);
    }
	  
    double upperLimit() {
	double b1,b2,b3;
	b1=a;
	b2=Math.cos(Math.PI/a1);
	b3=Math.sin(Math.PI/a1)*Math.cos(Math.PI/a2)/Math.sin(Math.PI/a2);
	b3=b3*Math.sqrt(1.0-a*a);
        return((b2-b3)/b1);
    }
	       

    double test(double u) {
	double d1,d2,d3,d4;
	Triangle T=this;
	double t=1.0;
	Complex z=new Complex();
	d1=lowerLimit();
	d2=upperLimit();
	d3=(d1+d2)/2.0;   /*center*/
	d4=d2-d3;         /*radius*/



	z.x=d3+d4*Math.cos(Math.PI*u);
        z.y=-d4*Math.sin(Math.PI*u);
	z=z.inverse(z);
	if(z.norm(z)<1.0) {
	    T.b=z;
	    Vector V=T.angle2();
	    t=-a3+V.z.x;
	}
	return(t);
    }


    Complex convert(double u) {
	double d1,d2,d3,d4;
	Complex z=new Complex();
	d1=lowerLimit();
	d2=upperLimit();
	d3=(d1+d2)/2.0;   /*center*/
	d4=(d2-d1)/2.0;      /*radius*/
	z.x=d3+d4*Math.cos(Math.PI*u);
        z.y=d4*Math.sin(Math.PI*u);
	z=z.inverse(z);
	return(z);
    }





    Triangle flow() {
	Triangle T=this;
	double u1=0.0;
	double u2=1.0;
	double u3=0.5;
	double test=0.0;
	for(int i=1;i<=50;++i) {
	    u3=(u1+u2)/2.0;
	    test=T.test(u3);
	    if(test<0) 	u2=u3;
            if(test>=0) u1=u3;
	}
	Complex z=this.convert(u3);
	T.b=z;
	return(T);
    }


    int hypTest(double u) {
	Triangle T=new Triangle();
	T.a=u*a;
	T.b=b;
	T.x=x;
	T.a1=a1;
	T.a2=a2;
	T.a3=a3;
	T=T.flow();
	TriangleGroup G=new TriangleGroup(T);
	int test1=G.hypTest();
	int test2=T.match();
	int test3=1;
	if((test1==0)&&(test2==0)) test3=0;
	return(test3);
    }


    
    double parabolicParameter() {
        double u1=0.0;
	double u2=1.0;
	double u3=0.5;
	double test=0.0;
	for(int i=1;i<=50;++i) {
	    u3=(u1+u2)/2.0;
	    test=hypTest(u3);
	    if(test==0) u2=u3;
            if(test==1) u1=u3;
	}
	return(u3);
    }


}














   
class WordSelector extends DBCanvas implements MouseListener {
    Word W;
    GroupSelector X;
    int n;
    Color C1,C2,C3;
    WordSelector(GroupSelector X,int n,Color C1,Color C2,Color C3) { 
	this.X=X;
	this.n=n;
	this.C1=C1;
	this.C2=C2;
	this.C3=C3;
	W=new Word();
	W=W.reset();
	this.setSize(n,20);
	addMouseListener(this);
    }


    public void paint(Graphics g) {   
	g.setColor(C1);
	g.fillRect(0,0,n,20);
	g.setColor(C2);
	g.fillRect(0,0,n-100,20);
	g.setColor(C3);
	g.translate(n-20,0);
	g.drawRect(1,1,18,18); 
	g.drawString("*",5,15);
	g.translate(-20,0);    
	g.drawRect(1,1,18,18); 
        g.drawString("3",5,15);
	g.translate(-20,0);    
	g.drawRect(1,1,18,18);  
        g.drawString("2",5,15);
        g.translate(-20,0);  
        g.drawRect(1,1,18,18);          
        g.drawString("1",5,15);  
        g.translate(-20,0);  
        g.drawRect(1,1,18,18);          
        g.drawString("-",5,15);  
	g.translate(-n+100,0);
        g.drawRect(0,0,n-102,19);
	W.render(g,n);
    }                     


    public void mousePressed(MouseEvent e) {}
    public void mouseReleased(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 val;
	val=0;
	if((P.x>n-20)&&(P.x<n)&&(P.y>0)&&(P.y<20))  val=4;
        if((P.x>n-40)&&(P.x<n-20)&&(P.y>0)&&(P.y<20)) val=3;
        if((P.x>n-60)&&(P.x<n-40)&&(P.y>0)&&(P.y<20)) val=2;
        if((P.x>n-80)&&(P.x<n-60)&&(P.y>0)&&(P.y<20)) val=1;
        if((P.x>n-100)&&(P.x<n-80)&&(P.y>0)&&(P.y<20)) val=0;
        if(val==0) W=W.strip();
	if(val==1) W=W.compose1();
	if(val==2) W=W.compose2();
	if(val==3) W=W.compose3();
	if(val==4) W=W.reset();
	repaint();
    }
}


class Word {
    int l;
    int[] n=new int[300];
    Word() {
	l=0;
    }

    Word reset() {
	Word w=this;
	w.l=0;
	return(w);
    }

    Word strip() {
	Word w=this;
        if(w.l>0) --w.l;
	return(w);
    }

    Word compose1() {
	Word w=this;
	int ll=l;
	if(n[ll]==1) w.l=l-1;
	if(n[ll]!=1) {w.l=l+1;w.n[l]=1;}
	return(w);
    }

    Word compose2() {
	Word w=this;
	int ll=l; 
	if(n[ll]==2) w.l=l-1;
	if(n[ll]!=2) {w.l=l+1;w.n[l]=2;}
	return(w);
    }


    Word compose3() {
	Word w=this;
	int ll=l;
	if(n[ll]==3) w.l=l-1;
	if(n[ll]!=3) {w.l=l+1;w.n[l]=3;}
	return(w);
    }

    void render(Graphics g,int nn) {
	g.setColor(Color.white);
	if(l==0) g.drawString("e",nn-115,15);
	int ll=1;
	int space=0;
	while(ll<=l) {
	    if(n[ll]==1) g.drawString("1",nn-115-space,15);
            if(n[ll]==2) g.drawString("2",nn-115-space,15);
            if(n[ll]==3) g.drawString("3",nn-115-space,15);
	    space=space+8;
	    ++ll;
	}
    }
}









class TriangleSelector extends DBCanvas implements MouseListener {
    GroupSelector X;
    ParameterSelector P; 
    int a,b,c;
    Color C1,C2,C3;
    Color[] COL=new Color[4];
    String S;
    int error;
    ListenSquare[][] L=new ListenSquare[4][6];


    TriangleSelector(GroupSelector X,
        Color C1,Color C2, int a,int b,int c) {
	S=new String();
	this.X=X;
	this.a=a;
        this.b=b;  
        this.c=c;
	this.C1=C1;
	this.C2=C2;
	error=0;

	COL[1]=new Color(255,0,0);
	COL[2]=new Color(0,0,255);
	COL[3]=new Color(0,230,0);


	S="";
	addMouseListener(this);
	this.setSize(400,17);

	for(int j=1;j<=3;++j) {
	for(int i=1;i<=2;++i) {
	    L[j][i]=new ListenSquare(150*j-150+16*i-16,1,14,15);
	}}

	for(int j=1;j<=3;++j) {
	for(int i=3;i<=4;++i) {
	    L[j][i]=new ListenSquare(150*j-120+16*i-16,1,14,15);
	}}


    }

    public void paint(Graphics g) {
	g.setColor(Color.black);
	g.fillRect(0,0,400,20);
	g.setColor(COL[1].darker());
	g.fillRect(0,0,93,17);
	g.setColor(COL[2].darker());
	g.fillRect(150,0,93,17);
	g.setColor(COL[3].darker());
	g.fillRect(300,0,93,17);


	for(int j=1;j<=3;++j) {
	for(int i=1;i<=4;++i) {
              L[j][i].render(g,COL[j]);
	}}
	g.setColor(Color.white);
        g.setFont(new Font("TimesRoman",Font.PLAIN,14));
	Integer aa=new Integer(a);
	Integer bb=new Integer(b);
	Integer cc=new Integer(c);
	g.drawString(aa.toString(a),35,15);
	g.drawString(bb.toString(b),185,15);
	g.drawString(cc.toString(c),335,15);

	if(error==1) g.drawString("error",105,12);
    }


    public void mouseClicked(MouseEvent e) {
	e.consume();
	Point p=new Point();	
        p.x=e.getX();
	p.y=e.getY();

	if(L[1][1].inside(p)==1) a=a-10;
	if(L[1][2].inside(p)==1) a=a-1;
	if(L[1][3].inside(p)==1) a=a+1;
	if(L[1][4].inside(p)==1) a=a+10;

	if(L[2][1].inside(p)==1) b=b-10;
	if(L[2][2].inside(p)==1) b=b-1;
	if(L[2][3].inside(p)==1) b=b+1;
	if(L[2][4].inside(p)==1) b=b+10;

	if(L[3][1].inside(p)==1) c=c-10;
	if(L[3][2].inside(p)==1) c=c-1;
	if(L[3][3].inside(p)==1) c=c+1;
	if(L[3][4].inside(p)==1) c=c+10;

	if(a<3) a=3;
	if(b<3) b=3;
	if(c<3) c=3;
	if(a>999) a=999;
	if(b>999) b=999;
	if(c>999) c=999;
	if((a==3)&&(b==3)&&(c==3)) {
	    a=3;b=3;c=4;
	}

	repaint();
	X.T=new Triangle(a,b,c);
	X.G=new TriangleGroup(X.T);
	X.PS.parameter=1.0;
	X.PS.H.POS=383;
	X.PS.repaint();
	X.K.repaint();

    }

    public void mouseReleased(MouseEvent e) {}
    public void mouseEntered(MouseEvent e) {}
    public void mouseExited(MouseEvent e) {}
    public void mousePressed(MouseEvent e) {}



}









class ParameterSelector extends DBCanvas implements MouseListener {
    int par[]=new int[20];
    double parameter;
    GroupSelector X;
    HorizontalSlider H;
    ListenSquare L1,L2;
    ParameterSelector(GroupSelector X) {
	addMouseListener(this);
	this.setSize(400,16);
	this.X=X;
	H=new HorizontalSlider(17,0,366,16,383,new Color(100,0,150));
	L1=new ListenSquare(0,1,15,17);
	L2=new ListenSquare(385,1,17,17);

    }

    
    public void paint(Graphics g) {
	g.setColor(Color.black);
	g.fillRect(0,0,400,20);
	H.render(g);
	L1.render(g,new Color(0,150,100));
	L2.render(g,new Color(0,150,100));
	g.setColor(new Color(140,220,200));
	g.setFont(new Font("TimesRoman",Font.PLAIN,12));
	g.drawString("parameter",30,10);

    }





    public void mousePressed(MouseEvent e) {
	e.consume();	
        Point p=new Point();
	p.x=e.getX();
	p.y=e.getY();

	if(H.inside(p)==1) H.ACTIVE=1;
    }


    public void mouseEntered(MouseEvent e) {}
    public void mouseExited(MouseEvent e) {}
    public void mouseClicked(MouseEvent e) {}

    public void mouseReleased(MouseEvent e) {
	e.consume();	
        Point p=new Point();
	p.x=e.getX();
	p.y=e.getY();
	if(L1.inside(p)==1) {
	    H.POS=17;
	    parameter=X.T.PARABOLIC;
	    repaint();
	}

	if(L2.inside(p)==1) {
	    H.POS=383;
	    parameter=1.0;
	    repaint();
	}

	if(H.ACTIVE==1) {
	    double pp=0.0;
	    H.configure(p);
	    repaint();
	    H.ACTIVE=0;
	    pp=1.0*(H.POS-H.x)/H.w;
	    parameter=(1.0-pp)*X.T.PARABOLIC+pp;
	}

	X.T=new Triangle(X.TS.a,X.TS.b,X.TS.c);
        X.T.a=parameter*X.T.a;
	repaint();
        X.T=X.T.flow();
	X.K.repaint();
	X.G=new TriangleGroup(X.T);
	double ev=0.0;
	
	int test=X.T.match();
	if(test==0) {X.TS.error=0;}
	if(test==1) {X.TS.error=1;}
	X.TS.repaint();
	X.C.init=1;
	X.C.repaint(0,0,500,120);
    }
}







class SketchPad extends DBCanvas {
    GroupSelector X;
    Complex[] z=new Complex[300];
    int count;
    SketchPad(GroupSelector X) {
	this.X=X;
	this.setSize(402,402);
	for(int i=0;i<=299;++i) z[i]=new Complex();
	count=1;
   
    }

    public void paint(Graphics g) {
	g.setColor(new Color(150,0,150));
	g.fillRect(0,0,400,400);
	g.setColor(Color.white);
	g.setFont(new Font("TimesRoman",Font.PLAIN,18));
	g.drawString("Rich: Applet 29",230,20);
	g.drawString("complex hyperbolic",230,40);
	g.drawString("triangle groups",230,60);

	g.setColor(Color.black);
	g.fillOval(-400,0,800,800);
	g.setColor(Color.white);
	g.drawOval(-400,0,800,800);


	g.translate(0,400);
	int x=(int)(400*X.T.b.x); 
        int y=(int)(-400*X.T.b.y);	
	double d1=1.0/X.T.lowerLimit();
	d1=400*d1;
	double d2=1.0/X.T.upperLimit();
	d2=400*d2;
	double d3=(-d1+d2)/2;
	if(d3<0) d3=-d3;
	double d4=d1;
	if (d2<d1) d4=d2;
	g.setColor(new Color(100,100,255));
	g.drawOval((int)(d4),(int)(-d3),(int)(2*d3),(int)(2*d3));
	int d5=(int)(X.T.a*400);
	g.setColor(Color.yellow);
	g.drawLine(0,0,d5,0);
	double d6=Math.cos(Math.PI/X.T.a1);
        double d7=Math.sin(Math.PI/X.T.a1);
	g.setColor(Color.red);
	g.drawLine(0,0,(int)(400*d6),(int)(-400*d7));
        g.fillOval(x-3,y-3,6,6);	
        g.translate(0,-400);
    }


}










class GroupSelector extends Container {
    TriangleGroup G;
    DisplayCanvas C;
    ParameterSelector PS;
    TriangleSelector TS;
    Triangle T;
    WordSelector[] W=new WordSelector[15];
    SketchPad K;
    GridBagLayout X;
    GridBagConstraints c;
    Color temp=Color.green;

    GroupSelector(DisplayCanvas C) {
	this.C=C;
	Color C1=new Color(150,0,0);
	Color C2=Color.blue;
	Color C3=Color.white; 
	T=new Triangle(4,4,4);
	G=new TriangleGroup(T);
	X=new GridBagLayout();
	c=new GridBagConstraints();  
        c.gridwidth=GridBagConstraints.REMAINDER; 
        setLayout(X);
	for(int i=1;i<=6;++i)  {
            W[i]=new WordSelector(this,400,C1,C2,C3);
	    X.setConstraints(W[i],c);
	    add(W[i]);
	}

	W[1].W.l=4;
	W[1].W.n[1]=1;
	W[1].W.n[2]=2;
	W[1].W.n[3]=1;
        W[1].W.n[4]=3;

	W[2].W.l=4;
	W[2].W.n[1]=2;
	W[2].W.n[2]=1;
	W[2].W.n[3]=2;
        W[2].W.n[4]=3;

	W[3].W.l=4;
	W[3].W.n[1]=3;
	W[3].W.n[2]=2;
	W[3].W.n[3]=3;
        W[3].W.n[4]=1;

	W[4].W.l=3;
	W[4].W.n[1]=1;
	W[4].W.n[2]=2;
	W[4].W.n[3]=3;


        PS=new ParameterSelector(this);
	TS=new TriangleSelector(this,new Color(0,150,0),C2,4,4,4);
	K=new SketchPad(this);
	K.setBackground(Color.black);
	X.setConstraints(TS,c);
        c.gridwidth=GridBagConstraints.REMAINDER; 
        X.setConstraints(PS,c);
	X.setConstraints(K,c);
        setLayout(X);
	add(K);		
        add(PS);  
        add(TS);

    }



}






class ListenTriangle {
    double x1,x2,x3;
    double y1,y2,y3;
    Color C;

    ListenTriangle() {
      this.x1=x1;
      this.x2=x2;
      this.x3=x3;
      this.y1=y1;
      this.y2=y2;
      this.y3=y3;
      this.C=C;
    }
    
    int inside(Point p)
    {
	double v1x,v1y,v2x,v2y;
	double A1,A2,A3;
	int val;
	v1x=p.x-this.x1;
	v1y=p.y-this.y1;
	v2x=p.x-this.x2;
	v2y=p.y-this.y2;
	A3=v1x*v2y-v1y*v2x;
	v1x=p.x-this.x2;
	v1y=p.y-this.y2;
	v2x=p.x-this.x3;
	v2y=p.y-this.y3;
	A1=v1x*v2y-v1y*v2x;
	v1x=p.x-this.x3;
	v1y=p.y-this.y3;
	v2x=p.x-this.x1;
	v2y=p.y-this.y1;
	A2=v1x*v2y-v1y*v2x;
	val=0;
	if((A1<0)&&(A2<0)&&(A3<0)) val=1;
	if((A1>0)&&(A2>0)&&(A3>0)) val=1;
	return(val);
    }
 
    int inside(Complex p)
    {
	double v1x,v1y,v2x,v2y;
	double A1,A2,A3;
	int val;
	v1x=p.x-this.x1;
	v1y=p.y-this.y1;
	v2x=p.x-this.x2;
	v2y=p.y-this.y2;
	A3=v1x*v2y-v1y*v2x;
	v1x=p.x-this.x2;
	v1y=p.y-this.y2;
	v2x=p.x-this.x3;
	v2y=p.y-this.y3;
	A1=v1x*v2y-v1y*v2x;
	v1x=p.x-this.x3;
	v1y=p.y-this.y3;
	v2x=p.x-this.x1;
	v2y=p.y-this.y1;
	A2=v1x*v2y-v1y*v2x;
	val=0;
	double tol=0.0;
	if((A1<tol)&&(A2<tol)&&(A3<tol)) val=1;
	if((A1>-tol)&&(A2>-tol)&&(A3>-tol)) val=1;
	return(val);
    }

    void render(Graphics g,Color C) {
	int x[]={(int)(x1),(int)(x2),(int)(x3)};
        int y[]={(int)(y1),(int)(y2),(int)(y3)};
	g.setColor(C);
	g.fillPolygon(x,y,3);
    }


}






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

    void render(Graphics g,Color C) {
	g.setColor(C);
	g.fillRect(x,y,w,h);
        g.drawRect(x,y,w,h);
	g.setColor(Color.black);
    }

    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 HorizontalSlider {
    int x,y,w,h;
    int ACTIVE;
    int POS;
    Color C;
    String S;
    HorizontalSlider(int x,int y,int w,int h,int POS,Color C) {
        this.x=x;
        this.y=y;
        this.h=h;
        this.w=w;
        this.POS=POS;
        this.C=C;
        ACTIVE=0;
    }

    void render(Graphics g) {
        g.setColor(C);
        g.fillRect(x,y,w,h);
        g.setColor(Color.black);
        g.drawRect(x,y,w,h);
        g.setColor(Color.white);
        g.fillRect(POS-1,y+1,2,h-2); 
        g.drawRect(POS-1,y+1,2,h-2); 
    }

    void configure(Point p) {
        if((ACTIVE==1)&&(p.x<x+w)&&(p.x>x)) POS=p.x;
    }

    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);
    }
}