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

public class ArithmeticGraphBox {
    int p,q;


    /*This class computes some quantities associated to the
      arithmetic graph and the hexagrid theorem.   These
      quantities are discussed in chapter 3 of the monograph*/


    public ArithmeticGraphBox(int pp,int qq) {
	p=pp;
	q=qq;
    }


    public GeneralPath arithmeticKite() { 
          GeneralPath gp=new GeneralPath();
	  float x1=0;
	  float y1=0;
	  float x2=0;
	  float y2=(float)(.5*(p+q));
	  float x3=(float)(p);
	  float y3=(float)(((p+q)*(p+q)-2.0*p*p)/(2.0*q));
	  float x4=(float)(2.0*p*q/(p+q));
	  float y4=(float)(((p+q)*(p+q)-4.0*p*p)/(2.0*(p+q)));
	  gp.moveTo(x1,y1);
	  gp.lineTo(x2,y2);
	  gp.lineTo(x3,y3);
	  gp.lineTo(x4,y4);
	  gp.closePath();
	  return(gp);
    }



    /* These are the same 2 vectors as in the monograph - V and W.  The
       vector V is the fundamental symmetry of the graph, and the vector W
       is parallel to the walls of the room grid.*/


    public double[] VectorV() {
	double[] X=new double[2];
	X[0]=1.0*q;
	X[1]=-1.0*p;
	return(X);
    }

    public double[] VectorW() {
	double[] X=new double[2];
        X[0]=1.0*(p*q)/(p+q);
	X[1]=X[0]+(q-p)/2.0;
	return(X);
    }

    public double[] VectorVprime() {
	double[] X=new double[2];
	X[0]=0;
	int test=(p*q)%2;
	X[1]=(p+q)*(p+q);
	if(test==1) X[1]=X[1]/4;
	return(X);
    }




    /*slope of the W vector.  The slope is defined even in the
      irrational case, while the vector itself is not defined.*/

    public static double slopeW(double A) {
	double s=1+0.5*(1+A)*(1-A)/A;
	return(s);
    }


    /*These routines are used for rotations*/

    public AffineTransform AFF1() {
	double[] m1=VectorV();
	double[] m2=VectorW();
	double a=m1[0];
	double b=m1[1];
	double c=m2[0];
	double d=m2[1];
	AffineTransform A=new AffineTransform(a,b,c,d,0,0);
	return(A);
    }

    public AffineTransform AFF2() {
	double[] m1=VectorV();
	double[] m2=VectorW();
	double a=-m1[0];
	double b=-m1[1];
	double c=m2[0];
	double d=m2[1];
	AffineTransform A=new AffineTransform(a,b,c,d,0,0);
	try {A=A.createInverse();}
	catch(Exception e) {}
	return(A);
    }

     public AffineTransform AFF3() {
         int[] x=MathRational.RPLUS(p,q); 
	 double x0=1.0*x[0];
	 double x1=1.0*x[1];
	 x0=x1*p/q;
         AffineTransform A=AffineTransform.getTranslateInstance(x1,-x0);
	 return(A);
     }


    public AffineTransform AFF4() {
	double xx=2.0;
	double[] m1=VectorV();
	double[] m2=VectorW();
	double a=m1[0];
	double b=m1[1];
	double c=xx*m2[0];
	double d=xx*m2[1];
	AffineTransform A=new AffineTransform(a,b,c,d,0,0);	
        try {A=A.createInverse();}
	catch(Exception e) {}
	return(A);
    }

    public AffineTransform AFF5() {
	int[] x=MathRational.pivot(p,q);
	double xx=1.0*(x[0]+x[2])/2.0;
	double yy=1.0*(x[1]+x[3])/2.0;
	AffineTransform B=AffineTransform.getTranslateInstance(-xx,-yy);
	return(B);
    }




    public GeneralPath pureReflect(GeneralPath gp1) {
	GeneralPath gp2=new GeneralPath(gp1);
	gp2.transform(AFF2());
	gp2.transform(AFF1());
	return(gp2);
    }

    public GeneralPath reflect(GeneralPath gp1) {
	GeneralPath gp2=new GeneralPath(gp1);
	gp2.transform(AFF2());
	gp2.transform(AFF1());
	gp2.transform(AFF3());
	return(gp2);
    }

    public GeneralPath straighten(GeneralPath gp1) {
	AffineTransform A1=AFF4();
	AffineTransform A2=AFF5();
	GeneralPath gp2=new GeneralPath(gp1);
	gp2.transform(A2);
	gp2.transform(A1);
	return(gp2);
    }



    /* Here is the period box */

    public GeneralPath periodBox() {
	double[] V=VectorV();
	double[] W=VectorVprime();

	double a0=V[0];
	double a1=V[1];
	double c0=W[0];
	double c1=W[1];
	double d0=a0+c0;
	double d1=a1+c1;

	GeneralPath gp=new GeneralPath();
	gp.moveTo(0,0);
	gp.lineTo((float)(a0),(float)(a1));
	gp.lineTo((float)(d0),(float)(d1));
	gp.lineTo((float)(c0),(float)(c1));
	gp.closePath();
	return(gp);
    }






    /* Here is a general parallogram whose sides are parallel to V and W.*/

    public GeneralPath parallelogram(double x1,double x2,double y) {
	double[] V=VectorV();
	double[] W=VectorW();

	double a0=V[0]*x1;
	double a1=V[1]*x1;
	double b0=V[0]*x2;
	double b1=V[1]*x2;
	double c0=W[0]*y;
	double c1=W[1]*y;
	double d0=a0+c0;
	double d1=a1+c1;
	double e0=b0+c0;
	double e1=b1+c1;

	GeneralPath gp=new GeneralPath();
	gp.moveTo((float)(a0),(float)(a1));
	gp.lineTo((float)(b0),(float)(b1));
	gp.lineTo((float)(e0),(float)(e1));
	gp.lineTo((float)(d0),(float)(d1));
	gp.closePath();
	return(gp);
    }

    /*This is the room, from the Room Lemma*/

    public GeneralPath basicBox() {
          GeneralPath gp=new GeneralPath();
	  if((p*q)%2==1) return(parallelogram(0,1,1));
	  return(parallelogram(-1,1,2));
    }





    /*These boxes are from the Decomposition Theorem */

    public GeneralPath sonBox1() {
        int[] c=MathRational.superiorPredecessor(p,q);  
        int[] a=MathRational.RPLUS(p,q);
	double h=(1.0*c[0]+1.0*c[1])/(p+q);
        double w=1.0*a[1]/q;
	return(parallelogram(0,w,h));
    }

    public GeneralPath fatherBox1() {
        int[] a=MathRational.RMINUS(p,q);
        double w=1.0*a[1]/q;
	return(parallelogram(-w,0,1));
    }

    public GeneralPath sonBox2() {
        int[] c=MathRational.superiorPredecessor(p,q);  
        int[] a=MathRational.RMINUS(p,q);
	double h=(1.0*c[0]+1.0*c[1])/(p+q);
        double w=1.0*a[1]/q;
	return(parallelogram(-w,0,h));
    }

    public GeneralPath fatherBox2() {
        int[] a=MathRational.RPLUS(p,q);
        double w=1.0*a[1]/q;
	return(parallelogram(0,w,1));
    }




    /*These parallelograms are part of the TRAPS defined in
      Part VI of the monograph*/


    public GeneralPath OddEvenBox1() {
        int[] c=MathRational.RPLUS(p,q);
	c=MathRational.oddPredecessor(c[0],c[1]);
        int[] a=MathRational.RMINUS(p,q);
	double h=(1.0*c[0]+1.0*c[1])/(p+q);
        double w=1.0*a[1]/q;
	return(parallelogram(-w,0,h));
    }

    public GeneralPath OddEvenBox2() {
        int[] c=MathRational.RMINUS(p,q);
	c=MathRational.oddPredecessor(c[0],c[1]);
        int[] a=MathRational.RPLUS(p,q);
	double h=(1.0*c[0]+1.0*c[1])/(p+q);
        double w=1.0*a[1]/q;
	return(parallelogram(0,w,h));
    }



    public GeneralPath EvenEvenBox1() {
        int[] c=MathRational.RMINUS(p,q);
	c=MathRational.oddPredecessor(c[0],c[1]);
        int[] a=MathRational.RPLUS(p,q);
	double h=(1.0*c[0]+1.0*c[1])/(p+q);
        double w=1.0*a[1]/q;
	return(parallelogram(0,w,h));
    }

    public GeneralPath EvenOddBox1() {
        int[] c=MathRational.RPLUS(p,q);
	double h=(1.0*c[0]+1.0*c[1])/(p+q);
        int[] a=MathRational.RMINUS(p,q);
        double w=1.0*a[1]/q;
	return(parallelogram(-w,0,h));
    }



    public GeneralPath EvenEvenBox2() {
        int[] c=MathRational.RPLUS(p,q);
	c=MathRational.oddPredecessor(c[0],c[1]);
        int[] a=MathRational.RMINUS(p,q);
	double h=(1.0*c[0]+1.0*c[1])/(p+q);
        double w=1.0*a[1]/q;
	return(parallelogram(-w,0,h));
    }

    public GeneralPath EvenOddBox2() {
        int[] c=MathRational.RMINUS(p,q);
	double h=(1.0*c[0]+1.0*c[1])/(p+q);
        int[] a=MathRational.RPLUS(p,q);
        double w=1.0*a[1]/q;
	return(parallelogram(0,w,h));
    }




    /*Here are two special families of lines, both parallel to the walls*/



    public GeneralPath iotaWall() {
          GeneralPath gp=new GeneralPath();
	  int[] a=MathRational.RPLUS(p,q);
          double x1=1.0*(p*q)/(p+q);
	  double y1=x1+(q-p)/2.0;
	  x1=x1*20;
	  y1=y1*20;
          gp.moveTo((float)(a[1]-x1),(float)(-a[0]-y1));
	  gp.lineTo((float)(a[1]+x1),(float)(-a[0]+y1));
	  gp.closePath();
	  return(gp);
    }



    public GeneralPath symmLine() {
          GeneralPath gp=new GeneralPath();
	  int[] a=MathRational.RPLUS(p,q);
          double x1=1.0*(p*q)/(p+q);
	  double y1=x1+(q-p)/2.0;
	  x1=x1*20;
	  y1=y1*20;
          gp.moveTo((float)(.5*a[1]-x1),(float)(-.5*a[0]-y1));
	  gp.lineTo((float)(.5*a[1]+x1),(float)(-.5*a[0]+y1));
	  gp.closePath();
	  return(gp);
    }



}