File:Straro10at.jpg

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
//using namespace std;
#include<complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"

DB Q=1;
z_type T(z_type z){ return z*(1.+z*z*(1.+z*Q));}

#include "nembran.cin"

z_type S=nembran(Q);

z_type F(z_type z){ z_type a,b,r,R ; a=Q-z; b=1. + 4.*Q*z; r = 27.*a*a + 4.*b*b*b ;
DB x,y; x=Re(z); y=Im(z);
if( x<=0 ) return -sqrt(r);
if( y > Im(S) ) return I*sqrt(-r);
if( y < - Im(S) ) return -I*sqrt(-r);
if( x*Im(S)< fabs(y)*Re(S) ) return -sqrt(r);
return sqrt(r);
}


int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
int M=1001,M1=M+1;
int N=501,N1=N+1;
DB X[M1],Y[N1]; DB *g, *f, *w; // w is working array.
g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
char v[M1*N1]; // v is working array
FILE *o;o=fopen("straro10a.eps","w"); ado(o,4002,4002);
fprintf(o,"2001 2001 translate\n 1000 1000 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
DO(m,M1) X[m]=-2+.004*(m-.5);
DO(n,N1) Y[n]=-2+.008*(n-.5);
//for(n=0;n<N1;n++) { Y[n]=1.09*sinh((3./200.)*(n-200)); printf("%3d %9.6f\n",n,Y[n]); }
for(m=-20;m<21;m+=5){M(.1*m,-2) L(.1*m,2) }
for(n=-20;n<21;n+=5){M( -2,.1*n) L(2,.1*n)}
 fprintf(o,".001 W 0 0 0 RGB S\n");

//z=nembran(Q);
x=Re(S);
y=Im(S);
M(x,-1)L(x,1)
M(-1,y)L(1,y)
M(-1,-y)L(1,-y)
fprintf(o,".004 W .5 .5 0 RGB S\n");
printf("x,y %18.15lf %18.15lf\n",x,y);


DO(m,M1)DO(n,N1){ g[m*N1+n]=99999999;
                  f[m*N1+n]=99999999;}
DO(m,M1){x=X[m]; if(m/10*10==m) printf("x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y); //if(abs(z+2.)>.019)

// c=-1./z;
// c=-(1.+3.*z*z)/(4.*z*z*z);

//c=Fru(z);
c=F(z);

// p=abs(c-z)/(abs(c)+abs(z)); p=-log(p)/log(10.); if(p>0 && p<17) g[m*N1+n]=p;
 p=Re(c); q=Im(c); if(p>-100000 && p<100000 && q>-100000 && q<100000 ){ g[m*N1+n]=p;f[m*N1+n]=q;}
       }}
fprintf(o,"1 setlinejoin 1 setlinecap\n");
 p=4;q=.5;

for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".001 W 0 .6 0 RGB S\n");
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".001 W .8 0 0 RGB S\n");
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".001 W 0 0 .8 RGB S\n");
for(m= 1;m<41;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".004 W .8 0 0 RGB S\n");
for(m= 1;m<41;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".004 W 0 0 .8 RGB S\n");
               conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".003 W .6 0 .6 RGB S\n");
for(m=-40;m<41;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".004 W 0 0 0 RGB S\n");
// fprintf(o,"0 setlinejoin 0 setlinecap\n");
// M(-10,0)L(0,0) fprintf(o,"1 1 1 RGB .02 W S\n");
//#include "plofu.cin"

x=Re(S);
y=Im(S);
M(x,y)L(0,0)
L(x,-y)
fprintf(o,".01 W 1 1 .5 RGB 0 setlinecap S\n");
printf("x,y %18.15lf %18.15lf\n",x,y);

fprintf(o,"showpage\n");
fprintf(o,"%c%cTrailer\n",'%','%');
fclose(o); free(f); free(g); free(w);

      system("epstopdf straro10a.eps");
      system( "open straro10a.pdf"); //for macintosh
      getchar(); system("killall Preview"); // For macintosh
}

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\oddsidemargin -80pt
\textheight 4800px
\parindent 0pt
\usepackage{graphicx}
\usepackage{rotating}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\begin{document}
\begin{picture}(4090,4050)
%\put(20,14){\ing{nembraplo}}
%\put(20,14){\ing{nembran}}
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\put(4110,-120){\sx{14}{$x$}}
\put(330,2000){\sx{14}{\bf cut}}
\put(1710,2000){\sx{14}{$v\!=\!0$}}
\put(3330,2000){\sx{14}{$v\!=\!0$}}
\put(2250,2060){\rot{80}\sx{14}{\bf cut}\ero}
%
\put(1120,3620){\rot{34}\sx{14}{$u\!=\!-40$}\ero}%
\put(2160,3100){\rot{52}\sx{14}{$u\!=\!-10$}\ero}%
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\put(3900,2600){\rot{80}\sx{14}{$u\!=\!40$}\ero}%
%
\put(800, 3040){\rot{-76}\sx{14}{$v\!=\!-10$}\ero}
\put(300, 1660){\rot{-6}\sx{14}{$u\!=\!-10$}\ero}
%
\put(760, 720){\rot{66}\sx{14}{$v\!=\!10$}\ero}
\put(1040, 600){\rot{58}\sx{14}{$v\!=\!0$}\ero}
\put(1320, 370){\rot{52}\sx{14}{$v\!=\!-10$}\ero}
%
\put(3300,3390){\rot{-17}\sx{14}{$v\!=\!40$}\ero}
\put(3190,2400){\rot{-8}\sx{14}{$v\!=\!10$}\ero}
\put(3190,1600){\rot{8}\sx{14}{$v\!=\!-10$}\ero}
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