File:Fig1802i.jpg

Demo of routine conrec6.cin:

extraction form picture

The only lines of constant real part of the function are drawn.

Generator

// Files «ado.cin», «conrec6.cin», «filog.cin», «tania.cin» should be loaded in order to compile the C++ code below.
//If saved as «Fig1802r.cc», the generator can be compiled with abracadabra //«c++ -std=c++11 Fig1802i.cc -O2 -o Fig1802i»

//c++ -std=c++11 Fig1802i.cc -O2 -o Fig1802i
#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 complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
#include "filog.cin"
#include "Conrec6.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=500,M1=M+1;
int N=501,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
//FILE *o;o=fopen("10.eps","w");ado(o,1020,1020);
FILE *o;o=fopen("Fig1802i.eps","w");ado(o,1020,1020);
fprintf(o,"510 510 translate\n 1000 1000 scale\n");
DO(m,M1) X[m]=-.5+.002*(m-.2);
DO(n,250)Y[n]=-.5+.002*n;
        Y[250]=-.00001;
        Y[251]= .00001;
for(n=252;n<N1;n++) Y[n]=-.5+.002*(n-1.);

for(m=-5;m<6;m++){M(.1*m,-.5)L(.1*m,.5)}
for(n=-5;n<6;n++){M( -.5,.1*n)L(.5,.1*n)}
fprintf(o,"2 setlinecap .001 W 0 0 0 RGB S\n");
M(exp(-1.),-.5)
L(exp(-1.), .5)
//M(M_PI/2.,-.5)
//L(M_PI/2., .5)
fprintf(o,".0007 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m+M1*n]=9999; f[m+M1*n]=9999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y); 
// c=Tania(z_type(-1.,-M_PI)+log(z))/(-z); 
//c=Filog(z);
c=Filog(z);
p=Re(c);q=Im(c); 
//if(p>-201. && p<201. && q>-201. && q<201. ){ g[m+N1*n]=p;f[m+N1*n]=q;}
if(p>-201. && p<201. && q>-201. && q<201. ){ g[m+M1*n]=p;f[m+M1*n]=q;}
       }}
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=5.;q=1;
// //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,".0008 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,".0008 W .9 0 0 RGB S\n");


for(m=-10;m<10;m++)for(n=2;n<10;n+=2)Conrec6(o,f,X,Y,M1,N1,(m+.1*n), q); fprintf(o,".0008 W 0 .6 0 RGB S\n");
//for(m=0;m<10;m++) for(n=2;n<10;n+=2)Conrec6(o,g,X,Y,M1,N1,-(m+.1*n), q); fprintf(o,".0008 W .9 0 0 RGB S\n");
//for(m=0;m<10;m++) for(n=2;n<10;n+=2)Conrec6(o,g,X,Y,M1,N1, (m+.1*n), q); fprintf(o,".0008 W 0 0 .9 RGB S\n");
for(m=1;m<20;m++) Conrec6(o,f,X,Y,M1,N1, (0.-m),p); fprintf(o,".002 W .9 0 0 RGB S\n");
for(m=1;m<20;m++) Conrec6(o,f,X,Y,M1,N1, (0.+m),p); fprintf(o,".002 W 0 0 .9 RGB S\n");
                  Conrec6(o,f,X,Y,M1,N1, (0. ),p); fprintf(o,".002 W .6 0 .6 RGB S\n");
//for(m=-20;m<21;m++) Conrec6(o,g,X,Y,M1,N1, (0.+m),p); fprintf(o,".002 W 0 0 0 RGB S\n");

p=10.;
/*
Conrec6(o,g,X,Y,M1,N1, 30 ,p); fprintf(o,".002 W 0 0 0 RGB S\n");
Conrec6(o,g,X,Y,M1,N1, 40 ,p); fprintf(o,".002 W 0 0 0 RGB S\n");
Conrec6(o,g,X,Y,M1,N1, 50 ,p); fprintf(o,".002 W 0 0 0 RGB S\n");
Conrec6(o,g,X,Y,M1,N1,-30 ,p); fprintf(o,".002 W 0 0 0 RGB S\n");
Conrec6(o,g,X,Y,M1,N1,-40 ,p); fprintf(o,".002 W 0 0 0 RGB S\n");
Conrec6(o,g,X,Y,M1,N1,-50 ,p); fprintf(o,".002 W 0 0 0 RGB S\n");
*/
Conrec6(o,f,X,Y,M1,N1,-30 ,p); fprintf(o,".002 W .9 0 0 RGB S\n");
Conrec6(o,f,X,Y,M1,N1,-40 ,p); fprintf(o,".002 W .9 0 0 RGB S\n");
Conrec6(o,f,X,Y,M1,N1,-50 ,p); fprintf(o,".002 W .9 0 0 RGB S\n");
Conrec6(o,f,X,Y,M1,N1, 30 ,p); fprintf(o,".002 W 0 0 .9 RGB S\n");
Conrec6(o,f,X,Y,M1,N1, 40 ,p); fprintf(o,".002 W 0 0 .9 RGB S\n");
Conrec6(o,f,X,Y,M1,N1, 50 ,p); fprintf(o,".002 W 0 0 .9 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
     system("epstopdf Fig1802i.eps"); 
     system(    "open Fig1802i.pdf"); //for mac
// getchar(); system("killall Preview"); // for mac
// Copyleft 2012-2025 by Dmitrii Kouznetsov
}

Warning

I load this picture by request from ChatGPT.

I have no idea as contours of only imaginary part of the function help to understand the meaning of routine conrec6.cin.

References

Keywords

ChatGPT, Conrec6 demo, Conrec6.cin