File:SincmapT100.png

Complex map of function sinc.

$f=\mathrm{sinc}(x+\mathrm i y) $ is shown in the $x$, $y$ plane with levels $u=\Re(f)=\mathrm {const}$ and levels $v=\Im(f)=\mathrm {const}$.

C++ generator of curves

// Files ado.cin and conto.cin ahould be loaded in the working directory in order to compile the C++ code below.

#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"
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=801,M1=M+1;
int N=401,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("sincmap.eps","w");ado(o,162,82);
fprintf(o,"81 41 translate\n 10 10 scale\n"); 
DO(m,400) X[m]=-8.+.02*m;
     X[400]=-.001;
     X[401]= .001;
for(m=402;m<M1;m++) X[m]=-8.+.02*(m-1.);
DO(n,200)Y[n]=-4.+.02*n;
      Y[200]=-.001;
      Y[201]= .001;
for(n=202;n<N1;n++) Y[n]=-4.+.02*(n-1.);
//DO(m,M1)X[m]=Y[m];
for(m=-8;m<9;m++){if(m==0){M(m,-4.1)L(m,4.1)} else{M(m,-4)L(m,4)}}
for(n=-4;n<5;n++){     M(  -8,n)L(8,n)}
fprintf(o,".01 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+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=sin(z)/z;
     p=Re(c);    q=Im(c);        
     if(p>-99. && p<99.
      &&     q>-99. && q<99 
     )
{g[m*N1+n]=p; 
 f[m*N1+n]=q;
}
                     }}
//#include "plodi.cin"
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.5;q=.5;
for(m=-11;m<11;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".01 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,".01 W .9 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,".01 W 0 0 .9 RGB S\n");
for(m=1;m<11;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".02 W .9 0 0 RGB S\n");
for(m=1;m<11;m++)  conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 .9 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0.  ),-2*p,2*p); fprintf(o,".02 W .6 0 .6 RGB S\n");
for(m=-9;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
    m=0;          conto(o,g,w,v,X,Y,M,N, (0.+m),-2*p,2*p); fprintf(o,".02 W 0 0 0 RGB S\n");
for(m=1;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
//#include "plofu.cin"
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
     system("epstopdf sincmap.eps");
     system(    "open sincmap.pdf");            
     getchar(); system("killall Preview");//for mac
}

Latex generator of labels

% File sincmap.pdf should be generated with the code above in order to compile the Lattex document below.

%<br> \documentclass[12pt]{article} %<br> \paperheight 838px %<br> \paperwidth 1644px %<br> \textwidth 1294px %<br> \textheight 1200px %<br> \topmargin -80px %<br> \oddsidemargin -80px %<br> \usepackage{graphics} %<br> \usepackage{rotating} %<br> %\usepackage{color}%<br> \newcommand \sx {\scalebox} %<br> \newcommand \rot {\begin{rotate}} %<br> \newcommand \ero {\end{rotate}} %<br> \newcommand \ing {\includegraphics} %<br> \newcommand \rmi {\mathrm{i}} %<br> \begin{document} %<br> \newcommand \zoomax { %<br> \put(16,820){\sx{4.4}{$y$}} %<br> \put(16,630){\sx{4}{$2$}} %<br> \put(16,430){\sx{4}{$0$}} %<br> \put(-4, 230){\sx{4}{$-\!2$}} %<br> \put(220, 5){\sx{4}{$-\!6$}} %<br> \put(420, 5){\sx{4}{$-\!4$}} %<br> \put(620, 5){\sx{4}{$-\!2$}} %<br> \put(843, 5){\sx{4}{$0$}} %<br> \put(1043, 5){\sx{4}{$2$}} %<br> \put(1243, 5){\sx{4}{$4$}} %<br> \put(1443, 5){\sx{4}{$6$}} %<br> \put(1631,6){\sx{4}{$x$}} %<br> } %<br> \parindent 0pt %<br> \begin{picture}(1616,816) %<br> \put(40,30){\sx{10}{\ing{sincmap}}} %<br> \zoomax %<br> \put(104,430){\sx{4}{\rot{0}$v\!=\!0$\ero}} %<br> \put(800,650){\sx{4}{$u\!=\!2$}} %<br> \put(865,500){\sx{4}{\rot{90}$v\!=\!0$\ero}} %<br> \put(872,446){\sx{4}{\rot{46}$u\!=\!1$\ero}} %<br> \put(862,420){\sx{4}{\rot{-46}$u\!=\!1$\ero}} %<br> \put(600,474){\sx{4}{\rot{0}$v\!=\!0.2$\ero}} %<br> \put(600,430){\sx{4}{\rot{0}$v\!=\!0$\ero}} \put(890,430){\sx{4}{\rot{0}$v\!=\!0$\ero}} %<br> \put(570,380){\sx{4}{\rot{0}$v\!=\!-0.2$\ero}} %<br> \put(550,390){\sx{4}{\rot{90}$u\!=\!0$\ero}} %<br> \put(90,390){\sx{4}{\rot{90}$u\!=\!0$\ero}} %<br> \put(233,390){\sx{4}{\rot{90}$u\!=\!0$\ero}} %<br> \put(362,366){\sx{3.8}{\rot{90}$u\!=\!-0.2$\ero}} %<br> \put(418,390){\sx{4}{\rot{90}$v\!=\!0$\ero}} %<br> \put(482,366){\sx{3.8}{\rot{90}$u\!=\!-0.2$\ero}} %<br> \put(1180,390){\sx{4}{\rot{90}$u\!=\!0$\ero}} %<br> \put(1270,360){\sx{3.8}{\rot{90}$u\!=\!-0.2$\ero}} %<br> \put(1318,390){\sx{4}{\rot{90}$v\!=\!0$\ero}} %<br> \put(1368,360){\sx{3.8}{\rot{90}$u\!=\!-0.2$\ero}} %<br> \put(1496,390){\sx{4}{\rot{90}$u\!=\!0$\ero}} %<br> \put(1642,390){\sx{4}{\rot{90}$v\!=\!0$\ero}} %<br> \end{picture} %<br> \end{document} %<br> %