File:TaniaMap100.png: Difference between revisions

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(== Summary == Importing file)
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== Summary ==
== Summary ==
{{Image_Details|user
Importing file
|description  = [[Complex map]] of the [[Tania function]], <math>y=\mathrm{Tania}(x)</math>.
|author      = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
|date-created = 2011 September 25
|pub-country  = Japan
|notes        = The generator of the figure uses files [[conto.cin]] and [[ado.cin]]
|versions    = http://tori.ils.uec.ac.jp/TORI/index.php/File:TaniaContourPlot100.png
}}
== Licensing ==
{{CC|by|3.0}}
 
== Generation==
First, the curves are generated with [[C++]] code below.
 
Then, the latex document uses these curves to generate the figure.
 
Then, the result can be converted to some *.png or any other format.
 
==[[C++]] generator of curves==
 
Files [[ado.cin]] and [[conto.cin]] are necessary for compilation of the generator of the curves below:
 
#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"
 
z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
 
z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
 
z_type TaniaTay(z_type z) { int n; z_type s;
s=1.+z*(.5+z*(1./16.+z*(-1./192.+z*(-1./3072.+z*(1.3/6144.+z*(-4.7/147456.
//+z*(7.3/4128768.) //some reserve term
)))))); DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
 
z_type TaniaNega(z_type z){int n;z_type s=exp(z-exp(z)+1.);
DO(n,4) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
 
z_type TaniaBig(z_type z){int n;z_type s=z; s=z-log(s)+1.;
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
 
z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t);
s=-1.+t*(3.+t*(-3.+t*(.75+t*(.3+t*(.9/16.+t*(-.3/7.+t*(-12.51/224. //+t*(-.9/28.)
)))))));
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
 
z_type Tania(z_type z){ z_type t;
if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);
if( abs(z)>7. || Re(z)>3.8 ) return TaniaBig(z);
if( Im(z) > .7 ) return TaniaS(z);
if( Im(z) < -.7) return conj(TaniaS(conj(z)));
return TaniaTay(z);
}
 
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=160,M1=M+1;
int N=161,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("taniamap.eps","w");ado(o,162,162);
fprintf(o,"81 81 translate\n 10 10 scale\n");
DO(m,M1) X[m]=-8.+.1*(m);
DO(n,80)Y[n]=-8.+.1*n;
        Y[80]=-.033;
        Y[81]= .033;
for(n=82;n<N1;n++) Y[n]=-8.+.1*(n-1.);
for(m=-8;m<9;m++){if(m==0){M(m,-8.5)L(m,8.5)} else{M(m,-8)L(m,8)}}
for(n=-8;n<9;n++){    M(  -8,n)L(8,n)}
fprintf(o,".008 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=Tania(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;}
        }}
fprintf(o,"1 setlinejoin 2 setlinecap\n");  p=.6;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,".01 W 0 .6 0 $
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 $
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 $
for(m=1;m<10;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".05 W .9 0 0 RGB S\n");
for(m=1;m<10;m++)  conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".05 W 0 0 .9 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".05 W .6 0 .6 RGB S\n");
for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".05 W 0 0 0 RGB S\n");
y= M_PI; for(m=0;m<60;m+=4) {x=-7.95+.1*m; M(x,y) L(x+.05,y)}
y=-M_PI; for(m=0;m<60;m+=4) {x=-7.95+.1*m; M(x,y) L(x+.05,y)}
fprintf(o,".07 W 1 .5 0 RGB S\n");
y= M_PI; for(m=2;m<60;m+=4) {x=-7.95+.1*m; M(x,y) L(x+.05,y)}
y=-M_PI; for(m=2;m<60;m+=4) {x=-7.95+.1*m; M(x,y) L(x+.05,y)}
fprintf(o,".07 W 0 .5 1 RGB S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf taniamap.eps");
      system(    "open taniamap.pdf");
      getchar(); system("killall Preview");
}
 
===[[Latex]] generator of the labels===
 
% Copyleft 2011 by Dmitrii Kouznetsov
\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating}
\paperwidth 854pt
\paperheight 844pt
\topmargin -96pt
\oddsidemargin -98pt
\textwidth 1100pt
\textheight 1100pt
\pagestyle {empty}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\begin{document}
\sx{5}{ \begin{picture}(164,165)
\put(6,5){\ing{taniamap}}
\put(2,162){\sx{.7}{$y$}}
\put(2,144){\sx{.6}{$6$}}
\put(2,124){\sx{.6}{$4$}}
\put(2,104){\sx{.6}{$2$}}
\put(3,116){\sx{.6}{$\pi$ ~ \bf cut}}
\put(23,100){\sx{.8}{$u\!=\!0$}}
\put(2, 84){\sx{.6}{$0$}}
\put(20, 84){\sx{.8}{$v\!=\!0$}}
\put(23,68){\sx{.8}{$u\!=\!0$}}
\put(-3,64){\sx{.6}{$-2$}}
\put(-3,53){\sx{.6}{$-\pi$ ~ \bf cut}}
\put(-3,44){\sx{.6}{$-4$}}
\put(-3,24){\sx{.6}{$-6$}}
\put( 22,0){\sx{.6}{$-6$}}
\put( 42,0){\sx{.6}{$-4$}}
\put( 62,0){\sx{.6}{$-2$}}
\put( 86,0){\sx{.6}{$0$}}
\put(106,0){\sx{.6}{$2$}}
\put(126,0){\sx{.6}{$4$}}
\put(146,0){\sx{.6}{$6$}}
\put(164,0){\sx{.7}{$x$}}
\put(139,154){\rot{-6}\sx{.8}{$v\!=\!6$}\ero}
\put(138,143){\rot{-6}\sx{.8}{$v\!=\!5$}\ero}
\put(137,132){\rot{-6}\sx{.8}{$v\!=\!4$}\ero}
\put(136,121){\rot{-6}\sx{.8}{$v\!=\!3$}\ero}
\put(135,109){\rot{-5}\sx{.8}{$v\!=\!2$}\ero}
\put( 89, 83){\rot{82}\sx{.8}{$u\!=\!1$}\ero}
\put(106, 81){\rot{84}\sx{.8}{$u\!=\!2$}\ero}
\put(134, 97){\rot{-4}\sx{.8}{$v\!=\!1$}\ero}
\put(134, 84){\rot{0}\sx{.8}{$v\!=\!0$}\ero}
\put(134, 72){\rot{3}\sx{.72}{$v\!=\!-\!1$}\ero}
\put(133, 60){\rot{3}\sx{.72}{$v\!=\!-\!2$}\ero}
\put(134, 48){\rot{3}\sx{.72}{$v\!=\!-\!3$}\ero}
\put(135, 36){\rot{3}\sx{.72}{$v\!=\!-\!4$}\ero}
\put(136, 25){\rot{3}\sx{.72}{$v\!=\!-\!5$}\ero}
\put(137, 14){\rot{3}\sx{.72}{$v\!=\!-\!6$}\ero}
\end{picture}
}
\end{document}

Latest revision as of 18:53, 11 March 2022

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