imported>Dmitrii Kouznetsov |
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| == 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}
| |
