File:AcomapT.png: Difference between revisions

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imported>Dmitrii Kouznetsov
({{Image_Details|user |description = Complex map of <i>u+iv</i>=ArcCos(<i>x+iy</i>) |author = ~~~ |date-created = 2012 March 17 |pub-country = Japan |notes = ==Generators== acomap.cc is used to generate the figure |versions = http://tori.ils.uec.ac.jp/TORI/index.php/File:AcomapT200.png }})
 
imported>Dmitrii Kouznetsov
(add generators)
Line 5: Line 5:
|date-created = 2012 March 17
|date-created = 2012 March 17
|pub-country  = Japan
|pub-country  = Japan
|notes        = ==Generators==
|notes        =  
acomap.cc is used to generate the figure
|versions    = http://tori.ils.uec.ac.jp/TORI/index.php/File:AcomapT200.png
|versions    = http://tori.ils.uec.ac.jp/TORI/index.php/File:AcomapT200.png
}}
}}
==C++ generator of curves==
==C++ generator of curves==
Files [[ado.cin]] and [[conto.cin]] should be loaded to the working directory
for compilation of the [[C++]] code 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 acos(z_type z){
  if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
                    else{return I*log( z - sqrt(z*z-1.) );}}
            if(Re(z)>=0){return -I*log( z + sqrt(z*z-1.) );}
                    else {return -I*log( z - sqrt(z*z-1.) );} }
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=401,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("acomap.eps","w");ado(o,82,82);
fprintf(o,"41 41 translate\n 10 10 scale\n");
//DO(m,M1) X[m]=-4.+.02*(m-.5);
DO(n,200)Y[n]=-4.+.02*n;
      Y[200]=-.002;
      Y[201]= .002;
for(n=202;n<N1;n++) Y[n]=-4.+.02*(n-1.);
DO(m,M1)X[m]=Y[m];
for(m=-4;m<5;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(  -4,n)L(4,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=acos(z);
//    c=ACip5(z);
//    p=abs((c-d)/(c+d));  p=-log(p)/log(10.);
      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 "plofu.cin"
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.8;q=.7;
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,".03 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,".03 W 0 0 .9 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".03 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,".03 W 0 0 0 RGB S\n");
//
M(-4.02,0)L(-1,0)
M(1,0)L(4.02,0)
fprintf(o,"0 setlinecap .028 W .9 1 .9 RGB S\n");
DO(m,31){x=-1.-.1*m; M(x,0) L(x-.05,0)}
DO(n,31){x= 1.+.1*n; M(x,0) L(x+.05,0)}
fprintf(o,".032 W 0 0 0 RGB S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf acomap.eps");
      system(    "open acomap.pdf");           
      getchar(); system("killall Preview");//for mac
}
==Latex generator of labels==
<!--<nowiki> !-->
\documentclass[12pt]{article} %<br>
\paperheight 838px %<br>
\paperwidth 844px %<br>
\textwidth 1294px %<br>
\textheight 1200px %<br>
\topmargin -80px %<br>
\oddsidemargin -80px %<br>
\usepackage{graphics} %<br>
\usepackage{rotating} %<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}{$-\!2$}} %<br>
\put(443,  5){\sx{4}{$0$}} %<br>
\put(643,  5){\sx{4}{$2$}} %<br>
\put(831,6){\sx{4}{$x$}}  %<br>
}%<br>
\parindent 0pt %<br>
%\sx{8}{\begin{picture}(86,86) \put(0,0){\ing{b271t0}} %<br>
\begin{picture}(816,816) %<br>
\put(40,30){\sx{10}{\ing{acomap}}} %<br>
\zoomax %<br>
\put(100,548){\sx{4}{\rot{-20}$u\!=\!2.8$\ero}} %<br>
\put(90,478){\sx{4}{\rot{-7}$u\!=\!3$\ero}} %<br>
\put(90,381){\sx{4}{\rot{8}$u\!=\!3$\ero}} %<br>
\put(312,120){\sx{4}{\rot{66}$u\!=\!2$\ero}} %<br>
%<br>
\put(540,620){\sx{4}{\rot{66}$u\!=\!1.2$\ero}} %<br>
\put(624,586){\sx{4}{\rot{48}$u\!=\!0.8$\ero}} %<br>
\put(644,548){\sx{4}{\rot{36}$u\!=\!0.6$\ero}} %<br>
\put(660,510){\sx{4}{\rot{22}$u\!=\!0.4$\ero}} %<br>
\put(670,472){\sx{4}{\rot{10}$u\!=\!0.2$\ero}} %<br>
%<br>
\put(90,432){\sx{4}{\bf cut}} %<br>
\put(690,432){\sx{4}{\bf cut}} %<br>
\put(400,795){\sx{4.1}{$v\!=\!-2$}} %<br>
\put(400,550){\sx{4}{$v\!=\!-1$}} %<br>
\put(411,431){\sx{3.8}{$v\!=\!0$}} %<br>
\put(410,313){\sx{4}{$v\!=\!1$}} %<br>
\put(410, 66){\sx{4}{$v\!=\!2$}} %<br>
\end{picture} %<br>
\end{document} %<br>
%<!-- </nowiki> %<br> !-->
== Licensing ==
== Licensing ==
{{CC|by|3.0}}
{{CC|by|3.0}}

Revision as of 03:55, 31 March 2012

Summary

Title / Description


Complex map of u+iv=ArcCos(x+iy)
Citizendium author
& Copyright holder


Copyright © Dmitrii Kouznetsov.
See below for licence/re-use information.
Date created


2012 March 17
Country of first publication


Japan
Notes


You can edit this page and add notes here which may be useful to people who wish to re-use this media.
Other versions


http://tori.ils.uec.ac.jp/TORI/index.php/File:AcomapT200.png
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C++ generator of curves

C++ generator of curves

Files ado.cin and conto.cin should be loaded to the working directory for compilation of the C++ code 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 acos(z_type z){
 if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} 
                    else{return I*log( z - sqrt(z*z-1.) );}}
            if(Re(z)>=0){return -I*log( z + sqrt(z*z-1.) );} 
                   else {return -I*log( z - sqrt(z*z-1.) );} }
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=401,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("acomap.eps","w");ado(o,82,82);
fprintf(o,"41 41 translate\n 10 10 scale\n");
//DO(m,M1) X[m]=-4.+.02*(m-.5);
DO(n,200)Y[n]=-4.+.02*n;
      Y[200]=-.002;
      Y[201]= .002;
for(n=202;n<N1;n++) Y[n]=-4.+.02*(n-1.);
DO(m,M1)X[m]=Y[m];
for(m=-4;m<5;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(  -4,n)L(4,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=acos(z);
//     c=ACip5(z);
//     p=abs((c-d)/(c+d));  p=-log(p)/log(10.);
      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 "plofu.cin"
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.8;q=.7;
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,".03 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,".03 W 0 0 .9 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".03 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,".03 W 0 0 0 RGB S\n");
//
M(-4.02,0)L(-1,0)
M(1,0)L(4.02,0)
fprintf(o,"0 setlinecap .028 W .9 1 .9 RGB S\n");
DO(m,31){x=-1.-.1*m; M(x,0) L(x-.05,0)}
DO(n,31){x= 1.+.1*n; M(x,0) L(x+.05,0)}
fprintf(o,".032 W 0 0 0 RGB S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf acomap.eps");
      system(    "open acomap.pdf");            
      getchar(); system("killall Preview");//for mac
}

Latex generator of labels

\documentclass[12pt]{article} %
\paperheight 838px %
\paperwidth 844px %
\textwidth 1294px %
\textheight 1200px %
\topmargin -80px %
\oddsidemargin -80px %
\usepackage{graphics} %
\usepackage{rotating} %
\newcommand \sx {\scalebox} %
\newcommand \rot {\begin{rotate}} %
\newcommand \ero {\end{rotate}} %
\newcommand \ing {\includegraphics} %
\newcommand \rmi {\mathrm{i}} %
\begin{document} %
\newcommand \zoomax { %
\put(16,820){\sx{4.4}{$y$}} %
\put(16,630){\sx{4}{$2$}} %
\put(16,430){\sx{4}{$0$}} %
\put(-4, 230){\sx{4}{$-\!2$}} %
\put(220, 5){\sx{4}{$-\!2$}} %
\put(443, 5){\sx{4}{$0$}} %
\put(643, 5){\sx{4}{$2$}} %
\put(831,6){\sx{4}{$x$}}  %
}%
\parindent 0pt %
%\sx{8}{\begin{picture}(86,86) \put(0,0){\ing{b271t0}} %
\begin{picture}(816,816) %
\put(40,30){\sx{10}{\ing{acomap}}} %
\zoomax %
\put(100,548){\sx{4}{\rot{-20}$u\!=\!2.8$\ero}} %
\put(90,478){\sx{4}{\rot{-7}$u\!=\!3$\ero}} %
\put(90,381){\sx{4}{\rot{8}$u\!=\!3$\ero}} %
\put(312,120){\sx{4}{\rot{66}$u\!=\!2$\ero}} %
%
\put(540,620){\sx{4}{\rot{66}$u\!=\!1.2$\ero}} %
\put(624,586){\sx{4}{\rot{48}$u\!=\!0.8$\ero}} %
\put(644,548){\sx{4}{\rot{36}$u\!=\!0.6$\ero}} %
\put(660,510){\sx{4}{\rot{22}$u\!=\!0.4$\ero}} %
\put(670,472){\sx{4}{\rot{10}$u\!=\!0.2$\ero}} %
%
\put(90,432){\sx{4}{\bf cut}} %
\put(690,432){\sx{4}{\bf cut}} %
\put(400,795){\sx{4.1}{$v\!=\!-2$}} %
\put(400,550){\sx{4}{$v\!=\!-1$}} %
\put(411,431){\sx{3.8}{$v\!=\!0$}} %
\put(410,313){\sx{4}{$v\!=\!1$}} %
\put(410, 66){\sx{4}{$v\!=\!2$}} %
\end{picture} %
\end{document} %
%


Licensing

This media, AcomapT.png, is licenced under the Creative Commons Attribution 3.0 Unported License

You are free: To Share — To copy, distribute and transmit the work; To Remix — To adapt the work.
Under the following conditions: Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
For any reuse or distribution, you must make clear to others the licence terms of this work (the best way to do this is with a link to this licence's web page). Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this licence impairs or restricts the author's moral rights.
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Date/TimeThumbnailDimensionsUserComment
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