imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = [[Complex map]] of <i>u+iv</i>=[[ArcCos]](<i>x+iy</i>)
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = 2012 March 17
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| |pub-country = Japan
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| |notes =
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| |versions = http://tori.ils.uec.ac.jp/TORI/index.php/File:AcomapT200.png
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| }}
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| | |
| ==C++ generator of curves==
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| Files [[ado.cin]] and [[conto.cin]] should be loaded to the working directory
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| for compilation of the [[C++]] code below
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| | |
| #include <math.h>
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| #include <stdio.h>
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| #include <stdlib.h>
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| #define DB double
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| #define DO(x,y) for(x=0;x<y;x++)
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| using namespace std;
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| #include <complex>
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| typedef complex<double> z_type;
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| #define Re(x) x.real()
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| #define Im(x) x.imag()
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| #define I z_type(0.,1.)
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| #include "conto.cin"
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| | |
| z_type acos(z_type z){
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| if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
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| else{return I*log( z - sqrt(z*z-1.) );}}
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| if(Re(z)>=0){return -I*log( z + sqrt(z*z-1.) );}
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| else {return -I*log( z - sqrt(z*z-1.) );} }
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| | |
| main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
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| int M=401,M1=M+1;
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| int N=401,N1=N+1;
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| DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
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| char v[M1*N1]; // v is working array
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| FILE *o;o=fopen("acomap.eps","w");ado(o,82,82);
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| fprintf(o,"41 41 translate\n 10 10 scale\n");
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| //DO(m,M1) X[m]=-4.+.02*(m-.5);
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| DO(n,200)Y[n]=-4.+.02*n;
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| Y[200]=-.002;
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| Y[201]= .002;
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| for(n=202;n<N1;n++) Y[n]=-4.+.02*(n-1.);
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| DO(m,M1)X[m]=Y[m];
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| for(m=-4;m<5;m++){if(m==0){M(m,-4.1)L(m,4.1)} else{M(m,-4)L(m,4)}}
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| for(n=-4;n<5;n++){ M( -4,n)L(4,n)}
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| fprintf(o,".01 W 0 0 0 RGB S\n");
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| DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
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| DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
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| DO(n,N1){y=Y[n]; z=z_type(x,y);
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| c=acos(z);
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| // c=ACip5(z);
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| // p=abs((c-d)/(c+d)); p=-log(p)/log(10.);
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| p=Re(c);
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| q=Im(c);
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| if(p>-99. && p<99.
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| && q>-99. && q<99
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| )
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| {g[m*N1+n]=p;
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| f[m*N1+n]=q;
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| }
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| }}
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| //
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| // #include "plofu.cin"
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| fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.8;q=.7;
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| 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");
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| 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");
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| 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");
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| 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");
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| 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");
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| conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".03 W .6 0 .6 RGB S\n");
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| 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");
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| //
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| M(-4.02,0)L(-1,0)
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| M(1,0)L(4.02,0)
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| fprintf(o,"0 setlinecap .028 W .9 1 .9 RGB S\n");
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| DO(m,31){x=-1.-.1*m; M(x,0) L(x-.05,0)}
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| DO(n,31){x= 1.+.1*n; M(x,0) L(x+.05,0)}
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| fprintf(o,".032 W 0 0 0 RGB S\n");
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| fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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| system("epstopdf acomap.eps");
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| system( "open acomap.pdf");
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| getchar(); system("killall Preview");//for mac
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| }
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| | |
| ==Latex generator of labels==
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| | |
| <!--<nowiki> !-->
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| \documentclass[12pt]{article} %<br>
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| \paperheight 838px %<br>
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| \paperwidth 844px %<br>
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| \textwidth 1294px %<br>
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| \textheight 1200px %<br>
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| \topmargin -80px %<br>
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| \oddsidemargin -80px %<br>
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| \usepackage{graphics} %<br>
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| \usepackage{rotating} %<br>
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| \newcommand \sx {\scalebox} %<br>
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| \newcommand \rot {\begin{rotate}} %<br>
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| \newcommand \ero {\end{rotate}} %<br>
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| \newcommand \ing {\includegraphics} %<br>
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| \newcommand \rmi {\mathrm{i}} %<br>
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| \begin{document} %<br>
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| \newcommand \zoomax { %<br>
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| \put(16,820){\sx{4.4}{$y$}} %<br>
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| \put(16,630){\sx{4}{$2$}} %<br>
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| \put(16,430){\sx{4}{$0$}} %<br>
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| \put(-4, 230){\sx{4}{$-\!2$}} %<br>
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| \put(220, 5){\sx{4}{$-\!2$}} %<br>
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| \put(443, 5){\sx{4}{$0$}} %<br>
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| \put(643, 5){\sx{4}{$2$}} %<br>
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| \put(831,6){\sx{4}{$x$}} %<br>
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| }%<br>
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| \parindent 0pt %<br>
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| %\sx{8}{\begin{picture}(86,86) \put(0,0){\ing{b271t0}} %<br>
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| \begin{picture}(816,816) %<br>
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| \put(40,30){\sx{10}{\ing{acomap}}} %<br>
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| \zoomax %<br>
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| \put(100,548){\sx{4}{\rot{-20}$u\!=\!2.8$\ero}} %<br>
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| \put(90,478){\sx{4}{\rot{-7}$u\!=\!3$\ero}} %<br>
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| \put(90,381){\sx{4}{\rot{8}$u\!=\!3$\ero}} %<br>
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| \put(312,120){\sx{4}{\rot{66}$u\!=\!2$\ero}} %<br>
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| %<br>
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| \put(540,620){\sx{4}{\rot{66}$u\!=\!1.2$\ero}} %<br>
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| \put(624,586){\sx{4}{\rot{48}$u\!=\!0.8$\ero}} %<br>
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| \put(644,548){\sx{4}{\rot{36}$u\!=\!0.6$\ero}} %<br>
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| \put(660,510){\sx{4}{\rot{22}$u\!=\!0.4$\ero}} %<br>
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| \put(670,472){\sx{4}{\rot{10}$u\!=\!0.2$\ero}} %<br>
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| %<br>
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| \put(90,432){\sx{4}{\bf cut}} %<br>
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| \put(690,432){\sx{4}{\bf cut}} %<br>
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| \put(400,795){\sx{4.1}{$v\!=\!-2$}} %<br>
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| \put(400,550){\sx{4}{$v\!=\!-1$}} %<br>
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| \put(411,431){\sx{3.8}{$v\!=\!0$}} %<br>
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| \put(410,313){\sx{4}{$v\!=\!1$}} %<br>
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| \put(410, 66){\sx{4}{$v\!=\!2$}} %<br>
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| \end{picture} %<br>
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| \end{document} %<br>
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| %<!-- </nowiki> %<br> !-->
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| == Licensing ==
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| {{CC|by|3.0}}
| |
