path: root/Master/texmf-dist/doc/latex/lshort-russian/src/graphic.tex

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\setcounter{chapter}{4}
\newcommand{\graphicscompanion}{\emph{The \LaTeX{} Graphics Companion}~\cite{graphicscompanion}} 
\newcommand{\hobby}{\emph{òÕËÏ×ÏÄÓÔ×Ï ÐÏÌØÚÏ×ÁÔÅÌÑ MetaPost}~\cite{metapost}}
\newcommand{\hoenig}{\emph{\TeX{} Unbound}~\cite{unbound}}
\newcommand{\graphicsinlatex}{\emph{çÒÁÆÉËÁ ×  \LaTeXe{}}~\cite{ursoswald}}

\chapter{çÅÎÅÒÁÃÉÑ ÍÁÔÅÍÁÔÉÞÅÓËÏÊ ÇÒÁÆÉËÉ}

\begin{intro}
âÏÌØÛÉÎÓÔ×Ï ÌÀÄÅÊ ÐÏÌØÚÕÀÔÓÑ \LaTeX\ ÄÌÑ ×ÅÒÓÔËÉ ÔÅËÓÔÁ. îÏ \LaTeX{} ÔÁËÖÅ
ÐÒÅÄÌÁÇÁÅÔ, ÈÏÔÑ É ÏÇÒÁÎÉÞÅÎÎÕÀ, ×ÏÚÍÏÖÎÏÓÔØ ÇÅÎÅÒÁÃÉÉ ÇÒÁÆÉËÉ ÐÏ
ÔÅËÓÔÏ×ÏÍÕ ÏÐÉÓÁÎÉÀ. âÏÌÅÅ ÔÏÇÏ, ÓÕÝÅÓÔ×ÕÅÔ ÍÎÏÖÅÓÔ×Ï ÒÁÓÛÉÒÅÎÉÊ \LaTeX{},
ÏÂÈÏÄÑÝÉÈ ÜÔÉ ÏÇÒÁÎÉÞÎÉÑ. üÔÁ ÇÌÁ×Á ÒÁÓÓËÁÖÅÔ Ï ÎÅÓËÏÌØËÉÈ ÉÚ ÎÉÈ.
\end{intro}

\section{ïÂÚÏÒ}

ïËÒÕÖÅÎÉÅ \ei{picture} ÐÏÚ×ÏÌÑÅÔ ÐÒÏÇÒÁÍÍÉÒÏ×ÁÔØ ËÁÒÔÉÎËÉ ÐÒÑÍÏ ×
ÓÒÅÄÅ \LaTeX. ðÏÄÒÏÂÎÏÅ ÏÐÉÓÁÎÉÅ ÐÒÉ×ÏÄÉÔÓÑ × \manual. ó ÏÄÎÏÊ
ÓÔÏÒÏÎÙ, ÐÒÉ ÜÔÏÍ ÅÓÔØ ÄÏ×ÏÌØÎÏ ÓÅÒØÅÚÎÙÅ ÏÇÒÁÎÉÞÅÎÉÑ, ÐÏÓËÏÌØËÕ ËÁË
ÎÁËÌÏÎÙ ÏÔÒÅÚËÏ×, ÔÁË É ÒÁÄÉÕÓÙ ÄÕÇ ÓÉÌØÎÏ ÏÇÒÁÎÉÞÅÎÙ × ×ÏÚÍÏÖÎÙÈ
ÚÎÁÞÅÎÉÑÈ. ó ÄÒÕÇÏÊ ÓÔÏÒÏÎÙ, × ÏËÒÕÖÅÎÉÉ \ei{picture} ÓÕÝÅÓÔ×ÕÀÅÔ
ËÏÍÁÎÄÁ \ci{qbezier}, ÇÄÅ <<\texttt{q}>> ÏÚÎÁÞÁÅÔ
<<Ë×ÁÄÒÁÔÉÞÎÙÊ>>. íÎÏÖÅÓÔ×Ï ÞÁÓÔÏ ÉÓÐÏÌØÚÕÅÍÙÈ ËÒÉ×ÙÈ, ÔÁËÉÈ ËÁË
ÏËÒÕÖÎÏÓÔÉ, ÜÌÌÉÐÓÙ ÉÌÉ ÃÅÐÎÙÅ ÌÉÎÉÉ, ÍÏÖÎÏ ÕÄÏ×ÌÅÔ×ÏÒÉÔÅÌØÎÏ
ÁÐÐÒÏËÓÉÍÉÒÏ×ÁÔØ Ë×ÁÄÒÁÔÉÞÎÙÍÉ ËÒÉ×ÙÍÉ âÅÚØÅ, ÈÏÔÑ ÄÌÑ ÜÔÏÇÏ É
ÔÒÅÂÕÀÔÓÑ ÎÅËÏÔÏÒÙÅ ÍÁÔÅÍÁÔÉÞÅÓËÉÅ ÕÓÉÌÉÑ. ëÒÏÍÅ ÔÏÇÏ, ËÏÇÄÁ ÂÌÏËÉ
ËÏÍÁÎÄ \ci{qbezier} ÇÅÎÅÒÉÒÕÀÔÓÑ ÉÚ ÑÚÙËÁ ÐÒÏÇÒÁÍÍÉÒÏ×ÁÎÉÑ, ÓËÁÖÅÍ,
Java, ÏËÒÕÖÅÎÉÅ \ei{picture} ÓÔÁÎÏ×ÉÔÓÑ ÄÏ×ÏÌØÎÏ ÍÏÝÎÙÍ.

èÏÔÑ ÐÒÏÇÒÁÍÍÉÒÏ×ÁÎÉÅ ËÁÒÔÉÎÏË ÐÒÑÍÏ ÉÚ \LaTeX{} ÓÅÒØÅÚÎÏ ÏÇÒÁÎÉÞÅÎÏ É
ÞÁÓÔÏ ÄÏ×ÏÌØÎÏ ÕÔÏÍÉÔÅÌØÎÏ, ÏÎÏ ×ÓÅ ÖÅ ÂÙ×ÁÅÔ ÐÏÌÅÚÎÙÍ. ðÏÌÕÞÅÎÎÙÅ
ÔÁËÉÍ ÏÂÒÁÚÏÍ ÄÏËÕÍÅÎÔÙ ÐÏÌÕÞÁÀÔÓÑ ËÏÍÐÁËÔÎÙÍÉ, É ÎÅÔ ÎÅÏÂÈÏÄÉÍÏÓÔÉ
ÐÒÉÌÁÇÁÔØ Ë ÄÏËÕÍÅÎÔÕ ÇÒÁÆÉÞÅÓËÉÅ ÆÁÊÌÙ.

ðÁËÅÔÙ ÎÁÐÏÄÏÂÉÅ \pai{epic} É \pai{eepic} (ÏÐÉÓÁÎÎÙÅ, ÎÁÐÒÉÍÅÒ, ×
\companion) ÉÌÉ \pai{pstricks} ÐÏÍÏÇÁÀÔ ÓÎÑÔØ ÏÇÒÁÎÉÞÅÎÉÑ
ÏÒÉÇÉÎÁÌØÎÏÇÏ ÏËÒÕÖÅÎÉÑ \ei{picture} É ÓÉÌØÎÏ ÒÁÚ×É×ÁÀÔ ÇÒÁÆÉÞÅÓËÉÅ
×ÏÚÍÏÖÎÏÓÔÉ \LaTeX{}.

ôÏÇÄÁ ËÁË ÐÅÒ×ÙÅ Ä×Á ÐÁËÅÔÁ ÐÒÏÓÔÏ ÕÌÕÞÛÁÀÔ ÏËÒÕÖÅÎÉÅ \ei{picture},
ÐÁËÅÔ \pai{pstricks} ÉÍÅÅÔ ÓÏÂÓÔ×ÅÎÎÏÅ ÏËÒÕÖÅÎÉÅ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ,
\ei{pspicture}. ÷ÏÚÍÏÖÎÏÓÔÉ \pai{pstricks} ÐÒÏÉÓÔÅËÁÀÔ ÉÈ ÔÏÇÏ, ÞÔÏ ÏÎ
ÛÉÒÏËÏ ÉÓÐÏÌØÚÕÅÔ ÆÕÎËÃÉÏÎÁÌØÎÏÓÔØ \PSi{}. ëÒÏÍÅ ÜÔÏÇÏ ÐÁËÅÔÁ,
ÓÕÝÅÓÔ×ÕÅÔ É ÍÎÏÖÅÓÔ×Ï ÄÒÕÇÉÈ, ÎÁÐÉÓÁÎÎÙÈ ÄÌÑ ËÏÎËÒÅÔÎÙÈ ÚÁÄÁÞ. ïÄÎÉÍ
ÉÚ ÎÉÈ Ñ×ÌÑÅÔÓÑ ÐÁËÅÔ \texorpdfstring{\Xy}{Xy}-pic, ÏÐÉÓÁÎÎÙÊ × ËÏÎÃÅ
ÜÔÏÊ ÇÌÁ×Ù. íÎÏÖÅÓÔ×Ï ÔÁËÉÈ ÐÁËÅÔÏ× ÄÅÔÁÌØÎÏ ÏÐÉÓÁÎÏ ×
\graphicscompanion{} (ÎÅ ÐÕÔÁÔØ Ó \companion).

÷ÏÚÍÏÖÎÏ, ÓÁÍÙÍ ÍÏÝÎÙÍ ÇÒÁÆÉÞÅÓËÉÍ ÉÎÓÔÒÕÍÅÎÔÏÍ, Ó×ÑÚÁÎÎÙÍ Ó \LaTeX{},
Ñ×ÌÑÅÔÓÑ \MP, ÐÒÏÇÒÁÍÍÁ-ÂÌÉÚÎÅà ÎÁÐÉÓÁÎÎÏÊ Donald E. Knuth ÐÒÏÇÒÁÍÍÙ
\texttt{METAFONT}. \MP{} ÉÓÐÏÌØÚÕÅÔ ÏÞÅÎØ ÍÏÝÎÙÊ É ÍÁÔÅÍÁÔÉÞÅÓËÉ
ÉÚÏÝÒÅÎÎÙÊ ÑÚÙË \texttt{METAFONT}. ÷ ÏÔÌÉÞÉÅ ÖÅ ÏÔ \texttt{METAFONT},
ÇÅÎÅÒÉÒÕÀÝÅÇÏ ÒÁÓÔÒÙ, \MP{} ÇÅÎÅÒÉÒÕÅÔ ÆÁÊÌÙ \EPSi{}, ËÏÔÏÒÙÅ ÍÏÖÎÏ
ÉÍÐÏÒÔÉÒÏ×ÁÔØ × \LaTeX{}. äÁÌÅÅ ÓÍÏÔÒÉÔÅ \hobby, ÉÌÉ ××ÅÄÅÎÉÅ ×
\cite{ursoswald}. 

ïÞÅÎØ ÐÏÄÒÏÂÎÏ ÒÁÂÏÔÁ Ó ÇÒÁÆÉËÏÊ (É ÛÒÉÆÔÁÍÉ) × \LaTeX{} É \TeX{}
ÏÐÉÓÁÎÁ × \hoenig.

\section{ïËÒÕÖÅÎÉÅ \texttt{picture}}
\secby{Urs Oswald}{osurs@bluewin.ch}

\subsection{ïÓÎÏ×ÎÙÅ ËÏÍÁÎÄÙ}

ïËÒÕÖÅÎÉÅ \ei{picture} ÓÏÚÄÁÅÔÓÑ ÏÄÎÏÊ ÉÚ Ä×ÕÈ ËÏÍÁÎÄ:
\begin{lscommand}
\ci{begin}\verb|{picture}(|$x,y$\verb|)|\ldots\ci{end}\verb|{picture}|
\end{lscommand}
\noindent ÌÉÂÏ
\begin{lscommand}
\ci{begin}\verb|{picture}(|$x,y$\verb|)(|$x_0,y_0$\verb|)|\ldots\ci{end}\verb|{picture}|
\end{lscommand}

þÉÓÌÁ $x,\,y,\,x_0,\,y_0$ ÉÚÍÅÒÑÀÔÓÑ × ÒÁÚÍÅÒÎÏÓÔÉ \ci{unitlength},
ËÏÔÏÒÕÀ ÍÏÖÎÏ ÍÅÎÑÔØ × ÌÀÂÏÊ ÍÏÍÅÎÔ (ÎÏ ÎÅ ×ÎÕÔÒÉ ÏËÒÕÖÅÎÉÑ
\ei{picture}) ËÏÍÁÎÄÁÍÉ ÎÁÐÏÄÏÂÉÅ
\begin{lscommand}
\ci{setlength}\verb|{|\ci{unitlength}\verb|}{1.2cm}|
\end{lscommand}

úÎÁÞÅÎÉÅ \ci{unitlength} ÐÏ ÕÍÏÌÞÁÎÉÀ ÓÏÓÔÁ×ÌÑÅÔ 1pt. ðÅÒ×ÁÑ ÐÁÒÁ,
$(x,y)$, ÄÉËÔÕÅÔ ÒÅÚÅÒ×ÉÒÏ×ÁÎÉÅ ÄÌÑ ËÁÒÔÉÎËÉ ÐÒÑÍÏÕÇÏÌØÎÏÇÏ
ÐÒÏÓÔÒÁÎÓÔ×Á ×ÎÕÔÒÉ ÄÏËÕÍÅÎÔÁ. îÅÏÂÑÚÁÔÅÌØÎÁÑ ×ÔÏÒÁÑ ÐÁÒÁ,
$(x_0,y_0)$, ÐÒÉÓ×ÁÉ×ÁÅÔ ÐÒÏÉÚ×ÏÌØÎÙÅ ËÏÏÒÄÉÎÁÔÙ ÎÉÖÎÅÍÕ ÌÅ×ÏÍÕ ÕÇÌÕ
ÚÁÒÅÚÅÒ×ÉÒÏ×ÁÎÎÏÇÏ ÐÒÑÍÏÕÇÏÌØÎÉËÁ.

âÏÌØÛÉÎÓÔ×Ï ËÏÍÁÎÄ ÒÉÓÏ×ÁÎÉÑ ÉÍÅÀÔ ÏÄÎÕ ÉÚ Ä×ÕÈ ÆÏÒÍ:
\begin{lscommand}
\ci{put}\verb|(|$x,y$\verb|){|\emph{ÏÂßÅËÔ}\verb|}|
\end{lscommand}
\noindent ÉÌÉ
\begin{lscommand}
\ci{multiput}\verb|(|$x,y$\verb|)(|$\Delta x,\Delta y$\verb|){|$n$\verb|}{|\emph{ÏÂßÅËÔ}\verb|}|\end{lscommand}

ëÒÉ×ÙÅ âÅÚØÅ Ñ×ÌÑÀÔÓÑ ÉÓËÌÀÞÅÎÉÅÍ. éÈ ÒÉÓÕÀÔ ËÏÍÁÎÄÏÊ
\begin{lscommand}
\ci{qbezier}\verb|(|$x_1,y_1$\verb|)(|$x_2,y_2$\verb|)(|$x_3,y_3$\verb|)|
\end{lscommand}

\subsection{ïÔÒÅÚËÉ}

\begin{example}
\setlength{\unitlength}{5cm}
\begin{picture}(1,1)
  \put(0,0){\line(0,1){1}}
  \put(0,0){\line(1,0){1}}  
  \put(0,0){\line(1,1){1}}  
  \put(0,0){\line(1,2){.5}}
  \put(0,0){\line(1,3){.3333}}
  \put(0,0){\line(1,4){.25}}  
  \put(0,0){\line(1,5){.2}}
  \put(0,0){\line(1,6){.1667}}
  \put(0,0){\line(2,1){1}}
  \put(0,0){\line(2,3){.6667}}
  \put(0,0){\line(2,5){.4}}
  \put(0,0){\line(3,1){1}}  
  \put(0,0){\line(3,2){1}}
  \put(0,0){\line(3,4){.75}}
  \put(0,0){\line(3,5){.6}}
  \put(0,0){\line(4,1){1}}
  \put(0,0){\line(4,3){1}}  
  \put(0,0){\line(4,5){.8}}
  \put(0,0){\line(5,1){1}}
  \put(0,0){\line(5,2){1}}
  \put(0,0){\line(5,3){1}}
  \put(0,0){\line(5,4){1}}
  \put(0,0){\line(5,6){.8333}}
  \put(0,0){\line(6,1){1}}
  \put(0,0){\line(6,5){1}}
\end{picture}
\end{example}
ïÔÒÅÚËÉ ÒÉÓÕÀÔÓÑ ËÏÍÁÎÄÏÊ
\begin{lscommand}
\ci{put}\verb|(|$x,y$\verb|){|\ci{line}\verb|(|$x_1,y_1$\verb|){|$length$\verb|}}|
\end{lscommand}
ëÏÍÁÎÄÁ \ci{line} ÉÍÅÅÔ Ä×Á ÁÒÇÕÍÅÎÔÁ:
\begin{enumerate}
 \item ×ÅËÔÏÒ ÎÁÐÒÁ×ÌÅÎÉÑ,
 \item ÄÌÉÎÁ.
\end{enumerate}
ëÏÍÐÏÎÅÎÔÙ ×ÅËÔÏÒÁ ÏÇÒÁÎÉÞÅÎÙ × Ó×ÏÅÍ ÚÎÁÞÅÎÉÉ ÎÁÂÏÒÏÍ ÃÅÌÙÈ ÞÉÓÅÌ
\[
 -6,\,-5\,\ldots,\,5,\,6,
\]
É ÏÎÉ ÏÂÑÚÁÎÙ ÂÙÔØ ×ÚÁÉÍÎÏ ÐÒÏÓÔÙÍÉ (ÎÅ ÉÍÅÔØ ÏÂÝÅÇÏ ÄÅÌÉÔÅÌÑ, ËÒÏÍÅ
1). éÌÌÀÓÔÒÁÃÉÑ ÐÏËÁÚÙ×ÁÅÔ ×ÓÅ 25 ×ÏÚÍÏÖÎÙÈ ÚÎÁÞÅÎÉÊ ÎÁËÌÏÎÁ × ÐÅÒ×ÏÍ
Ë×ÁÄÒÁÎÔÅ. äÌÉÎÁ ×ÙÒÁÖÁÅÔÓÑ × ÅÄÉÎÉÃÁÈ \ci{unitlength}. áÒÇÕÍÅÎÔ ÄÌÉÎÙ
ÚÁÄÁÅÔ ×ÅÒÔÉËÁÌØÎÕÀ ËÏÏÒÄÉÎÁÔÕ × ÓÌÕÞÁÅ ×ÅÒÔÉËÁÌØÎÏÇÏ ÏÔÒÅÚËÁ É
ÇÏÒÉÚÏÎÔÁÌØÎÕÀ~--- ×Ï ×ÓÅÈ ÏÓÔÁÌØÎÙÈ ÓÌÕÞÁÑÈ.

\subsection{÷ÅËÔÏÒÙ}

\begin{example}
\setlength{\unitlength}{1mm}
\begin{picture}(60,40)
  \put(30,20){\vector(1,0){30}}
  \put(30,20){\vector(4,1){20}}
  \put(30,20){\vector(3,1){25}}
  \put(30,20){\vector(2,1){30}}
  \put(30,20){\vector(1,2){10}}
  \thicklines
  \put(30,20){\vector(-4,1){30}}
  \put(30,20){\vector(-1,4){5}}
  \thinlines
  \put(30,20){\vector(-1,-1){5}}
  \put(30,20){\vector(-1,-4){5}}
\end{picture}
\end{example}
÷ÅËÔÏÒÙ ÒÉÓÕÀÔÓÑ ËÏÍÁÎÄÏÊ
\begin{lscommand}
\ci{put}\verb|(|$x,y$\verb|){|\ci{vector}\verb|(|$x_1,y_1$\verb|){|$length$\verb|}}|
\end{lscommand}
äÌÑ ×ÅËÔÏÒÏ× ÚÎÁÞÅÎÉÑ ×ÅËÔÏÒÁ ÎÁÐÒÁ×ÌÅÎÉÑ ÅÝÅ ÂÏÌÅÅ ÏÇÒÁÎÉÞÅÎÙ ×
ÚÎÁÞÅÎÉÑÈ, ÞÅÍ ÄÌÑ ÏÔÒÅÚËÏ×, Á ÉÍÅÎÎÏ~--- ÞÉÓÌÁÍÉ
\[
  -4,\,-3,\,\ldots,\,3,\,4.
\]
ëÏÍÐÏÎÅÎÔÙ ÔÁËÖÅ ÏÂÑÚÁÎÙ ÂÙÔØ ×ÚÁÉÍÎÏ ÐÒÏÓÔÙÍÉ (ÎÅ ÉÍÅÔØ ÏÂÝÅÇÏ
ÄÅÌÉÔÅÌÑ, ËÒÏÍÅ 1). úÁÍÅÔØÔÅ ÜÆÆÅËÔ ËÏÍÁÎÄÙ \ci{thicklines} ÎÁ Ä×ÕÈ
×ÅËÔÏÒÁÈ, ÕËÁÚÙ×ÁÀÝÉÈ × ×ÅÒÈÎÉÊ ÌÅ×ÙÊ ÕÇÏÌ.

\subsection{ïËÒÕÖÎÏÓÔÉ}

\begin{example}
\setlength{\unitlength}{1mm}
\begin{picture}(60, 40)
  \put(20,30){\circle{1}}
  \put(20,30){\circle{2}}
  \put(20,30){\circle{4}}
  \put(20,30){\circle{8}}
  \put(20,30){\circle{16}}
  \put(20,30){\circle{32}}
  
  \put(40,30){\circle{1}}
  \put(40,30){\circle{2}}
  \put(40,30){\circle{3}}
  \put(40,30){\circle{4}}
  \put(40,30){\circle{5}}
  \put(40,30){\circle{6}}
  \put(40,30){\circle{7}}
  \put(40,30){\circle{8}}
  \put(40,30){\circle{9}}
  \put(40,30){\circle{10}}
  \put(40,30){\circle{11}}
  \put(40,30){\circle{12}}
  \put(40,30){\circle{13}}
  \put(40,30){\circle{14}}
  
  \put(15,10){\circle*{1}}
  \put(20,10){\circle*{2}}
  \put(25,10){\circle*{3}}
  \put(30,10){\circle*{4}}
  \put(35,10){\circle*{5}}
\end{picture}
\end{example}
ëÏÍÁÎÄÁ
\begin{lscommand}
  \ci{put}\verb|(|$x,y$\verb|){|\ci{circle}\verb|{|\emph{ÄÉÁÍÅÔÒ}\verb|}}|
\end{lscommand}
\noindent ÒÉÓÕÅÔ ÏËÒÕÖÎÏÓÔØ Ó ÃÅÎÔÒÏÍ × ÔÏÞËÅ $(x,y)$ É ÄÉÁÍÅÔÒÏÍ (ÎÅ
ÒÁÄÉÕÓÏÍ!) \emph{ÄÉÁÍÅÔÒ}. ïËÒÕÖÅÎÉÅ \ei{picture} ÐÏÚ×ÏÌÑÅÔ ÒÉÓÏ×ÁÔØ
ÏËÒÕÖÎÏÓÔÉ ÄÉÁÍÅÔÒÏÍ ÎÅ ÂÏÌÅÅ ÐÒÉÍÅÒÎÏ 14\,ÍÍ, É ÄÁÖÅ × ÜÔÉÈ ÐÒÅÄÅÌÁÈ
ÄÏÐÕÓÔÉÍÙ ÎÅ ×ÓÅ ÄÉÁÍÅÔÒÙ. ëÏÍÁÎÄÁ \ci{circle*} ÒÉÓÕÅÔ ËÒÕÇ
(ÚÁÐÏÌÎÅÎÎÕÀ ÏËÒÕÖÎÏÓÔØ).

ëÁË É × ÓÌÕÞÁÅ ÏÔÒÅÚËÏ×, ×Ù ÍÏÖÅÔÅ ÐÒÉÂÅÇÁÔØ Ë ÐÏÍÏÝÉ ÄÏÐÏÌÎÉÔÅÌØÎÙÈ
ÐÁËÅÔÏ×, ÔÁËÉÈ, ËÁË \pai{eepic} ÉÌÉ \pai{pstricks}.
ðÏÄÒÏÂÎÏÅ ÏÐÉÓÁÎÉÅ ÜÔÉÈ ÐÁËÅÔÏ× ÐÒÉ×ÅÄÅÎÏ × \graphicscompanion.

óÕÝÅÓÔ×ÕÅÔ ÔÁËÖÅ É ×ÙÈÏÄ × ÒÁÍËÁÈ ÏËÒÕÖÅÎÉÑ \ei{picture}. åÓÌÉ ×Ù ÎÅ
ÂÏÉÔÅÓØ ×ÙÐÏÌÎÅÎÉÑ ÎÅÏÂÈÏÄÉÍÙÈ ×ÙÞÉÓÌÅÎÉÊ (ÉÌÉ ×ÏÚÌÁÇÁÅÔÅ ÉÈ ÎÁ
ÐÒÏÇÒÁÍÍÕ), ÔÏ ÍÏÖÎÏ ÉÚÏÂÒÁÖÁÔØ ÐÒÏÉÚ×ÏÌØÎÙÅ ÏËÒÕÖÎÏÓÔÉ É ÜÌÌÉÐÓÙ ÐÒÉ
ÐÏÍÏÝÉ ËÒÉ×ÙÈ âÅÚØÅ. ðÒÉÍÅÒÙ É ÉÓÈÏÄÎÙÅ ÔÅËÓÔÙ ÎÁ Java ÐÒÉ×ÅÄÅÎÙ ×
\graphicsinlatex.

\subsection{ôÅËÓÔ É ÆÏÒÍÕÌÙ}

\begin{example}
\setlength{\unitlength}{1cm}
\begin{picture}(6,5)
  \thicklines
  \put(1,0.5){\line(2,1){3}}
  \put(4,2){\line(-2,1){2}}
  \put(2,3){\line(-2,-5){1}}
  \put(0.7,0.3){$A$}
  \put(4.05,1.9){$B$}
  \put(1.7,2.95){$C$}
  \put(3.1,2.5){$a$}
  \put(1.3,1.7){$b$}
  \put(2.5,1.05){$c$}
  \put(0.3,4){$F=
    \sqrt{s(s-a)(s-b)(s-c)}$}  
  \put(3.5,0.4){$\displaystyle
    s:=\frac{a+b+c}{2}$}
\end{picture}
\end{example}
ëÁË ÐÏËÁÚÙ×ÁÅÔ ÜÔÏÔ ÐÒÉÍÅÒ, ÔÅËÓÔ É ÆÏÒÍÕÌÙ ÍÏÇÕÔ ÒÁÚÍÅÝÁÔØÓÑ ×
ÏËÒÕÖÅÎÉÉ \ei{picture} ÏÂÙÞÎÙÍ ÓÐÏÓÏÂÏÍ~--- ËÏÍÁÎÄÏÊ \ci{put}.

\subsection{ëÏÍÁÎÄÙ \ci{multiput} É \ci{linethickness}}

\begin{example}
\setlength{\unitlength}{2mm}
\begin{picture}(30,20)
  \linethickness{0.075mm}
  \multiput(0,0)(1,0){31}%
    {\line(0,1){20}}
  \multiput(0,0)(0,1){21}%
    {\line(1,0){30}}
  \linethickness{0.15mm}    
  \multiput(0,0)(5,0){7}%
    {\line(0,1){20}}
  \multiput(0,0)(0,5){5}%
    {\line(1,0){30}}
  \linethickness{0.3mm}    
  \multiput(5,0)(10,0){3}%
    {\line(0,1){20}}
  \multiput(0,5)(0,10){2}%
    {\line(1,0){30}}
\end{picture}
\end{example}
ëÏÍÁÎÄÁ
\begin{lscommand}
  \ci{multiput}\verb|(|$x,y$\verb|)(|$\Delta x,\Delta y$\verb|){|$n$\verb|}{|\emph{ÏÂßÅËÔ}\verb|}|
\end{lscommand}
\noindent ÉÍÅÅÔ 4 ÁÒÇÕÍÅÎÔÁ: ÎÁÞÁÌØÎÁÑ ÔÏÞËÁ, ×ÅËÔÏÒ ÐÅÒÅÈÏÄÁ ÏÔ
ÏÄÎÏÇÏ ÏÂßÅËÔÁ Ë ÓÌÅÄÕÀÝÅÍÕ, ÞÉÓÌÏ ÏÂßÅËÔÏ× É ÓÏÂÓÔ×ÅÎÎÏ ÏÂßÅËÔ ÄÌÑ
ÒÉÓÏ×ÁÎÉÑ. ëÏÍÁÎÄÁ \ci{linethickness} ÏÔÎÏÓÉÔÓÑ Ë ÇÏÒÉÚÏÎÔÁÌØÎÙÍ É
×ÅÒÔÉËÁÌØÎÙÍ ÏÔÒÅÚËÁÍ, ÎÏ ÎÉËÏÇÄÁ~--- Ë ÎÁËÌÏÎÎÙÍ ÉÌÉ
ÏËÒÕÖÎÏÓÔÑÍ. ïÎÁ, ÏÄÎÁËÏ ÏÔÎÏÓÉÔÓÑ ÔÁËÖÅ É Ë Ë×ÁÄÒÁÔÉÞÎÙÍ ËÒÉ×ÙÍ
âÅÚØÅ! 

\subsection{ï×ÁÌÙ. ëÏÍÁÎÄÙ \ci{thinlines} É \ci{thicklines}}

\begin{example}
\setlength{\unitlength}{1cm}
\begin{picture}(6,4)
  \linethickness{0.075mm}
  \multiput(0,0)(1,0){7}%
    {\line(0,1){4}}
  \multiput(0,0)(0,1){5}%
    {\line(1,0){6}}
  \thicklines
  \put(2,3){\oval(3,1.8)} 
  \thinlines
  \put(3,2){\oval(3,1.8)} 
  \thicklines
  \put(2,1){\oval(3,1.8)[tl]} 
  \put(4,1){\oval(3,1.8)[b]} 
  \put(4,3){\oval(3,1.8)[r]} 
  \put(3,1.5){\oval(1.8,0.4)}     
\end{picture}
\end{example}
ëÏÍÁÎÄÁ
\begin{lscommand}
  \ci{put}\verb|(|$x,y$\verb|){|\ci{oval}\verb|(|$w,h$\verb|)}|
\end{lscommand}
\noindent ÉÌÉ
\begin{lscommand}
  \ci{put}\verb|(|$x,y$\verb|){|\ci{oval}\verb|(|$w,h$\verb|)[|\emph{ÐÏÚÉÃÉÑ}\verb|]}|
\end{lscommand}
\noindent ×Ù×ÏÄÉÔ Ï×ÁÌ Ó ÃÅÎÔÒÏÍ × $(x,y)$, ÉÍÅÀÝÉÊ ÄÌÉÎÕ $w$ É ×ÙÓÏÔÕ
$h$. îÅÏÂÑÚÁÔÅÌØÎÙÊ ÁÒÇÕÍÅÎÔ \emph{ÐÏÚÉÃÉÑ} ÍÏÖÅÔ ÐÒÉÎÉÍÁÔØ ÚÎÁÞÅÎÉÑ
\texttt{b}, \texttt{t}, \texttt{l} É \texttt{r} (×ÎÉÚ/××ÅÒÈ/×ÌÅ×Ï/×ÐÒÁ×Ï)
É ÍÏÖÅÔ ÓÏÞÅÔÁÔØ ÜÔÉ ÚÎÁÞÅÎÉÑ, ËÁË ÎÁ ÐÒÉ×ÅÄÅÎÎÏÍ ÐÒÉÍÅÒÅ.

ôÏÌÝÉÎÁ ÌÉÎÉÊ ÍÏÖÅÔ ÕÐÒÁ×ÌÑÔØÓÑ ÏÄÎÏÊ ÉÚ Ä×ÕÈ ËÏÍÁÎÄ:\\
\ci{linethickness}\verb|{|\emph{ÄÌÉÎÁ}\verb|}|
Ó ÏÄÎÏÊ ÓÔÏÒÏÎÙ, É \ci{thinlines} É \ci{thicklines}~--- Ó ÄÒÕÇÏÊ. ÷ ÔÏ
×ÒÅÍÑ, ËÁË \ci{linethickness}\verb|{|\emph{ÄÌÉÎÁ}\verb|}| ×ÌÉÑÅÔ
ÔÏÌØËÏ ÎÁ ÇÏÒÉÚÏÎÔÁÌØÎÙÅ É ×ÅÒÔÉËÁÌØÎÙÅ ÌÉÎÉÉ (É Ë×ÁÄÒÁÔÉÞÎÙÅ ËÒÉ×ÙÅ
âÅÚØÅ), \ci{thinlines} É \ci{thicklines} ×ÌÉÑÅÔ ÎÁ ÎÁËÌÏÎÎÙÅ ÏÔÒÅÚËÉ,
ÏËÒÕÖÎÏÓÔÉ É Ï×ÁÌÙ.

\subsection{ðÏ×ÔÏÒÎÏÅ ÉÓÐÏÌØÚÏ×ÁÎÉÅ ÂÌÏËÏ× ËÁÒÔÉÎËÉ}

\begin{example}
\setlength{\unitlength}{0.5mm}
\begin{picture}(120,168)
\newsavebox{\foldera}% ÏÂßÑ×ÌÅÎÉÅ
\savebox{\foldera}
  (40,32)[bl]{% ÏÐÒÅÄÅÌÅÎÉÅ 
  \multiput(0,0)(0,28){2}
    {\line(1,0){40}}
  \multiput(0,0)(40,0){2}
    {\line(0,1){28}}
  \put(1,28){\oval(2,2)[tl]}
  \put(1,29){\line(1,0){5}}
  \put(9,29){\oval(6,6)[tl]}
  \put(9,32){\line(1,0){8}}
  \put(17,29){\oval(6,6)[tr]}
  \put(20,29){\line(1,0){19}}
  \put(39,28){\oval(2,2)[tr]}  
}
\newsavebox{\folderb}% ÏÂßÑ×ÌÅÎÉÅ
\savebox{\folderb}
  (40,32)[l]{%        ÏÐÒÅÄÅÌÅÎÉÅ 
  \put(0,14){\line(1,0){8}}
  \put(8,0){\usebox{\foldera}}
}
\put(34,26){\line(0,1){102}} 
\put(14,128){\usebox{\foldera}}
\multiput(34,86)(0,-37){3}
  {\usebox{\folderb}} 
\end{picture}
\end{example}
âÌÏË ÒÉÓÕÎËÁ ÍÏÖÅÔ ÂÙÔØ \emph{ÏÂßÑ×ÌÅÎ} ËÏÍÁÎÄÏÊ
\begin{lscommand}
  \ci{newsavebox}\verb|{|\emph{ÎÁÚ×ÁÎÉÅ}\verb|}|
\end{lscommand}
\noindent Á ÚÁÔÅÍ \emph{ÏÐÒÅÄÅÌÅÎ} ËÏÍÁÎÄÏÊ
\begin{lscommand}
  \ci{savebox}\verb|{|\emph{ÎÁÚ×ÁÎÉÅ}\verb|}(|\emph{ÛÉÒÉÎÁ,×ÙÓÏÔÁ}\verb|)[|\emph{ÐÏÚÉÃÉÑ}\verb|]{|\emph{ÓÏÄÅÒÖÁÎÉÅ}\verb|}|
\end{lscommand}
\noindent É, ÎÁËÏÎÅÃ, ÓËÏÌØËÏ ÕÇÏÄÎÏ ÒÁÚ \emph{ÎÁÒÉÓÏ×ÁÎ} ËÏÍÁÎÄÏÊ
\begin{lscommand}
  \ci{put}\verb|(|$x,y$\verb|)|\ci{usebox}\verb|{|\emph{ÎÁÚ×ÁÎÉÅ}\verb|}|
\end{lscommand}

îÅÏÂÑÚÁÔÅÌØÎÙÊ ÁÒÇÕÍÅÎÔ \emph{ÐÏÚÉÃÉÑ} ÏÐÒÅÄÅÌÑÅÔ ÔÏÞËÕ ÐÒÉ×ÑÚËÉ
ÂÌÏËÁ. ÷ ÐÒÉ×ÅÄÅÎÎÏÍ ÐÒÉÍÅÒÅ ÏÎ ÕÓÔÁÎÏ×ÌÅÎ × ÚÎÁÞÅÎÉÅ \texttt{bl}, ÞÔÏ
ÐÏÍÅÝÁÅÔ ÔÏÞËÕ ÐÒÉ×ÑÚËÉ × ÎÉÖÎÉÊ ÌÅ×ÙÊ ÕÇÏÌ ÂÌÏËÁ. äÒÕÇÉÅ ×ÁÒÉÁÎÔÙ
ÚÎÁÞÅÎÉÑ~--- \texttt{t} (××ÅÒÈ) É \texttt{r} (×ÐÒÁ×Ï).

áÒÇÕÍÅÎÔ \emph{ÎÁÚ×ÁÎÉÅ} ÆÁËÔÉÞÅÓËÉ Ñ×ÌÑÅÔÓÑ ËÏÍÁÎÄÏÊ \LaTeX{} (ÏÔÓÀÄÁ
É ÏÂÒÁÔÎÁÑ ËÏÓÁÑ ÞÅÒÔÁ ÐÅÒÅÄ ÎÉÍ × ÒÁÓÓÍÁÔÒÉ×ÁÅÍÏÍ ÐÒÉÍÅÒÅ). âÌÏËÉ
ÍÏÇÕÔ ÂÙÔØ ×ÌÏÖÅÎÎÙÍÉ: × ÜÔÏÍ ÐÒÉÍÅÒÅ ×ÎÕÔÒÉ ÏÐÒÅÄÅÌÅÎÉÑ \ci{folderb}
ÉÓÐÏÌØÚÕÅÔÓÑ \ci{foldera}.

ëÏÍÁÎÄÕ \ci{oval} ÐÒÉÛÌÏÓØ ÐÒÉÍÅÎÉÔØ ÐÏÔÏÍÕ ÞÔÏ ËÏÍÁÎÄÁ \ci{line} ÎÅ
ÒÁÂÏÔÁÅÔ, ÅÓÌÉ ÄÌÉÎÁ ÏÔÒÅÚËÁ ÍÅÎØÛÅ ÐÒÉÍÅÒÎÏ 3\,ÍÍ.

\subsection{ë×ÁÄÒÁÔÉÞÎÙÅ ËÒÉ×ÙÅ âÅÚØÅ}

\begin{example}
\setlength{\unitlength}{1cm}
\begin{picture}(6,4)
  \linethickness{0.075mm}
  \multiput(0,0)(1,0){7}
    {\line(0,1){4}}
  \multiput(0,0)(0,1){5}
    {\line(1,0){6}}
  \thicklines
  \put(0.5,0.5){\line(1,5){0.5}}    
  \put(1,3){\line(4,1){2}} 
  \qbezier(0.5,0.5)(1,3)(3,3.5)
  \thinlines   
  \put(2.5,2){\line(2,-1){3}}
  \put(5.5,0.5){\line(-1,5){0.5}}
  \linethickness{1mm}
  \qbezier(2.5,2)(5.5,0.5)(5,3)
  \thinlines
  \qbezier(4,2)(4,3)(3,3)
  \qbezier(3,3)(2,3)(2,2)
  \qbezier(2,2)(2,1)(3,1)
  \qbezier(3,1)(4,1)(4,2)
\end{picture}
\end{example}
ëÁË ÐÏËÁÚÙ×ÁÅÔ ÜÔÏÔ ÐÒÉÍÅÒ, ÒÁÚÂÉÅÎÉÅ ÏËÒÕÖÎÏÓÔÉ ÎÁ ÞÅÔÙÒÅ Ë×ÁÄÒÁÔÉÞÎÙÈ
ËÒÉ×ÙÈ âÅÚØÅ ÄÁÅÔ ÎÅÕÄÏ×ÌÅÔ×ÏÒÉÔÅÌØÎÙÊ ÒÅÚÕÌØÔÁÔ. ôÒÅÂÕÅÔÓÑ ËÁË
ÍÉÎÉÍÕÍ ×ÏÓÅÍØ. éÌÌÀÓÔÒÁÃÉÑ ÓÎÏ×Á ÐÏËÁÚÙ×ÁÅÔ ×ÌÉÑÎÉÅ ËÏÍÁÎÄÙ
\ci{linethickness} ÎÁ ÇÏÒÉÚÏÎÔÁÌØÎÙÅ É ×ÅÒÔÉËÁÌØÎÙÅ ÌÉÎÉÉ, Á ËÏÍÁÎÄ
\ci{thinlines} É \ci{thicklines}~--- ÎÁ ÎÁËÌÏÎÎÙÅ ÏÔÒÅÚËÉ. ïÎÁ ÔÁËÖÅ
ÐÏËÁÚÙ×ÁÅÔ, ÞÔÏ ÏÂÅ ËÏÍÁÎÄÙ ×ÌÉÑÀÔ ÎÁ Ë×ÁÄÒÁÔÉÞÎÙÅ ËÒÉ×ÙÅ âÅÚØÅ, É
ËÁÖÄÁÑ ÓÌÅÄÕÀÝÁÑ ËÏÍÁÎÄÁ ÏÔÍÅÎÑÅÔ ÒÅÚÕÌØÔÁÔÙ ÐÒÅÄÙÄÕÝÉÈ.

ðÕÓÔØ $P_1=(x_1,\,y_1),\,P_2=(x_2,\,y_2)$ ÚÁÄÁÀÔ ËÏÎÅÞÎÙÅ ÔÏÞËÉ, Á
$m_1,\,m_2$~--- ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÅ ÎÁËÌÏÎÙ % ËÁÓÁÔÅÌØÎÙÅ?
Ë×ÁÄÒÁÔÉÞÎÏÊ ËÒÉ×ÏÊ âÅÚØÅ. ôÏÇÄÁ ÐÒÏÍÅÖÕÔÏÞÎÁÑ ÕÐÒÁ×ÌÑÀÝÁÑ ÔÏÞËÁ
$S=(x,\,y)$ ÚÁÄÁÅÔÓÑ ÕÒÁ×ÎÅÎÉÅÍ
\begin{equation} \label{zwischenpunkt}
  \left\{
    \begin{array}{rcl}
      x & = & \displaystyle \frac{m_2 x_2-m_1x_1-(y_2-y_1}{m_2-m_1}, \\
      y & = & y_i+m_i(x-x_i)\qquad (i=1,\,2).
    \end{array}
  \right.
\end{equation}
\noindent ÷ \graphicsinlatex\ ÐÒÉ×ÅÄÅÎÁ Java-ÐÒÏÇÒÁÍÍÁ, ÇÅÎÉÒÕÀÝÁÑ
    ÎÅÏÂÈÏÄÉÍÙÅ ËÏÍÁÎÄÙ  \ci{qbezier}.

\subsection{ãÅÐÎÁÑ ÌÉÎÉÑ}

\begin{example}
\setlength{\unitlength}{1.3cm}
\begin{picture}(4.3,3.6)(-2.5,-0.25)
  \put(-2,0){\vector(1,0){4.4}}
  \put(2.45,-.05){$x$}
  \put(0,0){\vector(0,1){3.2}}
  \put(0,3.35){\makebox(0,0){$y$}}
  \qbezier(0.0,0.0)(1.2384,0.0)
    (2.0,2.7622) 
  \qbezier(0.0,0.0)(-1.2384,0.0)
    (-2.0,2.7622)
  \linethickness{.075mm}
  \multiput(-2,0)(1,0){5}
    {\line(0,1){3}}
  \multiput(-2,0)(0,1){4}
    {\line(1,0){4}}
  \linethickness{.2mm}
  \put( .3,.12763){\line(1,0){.4}}
  \put(.5,-.07237){\line(0,1){.4}}
  \put(-.7,.12763){\line(1,0){.4}}
  \put(-.5,-.07237){\line(0,1){.4}}
  \put(.8,.54308){\line(1,0){.4}}
  \put(1,.34308){\line(0,1){.4}}
  \put(-1.2,.54308){\line(1,0){.4}}
  \put(-1,.34308){\line(0,1){.4}}
  \put(1.3,1.35241){\line(1,0){.4}}
  \put(1.5,1.15241){\line(0,1){.4}}
  \put(-1.7,1.35241){\line(1,0){.4}}
  \put(-1.5,1.15241){\line(0,1){.4}}
  \put(-2.5,-0.25){\circle*{0.2}}
\end{picture}
\end{example}

îÁ ÜÔÏÊ ÉÌÌÀÓÔÒÁÃÉÉ ËÁÖÄÁÑ ÓÉÍÍÅÔÒÉÞÎÁÑ ÐÏÌÏ×ÉÎÁ ÃÅÐÎÏÊ ÌÉÎÉÉ $y=\cosh
x -1$ ÁÐÐÒÏËÓÉÍÉÒÏ×ÁÎÁ Ë×ÁÄÒÁÔÉÞÎÏÊ ËÒÉ×ÏÊ âÅÚØÅ. ðÒÁ×ÁÑ ÐÏÌÏ×ÉÎÁ
ËÒÉ×ÏÊ ÚÁËÁÎÞÉ×ÁÅÔÓÑ × ÔÏÞËÅ \((2,\,2.7622)\), ÎÁËÌÏÎ × ËÏÔÏÒÏÊ ÉÍÅÅÔ
ÚÎÁÞÅÎÉÅ \(m=3.6269\). ÷ÎÏ×Ø ÉÓÐÏÌØÚÕÑ ÕÒÁ×ÎÅÎÉÅ
(\ref{zwischenpunkt}), ÍÙ ÍÏÖÅÍ ×ÙÞÉÓÌÉÔØ ×ÎÕÔÒÅÎÎÉÅ ÕÐÒÁ×ÌÑÀÝÉÅ
ÔÏÞËÉ. éÍÉ ÏËÁÚÁÌÉÓØ $(1.2384,\,0)$ É $(-1.2384,\,0)$. ëÒÅÓÔÉËÉ
ÏÔÍÅÞÁÀÔ ÔÏÞËÉ \emph{ÎÁÓÔÏÑÝÅÊ} ÃÅÐÎÏÊ ÌÉÎÉÉ. ïÛÉÂËÁ ÅÄ×Á ÚÁÍÅÔÎÁ,
ÂÕÄÕÞÉ ÍÅÎØÛÅ ÏÄÎÏÇÏ ÐÒÏÃÅÎÔÁ.

üÔÏÔ ÐÒÉÍÅÒ ÐÏËÁÚÙ×ÁÅÔ ÉÓÐÏÌØÚÏ×ÁÎÉÅ ÎÅÏÂÑÚÁÔÅÌØÎÏÇÏ ÁÒÇÕÍÅÎÔÁ ËÏÍÁÎÄÙ
\verb|\begin{picture}|. ëÁÒÔÉÎËÁ ÏÐÒÅÄÅÌÅÎÁ × ÕÄÏÂÎÙÈ
<<ÍÁÔÅÍÁÔÉÞÅÓËÉÈ>> ËÏÏÒÄÉÎÁÔÁÈ, ÔÏÇÄÁ ËÁË ËÏÍÁÎÄÁ
\begin{lscommand} 
  \ci{begin}\verb|{picture}(4.3,3.6)(-2.5,-0.25)|
\end{lscommand}
\noindent ÐÒÉÓ×ÁÉ×ÁÅÔ ÅÅ ÎÉÖÎÅÍÕ ÌÅ×ÏÍÕ ÕÇÌÕ (ÏÔÍÅÞÅÎÎÏÍÕ ÞÅÒÎÙÍ
ËÒÕÖËÏÍ) ËÏÏÒÄÉÎÁÔÙ $(-2.5,-0.25)$. 

\subsection{óËÏÒÏÓÔØ × ÓÐÅÃÉÁÌØÎÏÊ ÔÅÏÒÉÉ ÏÔÎÏÓÉÔÅÌØÎÏÓÔÉ}

\begin{example}
\setlength{\unitlength}{1cm}
\begin{picture}(6,4)(-3,-2)
  \put(-2.5,0){\vector(1,0){5}}
  \put(2.7,-0.1){$\chi$}
  \put(0,-1.5){\vector(0,1){3}}
  \multiput(-2.5,1)(0.4,0){13}
    {\line(1,0){0.2}}
  \multiput(-2.5,-1)(0.4,0){13}
    {\line(1,0){0.2}}
  \put(0.2,1.4)
    {$\beta=v/c=\tanh\chi$}
  \qbezier(0,0)(0.8853,0.8853)
    (2,0.9640)
  \qbezier(0,0)(-0.8853,-0.8853)
    (-2,-0.9640)
  \put(-3,-2){\circle*{0.2}}
\end{picture}
\end{example}

õÐÒÁ×ÌÑÀÝÉÅ ÔÏÞËÉ Ä×ÕÈ ËÒÉ×ÙÈ âÅÚØÅ ÂÙÌÉ ×ÙÞÉÓÌÅÎÙ ÐÏ ÆÏÒÍÕÌÁÍ
(\ref{zwischenpunkt}). ðÏÌÏÖÉÔÅÌØÎÁÑ ×ÅÔËÁ ÏÐÒÅÄÅÌÑÅÔÓÑ
$P_1=(0,\,0),\,m_1=1$ É $P_2=(2,\,\tanh 2),\,m_2=1/\cosh^2
2$. ëÁÒÔÉÎËÁ ×ÎÏ×Ø ÏÐÒÅÄÅÌÑÅÔÓÑ × ÍÁÔÅÍÁÔÉÞÅÓËÉ ÕÄÏÂÎÙÈ ËÏÏÒÄÉÎÁÔÁÈ, Á
ÎÉÖÎÉÊ ÌÅ×ÙÊ ÕÇÏÌ ÐÏÌÕÞÁÅÔ ÍÁÔÅÍÁÔÉÞÅÓËÉÅ ËÏÏÒÄÉÎÁÔÙ $(-3,-2)$ (ÞÅÒÎÙÊ
ËÒÕÖÏË). 

\section{\texorpdfstring{\Xy}{Xy}-pic}
\secby{Alberto Manuel Brand\~ao Sim\~oes}{albie@alfarrabio.di.uminho.pt}
\pai{xy}~--- ÜÔÏ ÓÐÅÃÉÁÌØÎÙÊ ÐÁËÅÔ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ ÄÉÁÇÒÁÍÍ. äÌÑ ÅÇÏ
ÉÓÐÏÌØÚÏ×ÁÎÉÑ ÐÒÏÓÔÏ ÄÏÂÁ×ØÔÅ Ë ÐÒÅÁÍÂÕÌÅ ÄÏËÕÍÅÎÔÁ ÓÌÅÄÕÀÝÕÀ ÓÔÒÏÞËÕ:
\begin{lscommand}
\verb|\usepackage[|\emph{ÏÐÃÉÉ}\verb|]{xy}|
\end{lscommand}
\noindent ÇÄÅ \emph{ÏÐÃÉÉ}~--- ÓÐÉÓÏË ÚÁÇÒÕÖÁÅÍÙÈ ÆÕÎËÃÉÊ \Xy-pic. üÔÉ
ÏÐÃÉÉ ÐÏÌÅÚÎÙ, × ÐÅÒ×ÕÀ ÏÞÅÒÅÄØ, ÄÌÑ ÏÔÌÁÄËÉ ÐÁËÅÔÁ. òÅËÏÍÅÎÄÕÅÔÓÑ
ÉÓÐÏÌØÚÏ×ÁÔØ ÏÐÃÉÀ \verb!all!, ÉÎÓÔÒÕËÔÉÒÕÑ \LaTeX{} ÚÁÇÒÕÚÉÔØ ×ÓÅ
ËÏÍÁÎÄÙ \Xy{}. 

äÉÁÇÒÁÍÍÙ \Xy-pic ÒÉÓÕÀÔÓÑ × ÍÁÔÒÉÞÎÏÊ ËÁÎ×Å, ÇÄÅ ËÁÖÄÙÊ ÜÌÅÍÅÎÔ
ÄÉÁÇÒÁÍÍÙ ÐÏÍÅÝÁÅÔÓÑ × ÏÐÒÅÄÅÌÅÎÎÕÀ ËÌÅÔËÕ ÍÁÔÒÉÃÙ:
\begin{example}
\begin{displaymath}
\xymatrix{A & B \\
          C & D }
\end{displaymath}
\end{example}
ëÏÍÁÎÄÁ \ci{xymatrix} ÄÏÌÖÎÁ ÉÓÐÏÌØÚÏ×ÁÔØÓÑ × ÍÁÔÅÍÁÔÉÞÅÓËÏÍ
ÒÅÖÉÍÅ. úÄÅÓØ ÍÙ ÚÁÄÁÌÉ Ä×Å ÓÔÒÏËÉ É Ä×Á ÓÔÏÌÂÃÁ. þÔÏÂÙ ÉÚ ÜÔÏÊ
ÍÁÔÒÉÃÙ ÓÄÅÌÁÔØ ÄÉÁÇÒÁÍÍÕ, ÄÏÂÁ×ÉÍ ÓÔÒÅÌËÉ ×ÅËÔÏÒÏ× ËÏÍÁÎÄÏÊ \ci{ar}. 
\begin{example}
\begin{displaymath}
\xymatrix{ A \ar[r] & B \ar[d] \\
           D \ar[u] & C \ar[l] }
\end{displaymath}
\end{example}
ëÏÍÁÎÄÁ ÒÉÓÏ×ÁÎÉÑ ×ÅËÔÏÒÁ ÐÏÍÅÝÁÅÔÓÑ × ËÌÅÔËÕ, ÏÔËÕÄÁ ÉÓÈÏÄÉÔ
×ÅËÔÏÒ. áÒÇÕÍÅÎÔÏÍ Ñ×ÌÑÅÔÓÑ ÎÁÐÒÁ×ÌÅÎÉÅ, ËÕÄÁ ÐÏËÁÚÙ×ÁÅÔ ×ÅËÔÏÒ
(\texttt{u}p, \texttt{d}own, \texttt{r}ight É \texttt{l}eft).
\begin{example}
\begin{displaymath}
\xymatrix{
  A \ar[d] \ar[dr] \ar[r] & B \\
  D                       & C }
\end{displaymath}
\end{example}
äÌÑ ÒÉÓÏ×ÁÎÉÑ ÄÉÁÇÏÎÁÌÅÊ ÕËÁÖÉÔÅ ÂÏÌØÛÅ ÏÄÎÏÇÏ ÎÁÐÒÁ×ÌÅÎÉÑ. ÷Ù ÔÁËÖÅ
ÍÏÖÅÔÅ ÐÏ×ÔÏÒÑÔØ ÚÎÁË ÎÁÐÒÁ×ÌÅÎÉÑ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ Â\'ÏÌØÛÉÈ ×ÅËÔÏÒÏ×.
\begin{example}
\begin{displaymath}
\xymatrix{
  A \ar[d] \ar[dr] \ar[drr] & & \\
  B                      & C & D }
\end{displaymath}
\end{example}

íÏÖÎÏ ÒÉÓÏ×ÁÔØ ÅÝÅ ÂÏÌÅÅ ÉÎÔÅÒÅÓÎÙÅ ÄÉÁÇÒÁÍÍÙ, ÄÏÂÁ×ÌÑÑ Ë ×ÅËÔÏÒÁÍ
ÍÅÔËÉ. äÌÑ ÜÔÏÇÏ ÉÓÐÏÌØÚÕÀÔÓÑ  ÏÂÙÞÎÙÅ ÏÐÅÒÁÔÏÒÙ ÎÉÖÎÉÈ É ×ÅÒÈÎÉÈ
ÉÎÄÅËÓÏ×. 
\begin{example}
\begin{displaymath}
\xymatrix{
  A \ar[r]^f \ar[d]_g &
             B \ar[d]^{g'} \\
  D \ar[r]_{f'}       & C }
\end{displaymath}
\end{example}

ëÁË ÐÏËÁÚÁÎÏ ×ÙÛÅ, ÜÔÉ ÏÐÅÒÁÔÏÒÙ ÉÓÐÏÌØÚÕÀÔÓÑ ËÁË × ÍÁÔÅÍÁÔÉÞÅÓËÏÍ
ÒÅÖÉÍÅ. åÄÉÎÓÔ×ÅÎÎÁÑ ÒÁÚÎÉÃÁ ÚÁËÌÀÞÁÅÔÓÑ × ÔÏÍ, ÞÔÏ ×ÅÒÈÎÉÊ ÉÎÄÅËÓ
ÏÚÎÁÞÁÅÔ <<ÎÁÄ ÓÔÒÅÌËÏÊ ×ÅËÔÏÒÁ>>, Á ÎÉÖÎÉÊ~--- <<ÐÏÄ ÓÔÒÅÌËÏÊ>>.
åÓÔØ ÅÝÅ ÔÒÅÔÉÊ ÏÐÅÒÁÔÏÒ, ×ÅÒÔÉËÁÌØÎÁÑ ÞÅÒÔÁ: \verb+|+. ïÎ ÐÏÍÅÝÁÅÔ
ÔÅËÓÔ \emph{×} ÓÔÒÅÌËÕ.
\begin{example}
\begin{displaymath}
\xymatrix{
  A \ar[r]|f \ar[d]|g &
             B \ar[d]|{g'} \\
  D \ar[r]|{f'}       & C }
\end{displaymath}
\end{example}

þÔÏÂÙ ÎÁÒÉÓÏ×ÁÔØ ÓÔÒÅÌËÕ Ó ÐÒÏÂÅÌÏÍ × ÎÅÊ, ÐÏÌØÚÕÊÔÅÓØ ËÏÍÁÎÄÏÊ
\verb!\ar[...]|\hole!. ÷ ÎÅËÏÔÏÒÙÈ ÓÌÕÞÁÑÈ ×ÁÖÎÏ ÒÁÚÌÉÞÁÔØ ÎÅÓËÏÌØËÏ
×ÉÄÏ× ÓÔÒÅÌÏË. üÔÏÇÏ ÍÏÖÎÏ ÄÏÂÉÔØÓÑ, ÐÏÍÅÝÁÑ ÎÁ ÎÉÈ ÍÅÔËÉ ÉÌÉ ÍÅÎÑÑ ÉÈ
×ÉÄ: 
\begin{example}
\shorthandoff{"}
\begin{displaymath}
\xymatrix{
 \bullet\ar@{->}[rr] && \bullet\\
 \bullet\ar@{.<}[rr] && \bullet\\
 \bullet\ar@{~)}[rr] && \bullet\\
 \bullet\ar@{=(}[rr] && \bullet\\
 \bullet\ar@{~/}[rr]  && \bullet\\
 \bullet\ar@{^{(}->}[rr]  && \bullet\\
 \bullet\ar@2{->}[rr]  && \bullet\\
 \bullet\ar@3{->}[rr]  && \bullet\\
 \bullet\ar@{=+}[rr]   && \bullet
}
\end{displaymath}
\shorthandon{"}
\end{example}

ïÔÍÅÔØÔÅ ÒÁÚÎÉÃÕ ÍÅÖÄÕ ÓÌÅÄÕÀÝÉÍÉ Ä×ÕÍÑ ÄÉÁÇÒÁÍÍÁÍÉ:
\begin{example}
\begin{displaymath}
\xymatrix{
 \bullet \ar[r] 
         \ar@{.>}[r] & 
 \bullet
}
\end{displaymath}
\end{example}

\begin{example}
\begin{displaymath}
\xymatrix{
 \bullet \ar@/^/[r] 
         \ar@/_/@{.>}[r] &
 \bullet
}
\end{displaymath}
\end{example}

íÏÄÉÆÉËÁÔÏÒÙ ÍÅÖÄÕ ËÏÓÙÍÉ ÞÅÒÔÁÍÉ ÏÐÒÅÄÅÌÑÀÔ, ËÁË ÂÕÄÕÔ ÒÉÓÏ×ÁÔØÓÑ
ËÒÉ×ÙÅ. \Xy-pic ÐÒÅÄÌÁÇÁÅÔ ÍÎÏÖÅÓÔ×Ï ÓÐÏÓÏÂÏ× ÉÚÍÅÎÉÔØ ÓÐÏÓÏÂ
ÒÉÓÏ×ÁÎÉÑ ËÒÉ×ÙÈ; ÐÏÄÒÏÂÎÏÓÔÉ ÓÍÏÔÒÉÔÅ × ÄÏËÕÍÅÎÔÁÃÉÉ ÎÁ \Xy-pic.

% \begin{example}
% \begin{lscommand}
% \ci{dum}
% \end{lscommand}
% \end{example}