From 77adc9bb9bc69b5b61af7c5681ead56321b565e2 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Tue, 19 May 2009 18:34:32 +0000 Subject: move xypic-tut-pt out of texmf-doc git-svn-id: svn://tug.org/texlive/trunk@13246 c570f23f-e606-0410-a88d-b1316a301751 --- .../texmf-doc/doc/portuguese/xypic-tut-pt/README | 3 - .../doc/portuguese/xypic-tut-pt/grafico.eps | 460 --- .../doc/portuguese/xypic-tut-pt/xypic-tutorial.pdf | 3011 -------------------- .../doc/portuguese/xypic-tut-pt/xypictutorial.tex | 1954 ------------- 4 files changed, 5428 deletions(-) delete mode 100644 Master/texmf-doc/doc/portuguese/xypic-tut-pt/README delete mode 100644 Master/texmf-doc/doc/portuguese/xypic-tut-pt/grafico.eps delete mode 100644 Master/texmf-doc/doc/portuguese/xypic-tut-pt/xypic-tutorial.pdf delete mode 100644 Master/texmf-doc/doc/portuguese/xypic-tut-pt/xypictutorial.tex (limited to 'Master/texmf-doc') diff --git a/Master/texmf-doc/doc/portuguese/xypic-tut-pt/README b/Master/texmf-doc/doc/portuguese/xypic-tut-pt/README deleted file mode 100644 index 6bb13df8cc1..00000000000 --- a/Master/texmf-doc/doc/portuguese/xypic-tut-pt/README +++ /dev/null @@ -1,3 +0,0 @@ -A tutorial of the Xy-pic graphics package for LaTeX (in -portuguese). 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-\usepackage[english,brazil]{babel} -\usepackage[latin1]{inputenc} - -\usepackage{indentfirst} -\usepackage{graphicx} -\usepackage{url} - -\usepackage[all,knot,arc,import,poly]{xy} - -\title{Tutorial de \Xy-pic} -\author{Carlos A. P. Campani \\ {\tt campani@ufpel.edu.br}} - -\begin{document} - -\maketitle - -\section{Introduo} - -\Xy-pic{} um pacote para tipografar grficos e diagramas em -\TeX. O pacote \Xy-pic pode ser usado com \TeX{} e \LaTeX{} e permite -desenhar diversos tipos diferentes de grficos e diagramas, incluindo -polgonos, ns e diagramas em matriz. Ele implementado em torno de um -\emph{kernel de linguagem grfica}, que fornece uma notao -mnemnica e consistente, baseada na composio lgica de -componentes visuais. - -Este tutorial tem o objetivo de ser uma introduo breve e -a\-ces\-s\-vel ao uso do \Xy-pic{}. Estamos longe de pretender apresentar todos os recursos -disponveis. Ele complementa o \emph{\Xy-pic{} Reference -Manual}, de \mbox{Kristoffer} H. Rose e Ross Moore \cite{bib:manual}, e o \emph{\Xy-pic{} User's -Guide}, de Kristoffer H. Rose \cite{bib:guia}, que podem ser obtidos em -\url{http://www.tug.org/applications/Xy-pic/}. Ainda h o timo livro \emph{The \LaTeX{} Graphics Companion}, de -Goossens, Rahtz, e Mittelbach \cite{bib:goossens}. Recomendamos a leitura de todos estes textos -para aqueles que desejam usar intensamente o \Xy-pic. - -Para carregar o pacote \Xy-pic{} no \TeX{} usam-se os comandos -\verb+\input xy+ e \verb+\xyoption{all}+, que carrega todos os -recursos, o que pode tornar a execuo do \TeX{} lenta. Para aumentar -o desempenho do \TeX{} recomenda-se carregar apenas os recursos que -sero usados. Da mesma forma que no \TeX{}, para carregar o \Xy-pic{} no -\LaTeX{} usa-se o comando \verb+\usepackage[all]{xy}+ no cabealho do arquivo. - -Caso se queira produzir grficos de ns e arcos, deve-se incluir -adicionalmente as opes -\verb+knot+ e \verb+arc+. Tambm precisamos declarar as opes -\verb+import+ e \verb+poly+ se quisermos importar imagens -\emph{postscript} e desenhar polgonos nos diagramas. Para isto basta -usar, no cabealho do arquivo \LaTeX{}, o comando \verb+\usepackage[all,knot,arc,import,poly]{xy}+. - -Problemas podem ocorrer devido a flexibilidade do formato de entrada do -\TeX. Isto causa algumas situaes complicadas de conflito. Um exemplo - o uso do \Xy-pic{} junto com o pacote \emph{babel}, em portugus e outras lnguas que redefinem -as aspas, como o caso tambm do alemo, o que povoca conflito quando -se deseja salvar posies em um diagrama. Este problema pode ser -resolvido ao usarmos \verb+$$ \shorthandoff{"} \xy ... \endxy $$+, -protegendo os comandos \Xy-pic{} definidos dentro de \verb+\xy ... \endxy+. - - -Outro problema o conflito do caracter \verb+&+ quando usado em um diagrama -do \Xy-pic{} dentro de um ambiente \emph{tabular}. Neste caso, -possvel resolver o problema protegendo os comandos \Xy-pic{} dentro -de um par \verb+{+ e \verb+}+. - -\section{Conceitos Bsicos} - -A estrutura geral de uma \Xy-figura \verb+\xy ... \endxy+, -que constri uma caixa (\emph{box}) com uma \Xy-figura (usurios \LaTeX{} podem -substituir este comando por \verb+\begin{xy} ... \end{xy}+). Nesta -estrutura podem ser declarados comandos da ``linguagem grfica'' do -\Xy-pic. - -No h necessidade de colocar a \Xy-figura explicitamente em modo -ma\-te\-m\-ti\-co, pois a declarao \verb+\xy ... \endxy+ j o faz. Caso -haja necessidade de apresentar texto dentro da \Xy-figura, basta -usar o comando \verb+\txt{ ... }+. - -Os elementos que formam a linguagem do \Xy-pic{} so: -\begin{description} -\item [Posies] Representam coordenadas de pontos dentro da \emph{caixa} da - \Xy-figura; -\item [Objetos] Um objeto como uma caixa (\emph{box}) do \TeX{} que pode ser - posto em uma posio, exceto que ele possui uma \emph{borda} (\emph{edge}); -\item [Conexes] Junto com a capacidade de colocar objetos em - posies, todos os objetos podem ser usados para conectar duas - posies; -\item [Decoraes] Sempre que o \Xy-pic{} encontra algo que no pode - ser interpretado como uma posio, ele interpreta o que se segue - como uma \emph{de\-co\-ra\-o}, ou seja, um conjunto restrito de - comandos a ser adicionado figura. -\end{description} - -Posies podem ser representadas por pares \verb+(x,y)+, cujos valores -$x$ crescem da esquerda para a direita, e os valores $y$ de baixo para -cima. Assim, a origem do sistema de coordenadas o ponto $(0,0)$ -(tambm representado como \verb+0+), -e a \Xy-figura est contida no seguinte retngulo: -$$ - \shorthandoff{"} -\xy -(0,0)*{}="A"; (40,0)*{}="B"; (0,30)*{}="C"; (40,30)*{}="D"; -"A";"B" **\dir{-}; -"A";"C" **\dir{-}; -"B";"D" **\dir{-}; -"C";"D" **\dir{-}; -{\ar@{<->} (0,10)*{};(40,10)*{}}; -{\ar@{<->} (15,0)*{};(15,30)*{}}; -(15,10)*{\bullet}; -(15,10)*{};(25,14)*{0} **\dir{.}; -(22,25)*{Y_{\mathrm{max}}}; -(22,5)*{Y_{\mathrm{min}}}; -(7,7)*{X_{\mathrm{min}}}; -(32,7)*{X_{\mathrm{max}}}; -(-40,5)*{\txt{ponto de referncia \TeX}}; -(-17,6)*{};(0,10)*{} **\dir{.}; -\endxy -$$ - -A forma mais simples de colocar coisas em uma \Xy-figura ``largar'' -um objeto em uma posio. Para definir posies e ``largar'' objetos -usa-se o operador \verb+*+. Por exemplo, -\begin{verbatim} -(0,0)*{A} -\end{verbatim} -coloca o rtulo \verb+A+ na posio $(0,0)$. - -Alm de poder ``largar'' objetos em uma posio da \Xy-figura, podemos -\emph{conectar} os dois objetos correntes do \emph{estado}, formado -pelas posies $p$ -(posio prvia) e -$c$ (posio corrente). Para definir conexes usa-se o operador \verb+**+. Assim, -\begin{verbatim} -\xy -(0,0)*{};(10,0)*{} **\dir{-} -\endxy -\end{verbatim} -define a posio prvia $p=(0,0)$ e a posio corrente $c=(10,0)$ e -conecta ambas com um \emph{direcional} definido por -\verb+**\dir{-}+. Qualquer objeto pode ser usado como conector e, -neste caso, foi usado o \verb+-+, indicando que as duas posies devem -ser conectadas por uma linha simples. Observe que \verb+(0,0)*{}+ e \verb+(10,0)*{}+ -define as posies prvia e corrente, sem ``largar'' nenhum objeto -nelas. - -O operador \verb+;+ indica que deve-se atualizar as posies -prvia e corrente, trocando a corrente anterior pela prvia e fazendo -da ltima posio inserida a nova corrente. Assim, em -\begin{verbatim} -\xy -(0,0)*{};(10,0)*{} **\dir{-}; -(10,10)*{} **\dir{-} -\endxy -\end{verbatim} -O primeiro \verb+;+ define as posies $p=(0,0)$ e $c=(10,0)$. O -segundo \verb+;+ atribui a $p$ o valor -anterior de $c$, $(10,0)$, e faz $c=(10,10)$. Ento so traadas duas -linhas, uma entre $(0,0)$ e $(10,0)$ e outra entre $(10,0)$ e -$(10,10)$. - -Objetos possuem uma \emph{borda} (\emph{edge}). Assim, um objeto pode -ser entendido como uma \emph{caixa} (\emph{box}) \TeX{}, com -uma \emph{forma} (\emph{shape}), e com \emph{dimenses} $L$, $U$, $R$ -e $D$. A forma do objeto fora a forma de sua borda. O kernel do -\Xy-pic fornece trs formas (shapes), nomeadas \verb+[.]+, \verb+[]+ e -\verb+[o]+, correspondendo a: -$$ - \shorthandoff{"} -\xy (0,0)*{}; (1,0)*{} **\dir{} *\dir{x} \endxy \qquad , \qquad -\xy -(0,-6)*{}="A"; (20,-6)*{}="B"; (0,9)*{}="C"; (20,9)*{}="D"; -"A";"B" **\dir{-}; -"A";"C" **\dir{-}; -"B";"D" **\dir{-}; -"C";"D" **\dir{-}; -{\ar@{.} (0,0)*{};(20,0)*{}}; -{\ar@{.} (7,-6)*{};(7,9)*{}}; -(3,0)*{L}; -(7,4)*{U}; -(13,0)*{R}; -(7,-3)*{D}; -(0,0)*{}; (7,0)*{} **\dir{} ?>* \dir{x} -\endxy \qquad \mathrm{e} \qquad -\xy -{\ar@{.} (0,0)*{};(16,0)*{}}; -{\ar@{.} (8,-8)*{};(8,8)*{}}; -(3,0)*{L}; -(8,4)*{U}; -(13,0)*{R}; -(8,-3)*{D}; -(0,0)*{}; (8,0)*{} **\dir{} ?>* \dir{x}; -(8,0)*{} *\cir<25pt>{} -\endxy -$$ - -A forma (shape) \emph{default} dos objetos \verb+[]+. - -O \Xy-pic fornece um conjunto de \emph{direcionais}, como no exemplo anterior -o \verb+**\dir{-}+. Os direcionais so -elementos grficos que podem -ser tanto \emph{conectores} quanto \emph{pontas} (que terminam as -extremidades de uma conexo). - -Os conceitos apresentados de forma breve nesta seo sero melhor -desenvolvidos nas prximas sees. Particularmente a seo seguinte -tratar dos recursos do kernel do \Xy-pic, e mostrar por meio de -exemplos o uso de posies, objetos e conexes. - -\section{Usando o Kernel do \Xy-pic} - -Nesta seo mostraremos o uso do kernel do \Xy-pic{} por meio de -exemplos comentados. Sero introduzidos os recursos bsicos -disponveis no kernel, e nas sees seguintes sero explorados -aspectos mais avanados. - -A coisa mais simples que podemos fazer com o \Xy-pic{} definir duas -posies e conecta-las. Isto mostrado no exemplo seguinte, onde -produzida uma linha simples conectando as posies $(0,0)$ e $(10,0)$: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -(0,0)*{};(10,0)*{} **\dir{-} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*{};(10,0)*{} **\dir{-} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Podemos tambm ``largar'' objetos nas posies. Isto feito neste -outro exemplo, em que definimos dois objetos com rtulos $A$ e $B$, e -traamos uma linha na diagonal ligando estes dois rtulos: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{-} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{-} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -O operador \verb+*+ usado para definir posies e ``largar'' -objetos, e o operador \verb+**+ usado para definir conexes. - -Neste ltimo exemplo, observa-se o \emph{modificador} \verb=+= usado -em \verb=(0,0)*+{A}= e \verb=(10,10)*+{B}=. Este modificador serve -para obter espao adicional em torno do objeto, evitando que o -conector fique muito prximo ao objeto, como seria o caso de: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -(0,0)*{A};(10,10)*{B} **\dir{-} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*{A};(10,10)*{B} **\dir{-} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Podemos usar qualquer objeto como conector, como vemos no exemplo a -seguir: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{>} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{>} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Podemos definir trs posies em seqncia e conecta-las. Como se -explicou na seo anterior, o direcional \verb+**\dir{-}+ conecta as -posies $p$ e $c$ do estado do \Xy-pic{}. O operador \verb+;+ usado -para mudar o estado, trocando as posies $p$ e $c$ e atualizando a -$c$. Mostramos isso no seguinte exemplo: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -(0,0)*{};(10,0)*{} **\dir{-}; -(10,10)*{} **\dir{-} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*{};(10,0)*{} **\dir{-}; -(10,10)*{} **\dir{-} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Neste exemplo, a sequncia de mudanas de estado e aes do \Xy-pic{}, -associada aos comandos que as executam, apresentada na Tabela~\ref{tab:seq}. -\vspace{10pt} - -\begin{table} -\begin{center} -\begin{tabular}{c|c|c}\hline - & Ao & Comando \\ \hline\hline -1 & $c\leftarrow (0,0)$ & \verb+(0,0)*{}+ \\ \hline -2 & $p\leftarrow c$ & \verb+;+ \\ \hline -3 & $c\leftarrow (10,0)$ & \verb+(10,0)*{}+ \\ \hline -4 & traa linha entre $(0,0)$ e $(10,0)$ & \verb+**\dir{-}+ \\ \hline -5 & $p\leftarrow c$ & \verb+;+ \\ \hline -6 & $c\leftarrow (10,10)$ & \verb+(10,10)*{}+ \\ \hline -7 & traa linha entre $(10,0)$ e $(10,10)$ & \verb+**\dir{-}+ \\ \hline -\end{tabular} -\end{center} -\caption{Exemplo de execuo do \Xy-pic{}}\label{tab:seq} -\end{table} - -Textos podem ser postos em uma \Xy-figura usando o comando \verb+\txt+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -(5,5)*{A};(15,15)*{B} **\dir{-}; -(0,0)*{\txt{texto qualquer}} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(5,5)*{A};(15,15)*{B} **\dir{-}; -(0,0)*{\txt{texto qualquer}} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Este novo exemplo mostra o uso de conexes com \emph{pontas}: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{-} ?>* \dir{>} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{-} ?>* \dir{>} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Direcionais podem ser do tipo \emph{conectores} ou \emph{pontas}. No exemplo dado, -\verb+**\dir{-}+ um \emph{direcional conector}, e \verb+\dir{>}+ -um \emph{direcional ponta}. - -O \verb+?>*+ serve para indicar a posio -da ponta no conector. O operador \verb+?+ -serve para ``pegar'' o lugar da conexo mais recente definida por um -\verb+**+. O modificador \verb+>+ move posies, neste caso para o -extremo final da conexo. - -Poderamos posicionar a ponta no outro extremo do conector usando \verb+?<*+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{-} ?<* \dir{>} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{-} ?<* \dir{>} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Para melhorar o exemplo anterior poderamos usar espao adicional em -torno dos objetos: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*++{A};(10,10)*++{B} **\dir{-} ?<* \dir{>} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*++{A};(10,10)*++{B} **\dir{-} ?<* \dir{>} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Cada modificador \verb=+= dobra o valor do espao em torno de um -objeto. Assim, ao usar, por exemplo, \verb=(0,0)*++{A}= estamos -introduzindo um espao 4 vezes maior. - -Agora podemos inverter a ponta, como fazemos no exemplo seguinte: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{-} ?<* \dir{<} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*+{A};(10,10)*+{B} **\dir{-} ?<* \dir{<} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -As Figuras~\ref{fig:conectores} e \ref{fig:pontas} apresentam os -direcionais (conectores e pontas). Observe-se o recurso de fazer o -conector duplo ou triplo por meio de \verb+\dir2+ e \verb+\dir3+, e -as variaes de pontas usando-se \verb+\dir^+ ou \verb+\dir_+. - -\begin{figure}[!tp] -\begin{center} -\begin{tabular}{cccccc} -\verb=\dir{-}= & \xy (0,0)*{};(10,10)*{}; **\dir{-}; \endxy & -\verb=\dir2{-}= & \xy (0,0)*{};(10,10)*{}; **\dir2{-}; \endxy & -\verb=\dir3{-}= & \xy (0,0)*{};(10,10)*{}; **\dir3{-}; \endxy \\ -\verb=\dir{.}= & \xy (0,0)*{};(10,10)*{}; **\dir{.}; \endxy & -\verb=\dir2{.}= & \xy (0,0)*{};(10,10)*{}; **\dir2{.}; \endxy & -\verb=\dir3{.}= & \xy (0,0)*{};(10,10)*{}; **\dir3{.}; \endxy \\ -\verb=\dir{~}= & \xy (0,0)*{};(10,10)*{}; **\dir{~}; \endxy & -\verb=\dir2{~}= & \xy (0,0)*{};(10,10)*{}; **\dir2{~}; \endxy & -\verb=\dir3{~}= & \xy (0,0)*{};(10,10)*{}; **\dir3{~}; \endxy \\ -\verb=\dir{--}= & \xy (0,0)*{};(10,10)*{}; **\dir{--}; \endxy & -\verb=\dir2{--}= & \xy (0,0)*{};(10,10)*{}; **\dir2{--}; \endxy & -\verb=\dir3{--}= & \xy (0,0)*{};(10,10)*{}; **\dir3{--}; \endxy \\ -\verb=\dir{~~}= & \xy (0,0)*{};(10,10)*{}; **\dir{~~}; \endxy & -\verb=\dir2{~~}= & \xy (0,0)*{};(10,10)*{}; **\dir2{~~}; \endxy & -\verb=\dir3{~~}= & \xy (0,0)*{};(10,10)*{}; **\dir3{~~}; \endxy -\end{tabular} -\end{center} -\caption{Direcionais (conectores)}\label{fig:conectores} -\end{figure} - -\begin{figure}[!tp] -\begin{center} -\begin{tabular}{cccccc} -\verb=\dir{>}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{>} \endxy & -\verb=\dir^{>}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{>} \endxy & -\verb=\dir_{>}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{>} \endxy \\ -\verb=\dir{<}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{<} \endxy & -\verb=\dir^{<}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{<} \endxy & -\verb=\dir_{<}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{<} \endxy \\ -\verb=\dir{|}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{|} \endxy & -\verb=\dir^{|}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{|} \endxy & -\verb=\dir_{|}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{|} \endxy \\ -\verb=\dir{(}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{(} \endxy & -\verb=\dir^{(}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{(} \endxy & -\verb=\dir_{(}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{(} \endxy \\ -\verb=\dir{)}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{)} \endxy & -\verb=\dir^{)}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{)} \endxy & -\verb=\dir_{)}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{)} \endxy \\ - & & -\verb=\dir^{`}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{`} \endxy & -\verb=\dir_{`}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{`} \endxy \\ - & & -\verb=\dir^{'}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{'} \endxy & -\verb=\dir_{'}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{'} \endxy \\ -\verb=\dir{>>}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{>>} \endxy & -\verb=\dir^{>>}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{>>} \endxy & -\verb=\dir_{>>}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{>>} \endxy \\ -\verb=\dir{<<}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{<<} \endxy & -\verb=\dir^{<<}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{<<} \endxy & -\verb=\dir_{<<}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{<<} \endxy \\ -\verb=\dir{||}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{||} \endxy & -\verb=\dir^{||}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{||} \endxy & -\verb=\dir_{||}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{||} \endxy \\ -\verb=\dir{|-}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{|-} \endxy & -\verb=\dir^{|-}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir^{|-} \endxy & -\verb=\dir_{|-}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir_{|-} \endxy \\ -\verb=\dir{>|}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{>|} \endxy & -\verb=\dir{>>|}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{>>|} \endxy & -\verb=\dir{|<}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{|<} \endxy \\ -\verb=\dir{|<<}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{|<<} \endxy & -\verb=\dir{*}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{*} \endxy & -\verb=\dir{o}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{o} \endxy \\ -\verb=\dir{+}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{+} \endxy & -\verb=\dir{x}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{x} \endxy & -\verb=\dir{/}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{/} \endxy \\ -\verb=\dir{//}= & \xy (0,0)*{};(5,5)*{} **\dir{.} ?>* \dir{//} \endxy & - & & & -\end{tabular} -\end{center} -\caption{Direcionais (pontas)}\label{fig:pontas} -\end{figure} - -Podemos produzir setas com o \Xy-pic. Para isto usamos o comando \verb+\ar+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -{\ar (0,0)*+{A}; (10,10)*+{B}} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -{\ar (0,0)*+{A}; (10,10)*+{B}} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -A Figura~\ref{fig:setas} apresenta as setas que podem ser usadas em -uma \Xy-figura. De\-ve\-mos observar que \verb+\ar@{=>}+ e \verb+\ar@{:>}+ so -abreviaturas de \verb+\ar@2{->}+ e \verb+\ar@2{.>}+. - -\begin{figure} -\begin{center} -\begin{tabular}{cccccc} -\verb+\ar@{-}+ & \xy {\ar@{-} (0,0)*{}; (10,10)*{}}\endxy & -\verb+\ar@{->}+ & \xy {\ar@{->} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{->>}+ & \xy {\ar@{->>} (0,0)*{}; (10,10)*{}}\endxy \\ -\verb+\ar@{<-}+ & \xy {\ar@{<-} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{<->}+ & \xy {\ar@{<->} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@2{->}+ & \xy {\ar@2{->} (0,0)*{}; (10,10)*{}} \endxy \\ -\verb+\ar@{=>}+ & \xy {\ar@{=>} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@3{->}+ & \xy {\ar@3{->} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{-<}+ & \xy {\ar@{-<} (0,0)*{}; (10,10)*{}} \endxy \\ -\verb+\ar@{-|}+ & \xy {\ar@{-|} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{-)}+ & \xy {\ar@{-)} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{-o}+ & \xy {\ar@{-o} (0,0)*{}; (10,10)*{}} \endxy \\ -\verb+\ar@^{->}+ & \xy {\ar@^{->} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@_{->}+ & \xy {\ar@_{->} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{|->}+ & \xy {\ar@{|->} (0,0)*{}; (10,10)*{}} \endxy \\ -\verb+\ar@{.>}+ & \xy {\ar@{.>} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@2{.>}+ & \xy {\ar@2{.>} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{:>}+ & \xy {\ar@{:>} (0,0)*{}; (10,10)*{}} \endxy \\ -\verb+\ar@3{.>}+ & \xy {\ar@3{.>} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{~>}+ & \xy {\ar@{~>} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@2{~>}+ & \xy {\ar@2{~>} (0,0)*{}; (10,10)*{}} \endxy \\ -\verb+\ar@3{~>}+ & \xy {\ar@3{~>} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{-->}+ & \xy {\ar@{-->} (0,0)*{}; (10,10)*{}} \endxy & -\verb+\ar@{~~>}+ & \xy {\ar@{~~>} (0,0)*{}; (10,10)*{}} \endxy \\ - -\end{tabular} -\end{center} -\caption{Setas}\label{fig:setas} -\end{figure} - -Podemos curvar uma seta, como por exemplo em: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -{\ar@/^1pc/ (0,0)*+{A}; (10,10)*+{B}} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -{\ar@/^1pc/ (0,0)*+{A}; (10,10)*+{B}} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -O \verb+/^1pc/+ um \emph{vetor}, normalmente usado para denotar um -deslocamento, e que neste caso usado para especificar a curvatura da seta. A -curvatura especificada no exemplo de 1pc=12pt (pontos). Outras unidades de -medida usadas pelo \TeX{} so \emph{ex} (correspondendo altura da letra -``x''), \emph{mm}, \emph{cm} e \emph{in} (polegadas). O \verb+^+ -indica a direo da curvatura (para cima). - -Poderamos curvar a seta para baixo, como em: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -{\ar@/_1pc/ (0,0)*+{A}; (10,10)*+{B}} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -{\ar@/_1pc/ (0,0)*+{A}; (10,10)*+{B}} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -\Xy-pic{} fornece a facilidade de rtulos para indicar -posies. Assim, com \verb+(0,0)*{}="A"+ podemos criar o rtulo \verb+A+ para indicar a -posio $(0,0)$. No seguinte exemplo definimos trs rtulos para -indicar posies dos vrtices do tringulo que ser traado: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*{}="A"; (10,0)*{}="B"; (10,10)*{}="C"; -"A";"B" **\dir{-}; -"A";"C" **\dir{-}; -"B";"C" **\dir{-}; -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*{}="A"; (10,0)*{}="B"; (10,10)*{}="C"; -"A";"B" **\dir{-}; -"A";"C" **\dir{-}; -"B";"C" **\dir{-}; -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -A operao \verb+!{pos1,pos2}+ permite encontrar o ponto em que a ltima conexo -intercepta uma linha definida pelas posies \verb+pos1+ e \verb+pos2+. Por exem\-plo: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,5)*{1}="1"; (17,15)*{2}="2" **\dir{.}; -(6,0)*{A}="A"; (13,18)*{B}="B" **\dir{-} -?!{"1";"2"} *{\bullet} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,5)*{1}="1"; (17,15)*{2}="2" **\dir{.}; -(6,0)*{A}="A"; (13,18)*{B}="B" **\dir{-} -?!{"1";"2"} *{\bullet} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -No comando \verb+?!{"1";"2"} *{\bullet}+, o operador \verb+?+ ``pega'' a posio da ltima conexo definida -(neste caso a que liga as posies \verb+"A"+ e \verb+"B"+), e a seguir a operao \verb+!{"1";"2"}+ encontra o -ponto de interceptao desta conexo com a linha que liga as posies -\verb+"1"+ e \verb+"2"+. Ento posto um $\bullet$ (``bullet'') no ponto de interceptao. - -Podemos definir diagramas aninhados, ou seja, diagramas dentro de -ou\-tros diagramas. Para isto basta usar um diagrama como se fosse um -objeto ou um direcional. Neste exemplo ilustramos o uso deste recurso: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{9cm} -\begin{verbatim} -\xy -(0,0)*++{ -\xy -(0,0)*+{A}; (0,10)*+{B} **\dir{-} ?>* \dir{>} -\endxy -}="x"; -(20,0)*++{ -\xy -(0,0)*+{A}; (0,10)*+{B} **\dir{-} ?<* \dir{<} -\endxy -}="y"; -{\ar@{=>} "x";"y"}; -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*++{ -\xy -(0,0)*+{A}; (0,10)*+{B} **\dir{-} ?>* \dir{>} -\endxy -}="x"; -(20,0)*++{ -\xy -(0,0)*+{A}; (0,10)*+{B} **\dir{-} ?<* \dir{<} -\endxy -}="y"; -{\ar@{=>} "x";"y"}; -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Observe que -\begin{verbatim} -\xy -(0,0)*+{A}; (0,10)*+{B} **\dir{-} ?>* \dir{>} -\endxy -\end{verbatim} - atribuido a \verb+"x"+ e usado como objeto posicionado em $(0,0)$ e -\begin{verbatim} -\xy -(0,0)*+{A}; (0,10)*+{B} **\dir{-} ?<* \dir{<} -\endxy -\end{verbatim} - atribuido a \verb+"y"+ e usado como objeto posicionado em -$(20,0)$. Ambos os objetos so conectados pela seta dupla definida por \verb+{\ar@{=>} "x";"y"}+. - -Podemos usar macros \TeX{} em \Xy-figuras. Por exemplo: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{9cm} -\begin{verbatim} -\def\grafo{\xy (0,10)*+{A}; (0,0)*+{B} **\dir{-} -?>* \dir{>} \endxy} -\xy -{\ar@{=>} (0,0)*{\grafo};(15,0)*{\grafo}} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\def\grafo{\xy (0,10)*+{A}; (0,0)*+{B} **\dir{-} -?>* \dir{>} \endxy} -\xy -{\ar@{=>} (0,0)*{\grafo};(15,0)*{\grafo}} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Neste diagrama, -\begin{verbatim} -\def\grafo{\xy (0,10)*+{A}; (0,0)*+{B} **\dir{-} -?>* \dir{>} \endxy} -\end{verbatim} -define uma macro \TeX, referenciada como \verb+\grafo+, que usada duas -vezes a\-ninha\-da no diagrama. - -\section{Extenses} - -Nesta seo so descritas algumas extenses ao kernel do -\Xy-pic. Apresentaremos curvas, crculos, frames e -importao de grficos externos. - -\vspace{10pt} -Usando-se o comando \verb+\crv+ podemos criar curvas com mltiplos pontos tangentes: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -(0,0)*{}="A"; -(10,0)*{}="B"; -"A"; "B" **\crv{(5,5)}; -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*{}="A"; -(10,0)*{}="B"; -"A"; "B" **\crv{(5,5)}; -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Neste exemplo, a curva foi definida tendo apenas um ponto tangente, o $(5,5)$. - -Podemos definir curvas com mais pontos tangentes: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*{}="A"; -(25,0)*{}="B"; -"A"; "B" **\crv{(5,-17) & (12,8)}; -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{ -$$ - \shorthandoff{"} -\xy -(0,0)*{}="A"; -(25,0)*{}="B"; -"A"; "B" **\crv{(5,-17) & (12,8)}; -\endxy -$$ -} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Uma facilidade para desenvolver curvas tornar os pontos tangentes -visveis. Para isto usa-se \verb+~pC+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*{}="A"; -(25,0)*{}="B"; -"A"; "B" **\crv~pC{(5,-17) & (12,8)}; -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{ -$$ - \shorthandoff{"} -\xy -(0,0)*{}="A"; -(25,0)*{}="B"; -"A"; "B" **\crv~pC{(5,-17) & (12,8)}; -\endxy -$$ -} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Para produzir crculos usamos o comando \verb+\cir+. O tamanho -\emph{default} do crculo o tamanho do objeto que ele -envolver. Este exemplo ilustra isto: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*+{A}; (10,0)*+{B}*\cir{} **\dir{-} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*+{A}; (10,0)*+{B}*\cir{} **\dir{-} -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Podemos especificar um raio para o crculo. Por exemplo, se o crculo -deve ter \verb+20pt+ de raio, usamos \verb+\cir<20pt>{}+. - -Segmentos de crculo podem ser obtidos especificando-se as direes -dos vetores tangentes e um giro em sentido horrio (usando \verb+_+) -ou sentido anti-horrio (usando \verb+^+). As direes que podem ser -especificadas so: -$$ - \shorthandoff{"} -\xy -(0,0)*\cir<10pt>{}; -{\ar@{->} (-4,0)*{}; (-14,0)*+{l}}; -{\ar@{->} (4,0)*{}; (14,0)*+{r}}; -{\ar@{->} (0,4)*{}; (0,14)*+{u}}; -{\ar@{->} (0,-4)*{}; (0,-14)*+{d}}; -{\ar@{->} (3,3)*{}; (12,12)*+{ur=ru}}; -{\ar@{->} (-3,3)*{}; (-12,12)*+{ul=lu}}; -{\ar@{->} (-3,-3)*{}; (-12,-12)*+{dl=ld}}; -{\ar@{->} (3,-3)*{}; (12,-12)*+{dr=rd}}; -\endxy -$$ - -Exemplos de segmentos de crculo: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\verb+\xy *\cir<5pt>{l^r} \endxy+ & \xy *\cir<5pt>{l^r} \endxy \\ -\verb+\xy *\cir<5pt>{dl_u} \endxy+ & \xy *\cir<5pt>{dl_u} \endxy \\ -\verb+\xy *\cir<5pt>{dr^ur} \endxy+ & \xy *\cir<5pt>{dr^ur} \endxy \\ -\verb+\xy *\cir<5pt>{dr_ur} \endxy+ & \xy *\cir<5pt>{dr_ur} \endxy \\ -\verb+\xy *\cir<5pt>{ur^dr} \endxy+ & \xy *\cir<5pt>{ur^dr} \endxy -\end{tabular} - -\vspace{10pt} -Se so dadas a mesma diagonal duas vezes, ento nada produzido, como -em \verb+\xy *\cir<5pt>{d^d} \endxy+, que produz ``\ ''. - -No prximo exemplo produziremos um ``\emph{smile}'' usando crculo, -vetores, e os operadores \verb+?+, \verb+_+ e \verb+!+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*{};(4,0)*{} **\dir{} ? *_!/3pt/\dir{)} -*_!/7pt/\dir{:}; (2,2)*\cir<5pt>{}; -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*{};(4,0)*{} **\dir{} ? *_!/3pt/\dir{)} -*_!/7pt/\dir{:}; (2,2)*\cir<5pt>{}; -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -O operador \verb+?+, que j explicamos anteriormente, serve para ``pegar'' a posio da -ltima conexo. O operador \verb+_+ serve para girar um objeto $90^o$ -em sentido horrio (para o sentido anti-horrio usaramos o operador -\verb+^+). O operador \verb+!+ serve para tornar a direo oblqua ao -direcional usado (\emph{skew}). Finalmente, os vetores \verb+/3pt/+ e \verb+/7pt/+ -servem para deslocar os objetos ``\verb+)+'' e ``\verb+:+'' sobre a direo. - -Vamos explicar passo a passo a construo do smile do nosso exemplo. - -Em primeiro lugar, usamos o operador \verb+?+ para ``pegar'' a -posio do direcional ``vazio'' (\emph{dummy}) que conecta $(0,0)$ e -$(4,0)$. Sobre esta direo ser posto o ``\verb+)+''. Ilustramos isto, -mostrando o direcional vazio como uma linha pontilhada para melhor visualizao: -$$ - \shorthandoff{"} -\xy -(0,0)*{}; (4,0)*{} **\dir{.} ?*{)} -\endxy -$$ - -Para produzirmos a boca do smile devemos girar o ``\verb+)+'' em um ngulo de -$90^o$ em sentido horrio, e para isto usamos o operador \verb+_+, -resultando em: -$$ - \shorthandoff{"} -\xy -(0,0)*{}; (4,0)*{} **\dir{.} ?*_\dir{)} -\endxy -$$ - -Usamos o operador \verb+!+ para indicar a direo oblqua ao - direcional (para que possamos depois deslocar). Ilustramos com uma - seta pontilhada esta nova direo: -$$ - \shorthandoff{"} -\xy -(0,0)*{}; (4,0)*{} **\dir{.} ?*_\dir{)}; -(2,-3)*{}; (2,5)*{} **\dir{.} ?>* \dir{>} -\endxy -$$ - -As mesmas operaes so feitas sobre o ``\verb+:+'', que formar os olhos do smile. - -Finalmente, deslocamos o ``\verb+)+'' e o ``\verb+:+'' na nova direo, usando os vetores \verb+/3pt/+ e -\verb+/7pt/+, res\-pec\-ti\-va\-men\-te: -$$ - \shorthandoff{"} -\xy -(0,0)*{}; (4,0)*{} **\dir{.} ?*_!/3pt/\dir{)} *_!/7pt/\dir{:}; -\endxy -$$ - -O crculo foi usado como ``toque final'' para completar o smile. - -Poderamos tambm desenhar um smile usando um segmento de crculo, como -em: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*{};(4,0)*{} **\dir{} ? *_!/7pt/\dir{:}; -(2,2)*\cir<5pt>{}; -(2,2)*\cir<3pt>{dr^ur}; -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*{};(4,0)*{} **\dir{} ? *_!/7pt/\dir{:}; -(2,2)*\cir<5pt>{}; -(2,2)*\cir<3pt>{dr^ur}; -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{10pt} -Observe que a boca, tendo sido feita com um segmento de crculo, -resultou em um smile um pouco diferente ao do exemplo anterior. - -\emph{Frames} so molduras que podem ser postas em \Xy-figuras. Uma moldura -(frame) um objeto \Xy-pic{} na forma \verb+\frm{ ... }+. Na -Figura~\ref{fig:frames} so mostrados alguns tipos de molduras -disponveis (para mais veja o \emph{\Xy-pic{} Reference Manual}). - -\begin{figure}[!tp] -\begin{center} -\begin{tabular}{ccc} -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{\}}}}*\frm{} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{.\}}}}*\frm{.} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm<44pt>\{.\}}}}*\frm<44pt>{.} \endxy \\ - & & \\ -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{-\}}}}*\frm{-} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm<8pt>\{-\}}}}*\frm<8pt>{-} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm<44pt>\{-\}}}}*\frm<44pt>{-} \endxy \\ - & & \\ -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{--\}}}}*\frm{--} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{o-\}}}}*\frm{o-} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm<44pt>\{--\}}}}*\frm<44pt>{--} \endxy \\ - & & \\ -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{,\}}}}*\frm{,} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm<5pt>\{,\}}}}*\frm<5pt>{,} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{-,\}}}}*\frm{-,} \endxy \\ - & & \\ -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{o\}}}}*\frm{o} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm<8pt>\{o\}}}}*\frm<8pt>{o} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{.o\}}}}*\frm{.o} \endxy \\ - & & \\ -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{ee\}}}}*\frm{ee} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm<20pt,8pt>\{ee\}}}}*\frm<20pt,8pt>{ee} \endxy & -\xy (0,0)*{\txt{Usando \\ $\backslash${\tt frm\{-e\}}}}*\frm<44pt>{-e} -\endxy -\end{tabular} -\end{center} -\caption{Molduras (frames)}\label{fig:frames} -\end{figure} - -Podemos agora, usando curvas e molduras (frames), construir o seguinte diagrama: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy -(0,0)*++{\txt{Redondo}}*\frm{oo}="r"; -(30,30)*++{\txt{Quadrado}}*\frm{-,}="q"; -"r";"q" **\dir{} ? *++{\txt{Liga}}*\frm{.}="l"; -"r";"l" **\crv{(15,0)}; -"l";"q" **\crv{(15,30)} ?>* \dir{>}; -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -$$ - \shorthandoff{"} -\xy -(0,0)*++{\txt{Redondo}}*\frm{oo}="r"; -(30,30)*++{\txt{Quadrado}}*\frm{-,}="q"; -"r";"q" **\dir{} ? *++{\txt{Liga}}*\frm{.}="l"; -"r";"l" **\crv{(15,0)}; -"l";"q" **\crv{(15,30)} ?>* \dir{>}; -\endxy -$$ -\end{minipage} -\end{tabular} - -\vspace{20pt} -Observe neste exemplo como o \verb+Liga+ posicionado usando-se o -operador \verb+?+ para obter a posio da ligao entre \verb+"r"+ e \verb+"q"+. - -Para importar imagens \emph{postscript} devemos declarar a opo -\verb+import+ na declarao -\verb+\usepackage[all,import]{xy}+. Podemos usar qualquer pacote -para importar a imagem, como por exemplo, \verb+graphicx+, \verb+graphics+, \verb+epsf+ ou -\verb+epsfig+. Neste caso, usamos o \verb+graphicx+, e para isto -devemos declarar o uso do pacote com o comando -\verb+\usepackage{graphicx}+. - -Usamos \verb+\xyimport+ para estabelecer um sistema de coordenadas -para uma imagem em particular, permitindo que qualquer comando do -\Xy-pic{} seja u\-sa\-do, com as posies relativas ao sistema de -coordenadas definido. Para isto, o comando -\verb+\xyimport(larg,alt){imagem}+ exige que se defina uma largura e uma -altura, que fornece uma distncia em unidades de coordenadas, -iniciando no canto inferior esquerdo, onde o sistema de coordenadas -usualmente deve estar localizado. - -Assim, usando a imagem apresentada -na Figura~\ref{fig:semxy}, podemos produzir o que se pode ver na -Figura~\ref{fig:import}, usando o seguinte cdigo: -\begin{verbatim} -\def\grafico{\includegraphics[width=9cm]{grafico.eps}} -\xy -\xyimport(100,100){\grafico} -{\ar (75,85)*+{\txt{Astride}}; (60,75)*{}} -{\ar (75,25)*+{\txt{Elipse}}; (80,37)*{}} -\endxy -\end{verbatim} - -Observe-se que -\begin{verbatim} -\def\grafico{\includegraphics[width=9cm]{grafico.eps}} -\end{verbatim} - uma -macro \TeX{} para definir a imagem a ser importada. - -\begin{figure}[!tp] -\begin{center} -\includegraphics[width=9cm]{grafico.eps} -\end{center} -\caption{Imagem sem comandos \Xy}\label{fig:semxy} -\end{figure} - -\begin{figure}[!tp] -\[ -\def\grafico{\includegraphics[width=9cm]{grafico.eps}} -\xy -\xyimport(100,100){\grafico} -{\ar (75,85)*+{\txt{Astride}}; (60,75)*{}} -{\ar (75,25)*+{\txt{Elipse}}; (80,37)*{}} -\endxy -\] -\caption{Importando uma imagem}\label{fig:import} -\end{figure} - -\section{Usando Polgonos e Elipses} - -Para usar polgonos em diagramas necessrio carregar o \Xy-pic declarando a opo -\verb+poly+, usando o comando \verb+\usepackage[all,poly]{xy}+. - -Polgonos podem ser produzidos usando-se o comando -\verb+\xypolygon+. Por exemplo, podemos criar um hexgono usando: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xy -/r4pc/:{\xypolygon6{\circ}} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xy -/r4pc/:{\xypolygon6{\circ}} -\endxy -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Observe-se que \verb+/r4pc/+ especifica o tamanho do polgono em 4pc -(48pt). O nmero de lados do polgono declarado por meio de um valor -inteiro aps o comando \verb+\xypolygon+. Assim, especificamos o -hexgono com \verb+\xypolygon6+. Alm disto, o argumento \verb+\circ+ indica que os vrtices do -polgono devero ser crculos. - -Alguns outros exemplos de polgonos so: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy /r8mm/: -, 0 ,{\xypolygon6{}} -,+/r18mm/,{\xypolygon8{@{o}}} -,+/r18mm/,{*@{o}\xypolygon6{@{*}}} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xy /r8mm/: -, 0 ,{\xypolygon6{}} -,+/r18mm/,{\xypolygon8{@{o}}} -,+/r18mm/,{*@{o}\xypolygon6{@{*}}} -\endxy -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Nestes exemplos, \verb+0+ (origem) e -\verb=+/r18mm/= (deslocamento) -especificam o posicionamento dos trs polgonos, e os \verb+@{o}+ e -\verb+@{*}+ especificam os vrtices. - -Mais exemplos: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xy /r8mm/: -, 0 ,{\xypolygon6{~*{\dir{*}}}} -,+/r18mm/, -{\xypolygon8{~<{.}~>{}~={45}{\dir{*}}}} -,+/r18mm/, -{\xypolygon6{~<{=}~>{:}{\dir{*}}}} -\endxy -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xy /r8mm/: -, 0 ,{\xypolygon6{~*{\dir{*}}}} -,+/r18mm/, -{\xypolygon8{~<{.}~>{}~={45}{\dir{*}}}} -,+/r18mm/, -{\xypolygon6{~<{=}~>{:}{\dir{*}}}} -\endxy -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Neste exemplo, observamos o uso de \verb+~<+, \verb+~>+ e \verb+~=+ -para indicar conexes entre os vrtices do polgono. - -Para produzir elipses usamos \verb+xycircle+. Assim, -\verb+(0,0)*\xycircle(7,2){.}+ produz uma elipse centrada em $(0,0)$, -com largura $7$ e altura $2$, e pontilhada: -\[ -\xy -(0,0)*\xycircle(7,2){.} -\endxy -\] - -\section{Produzindo Diagramas em Matriz} - -O \Xy-pic oferece uma facilidade (\emph{feature}) para tipografar -diagramas em forma de matriz. Este tipo de diagrama tem -aplicao em diversas reas da matemtica e de cincia da computao, como por exemplo em teoria dos autmatos e teoria das categorias. Para -produzir um diagrama deste tipo usamos o comando -\verb+\xymatrix{ ... }+. - -O diagrama ser formado pelas entradas de uma matriz, organizadas em -linhas e colunas. Cada entrada pode conter uma expresso matemtica -(produzida usando o modo matemtico). - -Usa-se \verb+&+ para separar as colunas e \verb+\\+ para indicar nova -linha, em uma notao semelhante ao ambiente \emph{array} do modo -matemtico do \LaTeX. Assim, se desejamos produzir uma matriz com duas linhas e duas -colunas, usamos: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xymatrix{ -1 & 2 \\ -3 & 4 -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -1 & 2 \\ -3 & 4 -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Poderamos omitir entradas direita que no fossem necessrias no -diagrama, como em: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xymatrix{ -1 & 2 \\ -3 -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -1 & 2 \\ -3 -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Tambm podemos deixar entradas em branco na matriz, como em: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xymatrix{ -1 & 2 \\ - & 4 -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -1 & 2 \\ - & 4 -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Para conectar entradas por setas usamos \verb+\ar+. O destino da seta -definido de forma relativa origem por meio de uma seqncia de \verb+u+ (acima), \verb+d+ (abaixo), -\verb+l+ (esquerda) e \verb+r+ (direita), colocados entre colchetes. Assim, para conectar a -entrada da primeira linha e coluna com a da segunda linha e coluna usamos \verb+\ar[dr]+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xymatrix{ -1 \ar[dr] & 2 \\ -3 & 4 -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -1 \ar[dr] & 2 \\ -3 & 4 -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -As setas da Figura~\ref{fig:setas} funcionaro tambm com o -\verb+\xymatrix+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -{\bullet} \ar@{:>}[r] \ar@{-->}[dr] & {\bullet} -\ar@{=>}[d] \\ -{\bullet} \ar@{-}[u] \ar@{.>}[r] & {\bullet} -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -{\bullet} \ar@{:>}[r] \ar@{-->}[dr] & {\bullet} -\ar@{=>}[d] \\ -{\bullet} \ar@{-}[u] \ar@{.>}[r] & {\bullet} -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Este um exemplo com uma matriz trs por trs: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -2\times 4 \ar[ddrr] & \sqrt{2} \ar[ddl] -& 2^2 \ar[dl] \\ -2 & 4 & 6 \\ -1.414 & 2.7 & 8 -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -2\times 4 \ar[ddrr] & \sqrt{2} \ar[ddl] -& 2^2 \ar[dl] \\ -2 & 4 & 6 \\ -1.414 & 2.7 & 8 -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Observe que a seta que liga $2\times 4$ e $8$ passa sobre o $4$, o que pode ser inconveniente. Para evitar isto podemos -curvar a seta para cima, usando ``\verb+@/^/+'', ou para baixo, usando -``\verb+@/_/+''. Neste caso, curvaremos para baixo: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -2\times 4 \ar@/_/[ddrr] & \sqrt{2} \ar[ddl] -& 2^2 \ar[dl] \\ -2 & 4 & 6 \\ -1.414 & 2.7 & 8 -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -2\times 4 \ar@/_/[ddrr] & \sqrt{2} \ar[ddl] -& 2^2 \ar[dl] \\ -2 & 4 & 6 \\ -1.414 & 2.7 & 8 -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Para uma curvatura maior poderiamos usar, por exemplo, \verb+@/_1pc/+. - -Podemos colocar um rtulo acima (ou abaixo) de uma seta. Para isto -basta usar ``\verb+^+'' (ou ``\verb+_+''). Neste exemplo mostramos -isto: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -A \ar[dr]^{a} \\ -B & C -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -A \ar[dr]^{a} \\ -B & C -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Observe que ``acima'' pode no significar exatamente acima da seta, se a -seta est voltada para a esquerda: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -A & B\ar[dl]^{a} \\ -C -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -A & B\ar[dl]^{a} \\ -C -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Tambm podemos posicionar o rtulo da seta sobre a seta, ou no ``meio'', usando -\verb+|+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -A\ar[r]|a & B -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -A\ar[r]|a & B -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -O ``\verb+|+'' pode ser til para fazer ``buracos'' nas setas (por -exemplo, para passar outras setas sem que se cruzem). Para isto usamos -\verb+\hole+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -A\ar[r]|\hole & B -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -A\ar[r]|\hole & B -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -O seguinte diagrama a definio de produto fibrado em teoria das -categorias. Nele usamos vrios dos recursos do \verb+\xymatrix+ j apresentados: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -d\ar@/_/[ddr]_h\ar[dr]|{_a} -\ar@/^/[drr]^k \\ - & {b\times_a c}\ar[d]^p\ar[r]_q & -c\ar[d]^g\\ - & b\ar[r]^f & a -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -d\ar@/_/[ddr]_h\ar[dr]|{_a} -\ar@/^/[drr]^k \\ - & {b\times_a c}\ar[d]^p\ar[r]_q & -c\ar[d]^g\\ - & b\ar[r]^f & a -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -O comando \verb+\xymatrix+ permite especificar a forma com que -o diagrama ser tipografado. A especificao uma seqncia de -\verb+@+ que antecedem os comandos dentro do -\verb+\xymatrix+. Assim, por exemplo, \verb+\xymatrix@1{ ... }+ -especifica que o diagrama deve ser tipografado em uma linha, como em -\verb+\xymatrix@1{A\ar[r]^f & B}+, que produz \xymatrix@1{A\ar[r]^f & - B}. Isto til para produzir pequenos diagramas que aparecero -dentro do pargrafo do texto. - -Da mesma forma podemos modificar o espaamento das linhas e das colunas por -meio das especificaes \verb+@R+ e/ou \verb+@C+, como por -exemplo em -\verb+\xymatrix@R10pt@C5pt{ ... }+, que especifica 10pt para o -espaamento das linhas e 5pt para o das colunas. - -Podemos explicitamente posicionar o rtulo sobre a seta: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\verb+\xymatrix{A\ar[r]^<{f} & B}+ & {\xymatrix{A\ar[r]^<{f} & B}} \\ -\verb+\xymatrix{A\ar[r]^>{f} & B}+ & {\xymatrix{A\ar[r]^>{f} & B}} \\ -\verb+\xymatrix{A\ar[r]^(.4){f} & B}+ & {\xymatrix{A\ar[r]^(.4){f} & B}} -\end{tabular} - -\vspace{10pt} -Observe-se que, no ltimo caso, podemos usar um valor entre $0$ e $1$ -como fator para posicionar o rtulo (foi usado 0,4 como exemplo). O -fator $0$ representa o incio da seta, e o fator $1$ representa o fim. - -Finalmente, outra possibilidade usar \verb+!{t1;t2}+, que posiciona -o rtulo no ponto em que a seta cruza a linha que liga os lugares -\verb+t1+ e \verb+t2+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -A \ar[rr]^f \ar[dr]_(.3)g |!{[d];[rr]}\hole -& & B \\ -C \ar[rru]_(.7)h \ar[r]_i & D -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -A \ar[rr]^f \ar[dr]_(.3)g |!{[d];[rr]}\hole -& & B \\ -C \ar[rru]_(.7)h \ar[r]_i & D -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Neste ltimo exemplo, o \verb+!{[d];[rr]}+ determina o ponto em que a -seta que liga $A$ e $D$ se cruza com a que liga $C$ e $B$. Neste ponto - posto o \verb+\hole+. - -Podemos indicar a posio que a seta deve entrar ou sair de uma entrada -usando as seguintes direes, que j haviam sido mostradas, e -repetimos aqui para facilitar: -$$ - \shorthandoff{"} -\xy -(0,0)*\cir<10pt>{}; -{\ar@{->} (-4,0)*{}; (-14,0)*+{l}}; -{\ar@{->} (4,0)*{}; (14,0)*+{r}}; -{\ar@{->} (0,4)*{}; (0,14)*+{u}}; -{\ar@{->} (0,-4)*{}; (0,-14)*+{d}}; -{\ar@{->} (3,3)*{}; (12,12)*+{ur=ru}}; -{\ar@{->} (-3,3)*{}; (-12,12)*+{ul=lu}}; -{\ar@{->} (-3,-3)*{}; (-12,-12)*+{dl=ld}}; -{\ar@{->} (3,-3)*{}; (12,-12)*+{dr=rd}}; -\endxy -$$ - -Isto nos permite fazer uma seta ``reflexiva'', especificando a seta -usando o comando -\verb+\ar@(sada,entrada)[]+. O \verb+[]+ indica que a seta apontar -para a prpria entrada, e a especificao \verb+@(sada,entrada)+ -define as direes de sada e entrada da seta. Assim, -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xymatrix{ -1 \ar@(ul,ur)[]^{id} \ar[r]_f & -2 \ar@(ul,ur)[]^{id} -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -1 \ar@(ul,ur)[]^{id} \ar[r]_f & -2 \ar@(ul,ur)[]^{id} -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Podemos produzir setas paralelas, usando uma \emph{dimenso} para -separa-las, definida por \verb+@+: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xymatrix{ -A\ar@<1ex>[r]^a_{.} & B\ar@<1ex>[l]^b -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -A\ar@<1ex>[r]^a_{.} & B\ar@<1ex>[l]^b -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -A dimenso de 1ex, adotada neste caso, conveniente pois corresponde - altura da letra ``x''. - -Os recursos de frames (molduras) que podem ser usados nos objetos do diagrama so -apresentados na Figura~\ref{tab:framematriz}. Os modificadores -\verb=+= e \verb=-= podem ser usados para aumentar ou diminuir o -tamanho da moldura. - -\begin{figure}[!tp] -\begin{center} -\begin{tabular}{cccc} -\verb+[F]+ & {\xymatrix{*+[F]{\txt{Simples}}}} & \verb+[F=]+ & - {\xymatrix{*+[F=]{\txt{Duplo}}}} \\ - & & & \\ -\verb+[F.]+ & {\xymatrix{*+[F.]{\txt{Pontilhado}}}} & \verb+[F--]+ & - {\xymatrix{*+[F--]{\txt{Tracejado}}}} \\ - & & & \\ -\verb+[F-,]+ & {\xymatrix{*+[F-,]{\txt{Sombra}}}} & \verb+[F-:<3pt>]+ & - {\xymatrix{*+[F-:<3pt>]{\txt{Arredondado}}}} \\ - & & & \\ -\verb+[o][F-]+ & {\xymatrix{*+[o][F-]{\txt{Redondo}}}} -\end{tabular} -\end{center} -\caption{Frames em diagramas em matriz}\label{tab:framematriz} -\end{figure} - -Um exemplo usando frames : -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -*+[F-,]{\int_{-\infty}^{+\infty} -f(x)\mathrm{d}x } \ar[dr] \\ -*+[o][F-]{\txt{pi}} & 10 -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -*+[F-,]{\int_{-\infty}^{+\infty} -f(x)\mathrm{d}x } \ar[dr] \\ -*+[o][F-]{\txt{pi}} & 10 -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -O exemplo a seguir um diagrama que representa um autmato finito: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{8cm} -\begin{verbatim} -\xymatrix{ -*++[o][F-]{1} \ar@(ul,ul)[] \ar[r]^{1} -\ar[d]^{0} & *++[o][F=]{3} \\ -*++[o][F-]{2} \ar[ur]_{1} \ar@(dl,d)[]_{0}} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -*++[o][F-]{1} \ar@(ul,ul)[] \ar[r]^{1} -\ar[d]^{0} & *++[o][F=]{3} \\ -*++[o][F-]{2} \ar[ur]_{1} \ar@(dl,d)[]_{0}} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Outro exemplo: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xymatrix{ -{\txt{Oceano}} -\ar@/^3pc/[rr]^{\txt{evaporao}} -& *+[F-]{H_2O} -& {\txt{Atmosfera}} -\ar@/^3pc/[ll]^{\txt{precipitao}} -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -{\txt{Oceano}} -\ar@/^3pc/[rr]^{\txt{evaporao}} -& *+[F-]{H_2O} -& {\txt{Atmosfera}} -\ar@/^3pc/[ll]^{\txt{precipitao}} -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Ainda possvel colocar entradas extras, que estaro fora da matriz, -usando o comando \verb+\save ... \restore+. Neste caso, o que fica -dentro do comando no far parte de nenhuma entrada da matriz: -\vspace{10pt} - -\noindent \begin{tabular}{lr} -\begin{minipage}{7cm} -\begin{verbatim} -\xymatrix{ -A \ar@{-}[dr] & -\save[]+<3cm,0cm>*\txt<8pc>{ -Este um longo comentrio que -no ocupar nenhuma entrada -da matriz} -\ar[l]\ar[d] -\restore \\ - & B\ar@{-}[r] & C -} -\end{verbatim} -\end{minipage} & -\begin{minipage}{6cm} -{$$ - \shorthandoff{"} -\xymatrix{ -A \ar@{-}[dr] & -\save[]+<3cm,0cm>*\txt<8pc>{ -Este um longo comentrio que -no ocupar nenhuma entrada -da matriz} -\ar[l]\ar[d] -\restore \\ - & B\ar@{-}[r] & C -} -$$} -\end{minipage} -\end{tabular} - -\vspace{10pt} -Observe-se que a seta \verb+\ar[d]+, que parte do comentrio, no -necessariamente ``para baixo''. - -\begin{thebibliography}{1} -\bibitem {bib:guia} Rose, K. H. \emph{\Xy-pic User's Guide}. Disponvel em: \url{http://tug.org/applications/Xy-pic/soft/xyguide.ps.gz}. -\bibitem {bib:manual} Rose, K. H. \& Moore, R. \emph{\Xy-pic Reference - Manual}. Disponvel em: \url{http://tug.org/applications/Xy-pic/soft/xyrefer.ps.gz}. -\bibitem {bib:goossens} Goossens, M. \& Rahtz, S. \& Mittelbach, - F. \emph{The \LaTeX{} Graphics Companion}, Addison-Wesley, 1997. -\end{thebibliography} - -\newpage - -Copyright \copyright 2006 Carlos A. P. Campani. - - garantida a permisso para copiar, distribuir e/ou modificar este documento sob os termos da Licena de Documentao Livre GNU (GNU Free Documentation License), Verso 1.2 ou qualquer verso posterior publicada pela Free Software Foundation; sem Sees Invariantes, Textos de Capa Frontal, e sem Textos de Quarta Capa. Uma cpia da licena includa na seo intitulada ``GNU Free Documentation License''. - -veja: \url{http://www.ic.unicamp.br/~norton/fdl.html}. - -\end{document} -- cgit v1.2.3