diff options
Diffstat (limited to 'Master')
-rw-r--r-- | Master/texmf-doc/doc/portuguese/xypic-tut-pt/README | 3 | ||||
-rw-r--r-- | Master/texmf-doc/doc/portuguese/xypic-tut-pt/grafico.eps | 460 | ||||
-rw-r--r-- | Master/texmf-doc/doc/portuguese/xypic-tut-pt/xypic-tutorial.pdf | 3011 | ||||
-rw-r--r-- | Master/texmf-doc/doc/portuguese/xypic-tut-pt/xypictutorial.tex | 1954 | ||||
-rw-r--r-- | Master/texmf-doc/tpm/xypic-tut-pt.tpm | 24 | ||||
-rw-r--r-- | Master/texmf/lists/xypic-tut-pt | 8 | ||||
-rw-r--r-- | Master/texmf/tpm/collection-documentation-portuguese.tpm | 3 |
7 files changed, 5462 insertions, 1 deletions
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b/Master/texmf-doc/doc/portuguese/xypic-tut-pt/xypictutorial.tex new file mode 100644 index 00000000000..e48c9271b2f --- /dev/null +++ b/Master/texmf-doc/doc/portuguese/xypic-tut-pt/xypictutorial.tex @@ -0,0 +1,1954 @@ +\documentclass[12pt]{article} + +\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]|{<h,k>_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} +{$$ + \shorthandoff{"} +\xymatrix{ +d\ar@/_/[ddr]_h\ar[dr]|{<h,k>_a} +\ar@/^/[drr]^k \\ + & {b\times_a c}\ar[d]^p\ar[r]_q & +c\ar[d]^g\\ + & b\ar[r]^f & a +} +$$} +\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+@<especificao>+ 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<dim>+ e/ou \verb+@C<dim>+, 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+@<dim>+: +\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} diff --git a/Master/texmf-doc/tpm/xypic-tut-pt.tpm b/Master/texmf-doc/tpm/xypic-tut-pt.tpm new file mode 100644 index 00000000000..809e276e760 --- /dev/null +++ b/Master/texmf-doc/tpm/xypic-tut-pt.tpm @@ -0,0 +1,24 @@ +<!DOCTYPE rdf:RDF SYSTEM "../../support/tpm.dtd"> +<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:TPM="http://texlive.dante.de/"> + <rdf:Description about="http://texlive.dante.de/texlive/Documentation/xypic-tut-pt.zip"> + <TPM:Name>xypic-tut-pt</TPM:Name> + <TPM:Type>Documentation</TPM:Type> + <TPM:Date>2006/05/04 10:57:00</TPM:Date> + <TPM:Version></TPM:Version> + <TPM:Creator>karl</TPM:Creator> + <TPM:Title>The xypic-tut-pt package.</TPM:Title> + <TPM:Description></TPM:Description> + <TPM:Author></TPM:Author> + <TPM:Size>306794</TPM:Size> + <TPM:Build/> + <TPM:RunFiles size="957">texmf-doc/tpm/xypic-tut-pt.tpm</TPM:RunFiles> + <TPM:DocFiles size="306794"> +texmf-doc/doc/portuguese/xypic-tut-pt/README +texmf-doc/doc/portuguese/xypic-tut-pt/grafico.eps +texmf-doc/doc/portuguese/xypic-tut-pt/xypic-tutorial.pdf +texmf-doc/doc/portuguese/xypic-tut-pt/xypictutorial.tex + </TPM:DocFiles> + <TPM:Provides>Documentation/xypic-tut-pt</TPM:Provides> + </rdf:Description> +</rdf:RDF> + diff --git a/Master/texmf/lists/xypic-tut-pt b/Master/texmf/lists/xypic-tut-pt new file mode 100644 index 00000000000..23d1107f16f --- /dev/null +++ b/Master/texmf/lists/xypic-tut-pt @@ -0,0 +1,8 @@ +texmf-doc/doc/portuguese/xypic-tut-pt/README +texmf-doc/doc/portuguese/xypic-tut-pt/grafico.eps +texmf-doc/doc/portuguese/xypic-tut-pt/xypic-tutorial.pdf +texmf-doc/doc/portuguese/xypic-tut-pt/xypictutorial.tex + +texmf-doc/tpm/xypic-tut-pt.tpm + +texmf/lists/xypic-tut-pt diff --git a/Master/texmf/tpm/collection-documentation-portuguese.tpm b/Master/texmf/tpm/collection-documentation-portuguese.tpm index e61b2d457c1..8d70640ce57 100644 --- a/Master/texmf/tpm/collection-documentation-portuguese.tpm +++ b/Master/texmf/tpm/collection-documentation-portuguese.tpm @@ -21,8 +21,9 @@ texmf/tpm/collection-documentation-portuguese.tpm texmf/tpm/collection-documentation-portuguese.tpm </TPM:RunFiles> <TPM:Requires> - <TPM:Documentation name="lshort-portuguese"/> <TPM:Documentation name="beamer-tut-pt"/> + <TPM:Documentation name="lshort-portuguese"/> + <TPM:Documentation name="xypic-tut-pt"/> <TPM:TLCore name="collection-documentation-base"/> </TPM:Requires> <TPM:Provides>TLCore/collection-documentation-portuguese</TPM:Provides> |