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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /graphics/pgf/base/doc/text-en/pgfmanual-en-tutorial-nodes.tex |
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diff --git a/graphics/pgf/base/doc/text-en/pgfmanual-en-tutorial-nodes.tex b/graphics/pgf/base/doc/text-en/pgfmanual-en-tutorial-nodes.tex new file mode 100644 index 0000000000..26f9805b6a --- /dev/null +++ b/graphics/pgf/base/doc/text-en/pgfmanual-en-tutorial-nodes.tex @@ -0,0 +1,1072 @@ +% Copyright 2006 by Till Tantau +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Free Documentation License. +% +% See the file doc/generic/pgf/licenses/LICENSE for more details. + + +\section{Tutorial: A Petri-Net for Hagen} + +In this second tutorial we explore the node mechanism of \tikzname\ and +\pgfname. + +Hagen must give a talk tomorrow about his favorite formalism for distributed +systems: Petri nets! Hagen used to give his talks using a blackboard and +everyone seemed to be perfectly content with this. Unfortunately, his audience +has been spoiled recently with fancy projector-based presentations and there +seems to be a certain amount of peer pressure that his Petri nets should also +be drawn using a graphic program. One of the professors at his institute +recommends \tikzname\ for this and Hagen decides to give it a try. + + +\subsection{Problem Statement} + +For his talk, Hagen wishes to create a graphic that demonstrates how a net with +place capacities can be simulated by a net without capacities. The graphic +should look like this, ideally: +% +\begin{quote} +\begin{tikzpicture} + [node distance=1.3cm,>=stealth',bend angle=45,auto, + place/.style={circle,thick,draw=blue!75,fill=blue!20,minimum size=6mm}, + red place/.style={place,draw=red!75,fill=red!20}, + transition/.style={rectangle,thick,draw=black!75,fill=black!20,minimum size=4mm}, + every label/.style={red},on grid] + + \begin{scope} + % First net + \node [place,tokens=1] (w1) {}; + \node [place] (c1) [below=of w1] {}; + \node [place] (s) [below=of c1,label=above:$s\le 3$] {}; + \node [place] (c2) [below=of s] {}; + \node [place,tokens=1] (w2) [below=of c2] {}; + + \node [transition] (e1) [left=of c1] {} + edge [pre,bend left] (w1) + edge [post,bend right] (s) + edge [post] (c1); + + \node [transition] (e2) [left=of c2] {} + edge [pre,bend right] (w2) + edge [post,bend left] (s) + edge [post] (c2); + + \node [transition] (l1) [right=of c1] {} + edge [pre] (c1) + edge [pre,bend left] (s) + edge [post,bend right] node[swap] {2} (w1); + + \node [transition] (l2) [right=of c2] {} + edge [pre] (c2) + edge [pre,bend right] (s) + edge [post,bend left] node {2} (w2); + \end{scope} + + \begin{scope}[xshift=6cm] + % Second net + \node [place,tokens=1] + (w1') {}; + \node [place] (c1') [below=of w1'] {}; + \node [red place] (s1') [below=of c1',xshift=-5mm,label=left:$s$] {}; + \node [red place,tokens=3] + (s2') [below=of c1',xshift=5mm,label=right:$\bar s$] {}; + \node [place] (c2') [below=of s1',xshift=5mm] {}; + \node [place,tokens=1] + (w2') [below=of c2'] {}; + + \node [transition] (e1') [left=of c1'] {} + edge [pre,bend left] (w1') + edge [post] (s1') + edge [pre] (s2') + edge [post] (c1'); + + \node [transition] (e2') [left=of c2'] {} + edge [pre,bend right] (w2') + edge [post] (s1') + edge [pre] (s2') + edge [post] (c2'); + + \node [transition] (l1') [right=of c1'] {} + edge [pre] (c1') + edge [pre] (s1') + edge [post] (s2') + edge [post,bend right] node[swap] {2} (w1'); + + \node [transition] (l2') [right=of c2'] {} + edge [pre] (c2') + edge [pre] (s1') + edge [post] (s2') + edge [post,bend left] node {2} (w2'); + \end{scope} + + \begin{scope}[on background layer] + \node (r1) [fill=black!10,rounded corners,fit=(w1)(w2)(e1)(e2)(l1)(l2)] {}; + \node (r2) [fill=black!10,rounded corners,fit=(w1')(w2')(e1')(e2')(l1')(l2')] {}; + \end{scope} + + \draw [shorten >=1mm,-to,thick,decorate,decoration={snake,amplitude=.4mm,segment + length=2mm,pre=moveto,pre length=1mm,post length=2mm}] + (r1) -- (r2) + node [above=1mm,midway,text width=3cm,align=center] + {replacement of the \textcolor{red}{capacity} by \textcolor{red}{two places}}; + +\end{tikzpicture} +\end{quote} + + +\subsection{Setting up the Environment} + +For the picture Hagen will need to load the \tikzname\ package as did Karl in +the previous tutorial. However, Hagen will also need to load some additional +\emph{library packages} that Karl did not need. These library packages contain +additional definitions like extra arrow tips that are typically not needed in a +picture and that need to be loaded explicitly. + +Hagen will need to load several libraries: The |arrows| library for the special +arrow tip used in the graphic, the |decorations.pathmorphing| library for the +``snaking line'' in the middle, the |backgrounds| library for the two +rectangular areas that are behind the two main parts of the picture, the |fit| +library to easily compute the sizes of these rectangles, and the |positioning| +library for placing nodes relative to other nodes. + + +\subsubsection{Setting up the Environment in \LaTeX} + +When using \LaTeX\ use: +% +\begin{codeexample}[code only] +\documentclass{article} % say + +\usepackage{tikz} +\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,positioning,fit,petri} + +\begin{document} +\begin{tikzpicture} + \draw (0,0) -- (1,1); +\end{tikzpicture} +\end{document} +\end{codeexample} + + +\subsubsection{Setting up the Environment in Plain \TeX} + +When using plain \TeX\ use: +% +\begin{codeexample}[code only] +%% Plain TeX file +\input tikz.tex +\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,positioning,fit,petri} +\baselineskip=12pt +\hsize=6.3truein +\vsize=8.7truein +\tikzpicture + \draw (0,0) -- (1,1); +\endtikzpicture +\bye +\end{codeexample} + + +\subsubsection{Setting up the Environment in Con\TeX t} + +When using Con\TeX t, use: +% +\begin{codeexample}[code only] +%% ConTeXt file +\usemodule[tikz] +\usetikzlibrary[arrows,decorations.pathmorphing,backgrounds,positioning,fit,petri] + +\starttext + \starttikzpicture + \draw (0,0) -- (1,1); + \stoptikzpicture +\stoptext +\end{codeexample} + + +\subsection{Introduction to Nodes} + +In principle, we already know how to create the graphics that Hagen desires +(except perhaps for the snaked line, we will come to that): We start with big +light gray rectangle and then add lots of circles and small rectangle, plus +some arrows. + +However, this approach has numerous disadvantages: First, it is hard to change +anything at a later stage. For example, if we decide to add more places to the +Petri nets (the circles are called places in Petri net theory), all of the +coordinates change and we need to recalculate everything. Second, it is hard to +read the code for the Petri net as it is just a long and complicated list of +coordinates and drawing commands -- the underlying structure of the Petri net +is lost. + +Fortunately, \tikzname\ offers a powerful mechanism for avoiding the above +problems: nodes. We already came across nodes in the previous tutorial, where +we used them to add labels to Karl's graphic. In the present tutorial we will +see that nodes are much more powerful. + +A node is a small part of a picture. When a node is created, you provide a +position where the node should be drawn and a \emph{shape}. A node of shape +|circle| will be drawn as a circle, a node of shape |rectangle| as a rectangle, +and so on. A node may also contain some text, which is why Karl used nodes to +show text. Finally, a node can get a \emph{name} for later reference. + +In Hagen's picture we will use nodes for the places and for the transitions of +the Petri net (the places are the circles, the transitions are the rectangles). +Let us start with the upper half of the left Petri net. In this upper half we +have three places and two transitions. Instead of drawing three circles and two +rectangles, we use three nodes of shape |circle| and two nodes of shape +|rectangle|. +% +\begin{codeexample}[] +\begin{tikzpicture} + \path ( 0,2) node [shape=circle,draw] {} + ( 0,1) node [shape=circle,draw] {} + ( 0,0) node [shape=circle,draw] {} + ( 1,1) node [shape=rectangle,draw] {} + (-1,1) node [shape=rectangle,draw] {}; +\end{tikzpicture} +\end{codeexample} + +Hagen notes that this does not quite look like the final picture, but it seems +like a good first step. + +Let us have a more detailed look at the code. The whole picture consists of a +single path. Ignoring the |node| operations, there is not much going on in this +path: It is just a sequence of coordinates with nothing ``happening'' between +them. Indeed, even if something were to happen like a line-to or a curve-to, +the |\path| command would not ``do'' anything with the resulting path. So, all +the magic must be in the |node| commands. + +In the previous tutorial we learned that a |node| will add a piece of text at +the last coordinate. Thus, each of the five nodes is added at a different +position. In the above code, this text is empty (because of the empty |{}|). +So, why do we see anything at all? The answer is the |draw| option for the +|node| operation: It causes the ``shape around the text'' to be drawn. + +So, the code |(0,2) node [shape=circle,draw] {}| means the following: ``In the +main path, add a move-to to the coordinate |(0,2)|. Then, temporarily suspend +the construction of the main path while the node is built. This node will be a +|circle| around an empty text. This circle is to be |draw|n, but not filled or +otherwise used. Once this whole node is constructed, it is saved until after +the main path is finished. Then, it is drawn.'' The following +|(0,1) node [shape=circle,draw] {}| then has the following effect: ``Continue +the main path with a move-to to |(0,1)|. Then construct a node at this position +also. This node is also shown after the main path is finished.'' And so on. + + +\subsection{Placing Nodes Using the At Syntax} + +Hagen now understands how the |node| operation adds nodes to the path, but it +seems a bit silly to create a path using the |\path| operation, consisting of +numerous superfluous move-to operations, only to place nodes. He is pleased to +learn that there are ways to add nodes in a more sensible manner. + +First, the |node| operation allows one to add |at (|\meta{coordinate}|)| in +order to directly specify where the node should be placed, sidestepping the +rule that nodes are placed on the last coordinate. Hagen can then write the +following: +% +\begin{codeexample}[] +\begin{tikzpicture} + \path node at ( 0,2) [shape=circle,draw] {} + node at ( 0,1) [shape=circle,draw] {} + node at ( 0,0) [shape=circle,draw] {} + node at ( 1,1) [shape=rectangle,draw] {} + node at (-1,1) [shape=rectangle,draw] {}; +\end{tikzpicture} +\end{codeexample} + +Now Hagen is still left with a single empty path, but at least the path no +longer contains strange move-to's. It turns out that this can be improved +further: The |\node| command is an abbreviation for |\path node|, which allows +Hagen to write: +% +\begin{codeexample}[] +\begin{tikzpicture} + \node at ( 0,2) [circle,draw] {}; + \node at ( 0,1) [circle,draw] {}; + \node at ( 0,0) [circle,draw] {}; + \node at ( 1,1) [rectangle,draw] {}; + \node at (-1,1) [rectangle,draw] {}; +\end{tikzpicture} +\end{codeexample} + +Hagen likes this syntax much better than the previous one. Note that Hagen has +also omitted the |shape=| since, like |color=|, \tikzname\ allows you to omit +the |shape=| if there is no confusion. + + +\subsection{Using Styles} + +Feeling adventurous, Hagen tries to make the nodes look nicer. In the final +picture, the circles and rectangle should be filled with different colors, +resulting in the following code: +% +\begin{codeexample}[] +\begin{tikzpicture}[thick] + \node at ( 0,2) [circle,draw=blue!50,fill=blue!20] {}; + \node at ( 0,1) [circle,draw=blue!50,fill=blue!20] {}; + \node at ( 0,0) [circle,draw=blue!50,fill=blue!20] {}; + \node at ( 1,1) [rectangle,draw=black!50,fill=black!20] {}; + \node at (-1,1) [rectangle,draw=black!50,fill=black!20] {}; +\end{tikzpicture} +\end{codeexample} + +While this looks nicer in the picture, the code starts to get a bit ugly. +Ideally, we would like our code to transport the message ``there are three +places and two transitions'' and not so much which filling colors should be +used. + +To solve this problem, Hagen uses styles. He defines a style for places and +another style for transitions: +% +\begin{codeexample}[] +\begin{tikzpicture} + [place/.style={circle,draw=blue!50,fill=blue!20,thick}, + transition/.style={rectangle,draw=black!50,fill=black!20,thick}] + \node at ( 0,2) [place] {}; + \node at ( 0,1) [place] {}; + \node at ( 0,0) [place] {}; + \node at ( 1,1) [transition] {}; + \node at (-1,1) [transition] {}; +\end{tikzpicture} +\end{codeexample} + + +\subsection{Node Size} + +Before Hagen starts naming and connecting the nodes, let us first make sure +that the nodes get their final appearance. They are still too small. Indeed, +Hagen wonders why they have any size at all, after all, the text is empty. The +reason is that \tikzname\ automatically adds some space around the text. The +amount is set using the option |inner sep|. So, to increase the size of the +nodes, Hagen could write: +% +\begin{codeexample}[] +\begin{tikzpicture} + [inner sep=2mm, + place/.style={circle,draw=blue!50,fill=blue!20,thick}, + transition/.style={rectangle,draw=black!50,fill=black!20,thick}] + \node at ( 0,2) [place] {}; + \node at ( 0,1) [place] {}; + \node at ( 0,0) [place] {}; + \node at ( 1,1) [transition] {}; + \node at (-1,1) [transition] {}; +\end{tikzpicture} +\end{codeexample} + +However, this is not really the best way to achieve the desired effect. It is +much better to use the |minimum size| option instead. This option allows Hagen +to specify a minimum size that the node should have. If the node actually needs +to be bigger because of a longer text, it will be larger, but if the text is +empty, then the node will have |minimum size|. This option is also useful to +ensure that several nodes containing different amounts of text have the same +size. The options |minimum height| and |minimum width| allow you to specify the +minimum height and width independently. + +So, what Hagen needs to do is to provide |minimum size| for the nodes. To be on +the safe side, he also sets |inner sep=0pt|. This ensures that the nodes will +really have size |minimum size| and not, for very small minimum sizes, the +minimal size necessary to encompass the automatically added space. +% +\begin{codeexample}[] +\begin{tikzpicture} + [place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, + transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}] + \node at ( 0,2) [place] {}; + \node at ( 0,1) [place] {}; + \node at ( 0,0) [place] {}; + \node at ( 1,1) [transition] {}; + \node at (-1,1) [transition] {}; +\end{tikzpicture} +\end{codeexample} + + +\subsection{Naming Nodes} + +Hagen's next aim is to connect the nodes using arrows. This seems like a tricky +business since the arrows should not start in the middle of the nodes, but +somewhere on the border and Hagen would very much like to avoid computing these +positions by hand. + +Fortunately, \pgfname\ will perform all the necessary calculations for him. +However, he first has to assign names to the nodes so that he can reference +them later on. + +There are two ways to name a node. The first is to use the |name=| option. The +second method is to write the desired name in parentheses after the |node| +operation. Hagen thinks that this second method seems strange, but he will soon +change his opinion. +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +% ... set up styles +\begin{tikzpicture} + \node (waiting 1) at ( 0,2) [place] {}; + \node (critical 1) at ( 0,1) [place] {}; + \node (semaphore) at ( 0,0) [place] {}; + \node (leave critical) at ( 1,1) [transition] {}; + \node (enter critical) at (-1,1) [transition] {}; +\end{tikzpicture} +\end{codeexample} +} + +Hagen is pleased to note that the names help in understanding the code. Names +for nodes can be pretty arbitrary, but they should not contain commas, periods, +parentheses, colons, and some other special characters. However, they can +contain underscores and hyphens. + +The syntax for the |node| operation is quite liberal with respect to the order +in which node names, the |at| specifier, and the options must come. Indeed, you +can even have multiple option blocks between the |node| and the text in curly +braces, they accumulate. You can rearrange them arbitrarily and perhaps the +following might be preferable: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting 1) at ( 0,2) {}; + \node[place] (critical 1) at ( 0,1) {}; + \node[place] (semaphore) at ( 0,0) {}; + \node[transition] (leave critical) at ( 1,1) {}; + \node[transition] (enter critical) at (-1,1) {}; +\end{tikzpicture} +\end{codeexample} +} + + +\subsection{Placing Nodes Using Relative Placement} + +Although Hagen still wishes to connect the nodes, he first wishes to address +another problem again: The placement of the nodes. Although he likes the |at| +syntax, in this particular case he would prefer placing the nodes ``relative to +each other''. So, Hagen would like to say that the |critical 1| node should be +below the |waiting 1| node, wherever the |waiting 1| node might be. There are +different ways of achieving this, but the nicest one in Hagen's case is the +|below| option: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; +\end{tikzpicture} +\end{codeexample} +} + +With the |positioning| library loaded, when an option like |below| is followed +by |of|, then the position of the node is shifted in such a manner that it is +placed at the distance |node distance| in the specified direction of the given +direction. The |node distance| is either the distance between the centers of +the nodes (when the |on grid| option is set to true) or the distance between +the borders (when the |on grid| option is set to false, which is the default). + +Even though the above code has the same effect as the earlier code, Hagen can +pass it to his colleagues who will be able to just read and understand it, +perhaps without even having to see the picture. + + +\subsection{Adding Labels Next to Nodes} + +Before we have a look at how Hagen can connect the nodes, let us add the +capacity ``$s \le 3$'' to the bottom node. For this, two approaches are +possible: +% +\begin{enumerate} + \item Hagen can just add a new node above the |north| anchor of the + |semaphore| node. +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; + + \node [red,above] at (semaphore.north) {$s\le 3$}; +\end{tikzpicture} +\end{codeexample} +} + % + This is a general approach that will ``always work''. + + \item Hagen can use the special |label| option. This option is given to a + |node| and it causes \emph{another} node to be added next to the node + where the option is given. Here is the idea: When we construct the + |semaphore| node, we wish to indicate that we want another node with + the capacity above it. For this, we use the option + |label=above:$s\le 3$|. This option is interpreted as follows: We want + a node above the |semaphore| node and this node should read ``$s \le + 3$''. Instead of |above| we could also use things like |below left| + before the colon or a number like |60|. + % +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical, + label=above:$s\le3$] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; +\end{tikzpicture} +\end{codeexample} +} + % + It is also possible to give multiple |label| options, this causes + multiple labels to be drawn. + % +\begin{codeexample}[] +\tikz + \node [circle,draw,label=60:$60^\circ$,label=below:$-90^\circ$] {my circle}; +\end{codeexample} + % + Hagen is not fully satisfied with the |label| option since the label + is not red. To achieve this, he has two options: First, he can + redefine the |every label| style. Second, he can add options to the + label's node. These options are given following the |label=|, so he + would write |label=[red]above:$s\le3$|. However, this does not quite + work since \TeX\ thinks that the |]| closes the whole option list of + the |semaphore| node. So, Hagen has to add braces and writes + |label={[red]above:$s\le3$}|. Since this looks a bit ugly, Hagen + decides to redefine the |every label| style. + % +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture}[every label/.style={red}] + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical, + label=above:$s\le3$] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; +\end{tikzpicture} +\end{codeexample} +} +\end{enumerate} + + +\subsection{Connecting Nodes} + +It is now high time to connect the nodes. Let us start with something simple, +namely with the straight line from |enter critical| to |critical|. We want this +line to start at the right side of |enter critical| and to end at the left side +of |critical|. For this, we can use the \emph{anchors} of the nodes. Every node +defines a whole bunch of anchors that lie on its border or inside it. For +example, the |center| anchor is at the center of the node, the |west| anchor is +on the left of the node, and so on. To access the coordinate of a node, we use +a coordinate that contains the node's name followed by a dot, followed by the +anchor's name: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; + \draw [->] (critical.west) -- (enter critical.east); +\end{tikzpicture} +\end{codeexample} +} + +Next, let us tackle the curve from |waiting| to |enter critical|. This can be +specified using curves and controls: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; + \draw [->] (enter critical.east) -- (critical.west); + \draw [->] (waiting.west) .. controls +(left:5mm) and +(up:5mm) + .. (enter critical.north); +\end{tikzpicture} +\end{codeexample} +} + +Hagen sees how he can now add all his edges, but the whole process seems a but +awkward and not very flexible. Again, the code seems to obscure the structure +of the graphic rather than showing it. + +So, let us start improving the code for the edges. First, Hagen can leave out +the anchors: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; + \draw [->] (enter critical) -- (critical); + \draw [->] (waiting) .. controls +(left:8mm) and +(up:8mm) + .. (enter critical); +\end{tikzpicture} +\end{codeexample} +} + +Hagen is a bit surprised that this works. After all, how did \tikzname\ know +that the line from |enter critical| to |critical| should actually start on the +borders? Whenever \tikzname\ encounters a whole node name as a ``coordinate'', +it tries to ``be smart'' about the anchor that it should choose for this node. +Depending on what happens next, \tikzname\ will choose an anchor that lies on +the border of the node on a line to the next coordinate or control point. The +exact rules are a bit complex, but the chosen point will usually be correct -- +and when it is not, Hagen can still specify the desired anchor by hand. + +Hagen would now like to simplify the curve operation somehow. It turns out that +this can be accomplished using a special path operation: the |to| operation. +This operation takes many options (you can even define new ones yourself). One +pair of options is useful for Hagen: The pair |in| and |out|. These options +take angles at which a curve should leave or reach the start or target +coordinates. Without these options, a straight line is drawn: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; + \draw [->] (enter critical) to (critical); + \draw [->] (waiting) to [out=180,in=90] (enter critical); +\end{tikzpicture} +\end{codeexample} +} + +There is another option for the |to| operation, that is even better suited to +Hagen's problem: The |bend right| option. This option also takes an angle, but +this angle only specifies the angle by which the curve is bent to the right: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {}; + \draw [->] (enter critical) to (critical); + \draw [->] (waiting) to [bend right=45] (enter critical); + \draw [->] (enter critical) to [bend right=45] (semaphore); +\end{tikzpicture} +\end{codeexample} +} + +It is now time for Hagen to learn about yet another way of specifying edges: +Using the |edge| path operation. This operation is very similar to the |to| +operation, but there is one important difference: Like a node the edge +generated by the |edge| operation is not part of the main path, but is added +only later. This may not seem very important, but it has some nice +consequences. For example, every edge can have its own arrow tips and its own +color and so on and, still, all the edges can be given on the same path. This +allows Hagen to write the following: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +\begin{tikzpicture} + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + \node[transition] (leave critical) [right=of critical] {}; + \node[transition] (enter critical) [left=of critical] {} + edge [->] (critical) + edge [<-,bend left=45] (waiting) + edge [->,bend right=45] (semaphore); +\end{tikzpicture} +\end{codeexample} +} + +Each |edge| caused a new path to be constructed, consisting of a |to| between +the node |enter critical| and the node following the |edge| command. + +The finishing touch is to introduce two styles |pre| and |post| and to use the +|bend angle=45| option to set the bend angle once and for all: +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}} +\begin{codeexample}[] +% Styles place and transition as before +\begin{tikzpicture} + [bend angle=45, + pre/.style={<-,shorten <=1pt,>=stealth',semithick}, + post/.style={->,shorten >=1pt,>=stealth',semithick}] + + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + + \node[transition] (leave critical) [right=of critical] {} + edge [pre] (critical) + edge [post,bend right] (waiting) + edge [pre, bend left] (semaphore); + \node[transition] (enter critical) [left=of critical] {} + edge [post] (critical) + edge [pre, bend left] (waiting) + edge [post,bend right] (semaphore); +\end{tikzpicture} +\end{codeexample} +} + + +\subsection{Adding Labels Next to Lines} + +The next thing that Hagen needs to add is the ``$2$'' at the arcs. For this +Hagen can use \tikzname's automatic node placement: By adding the option +|auto|, \tikzname\ will position nodes on curves and lines in such a way that +they are not on the curve but next to it. Adding |swap| will mirror the label +with respect to the line. Here is a general example: +% +{ +\begin{codeexample}[] +\begin{tikzpicture}[auto,bend right] + \node (a) at (0:1) {$0^\circ$}; + \node (b) at (120:1) {$120^\circ$}; + \node (c) at (240:1) {$240^\circ$}; + + \draw (a) to node {1} node [swap] {1'} (b) + (b) to node {2} node [swap] {2'} (c) + (c) to node {3} node [swap] {3'} (a); +\end{tikzpicture} +\end{codeexample} +} + +What is happening here? The nodes are given somehow inside the |to| operation! +When this is done, the node is placed on the middle of the curve or line +created by the |to| operation. The |auto| option then causes the node to be +moved in such a way that it does not lie on the curve, but next to it. In the +example we provide even two nodes on each |to| operation. + +For Hagen that |auto| option is not really necessary since the two ``2'' labels +could also easily be placed ``by hand''. However, in a complicated plot with +numerous edges automatic placement can be a blessing. +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}, +pre/.style={<-,shorten <=1pt,>=stealth',semithick}, +post/.style={->,shorten >=1pt,>=stealth',semithick}} +\begin{codeexample}[] +% Styles as before +\begin{tikzpicture}[bend angle=45] + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + + \node[transition] (leave critical) [right=of critical] {} + edge [pre] (critical) + edge [post,bend right] node[auto,swap] {2} (waiting) + edge [pre, bend left] (semaphore); + \node[transition] (enter critical) [left=of critical] {} + edge [post] (critical) + edge [pre, bend left] (waiting) + edge [post,bend right] (semaphore); +\end{tikzpicture} +\end{codeexample} +} + + +\subsection{Adding the Snaked Line and Multi-Line Text} + +With the node mechanism Hagen can now easily create the two Petri nets. What he +is unsure of is how he can create the snaked line between the nets. + +For this he can use a \emph{decoration}. To draw the snaked line, Hagen only +needs to set the two options |decoration=snake| and |decorate| on the path. +This causes all lines of the path to be replaced by snakes. It is also possible +to use snakes only in certain parts of a path, but Hagen will not need this. +% +\begin{codeexample}[] +\begin{tikzpicture} + \draw [->,decorate,decoration=snake] (0,0) -- (2,0); +\end{tikzpicture} +\end{codeexample} + +Well, that does not look quite right, yet. The problem is that the snake +happens to end exactly at the position where the arrow begins. Fortunately, +there is an option that helps here. Also, the snake should be a bit smaller, +which can be influenced by even more options. +% +\begin{codeexample}[] +\begin{tikzpicture} + \draw [->,decorate, + decoration={snake,amplitude=.4mm,segment length=2mm,post length=1mm}] + (0,0) -- (3,0); +\end{tikzpicture} +\end{codeexample} + +Now Hagen needs to add the text above the snake. This text is a bit challenging +since it is a multi-line text. Hagen has two options for this: First, he can +specify an |align=center| and then use the |\\| command to enforce the line +breaks at the desired positions. +% +\begin{codeexample}[] +\begin{tikzpicture} + \draw [->,decorate, + decoration={snake,amplitude=.4mm,segment length=2mm,post length=1mm}] + (0,0) -- (3,0) + node [above,align=center,midway] + { + replacement of\\ + the \textcolor{red}{capacity}\\ + by \textcolor{red}{two places} + }; +\end{tikzpicture} +\end{codeexample} + +Instead of specifying the line breaks ``by hand'', Hagen can also specify a +width for the text and let \TeX\ perform the line breaking for him: +% +\begin{codeexample}[] +\begin{tikzpicture} + \draw [->,decorate, + decoration={snake,amplitude=.4mm,segment length=2mm,post length=1mm}] + (0,0) -- (3,0) + node [above,text width=3cm,align=center,midway] + { + replacement of the \textcolor{red}{capacity} by + \textcolor{red}{two places} + }; +\end{tikzpicture} +\end{codeexample} + + +\subsection{Using Layers: The Background Rectangles} + +Hagen still needs to add the background rectangles. These are a bit tricky: +Hagen would like to draw the rectangles \emph{after} the Petri nets are +finished. The reason is that only then can he conveniently refer to the +coordinates that make up the corners of the rectangle. If Hagen draws the +rectangle first, then he needs to know the exact size of the Petri net -- which +he does not. + +The solution is to use \emph{layers}. When the background library is loaded, +Hagen can put parts of his picture inside a scope with the +|on background layer| option. Then this part of the picture becomes part of the +layer that is given as an argument to this environment. When the +|{tikzpicture}| environment ends, the layers are put on top of each other, +starting with the background layer. This causes everything drawn on the +background layer to be behind the main text. + +The next tricky question is, how big should the rectangle be? Naturally, Hagen +can compute the size ``by hand'' or using some clever observations concerning +the $x$- and $y$-coordinates of the nodes, but it would be nicer to just have +\tikzname\ compute a rectangle into which all the nodes ``fit''. For this, the +|fit| library can be used. It defines the |fit| options, which, when given to a +node, causes the node to be resized and shifted such that it exactly covers all +the nodes and coordinates given as parameters to the |fit| option. +% +{ +\tikzset{place/.style={circle,draw=blue!50,fill=blue!20,thick, + inner sep=0pt,minimum size=6mm}, +transition/.style={rectangle,draw=black!50,fill=black!20,thick, + inner sep=0pt,minimum size=4mm}, +pre/.style={<-,shorten <=1pt,>=stealth',semithick}, +post/.style={->,shorten >=1pt,>=stealth',semithick}} +\begin{codeexample}[] +% Styles as before +\begin{tikzpicture}[bend angle=45] + \node[place] (waiting) {}; + \node[place] (critical) [below=of waiting] {}; + \node[place] (semaphore) [below=of critical] {}; + + \node[transition] (leave critical) [right=of critical] {} + edge [pre] (critical) + edge [post,bend right] node[auto,swap] {2} (waiting) + edge [pre, bend left] (semaphore); + \node[transition] (enter critical) [left=of critical] {} + edge [post] (critical) + edge [pre, bend left] (waiting) + edge [post,bend right] (semaphore); + + \begin{scope}[on background layer] + \node [fill=black!30,fit=(waiting) (critical) (semaphore) + (leave critical) (enter critical)] {}; + \end{scope} +\end{tikzpicture} +\end{codeexample} +} + + +\subsection{The Complete Code} + +Hagen has now finally put everything together. Only then does he learn that +there is already a library for drawing Petri nets! It turns out that this +library mainly provides the same definitions as Hagen did. For example, it +defines a |place| style in a similar way as Hagen did. Adjusting the code so +that it uses the library shortens Hagen code a bit, as shown in the following. + +First, Hagen needs less style definitions, but he still needs to specify the +colors of places and transitions. +% +\begin{codeexample}[code only] +\begin{tikzpicture} + [node distance=1.3cm,on grid,>=stealth',bend angle=45,auto, + every place/.style= {minimum size=6mm,thick,draw=blue!75,fill=blue!20}, + every transition/.style={thick,draw=black!75,fill=black!20}, + red place/.style= {place,draw=red!75,fill=red!20}, + every label/.style= {red}] +\end{codeexample} + +Now comes the code for the nets: +% +{ +\tikzset{ + every place/.style={minimum size=6mm,thick,draw=blue!75,fill=blue!20}, + every transition/.style={thick,draw=black!75,fill=black!20}, + red place/.style={place,draw=red!75,fill=red!20}, + every label/.style={red}, + every picture/.style={on grid,node distance=1.3cm,>=stealth',bend angle=45,auto}} +\tikzexternaldisable +\begin{codeexample}[pre=\begin{tikzpicture},post=\end{tikzpicture}] + \node [place,tokens=1] (w1) {}; + \node [place] (c1) [below=of w1] {}; + \node [place] (s) [below=of c1,label=above:$s\le 3$] {}; + \node [place] (c2) [below=of s] {}; + \node [place,tokens=1] (w2) [below=of c2] {}; + + \node [transition] (e1) [left=of c1] {} + edge [pre,bend left] (w1) + edge [post,bend right] (s) + edge [post] (c1); + \node [transition] (e2) [left=of c2] {} + edge [pre,bend right] (w2) + edge [post,bend left] (s) + edge [post] (c2); + \node [transition] (l1) [right=of c1] {} + edge [pre] (c1) + edge [pre,bend left] (s) + edge [post,bend right] node[swap] {2} (w1); + \node [transition] (l2) [right=of c2] {} + edge [pre] (c2) + edge [pre,bend right] (s) + edge [post,bend left] node {2} (w2); +\end{codeexample} +} + +{ +\tikzset{ +every place/.style={minimum size=6mm,thick,draw=blue!75,fill=blue!20}, +every transition/.style={thick,draw=black!75,fill=black!20}, +red place/.style= {place,draw=red!75,fill=red!20}, +every label/.style={red}, +every picture/.style={on grid,node distance=1.3cm,>=stealth',bend angle=45,auto}} +\tikzexternaldisable +\begin{codeexample}[pre=\begin{tikzpicture},post=\end{tikzpicture}] + \begin{scope}[xshift=6cm] + \node [place,tokens=1] (w1') {}; + \node [place] (c1') [below=of w1'] {}; + \node [red place] (s1') [below=of c1',xshift=-5mm] + [label=left:$s$] {}; + \node [red place,tokens=3] (s2') [below=of c1',xshift=5mm] + [label=right:$\bar s$] {}; + \node [place] (c2') [below=of s1',xshift=5mm] {}; + \node [place,tokens=1] (w2') [below=of c2'] {}; + + \node [transition] (e1') [left=of c1'] {} + edge [pre,bend left] (w1') + edge [post] (s1') + edge [pre] (s2') + edge [post] (c1'); + \node [transition] (e2') [left=of c2'] {} + edge [pre,bend right] (w2') + edge [post] (s1') + edge [pre] (s2') + edge [post] (c2'); + \node [transition] (l1') [right=of c1'] {} + edge [pre] (c1') + edge [pre] (s1') + edge [post] (s2') + edge [post,bend right] node[swap] {2} (w1'); + \node [transition] (l2') [right=of c2'] {} + edge [pre] (c2') + edge [pre] (s1') + edge [post] (s2') + edge [post,bend left] node {2} (w2'); + \end{scope} +\end{codeexample} +} + +The code for the background and the snake is the following: +% +\begin{codeexample}[code only] + \begin{scope}[on background layer] + \node (r1) [fill=black!10,rounded corners,fit=(w1)(w2)(e1)(e2)(l1)(l2)] {}; + \node (r2) [fill=black!10,rounded corners,fit=(w1')(w2')(e1')(e2')(l1')(l2')] {}; + \end{scope} + + \draw [shorten >=1mm,-to,thick,decorate, + decoration={snake,amplitude=.4mm,segment length=2mm, + pre=moveto,pre length=1mm,post length=2mm}] + (r1) -- (r2) node [above=1mm,midway,text width=3cm,align=center] + {replacement of the \textcolor{red}{capacity} by \textcolor{red}{two places}}; +\end{tikzpicture} +\end{codeexample} |