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+% 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 concent 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 this Petri nets should also be drawn using a
+graphic program. One of the professors at his institutes 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]
+
+ \tikzstyle{place}=[circle,thick,draw=blue!75,fill=blue!20,minimum size=6mm]
+ \tikzstyle{red place}=[place,draw=red!75,fill=red!20]
+ \tikzstyle{transition}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=4mm]
+
+ \tikzstyle{every label}=[red]
+
+ \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}
+
+ \draw [-to,thick,snake=snake,segment amplitude=.4mm,segment length=2mm,line after snake=1mm]
+ ([xshift=5mm]s -| l1) -- ([xshift=-5mm]s1' -| e1')
+ node [above=1mm,midway,text width=3cm,text centered]
+ {replacement of the \textcolor{red}{capacity} by \textcolor{red}{two places}};
+
+ \begin{pgfonlayer}{background}
+ \filldraw [line width=4mm,join=round,black!10]
+ (w1.north -| l1.east) rectangle (w2.south -| e1.west)
+ (w1'.north -| l1'.east) rectangle (w2'.south -| e1'.west);
+ \end{pgfonlayer}
+\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 three libraries: The arrow tip library for the
+special arrow tip used in the graphic, the snake library with the
+``snaking line'' in the middle, and the background library for the two
+rectangular areas that are behind the two main parts of the picture.
+
+
+\subsubsection{Setting up the Environment in \LaTeX}
+
+When using \LaTeX\ use:
+
+\begin{codeexample}[code only]
+\documentclass{article} % say
+
+\usepackage{tikz}
+\usetikzlibrary{arrows,snakes,backgrounds}
+
+\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,snakes,backgrounds}
+\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\ use:
+\begin{codeexample}[code only]
+%% ConTeXt file
+\usemodule[tikz]
+\usetikzlibrary[arrows,snakes,backgrounds]
+
+\starttext
+ \starttikzpicture
+ \draw (0,0) -- (1,1);
+ \stoptikzpicture
+\startext
+\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 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 same 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 Petir 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 build. 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.'' Then 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-tos. 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}[]
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick]
+\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick]
+\begin{tikzpicture}
+ \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 than \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}[]
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick]
+\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick]
+\begin{tikzpicture}[inner sep=2mm]
+ \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 nodes 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}[]
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick,
+ inner sep=0pt,minimum size=4mm]
+\begin{tikzpicture}
+ \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 the 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.
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick,
+ inner sep=0pt,minimum size=4mm]
+\begin{codeexample}[]
+% ... setup 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:
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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 of| option:
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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}
+}
+
+The |below of| and similar options setup the position of the node 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 the
+distance between the centers of the nodes, not between the borders.
+
+Even though the above code has the same effect the earlier code, Hagen
+can pass it to his colleagues how 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.
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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|.
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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, has 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.
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick,
+ inner sep=0pt,minimum size=4mm]
+\begin{codeexample}[]
+\begin{tikzpicture}
+ \tikzstyle{every label}=[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:
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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:
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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:
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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 option 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:
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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 bend to the right:
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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 is has some nice consequences. For example, every edge can have
+its own arrow tips and its own color and so one and, still, all the
+edges can be given on the same path. This allows Hagen to write the
+following:
+
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[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:
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick,
+ inner sep=0pt,minimum size=4mm]
+\begin{codeexample}[]
+% Styles place and transition as before
+\tikzstyle{pre}=[<-,shorten <=1pt,>=stealth',semithick]
+\tikzstyle{post}=[->,shorten >=1pt,>=stealth',semithick]
+\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] (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.
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick,
+ inner sep=0pt,minimum size=4mm]
+\tikzstyle{pre}=[<-,shorten <=1pt,>=stealth',semithick]
+\tikzstyle{post}=[->,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{snake}. Snakes a called thus since the
+most basic form of a snake looks exactly like a snake. However, and
+repeating pattern can be used as a snake like bumps or a saw or even
+much more complicated stuff.
+
+To draw the snake, Hagen only needs to set the |snake=snake| option on
+the path. This causes all straight 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 [->,snake=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 [->,snake=snake,
+ segment amplitude=.4mm,
+ segment length=2mm,
+ line after snake=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. To typeset such text, Hagen
+needs to specify a width for the text and he needs to specify that the
+text should be centered.
+
+
+\begin{codeexample}[]
+\begin{tikzpicture}
+ \draw [->,snake=snake,
+ segment amplitude=.4mm,
+ segment length=2mm,
+ line after snake=1mm] (0,0) -- (3,0)
+ node [above,text width=3cm,text centered,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 |{pgfonlayer}|
+environment. 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.
+
+
+{
+\tikzstyle{place}=[circle,draw=blue!50,fill=blue!20,thick,
+ inner sep=0pt,minimum size=6mm]
+\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick,
+ inner sep=0pt,minimum size=4mm]
+\tikzstyle{pre}=[<-,shorten <=1pt,>=stealth',semithick]
+\tikzstyle{post}=[->,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{pgfonlayer}{background}
+ \filldraw [fill=black!30,draw=red]
+ (semaphore.south -| enter critical.west)
+ rectangle (waiting.north -| leave critical.east);
+ \end{pgfonlayer}
+\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]
+\tikzstyle{every place}= [minimum size=6mm,thick,draw=blue!75,fill=blue!20]
+\tikzstyle{every transition}=[thick,draw=black!75,fill=black!20]
+
+\tikzstyle{red place}= [place,draw=red!75,fill=red!20]
+
+\tikzstyle{every label}= [red]
+\begin{tikzpicture}[node distance=1.3cm,>=stealth',bend angle=45,auto]
+\end{codeexample}
+
+Now comes the code for the nets:
+
+{
+\tikzstyle{every place}=[minimum size=6mm,thick,draw=blue!75,fill=blue!20]
+\tikzstyle{every transition}=[thick,draw=black!75,fill=black!20]
+
+\tikzstyle{red place}= [place,draw=red!75,fill=red!20]
+
+\tikzstyle{every label}=[red]
+
+\tikzstyle{every picture}=[node distance=1.3cm,>=stealth',bend angle=45,auto]
+\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}
+}
+
+{
+\tikzstyle{every place}= [minimum size=6mm,thick,draw=blue!75,fill=blue!20]
+\tikzstyle{every transition}=[thick,draw=black!75,fill=black!20]
+
+\tikzstyle{red place}= [place,draw=red!75,fill=red!20]
+
+\tikzstyle{every label}=[red]
+
+\tikzstyle{every picture}=[node distance=1.3cm,>=stealth',bend angle=45,auto]
+\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]
+ \draw [-to,thick,snake=snake,segment amplitude=.4mm,segment length=2mm,line after snake=1mm]
+ ([xshift=5mm]s -| l1) -- ([xshift=-5mm]s1' -| e1')
+ node [above=1mm,midway,text width=3cm,text centered]
+ {replacement of the \textcolor{red}{capacity} by \textcolor{red}{two places}};
+
+ \begin{pgfonlayer}{background}
+ \filldraw [line width=4mm,join=round,black!10]
+ (w1.north -| l1.east) rectangle (w2.south -| e1.west)
+ (w1'.north -| l1'.east) rectangle (w2'.south -| e1'.west);
+ \end{pgfonlayer}
+\end{tikzpicture}
+\end{codeexample}