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+% Copyright 2019 by Renée Ahrens, Olof Frahm, Jens Kluttig, Matthias Schulz, Stephan Schuster
+% Copyright 2019 by Till Tantau
+% Copyright 2019 by Jannis Pohlmann
+%
+% 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{The Algorithm Layer}
+\label{section-gd-algorithm-layer}
+
+\noindent{\emph{by Till Tantau}}
+
+\ifluatex
+\else
+ This section of the manual can only be typeset using Lua\TeX.
+ \expandafter\endinput
+\fi
+
+
+\subsection{Overview}
+
+The present section is addressed at readers interested in implementing new
+graph drawing algorithms for the graph drawing system. Obviously, in order to
+do so, you need to have an algorithm in mind and also some programming skills;
+but fortunately only in the Lua programming language: Even though the graph
+drawing system was originally developed as an extension of \tikzname, is has
+been restructured so that the ``algorithm layer'' where you define algorithms
+is scrupulously separated from \tikzname. In particular, an algorithm declared
+and implemented on this layer can be used in with every ``display layers'', see
+Section~\ref{section-gd-display-layer}, without change. Nevertheless, in the
+following we will use the \tikzname\ display layer and syntax in our examples.
+
+Normally, new graph drawing algorithms can and must be implemented in the Lua
+programming language, which is a small, easy-to-learn (and quite beautiful)
+language integrated into current versions of \TeX. However, as explained in
+Section~\ref{section-algorithms-in-c}, you can also implement algorithms in C
+or C++ (and, possibly, in the future also in other languages), but this comes
+at a great cost concerning portability. In the present section, I assume that
+you are only interested in writing an algorithm using Lua.
+
+In the following, after a small ``hello world'' example of graph drawing and a
+discussion of technical details like how to name files so that \TeX\ will find
+them, we have a look at the main parts of the algorithm layer:
+%
+\begin{itemize}
+ \item Section~\ref{section-gd-namespaces} gives and overview of the
+ available namespaces and also of naming conventions used in the graph
+ drawing system.
+ \item Section~\ref{section-gd-gd-scope} explores what graph drawing scopes
+ ``look like on the algorithm layer''. As the graph of a graph drawing
+ scope is being parsed on the display layer, a lot of information is
+ gathered: The nodes and edges of the graph are identified and the
+ object-oriented model is built, but other information is also
+ collected. For instance, a sequence of \emph{events} is created during
+ the parsing process. As another example, numerous kinds of
+ \emph{collections} may be identified by the parser. The parsed graph
+ together with the event sequence and the collections are all gathered
+ in a single table, called the \emph{scope table} of the current graph
+ drawing scope. Algorithms can access this table to retrieve information
+ that goes beyond the ``pure'' graph model.
+
+ One entry in this table is of particular importance: The
+ \emph{syntactic digraph.} While most graph drawing algorithms are not
+ really interested in the ``details'' of how a graph was specified, for
+ some algorithms it makes a big difference whether you write |a -> b| or
+ |b <- a| in your specification of the graph. These algorithms can
+ access the ``fine details'' of how the input graph was specified
+ through the syntactic digraph; all other algorithms can access their
+ |digraph| or |ugraph| fields and do not have to worry about the
+ difference between |a -> b| and |b <- a|.
+ \item Section~\ref{section-gd-models} explains the object-oriented model of
+ graphs used throughout the graph drawing system. Graph drawing
+ algorithms do not get the ``raw'' specification used by the user to
+ specify a graph (like |{a -> {b,c}}| in the |graph| syntax). Instead,
+ what a graph drawing algorithm sees is ``just'' a graph object that
+ provides methods for accessing the vertices and arcs.
+ \item Section~\ref{section-gd-transformations} explains how the information
+ in the graph drawing scope is processed. One might expect that we
+ simply run the algorithm selected by the user; however, things are more
+ involved in practice. When the layout of a graph needs to be computed,
+ only very few algorithms will actually be able to compute positions for
+ the nodes of \emph{every} graph. For instance, most algorithms
+ implicitly assume that the input graph is connected; algorithms for
+ computing layouts for trees assume that the input is, well, a tree; and
+ so on. For this reason, graph drawing algorithms will not actually need
+ the original input graph as their input, but some \emph{transformed}
+ version of it. Indeed, \emph{all} graph drawing algorithms are treated
+ as graph transformations by the graph drawing engine.
+
+ This section explains how transformations are chosen and which
+ transformations are applied by default.
+ \item Section~\ref{section-gd-interface-to-algorithms} documents the
+ interface-to-algorithm class. This interface encapsulates all that an
+ algorithm ``sees'' of the graph drawing system (apart from the classes
+ in |model| and |lib|).
+ \item Section~\ref{section-gd-examples} provides a number of complete
+ examples that show how graph drawing algorithms can, actually, be
+ implemented.
+ \item Section~\ref{section-gd-libs} documents the different libraries
+ functions that come with the graph drawing engine. For instance, there
+ are library functions for computing the (path) distance of nodes in a
+ graph; a parameter that is needed by some algorithms.
+\end{itemize}
+
+
+\subsection{Getting Started}
+
+In this section, a ``hello world'' example of a graph drawing algorithm is
+given, followed by an overview of the organization of the whole engine.
+
+
+\subsubsection{The Hello World of Graph Drawing}
+
+Let us start our tour of the algorithm layer with a ``hello world'' version of
+graph drawing: An algorithm that simply places all nodes of a graph in a circle
+of a fixed radius. Naturally, this is not a particularly impressive or
+intelligent graph drawing algorithm; but neither is the classical ``hello
+world''$\dots$\ Here is a minimal version of the needed code (this is not the
+typical way of formulating the code, but it is the shortest; we will have a
+look at the more standard and verbose way in a moment):
+%
+\begin{codeexample}[code only, tikz syntax=false]
+pgf.gd.interface.InterfaceToAlgorithms.declare {
+ key = "very simple demo layout",
+ algorithm = {
+ run =
+ function (self)
+ local alpha = (2 * math.pi) / #self.ugraph.vertices
+ for i,vertex in ipairs(self.ugraph.vertices) do
+ vertex.pos.x = math.cos(i * alpha) * 25
+ vertex.pos.y = math.sin(i * alpha) * 25
+ end
+ end
+ }
+}
+\end{codeexample}
+\directlua{
+pgf.gd.interface.InterfaceToAlgorithms.declare {
+ key = "very simple demo layout",
+ algorithm = {
+ run =
+ function (self)
+ local alpha = (2 * math.pi) / \luaescapestring{#}self.ugraph.vertices
+ for i,vertex in ipairs(self.ugraph.vertices) do
+ vertex.pos.x = math.cos(i * alpha) * 25
+ vertex.pos.y = math.sin(i * alpha) * 25
+ end
+ end
+ }
+}
+}
+
+This code \emph {declares} a new algorithm (|very simple demo layout|) and
+includes an implementation of the algorithm (through the |run| field of the
+|algorithm| field). When the |run| method is called, the |self| parameter will
+contain the to-be-drawn graph in its |ugraph| field. It is now the job of the
+code to modify the positions of the vertices in this graph (in the example,
+this is done by assigning values to |vertex.pos.x| and |vertex.pos.y|).
+
+In order to actually \emph{use} the algorithm, the above code first needs to be
+executed somehow. For \tikzname, one can just call |\directlua| on it or put it
+in a file and then use |\directlua| plus |require| (a better alternative) or
+you put it in a file like |simpledemo.lua| and use |\usegdlibrary{simpledemo}|
+(undoubtedly the ``best'' way). For another display layer, like a graphical
+editor, the code could also be executed through the use of |require|.
+
+Executing the code ``just'' declares the algorithm, this is what the |declare|
+function does. Inside some internal tables, the algorithm layer will store the
+fact that a |very simple demo layout| is now available. The algorithm layer
+will also communicate with the display layer through the binding layer to
+advertise this fact to the ``user''. In the case of \tikzname, this means that
+the option key |very simple demo layout| becomes available at this point and we
+can use it like this:
+%
+\begin{codeexample}[]
+\tikz [very simple demo layout]
+ \graph { f -> c -> e -> a -> {b -> {c, d, f}, e -> b}};
+\end{codeexample}
+
+It turns out, that our little algorithm is already more powerful than one might
+expect. Consider the following example:
+%
+\begin{codeexample}[]
+\tikz [very simple demo layout, componentwise]
+ \graph {
+ 1 -> 2 ->[orient=right] 3 -> 1;
+ a -- b --[orient=45] c -- d -- a;
+ };
+\end{codeexample}
+
+Note that, in our algorithm, we ``just'' put all nodes on a circle around the
+origin. Nevertheless, the graph gets decomposed into two connected components,
+the components are rotated so that the edge from node |2| to node |3| goes from
+left to right and the edge from |b| to |c| goes up at an angle of $45^\circ$,
+and the components are placed next to each other so that some spacing is
+achieved.
+
+The ``magic'' that achieves all this behind the scenes is called ``graph
+transformations''. They will heavily pre- and postprocess the input and output
+of graph drawing algorithms to achieve the above results.
+
+Naturally, some algorithms may not wish their inputs and/or outputs to be
+``tampered'' with. An algorithm can easily configure which transformations
+should be applied, by passing appropriate options to |declare|.
+
+
+\subsubsection{Declaring an Algorithm}
+
+Let us now have a look at how one would ``really'' implement the example
+algorithm. First of all, we place our algorithm in a separate file called, say,
+|ExampleLayout.lua|. This way, by putting it in a separate file, all display
+layers can easily install the algorithm at runtime by saying
+|require "ExampleLayout"|.
+
+Next, the |declare| function is needed quite often, so it makes sense to create
+a short local name for it:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+-- This is the file ExampleLayout.lua
+local declare = require "pgf.gd.interface.InterfaceToAlgorithms".declare
+\end{codeexample}
+
+The |declare| function is the work-horse of the algorithm layer. It takes a
+table that contains at least a |key| field, which must be a unique string, and
+some other fields that specify in more detail what kind of key is declared.
+Once declared through a call of |declare|, the ``key'' can be used on the
+display layer.
+
+For declaring an algorithm, the table passed to |declare| must contain a field
+|algorithm|. This field, in turn, must (normally) be set to a table that will
+become the algorithm class. In the above example, our algorithm was so simple
+that we could place the whole definition of the class inside the call of
+|declare|, but normally the class is defined in more detail after the call to
+|declare|:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+local ExampleClass = {} -- A local variable holding the class table
+
+declare {
+ key = "very simple demo layout",
+ algorithm = ExampleClass
+}
+
+function ExampleClass:run ()
+ local alpha = (2 * math.pi) / #self.ugraph.vertices
+ ...
+end
+\end{codeexample}
+
+The effect of the |declare| will be that the table stored in |ExampleClass| is
+setup to form a class in the sense of object-oriented programming. In
+particular, a static |new| function is installed.
+
+Now, whenever the user uses the key |very simple demo layout| on a graph, at
+some point the graph drawing engine will create a new instance of the
+|ExampleClass| using |new| and will then call the |run| method of this class.
+The class can have any number of other methods, but |new| and |run| are the
+only ones directly called by the graph drawing system.
+
+
+\subsubsection{The Run Method}
+
+The |run| method of an algorithm classes lies at the heart of any graph drawing
+algorithm. This method will be called whenever a graph needs to be laid out.
+Upon this call, the |self| object will have some important fields set:
+%
+\begin{itemize}
+ \item |ugraph| This stands for ``undirected graph'' and is the
+ ``undirected'' version of the to-be-laid out graph. In this graph,
+ whenever there is an arc between $u$ and $v$, there is also an arc
+ between $v$ and $u$. It is obtained by considering the syntactic
+ digraph and then ``forgetting'' about the actual direction of the
+ edges.
+
+ When you have set certain |preconditions| in your algorithm class, like
+ |connected=true|, the |ugraph| will satisfy these conditions. In
+ particular, the |ugraph| typically will not be the underlying
+ undirected graph of the complete syntactic digraph, but rather of some
+ part of it. The use of (sub)layouts will also modify the syntactic
+ digraph is fancy ways.
+
+ Refer to this graph whenever your algorithm is ``most comfortable''
+ with an undirected graph, as is the case for instance for most
+ force-base algorithms.
+ \item |digraph| This stands for ``directed graph'' and is the
+ ``semantically directed'' version of the to-be-laid out graph.
+ Basically, when happens is that reverse edges in the syntactic digraph
+ (an edge like |b <- a|) will yield an |Arc| from |a| to |b| in the
+ |digraph| while they yield a |b| to |a| arc and edge in the syntactic
+ digraph. Also, undirected edges like |a -- b| are replaced by directed
+ edges in both directions between the vertices.
+ \item |scope| The graph drawing scope.
+ \item |layout| The layout object for this graph. This is a collection of
+ kind |layout|.
+\end{itemize}
+
+
+\subsubsection{Loading Algorithms on Demand}
+
+In order to use the |very simple demo layout| on the display layer, |declare|
+must have been called for this key. However, we just saw that the |declare|
+function takes the actual class table as parameter and, thus, whenever an
+algorithm is declared, it is also completely loaded and compiled at this point.
+
+This is not always desirable. A user may wish to include a number of libraries
+in order to declare a large number of potentially useful algorithms, but will
+not actually use all of them. Indeed, at least for large, complex algorithms,
+it is preferable that the algorithm's code is loaded only when the algorithm is
+used for the first time.
+
+Such a ``loading of algorithms on demand'' is supported through the option of
+setting the |algorithm| field in a |declare| to a string. This string must now
+be the file name of a Lua file that contains the code of the actual algorithm.
+When the key is actually used for the first time, this file will be loaded. It
+must return a table that will be plugged into the |algorithm| field; so
+subsequent usages of the key will not load the file again.
+
+The net effect of all this is that you can place implementations of algorithms
+in files separate from interface files that just contain the |declare| commands
+for these algorithms. You will typically do this only for rather large
+algorithms.
+
+For our example, the code would look like this:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+-- File ExampleLayout.lua
+local declare = require "pgf.gd.interface.InterfaceToAlgorithms".declare
+declare {
+ key = "very simple demo layout",
+ algorithm = "ExampleLayoutImplementation"
+}
+\end{codeexample}
+
+\begin{codeexample}[code only, tikz syntax=false]
+-- File ExampleLayoutImplementation.lua
+local ExampleClass = {}
+function ExampleClass:run ()
+ local alpha = (2 * math.pi) / #self.ugraph.vertices
+ ...
+end
+return ExampleClass
+\end{codeexample}
+
+
+\subsubsection{Declaring Options}
+
+Let us now make our example algorithm a bit more ``configurable''. For this, we
+use |declare| once more, but instead of the |algorithm| field, we use a |type|
+field. This tells the display layer that the key is not used to select an
+algorithm, but to configure ``something'' about the graph or about nodes or
+edges.
+
+In our example, we may wish to configure the radius of the graph. So, we
+introduce a |radius| key (actually, this key already exists, so we would not
+need to declare it, but let us do so anyway for example purposes):
+%
+\begin{codeexample}[code only, tikz syntax=false]
+declare {
+ key = "radius",
+ type = "length",
+ initial = "25pt"
+}
+\end{codeexample}
+
+This tells the display layer that there is now an option called |radius|, that
+users set it to some ``length'', and that if it is not set at all, then the
+25pt should be used.
+
+To access what the user has specified for this key, an algorithm can access the
+|options| field of a graph, vertex, or arc at the key's name:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+ vertex.pos.x = math.cos(i * alpha) * vertex.options.radius
+ vertex.pos.y = math.sin(i * alpha) * vertex.options.radius
+\end{codeexample}
+
+
+\subsubsection{Adding Inline Documentation}
+
+You should always document the keys you |declare|. For this, the |declare|
+function allows you to add three fields to its argument table:
+%
+\begin{itemize}
+ \item |summary| This should be a string that succinctly summarizes the
+ effect this key has. The idea is that this text will be shown as a
+ ``tooltip'' in a graphical editor or will be printed out by a command
+ line tool when a user requests help about the key. You can profit from
+ using Lua's |[[| and |]]| syntax for specifying multi-line strings.
+
+ Also, when the file containing the key is parsed for this manual, this
+ text will be shown.
+ \item |documentation| When present, this field contains a more extensive
+ documentation of the key. It will also be shown in this manual, but
+ typically not as a tool tip.
+ \item |examples| This should either be a single string or an array of
+ strings. Each string should be an example demonstrating how the key is
+ used in \tikzname. They will all be included in the manual, each
+ surrounded by a |codeexample| environment.
+\end{itemize}
+
+Let us augment our |radius| key with some documentation. The three dashes
+before the |declare| are only needed when the declaration is part of this
+manual and they will trigger an inclusion of the key in the manual.
+%
+\begin{codeexample}[code only, tikz syntax=false]
+---
+declare {
+ key = "radius",
+ type = "length",
+ initial = "25pt",
+ summary = [[
+ Specifies the radius of a circle on which the nodes are placed when
+ the |very simple example layout| is used. Each vertex can have a
+ different radius.
+ ]],
+ examples = [[
+ \tikz \graph [very simple example layout, radius=2cm] {
+ a -- b -- c -- d -- e;
+ };
+ ]]
+}
+\end{codeexample}
+
+As a courtesy, all of the strings given in the documentation can start and end
+with quotation marks, which will be removed. (This helps syntax highlighting
+with editors that do not recognize the |[[| to |]]| syntax.) Also, the
+indentation of the strings is removed (we compute the minimum number of leading
+spaces on any line and remove this many spaces from all lines).
+
+
+\subsubsection{Adding External Documentation}
+\label{section-gd-documentation-in}
+
+As an alternative to inlining documentation, you can also store the
+documentation of keys in a separate file that is loaded only when the
+documentation is actually accessed. Since this happens only rarely (for
+instance, not at all, when \tikzname\ is run, except for this manual), this
+will save time and space. Also, for C code, it is impractical to store
+multi-line documentation strings directly in the C file.
+
+In order to store documentation externally, instead of the |summary|,
+|documentation|, and |examples| keys, you provide the key |documentation_in|.
+The |documentation_in| key must be set to a string that is input using
+|require|.
+
+In detail, when someone tries to access the |summary|, |documentation|, or
+|examples| field of a key and these keys are not (yet) defined, the system
+checks whether the |documentation_in| key is set. If so, we apply |require| to
+the string stored in this field. The file loaded in this way can now setup the
+missing fields of the current key and, typically, also of all other keys
+defined in the same file as the current key. For this purpose, it is advisable
+to use the |pgf.gd.doc| class:
+
+\includeluadocumentationof{pgf.gd.doc}
+
+As a longer example, consider the following declarations:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+---
+declare {
+ key = "very simple demo layout",
+ algorithm = ExampleClass,
+ documentation_in = "documentation_file"
+}
+
+---
+declare {
+ key = "radius",
+ type = "length",
+ initial = "25",
+ documentation_in = "documentation_file"
+}
+\end{codeexample}
+
+The file |documentation_file.lua| would look like this:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+-- File documentation_file.lua
+local key = require 'pgf.gd.doc'.key
+local documentation = require 'pgf.gd.doc'.documentation
+local summary = require 'pgf.gd.doc'.summary
+local example = require 'pgf.gd.doc'.example
+
+key "very simple demo layout"
+documentation "This layout is a very simple layout that, ..."
+
+key "radius"
+summary "Specifies the radius of a circle on which the nodes are placed."
+documentation
+[[
+This key can be used together with |very simple example layout|. An
+important feature ist that...
+]]
+example
+[[
+\tikz \graph [very simple example layout, radius=2cm]
+{ a -- b -- c -- d -- e; };
+]]
+\end{codeexample}
+
+
+\subsection{Namespaces and File Names}
+\label{section-gd-namespaces}
+
+\subsubsection{Namespaces}
+
+All parts of the |graphdrawing| library reside in the Lua ``namespace''
+|pgf.gd|, which is itself a ``sub-namespace'' of |pgf|. For your own
+algorithms, you are free to place them in whatever namespace you like; only for
+the official distribution of \pgfname\ everything has been put into the correct
+namespace.
+
+Let us now have a more detailed look at these namespaces. A namespace is just a
+Lua table, and sub-namespaces are just subtables of namespace tables. Following
+the Java convention, namespaces are in lowercase letters. The following
+namespaces are part of the core of the graph drawing engine:
+%
+\begin{itemize}
+ \item |pgf| This namespace is the main namespace of \pgfname. Other parts
+ of \pgfname\ and \tikzname\ that also employ Lua should put an entry
+ into this table. Since, currently, only the graph drawing engine
+ adheres to this rule, this namespace is declared inside the graph
+ drawing directory, but this will change.
+
+ The |pgf| table is the \emph{only} entry into the global table of Lua
+ generated by the graph drawing engine (or, \pgfname, for that matter).
+ If you intend to extend the graph drawing engine, do not even
+ \emph{think} of polluting the global namespace. You will be fined.
+ \item |pgf.gd| This namespace is the main namespace of the graph drawing
+ engine, including the object-oriented models of graphs and the layout
+ pipeline. Algorithms that are part of the distribution are also inside
+ this namespace, but if you write your own algorithms you do not need
+ place them inside this namespace. (Indeed, you probably should not
+ before they are made part of the official distribution.)
+ \item |pgf.gd.interface| This namespace handles, on the one hand, the
+ communication between the algorithm layer and the binding layer and, on
+ the other hand, the communication between the display layer (\tikzname)
+ and the binding layer.
+ \item |pgf.gd.binding| So-called ``bindings'' between display layers and
+ the graph drawing system reside in this namespace.
+ \item |pgf.gd.lib| Numerous useful classes that ``make an algorithm's your
+ life easier'' are collected in this namespace. Examples are a class for
+ decomposing a graph into connected components or a class for computing
+ the ideal distance between two sibling nodes in a tree, taking all
+ sorts of rotations and separation parameters into account.
+ \item |pgf.gd.model| This namespace contains all Lua classes that are part
+ of the object-oriented model of graphs employed throughout the graph
+ drawing engine. For readers familiar with the model--view--controller
+ pattern: This is the namespace containing the model-part of this
+ pattern.
+ \item |pgf.gd.control| This namespace contains the ``control logic'' of the
+ graph drawing system. It will transform graphs according to rules,
+ disassemble layouts and sublayouts and will call the appropriate
+ algorithms. For readers still familiar with the model--view--controller
+ pattern: This is the namespace containing the control-part of this
+ pattern.
+ \item |pgf.gd.trees| This namespace contains classes that are useful for
+ dealing with graphs that are trees. In particular, it contains a class
+ for computing a spanning tree of an arbitrary connected graph; an
+ operation that is an important preprocessing step for many algorithms.
+
+ In addition to providing ``utility functions for trees'', the namespace
+ \emph{also} includes actual algorithms for computing graph layouts like
+ |pgf.gd.trees.ReingoldTilford1981|. It may seem to be a bit of an
+ ``impurity'' that a namespace mixes utility classes and ``real''
+ algorithms, but experience has shown that it is better to keep things
+ together in this way.
+
+ Concluding the analogy to the model--view--controller pattern, a graph
+ drawing algorithm is, in a loose sense, the ``view'' part of the
+ pattern.
+ \item |pgf.gd.layered| This namespace provides classes and functions for
+ ``layered'' layouts; the Sugiyama layout method being the most
+ well-known one. Again, the namespace contains both algorithms to be
+ used by a user and utility functions.
+ \item |pgf.gd.force| Collects force-based algorithms and, again, also
+ utility functions and classes.
+ \item |pgf.gd.examples| Contains some example algorithms. They are
+ \emph{not} intended to be used directly, rather they should serve as
+ inspirations for readers wishing to implement their own algorithms.
+\end{itemize}
+
+There are further namespaces that also reside in the |pgf.gd| namespace, these
+namespaces are used to organize different graph drawing algorithms into
+categories.
+
+In Lua, similarly to Java, when a class |SomeClass| is part of, say, the
+namespace |pgf.gd.example|, it is customary to put the class's code in a file
+|SomeClass.lua| and then put this class in a directory |example|, that is a
+subdirectory of a directory |gd|, which is in turn a subdirectory of a
+directory |pgf|. When you write \texttt{require "pgf.gd.example.SomeClass"} the
+so-called \emph{loader} will turn this into a request for the file
+\texttt{pgf/gd/example/SomeClass.lua} (for Unix systems).
+
+
+\subsubsection{Defining and Using Namespaces and Classes}
+
+There are a number of rules concerning the structure and naming of namespaces
+as well as the naming of files. Let us start with the rules for naming
+namespaces, classes, and functions. They follow the ``Java convention'':
+%
+\begin{enumerate}
+ \item A namespace is a short lowercase |word|.
+ \item A function in a namespace is in
+ |lowercase_with_underscores_between_words|.
+ \item A class name is in |CamelCaseWithAnUppercaseFirstLetter|.
+ \item A class method name is in |camelCaseWithALowercaseFirstLetter|.
+\end{enumerate}
+
+From Lua's point of view, every namespace and every class is just a table.
+However, since these tables will be loaded using Lua's |require| function, each
+namespace and each class must be placed inside a separate file (unless you
+modify the |package.loaded| table, but, then, you know what you are doing
+anyway). Inside such a file, you should first declare a local variable whose
+name is the name of the namespace or class that you intend to define and then
+assign a (possibly empty) table to this variable:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+-- File pgf.gd.example.SomeClass.lua:
+local SomeClass = {}
+\end{codeexample}
+%
+Next, you should add your class to the encompassing namespace. This is achieved
+as follows:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+require("pgf.gd.example").SomeClass = SomeClass
+\end{codeexample}
+%
+The reason this works is that the |require| will return the table that is the
+namespace |pgf.gd.example|. So, inside this namespace, the |SomeClass| field
+will be filled with the table stored in the local variable of the same name --
+which happens to be the table representing the class.
+
+At the end of the file, you must write
+%
+\begin{codeexample}[code only, tikz syntax=false]
+return SomeClass
+\end{codeexample}
+%
+This ensures that the table that is defined in this file gets stored by Lua in
+the right places. Note that you need and should not use Lua's |module| command.
+The reason is that this command has disappeared in the new version of Lua and
+that it is not really needed.
+
+Users of your class can import and use your class by writing:
+%
+\begin{codeexample}[code only, tikz syntax=false]
+...
+local SomeClass = require "pgf.gd.examples.SomeClass"
+...
+\end{codeexample}
+
+
+\subsection{The Graph Drawing Scope}
+\label{section-gd-gd-scope}
+
+\includeluadocumentationof{pgf.gd.interface.Scope}
+
+
+\subsection{The Model Classes}
+\label{section-gd-models}
+
+All that a graph drawing algorithm will ``see'' of the graph specified by the
+user is a ``graph object''. Such an object is an object-oriented model of the
+user's graph that no longer encodes the specific way in which the user
+specified the graph; it only encodes which nodes and edges are present. For
+instance, the \tikzname\ graph specification
+%
+\begin{codeexample}[code only]
+graph { a -- {b, c} }
+\end{codeexample}
+%
+\noindent and the graph specification
+%
+\begin{codeexample}[code only]
+node (a) { a }
+child { node (b) {b} }
+child { node (c) {c} }
+\end{codeexample}
+%
+will generate exactly the same graph object.
+
+\begin{luanamespace}{pgf.gd.}{model}
+ This namespace contains the classes modeling graphs, nodes, and edges.
+ Also, the |Coordinate| class is found here, since coordinates are also part
+ of the modeling.
+\end{luanamespace}
+
+
+\subsubsection{Directed Graphs (Digraphs)}
+
+Inside the graph drawing engine, the only model of a graph that is available
+treats graphs as
+%
+\begin{enumerate}
+ \item directed (all edges have a designated head and a designated tail) and
+ \item simple (there can be at most one edge between any pair of nodes).
+\end{enumerate}
+%
+These two properties may appear to be somewhat at odds with what users can
+specify as graphs and with what some graph drawing algorithms might expect as
+input. For instance, suppose a user writes
+%
+\begin{codeexample}[code only]
+graph { a -- b --[red] c, b --[green, bend right] c }
+\end{codeexample}
+%
+In this case, it seems that the input graph for a graph drawing algorithm
+should actually be an \emph{undirected} graph in which there are
+\emph{multiple} edges (namely $2$) between |b| and~|c|. Nevertheless, the graph
+drawing engine will turn the user's input a directed simple graph in ways
+described later. You do not need to worry that information gets lost during
+this process: The \emph{syntactic digraph,} which is available to graph drawing
+algorithms on request, stores all the information about which edges are present
+in the original input graph.
+
+The main reasons for only considering directed, simple graphs are speed and
+simplicity: The implementation of these graphs has been optimized so that all
+operations on these graphs have a guaranteed running time that is small in
+practice.
+
+\includeluadocumentationof{pgf.gd.model.Digraph}
+
+
+\subsubsection{Vertices}
+
+\includeluadocumentationof{pgf.gd.model.Vertex}
+
+
+\subsubsection{Arcs}
+\label{section-gd-arc-model}
+
+\includeluadocumentationof{pgf.gd.model.Arc}
+
+
+\subsubsection{Edges}
+
+\includeluadocumentationof{pgf.gd.model.Edge}
+
+
+\subsubsection{Collections}
+
+\includeluadocumentationof{pgf.gd.model.Collection}
+
+
+\subsubsection{Coordinates, Paths, and Transformations}
+
+\includeluadocumentationof{pgf.gd.model.Coordinate}
+\includeluadocumentationof{pgf.gd.model.Path}
+\includeluadocumentationof{pgf.gd.lib.Transform}
+
+
+\subsubsection{Options and Data Storages for Vertices, Arcs, and Digraphs}
+
+Many objects in the graph drawing system have an |options| table attached to
+them. These tables will contain the different kinds options specified by the
+user for the object. For efficiency reasons, many objects may share the same
+options table (since, more often than not, almost all objects have exactly the
+same |options| table). For this reason, you cannot store anything in an options
+table, indeed, you should never attempt to write anything into an options
+table. Instead, you should use a |Storage|.
+
+\includeluadocumentationof{pgf.gd.lib.Storage}
+
+
+\subsubsection{Events}
+
+\includeluadocumentationof{pgf.gd.lib.Event}
+
+
+\subsection{Graph Transformations}
+\label{section-gd-transformations}
+
+\subsubsection{The Layout Pipeline}
+
+\includeluadocumentationof{pgf.gd.control.LayoutPipeline}
+
+
+\subsubsection{Hints For Edge Routing}
+
+\includeluadocumentationof{pgf.gd.routing.Hints}
+
+
+\subsection{The Interface To Algorithms}
+\label{section-gd-interface-to-algorithms}
+
+\includeluadocumentationof{pgf.gd.interface.InterfaceToAlgorithms}
+
+
+\subsection{Examples of Implementations of Graph Drawing Algorithms}
+\label{section-gd-examples}
+
+\includeluadocumentationof{pgf.gd.examples.library}
+\includeluadocumentationof{pgf.gd.examples.SimpleDemo}
+\includeluadocumentationof{pgf.gd.examples.SimpleEdgeDemo}
+\includeluadocumentationof{pgf.gd.examples.SimpleHuffman}
+
+
+\subsection{Support Libraries}
+\label{section-gd-libs}
+
+The present section lists a number of general-purpose libraries that are used
+by different algorithms.
+
+\subsubsection{Basic Functions}
+
+\includeluadocumentationof{pgf}
+
+\includeluadocumentationof{pgf.gd.lib}
+
+
+\subsubsection{Lookup Tables}
+
+\includeluadocumentationof{pgf.gd.lib.LookupTable}
+
+
+\subsubsection{Computing Distances in Graphs}
+
+\emph{Still needs to be ported to digraph classes!}
+
+%\includeluadocumentationof{pgf.gd.lib.PathLengths}
+
+
+\subsubsection{Priority Queues}
+
+\includeluadocumentationof{pgf.gd.lib.PriorityQueue}