% Copyright 2019 by Till Tantau and Mark Wibrow
%
% 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{Decorations}
\label{section-base-decorations}

\begin{pgfmodule}{decorations}
    The commands for creating decorations are defined in this module, so you
    need to load this module to use decorations. This module is automatically
    loaded by the different decoration libraries.
\end{pgfmodule}


\subsection{Overview}

Decorations are a general way of creating graphics by ``moving along'' a path
and, while doing so, either drawing something or constructing a new path. This
could be as simple as extending a path with a ``zigzagged'' line\ldots
%
\begin{codeexample}[preamble={\usetikzlibrary{decorations,decorations.pathmorphing}}]
\tikz \draw decorate[decoration=zigzag] {(0,0) -- (3,0)};
\end{codeexample}
%
\ldots but could also be as complex as typesetting text along a path:
%
{\catcode`\|12
\begin{codeexample}[preamble={\usetikzlibrary{decorations,decorations.text}}]
\tikz \path decorate [decoration={text along path,
     text={Some text along a path}}]
   { (0,2) .. controls (2,2) and (1,0) .. (3,0) };
\end{codeexample}
}

The workflow for using decorations is the following:
%
\begin{enumerate}
    \item You define a decoration using the |\pgfdeclaredecoration| command.
        Different useful decorations are already declared in libraries like
        |decorations.shapes|.
    \item You use normal path construction commands like |\pgfpathlineto| to
        construct a path. Let us call this path the \emph{to-be-decorated}
        path.
    \item You place the path construction commands inside the environment
        |{pgfdecoration}|. This environment takes the name of a previously
        declared decoration as a parameter. It will then start ``walking
        along'' the to-be-decorated path. As it does this, a special finite
        automaton called a \emph{decoration automaton} produces new path
        commands as its output (or even other outputs). These outputs replace
        the to-be-decorated path; indeed, after the to-be-decorated path has
        been fully walked along it is thrown away, only the output of the
        automaton persists.
\end{enumerate}

In the present section the process of how decoration automata work is explained
first. Then the command(s) for declaring decoration automata and for using them
are covered.


\subsection{Decoration Automata}

Decoration automata (and the closely related meta-decoration automata) are a
general concept for creating graphics ``along paths''. For straight lines, this
idea was first proposed by Till Tantau in an earlier version of \pgfname, the
idea to extend this to arbitrary path was proposed and implemented by Mark
Wibrow. Further versatility is provided by ``meta-decorations''. These are
automata that decorate a path with decorations.

In the present subsection the different ideas underlying decoration automata
are presented.


\subsubsection{The Different Paths}

In order to prevent confusion with different types of paths, such as those that
are extended, those that are decorated and those that are created, the
following conventions will be used:
%
\begin{itemize}
    \item The \emph{preexisting} path refers to the current path in existence
        before a decoration environment. (Possibly this path has been created
        by another decoration used earlier, but we will still call this path
        the preexisting path also in this case.)
    \item The \emph{input} path refers to the to-be-decorated path that the
        decoration automaton moves along. The input path may consist of many
        line and curve input segments (for example, a circle or an ellipse
        consists of four curves). It is specified inside the decoration
        environment.
    \item The \emph{output} path refers to the path that the decoration
        creates. Depending on the decoration, this path may or may not be empty
        (a decoration can also choose to use side-effects instead of producing
        an output path). The input path is always consumed by the decoration
        automaton, that is, it is no longer available in any way after the
        decoration automaton has finished.
\end{itemize}

The effect of a decoration environment is the following: The input path, which
is specified inside the environment, is constructed and stored. This process
does not alter the preexisting path in any way. Then the decoration automaton
is started (as described later) and it produces an output path (possibly
empty). Whenever part of the output path is produced, it is concatenated with
the preexisting path. After the environment, the current path will equal the
original preexisting path followed by the output path.

It is permissible that a decoration issues a |\pgfusepath| command. As usual,
this causes the current path to be filled or stroked or some other action to be
taken and the current path is set to the empty path. As described above, when
the decoration automaton starts, the current path is the preexisting path and
as the automaton progresses, the current path is constantly being extended by
the output path. This means that first time a |\pgfusepath| command is used on
a decoration, the preexisting path is part of the path this command operates
on; in subsequent calls only the part of the output path constructed since the
last |\pgfusepath| command will be used.

You can use this mechanism to stroke or fill different parts of the output path
in different colors, line widths, fills and shades; all within the same
decoration. Alternatively, a decoration can choose to produce no output path at
all: the |text| decoration simply typesets text along a path.


\subsubsection{Segments and States}

The most common use of a decoration is to ``repeat something along a path''
(for example, the |zigzag| decoration repeats
%
\tikz\draw decorate[decoration=zigzag] {(0,0)--(\pgfdecorationsegmentlength,0)};
%
along a path). However, it not necessarily the case that only one thing is
repeated: a decoration can consist of different parts, or \emph{segments},
repeated in a particular order.

When you declare a decoration, you provide a description of how their different
segments will be rendered. The description of each segment should be given in a
way as if the ``$x$-axis'' of the segment is the tangent to the path at a
particular point, and that point is the origin of the segment. Thus, for
example, the segment of the |zigzag| decoration might be defined using the
following code:
%
\begin{codeexample}[code only]
\pgfpathlineto{\pgfpoint{5pt}{5pt}}
\pgfpathlineto{\pgfpoint{15pt}{-5pt}}
\pgfpathlineto{\pgfpoint{20pt}{0pt}}
\end{codeexample}

\pgfname\ will ensure that an appropriate coordinate transformation is in place
when the segment is rendered such that the segment actually points in the right
direction. Also, subsequent segments will be transformed such that they are
``further along the path'' toward the end of the path. All transformations are
set up automatically.

Note that we did not use a |\pgfpathmoveto{\pgfpointorigin}| at the beginning
of the segment code. Doing so would subdivide the path into numerous subpaths.
Rather, we assume that the previous segment caused the current point to be at
the origin.

The width of a segment can (and must) be specified explicitly. \pgfname\ will
use this width to find out the start point of the next segment and the correct
rotation. The width the you provide need not be the ``real'' width of the
segment, which allows decoration segments to overlap or to be spaced far apart.

The |zigzag| decoration only has one segment that is repeated again and again.
However, we might also like to have \emph{different} segments and use rules to
describe which segment should be used where. For example, we might have special
segments at the start and at the end.

Decorations use a mechanism known in theoretical in computer science as
\emph{finite state automata} to describe which segment is used at a particular
point. The idea is the following: For the first segment we start in a special
\emph{state} called the \emph{initial state}. In this state, and also in all
other states later, \pgfname\ first computes how much space is left on the
input path. That is, \pgfname\ keeps track of the distance to the end of the
input path. Attached to each state there is a set of rules of the following
form: ``If the remaining distance on the input path is less than $x$, switch to
state~$q$.'' \pgfname\ checks for each of these rules whether it applies and,
if so, immediately switches to state~$q$.

Only if none of the rules tell us to switch to another state, \pgfname\ will
execute the state's code. This code will (typically) add a segment to the
output path. In addition to the rules there is also a width parameter attached
to each state. \pgfname\ then translates the coordinate system by this width
and reduces the remaining distance on the input path. Then, \pgfname\ either
stays in the current state or switches to another state, depending on yet
another property attached of the state.

The whole process stops when a special state called |final| is reached. The
segment of this state is immediately added to the output path (it is often
empty, though) and the process ends.


\subsection{Declaring Decorations}

The following command is used to declare a decoration. Essentially, this
command describes the decoration automaton.

\begin{command}{\pgfdeclaredecoration\marg{name}\marg{initial state}\marg{states}}
    This command declares a new decoration called \meta{name}. The
    \meta{states} argument contains a description of the decoration automaton's
    states and the transitions between them. The \meta{initial state} is the
    state in which the automaton starts.

    When the automaton is later applied to an input path, it keeps track of a
    certain position on the input path. This current point will ``travel along
    the path'', each time being moved along by a certain distance. This will
    also work if the path is not a straight line. That is, it is permissible
    that the path curves are veers at a sharp angle.  It is also permissible
    that while traveling along the input path, the current input segment ends
    and a new input segment starts. In this case, the remaining distance on the
    first input segment is subtracted from the \meta{dimension} and then we
    travel along the second input segment for the remaining distance. This
    input segment may also end early, in which case we travel along the next
    input segment, and so on. Note that it cannot happen that we travel past
    the end of the input path since this would have caused an immediate switch
    to the |final| state.

    Note that the computation of the path lengths has only a low accuracy
    because of \TeX's small math capabilities. Do not expect high accuracy
    alignments when using decorations (unless the input path consists only of
    horizontal and vertical lines).

    The \meta{states} argument should consist of |\state| commands, one for
    each state of the decoration automaton. The |\state| command is defined
    only when the \meta{states} argument is executed.

    \begin{command}{\state\marg{name}\oarg{options}\marg{code}}
        This command declares a new state inside the current decoration
        automaton. The state is named \meta{name}.

        When the decoration automaton is in state \meta{name}, the following
        things happen:
        %
        \begin{enumerate}
            \item The \meta{options} are parsed. This may lead to a state
                switch, see below. When this happens, the following steps are
                not executed. The \meta{options} are executed one after the
                other in the given order. If an option causes a state switch,
                the switch is immediate, even if later options might cause a
                different state switch.
            \item The \meta{code} is executed in a \TeX-group with the current
                transformation matrix set up in such a way that the origin is
                on the input path at the current point (the point at the
                distance traveled up to now) and the coordinate system is
                rotated in such a way that the positive $x$-axis points in the
                direction of the tangent to the input path at the current
                point, while the positive $y$-axis points to the left of this
                tangent.

                As described earlier, the \meta{code} can have two different
                effects: If it just contains path construction commands, the
                decoration will produce an output path, that is, it extends the
                preexisting path. Here is an example:
                %
\begin{codeexample}[preamble={\usetikzlibrary{decorations}}]
\pgfdeclaredecoration{example}{initial}
{
  \state{initial}[width=10pt]
  {
    \pgfpathlineto{\pgfpoint{0pt}{5pt}}
    \pgfpathlineto{\pgfpoint{5pt}{5pt}}
    \pgfpathlineto{\pgfpoint{5pt}{-5pt}}
    \pgfpathlineto{\pgfpoint{10pt}{-5pt}}
    \pgfpathlineto{\pgfpoint{10pt}{0pt}}
  }
  \state{final}
  {
    \pgfpathlineto{\pgfpointdecoratedpathlast}
  }
}
\tikz[decoration=example]
{
  \draw [decorate]     (0,0) -- (3,0);
  \draw [red,decorate] (0,0) to [out=45,in=135] (3,0);
}
\end{codeexample}

                Alternatively, the \meta{code} can also contain the
                |\pgfusepath| command. This will use the path in the usual
                manner, where ``the path'' is the preexisting path plus a part
                of the output path for the first invocation and the different
                parts of the rest of the output path for the following
                invocation. Here is an example:
                %
\begin{codeexample}[pre={\pgfmathsetseed{1}},preamble={\usetikzlibrary{decorations,shapes.geometric}}]
\pgfdeclaredecoration{stars}{initial}{
  \state{initial}[width=15pt]
  {
    \pgfmathparse{round(rnd*100)}
    \pgfsetfillcolor{yellow!\pgfmathresult!orange}
    \pgfsetstrokecolor{yellow!\pgfmathresult!red}
    \pgfnode{star}{center}{}{}{\pgfusepath{stroke,fill}}
  }
  \state{final}
  {
    \pgfpathmoveto{\pgfpointdecoratedpathlast}
  }
}
\tikz\path[decorate, decoration=stars, star point ratio=2, star points=5,
           inner sep=0, minimum size=rnd*10pt+2pt]
  (0,0) .. controls (0,2)  and (3,2)  .. (3,0)
        .. controls (3,-3) and (0,0)  .. (0,-3)
        .. controls (0,-5) and (3,-5) .. (3,-3);
\end{codeexample}
                %
            \item After the \meta{code} has been executed (possibly more than
                once, if the |repeat state| option is used), the state switches
                to whatever state has been specified inside the \meta{options}
                using the |next state| option. If no |next state| has been
                specified, the state stays the same.
        \end{enumerate}

        The \meta{options} are executed with the key path set to
        |/pgf/decoration automaton|. The following keys are defined:
        %
        \begin{key}{/pgf/decoration automaton/switch if less than=\meta{dimension}\texttt{ to }\meta{new state}}
            When this key is encountered, \pgfname\ checks whether the
            remaining distance to the end of the input path is less than
            \meta{dimension}. If so, an immediate state switch to \meta{new
            state} occurs.
        \end{key}
        %
        \begin{key}{/pgf/decoration automaton/switch if input segment less than=\\\meta{dimension}\texttt{ to }\meta{new state}}
            When this key is encountered, \pgfname\ checks whether the
            remaining distance to the end of the current input segment of the
            input path is less than \meta{dimension}. If so, an immediate state
            switch to \meta{new state} occurs.
        \end{key}
        %
        \begin{key}{/pgf/decoration automaton/width=\meta{dimension}}
            First, this option causes an immediate switch to the state |final|
            if the remaining distance on the input path is less than
            \meta{dimension}. The effect is the same as if you had said 
            |switch if less than=|\meta{dimension}| to final| just before the
            |width| option.

            If no switch occurs, this option tells \pgfname\ the width of the
            segment. The current point will travel along the input path (as
            described earlier) by this distance.
        \end{key}
        %
        \begin{key}{/pgf/decoration automaton/repeat state=\meta{repetitions} (initially 0)}
            Tells \pgfname\ how long the automaton stays ``normally'' in the
            current state. This count is reset to \meta{repetitions} each time
            one of the |switch if| keys causes a state switch. If no state
            switches occur, the \meta{code} is executed and the repetition
            counter is decreased. Then, there is once more a chance of a state
            change caused by any of the \meta{options}. If no repetition
            occurs, the \meta{code} is executed once more and the counter is
            decreased once more. When the counter reaches zero, the \meta{code}
            is executed once more, but, then, a different state is entered, as
            specified by the |next state| option.

            Note, that the maximum number of times the state will be executed
            is $\meta{repetitions}+1$.
        \end{key}
        %
        \begin{key}{/pgf/decoration automaton/next state=\meta{new state}}
            After the \meta{code} for state has been executed for the last
            time, a state switch to \meta{new state} is performed. If this
            option is not given, the next state is the same as the current
            state.
        \end{key}

        \begin{key}{/pgf/decoration automaton/if input segment is closepath=\meta{options}}
            This key checks whether the current input segment is a closepath
            operation. If so, the \meta{options} get executed; otherwise
            nothing happens. You can use this option to handle a closepath in
            some special way, for instance, switching to a new state in which
            |\pgfpathclose| is executed.
        \end{key}

        \begin{key}{/pgf/decoration automaton/auto end on length=\meta{dimension}}
            This key is just included for convenience, it does nothing that
            cannot be achieved using the previous options. The effect is the
            following: If the remaining input path's length is at most
            \meta{dimension}, the decorated path is ended with a straight line
            to the end of the input path and, possibly, it is closed, namely if
            the input path ended with a closepath operation. Otherwise, it is
            checked whether the current input segment is a closepath segment
            and whether the remaining distance on the current input segment is
            at most \meta{distance}. If so, then a closepath operation is used
            to close the decorated path and the automaton continues with the
            next subpath, remaining in the current state.

            In all other cases, nothing happens.
        \end{key}

        \begin{key}{/pgf/decoration automaton/auto corner on length=\meta{dimension}}
            This key has the following effect: Firstly, in case the \TeX-if
            |\ifpgfdecoratepathhascorners| is false, nothing happens.
            Otherwise, it is tested whether the remaining distance on the
            current input segment is at most \meta{dimension}. If so, a
            |lineto| operation is used to reach the end of this input segment
            and the automaton continues with the next input segment, but
            remains in the current state.

            The main idea behind this option is to avoid having decoration
            segments ``overshoot'' past a corner.
        \end{key}

        You may sometimes wish to do computations outside the transformational
        \TeX-group of the current segment, so that these results of these
        computations are available in the next state. For this, the following
        two options are useful:

        \begin{key}{/pgf/decoration automaton/persistent precomputation=\meta{precode}}
            If the \meta{code} of the state is executed, the \meta{precode} is
            executed first and it is executed outside the \TeX-group of the
            \meta{code}. Note that when the \meta{precode} is executed, the
            transformation matrix is not set up.
        \end{key}

        \begin{key}{/pgf/decoration automaton/persistent postcomputation=\meta{postcode}}
            Works like the |persistent precomputation| option, only the
            \meta{postcode} is executed after (and also outside) the \TeX-group
            of the main \meta{code}.
        \end{key}

        There are a number of macros and dimensions which may be useful inside
        a decoration automaton. The following macros are available:

        \begin{command}{\pgfdecoratedpathlength}
            The length of the input path. If the input path consists of several
            input segments, this number is the sum of the lengths of the input
            segments.
        \end{command}

        \begin{command}{\pgfdecoratedinputsegmentlength}
            The length of the current input segment of the input path.
            ``Current input segment''  refers to the input segment on which the
            current point lies.
        \end{command}

        \begin{command}{\pgfpointdecoratedpathlast}
            The final point of the input path.
        \end{command}

        \begin{command}{\pgfpointdecoratedinputsegmentlast}
            The final point of the current input segment of the input path.
        \end{command}

        \begin{command}{\pgfdecoratedangle}
            The angle of the tangent to the decorated path at the \emph{origin}
            of the current segment. The transformation matrix applied at the
            beginning of a state includes a rotation equivalent to this angle.
        \end{command}

        The following \TeX\ dimension registers are also available inside the
        automaton:

        \begin{command}{\pgfdecoratedremainingdistance}
            The remaining distance on the input path.
        \end{command}

        \begin{command}{\pgfdecoratedcompleteddistance}
            The completed distance on the input path.
        \end{command}

        \begin{command}{\pgfdecoratedinputsegmentremainingdistance}
            The remaining distance on the current input segment of the input path.
        \end{command}

        \begin{command}{\pgfdecoratedinputsegmentcompleteddistance}
            The completed distance on the current input segment of the input path.
        \end{command}

        Further keys and macros are defined and used by the decoration
        libraries, see Section~\ref{section-library-decorations}.

        The following example shows how these options can be used:
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations}}]
\pgfdeclaredecoration{complicated example decoration}{initial}
{
  \state{initial}[width=5pt,next state=up]
  { \pgfpathlineto{\pgfpoint{5pt}{0pt}} }

  \state{up}[width=5pt,next state=down]
  {
    \ifdim\pgfdecoratedremainingdistance>\pgfdecoratedcompleteddistance
      % Growing
      \pgfpathlineto{\pgfpoint{0pt}{\pgfdecoratedcompleteddistance}}
      \pgfpathlineto{\pgfpoint{5pt}{\pgfdecoratedcompleteddistance}}
      \pgfpathlineto{\pgfpoint{5pt}{0pt}}
    \else
      % Shrinking
      \pgfpathlineto{\pgfpoint{0pt}{\pgfdecoratedremainingdistance}}
      \pgfpathlineto{\pgfpoint{5pt}{\pgfdecoratedremainingdistance}}
      \pgfpathlineto{\pgfpoint{5pt}{0pt}}
    \fi%
  }
  \state{down}[width=5pt,next state=up]
  {
    \ifdim\pgfdecoratedremainingdistance>\pgfdecoratedcompleteddistance
      % Growing
      \pgfpathlineto{\pgfpoint{0pt}{-\pgfdecoratedcompleteddistance}}
      \pgfpathlineto{\pgfpoint{5pt}{-\pgfdecoratedcompleteddistance}}
      \pgfpathlineto{\pgfpoint{5pt}{0pt}}
    \else
      % Shrinking
      \pgfpathlineto{\pgfpoint{0pt}{-\pgfdecoratedremainingdistance}}
      \pgfpathlineto{\pgfpoint{5pt}{-\pgfdecoratedremainingdistance}}
      \pgfpathlineto{\pgfpoint{5pt}{0pt}}
    \fi%
  }
  \state{final}
  {
    \pgfpathlineto{\pgfpointdecoratedpathlast}
  }
}
\begin{tikzpicture}[decoration=complicated example decoration]
  \draw decorate{ (0,0) -- (3,0)};
  \fill [red!50,rounded corners=2pt]
    decorate {(.5,-2) -- ++(2.5,-2.5)} -- (3,-5) -| (0,-2) -- cycle;
\end{tikzpicture}
\end{codeexample}
    \end{command}
\end{command}


\subsubsection{Predefined Decorations}

The three decorations |moveto|, |lineto|, and |curveto| are predefined and
``always available''. They are mostly useful in conjunction with
meta-decorations. They are documented in
Section~\ref{section-library-decorations} alongside the other decorations.


\subsection{Using Decorations}

Once a decoration has been declared, it can be used.

\begin{environment}{{pgfdecoration}\marg{decoration list}}
    The \meta{environment contents} should contain commands for creating an
    path. This path is the basis for the \emph{input paths} for the decorations
    in the \meta{decoration list}. In detail, the following happens:
    %
    \begin{enumerate}
        \item The preexisting unused path is saved.
        \item The path commands specified in \meta{environment contents} are
            executed and this resulting path is saved. The path is then divided
            into different \emph{input paths} as follows: The format for each
            item in \marg{decoration list} is
            %
            \begin{quote}
                \marg{decoration}\marg{length}\opt{\marg{before code}\marg{after code}}
            \end{quote}
            %
            The \meta{before code} and the \meta{after code} are optional. The
            input path is divided into input paths as follows: The first input
            path consists of the first lines of the path specified in the
            \meta{environment contents} until the \meta{length}  of the first
            element of the \meta{decoration list} is reached. If this length is
            reached in the middle of a line, the line is broken up at this
            exact position. Then the second input path has the \meta{length} of
            the second element in the \meta{decoration list} and consists of
            the lines making up the following \meta{length} part of the path in
            the \meta{environment contents}, and so on.

            If the lengths in the \meta{decoration list} do not add up to the
            total length of the path in the \meta{environment contents}, either
            some  decorations are dropped (if their lengths add up to more than
            the length of the \meta{environment contents}) or the input path is
            not fully used (if their lengths  add up to less).
        \item The preexisting path is reinstalled.
        \item The decoration automata move along the input paths, thus creating
            (and  possibly using) the output paths. These output paths extend
            the current path (unless they are used).
    \end{enumerate}

    Some important points should be noted regarding the use of this
    environment:
    %
    \begin{itemize}
        \item If \meta{environment contents} does not begin with
            |\pgfpathmoveto|, the last known point on the preexisting path is
            assumed as the starting point.
        \item All except the last of any sequence of consecutive move-to
            commands in \meta{environment contents} are discarded.
        \item Any move-to commands at the end of \meta{environment contents}
            are ignored.
        \item Any close-path commands on the input path are interpreted as
            straight lines. Internally, something a little more complicated is
            going on, however, a closed path on the input path has no effect on
            the output path, other than causing the automaton to travel in a
            straight line towards the location of the last move-to command on
            the input path.
        \item Although tangent computations for the input path work with the
            last point on the preexisting path, no automatic move-to operations
            are issued for the output path. If an output path starts with a
            line-to or curve-to when the existing path is empty, an appropriate
            move-to command should be inserted before the decoration starts.
        \item If a decoration uses its own path, the first time this happens
            the preexisting path is part of the path that is used at this
            point.
    \end{itemize}

    Before the automata start to ``work on'' their respective inputs paths,
    \meta{before code} is executed. After the decoration automaton has
    finished, \meta{after code} is executed.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations,decorations.pathmorphing}}]
\begin{tikzpicture}[decoration={segment length=5pt}]
  \draw [help lines] grid (3,2);
  \begin{pgfdecoration}{{curveto}{1cm},{zigzag}{2cm},{curveto}{1cm}}
    \pgfpathmoveto{\pgfpointorigin}
    \pgfpathcurveto
      {\pgfpoint{0cm}{2cm}}{\pgfpoint{3cm}{2cm}}{\pgfpoint{3cm}{0cm}}
  \end{pgfdecoration}
\pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}

    When the lengths are evaluated, the dimension
    |\pgfdecoratedremainingdistance| holds the remaining distance on the entire
    decorated path, and |\pgfdecoratedpathlength| holds the total length of the
    path. Thus, it is possible to specify lengths like
    |\pgfdecoratedpathlength/3|.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations,decorations.pathmorphing}}]
\begin{tikzpicture}[decoration={segment length=5pt}]
  \draw [help lines] grid (3,2);
  \begin{pgfdecoration}{
      {curveto}{\pgfdecoratedpathlength/3},
      {zigzag}{\pgfdecoratedpathlength/3},
      {curveto}{\pgfdecoratedremainingdistance}
    }
    \pgfpathmoveto{\pgfpointorigin}
    \pgfpathcurveto
      {\pgfpoint{0cm}{2cm}}{\pgfpoint{3cm}{2cm}}{\pgfpoint{3cm}{0cm}}
  \end{pgfdecoration}
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}

    When \meta{before code} is executed, the following macro is useful:
    %
    \begin{command}{\pgfpointdecoratedpathfirst}
        Returns the point corresponding to the start of the current input path.
    \end{command}
    %
    When \meta{after code} is executed, the following macro can be used:
    %
    \begin{command}{\pgfpointdecoratedpathlast}
        Returns the point corresponding to the end of the current input path.
    \end{command}
    %
    This means that if decorations do not use their own path, it is possible to
    do something with them and continue from the correct place.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations,decorations.pathmorphing}}]
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \begin{pgfdecoration}{
      {curveto}{\pgfdecoratedpathlength/3}
      {}
      {
        \pgfusepath{stroke}
      },
      {zigzag}{\pgfdecoratedpathlength/3}
      {
        \pgfpathmoveto{\pgfpointdecoratedpathfirst}
        \pgfdecorationsegmentlength=5pt
      }
      {
        \pgfsetstrokecolor{red}
        \pgfusepath{stroke}
        \pgfpathmoveto{\pgfpointdecoratedpathlast}
        \pgfsetstrokecolor{black}
      },
      {curveto}{\pgfdecoratedremainingdistance}
    }
    \pgfpathmoveto{\pgfpointorigin}
    \pgfpathcurveto
      {\pgfpoint{0cm}{2cm}}{\pgfpoint{3cm}{2cm}}{\pgfpoint{3cm}{0cm}}
  \end{pgfdecoration}
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}

    After the |{decoration}| environment has finished, the following macros are
    available:

    \begin{command}{\pgfdecorateexistingpath}
        The preexisting path before the environment was entered.
    \end{command}

    \begin{command}{\pgfdecoratedpath}
        The (total) input path (that is, the path created by the environment
        contents).
    \end{command}

    \begin{command}{\pgfdecorationpath}
        The output path. If the path is used, this macro contains only the last
        unused part of the output path.
    \end{command}

    \begin{command}{\pgfpointdecoratedpathlast}
        The final point of the input path.
    \end{command}

    \begin{command}{\pgfpointdecorationpathlast}
        The final point of the output path.
    \end{command}

    The following style is executed each time a decoration is used. You may use
    it to set up default options for decorations.
    %
    \begin{stylekey}{/pgf/every decoration (initially \normalfont empty)}
        This style is executed for every decoration.
    \end{stylekey}
\end{environment}

\begin{plainenvironment}{{pgfdecoration}\marg{name}}
    The plain-\TeX{} version of the |{pgfdecorate}| environment.
    \todosp{`pgfdecorate' right or `pgfdecoration'? really no idea}
\end{plainenvironment}

\begin{contextenvironment}{{pgfdecoration}\marg{name}}
    The Con\TeX t version of the |{pgfdecoration}| environment.
\end{contextenvironment}

For convenience, the following macros provide a ``shorthand'' for decorations
(internally, they all use the |{pgfdecoration}| environment).

\begin{command}{\pgfdecoratepath\marg{name}\marg{path commands}}
    Decorate the path described by \meta{path commands} with the decoration
    \meta{name}. This is equivalent to
    %
\begin{codeexample}[code only]
\pgfdecoration{{name}{\pgfdecoratedpathlength}
               {\pgfdecoratebeforecode}{\pgfdecorateaftercode}}
  // the path commands.
\endpgfdecoration
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfdecoratecurrentpath\marg{name}}
    Decorate the preexisting path with the decoration \meta{name}.
\end{command}

Both the above commands use the current definitions of the following macros:

\begin{command}{\pgfdecoratebeforecode}
    Code executed as \meta{before code}, see the description of
    |\pgfdecoration|.
\end{command}

\begin{command}{\pgfdecorateaftercode}
    Code executed as \meta{after code}, see the description of
    |\pgfdecoration|.
\end{command}

It may sometimes be useful to add an additional transformation for each segment
of a decoration. The following command allows you to define such a ``last
minute transformation''.

\begin{command}{\pgfsetdecorationsegmenttransformation\marg{code}}
    The \meta{code} will be executed at the very beginning of each segment.
    Note when applying multiple decorations, this will be reset between
    decorations, so it needs to be specified for each segment.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations,decorations.pathmorphing}}]
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \begin{pgfdecoration}{
      {curveto}{\pgfdecoratedpathlength/3},
      {zigzag}{\pgfdecoratedpathlength/3}
      {
        \pgfdecorationsegmentlength=5pt
        \pgfsetdecorationsegmenttransformation{\pgftransformyshift{.5cm}}
      },
      {curveto}{\pgfdecoratedremainingdistance}
    }
    \pgfpathmoveto{\pgfpointorigin}
    \pgfpathcurveto
      {\pgfpoint{0cm}{2cm}}{\pgfpoint{3cm}{2cm}}{\pgfpoint{3cm}{0cm}}
  \end{pgfdecoration}
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}


\subsection{Meta-Decorations}
\label{section-base-meta-decorations}

A meta-decoration provides an alternative way to decorate a path with multiple
decorations. It is, in essence, an automaton that decorates an input path with
decoration automatons. In general, however, the end effect is still that a path
is decorated with other paths, and the input path should be thought of as being
divided into sub-input-paths, each with their own decoration. Like ordinary
decorations, a meta-decoration must be declared before it can be used.


\subsubsection{Declaring Meta-Decorations}

\begin{command}{\pgfdeclaremetadecorate\marg{name}\marg{initial state}\marg{states}}
    This command declares a new meta-decoration called \meta{name}. The
    \meta{states} argument contains a description of the meta-decoration
    automaton's states and the transitions between them. The \meta{initial
    state} is the state in which the automaton starts.

    The |\state| command is similar to the one found in decoration
    declarations, and takes the same form:

    \begin{command}{\state\marg{name}\oarg{options}\marg{code}} Declares the
        state \meta{name} inside the current meta-decoration automaton. Unlike
        decorations, states in meta-decorations are not executed within a
        group, which makes the persistent computation options superfluous.
        Consider using an initial state with |width=0pt| to do precalculations
        that could speed the execution of the meta-decoration.

        The \meta{options} are executed with the key path set to
        |/pgf/meta-decorations automaton/|, and the following keys are defined
        for this path:

        \begin{key}{/pgf/meta-decoration automaton/switch if less than=\meta{dimension}| to |\meta{new state}}
            This causes \pgfname\ to check whether the remaining distance to
            the end of the input path is less than \meta{dimension}, and, if
            so, to immediately switch to the state \meta{new state}. When this
            key is evaluated, the macro |\pgfmetadecoratedpathlength| will be
            defined as the total length of the decoration path, allowing for
            values such as |\pgfmetadecoratedpathlength/8|.
        \end{key}

        \begin{key}{/pgf/meta-decoration automaton/width=\meta{dimension}}
            As always, this option will cause an immediate switch to the state
            |final| if the remaining distance on the input path is less than
            \meta{dimension}.

            Otherwise, this option tells \pgfname\ the width of the
            ``meta-segment'', that is, the length of the sub-input-path which
            the decoration automaton specified  in \meta{code} will decorate.
        \end{key}

        \begin{key}{/pgf/meta-decoration automaton/next state=\meta{new state}}
            After the code for a state has been executed, a state switch to
            \meta{new state} is performed. If this option is not given, the
            next state is the same as the current state.
        \end{key}

        The code in \meta{code} is quite different from the code in a
        decoration state. In almost all cases only the following three macros
        will be required:

        \begin{command}{\decoration\marg{name}}
            This sets the decoration for the current state to \meta{name}. If
            this command is omitted, the |moveto| decoration will be used.
        \end{command}

        \begin{command}{\beforedecoration\marg{before code}}
            Defines \meta{before code} as (typically) \pgfname{} commands to be
            executed before the decoration is applied to the current segment.
            This command can be omitted. If you wish to set up some decoration
            specific parameters such as segment length, or segment amplitude,
            then they can be set in \meta{before code}.
        \end{command}

        \begin{command}{\afterdecoration\marg{after code}}
            Defines \meta{after code} as commands to be executed after the
            decoration has been applied to the current segment. This command
            can be omitted.
        \end{command}

        There are some macros that may be useful when creating meta-decorations
        (note that they are all macros):

        \begin{command}{\pgfpointmetadecoratedpathfirst}
            When the \meta{before code} is executed, this macro stores the
            first point on the current sub-input-path.
        \end{command}

        \begin{command}{\pgfpointmetadecoratedpathlast}
            When the \meta{after code} is executed, this macro stores the last
            point on the current sub-input-path.
        \end{command}

        \begin{command}{\pgfmetadecoratedpathlength}
            The entire length of the entire input path.
        \end{command}

        \begin{command}{\pgfmetadecoratedcompleteddistance}
            The completed distance on the entire input path.
        \end{command}

        \begin{command}{\pgfmetadecoratedremainingdistance}
            The remaining distance on the entire input path.
        \end{command}

        \begin{command}{\pgfmetadecoratedinputsegmentcompleteddistance}
            The completed distance on the current input segment of the entire
            input path.
        \end{command}

        \begin{command}{\pgfmetadecoratedinputsegmentremainingdistance}
            The remaining distance on the current input segment of the entire
            input path.
        \end{command}
    \end{command}

    Here is a complete example of a meta-decoration:
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations,decorations.pathmorphing}}]
\pgfdeclaremetadecoration{arrows}{initial}{
  \state{initial}[width=0pt, next state=arrow]
  {
    \pgfmathdivide{100}{\pgfmetadecoratedpathlength}
    \let\factor\pgfmathresult
    \pgfsetlinewidth{1pt}
    \pgfset{/pgf/decoration/segment length=4pt}
  }
  \state{arrow}[
    switch if less than=\pgfmetadecorationsegmentlength to final,
    width=\pgfmetadecorationsegmentlength/3,
    next state=zigzag]
  {
    \decoration{curveto}
    \beforedecoration
    {
      \pgfmathparse{\pgfmetadecoratedcompleteddistance*\factor}
      \pgfsetcolor{red!\pgfmathresult!yellow}
      \pgfpathmoveto{\pgfpointmetadecoratedpathfirst}
    }
  }
  \state{zigzag}[width=\pgfmetadecorationsegmentlength/3, next state=end arrow]
  {
    \decoration{zigzag}
  }
  \state{end arrow}[width=\pgfmetadecorationsegmentlength/3, next state=move]
  {
    \decoration{curveto}
    \beforedecoration{\pgfpathmoveto{\pgfpointmetadecoratedpathfirst}}
    \afterdecoration
    {
      \pgfsetarrowsend{to}
      \pgfusepath{stroke}
    }
  }
  \state{move}[width=\pgfmetadecorationsegmentlength/2, next state=arrow]{}
  \state{final}{}
}

\tikz\draw[decorate,decoration={arrows,meta-segment length=2cm}]
  (0,0) .. controls (0,2)   and (3,2)   .. (3,0)
        .. controls (3,-2)  and (0,-2)  .. (0,-4)
        .. controls (0,-6)  and (3,-6)  .. (3,-8)
        .. controls (3,-10) and (0,-10) .. (0,-8);
\end{codeexample}
    %
\end{command}


\subsubsection{Predefined Meta-decorations}

There are no predefined meta-decorations loaded with \pgfname{}.


\subsubsection{Using Meta-Decorations}

Using meta-decorations is ``simpler'' than using decorations, because you can
only use one meta-decoration per path.

\begin{environment}{{pgfmetadecoration}\marg{name}}
    This environment decorates the input path described in \meta{environment
    contents}, with the meta-decoration \meta{name}.
\end{environment}

\begin{plainenvironment}{{pgfmetadecoration}\marg{name}}
    The plain \TeX{} version of the |{pgfmetadecoration}| environment.
\end{plainenvironment}

\begin{contextenvironment}{{pgfmetadecoration}\marg{name}}
    The Con\TeX t version of the |{pgfmetadecoration}| environment.
\end{contextenvironment}
