% Copyright 2019 by Mark Wibrow and 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{Decoration Library}
\label{section-library-decorations}


\subsection{Overview and Common Options}

The decoration libraries define a number of (more or less useful) decorations
that can be applied to paths. The usage of decorations is not covered in the
present section, please consult Sections~\ref{section-tikz-decorations}, which
explains how decorations are used in \tikzname, and
\ref{section-base-decorations}, which explains how new decorations can be
defined.

The decorations are influenced by a number of parameters that can be set using
the |decoration| option. These parameters are typically shared between
different decorations. In the following, the general options are documented
(they are defined directly in the |decoration| module), special-purpose keys
are documented with the decoration that uses it.

Since you are encouraged to use these keys to make your own decorations
configurable, it is indicated for each key where the value is stored (so that
you can access it). Note that some values are stored in \TeX\ dimension
registers while others are stored in macros.

\begin{key}{/pgf/decoration/amplitude=\meta{dimension} (initially 2.5pt)}
    This key determines the ``desired height'' (or amplitude) of decorations
    for which this makes sense. For instance, the initial value of |2.5pt|
    means that deforming decorations should deform a path by up to 2.5pt away
    from the original path.

    This key sets the \TeX-dimension |\pgfdecorationsegmentamplitude|.
\end{key}

\begin{key}{/pgf/decoration/meta-amplitude=\meta{dimension} (initially 2.5pt)}
    This key determines the amplitude for a meta-decoration.

    The key sets the \TeX-macro (!) |\pgfmetadecorationsegmentamplitude|.
\end{key}

\begin{key}{/pgf/decoration/segment length=\meta{dimension} (initially 10pt)}
    Many decorations are made up of small segments. This key determines the
    desired length of such segments.

    This key sets the \TeX-dimension |\pgfdecorationsegmentlength|.
\end{key}

\begin{key}{/pgf/decoration/meta-segment length=\meta{dimension} (initially 1cm)}
    This determined the length of the meta-segments from which a
    meta-decoration is made up.

    This key sets the \TeX-macro (!) |\pgfmetadecorationsegmentlength|.
\end{key}

\begin{key}{/pgf/decoration/angle=\meta{degree} (initially 45)}
    The way some decorations look like depends on a configurable angle. For
    instance, a |wave| decoration consists of arcs and the opening angle of
    these arcs is given by the |angle|.

    This key sets the \TeX-macro |\pgfdecorationsegmentangle|.
\end{key}

\begin{key}{/pgf/decoration/aspect=\meta{factor} (initially 0.5)}
    For some decorations there is a natural aspect ratio. For instance,
    for a |brace| decoration the aspect ratio determines where the brace
    point will be.

    This key sets the \TeX-macro |\pgfdecorationsegmentaspect|.
\end{key}

\begin{key}{/pgf/decoration/start radius=\meta{dimension} (initially 2.5pt)}
    For some decorations there is a natural start radius (of some circle,
    presumably).

    This key stores the value directly inside the key.
\end{key}

\begin{key}{/pgf/decoration/end radius=\meta{dimension} (initially 2.5pt)}
    For some decorations there is a natural end radius (of some circle,
    presumably).

    This key stores the value directly inside the key.
\end{key}

\begin{stylekey}{/pgf/decoration/radius=\meta{dimension}}
    Sets the start and end radius simultaneously.
\end{stylekey}

\begin{key}{/pgf/decoration/path has corners=\meta{boolean} (initially false)}
    This is a hint to the decoration code as to whether the path has corners or
    not. If a path has a sharp corner, setting this option to |true| may result
    in better rendering of the decoration because the joins of input segments
    are approached ``more carefully'' than when this key is set to false.
    However, if the path is, say, a smooth circle, setting this key to |true|
    will usually look worse. Most decorations ignore this key, anyway.
    Internally, it sets the \TeX-if |\ifpgfdecoratepathhascorners|.
\end{key}


\subsection{Handling ``Dimension too large'' errors}

In case you should run into a ``Dimension too large error'' when using the
|decorations| libraries, there is a pretty high chance that you can resolve
this by using the |fpu| library in combination with
|/pgf/fpu/install only={reciprocal}|. Please note that this key should only be
applied locally to avoid other errors (see also at the definition of this key
on page~\pageref{fpu-install-only}).
%
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings,fpu}}]
\begin{tikzpicture}
  \begin{scope}[/pgf/fpu/install only={reciprocal}]
    \draw[postaction=decorate,decoration={
        markings,mark=at position 0.52 with {
            \draw circle[radius=2pt];
        }},
    ] plot[smooth,variable=\x,domain=-1:1] (\x*\x*\x,\x*\x);
  \end{scope}
\end{tikzpicture}
\end{codeexample}


\subsection{Path Morphing Decorations}

\begin{pgflibrary}{decorations.pathmorphing}
    A \emph{path morphing decoration} ``morphs'' or ``deforms'' the
    to-be-decorated path. This means that what used to be a straight line might
    afterwards be a snaking curve and have bumps. However, a line is still a
    line and path deforming decorations do not change the number of subpaths.
    For instance, if the path used to consist of two circles and an open arc,
    the path will, after the decoration process, still consist of two closed
    subpaths and one open subpath.
\end{pgflibrary}


\subsubsection{Decorations Producing Straight Line Paths}

The following deformations use only straight lines in order to morph the paths.

\begin{decoration}{lineto}
    This decoration replaces the path by straight lines. For each curve, the
    path simply goes directly from the start point to the end point. In the
    following example, the arc actually consist of two subcurves.

    This decoration is actually always defined when the decoration module is
    loaded, but it is documented here for consistency.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations}}]
\begin{tikzpicture}[decoration=lineto]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{straight zigzag}
    This (meta-)decoration decorates the path by alternating between |curveto|
    and |zigzag| decorations. It always finishes with the |curveto| decoration.
    The following parameters influence the decoration:
    %
    \begin{itemize}
        \item |amplitude| determines how much the zigzag line raises above and
            falls below a straight line to the target point.
        \item |segment length| determines the length of a complete ``up-down''
            cycle.
    \item |meta-segment length| determines the length of the |curveto| and the
        |zigzag| decorations.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration={straight zigzag,meta-segment length=1.1cm}]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{random steps}
    This decoration consists of straight line segments. The line segments head
    towards the target, but each step is randomly shifted a little bit. The
    following parameters influence the decorations:
    %
    \begin{itemize}
        \item |segment length| determines the basic length of each step.
        \item |amplitude| The end of each step is perturbed both in $x$- and in
            $y$-direction by two values drawn uniformly from the interval
            $[-d,d]$, where $d$ is the value of |amplitude|.
    \end{itemize}
    %
\begin{codeexample}[pre={\pgfmathsetseed{1}},preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}
    [decoration={random steps,segment length=2mm}]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{saw}
    This decoration looks like the blade of a saw. The following parameters
    influence the decoration:
    %
    \begin{itemize}
        \item |amplitude| determines how much each spike raises above the
            straight line.
        \item |segment length| determines the length each spike.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration=saw]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{zigzag}
    This decoration looks like a zigzag line. The following parameters
    influence the decoration:
    %
    \begin{itemize}
        \item |amplitude| determines how much the zigzag line raises above and
            falls below a straight line to the target point.
        \item |segment length| determines the length of a complete ``up-down''
            cycle.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration=zigzag]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}


\subsubsection{Decorations Producing Curved Line Paths}

\begin{decoration}{bent}
    This decoration adds a slightly bent line from the start to the target. The
    amplitude of the bend is given |amplitude| (an amplitude of zero gives a
    straight line).
    %
    \begin{itemize}
        \item |amplitude| determines the amplitude of the bend.
        \item |aspect| determines how tight the bend is. A good value is around
            |0.3|.
    \end{itemize}
    %
    Note that this decoration makes only little sense for curves. You should
    apply it only to straight lines.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration=bent]
  \draw [help lines] grid (3,2);
  \draw [decorate] (0,0) -- (3,1) -- (1.5,2) -- (0,1);
\end{tikzpicture}
\end{codeexample}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration={bent,aspect=.3}]
  \draw [decorate,fill=yellow!80!black] (0,0) rectangle (3.5,2);
  \node[circle,draw] (A) at (.5,.5) {A};
  \node[circle,draw] (B) at (3,1.5) {B};
  \draw[->,decorate] (A) -- (B);
  \draw[->,decorate] (B) -- (A);
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{bumps}
    This decoration replaces the path by little half ellipses. The following
    parameters influence it.
    %
    \begin{itemize}
        \item |amplitude| determines the height of the half ellipse.
        \item |segment length| determines the width of the half ellipse.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration=bumps]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{coil}
    This decoration replaces the path by a coiled line. To understand how this
    works, imagine a three-dimensional spring. The spring's axis points along
    the path toward the target. Then, we ``view'' the spring from a certain
    angle. If we look ``straight from the side'' we will see a perfect sine
    curve, if we look ``more from the front'' we will see a coil. The following
    parameters influence the decoration:
    %
    \begin{itemize}
        \item |amplitude| determines how much the coil rises above the path and
            falls below it. Thus, this is the radius of the coil.
        \item |segment length| determines the distance between two consecutive
            ``curls''. Thus, when the spring is see ``from the side'' this will
            be the wave length of the sine curve.
        \item |aspect| determines the ``viewing direction''. A value of |0|
            means ``looking from the side'' and a value of |0.5|, which is the
            default, means ``look more from the front''.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration=coil]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}
    [decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{curveto}
    This decoration simply yields a line following the original path. This
    means that (ideally) it does not change the path and follows any curves in
    the path (hence the name). In reality, due to the internals of how
    decorations are implemented, this decoration actually replaces the path by
    numerous small straight lines.

    This decoration is mostly useful in conjunction with meta-decorations. It
    is also actually defined in the decoration module and is always available.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration=curveto]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{snake}
    This decoration replaces the path by a line that looks like a snake seen
    from above. More precisely, the snake is a sine wave with a ``softened''
    start and ending. The following parameters influence the snake:
    %
    \begin{itemize}
        \item |amplitude| determines the sine wave's amplitude.
        \item |segment length| determines the sine wave's wavelength.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathmorphing}}]
\begin{tikzpicture}[decoration=snake]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black]
    (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}


\subsection{Path Replacing Decorations}

\begin{pgflibrary}{decorations.pathreplacing}
    This library defines decorations that replace the to-be-decorated path by
    another path. Unlike morphing decorations, the replaced path might be quite
    different, for instance a straight line might be replaced by a set of
    circles. Note that filling a path that has been replaced using one of the
    decorations in this library typically does not fill the original area but,
    rather, the smaller area of the newly-created path segments.
\end{pgflibrary}

\begin{decoration}{border}
    This decoration adds straight lines to the path that are at a specific
    angle to the line toward the target. The idea is to add these little lines
    to indicate the ``border'' of an area. The following parameters influence
    the decoration:
    %
    \begin{itemize}
        \item |segment length| determines the distance between consecutive
            ticks.
        \item |amplitude| determines the length of the ticks.
        \item |angle| determines the angle between the ticks and the line of
            the path.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathreplacing}}]
\begin{tikzpicture}[decoration=border]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate,draw,red}]
        (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{brace}
    This decoration replaces a straight line path by a long brace. The left and
    right end of the brace will be exactly on the start and endpoint of the
    decoration. The decoration really only makes sense for paths that are a
    straight line.
    %
    \begin{itemize}
        \item |amplitude| determines how much the brace rises above the path.
        \item |aspect| determines the fraction of the total length where the
            ``middle part'' of the brace will be.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathreplacing}}]
\begin{tikzpicture}[decoration=brace]
  \draw [help lines] grid (3,2);
  \draw [decorate] (0,0) -- (3,1);
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{expanding waves}
    This decoration adds arcs to the path that get bigger along the line
    towards the target. The following parameters influence the decoration:
    %
    \begin{itemize}
        \item |segment length| determines the distance between consecutive
            arcs.
        \item |angle| determines the opening angle below and above the path.
            Thus, the total opening angle is twice this angle.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathreplacing}}]
\begin{tikzpicture}[decoration={expanding waves,angle=5}]
  \draw [help lines] grid (3,2);
  \draw [decorate] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{moveto}
    This decoration simply jumps to the end of the path using a move-to path
    operation. It is mainly useful as |pre=moveto| or |post=moveto|
    decorations.

    This decoration is actually always defined when the decoration module is
    loaded, but it is documented here for consistency.
\end{decoration}

\begin{decoration}{ticks}
    This decoration replaces the path by straight lines that are orthogonal to
    the path. The following parameters influence the decoration:
    %
    \begin{itemize}
        \item |segment length| determines the distance between consecutive
            ticks.
        \item |amplitude| determines half the length of the ticks.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathreplacing}}]
\begin{tikzpicture}[decoration=ticks]
  \draw [help lines] grid (3,2);
  \draw [decorate] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{waves}
    This decoration replaces the path by arcs that have a constant size. The
    following parameters influence the decoration:
    %
    \begin{itemize}
        \item |segment length| determines the distance between consecutive
            arcs.
        \item |angle| determines the opening angle below and above the path.
            Thus, the total opening angle is twice this angle.
        \item |radius| determines the radius of each arc.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathreplacing}}]
\begin{tikzpicture}[decoration={waves,radius=4mm}]
  \draw [help lines] grid (3,2);
  \draw [decorate] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{show path construction}
    This decoration allows ``something different'' to be done for each
    \emph{type} of input segment (i.e., moveto, lineto, curveto or closepath).
    Typically, each segment will be replaced with another path, but this need
    not necessarily be the case.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathreplacing}}]
\begin{tikzpicture}[>=stealth, every node/.style={midway, sloped, font=\tiny},
  decoration={show path construction,
    moveto code={
      \fill [red] (\tikzinputsegmentfirst) circle [radius=2pt]
        node [fill=none, below] {moveto};},
    lineto code={
      \draw [blue,->] (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast)
        node [above] {lineto};
    },
    curveto code={
      \draw [green!75!black,->] (\tikzinputsegmentfirst) .. controls
        (\tikzinputsegmentsupporta) and (\tikzinputsegmentsupportb)
        ..(\tikzinputsegmentlast) node [above] {curveto};
    },
    closepath code={
      \draw [orange,->] (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast)
        node [above] {closepath};}
  }]
  \draw [help lines] grid (3,2);
  \path [decorate] (0,0) -- (3,1) arc (0:180:1.5 and 1) -- cycle;
\end{tikzpicture}
\end{codeexample}

    The following keys can be used to specify the code to execute for each type
    of input segment.

    \begin{key}{/pgf/decoration/moveto code=\meta{code} (initially \char`\{\char`\})}
        Set the code to be executed for every moveto input segment. It is
        important to remember that the transformations applied by the
        decoration automaton are turned \emph{off} when \meta{code} is
        executed.
    \end{key}

    \begin{key}{/pgf/decoration/lineto code=\meta{code} (initially \char`\{\char`\})}
        Set the code to be executed for every lineto input segment.
    \end{key}

    \begin{key}{/pgf/decoration/curveto code=\meta{code} (initially \char`\{\char`\})}
        Set the code to be executed for every curveto input segment.
    \end{key}

    \begin{key}{/pgf/decoration/closepath code=\meta{code} (initially \char`\{\char`\})}
        Set the code to be executed for every closepath input segment.
    \end{key}

    Within \meta{code} the first and last points on the current input segment
    can be accessed using |\pgfpointdecoratedinputsegmentfirst| and
    |\pgfpointdecoratedinputsegmentlast|. For curves, the control (support)
    points can be accessed using |\pgfpointdecoratedinputsegmentsupporta| and
    |\pgfpointdecoratedinputsegmentsupportb|.

    In \tikzname, you can use the following macros inside a \tikzname{}
    coordinate.

    \begin{command}{\tikzinputsegmentfirst}
        The first point on the current input segment path.
    \end{command}

    \begin{command}{\tikzinputsegmentlast}
        The last point on the current input segment path.
    \end{command}

    \begin{command}{\tikzinputsegmentsupporta}
        The first support on the curveto input segment path.
    \end{command}

    \begin{command}{\tikzinputsegmentsupportb}
    The second support on the curveto input segment path.
    \end{command}
    %
{\ifpgfmanualexternalize\tikzexternaldisable\fi
\begin{codeexample}[preamble={\usetikzlibrary{decorations.pathreplacing,shapes.misc}}]
\tikzset{
  show curve controls/.style={
    decoration={
      show path construction,
      curveto code={
        \draw [blue, dashed]
          (\tikzinputsegmentfirst)    -- (\tikzinputsegmentsupporta)
          node [at end, cross out, draw, solid, red, inner sep=2pt]{};
        \draw [blue, dashed]
          (\tikzinputsegmentsupportb) -- (\tikzinputsegmentlast)
          node [at start, cross out, draw, solid, red, inner sep=2pt]{};
      }
    },decorate
  }
}

\begin{tikzpicture}
  \draw [postaction=show curve controls, thick]
    (0,2) .. controls (2.5,1.5) and (0.5,0.5) .. (3,0);
\end{tikzpicture}
\end{codeexample}
}%
    %
\end{decoration}


\subsection{Marking Decorations}

\subsubsection{Overview}

A \emph{marking on a path} is any kind of graphic that is placed on a specific
position on a path. Markings are useful in rather diverse situations: you can
use them to, say, place little ``footsteps'' along a path as if someone where
walking along the path; to place arrow tips on the middle of a path to indicate
the ``direction'' in which something is flowing; or you can use them to place
informative information at certain positions of a path.

For historical reasons there are three different libraries for placing marks on
a path. They differ in what kind of markings can be added to a path. We start
with the most general and most useful of these libraries.


\subsection{Arbitrary Markings}

\begin{pgflibrary}{decorations.markings}
    Markings are arbitrary ``marks'' that can be put on a path. Marks can be
    arrow tips or nodes or even whole pictures.
\end{pgflibrary}

\begin{decoration}{markings}
    A \emph{marking} can be thought of a ``little picture'' or more precisely
    of ``some scope contents'' that is placed ``on'' a path at a certain
    position. Suppose the marking should be a simple cross. We can produce this
    with the following code:
    %
\begin{codeexample}[code only]
\draw (-2pt,-2pt) -- (2pt,2pt);
\draw (2pt,-2pt) -- (-2pt,2pt);
\end{codeexample}
    %
    If we use this code as a marking at position |2cm| on a path, then the
    following happens: \pgfname\ determines the position on the path that is
    2cm along the path. Then it translates the coordinate system to this
    position and rotates it such that the positive $x$-axis is tangent to the
    path. Then a protective scope is created, inside which the above code is
    executed -- resulting in a little cross on the path.

    The |markings| decoration allows you to place one or more such markings on
    a path. The decoration destroys the input path (except in certain cases,
    detailed later), which means that it uses the path for determining
    positions on the path, but after the decoration is done this path is gone.
    You typically need to use a |postaction| to add markings.

    Let us start with the above example in real code:
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={
    markings,% switch on markings
    mark=% actually add a mark
      at position 2cm
      with
      {
        \draw (-2pt,-2pt) -- (2pt,2pt);
        \draw (2pt,-2pt) -- (-2pt,2pt);
      }
    }
    ]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate}] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}

    We can also add the cross repeatedly:
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={
    markings,% switch on markings
    mark=% actually add a mark
      between positions 0 and 1 step 5mm
      with
      {
        \draw (-2pt,-2pt) -- (2pt,2pt);
        \draw (2pt,-2pt) -- (-2pt,2pt);
      }
    }
    ]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate}] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}

    The |mark| decoration option is used to specify a marking. It comes in two
    versions:
    %
    \begin{key}{/pgf/decoration/mark=\texttt{at position }\meta{pos}\texttt{ with }\meta{code}}
        The options specifies that when a |marking| decoration is applied,
        there should be a marking at position \meta{pos} on the path whose code
        is given by \meta{code}.

        The \meta{pos} can have four different forms:
        %
        \begin{enumerate}
            \item It can be a non-negative dimension like |0pt| or |2cm| or
                |5cm/2|. In this case, it refers to the position along the path
                that is this far displaced from the start.
            \item It can be a negative dimension like |-1cm-2pt| or |-1sp|. In
                this case, the position is taken from the end of the path.
                Thus, |-1cm| is the position that is $-1$cm displaced from the
                end of the path.
            \item It can be a dimensionless non-negative number like |1/2| or
                |0.333+2*0.1|. In this case, the \meta{pos} is interpreted as a
                factor of the total path length. Thus, a \meta{pos} or |0.5|
                refers to the middle of the path, |0.1| is near the start, and
                so on.
            \item It can be a dimensionless negative number like |-0.1|. Then,
                again, the fraction of the path length counts ``from the end''.
        \end{enumerate}

        The \meta{pos} determines a position on the path. When the marking is
        applied, the (high level) coordinate system will have been transformed
        so that the origin lies at this position and the positive $x$-axis
        points along the path. For this coordinate system, the \meta{code} is
        executed. It can contain all sorts of graphic drawing commands,
        including (even named) nodes.

        If the position lies past the end of the path (for instance if
        \meta{pos} is set to |1.2|), the marking will not be drawn.

        It is possible to give the |mark| option several times, which causes
        several markings to be applied. In this case, however, it is necessary
        that the positions on the path are in increasing order. That is, it is
        not allowed (and will result in chaos) to have a marking that lies
        earlier on the path to follow a marking that is later on the path.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={
    markings,% switch on markings
    mark=at position 1cm  with \node[red]{1cm};,
    mark=at position .5   with \node[green]{mid};,
    mark=at position -1cm with {\node[blue,transform shape]{1cm from end};}}
    ]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate}] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}

        Here is an example that shows how markings can be used to place text on
        plots:
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[domain=0:4,label/.style={postaction={
      decorate,
      decoration={
        markings,
        mark=at position .75 with \node #1;}}}]
  \draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9);

  \draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
  \draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};

  \draw[red,label={[above left]{$f(x)=x$}}]                       plot (\x,\x);
  \draw[blue,label={[below left]{$f(x)=\sin x$}}]                 plot (\x,{sin(\x r)});
  \draw[orange,label={[right]{$f(x)= \frac{1}{20} \mathrm e^x$}}] plot (\x,{0.05*exp(\x)});
\end{tikzpicture}
\end{codeexample}

        When the \meta{code} is being executed, two special keys will have been
        set up, whose value may be of interest:
        %
        \begin{key}{/pgf/decoration/mark info/sequence number}
            This key can only be read. Its value (which can be obtained using
            the |\pgfkeysvalueof| command) is a ``sequence number'' of the
            mark. The first mark that is added to a path has number |1|, the
            second number |2|, and so on. This key is mainly useful in
            conjunction with repeated markings (see below).
        \end{key}
        %
        \begin{key}{/pgf/decoration/mark info/distance from start}
            This key can only be read. Its value is the distance of the marking
            from the start of the path in points. For instance, if the path
            length is 100pt and the marking is in the middle of the path, the
            value of this key would be |50.0pt|.
        \end{key}
    \end{key}

    A second way to use the |mark| key is the following:
    %
    \begin{key}{/pgf/decoration/mark=\texttt{between positions }\meta{start pos}\texttt{ and }\meta{end pos}\texttt{ step }\meta{stepping}\texttt{ with }\meta{code}}
        This works similarly to the |at position| version of this option, only
        multiple marks are placed, starting at \meta{start pos} and then spaced
        apart by \meta{stepping}. The \meta{start pos}, the \meta{end pos}, and
        also the \meta{stepping} may all be specified in the same way as for
        the |at position| version, that is, either using units or no units and
        also using positive or negative values.

        Let us start with a simple example in which we place ten crosses along
        a path starting with the beginning of the path ($\meta{start pos} = 0$)
        and ending at the end ($\meta{end pos} = 1$).
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={markings,
    mark=between positions 0 and 1 step 0.1
         with { \draw (-2pt,-2pt) -- (2pt,2pt);
                \draw (2pt,-2pt) -- (-2pt,2pt); }} ]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate}] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}

        In the next example we place arrow shapes on the path instead of
        crosses. Note the use of the |transform shape| option to ensure that
        the nodes are actually rotated.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings,shapes.arrows}}]
\begin{tikzpicture}[decoration={markings,
    mark=between positions 0 and 1 step 1cm
      with { \node [single arrow,fill=red,
                    single arrow head extend=3pt,transform shape] {};}}]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate}] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}

        Using the key |sequence number| we can also ``number'' the nodes and
        even refer to them later on.
        %
% FIXME: the automatic key highlighting fails here!
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={markings,
    mark=between positions 0 and 1 step 1cm with {
      \node [draw,
        name=mark-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number},
        transform shape]
      {\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}};}}]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate}] (0,0) -- (3,1) arc (0:180:1.5 and 1);
  \draw [red,->] (mark-3) -- (mark-7);
\end{tikzpicture}
\end{codeexample}

        In the following example we use the distance info to place ``length
        information'' on a path:
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={markings,
    % Main marks
    mark=between positions 0 and 1 step 40pt with
      { \draw [help lines] (0,0) -- (0,0.5)
        node[above,font=\tiny]{
          \pgfkeysvalueof{/pgf/decoration/mark info/distance from start}}; },
    mark=at position -0.1pt with
      { \draw [help lines] (0,0) -- (0,0.5)
        node[above,font=\tiny]{
          \pgfkeysvalueof{/pgf/decoration/mark info/distance from start}}; }}]
  \draw [help lines] grid (5,3);
  \draw [postaction={decorate}]  (0,0) .. controls (8,3) and (0,3) .. (5,0) ;
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/reset marks}
        Since |mark| options accumulate, there needs to be a way to ``reset''
        things, so that any |mark| options set in an enclosing scope do not
        interfere. This option does exactly this. Note that when the
        \meta{code} of a marking is executed, the markings are automatically
        reset.
    \end{key}

    As mentioned earlier, the decoration usually destroys the path. However,
    this is no longer the case when the following key is set:
    %
    \begin{key}{/pgf/decoration/mark connection node=\meta{node name} (initially empty)}
        When this key is set to a non-empty \meta{node name} while the
        decoration is being processed, the following happens: The marking code
        should, among possibly other things, define a node named \meta{node
        name}. Then, the output path of this decoration will contain a line-to
        to ``one end'' of this node, followed by a moveto to the ``other end''
        of the node. More precisely, the first end is given by the position on
        the border of \meta{node name} that lies in the direction ``from which
        the path heads toward the node'' while the other end lies on the border
        ``where the path heads away from the node''. Furthermore, this option
        causes the decoration to end with a line-to to the end instead of a
        move-to.

        The net effect of all this is that when you decorate a straight line
        with one or more markings that contain just a node, the line will
        effectively connect these nodes.

        Here are two examples that show how this works:
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={markings,
    mark connection node=my node,
    mark=at position .5 with
      {\node [draw,blue,transform shape] (my node) {my node};}}]
  \draw [help lines] grid (3,2);
  \draw decorate { (0,0) -- (3,2) };
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={markings,
    mark connection node=my node,
    mark=at position .25 with
      {\node [draw,red] (my node) {my node};}}]
  \draw [help lines] grid (3,2);
  \draw decorate { (0,0) -- (3,2) };
\end{tikzpicture}
\end{codeexample}
    \end{key}
\end{decoration}


\subsubsection{Arrow Tip Markings}

Frequent markings that are hard to create correctly are arrow tips. For them,
two special commands are available when the \meta{code} of a |mark| option is
executed. (They are only defined in this code):

\begin{command}{\arrow\opt{\oarg{options}}\marg{arrow end tip}}
    This command simply draws the \meta{arrow end tip} at the origin, pointing
    right. This is exactly what you need when you want to draw an arrow tip as
    a marking.

    The \meta{options} can only be given when \tikzname\ is used. In this case,
    they are executed in a scope that contains the arrow tip.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={
    markings,% switch on markings
    mark=at position 1cm  with {\node[red]{1cm};},
    mark=at position .75  with {\arrow[blue,line width=2mm]{>}},
    mark=at position -1cm with {\arrowreversed[black]{stealth}}}
    ]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate}] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}

    Here is a more useful example:
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.markings}}]
\begin{tikzpicture}[decoration={
    markings,% switch on markings
    mark=between positions 0 and .75 step 4mm with {\arrow{stealth}},
    mark=between positions .75 and 1 step 4mm with {\arrowreversed{stealth}}}
    ]
  \draw [help lines] grid (3,2);
  \draw [postaction={decorate}] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\arrowreversed\opt{\oarg{options}}\marg{arrow end tip}}
    As above, only the arrow end tip is flipped and points in the other
    direction.
\end{command}


\subsubsection{Footprint Markings}

\begin{pgflibrary}{decorations.footprints}
    The decorations of this library can be used to decorate a path with little
    footprints, as if someone had ``walked'' along the path.
\end{pgflibrary}

\begin{decoration}{footprints}
    The footprint decoration adds little footprints around the path. They start
    with the left foot.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.footprints}}]
\begin{tikzpicture}[decoration={footprints,foot length=5pt,stride length=10pt}]
  \draw [help lines] grid (3,3);
  \fill [decorate] (0,0) -- (3,2) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}
    %
    You can influence the way this decoration looks using the following
    options:
    %
    \begin{key}{/pgf/decoration/foot length (initially 10pt)}
        The length or size of the footprint itself. A larger value makes the
        footprint larger, but does not change the stride length.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.footprints}}]
\begin{tikzpicture}[decoration={footprints,foot length=20pt}]
  \fill [decorate] (0,0) -- (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}
    %
    \begin{key}{/pgf/decoration/stride length (initially 30pt)}
        The length of strides. This is the distance between the beginnings of
        left footprints along the path.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.footprints}}]
\begin{tikzpicture}[decoration={footprints,stride length=50pt}]
  \fill [decorate] (0,0) -- (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}
    %
    \begin{key}{/pgf/decoration/foot sep (initially 4pt)}
        The separation in the middle between the footprints. The footprints are
        moved away from the path by half this amount.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.footprints}}]
\begin{tikzpicture}[decoration={footprints,foot sep=10pt}]
  \fill [decorate] (0,0) -- (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}
    %
    \begin{key}{/pgf/decoration/foot angle (initially 10)}
        Footprints are rotated by this much.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.footprints}}]
\begin{tikzpicture}[decoration={footprints,foot angle=60}]
  \fill [decorate] (0,0) -- (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}
    %
    \begin{key}{/pgf/decoration/foot of (initially human)}
        The species whose footprints are shown. Possible values are:

        \def\render#1{
          \texttt{#1} &
          \tikz [baseline,decoration={footprints,foot of=#1}]
            \fill [decorate] (0,0) -- (6,0); \\[3em]
        }
        \begin{tabular}{ll}
            \emph{Species} & \emph{Result} \\[1em]
            \render{gnome}
            \render{human}
            \render{bird}
            \render{felis silvestris}
        \end{tabular}
    \end{key}
\end{decoration}


\subsubsection{Shape Background Markings}

The third library for adding markings uses the background paths of certain
shapes. This library is included mostly for historical reasons, using the
|markings| library is usually preferable.

\begin{pgflibrary}{decorations.shapes}
    This library defines decorations that use shapes or shape-like drawings to
    decorate a path. The following options are common options used by the
    decorations in this library:

    \begin{key}{/pgf/decoration/shape width=\meta{dimension}  (initially 2.5pt)}
        The desired width of the shapes. For decorations that support varying
        shape sizes, this key sets both the start and end width (which can be
        overwritten using options like |shape start width|).
    \end{key}

    \begin{key}{/pgf/decoration/shape height=\meta{dimension} (initially 2.5pt)}
        Works like the previous key, only for the height.
    \end{key}

    \begin{key}{/pgf/decoration/shape size=\meta{dimension}}
        Sets the desired width and height simultaneously.
    \end{key}

    For the exact places and macros where these keys store the values, please
    consult the beginning of the code of the library.
\end{pgflibrary}

\begin{decoration}{crosses}
    This decoration replaces the path by (diagonal) crosses. The following
    parameters influence the decoration:
    %
    \begin{itemize}
        \item |segment length| determines the distance between (the centers of)
            consecutive crosses.
        \item |shape height| determines the height of each cross.
        \item |shape width| determines the width of each cross.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes}}]
\begin{tikzpicture}[decoration=crosses]
  \draw [help lines] grid (3,2);
  \draw [decorate] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{triangles}
    This decoration replaces the path by triangles that point along the path.
    The following parameters influence the decoration:
    %
    \begin{itemize}
        \item |segment length| determines the distance between consecutive
            triangles.
        \item |shape height| determines the height of the triangle side that is
            orthogonal to the path.
        \item |shape width| determines the width of the triangle.
    \end{itemize}
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes}}]
\begin{tikzpicture}[decoration=triangles]
  \draw [help lines] grid (3,2);
  \draw [decorate,fill=yellow!80!black] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{shape backgrounds}
    This is a general decoration that replaces the to-be-decorated path by
    repeated copies of the background path of an arbitrary shape that has
    previously been defined using the |\pgfdeclareshape| command (that is, you
    can use any shape in the shape libraries).

    Please note that the background path of the shapes is used, but \emph{no
    nodes are created}. This means that \emph{you cannot have text inside the
    shapes of this path, you cannot name them, or refer to them.} Finally, this
    decoration \emph{will not work with shapes that depend  strongly on the
    size of the text box (like the arrow shapes).} If any of these restrictions
    pose a problem, use the |markings| library instead.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes,shapes.geometric}}]
\begin{tikzpicture}[decoration={shape backgrounds,shape=star,shape size=5pt}]
  \draw [help lines] grid (3,2);
  \draw [decorate] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes,shapes.geometric}}]
\tikzset{paint/.style={ draw=#1!50!black, fill=#1!50 },
         decorate with/.style=
           {decorate,decoration={shape backgrounds,shape=#1,shape size=2mm}}}
\begin{tikzpicture}
  \draw [decorate with=dart,      paint=red]    (0,1.5) -- (3,1.5);
  \draw [decorate with=diamond,   paint=green]  (0,1)   -- (3,1);
  \draw [decorate with=rectangle, paint=blue]   (0,0.5) -- (3,0.5);
  \draw [decorate with=circle,    paint=yellow] (0,0)   -- (3,0);
\end{tikzpicture}
\end{codeexample}

    All shapes are positioned by the anchor that is specified via the |anchor|
    decoration option:

    \begin{key}{/pgf/decoration/anchor=\meta{anchor} (initially center)}
        The anchor used to position the shape backgrounds.
    \end{key}

    A shape background path is added at the start point of the path and, if the
    distance between the shapes is appropriate, at the end point of the path.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes,shapes.geometric}}]
\begin{tikzpicture}[decoration={
      shape backgrounds,shape=regular polygon,shape size=4mm}]
  \draw [help lines] grid (3,2);
  \draw [thick] (0,0) -- (2,2) (1,0) -- (3,0);
  \draw [red, decorate, decoration={shape sep=.5cm}]  (1,0) -- (3,0);
  \draw [blue, decorate, decoration={shape sep=.5cm}] (0,0) -- (2,2);
\end{tikzpicture}
\end{codeexample}

    Keys for customizing specific shapes can be specified (e.g., |star points|,
    |cloud puffs|, |kite angles|, and so on). The size of the shape is
    ``enforced'' using transformations. This means that the shape is typeset
    with an empty text box and some default size values, resulting in an
    initial shape. This shape is then rescaled using coordinate transformations
    so that it has the desired size (which may vary as we travel along the
    to-be-decorated path). This means that settings involving angles and
    distances may not appear entirely accurate. More general options such as
    |inner sep| and |minimum size| will be ignored,  but transformations can be
    applied to each segment as described below.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes,shapes.geometric}}]
\tikzset{
  paint/.style={draw=#1!50!black, fill=#1!50},
  my star/.style={decorate,decoration={shape backgrounds,shape=star},
                  star points=#1}
}
\begin{tikzpicture}[decoration={shape sep=.5cm, shape size=.5cm}]
  \draw [my star=9, paint=red]                            (0,1.5) -- (3,1.5);
  \draw [my star=5, paint=blue]                           (0,.75) -- (3,.75);
  \draw [my star=5, paint=yellow, shape border rotate=30] (0,0) -- (3,0);
\end{tikzpicture}
\end{codeexample}

    There are various keys to control the drawing of the shape decoration.

    \begin{key}{/pgf/decoration/shape=\meta{shape name} (initially circle)}
        The shape whose background path is used.
    \end{key}

    \begin{key}{/pgf/decoration/shape sep=\meta{spacing} (initially {.25cm, between centers})}
        Set the spacing between the shapes on the decorations path. This can be
        just a distance on its own, but the additional keywords
        |between centers|, and |between borders| (which must be preceded by a
        comma), specify that the distance  is between the center anchors of the
        shapes or between the edges of the \emph{boundaries} of the shape
        borders.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes,shapes.symbols}}]
\begin{tikzpicture}[
    decoration={shape backgrounds,shape size=.5cm,shape=signal},
    signal from=west, signal to=east,
    paint/.style={decorate, draw=#1!50!black, fill=#1!50}]
  \draw [help lines] grid (3,2);
  \draw [paint=red, decoration={shape sep=.5cm}]
    (0,2) -- (3,2);
  \draw [paint=green, decoration={shape sep={1cm, between centers}}]
    (0,1) -- (3,1);
  \draw [paint=blue, decoration={shape sep={1cm, between borders}}]
    (0,0) -- (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/shape evenly spread=\meta{number}}
        This key overrides the |shape sep| key and forces the decoration to fit
        \meta{number} shapes evenly across the path. If \meta{number} is less
        than |1|, then no shapes will be used. If \meta{number} equals |1|,
        then one shape is put in the middle of the path. The additional
        keywords |by centers| (the default, if no keyword is specified) and
        |by borders| can be used (both preceded by a comma), to specify how the
        distance between shapes is determined. These keywords will only have a
        noticeable effect if the shapes sizes differ over time.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes}}]
\tikzset{
  paint/.style={draw=#1!50!black, fill=#1!50},
  spreading/.style={
    decorate,decoration={shape backgrounds, shape=rectangle,
    shape start size=4mm,shape end size=1mm,shape evenly spread={#1}}}
}
\begin{tikzpicture}
  \fill [paint=green,spreading={5, by borders},
         decoration={shape scaled}]            (0,2)   -- (3,2);
  \fill [paint=blue,spreading={5, by centers},
         decoration={shape scaled}]            (0,1.5) -- (3,1.5);
  \fill [paint=red,    spreading=5]            (0,1)   -- (3,1);
  \fill [paint=orange, spreading=4]            (0,.5)  -- (3,.5);
  \fill [paint=gray,    spreading=1]            (0,0)   -- (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/shape sloped=\opt{\meta{boolean}} (initially true)}
        By default, shapes are rotated to the slope of the decorations path. If
        \meta{boolean} is the value |false|, then this rotation is turned off.
        Internally this sets the \TeX-if |\ifpgfshapedecorationsloped|
        accordingly.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes,shapes.geometric}}]
\tikzset{
  paint/.style={draw=#1!50!black, fill=#1!50}
}
\begin{tikzpicture}[decoration={
    shape width=.65cm, shape height=.45cm,
    shape=isosceles triangle, shape sep=.75cm,
    shape backgrounds}]
  \draw [help lines] grid (3,2);
  \draw [paint=red,decorate] (0,0) -- (2,2);
  \draw [paint=blue,decorate,decoration={shape sloped=false}]
                             (1,0) -- (3,2);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    It is possible to scale the width and height of the shapes along the length
    of the decorations path. The shapes are scaled between the starting size
    and the ending size. The following keys customize the way the decoration
    shapes are scaled:

    \begin{key}{/pgf/decoration/shape scaled=\meta{boolean} (initially false)}
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes}}]
\tikzset{
  bigger/.style={decoration={shape start size=.125cm, shape end size=.5cm}},
  smaller/.style={decoration={shape start size=.5cm, shape end size=.125cm}},
  decoration={shape backgrounds,
              shape sep={.25cm, between borders},shape scaled}
}
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \fill [decorate, bigger, red!50]   (0,1) -- (3,2);
  \fill [decorate, smaller, blue!50] (0,0) -- (3,1);
\end{tikzpicture}
\end{codeexample}

        If this key is set to false (which is the default), then only the start
        width and height are used. Note that the keys |shape width| and
        |shape height| set the start and end height simultaneously.
    \end{key}

    \begin{key}{/pgf/decoration/shape start width=\meta{length} (initially 2.5pt)}
        The starting width of the shape.
    \end{key}%

    \begin{key}{/pgf/decoration/shape start height=\meta{length} (initially 2.5pt)}
        The starting height of the shape.
    \end{key}%

    \begin{stylekey}{/pgf/decoration/shape start size=\meta{length}}
        Sets both the start height and start width simultaneously.
    \end{stylekey}%

    \begin{key}{/pgf/decoration/shape end width=\meta{length} (initially 2.5pt)}
        The recommended ending width of the shape. Note that this is the width
        that a shape will take only if it is drawn exactly at the end of the
        path.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.shapes}}]
\tikzset{
  bigger/.style={decoration={shape start size=.25cm, shape end size=1cm}},
  smaller/.style={decoration={shape start size=1cm, shape end size=.25cm}},
  decoration={shape backgrounds,
              shape sep={.25cm, between borders},shape scaled}
}
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \fill [decorate,bigger,
         decoration={shape sep={.25cm, between borders}}, blue!50]
    (0,1.5) -- (3,1.5);
  \fill [decorate,smaller,
         decoration={shape sep={1cm, between centers}},   red!50]
    (0,.5)  -- (3,.5);
  \draw [gray, dotted] (0,1.625) -- (3,2)    (0,1.375) -- (3,1)
                       (0,1)     -- (3,.625) (0,0)     -- (3,.375);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/shape end height=\meta{length}}
        The recommended ending height of the shape.
    \end{key}

    \begin{stylekey}{/pgf/decoration/shape end size=\meta{length}}
        Set both the end height and end width simultaneously.
    \end{stylekey}
\end{decoration}


\subsection{Text Decorations}

\begin{pgflibrary}{decorations.text}
    The decoration in this library decorates the path with some text. This can
    be used to draw text that follows a curve.
\end{pgflibrary}

\begin{decoration}{text along path}
    This decoration decorates the path with text. This drawing of the text is a
    ``side effect'' of the decoration. The to-be-decorated path is only used to
    determine where the characters should be put and it is thrown away after
    the decoration is done. This is why no line is shown in the following
    example.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\catcode`\|12
\begin{tikzpicture}[decoration={text along path,
    text={Some long text along a ridiculously long curve that}}]
  \draw [help lines] grid (3,2);
  \draw [decorate] (0,0) -- (3,1) arc (0:180:1.5 and 1);
\end{tikzpicture}
\end{codeexample}

    \pgfname{} ``does its best'' to typeset the text, however you should note
    the following points:
    %
    \begin{itemize}
        \item Each character in the text is typeset in a separate |\hbox|. This
            means that if you want fancy things like kerning or ligatures you
            will have to manually annotate the characters in the decoration
            text within a group, for example, |W{\kern-1ptA}TER|.
        \item Each character is positioned using the center of its baseline. To
            move the text vertically (relative to the path), the additional
            decoration key |raise| should be used (see
            Section~\ref{section-decorations-adjust} for details).
        \item No attempt is made to ensure characters do not overlap when the
            angle between segments is considerably less than 180$^\circ$ (this
            is tricky to do in \TeX{} without a huge processing overhead). In
            general this should not be too much of a problem, but, once again,
            kerning can be used in most cases to overcome any undesirable
            effects.
        \item It is only possible to typeset text in math mode under
            considerable restrictions. Math mode is entered and exited using
            any character of category code 3 (e.g., in plain \TeX{} this is |$|). %$
            Math subscripts and superscripts need to be  contained within
            braces (e.g., |{^y_i}|) as do commands like |\times| or |\cdot|.
            However, even modestly complex mathematical  typesetting is
            unlikely to be successful along a path (or even desirable).
        \item Some inaccuracies in positioning may be particularly apparent at
            input segment boundaries. This can (unfortunately) only be solved
            on a case-by-case basis by individually kerning the offending
            characters within a group.
    \end{itemize}

    The following keys are used by the |text| decoration:
    %
    \begin{key}{/pgf/decoration/text=\meta{text} (initially \normalfont empty)}
        Sets the text to typeset along the curve. Consecutive spaces are
        ignored, so |\ | (or |\space| in \LaTeX) should be used to insert
        multiple spaces. It is possible to format the text using normal
        formatting commands, such as |\it|, |\bf| and |\color|, within
        customizable delimiters. Initially these delimiters are both
        {\tt\char`\|} (however, care will be needed regarding the category
        codes of delimiters -- see below).
        %
{\catcode`\|12
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\catcode`\|12
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \path [decorate,decoration={text along path,
           text={a big |\color{green}|green|| juicy apple.}}]
    (0,0) .. controls (0,2) and (3,0) .. (3,2);
\end{tikzpicture}
\end{codeexample}
}
        %
        By following the first delimiter with |+|, the formatting commands are
        added to any existing formatting.
        %
{\catcode`\|12
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \path [decorate,decoration={text along path,
           text={a |\large|big |+\bf\color{red}|red|| juicy apple.}}]
    (0,0) .. controls (0,2) and (3,0) .. (3,2);
\end{tikzpicture}
\end{codeexample}
}

        Internally, the text is stored in the macro |\pgfdecorationtext|. Any
        characters that have not been typeset when the end of the path has been
        reached will be stored in |\pgfdecorationrestoftext|.
    \end{key}

{\catcode`\|12
    \begin{key}{/pgf/decoration/text format delimiters=\marg{before}\marg{after} (initially \char`\{|\char`\}\char`\{\char`\})}
            \catcode`\|13

        Set the characters that the text decoration will use to parse
        formatting commands. If \meta{after} is empty, then \meta{before} will
        be used for both delimiters. In general you should stick to characters
        whose category codes are |11| or |12|. As |+| is used to indicate that
        the specified format commands are added  to any existing ones, you
        should avoid using |+| as a delimiter.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \path [decorate, decoration={text along path,text format delimiters={[}{]},
           text={A big [\color{red}]red[] and [\color{green}]green[] apple.}}]
    (0,0) .. controls (0,2) and (3,0) .. (3,2);
\end{tikzpicture}
\end{codeexample}
    \end{key}
}

    \begin{key}{/pgf/decoration/text color=\meta{color}  (initially black)}
        The color of the text.
    \end{key}

    \begin{key}{/pgf/decoration/reverse path=\meta{boolean} (initially false)}
        This key reverses the path. This is especially useful for typesetting
        text along different sides of curves.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \draw [gray, ->]
    [postaction={decoration={text along path,
      text={a big juicy apple}, text color=red}, decorate}]
    [postaction={decoration={text along path,
      text={a big juicy apple}, text color=blue, reverse path}, decorate}]
    (3,0) .. controls (3,2) and (0,2) .. (0,0);
\end{tikzpicture}
\end{codeexample}
        %
    \end{key}

    \begin{key}{/pgf/decoration/text align={\ttfamily\char`\{}\meta{alignment options}{\ttfamily\char`\}}}
        This changes the key path to |/pgf/decoration/text align| and executes
        \meta{alignment options}.
    \end{key}

    \begin{key}{/pgf/decoration/text align/align=\meta{alignment} (initially left)}
        Aligns the text according to \meta{alignment}, which should be one of
        |left|, |right|, or |center|.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}
\draw [help lines] grid (3,2);
\draw [red, dashed]
[postaction={decoration={text along path, text={a big juicy apple},
  text align={align=right}}, decorate}]
(0,0) .. controls (0,2) and (3,2) .. (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{stylekey}{/pgf/decoration/text align/left}
        Aligns the text to the left end of the path.
    \end{stylekey}

    \begin{stylekey}{/pgf/decoration/text align/right}
        Aligns the text to the right end of the path.
    \end{stylekey}

    \begin{stylekey}{/pgf/decoration/text align/center}
        Aligns the text to the center of the path.
    \end{stylekey}

    \begin{key}{/pgf/decoration/text align/left indent=\meta{length} (initially 0pt)}
        Specifies a distance which the automaton should move along before it
        starts typesetting the text.
    \end{key}

    \begin{key}{/pgf/decoration/text align/right indent=\meta{length} (initially 0pt)}
        Specifies a distance before the end of the path, where the automaton
        should stop typesetting the text.
    \end{key}

    \begin{key}{/pgf/decoration/text align/fit to path=\meta{boolean} (initially false)}
        This key makes the decoration automaton try to fit the text to the
        length of the path. The automaton shifts forward by a small amount
        between each character in order to fit the text to the path. If,
        however, the length of the text is longer than the length of the path
        (i.e., the automaton would have to shift \emph{backwards} between
        characters) this key will have no effect.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \draw [red, dashed]
    [postaction={decoration={text along path, text={a big juicy apple},
      text align=fit to path}, decorate}]
    (0,0) .. controls (0,2) and (3,2) .. (3,0);
\end{tikzpicture}
\end{codeexample}
        %
    \end{key}

    \begin{key}{/pgf/decoration/text align/fit to path stretching spaces=\meta{boolean} (initially false)}
        This key works like the previous key except the automaton shifts
        forward only for space characters (including |\space|, but
        \emph{excluding} |\ |).
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}
  \draw [help lines] grid (3,2);
  \draw [red, dashed]
    [postaction={decoration={text along path, text={a big juicy apple},
      text align={fit to path stretching spaces}}, decorate}]
    (0,0) .. controls (0,2) and (3,2) .. (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}
\end{decoration}

\begin{decoration}{text effects along path}
    This decoration is similar to the |text along path| decoration except that
    each character is inserted into the picture as a \tikzname\ node, and node
    options (such as |text|, |scale| and |opacity|) can be used to create `text
    effects'.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text,math}}]
\bfseries\large
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!}, text align=center,
  text effects/.cd,
    character count=\i, character total=\n,
    characters={evaluate={\c=\i/\n*100;}, text along path, text=red!\c!orange},
    character widths={text along path, xslant=0, yscale=1}}]

\path [postaction={decorate}, preaction={decorate,
  text effects={characters/.append={yscale=-1.5, opacity=0.5,
    text=gray, xslant=(\i/\n-0.5)*3}}}]
   (0,0) .. controls ++(2,1) and ++(-2,-1) .. (3,4);
\end{tikzpicture}
\end{codeexample}

    There are some important differences between this decoration and the
    |text along path| decoration:
    %
    \begin{itemize}
        \item formatting (e.g., font and color) cannot be specified in the
            decoration text. They can only be specified using the keys
            described below.
        \item as a consequence of using the \tikzname\ node options, this
            decoration is only available in \tikzname.
        \item due to the number of computations involved, this is quite a slow
            decoration.
    \end{itemize}

    The following keys are shared with the |text along path| decoration:

    \begin{key}{/pgf/decoration/text=\marg{text}}
        Set the text this decoration will use. Braces can be used to group
        multiple characters together, or commands that should not be expanded
        until they are typeset, for example |gr{\"o}{\ss}eren|. You should
        \emph{not} use the formatting delimiters or math mode characters that
        the |text along path| decoration  supports.
    \end{key}

    \begin{key}{/pgf/decoration/text align=\meta{align}}
        This sets the alignment of the text along the path. The \meta{align}
        argument should be |left|, |right| or |center|. Spreading the text out,
        or stretching the spaces between words is \emph{not} supported.
    \end{key}

    The decoration text can be thought of as consisting of \emph{characters}
    arranged in to sequences of \emph{letters} to make \emph{words} which are
    separated by a \emph{word separator}. This, however, does not mean that you
    are limited to using only natural language as the decoration text.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={000-001-010-011-100-101-110-111},
  text effects/.cd,
    path from text,
    word separator=-,
    every letter/.style={shape=rectangle, fill=blue!20, draw=blue!40}}]

\path [decorate] (0,0);
\end{tikzpicture}
\end{codeexample}

    In addition, it is possible to replace characters with \tikzname\ code:
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={000-001-010-011-100-101-110-111}, text align=center,
  text effects/.cd,
    word separator=-,
    replace characters=0 with {\fill [purple] circle [radius=2pt]; },
    replace characters=1 with {\fill [orange] circle [radius=2pt]; },
    replace characters=- with {\path circle [radius=2pt]; },
    every letter/.style={shape=rectangle, fill=blue!20, draw=blue!40}}]

\path [decorate] (0,0) .. controls ++(2,0) and ++(-2,0) .. (3,4);
\end{tikzpicture}
\end{codeexample}

    There are many keys and styles that can be used to add effects to the
    decoration text. Many of these keys have the parent path
    |/pgf/decoration/text effects/|, but for convenience, these keys can be
    accessed using the following key:

    \begin{key}{/tikz/text effects=\marg{options}}
    Execute every option in \marg{options} with the key path for each option
    temporarily set to |/pgf/decoration/text effects/|.
    \end{key}

    The following keys can be used to customise the
    appearance of text in the |text effects along path|
    decoration.

    \begin{stylekey}{/pgf/decoration/text effects/every character}
        Set the effects that will be applied to every character in the
        decoration text. The effects will typically be \tikzname\ node options.
        Initially, this style is empty so the decoration simply positions nodes
        at the appropriate position along the path. In order to make the text
        `follow the path' like the |text along path| decoration the following
        key can be added to the |every character| style.
    \end{stylekey}

    \begin{stylekey}{/pgf/decoration/text effects/text along path}
        This style automatically sets the \tikzname\ keys |transform shape| (to
        make the character slope with the path), |anchor=baseline| (to make the
        baseline of the characters `sit' on the path) and |inner xsep=0pt| (to
        horizontally fit each node to the character it contains, reducing the
        spacing between characters).
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
    text={text effects along path!}}]

\path [draw=red, dotted, postaction={decorate}]
  (0,0) .. controls ++(1,0) and ++(-1,0) .. (3,2);
\path [draw=blue, dotted, yshift=1cm, postaction={decorate},
  text effects={text along path}]
  (0,0) .. controls ++(1,0) and ++(-1,0) .. (3,2);
\end{tikzpicture}
\end{codeexample}
    \end{stylekey}

    \begin{key}{/pgf/decoration/text effects/characters=\marg{effects}}
        Shorthand for the |every character|.
    \end{key}

    \begin{stylekey}{/pgf/decoration/text effects/character \meta{number}}
        Specify additional effects for the character \meta{number}.
    \end{stylekey}

    \begin{stylekey}{/pgf/decoration/text effects/every letter}
        Specify additional effects for every letter (i.e., every character that
        isn't the word separator) in the decoration text.
    \end{stylekey}

    \begin{stylekey}{/pgf/decoration/text effects/letter \meta{number}}
        Specify the effects for letter \meta{number} in \emph{every} word.
    \end{stylekey}


\begin{stylekey}{/pgf/decoration/text effects/every first letter}
    Specify additional effects for the first letter in \emph{every} word.
\end{stylekey}

\begin{stylekey}{/pgf/decoration/text effects/every last letter}
    Specify additional effects for the last letter in \emph{every} word.
\end{stylekey}

\begin{stylekey}{/pgf/decoration/text effects/every word}
    Specify additional effects for every word in the decoration text.
\end{stylekey}

\begin{stylekey}{/pgf/decoration/text effects/word \meta{number}}
    Specify additional effects for word \meta{number} in the decoration text.
\end{stylekey}

\begin{stylekey}{/pgf/decoration/text effects/word \meta{m} letter \meta{n}}
    Specify additional effects for letter \meta{n} in word \meta{m} in the
    decoration text.
\end{stylekey}

\begin{stylekey}{/pgf/decoration/text effects/every word separator}
    Specify additional effects for every character that is a word separator.
\end{stylekey}

\begin{key}{/pgf/decoration/text effects/word separator=\meta{character} (initially space)}
    Specify the character that is to be used as the word separator. This
    \emph{must} be a single character such as |a| or |-| or the special value
    |space| (which should be used to indicate that spaces should be used as the
    separator).
\end{key}

    By default, the width for each character is calculated according to the
    bounding box of the node in which it is contained. However, if the node is
    rotated or slanted, or has a substantial |inner sep|, this bounding box
    will be quite big. The following key enables different effects to be
    applied to the node that is used to calculate the width.

    \begin{stylekey}{/pgf/decoration/text effects/every character width}
        This style is applied to the (invisible) nodes used for calculating the
        width of a character node.
    \end{stylekey}

    \begin{key}{/pgf/decoration/text effects/character widths=\marg{effects}}
        Shorthand for the |every character width| style.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!}, text align=center,
  text effects/.cd,
    character count=\i,
    characters={xslant=0.5, text along path, name=c-\i}}]

\path [decorate] (0,0) -- (3,2);
\path [decorate,
  text effects={character widths={inner xsep=0pt, xslant=0}}]
  (0,1) -- (3,3);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    It is possible to parameterize effects, perhaps for doing calculations, or
    labelling nodes based on the number of the character in the decoration
    text. To access the number of the character, and the total number of
    characters the following keys can be used. However, these keys should
    \emph{not} be used inside the style keys given above.

    \begin{key}{/pgf/decoration/text effects/character count=\meta{macro}}
        Store the number of the character being typeset in \meta{macro}.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text,
    character count=\i, every word separator/.style={fill=red!30},
    characters={text along path, shape=circle, fill=gray!50}}]

\path [decorate, text effects={characters/.append={label=above:\footnotesize\i}}] (0,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/text effects/character total=\meta{macro}}
        Store the total number of the characters in the decoration text in
        \meta{macro}. This key can be used with the |character count| key to
        produce some quite pleasing effects:
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text,math}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    character count=\i, character total=\n,
    characters={text along path, evaluate={\c=\i/\n*100;},
      text=orange!\c!blue, scale=\i/\n+0.5}}]

\path [decorate]
  (0,0) .. controls ++(1,0) and ++(-1,0) .. (3,2);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/text effects/letter count=\meta{macro}}
        Store the number of letter being typeset (i.e., the position of the
        character in the word) in \meta{macro}. Numbering starts at |1| and the
        character acting as a word separator is numbered |0|.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, letter count=\i, every word separator/.style={fill=red!30},
    characters={text along path, shape=circle, fill=gray!50}}]

\path [decorate, text effects={characters/.append={label=above:\footnotesize\i}}] (0,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/text/effetcs/letter total=\meta{macro}}
        Store the number of letters in the current word in \meta{macro}. When
        the character is the word separator, this value is |0|.
    \end{key}

    \begin{key}{/pgf/decoration/text effects/word count=\meta{macro}}
        Store the number of words in the decoration text in \meta{macro}.
        Numbering starts at |1|. When the character is the word separator,
        \meta{macro} takes the number of the previous word. If the decoration
        text starts with a word separator \meta{macro} will be |0|.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, word count=\i, every word separator/.style={fill=red!30},
    characters={text along path, shape=circle, fill=gray!50}}]

 \path [decorate, text effects={characters/.append={label=above:\footnotesize\i}}] (0,0);
\end{tikzpicture}
\end{codeexample}
        %
    \end{key}

    \begin{key}{/pgf/decoration/text effects/word total=\meta{macro}}
        Store the total number of words in the decoration text in \meta{macro}.
    \end{key}

    It is also possible to apply effects to specific characters such as
    coloring every instance of the character |a|, or changing the font of every
    |T| in the decoration text:

    \begin{key}{/pgf/decoration/text effects/style characters=\marg{characters} with \marg{effects}}
        This key enables \meta{effects} to be applied to every character in the
        decoration text that is specified in \meta{characters}.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={Falsches {\"U}ben von Xylophonmusik qu{\"a}lt jeden gr{\"o}{\ss}eren Zwerg},
  text effects/.cd,
    path from text,
    style characters=aeiou{\"U}{\"a}{\"o} with {text=blue},
    characters={text along path}}]

\path [decorate] (0,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/text effects/path from text=\opt{\marg{true or false}} (default true)}
        When this key is set to |true| and the decorated path consists only of
        a single point, the decoration will calculate the width of the
        decoration text using all the specified parameters as if the decorated
        path was actually a straight line starting from the given point. This
        `virtual' straight line is then decorated with the text.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text,
    character count=\i, character total=\n,
    characters={text along path, scale=\i/\n+0.5}}]

\path [decorate] (0,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/text effects/path from text angle=\meta{angle}}
        When used in conjunction with the |path from text| key, the straight
        line that is used as the decorated path is rotated by \meta{angle}
        around the starting point.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, path from text angle=60,
    character count=\i, character total=\n,
    characters={text along path, scale=\i/\n+0.5}}]

\path [decorate] (0,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/text effects/fit text to path=\opt{\meta{true or false}} (default true)}
        This key will make the decoration increase the space between characters
        so that the entire path is used by the decoration.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/every character/.style={text along path}}]

\path [draw=gray, postaction={decorate}, rotate=90]
  (0,0) .. controls ++(2,0) and ++(-1,0) .. (5,-1);
\path [draw=gray, postaction={decorate}, rotate=90, yshift=-1cm,
  text effects={fit text to path}]
  (0,0) .. controls ++(2,0) and ++(-1,0) .. (5,-1);
\end{tikzpicture}
\end{codeexample}
        %
    \end{key}

    \begin{key}{/pgf/decoration/text effects/scale text to path=\opt{\meta{true or false}} (default true)}
        This key will make the decoration scale the text so that the entire
        path is used by the decoration.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/every character/.style={text along path}}]

\path [draw=gray, postaction={decorate}, rotate=90]
  (0,0) .. controls ++(2,0) and ++(-1,0) .. (5,-1);
\path [draw=gray, postaction={decorate}, rotate=90, yshift=-1cm,
  text effects={scale text to path}]
  (0,0) .. controls ++(2,0) and ++(-1,0) .. (5,-1);
\end{tikzpicture}
\end{codeexample}
        %
    \end{key}

    \begin{key}{/pgf/decoration/text effects/reverse text}
        Reverse the order of the characters in the decoration text. This may be
        useful if using `right-to-left` languages. Unfortunately, any leading
        `soft' spaces in the original text will be lost.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, path from text angle=60,
    reverse text,
    character count=\i, character total=\n,
    characters={text along path, scale=\i/\n+0.5}}]

\path [decorate] (0,0) .. controls ++(1,0) and ++(-1,0) .. (3,2);
\end{tikzpicture}
\end{codeexample}

        It is important to note that the |reverse text| key reverses the text
        \emph{before} doing anything else. This means that the numbering of
        characters, letters and words will still be in the normal order, so any
        parameterized effects will have to take this into account.
        Alternatively, to get the numbering to follow the reversed text, it is
        possible to reverse the path and then invert the scale:
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, path from text angle=60,
    character count=\i, character total=\n,
    characters={text along path, scale=\i/\n+0.5}}]

\path [decorate, text effects={reverse text}] (0,0);
\path [blue, decorate, decoration={reverse path},
    text effects={characters/.append={scale=-1}}] (1,0);
\end{tikzpicture}
\end{codeexample}
        %
    \end{key}

    \begin{key}{/pgf/decoration/text effects/group letters}
        Group sequences of letters together so they are treated as a single
        `character'.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, path from text angle=60,
    every word separator/.style={fill=none},
    character count=\i, character total=\n,
    characters={text along path, fill=gray!50, scale=\i/\n+0.5}}]

\path [decorate] (0,0);
\path [decorate, text effects={group letters,
  characters/.append={fill=red!20}}]
  (1,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    The order in which the |reverse text| and |group letters| keys are applied
    is important:
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, path from text angle=60,
    every word separator/.style={fill=none},
    character count=\i, character total=\n,
    characters={text along path, fill=gray!50, scale=\i/\n+0.5}}]

\path [decorate, text effects={reverse text, group letters}] (0,0);
\path [decorate, text effects={group letters, reverse text,
  characters/.append={fill=red!20}}] (1,0);
\end{tikzpicture}
\end{codeexample}

    \begin{key}{/pgf/decoration/text effects/repeat text=\opt{\meta{times}}}
        Usually, when the decoration runs out of text, it simply stops. This
        key will make the decoration repeat the decoration text for the
        specified number of \meta{times}. If no value is given the text will be
        repeated until the path is finished. There are two points to remember
        however. Firstly the numbering of characters, letters and words will be
        restarted each time the text is repeated. Secondly, the options for
        alignment, scaling or fitting the text to the path, fitting the path to
        the text, and so on, are computed using the decoration text before the
        decoration starts. If any of these options are given the behavior of
        the |repeat text| key is undefined, but typically it will be ignored.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!\ },
  text effects/.cd,
    repeat text,
    character count=\m, character total=\n,
    characters={text along path, scale=0.5+\m/\n/2}}]

\path [draw=gray, ultra thin, postaction=decorate]
  (180:2) \foreach \a in {0,...,12}{ arc (180-\a*90:90-\a*90:1.5-\a/10) };
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/text effects/character command=\meta{macro}}
        This key specifies a command that is executed when each character is
        placed in the node. The \meta{macro} should be an ordinary \TeX\ macro
        which takes one argument. The argument will be a macro which when
        expanded will contain the current character.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\def\mycommand#1{#1$_\n$}
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, path from text angle=60, group letters,
    word count=\n,
    every word/.style={character command=\mycommand},
    characters={text along path}}]

\path [decorate] (0,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/decoration/text effects/replace characters=\meta{characters} with \marg{code}}
        Replace the node for each character in \meta{characters} with
        \meta{code}. The \meta{code} can be thought of as describing a little
        picture or marking which will be used instead of the character node.
        The origin will be the current point along the decoration path. Any
        transformations associated with the \meta{characters} (e.g., applied
        with the |every character| or |every letter| styles) will also be
        applied to \meta{code}.
        %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.text}}]
\begin{tikzpicture}[decoration={text effects along path,
  text={text effects along path!},
  text effects/.cd,
    path from text, path from text angle=60,
    replace characters=e with {\fill [red!20]   (0,1mm) circle [radius=1mm];},
    replace characters=a with {\fill [black!20] (0,1mm) circle [radius=1mm];},
    character count=\i, character total=\n,
    characters={text along path, scale=\i/\n+0.5}}]

\path [decorate] (0,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}
\end{decoration}


\subsection{Fractal Decorations}

\begin{pgflibrary}{decorations.fractals}
    The decorations of this library can be used to create fractal lines. To use
    them, you typically have to apply the decoration repeatedly to an
    originally straight path.
\end{pgflibrary}

\begin{decoration}{Koch curve type 1}
    This decoration replaces a straight line by a ``rectangular bump''. By
    repeatedly applying this replacement, different levels of the Koch curve
    fractal can be created. Its Hausdorff dimension is $\log 5/\log 3$.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.fractals}}]
\begin{tikzpicture}[decoration=Koch curve type 1]
  \draw decorate{ (0,0) -- (3,0) };
  \draw decorate{ decorate{ (0,-1.5) -- (3,-1.5) }};
  \draw decorate{ decorate{ decorate{ (0,-3) -- (3,-3) }}};
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{Koch curve type 2}
    This decoration replaces a straight line by a ``rectangular sine''. Its
    Hausdorff dimension is $3/2$.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.fractals}}]
\begin{tikzpicture}[decoration=Koch curve type 2]
  \draw decorate{ (0,0) -- (3,0) };
  \draw decorate{ decorate{ (0,-2) -- (3,-2) }};
  \draw decorate{ decorate{ decorate{ (0,-4) -- (3,-4) }}};
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{Koch snowflake}
    This decoration replaces a straight line by a ``line with a spike''. The
    Hausdorff dimension of Koch's snowflake's is $\log 4/\log 3$.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.fractals}}]
\begin{tikzpicture}[decoration=Koch snowflake]
  \draw decorate{ (0,0) -- (3,0) };
  \draw decorate{ decorate{ (0,-1) -- (3,-1) }};
  \draw decorate{ decorate{ decorate{ (0,-2) -- (3,-2) }}};
  \draw decorate{ decorate{ decorate{ decorate{ (0,-3) -- (3,-3) }}}};
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}

\begin{decoration}{Cantor set}
    This decoration replaces a straight line by a ``line with a gap in the
    middle''. The Hausdorff dimension of the Cantor set is $\log 2/\log 3$.
    %
\begin{codeexample}[preamble={\usetikzlibrary{decorations.fractals}}]
\begin{tikzpicture}[decoration=Cantor set,very thick]
  \draw decorate{ (0,0) -- (3,0) };
  \draw decorate{ decorate{ (0,-.5) -- (3,-.5) }};
  \draw decorate{ decorate{ decorate{ (0,-1) -- (3,-1) }}};
  \draw decorate{ decorate{ decorate{ decorate{ (0,-1.5) -- (3,-1.5) }}}};
\end{tikzpicture}
\end{codeexample}
    %
\end{decoration}
