% Copyright 2018 by Till Tantau
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Free Documentation License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.


\section{Plot Handler Library}
\label{section-library-plothandlers}

\begin{pgflibrary}{plothandlers}
    This library packages defines additional plot handlers, see
    Section~\ref{section-plot-handlers} for an introduction to plot handlers.
    The additional handlers are described in the following.

    This library is loaded automatically by \tikzname.
\end{pgflibrary}


\subsection{Curve Plot Handlers}

\begin{command}{\pgfplothandlercurveto}
    This handler will issue a |\pgfpathcurveto| command for each point of the
    plot, \emph{except} possibly for the first. As for the line-to handler,
    what happens with the first point can be specified using
    |\pgfsetmovetofirstplotpoint| or |\pgfsetlinetofirstplotpoint|.

    Obviously, the |\pgfpathcurveto| command needs, in addition to the points
    on the path, some control points. These are generated automatically using a
    somewhat ``dumb'' algorithm: Suppose you have three points $x$, $y$, and
    $z$ on the curve such that $y$ is between $x$ and $z$:
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlercurveto
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}

    In order to determine the control points of the curve at the point $y$, the
    handler computes the vector $z-x$ and scales it by the tension factor (see
    below). Let us call the resulting vector $s$. Then $y+s$ and $y-s$ will be
    the control points around $y$. The first control point at the beginning of
    the curve will be the beginning itself, once more; likewise the last
    control point is the end itself.
\end{command}

\begin{command}{\pgfsetplottension\marg{value}}
    Sets the factor used by the curve plot handlers to determine the distance
    of the control points from the points they control. The higher the
    curvature of the curve points, the higher this value should be. A value of
    $1$ will cause four points at quarter positions of a circle to be connected
    using a circle. The default is $0.5$.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfsetplottension{0.75}
  \pgfplothandlercurveto
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlerclosedcurve}
    This handler works like the curve-to plot handler, only it will add a new
    part to the current path that is a closed curve through the plot points.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerclosedcurve
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}


\begin{command}{\pgfplothandlermonotone}
    This handler will issue a |\pgfpathcurveto| command for each point of the
    plot, \emph{except} possibly for the first. As for the line-to handler,
    what happens with the first point can be specified using
    |\pgfsetmovetofirstplotpoint| or |\pgfsetlinetofirstplotpoint|.

    Obviously, the |\pgfpathcurveto| command needs, in addition to the points
    on the path, some control points. These are computed using The
    Fritsch-Carlson monotone cubic interpolation algorithm which roughly does
    the following:

    \begin{enumerate}
        \item Initialize tangent slopes at each input point as the
            average of the slopes of the neighboring secant lines.
        \item If the secants have opposite signes (because this is a local
            extremum), set the tangent slope to~$0$ to get an horizontal
            tangent and prevent overshoot. Same if one of the neighboring
            secants is horizontal.
        \item Adjust the tangent slopes to ensure strict monotonicity.
        \item Place the control points on the computed tangent lines,
            at one third of the $x$~distance of a secant line: if $a$, $b$
            and~$c$ are three consecutive input points and $m$~is the
            slope computed at~$B$, then the control points around~$b$ will
            be $u$~and~$v$ where $x_u = x_b - \frac{1}{3}(x_b-x_a)$,
            $y_u = y_b - \frac{1}{3} m (x_b-x_a)$,
            $x_v = x_b + \frac{1}{3}(x_c-x_b)$ and
            $y_v = y_b + \frac{1}{3} m (x_c-x_b)$.
    \end{enumerate}
\end{command}



\subsection{Constant Plot Handlers}

There are several plot handlers which produce piecewise constant interpolations
between successive points:

\begin{command}{\pgfplothandlerconstantlineto}
    This handler works like the line-to plot handler, only it will produce a
    connected, piecewise constant path to connect the points.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerconstantlineto
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlerconstantlinetomarkright}
    A variant of |\pgfplothandlerconstantlineto| which places its mark on the
    right line ends.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerconstantlinetomarkright
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlerconstantlinetomarkmid}
    A variant of |\pgfplothandlerconstantlineto| which places its mark on the
    center of the line.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerconstantlinetomarkmid
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
    The plot handler always connects two data points by a horizontal line
    starting from the previous data points, followed by a vertical line in the
    middle between the two data points, followed by a horizontal line between
    the middle and the current data point. This results in a symmetric constant
    plot handler for constant mesh width.
\end{command}

\begin{command}{\pgfplothandlerjumpmarkleft}
    This handler works like the line-to plot handler, only it will produce a
    non-connected, piecewise constant path to connect the points. If there are
    any plot marks, they will be placed on the left open pieces.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerjumpmarkleft
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlerjumpmarkright}
    This handler works like the line-to plot handler, only it will produce a
    non-connected, piecewise constant path to connect the points. If there are
    any plot marks, they will be placed on the right open pieces.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerjumpmarkright
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlerjumpmarkmid}
    This handler works like the |\pgfplothandlerconstantlinetomarkmid|, but it
    will produce a non-connected, piecewise constant path to connect the
    points. If there are any plot marks, they will be placed in the center of
    the horizontal line segment..
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerjumpmarkmid
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
    See |\pgfplothandlerconstantlinetomarkmid| for details.
\end{command}


\subsection{Comb Plot Handlers}

There are three ``comb'' plot handlers. Their name stems from the fact that the
plots they produce look like ``combs'' (more or less).

\begin{command}{\pgfplothandlerxcomb}
    This handler converts each point in the plot stream into a line from the
    $y$-axis to the point's coordinate, resulting in a ``horizontal comb''.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerxcomb
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlerycomb}
    This handler converts each point in the plot stream into a line from the
    $x$-axis to the point's coordinate, resulting in a ``vertical comb''.

    This handler is useful for creating ``bar diagrams''.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerycomb
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlerpolarcomb}
    This handler converts each point in the plot stream into a line from the
    origin to the point's coordinate.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerpolarcomb
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\pgfname\ bar or comb plots usually draw something from zero to the current
plot's coordinate. The ``zero'' offset can be changed using an input stream
which returns the desired offset successively for each processed coordinate.

There are two such streams, which can be configured independently. The first
one returns ``zeros'' for coordinate~$x$, the second one returns ``zeros'' for
coordinate~$y$. They are used as follows.
%
\begin{codeexample}[code only]
\pgfplotxzerolevelstreamstart
\pgfplotxzerolevelstreamnext % assigns \pgf@x
\pgfplotxzerolevelstreamnext
\pgfplotxzerolevelstreamnext
\pgfplotxzerolevelstreamend
\end{codeexample}
%
\begin{codeexample}[code only]
\pgfplotyzerolevelstreamstart
\pgfplotyzerolevelstreamnext % assigns \pgf@x
\pgfplotyzerolevelstreamend
\end{codeexample}
%
Different zero level streams can be implemented by overwriting these macros.

\begin{command}{\pgfplotxzerolevelstreamconstant\marg{dimension}}
    This zero level stream always returns \marg{dimension} instead of $x=0$pt.

    It is used for |xcomb| and |xbar|.
\end{command}

\begin{command}{\pgfplotyzerolevelstreamconstant\marg{dimension}}
    This zero level stream always returns \marg{dimension} instead of $y=0$pt.

    It is used for |ycomb| and |ybar|.
\end{command}


\subsection{Bar Plot Handlers}
\label{section-plotlib-bar-handlers}

While comb plot handlers produce a line-to operation to generate combs, bar
plot handlers employ rectangular shapes, allowing filled bars (or pattern
bars).

\begin{command}{\pgfplothandlerybar}
    This handler converts each point in the plot stream into a rectangle from
    the $x$-axis to the point's coordinate. The rectangle is placed centered at
    the $x$-axis.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerybar
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlerxbar}
    This handler converts each point in the plot stream into a rectangle from
    the $y$-axis to the point's coordinate. The rectangle is placed centered at
    the $y$-axis.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlerxbar
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\label{key-bar-width}%
\begin{key}{/pgf/bar width=\marg{dimension} (initially 10pt)}
\keyalias{tikz}
    Sets the width of |\pgfplothandlerxbar| and |\pgfplothandlerybar| to
    \marg{dimension}. The argument \marg{dimension} will be evaluated using the
    math parser.
\end{key}

\label{key-bar-shift}%
\begin{key}{/pgf/bar shift=\marg{dimension} (initially 0pt)}
\keyalias{tikz}
    Sets a shift used by |\pgfplothandlerxbar| and |\pgfplothandlerybar| to
    \marg{dimension}. It has the same effect as |xshift|, but it applies only
    to those bar plots. The argument \marg{dimension} will be evaluated using
    the math parser.
\end{key}

\begin{command}{\pgfplotbarwidth}
    Expands to the value of |/pgf/bar width|.
\end{command}

\begin{command}{\pgfplothandlerybarinterval}
    This handler is a variant of |\pgfplothandlerybar| which works with
    intervals instead of points.

    Bars are drawn between successive input coordinates and the width is
    determined relatively to the interval length.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,2) node {$x_1$} (1,1) node {$x_2$} (2,.5) node {$x_3$} (4,0.7) node {$x_4$};
  \pgfplothandlerybarinterval
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{2cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreampoint{\pgfpoint{4cm}{0.7cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}

    In more detail, if $(x_i,y_i)$ and $(x_{i+1},y_{i+1})$ denote successive
    input coordinates, the bar will be placed above the interval
    $[x_i,x_{i+1}]$, centered at
    %
        \[ x_i + \text{\meta{bar interval shift}} \cdot (x_{i+1} - x_i) \]
    %
    with width
    %
        \[ \text{\meta{bar interval width}} \cdot (x_{i+1} - x_i). \]
    %
    Here, \meta{bar interval shift} and \meta{bar interval width} denote the
    current values of the associated options.

    If you have $N+1$ input points, you will get $N$ bars (one for each
    interval). The $y$~value of the last point will be ignored.
\end{command}

\begin{command}{\pgfplothandlerxbarinterval}
    As |\pgfplothandlerybarinterval|, this handler provides bar plots with
    relative bar sizes and offsets, one bar for each $y$~coordinate interval.
\end{command}

\begin{key}{/pgf/bar interval shift=\marg{factor} (initially 0.5)}
\label{key-bar-interval-shift}%
\keyalias{tikz}
    Sets the \emph{relative} shift of |\pgfplothandlerxbarinterval| and
    |\pgfplothandlerybarinterval| to \meta{factor}. As
    |/pgf/bar interval width|, the argument is relative to the interval length
    of the input coordinates.

    The argument \marg{scale} will be evaluated using the math parser.
\end{key}

\begin{key}{/pgf/bar interval width=\marg{scale} (initially 1)}
\label{key-bar-interval-width}%
\keyalias{tikz}
    Sets the \emph{relative} width of |\pgfplothandlerxbarinterval| and
    |\pgfplothandlerybarinterval| to \marg{scale}. The argument is relative to
    $(x_{i+1} - x_i)$ for $y$~bar plots and relative to $(y_{i+1}-y_i)$ for
    $x$~bar plots.

    The argument \marg{scale} will be evaluated using the math parser.
    %
\begin{codeexample}[]
\begin{tikzpicture}[bar interval width=0.5]
  \draw[gray]
    (0,3) -- (0,-0.1)
    (1,3) -- (1,-0.1)
    (2,3) -- (2,-0.1)
    (4,3) -- (4,-0.1);
  \pgfplothandlerybarinterval
  \begin{scope}[bar interval shift=0.25,fill=blue]
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{2cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreampoint{\pgfpoint{4cm}{0.7cm}}
  \pgfplotstreamend
  \pgfusepath{fill}
  \end{scope}
  \begin{scope}[bar interval shift=0.75,fill=red]
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{3cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{0.2cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.7cm}}
  \pgfplotstreampoint{\pgfpoint{4cm}{0.2cm}}
  \pgfplotstreamend
  \pgfusepath{fill}
  \end{scope}
\end{tikzpicture}
\end{codeexample}
    %
    Please note that bars are always centered, so we have to use shifts $0.25$
    and $0.75$ instead of $0$ and $0.5$.
\end{key}


\subsection{Gapped Plot Handlers}
\label{section-plot-gapped}

\begin{command}{\pgfplothandlergaplineto}
    This handler will connect the points of the plots by straight line
    segments. However, at the start and the end of the lines there will be a
    small gap, given by the following key:
    %
    \begin{key}{/pgf/gap around stream point=\meta{dimension} (initially 1.5pt)}
        The \meta{dimension} by which the lines between consecutive stream
        points are shortened at the beginning and end.
    \end{key}
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \pgfplothandlergaplineto
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfplothandlergapcycle}
    Works like |\pgfplothandlergaplineto|, but the last point is connected to
    the first in the same fashion:
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \pgfplothandlergapcycle
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}


\subsection{Mark Plot Handler}
\label{section-plot-marks}

\begin{command}{\pgfplothandlermark\marg{mark code}}
    This command will execute the \meta{mark code} for some points of the plot,
    but each time the coordinate transformation matrix will be set up such that
    the origin is at the position of the point to be plotted. This way, if the
    \meta{mark code} draws a little circle around the origin, little circles
    will be drawn at some point of the plot.

    By default, a mark is drawn at all points of the plot. However, two
    parameters $r$ and $p$ influence this. First, only every $r$th mark is
    drawn. Second, the first mark drawn is the $p$th. These parameters can be
    influenced using the commands below.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlermark{\pgfpathcircle{\pgfpointorigin}{4pt}\pgfusepath{stroke}}
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}

    Typically, the \meta{code} will be |\pgfuseplotmark{|\meta{plot mark
    name}|}|, where \meta{plot mark name} is the name of a predefined plot
    mark.
\end{command}

\begin{command}{\pgfsetplotmarkrepeat\marg{repeat}}
    Sets the $r$ parameter to \meta{repeat}, that is, only every $r$th mark
    will be drawn.
\end{command}

\begin{command}{\pgfsetplotmarkphase\marg{phase}}
    Sets the $p$ parameter to \meta{phase}, that is, the first mark to be drawn
    is the $p$th, followed by the $(p+r)$th, then the $(p+2r)$th, and so on.
\end{command}

\begin{command}{\pgfplothandlermarklisted\marg{mark code}\marg{index list}}
    This command works similar to the previous one. However, marks will only be
    placed at those indices in the given \meta{index list}. The syntax for the
    list is the same as for the |\foreach| statement. For example, if you
    provide the list |1,3,...,25|, a mark will be placed only at every second
    point. Similarly, |1,2,4,8,16,32| yields marks only at those points that
    are powers of two.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlermarklisted
    {\pgfpathcircle{\pgfpointorigin}{4pt}\pgfusepath{stroke}}
    {1,3}
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfuseplotmark\marg{plot mark name}}
    Draws the given \meta{plot mark name} at the origin. The \meta{plot mark
    name} must have been previously declared using |\pgfdeclareplotmark|.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlermark{\pgfuseplotmark{pentagon}}
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfdeclareplotmark\marg{plot mark name}\marg{code}}
    Declares a plot mark for later used with the |\pgfuseplotmark| command.
    %
\begin{codeexample}[]
\pgfdeclareplotmark{my plot mark}
  {\pgfpathcircle{\pgfpoint{0cm}{1ex}}{1ex}\pgfusepathqstroke}
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfplothandlermark{\pgfuseplotmark{my plot mark}}
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfsetplotmarksize\marg{dimension}}
    This command sets the \TeX\ dimension |\pgfplotmarksize| to
    \meta{dimension}. This dimension is a ``recommendation'' for plot mark code
    at which size the plot mark should be drawn; plot mark code may choose to
    ignore this \meta{dimension} altogether. For circles, \meta{dimension}
    should  be the radius, for other shapes it should be about half the
    width/height.

    The predefined plot marks all take this dimension into account.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \draw[gray] (0,0) node {x} (1,1) node {y} (2,.5) node {z};
  \pgfsetplotmarksize{1ex}
  \pgfplothandlermark{\pgfuseplotmark{*}}
  \pgfplotstreamstart
  \pgfplotstreampoint{\pgfpoint{0cm}{0cm}}
  \pgfplotstreampoint{\pgfpoint{1cm}{1cm}}
  \pgfplotstreampoint{\pgfpoint{2cm}{0.5cm}}
  \pgfplotstreamend
  \pgfusepath{stroke}
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{textoken}{\pgfplotmarksize}
    A \TeX\ dimension that is a ``recommendation'' for the size of plot marks.
\end{textoken}

The following plot marks are predefined (the filling color has been set to
yellow):

\medskip
\begin{tabular}{lc}
    \plotmarkentry{*}
    \plotmarkentry{x}
    \plotmarkentry{+}
\end{tabular}


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