% Copyright 2019 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{Plots of Functions}
\label{section-tikz-plots}

A warning before we get started: \emph{If you are looking for an easy way to
create a normal plot of a function with scientific axes, ignore this section
and instead look at the |pgfplots| package or at the |datavisualization|
command from Part~\ref{part-dv}.}


\subsection{Overview}
\label{section-why-pgname-for-plots}

\tikzname\ can be used to create plots of functions, a job that is normally
handled by powerful programs like \textsc{gnuplot} or \textsc{mathematica}.
These programs can produce two different kinds of output: First, they can
output a complete plot picture in a certain format (like \pdf) that includes
all low-level commands necessary for drawing the complete plot (including axes
and labels). Second, they can usually also produce ``just plain data'' in the
form of a long list of coordinates. Most of the powerful programs consider it a
to be ``a bit boring'' to just output tabled data and very much prefer to
produce fancy pictures. Nevertheless, when coaxed, they can also provide the
plain data.

The advantage of creating plots directly using \tikzname\ is
\emph{consistency:} Plots created using \tikzname\ will automatically have the
same styling and fonts as those used in the rest of a document -- something
that is hard to do right when an external program gets involved. Other problems
people encounter with external programs include: Formulas will look different,
if they can be rendered at all; line widths will usually be too thick or too
thin; scaling effects upon inclusion can create a mismatch between sizes in the
plot and sizes in the text; the automatic grid generated by most programs is
mostly distracting; the automatic ticks generated by most programs are cryptic
numerics (try adding a tick reading ``$\pi$'' at the right point); most
programs make it very easy to create ``chart junk'' in a most convenient
fashion; arrows and plot marks will almost never match the arrows used in the
rest of the document. This list is not exhaustive, unfortunately.

There are basically three ways of creating plots using \tikzname:
%
\begin{enumerate}
    \item Use the |plot| path operation. How this works is explained in the
        present section. This is the most ``basic'' of the three options and
        forces you to do a lot of things ``by hand'' like adding axes or ticks.
    \item Use the |datavisualization| path command, which is documented in
        Part~\ref{part-dv}. This command is much more powerful than the |plot|
        path operation and produces complete plots including axes and ticks.
        The downside is that you cannot use it to ``just'' quickly plot a
        simple curve (or, more precisely, it is hard to use it in this way).
    \item Use the |pgfplots| package, which is basically an alternative to the
        |datavisualization| command. While the underlying philosophy of this
        package is not as ``ambitious'' as that of the command
        |datavisualization|, it is somewhat more mature, has a simpler design,
        and wider support base.
\end{enumerate}


\subsection{The Plot Path Operation}

The |plot| path operation can be used to append a line or curve to the path
that goes through a large number of coordinates. These coordinates are either
given in a simple list of coordinates, read from some file, or they are
computed on the fly.

The syntax of the |plot| comes in different versions.

\begin{pathoperation}{--plot}{\meta{further arguments}}
    This operation plots the curve through the coordinates specified in the
    \meta{further arguments}. The current (sub)path is simply continued, that
    is, a line-to operation to the first point of the curve is implicitly
    added. The details of the \meta{further arguments} will be explained in a
    moment.
\end{pathoperation}

\begin{pathoperation}{plot}{\meta{further arguments}}
    This operation plots the curve through the coordinates specified in the
    \meta{further arguments} by first ``moving'' to the first coordinate of the
    curve.
\end{pathoperation}

The \meta{further arguments} are used in different ways to specifying the
coordinates of the points to be plotted:
%
\begin{enumerate}
    \item \opt{|--|}|plot|\oarg{local
        options}\declare{|coordinates{|\meta{coordinate 1}\meta{coordinate
        2}\dots\meta{coordinate $n$}|}|}
    \item \opt{|--|}|plot|\oarg{local
        options}\declare{|file{|\meta{filename}|}|}
    \item \opt{|--|}|plot|\oarg{local options}\declare{\meta{coordinate
        expression}}
    \item \opt{|--|}|plot|\oarg{local options}\declare{|function{|\meta{gnuplot
        formula}|}|}
\end{enumerate}

These different ways are explained in the following.


\subsection{Plotting Points Given Inline}

Points can be given directly in the \TeX-file as in the following example:
%
\begin{codeexample}[]
\tikz \draw plot coordinates {(0,0) (1,1) (2,0) (3,1) (2,1) (10:2cm)};
\end{codeexample}

Here is an example showing the difference between |plot| and |--plot|:
%
\begin{codeexample}[]
\begin{tikzpicture}
  \draw (0,0) -- (1,1) plot coordinates {(2,0)  (4,0)};
  \draw[color=red,xshift=5cm]
        (0,0) -- (1,1) -- plot coordinates {(2,0)  (4,0)};
\end{tikzpicture}
\end{codeexample}


\subsection{Plotting Points Read From an External File}

The second way of specifying points is to put them in an external file named
\meta{filename}. Currently, the only file format that \tikzname\ allows is the
following: Each line of the \meta{filename} should contain one line starting
with two numbers, separated by a space. A line may also be empty or, if it
starts with |#| or |%| it is considered empty. For such lines, a ``new data
set'' is started, typically resulting in a new subpath being started in the
plot (see Section~\ref{section-plot-jumps} on how to change this behavior, if
necessary). For lines containing two numbers, they must be separated by a
space. They may be following by arbitrary text, which is ignored, \emph{except}
if it is |o| or |u|. In the first case, the point is considered to be an
\emph{outlier} and normally also results in a new subpath being started. In the
second case, the point is considered to be \emph{undefined}, which also results
in a new subpath being started. Again, see Section~\ref{section-plot-jumps} on
how to change this, if necessary. (This is exactly the format that
\textsc{gnuplot} produces when you say |set table|.)
%
\begin{codeexample}[]
\tikz \draw plot[mark=x,smooth] file {plots/pgfmanual-sine.table};
\end{codeexample}

The file |plots/pgfmanual-sine.table| reads:
%
\begin{codeexample}[code only]
#Curve 0, 20 points
#x y type
0.00000 0.00000  i
0.52632 0.50235  i
1.05263 0.86873  i
1.57895 0.99997  i
...
9.47368 -0.04889  i
10.00000 -0.54402  i
\end{codeexample}
%
It was produced from the following source, using |gnuplot|:
%
\begin{codeexample}[code only]
set table  "../plots/pgfmanual-sine.table"
set format "%.5f"
set samples 20
plot [x=0:10] sin(x)
\end{codeexample}

The \meta{local options} of the |plot| operation are local to each plot and do
not affect other plots ``on the same path''. For example, |plot[yshift=1cm]|
will locally shift the plot 1cm upward. Remember, however, that most options
can only be applied to paths as a whole. For example, |plot[red]| does not have
the effect of making the plot red. After all, you are trying to ``locally''
make part of the path red, which is not possible.


\subsection{Plotting a Function}
\label{section-tikz-plot}

When you plot a function, the coordinates of the plot data can be computed by
evaluating a mathematical expression. Since \pgfname\ comes with a mathematical
engine, you can specify this expression and then have \tikzname\ produce the
desired coordinates for you, automatically.

Since this case is quite common when plotting a function, the syntax is easy:
Following the |plot| command and its local options, you directly provide a
\meta{coordinate expression}. It looks like a normal coordinate, but inside you
may use a special macro, which is |\x| by default, but this can be changed
using the |variable| option. The \meta{coordinate expression} is then evaluated
for different values for |\x| and the resulting coordinates are plotted.

Note that you will often have to put the $x$- or $y$-coordinate inside braces,
namely whenever you use an expression involving a parenthesis.

The following options influence how the \meta{coordinate expression} is
evaluated:
%
\begin{key}{/tikz/variable=\meta{macro} (initially \string\x)}
    Sets the macro whose value is set to the different values when
    \meta{coordinate expression} is evaluated.
\end{key}

\begin{key}{/tikz/samples=\meta{number} (initially 25)}
    Sets the number of samples used in the plot.
\end{key}

\begin{key}{/tikz/domain=\meta{start}|:|\meta{end} (initially -5:5)}
    Sets the domain from which the samples are taken.
\end{key}

\begin{key}{/tikz/samples at=\meta{sample list}}
    This option specifies a list of positions for which the variable should be
    evaluated. For instance, you can say |samples at={1,2,8,9,10}| to have the
    variable evaluated exactly for values $1$, $2$, $8$, $9$, and $10$. You can
    use the |\foreach| syntax, so you can use |...| inside the \meta{sample
    list}.

    When this option is used, the |samples| and |domain| option are overruled.
    The other way round, setting either |samples| or |domain| will overrule
    this option.
\end{key}
%
\begin{codeexample}[]
\begin{tikzpicture}[domain=0:4]
  \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[color=red]    plot (\x,\x)             node[right] {$f(x) =x$};
  % \x r means to convert '\x' from degrees to _r_adians:
  \draw[color=blue]   plot (\x,{sin(\x r)})    node[right] {$f(x) = \sin x$};
  \draw[color=orange] plot (\x,{0.05*exp(\x)}) node[right] {$f(x) = \frac{1}{20} \mathrm e^x$};
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[]
\tikz \draw[scale=0.5,domain=-3.141:3.141,smooth,variable=\t]
  plot ({\t*sin(\t r)},{\t*cos(\t r)});
\end{codeexample}

\begin{codeexample}[]
\tikz \draw[domain=0:360,smooth,variable=\t]
  plot ({sin(\t)},\t/360,{cos(\t)});
\end{codeexample}


\subsection{Plotting a Function Using Gnuplot}
\label{section-tikz-gnuplot}

Often, you will want to plot points that are given via a function like $f(x) =
x \sin x$. Unfortunately, \TeX\ does not really have enough computational power
to generate the points of such a function efficiently (it is a text processing
program, after all). However, if you allow it, \TeX\ can try to call external
programs that can easily produce the necessary points. Currently, \tikzname\
knows how to call \textsc{gnuplot}.

When \tikzname\ encounters your operation
|plot[id=|\meta{id}|] function{x*sin(x)}| for the first time, it will create a
file called \meta{prefix}\meta{id}|.gnuplot|, where \meta{prefix} is
|\jobname.| by default, that is, the name of your main |.tex| file. If no
\meta{id} is given, it will be empty, which is alright, but it is better when
each plot has a unique \meta{id} for reasons explained in a moment. Next,
\tikzname\ writes some initialization code into this file followed by
|plot x*sin(x)|. The initialization code sets up things such that the |plot|
operation will write the coordinates into another file called
\meta{prefix}\meta{id}|.table|. Finally, this table file is read as if you had
said |plot file{|\meta{prefix}\meta{id}|.table}|.

For the plotting mechanism to work, two conditions must be met:
%
\begin{enumerate}
    \item You must have allowed \TeX\ to call external programs. This is often
        switched off by default since this is a security risk (you might,
        without knowing, run a \TeX\ file that calls all sorts of ``bad''
        commands). To enable this ``calling external programs'' a command line
        option must be given to the \TeX\ program. Usually, it is called
        something like |shell-escape| or |enable-write18|. For example, for my
        |pdflatex| the option |--shell-escape| can be given.
    \item You must have installed the |gnuplot| program and \TeX\ must find it
        when compiling your file.
\end{enumerate}

Unfortunately, these conditions will not always be met. Especially if you pass
some source to a coauthor and the coauthor does not have \textsc{gnuplot}
installed, he or she will have trouble compiling your files.

For this reason, \tikzname\ behaves differently when you compile your graphic
for the second time: If upon reaching |plot[id=|\meta{id}|] function{...}| the
file \meta{prefix}\meta{id}|.table| already exists \emph{and} if the
\meta{prefix}\meta{id}|.gnuplot| file contains what \tikzname\ thinks that it
``should'' contain, the |.table| file is immediately read without trying to
call a |gnuplot| program. This approach has the following advantages:
%
\begin{enumerate}
    \item If you pass a bundle of your |.tex| file and all |.gnuplot| and
        |.table| files to someone else, that person can \TeX\ the |.tex| file
        without having to have |gnuplot| installed.
    \item If the |\write18| feature is switched off for security reasons (a
        good idea), then, upon the first compilation of the |.tex| file, the
        |.gnuplot| will still be generated, but not the |.table| file. You can
        then simply call |gnuplot| ``by hand'' for each |.gnuplot| file, which
        will produce all necessary |.table| files.
    \item If you change the function that you wish to plot or its domain,
        \tikzname\ will automatically try to regenerate the |.table| file.
    \item If, out of laziness, you do not provide an |id|, the same |.gnuplot|
        will be used for different plots, but this is not a problem since the
        |.table| will automatically be regenerated for each plot on-the-fly.
        \emph{Note: If you intend to share your files with someone else, always
        use an id, so that the file can by typeset without having
        \textsc{gnuplot} installed.} Also, having unique ids for each plot will
        improve compilation speed since no external programs need to be called,
        unless it is really necessary.
\end{enumerate}

When you use |plot function{|\meta{gnuplot formula}|}|, the \meta{gnuplot
formula} must be given in the |gnuplot| syntax, whose details are beyond the
scope of this manual. Here is the ultra-condensed essence: Use |x| as the
variable and use the C-syntax for normal plots, use |t| as the variable for
parametric plots. Here are some examples:
%
\begin{codeexample}[]
\begin{tikzpicture}[domain=0:4]
  \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[color=red]    plot[id=x]   function{x}           node[right] {$f(x) =x$};
  \draw[color=blue]   plot[id=sin] function{sin(x)}      node[right] {$f(x) = \sin x$};
  \draw[color=orange] plot[id=exp] function{0.05*exp(x)} node[right] {$f(x) = \frac{1}{20} \mathrm e^x$};
\end{tikzpicture}
\end{codeexample}

The plot is influenced by the following options: First, the options |samples|
and |domain| explained earlier. Second, there are some more specialized
options.

\begin{key}{/tikz/parametric=\meta{boolean} (default true)}
    Sets whether the plot is a parametric plot. If true, then |t| must be used
    instead of |x| as the parameter and two comma-separated functions must be
    given in the \meta{gnuplot formula}. An example is the following:
    %
\begin{codeexample}[]
\tikz \draw[scale=0.5,domain=-3.141:3.141,smooth]
  plot[parametric,id=parametric-example] function{t*sin(t),t*cos(t)};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/range=\meta{start}|:|\meta{end}}
    This key sets the range of the plot. If set, all points whose
    $y$-coordinates lie outside this range will be considered to be outliers
    and will cause jumps in the plot, by default:
    %
\begin{codeexample}[]
\tikz \draw[scale=0.5,domain=-3.141:3.141, samples=100, smooth, range=-3:3]
  plot[id=tan-example] function{tan(x)};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/yrange=\meta{start}|:|\meta{end}}
    Same as |range|.
\end{key}

\begin{key}{/tikz/xrange=\meta{start}|:|\meta{end}}
    Set the $x$-range. This makes sense only for parametric plots.
    %
\begin{codeexample}[]
\tikz \draw[scale=0.5,domain=-3.141:3.141,smooth,xrange=0:1]
  plot[parametric,id=parametric-example-cut] function{t*sin(t),t*cos(t)};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/id=\meta{id}}
    Sets the identifier of the current plot. This should be a unique identifier
    for each plot (though things will also work if it is not, but not as well,
    see the explanations above). The \meta{id} will be part of a filename, so
    it should not contain anything fancy like |*| or |$|.%$
\end{key}

\begin{key}{/tikz/prefix=\meta{prefix}}
    The \meta{prefix} is put before each plot file name. The default is
    |\jobname.|, but if you have many plots, it might be better to use, say
    |plots/| and have all plots placed in a directory. You have to create the
    directory yourself.
\end{key}

\begin{key}{/tikz/raw gnuplot}
    This key causes the \meta{gnuplot formula} to be passed on to
    \textsc{gnuplot} without setting up the samples or the |plot| operation.
    Thus, you could write
    %
\begin{codeexample}[code only]
plot[raw gnuplot,id=raw-example] function{set samples 25; plot sin(x)}
\end{codeexample}
    %
    This can be useful for complicated things that need to be passed to
    \textsc{gnuplot}. However, for really complicated situations you should
    create a special external generating \textsc{gnuplot} file and use the
    |file|-syntax to include the table ``by hand''.
\end{key}

The following styles influence the plot:
%
\begin{stylekey}{/tikz/every plot (initially \normalfont empty)}
    This style is installed in each plot, that is, as if you always said
    %
\begin{codeexample}[code only]
  plot[every plot,...]
\end{codeexample}
    %
    This is most useful for globally setting a prefix for all plots by saying:
    %
\begin{codeexample}[code only]
\tikzset{every plot/.style={prefix=plots/}}
\end{codeexample}
    %
\end{stylekey}


\subsection{Placing Marks on the Plot}

As we saw already, it is possible to add \emph{marks} to a plot using the
|mark| option. When this option is used, a copy of the plot mark is placed on
each point of the plot. Note that the marks are placed \emph{after} the whole
path has been drawn/filled/shaded. In this respect, they are handled like text
nodes.

In detail, the following options govern how marks are drawn:
%
\begin{key}{/tikz/mark=\meta{mark mnemonic}}
    Sets the mark to a mnemonic that has previously been defined using the
    |\pgfdeclareplotmark|. By default, |*|, |+|, and |x| are available, which
    draw a filled circle, a plus, and a cross as marks. Many more marks become
    available when the library |plotmarks| is loaded.
    Section~\ref{section-plot-marks} lists the available plot marks.

    One plot mark is special: the |ball| plot mark is available only in
    \tikzname. The |ball color| option determines the balls's color. Do not use
    this option with a large number of marks since it will take very long to
    render in PostScript.

    \begin{tabular}{lc}
        Option & Effect \\
            \hline
        \vrule height14pt width0pt \plotmarkentrytikz{ball}
    \end{tabular}
\end{key}

\begin{key}{/tikz/mark repeat=\meta{r}}
    This option tells \tikzname\ that only every $r$th mark should be drawn.
    %
\begin{codeexample}[]
\tikz \draw plot[mark=x,mark repeat=3,smooth] file {plots/pgfmanual-sine.table};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/mark phase=\meta{p}}
    This option tells \tikzname\ that the first mark to be draw should be the
    $p$th, followed by the $(p+r)$th, then the $(p+2r)$th, and so on.
    %
\begin{codeexample}[]
\tikz \draw plot[mark=x,mark repeat=3,mark phase=6,smooth] file {plots/pgfmanual-sine.table};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/mark indices=\meta{list}}
    This option allows you to specify explicitly the indices at which a mark
    should be placed. Counting starts with 1. You can use the |\foreach|
    syntax, that is, |...| can be used.
    %
\begin{codeexample}[]
\tikz \draw plot[mark=x,mark indices={1,4,...,10,11,12,...,16,20},smooth]
  file {plots/pgfmanual-sine.table};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/mark size=\meta{dimension}}
    Sets the size of the plot marks. For circular plot marks, \meta{dimension}
    is the radius, for other plot marks \meta{dimension} should be about half
    the width and height.

    This option is not really necessary, since you achieve the same effect by
    specifying |scale=|\meta{factor} as a local option, where \meta{factor} is
    the quotient of the desired size and the default size. However, using
    |mark size| is a bit faster and more natural.
\end{key}

\begin{stylekey}{/tikz/every mark}
    This style is installed before drawing plot marks. For example, you can
    scale (or otherwise transform) the plot mark or set its color.
\end{stylekey}

\begin{key}{/tikz/mark options=\meta{options}}
    Redefines |every mark| such that it sets \marg{options}.
    %
\begin{codeexample}[]
\tikz \fill[fill=blue!20]
  plot[mark=triangle*,mark options={color=blue,rotate=180}]
    file{plots/pgfmanual-sine.table} |- (0,0);
\end{codeexample}
    %
\end{key}

\begin{stylekey}{/tikz/no marks}
    Disables markers (the same as |mark=none|).
\end{stylekey}
%
\begin{stylekey}{/tikz/no markers}
    Disables markers (the same as |mark=none|).
\end{stylekey}


\subsection{Smooth Plots, Sharp Plots, Jump Plots, Comb Plots and Bar Plots}

There are different things the |plot| operation can do with the points it reads
from a file or from the inlined list of points. By default, it will connect
these points by straight lines. However, you can also use options to change the
behavior of |plot|.

\begin{key}{/tikz/sharp plot}
    This is the default and causes the points to be connected by straight
    lines. This option is included only so that you can ``switch back'' if you
    ``globally'' install, say, |smooth|.
\end{key}

\begin{key}{/tikz/smooth}
    This option causes the points on the path to be connected using a smooth
    curve:
    %
\begin{codeexample}[]
\tikz\draw plot[smooth] file{plots/pgfmanual-sine.table};
\end{codeexample}

    Note that the smoothing algorithm is not very intelligent. You will get the
    best results if the bending angles are small, that is, less than about
    $30^\circ$ and, even more importantly, if the distances between points are
    about the same all over the plotting path.
\end{key}

\begin{key}{/tikz/tension=\meta{value}}
    This option influences how ``tight'' the smoothing is. A lower value will
    result in sharper corners, a higher value in more ``round'' curves. A value
    of $1$ results in a circle if four points at quarter-positions on a circle
    are given. The default is $0.55$. The ``correct'' value depends on the
    details of plot.
    %
\begin{codeexample}[]
\begin{tikzpicture}[smooth cycle]
  \draw                 plot[tension=0.2]
    coordinates{(0,0) (1,1) (2,0) (1,-1)};
  \draw[yshift=-2.25cm] plot[tension=0.5]
    coordinates{(0,0) (1,1) (2,0) (1,-1)};
  \draw[yshift=-4.5cm]  plot[tension=1]
    coordinates{(0,0) (1,1) (2,0) (1,-1)};
\end{tikzpicture}
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/smooth cycle}
    This option causes the points on the path to be connected using a closed
    smooth curve.
    %
\begin{codeexample}[]
\tikz[scale=0.5]
  \draw plot[smooth cycle] coordinates{(0,0) (1,0) (2,1) (1,2)}
        plot               coordinates{(0,0) (1,0) (2,1) (1,2)} -- cycle;
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/const plot}
    This option causes the points on the path to be connected using piecewise
    constant series of lines:
    %
\begin{codeexample}[]
\tikz\draw plot[const plot] file{plots/pgfmanual-sine.table};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/const plot mark left}
    Just an alias for |/tikz/const plot|.
    %
\begin{codeexample}[]
\tikz\draw plot[const plot mark left,mark=*] file{plots/pgfmanual-sine.table};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/const plot mark right}
    A variant of |/tikz/const plot| which places its mark on the right ends:
    %
\begin{codeexample}[]
\tikz\draw plot[const plot mark right,mark=*] file{plots/pgfmanual-sine.table};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/const plot mark mid}
    A variant of |/tikz/const plot| which places its mark in the middle of the
    horizontal lines:
    %
\begin{codeexample}[]
\tikz\draw plot[const plot mark mid,mark=*] file{plots/pgfmanual-sine.table};
\end{codeexample}
    %
    More precisely, it generates vertical lines in the middle between each pair
    of consecutive points. If the mesh width is constant, this leads to
    symmetrically placed marks (``middle'').
\end{key}

\begin{key}{/tikz/jump mark left}
    This option causes the points on the path to be drawn using piecewise
    constant, non-connected series of lines. If there are any marks, they will
    be placed on left open ends:
    %
\begin{codeexample}[]
\tikz\draw plot[jump mark left, mark=*] file{plots/pgfmanual-sine.table};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/jump mark right}
    This option causes the points on the path to be drawn using piecewise
    constant, non-connected series of lines. If there are any marks, they will
    be placed on right open ends:
    %
\begin{codeexample}[]
\tikz\draw plot[jump mark right, mark=*] file{plots/pgfmanual-sine.table};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/jump mark mid}
    This option causes the points on the path to be drawn using piecewise
    constant, non-connected series of lines. If there are any marks, they will
    be placed in the middle of the horizontal line segments:
    %
\begin{codeexample}[]
\tikz\draw plot[jump mark mid, mark=*] file{plots/pgfmanual-sine.table};
\end{codeexample}

    In case of non-constant mesh widths, the same remarks as for
    |const plot mark mid| apply.
\end{key}

\begin{key}{/tikz/ycomb}
    This option causes the |plot| operation to interpret the plotting points
    differently. Instead of connecting them, for each point of the plot a
    straight line is added to the path from the $x$-axis to the point,
    resulting in a sort of ``comb'' or ``bar diagram''.
    %
\begin{codeexample}[]
\tikz\draw[ultra thick] plot[ycomb,thin,mark=*] file{plots/pgfmanual-sine.table};
\end{codeexample}

\begin{codeexample}[]
\begin{tikzpicture}[ycomb]
  \draw[color=red,line width=6pt]
    plot coordinates{(0,1) (.5,1.2) (1,.6) (1.5,.7) (2,.9)};
  \draw[color=red!50,line width=4pt,xshift=3pt]
    plot coordinates{(0,1.2) (.5,1.3) (1,.5) (1.5,.2) (2,.5)};
\end{tikzpicture}
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/xcomb}
    This option works like |ycomb| except that the bars are horizontal.
    %
\begin{codeexample}[]
\tikz \draw plot[xcomb,mark=x] coordinates{(1,0) (0.8,0.2) (0.6,0.4) (0.2,1)};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/polar comb}
    This option causes a line from the origin to the point to be added to the
    path for each plot point.
    %
\begin{codeexample}[]
\tikz \draw plot[polar comb,
     mark=pentagon*,mark options={fill=white,draw=red},mark size=4pt]
   coordinates {(0:1cm) (30:1.5cm) (160:.5cm) (250:2cm) (-60:.8cm)};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/ybar}
    This option produces fillable bar plots. It is thus very similar to
    |ycomb|, but it employs rectangular shapes instead of line-to operations.
    It thus allows to use any fill or pattern style.
    %
\begin{codeexample}[]
\tikz\draw[draw=blue,fill=blue!60!black] plot[ybar] file{plots/pgfmanual-sine.table};
\end{codeexample}

\begin{codeexample}[]
\begin{tikzpicture}[ybar]
  \draw[color=red,fill=red!80,bar width=6pt]
    plot coordinates{(0,1) (.5,1.2) (1,.6) (1.5,.7) (2,.9)};
  \draw[color=red!50,fill=red!20,bar width=4pt,bar shift=3pt]
    plot coordinates{(0,1.2) (.5,1.3) (1,.5) (1.5,.2) (2,.5)};
\end{tikzpicture}
\end{codeexample}
    %
    The use of |bar width| and |bar shift| is explained in the |plothandlers|
    library documentation, section~\ref{section-plotlib-bar-handlers}. Please
    refer to page~\pageref{key-bar-width}.
\end{key}

\begin{key}{/tikz/xbar}
    This option works like |ybar| except that the bars are horizontal.
    %
\begin{codeexample}[preamble={\usetikzlibrary{patterns}}]
\tikz \draw[pattern=north west lines] plot[xbar]
   coordinates{(1,0) (0.4,1) (1.7,2) (1.6,3)};
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/ybar interval}
    As |/tikz/ybar|, this options produces vertical bars. However, bars are
    centered at coordinate \emph{intervals} instead of interval edges, and the
    bar's width is also determined relatively to the interval's length:
    %
\begin{codeexample}[]
\begin{tikzpicture}[ybar interval,x=10pt]
  \draw[color=red,fill=red!80]
    plot coordinates{(0,2) (2,1.2) (3,.3) (5,1.7) (8,.9) (9,.9)};
\end{tikzpicture}
\end{codeexample}
    %
    Since there are $N$ intervals $[x_i,x_{i+1}]$ for given $N+1$ coordinates,
    you will always have one coordinate more than bars. The last $y$ value will
    be ignored.

    You can configure relative shifts and relative bar widths, which is
    explained in the |plothandlers| library documentation,
    section~\ref{section-plotlib-bar-handlers}. Please refer to
    page~\pageref{key-bar-interval-width}.
\end{key}

\begin{key}{/tikz/xbar interval}
    Works like |ybar interval|, but for horizontal bar plots.
    %
\begin{codeexample}[]
\begin{tikzpicture}[xbar interval,x=0.5cm,y=0.5cm]
  \draw[color=red,fill=red!80]
    plot coordinates {(3,0) (2,1) (4,1.5) (1,4) (2,6) (2,7)};
\end{tikzpicture}
\end{codeexample}
    %
\end{key}

\begin{key}{/tikz/only marks}
    This option causes only marks to be shown; no path segments are added to
    the actual path. This can be useful for quickly adding some marks to a
    path.
    %
\begin{codeexample}[]
\tikz \draw (0,0) sin (1,1) cos (2,0)
  plot[only marks,mark=x] coordinates{(0,0) (1,1) (2,0) (3,-1)};
\end{codeexample}
\end{key}