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diff --git a/Master/texmf-dist/doc/generic/pgf/pgfmanual-en-base-plots.tex b/Master/texmf-dist/doc/generic/pgf/pgfmanual-en-base-plots.tex new file mode 100644 index 00000000000..d11922a09b7 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pgf/pgfmanual-en-base-plots.tex @@ -0,0 +1,587 @@ +% 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{Creating Plots} +\label{section-plots} + +This section describes the |plot| module. + +\begin{pgfmodule}{plot} + This module provides a set of commands that are intended to make it + reasonably easy to plot functions using \pgfname. It is loaded + automatically by |pgf|, but you can load it manually if you have only + included |pgfcore|. +\end{pgfmodule} + + +\subsection{Overview} + +There are different reasons for using \pgfname\ for creating plots rather than +some more powerful program such as \textsc{gnuplot} or \textsc{mathematica}, as +discussed in Section~\ref{section-why-pgname-for-plots}. So, let us assume that +-- for whatever reason -- you wish to use \pgfname\ for generating a plot. + +\pgfname\ (conceptually) uses a two-stage process for generating plots. First, +a \emph{plot stream} must be produced. This stream consists (more or less) of a +large number of coordinates. Second a \emph{plot handler} is applied to the +stream. A plot handler ``does something'' with the stream. The standard handler +will issue line-to operations to the coordinates in the stream. However, a +handler might also try to issue appropriate curve-to operations in order to +smooth the curve. A handler may even do something else entirely, like writing +each coordinate to another stream, thereby duplicating the original stream. + +Both for the creation of streams and the handling of streams different sets of +commands exist. The commands for creating streams start with |\pgfplotstream|, +the commands for setting the handler start with |\pgfplothandler|. + + +\subsection{Generating Plot Streams} + +\subsubsection{Basic Building Blocks of Plot Streams} + +A \emph{plot stream} is a (long) sequence of the following commands: +% +\begin{enumerate} + \item |\pgfplotstreamstart|, + \item |\pgfplotstreampoint|, + \item |\pgfplotstreampointoutlier|, + \item |\pgfplotstreampointundefined|, + \item |\pgfplotstreamnewdataset|, + \item |\pgfplotstreamspecial|, and + \item |\pgfplotstreamend|. +\end{enumerate} +% +Between calls of these commands arbitrary other code may be called. Obviously, +the stream should start with the first command and end with the last command. +Here is an example of a plot stream: +% +\begin{codeexample}[code only] +\pgfplotstreamstart +\pgfplotstreampoint{\pgfpoint{1cm}{1cm}} +\newdimen\mydim +\mydim=2cm +\pgfplotstreampoint{\pgfpoint{\mydim}{2cm}} +\advance \mydim by 3cm +\pgfplotstreampoint{\pgfpoint{\mydim}{2cm}} +\pgfplotstreamend +\end{codeexample} + +Streams are \emph{global}, meaning that they are not influenced by \TeX\ +groups. + +\begin{command}{\pgfplotstreamstart} + This command signals that a plot stream starts. The effect of this command + is to call the internal command |\pgf@plotstreamstart|, which is set by the + current plot handler to do whatever needs to be done at the beginning of + the plot. It will also reset the meaning of the internal commands like + |\pgf@plotstreampoint| to the initial setting for the plot handler (what + this means will be explained in a moment). +\end{command} + +\begin{command}{\pgfplotstreampoint\marg{point}} + This command adds a \meta{point} to the current plot stream. The effect of + this command is to call the internal command |\pgf@plotstreampoint|, which + is also set by the current plot handler. This command should now ``handle'' + the point in some sensible way. For example, a line-to command might be + issued for the point. + + When a plot handler is installed, it will setup the internal command + |\pgf@plotstreampoint| in some way. It is permissible to change the meaning + of this internal command during a stream. For instance, a handler might + setup |\pgf@plotstreampoint| in some sensible way for the first point and + then redefine it so that subsequent points are handled in some other way. + + As mentioned earlier, the |\pgfplotstreamstart| will always reset the + definition of the internal command to the initial meaning it had when the + handler was installed. This is true for the other commands mentioned in the + following. +\end{command} + +\begin{command}{\pgfplotstreampointoutlier\marg{point}} + An \emph{outlier} is a point that is ``out of bounds'' in some way. For + instance, it might have very large coordinates or the coordinates might + just be outside some specified range. Nevertheless, an outlier is still a + well-defined point. This command is issued, for instance, by + \textsc{gnuplot} when a value is outside the specified range. + + You can configure how outliers are treated using the following key: + % + \begin{key}{/pgf/handle outlier points in plots=\meta{how} (initially jump)} + \keyalias{tikz} + You can set \meta{how} to one of the following values: + % + \begin{itemize} + \item |plot| This will cause the outlier to be drawn normally, just + as if |\pgfplotstreampoint| had been used rather than this + command. + \item |ignore| The outlier will be completely ignored, just as if + the command had not been used at all. + \item |jump| This causes the internal macro |\pgf@plotstreamjump| + to be called. A ``jump'' in a stream is a position where a + ``gap'' is introduced. For instance, a simple line-to plot + handler will stop the current subpath at a jump position and + begin with a move-to operation at the next normal point of the + stream. + + The net effect of this setting is that at outlier points plots + get interrupted and ``restarted'' when the points are no longer + outliers. This is usually the behavior you will be looking for. + \end{itemize} + \end{key} +\end{command} + +\begin{command}{\pgfplotstreampointundefined} + This command indicated that the stream contains an ``undefined'' point like + a point where some coordinate results for a division by zero. Such a point + cannot be plotted, which is why it is not given as a parameter. However, + such a point \emph{can} result in a jump in the plot, depending on the + setting of the following key: + % + \begin{key}{/pgf/handle undefined points in plots=\meta{how} (initially jump)} + \keyalias{tikz} + You can set \meta{how} to one of the following values: + % + \begin{itemize} + \item |ignore| The undefined point will be completely ignored, just + as if the command had not been used at all. + \item |jump| This causes the internal macro |\pgf@plotstreamjump| + to be called. + \end{itemize} + \end{key} +\end{command} + +\begin{command}{\pgfplotstreamnewdataset} + This command indicated that in the stream a ``new data set'' starts. So, + the stream does not end, but there is a logical break in the data. For + example, when a table is read from a file, empty lines are interpreted as + indicating new data sets. What happens when a new data set is encountered + is governed by the following key: + % + \begin{key}{/pgf/handle new data sets in plots=\meta{how} (initially jump)} + \keyalias{tikz} + You can set \meta{how} to one of the following values: + % + \begin{itemize} + \item |ignore| The command will be completely ignored, just as if + the command had not been used at all. + \item |jump| This causes the internal macro |\pgf@plotstreamjump| + to be called. + \end{itemize} + \end{key} +\end{command} + +\begin{command}{\pgfplotstreamspecial\marg{text}} + This command causes |\pgf@plotstreamspecial| to be called with \meta{text} + as its parameter. This allows handler-specific information to be passed to + the handler. All normal handlers ignore this command. +\end{command} + +\begin{command}{\pgfplotstreamend} + This command signals that a plot stream ends. It calls + |\pgf@plotstreamend|, which should now do any necessary ``cleanup''. +\end{command} + +Note that plot streams are not buffered, that is, the different points are +handled immediately. However, using the recording handler, it is possible to +record a stream. + + +\subsubsection{Commands That Generate Plot Streams} +\label{section-plot-jumps} + +Plot streams can be created ``by hand'' as in the earlier example. However, +most of the time the coordinates will be produced internally by some command. +For example, the |\pgfplotxyfile| reads a file and converts it into a plot +stream. + +\begin{command}{\pgfplotxyfile\marg{filename}} + This command will try to open the file \meta{filename}. If this succeeds, + it will convert the file contents into a plot stream as follows: A + |\pgfplotstreamstart| is issued. Then, for each empty line a + |\pgfplotstreamnewdataset| is produced. Other lines in the file should + start with two numbers separated by a space, such as |0.1 1| or |100 -.3|. + The numbers may be followed by some text, which will be ignore + \emph{except} if it is exactly ``|u|'' or ``|o|''. For ``|u|'' the point + is considered to be undefined and |\pgfplotstreampointundefined| is called. + For ``|o|'' the point is considered to be an outlier and + |\pgfplotstreampointoutlier| is called. Otherwise, each pair \meta{x} and + \meta{y} of numbers is converted into one plot stream point in the + $xy$-coordinate system. Thus, a line like + % +\begin{codeexample}[code only, tikz syntax=false] +0 Nan u +1 1 some text +2 4 +3 9 + +4 16 o +5 25 oo +\end{codeexample} + % + is turned into + % +\begin{codeexample}[code only] +\pgfplotstreamstart +\pgfplotstreampointundefined +\pgfplotstreampoint{\pgfpointxy{1}{1}} +\pgfplotstreampoint{\pgfpointxy{2}{4}} +\pgfplotstreampoint{\pgfpointxy{3}{9}} +\pgfplotstreamnewdataset +\pgfplotstreampointoutlier{\pgfpointxy{4}{16}} +\pgfplotstreampoint{\pgfpointxy{5}{25}} +\pgfplotstreamend +\end{codeexample} + % + (Note that the last line is not an outlier because |oo| is not the same as + |o|). + + The two characters |%| and |#| are also allowed in a file and they are both + treated as comment characters. Thus, a line starting with either of them is + treated as empty. + + When the file has been read completely, |\pgfplotstreamend| is called. +\end{command} + +\begin{command}{\pgfplotxyzfile\marg{filename}} + This command works like |\pgfplotxyfile|, only \emph{three} numbers are + expected on each non-empty line. They are converted into points in the + $xyz$-coordinate system. Consider, the following file: + % +\begin{codeexample}[code only, tikz syntax=false] +% Some comments +# more comments +2 -5 1 first entry +2 -.2 2 o +2 -5 2 third entry +\end{codeexample} + % + It is turned into the following stream: + % +\begin{codeexample}[code only] +\pgfplotstreamstart +\pgfplotstreamnewdataset +\pgfplotstreamnewdataset +\pgfplotstreampoint{\pgfpointxyz{2}{-5}{1}} +\pgfplotstreampointoutlier{\pgfpointxyz{2}{-.2}{2}} +\pgfplotstreampoint{\pgfpointxyz{2}{-5}{2}} +\pgfplotstreamend +\end{codeexample} + % +\end{command} + +Currently, there is no command that can decide automatically whether the +$xy$-coordinate system should be used or whether the $xyz$-system should be +used. However, it would not be terribly difficult to write a ``smart file +reader'' that parses coordinate files a bit more intelligently. + +\begin{command}{\pgfplotfunction\marg{variable}\marg{sample list}\marg{point}} + This command will produce coordinates by iterating the \meta{variable} over + all values in \meta{sample list}, which should be a list in the |\foreach| + syntax. For each value of \meta{variable}, the \meta{point} is evaluated + and the resulting coordinate is inserted into the plot stream. + % +\begin{codeexample}[] +\begin{tikzpicture}[x=3.8cm/360] + \pgfplothandlerlineto + \pgfplotfunction{\x}{0,5,...,360}{\pgfpointxy{\x}{sin(\x)+sin(3*\x)}} + \pgfusepath{stroke} +\end{tikzpicture} +\end{codeexample} + +\begin{codeexample}[] +\begin{tikzpicture}[y=3cm/360] + \pgfplothandlerlineto + \pgfplotfunction{\y}{0,5,...,360}{\pgfpointxyz{sin(2*\y)}{\y}{cos(2*\y)}} + \pgfusepath{stroke} +\end{tikzpicture} +\end{codeexample} + + Be warned that if the expressions that need to evaluated for each point are + complex, then this command can be very slow. +\end{command} + +\begin{command}{\pgfplotgnuplot\oarg{prefix}\marg{function}} + This command will ``try'' to call the \textsc{gnuplot} program to generate + the coordinates of the \meta{function}. In detail, the following happens: + + This command works with two files: \meta{prefix}|.gnuplot| and + \meta{prefix}|.table|. If the optional argument \meta{prefix} is not + given, it is set to |\jobname|. + + Let us start with the situation where none of these files exists. Then + \pgfname\ will first generate the file \meta{prefix}|.gnuplot|. In this + file it writes + % +\begin{codeexample}[code only, tikz syntax=false] +set table "#1.table"; set format "%.5f" +\end{codeexample} + % + where |#1| is replaced by \meta{prefix}. Then, in a second line, it writes + the text \meta{function}. + + Next, \pgfname\ will try to invoke the program |gnuplot| with the argument + \meta{prefix}|.gnuplot|. This call may or may not succeed, depending on + whether the |\write18| mechanism (also known as shell escape) is switched + on and whether the |gnuplot| program is available. + + Assuming that the call succeeded, the next step is to invoke + |\pgfplotxyfile| on the file \meta{prefix}|.table|; which is exactly the + file that has just been created by |gnuplot|. + % +\begin{codeexample}[] +\begin{tikzpicture} + \draw[help lines] (0,-1) grid (4,1); + \pgfplothandlerlineto + \pgfplotgnuplot[plots/pgfplotgnuplot-example]{plot [x=0:3.5] x*sin(x)} + \pgfusepath{stroke} +\end{tikzpicture} +\end{codeexample} + + The more difficult situation arises when the |.gnuplot| file exists, which + will be the case on the second run of \TeX\ on the \TeX\ file. In this case + \pgfname\ will read this file and check whether it contains exactly what + \pgfname\ ``would have written'' into this file. If this is not the case, + the file contents is overwritten with what ``should be there'' and, as + above, |gnuplot| is invoked to generate a new |.table| file. However, if + the file contents is ``as expected'', the external |gnuplot| program is + \emph{not} called. Instead, the \meta{prefix}|.table| file is immediately + read. + + As explained in Section~\ref{section-tikz-gnuplot}, the net effect of the + above mechanism is that |gnuplot| is called as seldom as possible and that + when you pass along the |.gnuplot| and |.table| files with your |.tex| file + to someone else, that person can \TeX\ the |.tex| file without having + |gnuplot| installed and without having the |\write18| mechanism switched + on. + + \begin{key}{/pgf/plot/gnuplot call=\meta{gnuplot invocation} (initially gnuplot)} + This key can be used to change the way gnuplot is called. + + Some portable MiK\TeX{} distribution needs something like the + following. + % +\begin{codeexample}[code only] + \pgfkeys{/pgf/plot/gnuplot call="/Programs/gnuplot/binary/gnuplot"} +\end{codeexample} + \end{key} +\end{command} + + +\subsection{Plot Handlers} +\label{section-plot-handlers} + +A \emph{plot handler} determines what ``should be done'' with a plot stream. +You must set the plot handler before the stream starts. The following commands +install the most basic plot handlers; more plot handlers are defined in the +file |pgflibraryplothandlers|, which is documented in +Section~\ref{section-library-plothandlers}. + +All plot handlers work by setting or redefining the following three macros: +|\pgf@plotstreamstart|, |\pgf@plotstreampoint|, and |\pgf@plotstreamend|. + +\begin{command}{\pgfplothandlerlineto} + This handler will issue a |\pgfpathlineto| command for each point of the + plot, \emph{except} possibly for the first. What happens with the first + point can be specified using the two commands described below. + % +\begin{codeexample}[] +\begin{pgfpicture} + \pgfpathmoveto{\pgfpointorigin} + \pgfplothandlerlineto + \pgfplotstreamstart + \pgfplotstreampoint{\pgfpoint{1cm}{0cm}} + \pgfplotstreampoint{\pgfpoint{2cm}{1cm}} + \pgfplotstreampoint{\pgfpoint{3cm}{2cm}} + \pgfplotstreampoint{\pgfpoint{1cm}{2cm}} + \pgfplotstreamend + \pgfusepath{stroke} +\end{pgfpicture} +\end{codeexample} + % +\end{command} + +\begin{command}{\pgfsetmovetofirstplotpoint} + Specifies that the line-to plot handler (and also some other plot handlers) + should issue a move-to command for the first point of the plot instead of a + line-to. This will start a new part of the current path, which is not + always, but often, desirable. This is the default. +\end{command} + +\begin{command}{\pgfsetlinetofirstplotpoint} + Specifies that plot handlers should issue a line-to command for the first + point of the plot. + % +\begin{codeexample}[] +\begin{pgfpicture} + \pgfpathmoveto{\pgfpointorigin} + \pgfsetlinetofirstplotpoint + \pgfplothandlerlineto + \pgfplotstreamstart + \pgfplotstreampoint{\pgfpoint{1cm}{0cm}} + \pgfplotstreampoint{\pgfpoint{2cm}{1cm}} + \pgfplotstreampoint{\pgfpoint{3cm}{2cm}} + \pgfplotstreampoint{\pgfpoint{1cm}{2cm}} + \pgfplotstreamend + \pgfusepath{stroke} +\end{pgfpicture} +\end{codeexample} + % +\end{command} + +\begin{command}{\pgfplothandlerpolygon} + This handler works like the line-to plot handler, only the line is closed + at the end using |\pgfpathclose|, resulting in a polygon. +\end{command} + +\begin{command}{\pgfplothandlerdiscard} + This handler will simply throw away the stream. +\end{command} + +\begin{command}{\pgfplothandlerrecord\marg{macro}} + When this handler is installed, each time a plot stream command is called, + this command will be appended to \meta{macro}. Thus, at the end of the + stream, \meta{macro} will contain all the commands that were issued on the + stream. You can then install another handler and invoke \meta{macro} to + ``replay'' the stream (possibly many times). + % +\begin{codeexample}[] +\begin{pgfpicture} + \pgfplothandlerrecord{\mystream} + \pgfplotstreamstart + \pgfplotstreampoint{\pgfpoint{1cm}{0cm}} + \pgfplotstreampoint{\pgfpoint{2cm}{1cm}} + \pgfplotstreampoint{\pgfpoint{3cm}{1cm}} + \pgfplotstreampoint{\pgfpoint{1cm}{2cm}} + \pgfplotstreamend + \pgfplothandlerlineto + \mystream + \pgfplothandlerclosedcurve + \mystream + \pgfusepath{stroke} +\end{pgfpicture} +\end{codeexample} + % +\end{command} + + +\subsection{Defining New Plot Handlers} + +You can define new plot handlers using the following command: + +\begin{command}{\pgfdeclareplothandler\marg{macro}\marg{arguments}\marg{configuration}} + This command creates a new plot handler that can subsequently be called + using the macro \meta{macro}. This macro take the arguments given in + \meta{arguments}, which can be a list like |#1#2| if \meta{macro} should be + invoked with two arguments. Here is a typical example: + % +\begin{codeexample}[code only] +\pgfdeclareplothandler{\myhandler}{#1}{...} +... +\myhandler{foo} +\pgfplotstreamstart +... +\pgfplotstreamend +\end{codeexample} + + The \meta{configuration} is used to define the behavior of the handler. It + is a list of key--value pairs, where the following keys are allowed: + % + \begin{itemize} + \item |start=|\meta{code}. The \meta{code} will be executed whenever + |\pgfplotstreamstart| is used while the handler \meta{macro} is + selected. Inside the \meta{code}, you can use |#1|, |#2|, and so on + to refer to the parameters that were given to \meta{macro}: + % +\begin{codeexample}[width=6cm] +\pgfdeclareplothandler{\myhandler}{#1}{ + start = Hi #1., + end = Bye #1., +} +\myhandler{foo} +\pgfplotstreamstart +\pgfplotstreamend +\myhandler{bar} +\pgfplotstreamstart +\pgfplotstreamend +\end{codeexample} + % + \item |end=|\meta{code} Works just like |start|. + \item |point=|\meta{code}. The \meta{code} will be executed whenever + |\pgfplotstreampoint| is used while the handler \meta{macro} is in + force. Inside the \meta{code}, you can use |#1|, |#2|, and so on to + refer to the arguments give to \meta{macro}, while you can use + |##1| to refer to the argument given to |\pgfplotstreampoint| + itself (this will be the coordinate). + % +\begin{codeexample}[] +\pgfdeclareplothandler{\myhandler}{#1}{ + point=\pgfpathcircle{##1}{#1} % ##1 is the coordinate, + % #1 the parameter for \myhandler +} +\begin{pgfpicture} + \myhandler{1pt} + \pgfplotstreamstart + \pgfplotstreampoint{\pgfpoint{0pt}{0pt}} + \pgfplotstreampoint{\pgfpoint{3pt}{3pt}} + \pgfplotstreampoint{\pgfpoint{6pt}{3pt}} + \pgfplotstreampoint{\pgfpoint{9pt}{0pt}} + \pgfplotstreamend + \pgfusepath{stroke} + \myhandler{3pt} + \pgfplotstreamstart + \pgfplotstreampoint{\pgfpoint{0pt}{0pt}} + \pgfplotstreampoint{\pgfpoint{9pt}{0pt}} + \pgfplotstreamend + \pgfusepath{stroke} +\end{pgfpicture} +\end{codeexample} + % + The \meta{code} will also be called for + |\pgfplotstreampointoutlier| when this command has been configured + to |plot| the outliers. + \item |jump=|\meta{code} The \meta{code} will be called whenever a jump + has been requested indirectly via an outlier point, and undefined + point, or a new data set (for each of which the command needs to be + configured to |jump|). As always, inside the \meta{code} you can + access |#1| and so on. + \item |special=|\meta{code} Causes \meta{code} to be executed whenever + |\pgfplotstreamspecial|\marg{something} is used. Inside the + \meta{code}, you can access \meta{something} via |##1| and the + parameters of \meta{macro} as |#1|, |#2|, and so on. + \end{itemize} + + In addition to the above keys, there exist also ``code macro versions'' of + them: + % + \begin{itemize} + \item |point macro=|\meta{some macro}. Causes |\pgfplotstreampoint| to + call \meta{some macro} directly (actually, |\pgf@plotstreampoint| + is set to be equal to \meta{some macro}). Inside the \meta{some + macro} you can use |#1| to access the coordinate passed to + |\pgfplotstreampoint| and you can no longer access the parameters + passed to the original call to \meta{macro} that installed the + handler. So, \meta{some macro} must take exactly one argument, + namely |#1|. + \item |special macro=|\meta{some macro}. As |point macro|, only for + specials. + \item |start macro=|\meta{some macro}. Causes \meta{some macro} to be + executed at the start. This macro, like the below ones, may not + take any parameters and will not have access to the parameters + passed to the original \meta{macro}. + \item |end macro=|\meta{some macro}. As above. + \item |jump macro=|\meta{some macro}. As above. + \end{itemize} +\end{command} + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "pgfmanual" +%%% End: |