%%% File: mfpman.tex
%%% A part of mfpic 0.7a beta 2004/04/16
%%%
%  Documentation of mfpic macros
\documentclass[letterpaper]{article}

\usepackage{pslatex}

\usepackage{mfpdoc}
\pagestyle{mfpdoc}
\usepackage{verbatim}
\usepackage{makeidx}
\makeindex

\ifpdf
\usepackage[pdftex,colorlinks,pdfpagemode=none,pdfstartview=FitH,%
plainpages=false,hypertexnames=true]{hyperref}
\pdfstringdefDisableCommands{\def\cs#1{\otherbackslash#1}%
    \def\opt#1{#1}\def\prog#1{#1}}
\fi

\title{\Mfp: Pictures in \TeX\\ with Metafont and MetaPost}
\author{Dr Thomas E. Leathrum
\and Geoffrey Tobin\thanks{\email{G.Tobin@latrobe.edu.au}}
\and Daniel H. Luecking\thanks{\email {luecking@uark.edu}}}
\date{\mfpdate}

\begin{document}

\pagenumbering{roman}
\maketitle
\tableofcontents

\clearpage
\pagenumbering{arabic}

\section{Introduction}\label{introduction}

\subsection{Why?}\label{why}

Tom got the idea for \mfp%
    \footnote{If you're wondering how to pronounce `\mfp': I always say
    `em-eff-\textbf{pick}', speaking the first two letters. ---DHL.} %
mostly out of a feeling of frustration. Different output mechanisms for
printing or viewing \TeX{} DVI files each have their own ways to include
pictures.  More often than not, there are provisions for including
graphic objects into a \prog{DVI} file using \TeX{} \cs{special}'s.
However, this technique seemed far from \TeX's ideal of
device independence because different \TeX{} output drivers recognize
different \cs{special's}, and handle them in different ways.

\LaTeX's \env{picture} environment has a hopelessly limited supply of
available objects to draw---if you want to draw a graph of a polynomial
curve, you're out of luck.

There was, of course, \PiCTeX, which is wonderfully flexible and general,
but its most obvious feature was its speed---or rather lack of it.
Processing a single picture in \PiCTeX{} could often take several seconds.

It occurred to Tom that it might be possible to take advantage of the
fact that \MF{} is \emph{designed} for drawing things. The result of
pursuing this idea is \mfp, a set of macros for \TeX{} and
\MF{} which incorporate \MF-drawn pictures into a \TeX{} file.

With the creation of \MP{} by John Hobby, and the almost universal
availability of free \PS{} interpreters like \GS, some \mfp{} users
wanted to run their \mfp{} output through \MP, to produce \PS{}
pictures. Moreover, users wanted to be able to use \pdfTeX, which does
not get along well with PK fonts, but is quite happy with \MP{}
pictures. Unfortunately \file{grafbase.mf}, which contained the \MF{}
macros responsible for processing \mfp's output, was far too
pixel-oriented for \MP. A new file, \file{grafbase.mp} was created,
based very heavily on \file{grafbase.mf} but compatible with \MP. Now
when an \mfp{} output file says \mfc{input grafbase}, either \MF{} or
\MP{} may be run on it, and each program will select its own macros, and
produce (nearly) the same picture. This gets us away from device
independence, but many users were not so much concerned with that as
with having a convenient way to have text and pictures described in the
same document.

With the extra capabilities of \PS{} (e.g., color) and the corresponding
abilities of \MP, there was a demand for some \mfp{} interface to
access them. Consequently, switches (options) have been added to access
some of them. When these are used, output files may no longer be
compatible with \MF.

\subsection{Who?}\label{author}

\Mfp{} was written primarily by Tom Leathrum during the late
(northern hemisphere) spring and summer of 1992, while at Dartmouth
College. Different versions were being written and tested for nearly two
years after that, during which time Tom finished his Ph.D. and took a
job at Berry College, in Rome, GA.  Between fall of 1992 and fall of
1993, much of the development was carried out by others.  Those who
helped most in this process are credited in the Acknowledgements.

Somewhere in the mid 1990's the development passed to Geoffrey Tobin who
kept things going for several years.

The addition of \MP{} support was carried out by Dan Luecking around
1997--99. He is also responsible for all other additions and changes
since then, with help from Geoffrey and a few others mentioned in the
Acknowledgements.

\subsection{What?}\label{manifest}

See \file{README.txt} for a list and a brief explanation of each of
the files. Only five are actually needed for full access to
\mfp's capabilities: \file{mfpic.tex}, \file{mfpic.sty} (the
latter needed only for \LaTeX's \cs{usepackage}), \file{grafbase.mf}
(needed only if \MF{} will be processing the figures),
\file{grafbase.mp} and \file{dvipsnam.mp} (needed only if \MP{} will be
the processor).

The readme file that accompanies \mfp{} gives some guidence on the
proper location for the installation of these files.

\subsection{How?}\label{process}

Setting up \TeX{} and \MF{} to process these files will, to an extent,
depend on your local installation. The biggest problem you are likely to
have, regardless of your installation, will be convincing \TeX{} and its
output drivers to find \MF's output files. You should do whatever is
necessary (perhaps nothing!) to insure that \TeX{} looks in the current
directory for \file{.tfm} files, and that your dvi driver/viewer looks
in the current directory for \file{.pk} files. If you process your
pictures with \MP{} there is nothing to do in this regard.

Here is an example of the process: for the sample file
\file{pictures.tex}%
    \footnote{Read \file{mfpguide.pdf} for examples of minimal \mfp{}
    input files.}, %
first run \TeX{} on it (or run \LaTeX{} on \file{lapictures.tex}). You
may see a message from \mfp{} that there is no file \file{pics.tfm}, but
\TeX{} will continue processing the file anyway. When \TeX{} is
finished, you will now have a file called \file{pics.mf}. This is the
\MF{} file containing the descriptions of the pictures for
\file{pictures.tex}. You need to run \MF{} on \file{pics.mf}, with
\cs{mode:=localfont} set up.  (Read your \MF{} manual to see how to do
this.%
    \footnote{If you are new to running \MF, the document
    \textit{Metafont for Beginners}, by \hbox{Geoffrey Tobin}, is a good
    start. Fetch \file{CTAN/info/metafont-for-beginners.tex}.
    `\file{CTAN}' means the Comprehensive \TeX{} Archive Network. You
    can find the mirror nearest you by pointing your browser at
    \file{http://www.ctan.org/}.}) %
Typically, you just type
\begin{verbatim}
    mf pics.mf
\end{verbatim}
or, to use a particular printer mode such as \texttt{ljfour}, possibly
something like
\begin{verbatim}
    mf '\mode:=ljfour; input pics.mf'
\end{verbatim}
This produces a \file{pics.tfm} file and a GF file with a name something
like \file{pics.600gf}. The actual number may be different and the
extension may get truncated on some file systems. Then you run
\prog{gftopk} on the GF file to produce a PK font file. (Read your
\prog{gftopk} manual on how to do this.) Typically, you just run
\begin{verbatim}
    gftopk pics.600gf
\end{verbatim}
(or possibly \ \verb$gftopk pics.600gf pics.600pk$ \ or \
\verb$gftopk pics.600gf pics.pk$ ).

Now you have the font (the \file{.pk} file) and font metric file (the
\file{.tfm}) generated by \MF, reprocess the file \file{pictures.tex}
with \TeX. The resulting DVI file should now be complete, and you should
be able to print and view it at your computer (assuming your viewer and
print driver have been set up to be able to find the PK font generated
from \file{pics.mf}). You can delete \file{pics.600gf} and
\file{pics.log}.

If you use \mfp{} with the \opt{metapost} option (this would require you
to edit \file{pictures.tex} or \file{lapictures.tex}. See
chapter~\ref{options} for how to do this), then \file{pics.mp} is
produced, and you need to replace the \MF/\prog{gftopk} steps with the
single step of running \MP. (Read your \MP{} documentation on how to do
this.%
    \footnote{The document \textit{Some experiences on running Metafont
    and MetaPost}, by Peter Wilson, can be useful for beginners. Fetch
    \file{CTAN/info/metafp.pdf}.}) %
Typically just
\begin{verbatim}
    mpost pics.mp
\end{verbatim}
or possibly \ \verb$mp pics.mp$ .

After reprocessing \file{pictures.tex} with \TeX{} you should then be
able to run dvips on the resulting DVI file and print or view its \PS{}
output. It \pdfTeX{} is used instead of \TeX{} on the second run, you
should be able to view the resulting PDF file with the pictures
included.

It is not advisable to rely on automatic font generation to create the
\file{.tfm} and \file{.pk} files. (Different systems do this in
different ways, so here I will try to give a generic explanation.) The
reason: later editing of a figure will require new files to be built,
and most automatic systems will \emph{not} remake the files once they
have been created. This is not so much a problem with the \file{.tfm},
as \mfp{} never tries to load the font if the \file{.tfm} is absent and
therefore no automatic \file{.tfm}-making should ever be triggered.
However, if you forget to run \prog{gftopk}, then try to view your
resulting file, you may have to search your system and delete some
automatically generated \file{.pk} file (they can turn up in
unpredictable places) before you can see any later changes. It might
be wise to write a shell script (batch file) that (1)~runs \MF, (2)~runs
\prog{gftopk} if step~1 returns no error, (3)~deletes the \file{.tfm} if
the \file{.pk} file does not exist. That way, if anything goes wrong,
the \file{.dvi} will not contain the font (\mfp{} will draw a rectangle
and the figure number in place of the figure).

These processing steps---processing with \TeX, processing with
\MF/\prog{gftopk}, and reprocessing with \TeX---may not always be
necessary. In particular, if you change the \TeX{} document without
making any changes at all to the pictures, then there will be no need to
repeat the \MF{} or \MP{} steps.

There are also somewhat subtle circumstance under which you can skip the
second \TeX{} step after editing a file that has gone through the above
process. Listing the exact cirumstances is rather involved, so it is
recommended that you always repeat the \TeX{} step if changes have been
made.

What makes \mfp{} work? When you run \TeX{} on the file
\file{pictures.tex}, the \mfp{} macros issue \TeX{} \cs{write
commands}, writing \MF{} (or \MP) commands to a file \file{pics.mf} (or
\file{pics.mp}).  The user should never have to read or change the
file \file{pics.mf} directly---the \mfp{} macros take care of it.

The enterprising user can determine by examining the \mfp{} source and
the resulting \MF{} file, that \mfp{} drawing macros translate almost
directly into similar \MF/\MP{} commands, defined in one of the files
\file{grafbase.mf} or \file{grafbase.mp}. The labels and
captions, however, are placed on the graph by \TeX{} using box
placement techniques similar to those used in \LaTeX's \env{picture}
environment (except when option \opt{mplabels} is in effect, in which
case \MP{} places the labels).


\clearpage
\section{Options.}\label{options}

There are now several options to the \mfp{} package. These can be listed
in the standard \LaTeX{} \cs{usepackage} optional argument, or can be
turned on with certain provided commands (the only possibility for plain
\TeX). Some options can be switched off and on throughout the document.
Here we merely list them and provide a general description of their
purpose. More details may be found later in the discussion of the
features affected. The headings below give the option name, the
alternative macro and, if available, the command for turning off the
option. Any option not among those given below will be passed on to the
\prog{graphics} package, provided the \opt{metapost} option has been
used.

If the file \file{mfpic.cfg} exists, it will be input just before all
options are processed. You can create such a file containing an
\cs{ExecuteOptions} command to execute any options you would like to
have as default. Actual options to \cs{usepackage} will override these
defaults, of course. And so will any of the commands below.

If the file \file{mfpic.usr} exists, it will be input at the end of the
loading of \mfp. The user can create such a file containing any of the
commands of this section that he would like to have as default.

\subsection{\opt{metapost}, \cs{usemetapost}}\label{metapost}
\index{metapost@\opt{metapost}}\index{usemetapost@\cs{usemetapost}}

Selects \MP{} as the figure processor and makes specific features
available. It changes the extension used on the output file to
\file{.mp} to signal that it can no longer be processed with \MF. There
is also a \opt{metafont} option (command \cs{usemetafont}), but it is
redundant, as \MF{} is the default. Either command must come before the
\cs{opengraphsfile} command (see section~\ref{files}). They should not
be used together in the same document. (Actually, they can but one needs
to close one output file and open another. Moreover, it hasn't ever been
seriously tested, and it wasn't taken into consideration in writing most
of the macros.) If the command form \cs{usemetapost} is used in a
\LaTeXe{} document, it must come in the preamble. Because of the timing
of actions by the \prog{babel} package and by older versions of
\file{supp-pdf.tex} (input by \file{pdftex.def} in the \prog{graphics}
package), when \pdfLaTeX{} is used \mfp{} should be loaded and
\cs{usemetapost} (if used) declared before \prog{babel} is loaded.


\subsection{\opt{mplabels}, \cs{usemplabels},
\cs{nomplabels}}\label{mplabels}
\index{mplabels@\opt{mplabels}}\index{usemplabels@\cs{usemplabels}}%
\index{nomplabels@\cs{nomplabels}}

Causes all label creation commands to write their contents to the output
file. It has no effect on the \cs{tcaption} command. In this case labels
are handled by \MP{} and can be rotated. It requires \MP, and will be be
ignored without it (\MF{} cannot handle labels). It may also produce an
error either from \TeX{} or \MF. Otherwise the commands can come
anywhere and affect subsequent \cs{tlabel} commands. When this is in
effect, the labels become part of the figure and, in the default
handling, they may be clipped off or covered up by later drawing
elements. But see the next section on the \opt{overlaylabels} option.
Labels added to a picture contribute to the bounding box even if
\opt{truebbox} is not in effect.

The user is responsible for adding the appropriate \mfc{verbatimtex}
header to the output file if necessary. For this purpose, there is the
\cs{mfpverbtex} command, see section~\ref{labels}. If
the label text contains only valid plain \TeX{} macros, there is
generally no need for a \mfc{verbatimtex} preamble at all. If you add a
\mfc{verbatimtex} preamble of \LaTeX{} code take care to make sure \MP{}
calls \LaTeX{} (for example, by setting the environmental variable
\texttt{TEX} to \texttt{latex} in the command shell of your operating
system.).


\subsection{\opt{overlaylabels}, \cs{overlaylabels}, \cs{nooverlaylabels}}
\label{overlaylabels}
\index{overlaylabels@\opt{overlaylabels}}%
\index{overlaylabels@\cs{overlaylabels}}%
\index{nooverlaylabels@\cs{nooverlaylabels}}

In the past, under \opt{mplabels} all text labels created by \cs{tlabel}
and its relatives were added to the picture by \MP{} \emph{as they
occurred}. This made them subject to later drawing commands: they could
be covered up, erased, or clipped. With this option (or after the
command \cs{overlaylabels}) text labels are saved in a separate place
from the rest of a picture. When a picture is completed, the labels that
were saved are added on top of it. This is the way labels always behave
under the \opt{metafont} option, because then \TeX{} must add the labels
and there is no possibility for special effects involving clipping or
erasing (at the \MF{} level).

With the \opt{metapost} option, but without \opt{mplabels} it has been
decided to keep the same behavior (and the same code) as under the
\opt{metafont} option. However, when \opt{mplabels} is used, there is
the possibility for special effects with text, and it has always been
the behavior before this version to simply place the labels as they
occurred. It turns out that placing the labels at the end is cleaner and
simpler to code, so I experimented with it and rejected it as a default,
but now offer it as an option. With this option, \mfp{} labels have
almost the same behavior with or without \opt{mplabels}.


\subsection{\opt{truebbox}, \cs{usetruebbox},
\cs{notruebbox}}\label{truebbox}
\index{truebbox@\opt{truebbox}}\index{usetruebbox@\cs{usetruebbox}}%
\index{notruebbox@\cs{notruebbox}}

Normally \MP{} outputs an EPS file with the actual bounding box of the
figure. By default, \mfp{} \emph{overrides} this and sets the bounding
box to the dimensions specified by the \cs{mfpic} command that produced
it. (This used to be needed for \TeX{} is to handle \cs{tlabel} commands
correctly. Now, it is just for backward compatability, and for
compatability with \MF's behavior.) It is reasonable to let \MP{} have
its way, and that is what this option does. If one of the command forms
is used in an \env{mfpic} environment, it affects only that environment,
otherwise it affects all subsequent figures. This option currently has
no effect with \MF, but should cause no errors.


\subsection{\opt{clip}, \cs{clipmfpic}, \cs{noclipmfpic}}\label{clip}
\index{clip@\opt{clip}}\index{clipmfpic@\cs{clipmfpic}}%
\index{noclipmfpic@\cs{noclipmfpic}}

Causes all parts of the figure outside the rectangle specified by the
\cs{mfpic} command to be removed. The commands can come anywhere. If
issued inside an \env{mfpic} environment they affect the current figure
only. Otherwise all subsequent figures are affected. Note: this is a
rather rudimentary option. It has an often unexpected interaction with
truebbox. When both are in effect, \MP{} will produce a bounding box
that is the intersection of two rectangles: the true one \emph{without
clipping}, and the box specified in the \cs{mfpic} command. It is
possible that the actual figure will be much smaller (even empty!). This
is a property of the \MP{} \gbc{clip} command and we know of no way to
avoid it.


\subsection{\opt{centeredcaptions}, \cs{usecenteredcaptions},
\cs{nocenteredcaptions}}\label{centeredcaptions}
\index{centeredcaptions@\opt{centeredcaptions}}%
\index{usecenteredcaptions@\cs{usecenteredcaptions}}%
\index{nocenteredcaptions@\cs{nocenteredcaptions}}

Causes multiline captions created by \cs{tcaption} to have all lines
centered. This has no effect on the normal \LaTeX{} \cs{caption}
command.%
    \footnote{This writer [DHL] feels that \cs{tcaption} is too limited
    and users ought to apply the caption by other means, such as
    \LaTeX's \cs{caption} command, outside the \env{mfpic}
    environment.} %
The commands can be issued anywhere. If inside an \env{mfpic}
environment they should come before the \cs{tcaption} command and affect
only it, otherwise they affect all subsequent figures.

\subsection{\opt{debug}, \cs{mfpicdebugtrue},
\cs{mfpicdebugfalse}}\label{debug}
\index{debug@\opt{debug}}\index{mfpicdebugtrue@\cs{mfpicdebugtrue}}%
\index{mfpicdebugfalse@\cs{mfpicdebugfalse}}

Causes \mfp{} to write a rather large amount of information to the
\file{.log} file and sometimes to the terminal. Debug information
generated by \file{mfpic.tex} \emph{while loading} is probably of
interest only to developers, but can be turned on by giving a definition
to the command \cs{mfpicdebug} prior to loading.

\subsection{\opt{clearsymbols}, \cs{clearsymbols}, \cs{noclearsymbols}}
\index{clearsymbols@\opt{clearsymbols}}
\index{clearsymbols@\cs{clearsymbols}}
\index{noclearsymbols@\cs{noclearsymbols}}

\Mfp{} has two commands, \cs{point} and \cs{plotsymbol} that place a
small symbol at each of a list of points. The first can place either a
small filled disk or an open disk, the choice being dictated by the
setting of the boolean \cs{pointfilltrue} or \cs{pointfillfalse}. The
behavior of \cs{point} in the case of \cs{pointfillfalse} is to erase the
interior of the disk in addition to drawing its circumference.

The second command \cs{plotsymbol} can place a variety of shapes, some
open, some not. Its behavior until now was always simply to draw the
shape without erasing the interior. Two other commands that placed these
symbols, \cs{plotnodes} and \cs{plot}, had the same behavior. With this
option, two of these, \cs{plotsymbol} and \cs{plotnodes}, will erase the
interior of the open symbols before drawing them. Thus
\cs{plotsymbol}\marg{SolidCircle} still works just like
\cs{pointfilltrue}\cs{point}, and now with this option
\cs{plotsymbol}\marg{Circle} behaves the same as
\cs{pointfillfalse}\cs{point}. The \cs{plot} command is unaffected by
this option.


\subsection{\opt{draft}, \opt{final}, \opt{nowrite}, \cs{mfpicdraft},
    \cs{mfpicfinal}, \cs{mfpicnowrite}}\label{draft}
\index{draft@\opt{draft}}\index{final@\opt{final}}%
\index{nowrite@\opt{nowrite}}\index{mfpicdraft@\cs{mfpicdraft}}%
\index{mfpicfinal@\cs{mfpicfinal}}\index{mfpicnowrite@\cs{mfpicnowrite}}

Under the \opt{metapost} option, the various macros that include the
\EPS{} files emit rather large amounts of confusing error messages when
the files don't exist (especially in \LaTeX). For this reason, before
each picture is placed, \mfp{} checks for the existence of the
graphic before trying to include it. However, on some systems checking
for the existence of a nonexistent file can be very slow because the
entire \TeX{} search path will need to be checked. Therefore, \mfp{}
doesn't even attempt any inclusion on the first run. The first run is
detected by the non-existence of \file{\meta{file}.1}, where \meta{file}
is the name given in the \cs{opengraphsfile} command (but see also
section~\ref{files}). These options can be used to override this
automatic detection. All the command versions should come \emph{before}
the \cs{opengraphsfile} command. The \cs{mfpicnowrite} command
\emph{must} come before it.

These options might be used if, for example, the first figure has an
error and is not created by \MP, but you would like \mfp{} to go
ahead and include the remaining figures. Then use \opt{final}. It can
also be used to override a \LaTeX{} global \opt{draft} option. Or if
\file{\meta{file}.1} exists, but other figures still have errors and you
would like several runs to be treated as first runs until \MP{} has
stopped issuing error messages, then use \opt{draft}.  These commands
also work under the \opt{metafont} option, but time and error messages
are less of an issue then. If all the figures have been created and
debugged, some time might be saved (with either \opt{metafont} or
\opt{metapost}) by not writing the output file again, then \opt{nowrite}
can be used.


\subsection{Option Scoping Rules}\label{scoping}

Some of these options merely change \TeX{} behavior, others write
information to the output file for \MF{} or \MP. Changes in \TeX{}
behavior obey the normal \TeX{} grouping rules, the information written
to the output file obeys \MF{} grouping rules. Since each \env{mfpic}
environment is both a \TeX{} group and (corresponds to) a \MF{} group,
the following always holds: use of one of the command forms inside of an
\env{mfpic} environment makes the change local to that environment.

An effort has been made (as of version 0.7) to make this universal. That
is, any of the commands listed above for turning options on and off will
be global when issued outside an \env{mfpic} environment. The debug
commands are exceptions; they obey all \TeX{} scoping rules.

We have also tried to make all other \mfp{} commands for changing the
various parameters follow this rule: local inside \env{mfpic}
environment, global outside. However, as of this writing I don't
claim to have caught every one.

The following are special:
\cs{usemetapost}\index{usemetapost@\cs{usemetapost}},
\cs{usemetafont}\index{usemetafont@\cs{usemetafont}},
\cs{mfpicdraft}\index{mfpicdraft@\cs{mfpicdraft}},
\cs{mfpicfinal}\index{mfpicfinal@\cs{mfpicfinal}},
and
\cs{mfpicnowrite}\index{mfpicnowrite@\cs{mfpicnowrite}}.
Their effects are always global, partly because they should occur prior
to the initialization command \cs{opengraphsfile} (described in
section~\ref{files}). Note that \cs{usemetapost} may cause a file of
graphic inclusion macros to be input. If this command is issued inside a
group, some definitions in that file may be lost, breaking the graphic
inclusion code.

\clearpage
\section{The Macros.}\label{macros}

In these descriptions we will often refer to `\MF{}' when we really mean
`\MF{} or \MP{}'. This will especially be the case whenever we need to
refer to commands in the two languages which are substantially the same,
but occasionally we will even talk about running `\MF{}' when we mean
running one or the other to process the figures. If we need to
discriminate between the two processors, (for example when they have
different behavior) we will make the difference explicit.

A similar shorthand is used when referring to \TeX{}. It should not be
taken to mean plain\TeX, but rather whatever version of \TeX{} is used
to process the source file: \LaTeX, \pdfTeX, \pdfLaTeX, etc.

Many of the commands of \mfp{} have optional arguments. These are
denoted just as in \LaTeX, with square brackets. Thus, the command for
drawing a circle can be given
\begin{ex}
  \cs{circle}\marg{(0,0),1}
\end{ex}
having only the mandatory argument, or
\begin{ex}
  \cs{circle}\oarg{p}\marg{(0,0),1}
\end{ex}
Whenever an optional argument is omitted, the behavior is equivalent to
some choice of the optional argument. In this example, the two forms
have exactly the same behavior, drawing a circle centered at $(0,0)$
with radius $1$. In this case we will say that \oarg{p} is the
\emph{default}. Another example is \cs{point}\marg{(1,0)} versus
\cs{point}\oarg{3pt}\marg{(1,0)}. They both place a dot at the point
$(1,0)$. The second one explicitly request that it have diameter
\dim{3pt}; the first will examine the length command \cs{pointsize},
which the user can change, but it is initialized to \dim{2pt}. In this
case we will say the default is the value of \cs{pointsize},
\emph{initially \dim{2pt}}.

Optional arguments for \mfp{} commands may consist of empty brackets
(completely empty, no spaces) and the default will be used. This is
useful only for commands that have two optional arguments and one only
wants to change from the defaults in the second one. An optional
argument should normally not contain any spaces. Even when the argument
contains more than one piece of data, spaces should not separate the
parts. In many cases (perhaps most) this will cause no harm, but it
would be better to avoid doing it altogether.


\subsection{Files and Environments.}\label{files}

\begin{cd}
\cs{opengraphsfile}\marg{\meta{file}}\\
  \ $\ldots$\\
\cs{closegraphsfile}%
\index{opengraphsfile@\cs{opengraphsfile}}%
\index{closegraphsfile@\cs{closegraphsfile}}
\end{cd}

These macros open and close the \MF{} or \MP{} file which will contain
the pictures to be included in this document.  The name of the file will
be \file{\meta{file}.mf} (or \file{\meta{file}.mp}). Do \emph{not}
specify the extension, which is added automatically.

\emph{Note}: This command will cause \file{\meta{file}.mf} or
\file{\meta{file}.mp} to be overwritten if it already exists, so be sure
to consider that when selecting the name. Repeating the running of
\TeX{} will overwrite the file created on previous runs, but that should
be harmless. For if no changes are made to \env{mfpic} environments, the
identical file will be recreated, and if changes have been made, then
you want the file to be replaced with the new version.

It is possible (but \emph{has not} been seriously tested) to close one
file and open another, and even to change between \opt{metapost} and
\opt{metafont} in between. If anything goes wrong with this, contact the
maintainer and it might be fixed in some later version.

\begin{cd}
\cs{mfpic}\oarg{\meta{xscale}}\oarg{\meta{yscale}}%
  \marg{\meta{xmin}}\marg{\meta{xmax}}\marg{\meta{ymin}}\marg{\meta{ymax}}\\
  \ $\ldots$\\
\cs{endmfpic}%
\index{mfpic@\cs{mfpic}}\index{endmfpic@\cs{endmfpic}}
\end{cd}

These macros open and close the \env{mfpic} environment in which most of
the rest of the macros make sense. The \cs{mfpic} macro also sets up the
local coordinate system for the picture. The \meta{xscale} and
\meta{yscale} parameters establish the length of a coordinate system
unit, as a multiple of the \TeX{} dimension \cs{mfpicunit}. If neither
is specified, both are taken to be 1 (i.e., each coordinate system unit
is 1 \cs{mfpicunit}). If only one is specified, then they are assumed to
be equal. The \meta{xmin} and \meta{xmax} parameters establish the lower
and upper bounds for the $x$-axis coordinates; similarly, \meta{ymin}
and \meta{ymax} establish the bounds for the $y$-axis. These bounds are
expressed in local units---in other words, the actual width of the
picture will be $(\meta{xmax}-\meta{xmin})\cdot\meta{xscale}$ times
\cs{mfpicunit}, its height $(\meta{ymax}-\meta{ymin})\cdot\meta{yscale}$
times \cs{mfpicunit}, and its depth zero. One can scale all pictures
uniformly by changing \cs{mfpicunit}, and scale an individual picture by
changing \meta{xscale} and \meta{yscale}. After loading \mfp,
\cs{mfpicunit} has the value \dim{1pt}. One \texttt{pt} is a
\emph{printer's point}, which equals 1/72.27 inches or 0.35146
millimeters.

\emph{Note}: Changing \cs{mfpicunit} or the optional parameters will
scale the coordinate system, but not the values of certain parameters
that are defined in absolute units. Examples of these are the default
width of the drawing pen, the default lengths of arrowheads, the default
sizes of dashes and dots, etc. If you wish, you can set these to
multiples of \cs{mfpicunit}, but it is difficult (and probably unwise)
to get them to scale along with the scale parameters.

In addition to establishing the coordinate system, these scales and
bounds are used to establish the metric for the \MF{} character or
bounding box for the \MP{} figure described within the environment. If
any of these parameters are changed, the \file{.tfm} file (\MF) or the
bounding box (\MP) will be affected, so you will have to be sure to
reprocess the \TeX{} file after processing the \file{.mf} or \file{.mp}
file, even if no other changes are made in the figure.

\begin{cd}
\cs{mfpicnumber}\marg{\meta{num}}%
\index{mfpicnumber@\cs{mfpicnumber}}
\end{cd}

Normally, \cs{mfpic} assigns the number 1 to the first \env{mfpic}
environment, after which the number is increased by one for each new
\env{mfpic} environment. This number is used internally to include the
picture. It is also transmitted to the output file where it is used as
the argument to a \gbc{beginmfpic} command. In \MF{} this number becomes
the position of the character in the font file, while in \MP{} it is the
extension on the graphic file that is output. The above command tells
\mfp{} to ignore this sequence and number the next \env{mfpic}
figure with \meta{num} (and the one after that $\meta{num}+1$, etc.). It
is up to the user to make sure no number is repeated, as no checking is
done. Numbers greater than 255 may cause errors, as \TeX{} assumes that
characters are represented by 8-bit numbers. If the first figure is to
be numbered something other than $1$, then, under the \opt{metapost}
option, this command should come before \cs{opengraphsfile}, as that
command checks for the existence of the first numbered figure to
determine if there are figures to be included.

\begin{cd}
\cs{begin}\marg{mfpic}\texttt{...}\cs{end}\marg{mfpic}%
\index{begin@\cs{begin}\marg{mfpic}}
\end{cd}

In \LaTeX, instead of \cs{mfpic} and \cs{endmfpic}, you may prefer to
use \cs{begin}\marg{mfpic} and \cs{end}\marg{mfpic}. This is by no means
required: in \LaTeX{} \cs{begin}\marg{command} invokes \cs{command}, and
\cs{end}\marg{command} invokes \cs{endcommand}, for any environment
\env{command}.

The sample file \file{lapictures.tex} provided with \mfp{}
illustrates this use of an \env{mfpic} environment in \LaTeX.

\medskip
The rest of the \mfp{} macros do not affect the font metric file
(\file{\meta{file}.tfm}), and so if these commands are changed or added
in your document, you will not have to repeat the third step of
processing (reprocessing with \TeX) to complete your \TeX{} document.
The same is true when option \opt{metapost} is selected without the
\opt{truebbox} option, except under \pdfTeX{} or \pdfLaTeX. Those \TeX{}
programs will embed the figures right in the \file{.pdf} output. For
normal \LaTeX{} + \prog{dvips}, the figures are embedded by
\prog{dvips}, which must always be repeated.

\medskip
For the remainder of the macros, the numerical parameters are expressed
in the units of the local coordinate system specified by \cs{mfpic},
unless otherwise indicated.


\subsection{Figures.}\label{figures}

\subsubsection{\CMF{} Pairs.}\label{pairs}

Since many of the arguments of the \mfp{} drawing commands are
sent to \MF{} to be interpreted, it's useful to know something about
\MF{} concepts.

In particular, \MF{} has \mfc{pair} objects, which may be constants or
variables.  Pair constants have the form \mfc{($x$,$y$)}.  Pairs are
two-dimensional rectangular (cartesian) quantities, and are clearly
useful for representing both points and vectors on the plane.

Moreover, we herein often represent each pair by a brief name, such as
$p$, $v$ or $c$, the meanings of which are usually obvious in the
context of the macro. The succinctness of this notation also helps us to
think geometrically rather than only of coordinates.

\CMP{} has these same concepts, but also has color objects, which may
also be constants or variables. Color constants have the form
\mfc{($r$,$g$,$b$)} where $r$, $g$, and $b$ are numbers between $0$ and
$1$ determining the relative proportions of red, green and blue in the
color (rgb model). A color variable is a name, like \mfc{magenta} or
\mfc{RoyalBlue} (predefined). There are also color functions like
\mfc{cmyk($x$,$y$,$z$,$w$)} which is defined to convert cmyk values into
\MP's native rgb model.

Some commands depend on the value of separately defined parameters. All
these parameters are initialized when \mfp{} is loaded. In the following
descriptions we give the initial value of all the relevant parameters.
When \MP{} output is selected, figures can be drawn in any color.
Several of the above mentioned parameters are colors. \Mfp{} provides
commands to change any of these parameters.


\subsubsection{Points, Lines, and Rectangles.}\label{points}

\begin{cd}
\cs{pointdef}\marg{\meta{name}}\texttt{($x$,$y$)}%
\index{pointdef@\cs{pointdef}}
\end{cd}

Defines a symbolic name for points and their coordinates. \meta{name} is
any legal \TeX{} command name \emph{without} the backslash; $x$ and $y$
are any numbers. For example, after the command
\cs{pointdef}\marg{A}\texttt{(1,3)}, \cs{A} expands to \texttt{(1,3)}, while
\cs{Ax} and \cs{Ay} expand to \texttt{1} and \texttt{3}, respectively. Because
of the way \cs{tlabel} is defined (see section~\ref{labels} below), one
cannot use \cs{A} to specify where to place a label (unless
\opt{mplabels} is in effect), but must use \texttt{ (\cs{Ax},\cs{Ay})}. In
most other commands, one can use \cs{A} where a pair or point is
required.

\begin{cd}
\cs{point}\oarg{\meta{ptsize}}\marg{\meta{$p_0$},\meta{$p_1$},$\ldots$}%
\index{point@\cs{point}}
\end{cd}

Draws small disks centered at the points \meta{$p_0$}, \meta{$p_1$}, and
so on. If the optional argument \meta{ptsize} is present, it determines
the diameter of the disks, which otherwise equals the \TeX{} dimension
\cs{pointsize}, initially \dim{2pt}. The disks have a filled interior if
the command \cs{pointfilltrue} has been issued (the initial value),
\cs{pointfillfalse} causes the interior to be erased and an outline
drawn. The color of the circles is the value of the predefined variable
\gbc{pointcolor}, and the inside of the open circles is the value of
\mfc{background}.

\begin{cd}
\cs{plotsymbol}\oarg{\meta{size}}\marg{\meta{symbol}}%
\marg{\meta{$p_0$},\meta{$p_1$},$\ldots$}%
\index{plotsymbol@\cs{plotsymbol}}
\end{cd}

Draws small symbols centered at the points \meta{$p_0$}, \meta{$p_1$},
and so on. The symbols must be given by name, and the available symbols
are
\gbc{Asterisk}\index{Asterisk@\gbc{Asterisk}},
\gbc{Circle}\index{Circle@\gbc{Circle}},
\gbc{Diamond}\index{Diamond@\gbc{Diamond}},
\gbc{Square}\index{Square@\gbc{Square}},
\gbc{Triangle}\index{Triangle@\gbc{Triangle}},
\gbc{Star}\index{Star@\gbc{Star}},
\gbc{SolidCircle}\index{SolidCircle@\gbc{SolidCircle}},
\gbc{SolidDiamond}\index{SolidDiamond@\gbc{SolidDiamond}},
\gbc{SolidSquare}\index{SolidSquare@\gbc{SolidSquare}},
\gbc{SolidTriangle}\index{SolidTriangle@\gbc{SolidTriangle}},
\gbc{SolidStar}\index{SolidStar@\gbc{SolidStar}},
\gbc{Cross}\index{Cross@\gbc{Cross}} and
\gbc{Plus}\index{Plus@\gbc{Plus}}.
The names should be self-explanatory. Under \opt{metapost}, symbols are
drawn in \gbc{pointcolor}. The \meta{size} defaults to \cs{pointsize} as
in \cs{point} above. \gbc{Asterisk} consists of six
line segments while \gbc{Star} is the standard closed, ten-sided
polygon. The name `\cs{plotsymbol}' comes from the fact that the \cs{plot}
command, which was written first, utilizes these same symbols. The command
\cs{symbol} was already taken (standard \LaTeX).

The difference between \cs{pointfillfalse}\cs{point}$\ldots$ and
\cs{plotsymbol}\marg{Circle}$\ldots$ is that the inside of the circle
will not be erased in the second version (i.e., whatever else has already
been drawn in that area will remain visible). This is the default (for
backward compatibility), but that can be changed with the commands
below.

\begin{cd}
\cs{clearsymbols}\\
\cs{noclearsymbols}%
\index{clearsymbols@\cs{clearsymbols}}%
\index{noclearsymbols@\cs{noclearsymbols}}
\end{cd}

After the first of these two commands, subsequent \cs{plotsymbol}
commands will draw the open symbols with their interiors erased. After
the second, the default behavior (described above) will be restored.
These commands have no effect on \cs{point}. \cs{plotnodes} (see
subsection~\ref{drawing}) also responds to the settings made by these
commands. The \cs{plot} command (also in subsection~\ref{drawing}) does
not.

\begin{cd}
\cs{polyline}\marg{\meta{$p_0$},\meta{$p_1$},$\ldots$}\\
\cs{lines}\marg{\meta{$p_0$},\meta{$p_1$},$\ldots$}%
\index{polyline@\cs{polyline}}\index{lines@\cs{lines}}
\end{cd}

Draws the line segment with endpoints at \meta{$p_0$} and \meta{$p_1$},
then the line segment with endpoints at \meta{$p_1$} and \meta{$p_2$},
etc. The result is an open polygonal path through the specified points,
in the specified order. \cs{polyline} and \cs{lines} mean the same
thing.

\begin{cd}
\cs{polygon}\marg{\meta{$p_0$},\meta{$p_1$},$\ldots$}%
\index{polygon@\cs{polygon}}
\end{cd}

Draws a closed polygon with vertices at the specified points in the
specified order.

\begin{cd}
\cs{rect}\marg{\meta{$p_0$},\meta{$p_1$}}%
\index{rect@\cs{rect}}
\end{cd}

Draws the rectangle specified by the points \meta{$p_0$} and
\meta{$p_1$}, these being either pair of opposite corners of the
rectangle in any order.

It is occasionally helpful to know that connected paths like those
produced by \cs{polyline} or \cs{rect} have a \emph{sense} (a
direction). The sense of \cs{polyline} is the direction determined by
the order of the points. For \cs{rect} the sense may be clockwise or
anticlockwise depending on the corners used: it begins at the first of
the two points and goes horizontally from there.

\begin{cd}
\cs{regpolygon}\marg{\meta{num}}\marg{\meta{name}}%
\marg{\meta{eqn$_1$}}\marg{\meta{eqn$_2$}}%
\index{regpolygon@\cs{regpolygon}}
\end{cd}

This produces a regular polygon with \meta{num} sides. The second
argument, \meta{name} is a symbolic name. It can be used to refer to the
vertices later. The last two arguments should be equations that position
two of the vertices or one vertex and the center. The center is refered
to by \meta{name}\gbc{0} and the vertices by \meta{name}\gbc{1}
\meta{name}\gbc{2}, etc., going anticlockwise around the polygon. The
\meta{name} itself (without a number) will be a \MF{} variable assigned
the value of \meta{num}. For example,
\begin{ex}
\cs{regpolygon}\marg{5}\marg{Meg}\marg{Meg0=(0,1)}\marg{Meg1=(2,0)}
\end{ex}
will produce a regular pentagon with its center at $(0,1)$ and its first
vertex at $(2,0)$. One could later draw a star inside it with
\begin{ex}
\cs{polygon}\marg{Meg1,Meg3,Meg5,Meg2,Meg4}
\end{ex}
Moreover, \gbc{Meg} will equal $5$.
The name given becomes a \MF{} variable and care should be taken to make
the name distinctive so as not to redefine some internal variable.

\subsubsection{A Word on List Arguments}\label{list}

We have seen already four \mfp{} macros that take a mandatory argument
consisting of a list of coordinate pairs. There are many more, and some
that take a comma-separated lists of other types of items. If the lists
are long, especially if they are generated by a program, it might be
more convenient if one could simply refer to an external file for the
data. This is possible, and one does it the following way: instead of
\cs{lines}\marg{\meta{list}}, one can write\index{datafile@\cs{datafile}}
\begin{ex}
\cs{lines}\cs{datafile}\marg{\meta{filename}}
\end{ex}
where \meta{filename} is the full name of the file containing the data.
The required format of this file and the details of this usage can be
found in subsection~\ref{external}. This method is available for any
command that takes a comma-separated list of data as its last argument,
\emph{with the exception of those commands that adds text to the
picture}. Examples of the latter are \cs{plottext} and \cs{axislabels}
(subsection~\ref{text}).

\subsubsection{Axes, Axis Marks, and Grids.}\label{axes}

\begin{cd}
\cs{axes}\oarg{\meta{hlen}}\\
\cs{xaxis}\oarg{\meta{hlen}}\\
\cs{yaxis}\oarg{\meta{hlen}}%
\index{axes@\cs{axes}}%
\index{xaxis@\cs{xaxis}}%
\index{yaxis@\cs{yaxis}}
\end{cd}

These are retained for backward compatibility, but there are more
flexible alternatives below. They draw $x$- and  $y$-axes for the
coordinate system. The command \cs{axes} is equivalent to \cs{xaxis}
followed by \cs{yaxis} which produce the obvious. The $x$- and $y$-axes
extend the full width and height of the \env{mfpic} environment. The
optional \meta{hlen} sets the length of the arrowhead on each axis. The
default is the value of the \TeX{} dimension \cs{axisheadlen}, initially
\dim{5pt}. The shape of the arrowhead is determined as in the \cs{arrow}
macro (section~\ref{modifier}). The color of the head is the value of
\gbc{headcolor}, the shaft is \gbc{drawcolor}.

Unlike other commands that produce lines or curves, these do not respond
to the prefix macros of sections \ref{modifier}~and \ref{rendering}.
They always draw a solid line (with an arrowhead unless \cs{axisheadlen}
is \dim{0pt}). They \emph{do} respond to changes in the pen thickness
(see \cs{penwd} in section~\ref{parameters}) but that is pretty much the
only possibility for variation.

\begin{cd}
\cs{axis}\oarg{\meta{hlen}}\marg{\meta{one-axis}}\\
\cs{doaxes}\oarg{\meta{hlen}}\marg{\meta{axis-list}}%
\index{axis@\cs{axis}}
\index{doaxes@\cs{doaxes}}
\end{cd}

These produce any of 6 different axes. The parameter \meta{one-axis} can
be \texttt{x} or \texttt{y}, to produce (almost) the equivalent of \cs{xaxis}
and \cs{yaxis}; or it can be \texttt{l}, \texttt{b}, \texttt{r}, or \texttt{t} to
produce an axis on the border of the picture (left, bottom, right or
top, respectively). \cs{doaxes} takes a list of any or all of the six
letters (with either spaces or nothing in between) and produces the
appropriate axes. Example: \cs{doaxes}\marg{lbrt}. The optional argument
sets the length of the arrowhead. In the case of axes on the edges, the
default is the value of \cs{sideheadlen}, which \mfp{}
initializes to \dim{0pt}. For the $x$- and $y$-axis the default is
\cs{axisheadlen} as in \cs{xaxis} and \cs{yaxis} above.

The commands \cs{axis}\marg{x}, \cs{axis}\marg{y}, and
\cs{doaxes}\marg{xy} differ from the old \cs{xaxis}, \cs{yaxis} and
\cs{axes} in that these new versions respond to changes made by
\cs{setrender} (see subsection~\ref{default}). Moreover, prefix macros
may be applied to \cs{axis} without error (see sections
\ref{modifier}~and \ref{rendering}): \cs{dotted}\cs{axis}\marg{x} draws
a dotted $x$-axis, but \cs{dotted}\cs{xaxis} produces a \MF{} error. A
prefix macro applied to \cs{doaxes} generates no error, but only the
first axis in the list will be affected.

The side axes are drawn by default with a pen stroke along the very edge
of the picture (as determined by the parameters to \cs{mfpic}). This can
be changed with the command \cs{axismargin} described below.

Axes on the edges are drawn so that they don't cross each other.
\cs{doaxes}\marg{lbrt}, for example, produces a perfect rectangle. If the
$x$- and $y$-axis are drawn with \cs{axis} or \cs{doaxis}, then they
will not cross the side axes. For this to work properly, all the
following margin settings have to be done before the axes are drawn.

\begin{cd}
\cs{axismargin}\marg{\meta{axis}}\marg{\meta{num}}\\
\cs{setaxismargins}\marg{\meta{num}}\marg{\meta{num}}\marg{\meta{num}}\marg{\meta{num}}\\
\cs{setallaxismargins}\marg{\meta{num}}%
\index{axismargin@\cs{axismargin}}%
\index{setaxismargins@\cs{setaxismargins}}%
\index{setallaxismargins@\cs{setallaxismargins}}
\end{cd}

The \meta{axis} is one of the letters \texttt{l}, \texttt{b}, \texttt{r}, or \texttt{
t}. \cs{axismargin} causes the given axis to be shifted \emph{inward} by
the \meta{num} specified (in \emph{graph} coordinates). The second
command \cs{setaxismargins} takes 4 arguments, using them to set the
margins starting with the left and proceeding anticlockwise. The last
command sets all the axis margins to the same value.

A change to an axis margin affects not only the axis at that edge but
also the three axes perpendicular to it. For example, if the margins are
$M_{\mathrm{lft}}$, $M_{\mathrm{bot}}$, $M_{\mathrm{rt}}$ and
$M_{\mathrm{top}}$, then
\cs{axis b} draws a line starting $M_{\mathrm{lft}}$ graph units from the
left edge and ending $M_{\mathrm{rt}}$ units from the right edge. Of course,
the entire line is $M_{\mathrm{bot}}$  units above the bottom edge. The
margins are also respected by the $x$- and $y$-axis, but only when drawn
with \cs{axis}. The old \cs{xaxis}, \cs{yaxis} and \cs{axes} ignore
them.

Special effects can be achieved by lying to one axis about the other
margins.

\begin{cd}
\cs{xmarks}\oarg{\meta{len}}\marg{\meta{numberlist}}\\
\cs{tmarks}\oarg{\meta{len}}\marg{\meta{numberlist}}\\
\cs{bmarks}\oarg{\meta{len}}\marg{\meta{numberlist}}\\
\cs{ymarks}\oarg{\meta{len}}\marg{\meta{numberlist}}\\
\cs{lmarks}\oarg{\meta{len}}\marg{\meta{numberlist}}\\
\cs{rmarks}\oarg{\meta{len}}\marg{\meta{numberlist}}\\
\cs{axismarks}\marg{\meta{axis}}\oarg{\meta{len}}\marg{\meta{numberlist}}%
\index{xmarks@\cs{xmarks}}%
\index{tmarks@\cs{tmarks}}%
\index{bmarks@\cs{bmarks}}%
\index{ymarks@\cs{ymarks}}%
\index{lmarks@\cs{lmarks}}%
\index{rmarks@\cs{rmarks}}%
\index{axismarks@\cs{axismarks}}
\end{cd}

These macros place hash marks on the appropriate axes at the places
indicated by the values in the list. The optional \meta{len} gives the
length of the hash marks. If \meta{len} is not specified, the \TeX{}
dimension \cs{hashlen}, initially \dim{4pt}, is used. The marks on the
$x$- and $y$-axes are centered on the respective axis; the marks on the
border axes are drawn to the inside.  Both these behaviors can be
changed (see below). The commands may be repeated as often as desired.
(The timing of drawing commands can make a difference as outlined in
appendix~\ref{mpconsiderations}.) The command \cs{axismarks}\marg{x} is
equivalent to \cs{xmarks} and so on for each of the six axes. (I would
have used \cs{marks}, but e\kern-.16em\TeX{} makes that a primitive.)

The \meta{numberlist} is normally a comma-separated list of numbers. In
place of this, one can give a starting number, an increment and an
ending number as in the following example:
\begin{ex}
    \cs{xmarks}\marg{-2 step 1 until 2}
\end{ex}
is the equivalent of
\begin{ex}
    \cs{xmarks}\marg{-2,-1,0,1,2}
\end{ex}

One must use exactly the words \mfc{step} and \mfc{until}. There must be
spaces between, but the number of spaces is not
significant.%
    \footnote{Experienced \MF{} programmers may recognize that anything
    can be used that is permitted in \MF's \meta{forloop} syntax. Thus
    the given example can also be reworded \cs{xmarks}\marg{-2 upto 2},
    or even \cs{xmarks}\marg{2 downto -2}} %
Users should be aware that if any of the numbers are non-integral then
due to natural round-off effects, the last value might be overshot and a
mark not printed there.

\begin{cd}
\cs{setaxismarks}\marg{\meta{axis}}\marg{\meta{pos}}\\
\cs{setbordermarks}\marg{\meta{lpos}}\marg{\meta{bpos}}\marg{\meta{rpos}}\marg{\meta{tpos}}\\
\cs{setallbordermarks}\marg{\meta{pos}}\\
\cs{setxmarks}\marg{\meta{pos}}\\
\cs{setymarks}\marg{\meta{pos}}%
\index{setaxismarks@\cs{setaxismarks}}%
\index{setbordermarks@\cs{setbordermarks}}%
\index{setallbordermarks@\cs{setallbordermarks}}%
\index{setxmarks@\cs{setxmarks}}%
\index{setymarks@\cs{setymarks}}%
\end{cd}

These set the placement of the hash marks relative to the axis. The
parameter \meta{axis} is one of the letters \texttt{x}, \texttt{y}, \texttt{l},
\texttt{b}, \texttt{r}, or \texttt{t}, and \meta{pos} must be one of the literal
words \gbc{inside}, \gbc{outside}, \gbc{centered}, \gbc{onleft},
\gbc{onright}, \gbc{ontop} or \gbc{onbottom}. The second command takes
four arguments and sets the position of the marks on each border. The
third command sets the position on all four border axis to the same
value. The last two commands are abbreviations for
\cs{setaxismarks}\marg{x}\marg{\meta{pos}} and
\cs{setaxismarks}\marg{y}\marg{\meta{pos}}, respectively.

Not all combinations make sense (for example,
\cs{setaxismarks}\marg{r}\marg{ontop}). In these cases, no error message
is produced: \gbc{ontop} and \gbc{onleft} are considered to be
equivalent, as are \gbc{onbottom} and \gbc{onright}. The parameters
\gbc{inside} and \gbc{outside} make no sense for the $x$- and $y$-axes,
but if they are used then \gbc{inside} means \gbc{ontop} for the
$x$-axis and \gbc{onright} for the $y$-axis. These words are actually
\MF{} numeric variables defined in the file \file{grafbase.mf}, and the
variables \gbc{ontop} and \gbc{onleft}, for example, are given the same
value.

\begin{cd}
\cs{grid}\oarg{\meta{ptsize}}\marg{\meta{xsep},\meta{ysep}}\\
\cs{gridpoints}\oarg{\meta{ptsize}}\marg{\meta{xsep},\meta{ysep}}\\
\cs{lattice}\oarg{\meta{ptsize}}\marg{\meta{xsep},\meta{ysep}}\\
\cs{hgridlines}\marg{\meta{ysep}}\\
\cs{vgridlines}\marg{\meta{xsep}}\\
\cs{gridlines}\marg{\meta{xsep},\meta{ysep}}
\index{grid@\cs{grid}}%
\index{gridpoints@\cs{gridpoints}}%
\index{lattice@\cs{lattice}}%
\index{vgridlines@\cs{vgridlines}}%
\index{hgridlines@\cs{hgridlines}}%
\index{gridlines@\cs{gridlines}}%
\end{cd}

\cs{grid} draws a dot at every point for which the first coordinate is
an integer multiple of the \meta{xsep} and the second coordinate is an
integer multiple of \meta{ysep}. The diameter of the dot is determined
by \meta{ptsize}. The default is \dim{.5bp} and is hard coded in the
\MF{} macros that ultimately do the drawing. Under the \opt{metapost}
option, the color of the dot is \gbc{pointcolor}. The commands
\cs{gridpoints and \cs{lattice}} are synonyms for \cs{grid}.

\cs{hgridlines} draws the horizontal and \cs{vgridlines} the vertical
lines through these same points. \cs{gridlines} draws both sets of
lines. The thickness of the lines is set by \cs{penwd}. Authors are
recommended to either reduce the pen width or change \gbc{drawcolor} to
a lighter color for grids. Or omit them entirely: well-designed graphs
usually don't need them and almost never should both horizontals and
verticals be used.

\begin{cd}
\cs{plrgrid}\marg{\meta{rsep},\meta{anglesep}}\\
\cs{gridarcs}\marg{\meta{rsep}}\\
\cs{gridrays}\marg{\meta{anglesep}}\\
\cs{plrpatch}\marg{\meta{rmin},\meta{rmax},\meta{rsep},%
    \meta{tmin},\meta{tmax},\meta{tsep}}\\
\cs{plrgridpoints}\marg{\meta{rsep},\meta{anglesep}}%
\index{plrgrid@\cs{plrgrid}}%
\index{plrpatch@\cs{plrpatch}}%
\index{gridarcs@\cs{gridarcs}}%
\index{gridrays@\cs{gridrays}}%
\index{plrgridpoints@\cs{plrgridpoints}}%
\end{cd}

\cs{plrgrid} fills the graph with circular arcs and radial lines.
\cs{gridarcs} draws only the arcs, \cs{gridrays} only the radial lines.
\cs{plrgridpoints} places a dot at all the places the rays and arcs
would intersect.

The arcs are centered at $(0,0)$ and the lines emanate from $(0,0)$
(even if $(0,0)$ is not in the graph space). The corresponding \MF{}
commands actually draw enough to cover the graph area and then clip them
to the graph boundaries. If you don't want them clipped, use
\cs{plrpatch}.

\cs{plrpatch} draws arcs with radii starting at \meta{rmin}, stepping by
\meta{rsep} and ending with \meta{rmax}. Each arc goes from angle
\meta{tmin} to \meta{tmax}. It also draws radial lines with angles
starting at \meta{tmin}, stepping by \meta{tsep} and ending with
\meta{tmax}. Each line goes from radius \meta{rmin} to \meta{rmax}. If
$\meta{rmax}-\meta{rmin}$ doesn't happen to be a multiple of
\meta{rsep}, the arc with radius \meta{rmax} is drawn anyway. The same
is true of the line at angle \meta{tmax}, so that the entire boundary is
always drawn.

If \meta{tsep} is larger than \meta{tmax}${}-{}$\meta{tmin}, then only
the boundary rays will be drawn. If \meta{rsep} is larger than
\meta{rmax}${}-{}$\meta{rmin}, then only the boundary arcs will be
drawn.

The color used for rays and arcs is \gbc{drawcolor}, and for dots
\gbc{pointcolor}. The advice about \cs{gridlines} holds for \cs{plrgrid}
as well.


\subsubsection{Circles and Ellipses.}\label{circles}

\begin{cd}
\cs{circle}\oarg{\meta{format}}\marg{\meta{specification}}%
\index{circle@\cs{circle}}%
\end{cd}

Draws a circle. Starting with \mfp{} version 0.7, there are 4
different ways to specify a circle, so \cs{circle} can be given an
optional argument that determines what data is specified in the
mandatory argument.

\begin{cd}
\cs{circle}\oarg{p}\marg{\meta{$c$},\meta{$r$}}\\
\cs{circle}\oarg{c}\marg{\meta{$c$},\meta{$p$}}\\
\cs{circle}\oarg{t}\marg{\meta{$p_1$},\meta{$p_2$},\meta{$p_3$}}\\
\cs{circle}\oarg{s}\marg{\meta{$p_1$},\meta{$p_2$},\meta{$\theta$}}%
\index{circle@\cs{circle}}%
\end{cd}

The optional arguments produce circles according to the following
descriptions.

\begin{description}
\item[\oarg{p}] The \textit{Polar form} is the default. The data in the
mandatory argument should then be the center $c$ and radius $r$ of the
circle.

\item[\oarg{c}] The \textit{Center-point form}. In this case the data
should be the center and one point on the circumference.

\item[\oarg{t}] The \textit{Three-point form}. The data are three points
that do not lie in a straight line.

\item[\oarg{s}] The \textit{point-sweep}. The data are two points on the
circle, followed by the angle of arc between them.
\end{description}
These optional arguments are also used in the \cs{arc} command (see
subsection~\ref{arcs}). The \cs{circle} command draws the whole circle
which the equivalent \cs{arc} command draws only part of. The sense of
the circle produced is anticlockwise except in the case \texttt{[t]},
where it is the direction determined by the order of the three points,
and the case \texttt{[s]}, where it is determined by \meta{$\theta$}:
clockwise if negative, anticlockwise if positive.


\begin{cd}
\cs{ellipse}\oarg{\meta{$\theta$}}\marg{\meta{$c$},\meta{$r_x$},\meta{$r_y$}}%
\index{ellipse@\cs{ellipse}}%
\end{cd}

Draws an ellipse with the $x$ radius \meta{$r_x$} and $y$ radius
\meta{$r_y$}, centered at the point \meta{$c$}. The optional parameter
\meta{$\theta$} provides a way of rotating the ellipse by
\meta{$\theta$} degrees anticlockwise around its center.


\subsubsection{Curves.}\label{curves}

\begin{cd}
\cs{curve}\oarg{\meta{tension}}\marg{\meta{$p_0$},\meta{$p_1$},$\ldots$}%
\index{curve@\cs{curve}}%
\end{cd}

Draws a smooth path through the specified points, in the specified
order. It is `smooth' in two ways: it never changes direction abruptly
(no `corners' or `cusps' on the curve), and it tries to make turns that are
not too sharp. This latter property is acheived by specifying (to \MF) that
the tangent to the curve at each listed point is to be parallel to the
line from that point's predecessor to its successor.

The optional \meta{tension} influences \emph{how} smooth the curve is.
The special value \mfc{infinity} (in fact, usually anything greater than
about $10$), makes the curve not visibly different from a polyline. The
higher the value of tension, the sharper the corners on the curve and
the flatter the portions in between. \CMF{} requires the tension to be
larger than 0.75. The default value of the tension is $1$ when \mfp{} is
loaded, but that can be changed with the following command.

\begin{cd}
\cs{settension}\marg{\meta{num}}%
\index{settension@\cs{settension}}
\end{cd}

This sets the default tension for all commands that take an optional
tension parameter.

\begin{cd}
\cs{cyclic}\oarg{\meta{tension}}\marg{\meta{$p_0$},\meta{$p_1$},$\ldots$}%
\index{cyclic@\cs{cyclic}}%
\end{cd}

Draws a cyclic (i.e., closed) \MF{} B\'ezier curve through the specified
points, in the specified order. It uses the same procedure as
\cs{curve}, but treats the first listed point as having the last as its
predecessor and the last point has the first as its successor. The
\meta{tension} is as in the \cs{curve} command.

\medskip
Occasionally it is necessary to specify a sequence of points with
\emph{increasing} $x$ coordinates and draw a curve through them. One
would then like the resulting curve both to be smooth \textit{and} to
represent a function (that is, the curve always has increasing $x$
coordinate, never turning leftward). This cannot be guaranteed with the
\cs{curve} command unless the tension is \texttt{infinity}.

\begin{cd}
\cs{fcncurve}\oarg{\meta{tension}}\marg{($x_0$,$y_0$),($x_1$,$y_1$),$\ldots$}%
\index{fcncurve@\cs{fcncurve}}%
\end{cd}

Draws a curve through the points specified. If the points are listed
with increasing (or decreasing) $x$ coordinates, the curve will also
have increasing (resp., decreasing) $x$ coordinates. The \meta{tension}
is a number equal to or greater than $1.0$ which controls how tightly
the curve is drawn. Generally, the larger it is, the closer the curve is
to the polyline through the points. The default tension is typically $1.2$
(actually $1.2$ times the value set with \cs{settension}). For those who
know something about \MF, this `tension' is not the same as the \MF{}
notion of tension, the tension in the \cs{curve} command, but it
functions in a similar fashion. In this case it can be any positive
number, but only values greater than or equal to $1$ guarantee the
property of never doubling back.


\subsubsection{Circular Arcs.}\label{arcs}

\begin{cd}
\cs{arc}\oarg{\meta{format}}\marg{\meta{specification}}%
\index{arc@\cs{arc}}%
\end{cd}

Draws a circular arc specified as determined by the \meta{format}
optional parameter. This macro and \cs{circle} are unusual in that the
optional \meta{format} parameter determines the format of the other
parameter, as indicated below. The user is responsible for ensuring that
the parameter values make geometric sense.

\begin{cd}
\cs{arc}\oarg{s}\marg{\meta{$p_0$},\meta{$p_1$},\meta{sweep}}\\
\cs{arc}\oarg{t}\marg{\meta{$p_0$},\meta{$p_1$},\meta{$p_2$}}\\
\cs{arc}\oarg{p}\marg{\meta{$c$},\meta{$\theta_1$},\meta{$\theta_2$},\meta{$r$}}\\
\cs{arc}\oarg{a}\marg{\meta{$c$},\meta{$r$},\meta{$\theta_1$},\meta{$\theta_2$}}\\
\cs{arc}\oarg{c}\marg{\meta{$c$},\meta{$p_1$},\meta{$\theta$}}%
\index{arc@\cs{arc}}%
\end{cd}

The optional arguments produce arcs according to the following
descriptions.
\begin{description}
\item[\oarg{s}] The \textit{point-Sweep form} is the default format. It
draws the circular arc starting from the point \meta{$p_0$}, ending at
the point \meta{$p_1$}, and covering an arc angle of \meta{sweep}
degrees, measured anticlockwise around the center of the circle. If,
for example, the points \meta{$p_0$} and \meta{$p_1$} lie on a
horizontal line with \meta{$p_0$} to the \emph{left}, and \meta{sweep}
is between 0~and 360 (degrees), then the arc will sweep \emph{below} the
horizontal line (in order for the arc to be anticlockwise). A
negative value of \meta{sweep} gives a clockwise arc from \meta{$p_0$}
to \meta{$p_1$}.

\item[\oarg{t}] The \textit{Three-point form} draws the circular arc
which passes through all three points given, in the order given.
Internally, this is converted to two applications of the point-sweep
form.

\item[\oarg{p}] The \textit{Polar form} draws the arc of a circle with
center \meta{$c$} starting at the angle \meta{$\theta_1$} and ending at
the angle \meta{$\theta_2$}, with radius \meta{$r$}. Both angles are
measured anticlockwise from the positive $x$ axis.

\item[\oarg{a}] The \textit{Alternate polar form} draws the arc of a
circle with center \meta{$c$} and radius \meta{$r$}, starting at the
angle \meta{$\theta_1$} and ending at the angle \meta{$\theta_2$}. Both
angles are measured anticlockwise from the positive $x$ axis. This is
provided because it seems a more reasonable order of arguments, and
matches the order \cs{sector} requires (see subsection~\ref{other}
below). The \texttt{p} option is retained for backward compatibility.

\item[\oarg{c}] The \textit{Center-point form} draws the circular arc with
center \meta{$c$}, starting at the point \meta{$p_1$}, and sweeping an
angle of \meta{$\theta$} around the center from that point. (This and
the point sweep form are the basic methods of handling arcs---the
previous three formats are translated to one of these two before drawing.)
\end{description}


\subsubsection{Other Figures.}\label{other}

\begin{cd}
\cs{turtle}\marg{\meta{$p_0$},\meta{$v_1$},\meta{$v_2$},$\ldots$}%
\index{turtle@\cs{turtle}}%
\end{cd}

Draws a line segment, starting from the point \meta{$p_0$}, and
extending along the (2-dimen\-sional vector) displacement \meta{$v_1$}.
It then draws a line segment from the previous segment's endpoint, along
displacement \meta{$v_2$}. This continues for all listed displacements,
a process similar to `turtle graphics'.

\begin{cd}
\cs{sector}\marg{\meta{$c$},\meta{$r$},\meta{$\theta_1$},\meta{$\theta_2$}}%
\index{sector@\cs{sector}}%
\end{cd}

Draws the sector, from the angle \meta{$\theta_1$} to the angle
\meta{$\theta_2$} inside the circle with center at the point \meta{$c$}
and radius \meta{$r$}, where both angles are measured in degrees
anticlockwise from the direction parallel to the $x$ axis. The sector
forms a closed path. \emph{Note}: \cs{sector} and \cs{arc}\oarg{p} have
the same parameters, but \emph{in a different
order}.%
    \footnote{This apparently was unintended, but we now have to live
    with it so as not to break existing \file{.tex} files.}

\begin{cd}
\cs{makesector}
\index{makesector@\cs{makesector}}
\end{cd}
The \cs{sector} command requires the center of the arc as one of its
arguments. But if one doesn't know that center (say one only knows three
points the arc connects) then even though the arc can be drawn,
\cs{sector} cannot. The \cs{makesector} command, when followed by any
\cs{arc} command, will find the center and connect it to the two ends of
the arc. It will actually attempt to do the same with any path that
follows, but the `center' it finds (if it finds one) will usually be
meaningless.


\subsubsection{Bar Charts and Pie Charts.}\label{charts}

\begin{cd}
\cs{barchart}\oarg{\meta{start},\meta{sep},\meta{r}}\marg{\meta{h-or-v}}\marg{\meta{list}}\\
\cs{bargraph}$\ldots$\\
\cs{gantt}$\ldots$\\
\cs{histogram}$\ldots$\\
\cs{chartbar}\marg{\meta{num}}\\
\cs{graphbar}\marg{\meta{num}}\\
\cs{histobar}\marg{\meta{num}}%
\index{barchart@\cs{barchart}}%
\index{bargraph@\cs{bargraph}}%
\index{histogram@\cs{histogram}}%
\index{chartbar@\cs{chartbar}}%
\index{graphbar@\cs{graphbar}}%
\index{histobar@\cs{histobar}}%
\end{cd}

The macro \cs{barchart} computes a bar chart or a Gantt chart. It does
not draw the bars, but only defines their rectangular paths which the
user may then draw or fill or both using the \cs{chartbar} macros (see
below). Since bar charts have many names, \cs{bargraph} and
\cs{histogram} are provided as synonyms. The macro \cs{gantt} is also a
synonym; whether a Gantt chart or bar chart is created depends on the
data.

\meta{h-or-v} should be \texttt{v} if you want the ends of the bars to
be measured vertically from the $x$-axis, or \texttt{h} if they should
be measured horizontally from the $y$-axis. \meta{list} should be a
comma-separated list of numbers and/or pairs giving the coordinates of
the end(s) of each bar. A number $c$ is interpreted as the pair $(0,c)$;
a pair $(a,b)$ is interpreted as an interval giving the ends of the bar
(for Gantt diagrams). The rest of this description refers to the
\texttt{h} case; the \texttt{v} case is analogous.

By default the bars are 1 graph unit high (thickness), from $y = n-1$ to
$y = n$. Their width and location are determined by the data. The
optional parameter consists of three numeric parameters separated by
commas. \meta{start} is the $y$-coordinate of the bottom edge of the
first bar, \meta{sep} is the distance between the  bottom edges of
successive bars, and \meta{r} is the fraction of \meta{sep} occupied by
each bar. The default behavior corresponds to \texttt{[0,1,1]}. In
general, bar number $n$ will be from $y = \meta{start} +
(n-1)*\meta{sep}$ to $y = \meta{start} + (n-1 + \meta{r})*\meta{sep}$

Notice the bars are numbered in order from bottom to top. You can
reverse them by making \meta{sep} negative, and making \meta{start} the
top edge of the first bar.

The fraction \meta{r}  should be between -1 and 1. A negative value
reverses the direction from the `leading edge' of the bar to the
`trailing edge'. For example, if one bar chart is created with
\begin{ex}
  \cs{barchart}\oarg{1,1,-.4}\marg{h}\marg{..}
\end{ex}
and another with
\begin{ex}
  \cs{barchart}\oarg{1,1,.4}\marg{h}\marg{..}
\end{ex}
both having the same number of bars, then the first will have its first
bar from $y = 1$ to $y = 1 -.4 = .6$, while the second will have its
first bar adjacent to that one, from $1$ to $1 + .4$. Similarly the next
bars will be above and below $y=2$, etc. This makes it easy to draw bars
next to one another for comparison.

The macro \cs{chartbar} (synonyms \cs{graphbar}, \cs{ganttbar}, and
\cs{histobar}) takes a number from $1$ to the number of elements in the
\meta{list} and draws the rectangular path. This behaves just like any
other figure macro, and the prefix macros from section~\ref{rendering}
may be used to give adjacent bars contrasting colors, fills, etc.


\begin{cd}
\cs{piechart}\oarg{\meta{dir}\meta{angle}}\marg{\meta{$c$},\meta{$r$}}%
    \marg{\meta{list}}\\
\cs{piewedge}\oarg{\meta{spec}\meta{trans}}\marg{\meta{num}}%
\index{piechart@\cs{piechart}}%
\index{piewedge@\cs{piewedge}}%
\end{cd}

The macro \cs{piechart} also does not draw anything, but computes the
\cs{piewedge} regions described below. The first part of the optional
parameter, \meta{dir}, is a single letter which may be either \texttt{c} or
\texttt{a} which stand for \emph{clockwise} or \emph{anticlockwise},
respectively. It is common to draw piecharts with the largest wedge
starting at 12 o'clock (angle 90 degrees) and successive wedges
clockwise from there. This is the default. You can change the starting
angle from 90 with the \meta{angle} parameter, and the change the
direction to counter-clockwise by specifying \texttt{a} for \meta{dir}. It
is also traditional to arrange the wedges from largest to smallest,
except there is often a miscellaneous category which is usually last and
may be larger than some others. Therefore \cs{piechart} makes no attempt
to sort the data. The data is entered as a comma separated \meta{list}
of positive numbers in the second required parameter. These are only
used to determine the relative sizes of the wedges and are not printed
anywhere. The first required parameter should contain a pair \meta{c}
for the center and a positive number \meta{r} for the radius, separated
by a comma.

After a \cs{piechart} command has been issued, the individual wedges may
be drawn, filled, etc., using \cs{piewedge}\marg{1},
\cs{piewedge}\marg{2}, etc. Without the optional argument, the wedges
are located according to the arguments of the last \cs{piechart}
command. The optional argument to \cs{piewedge} can override this. The
parameter \meta{spec} is a single letter, which can be \texttt{x}, \texttt{s}
or \texttt{m}. The \texttt{x} stands for \emph{exploded} and it means the
wedge is moved directly out from the center of the pie a distance
\meta{trans}. \meta{trans} should then be a pure number and is
interpreted as a distance in graph units. The \texttt{s} stands for
\emph{shifted} and in this case \meta{trans} should be a pair of the
form \texttt{(\meta{dx},\meta{dy})} indicating the wedge should be shifted
\meta{dx} horizontally and \meta{dy} vertically (in graph units). The
\texttt{m} stands for \emph{move to}, and \meta{trans} is then the absolute
coordinates \texttt{(\meta{x},\meta{y})} in the graph where the point of
the wedge should be placed.

\subsubsection{Polar Coordinates to Rectangular.}\label{polar}

\begin{cd}
\cs{plr}\marg{(\meta{$r_0$},\meta{$\theta_0$}),
(\meta{$r_1$},\meta{$\theta_1$}), $\ldots$}%
\index{plr@\cs{plr}}%
\end{cd}

Replaces the specified list of polar coordinate pairs by the equivalent
list of rectangular (cartesian) coordinate pairs. Through \cs{plr},
commands designed for rectangular coordinates can be applied to data
represented in polar coordinates---and to data containing both
rectangular and polar coordinate pairs.


\subsection{Colors}\label{colors}

\subsubsection{Setting the Default Colors.}\label{defaultcolors}

\begin{cd}
\cs{drawcolor}\oarg{\meta{model}}\marg{\meta{colorspec}}\\
\cs{fillcolor}$\ldots$\\
\cs{hatchcolor}$\ldots$\\
\cs{pointcolor}$\ldots$\\
\cs{headcolor}$\ldots$\\
\cs{tlabelcolor}$\ldots$\\
\cs{backgroundcolor}$\ldots$%
\index{drawcolor@\cs{drawcolor}}%
\index{fillcolor@\cs{fillcolor}}%
\index{hatchcolor@\cs{hatchcolor}}%
\index{pointcolor@\cs{pointcolor}}%
\index{headcolor@\cs{headcolor}}%
\index{tlabelcolor@\cs{tlabelcolor}}%
\index{backgroundcolor@\cs{backgroundcolor}}%
\end{cd}

These macros set the default color for various drawing
elements. Any curve (with one exception, those drawn by \cs{plotdata}),
whether solid, dashed, dotted, or plotted in symbols, will be in the
color set by \cs{drawcolor}. Set the color used by \cs{gfill} with
\cs{fillcolor}. For all the hatching commands use \cs{hatchcolor}. For
the \cs{point}, \cs{plotsymbol} and \cs{grid} commands use
\cs{pointcolor}, and for arrowheads, \cs{headcolor}. When \opt{mplabels}
is in effect, the color of labels can be set with \cs{tlabelcolor}, and
one can set the color used by \cs{gclear} with \cs{backgroundcolor} (the
same color is used in the interior of unfilled points drawn with
\cs{point}). The optional \meta{model} may be one of \opt{rgb},
\opt{RGB}, \opt{cmyk}, \opt{gray}, and \opt{named}. The \meta{colorspec}
depends on the model, as outlined below. Each of these commands sets a
corresponding \MP{} color variable with the same name (except
\cs{backgroundcolor} sets the color \mfc{background}). Thus one can set
the filling color to the drawing color with
\cs{fillcolor}\marg{drawcolor}.

\subsubsection{\CMP{} Colors.}\label{mpcolors}

If the optional \meta{model} specification is omitted, the color
specification may be any expression recognized as a color by \MP. In
\MP, a color is a triple of numbers like \mfc{(1,.5,.5)}, with the
coordinates between 0 and 1, representing red, green and blue levels,
respectively. White is given by \mfc{(1,1,1)} and black by
\mfc{(0,0,0)}. \CMP{} also has color variables and several have been
predefined: \mfc{red}, \mfc{green}, \mfc{blue}, \mfc{yellow},
\mfc{cyan}, \mfc{magenta}, \mfc{white}, and \mfc{black}. All the names
in the \LaTeX{} \prog{color} package's \file{dvipsnam.def} are
predefined color variable names. Since \MP{} allows color expressions,
colors may be added and multiplied by numerics. Moreover, several \MP{}
color functions have been defined in \file{grafbase.mp}:

\begin{cd}
\mfc{cmyk($c$,$m$,$y$,$k$)}%
\index{cmyk@\mfc{cmyk($c$,$m$,$y$,$k$)}}
\end{cd}

Converts a \opt{cmyk} color specification to \MP's native \opt{rgb}. For
example, the command \mfc{cmyk(1,0,0,0)} yields \mfc{(0,1,1)}, which is
the definition of \mfc{cyan}.

\begin{cd}
\mfc{RGB($R$,$G$,$B$)}%
\index{RGB@\mfc{RGB($R$,$G$,$B$)}}
\end{cd}

Converts an \opt{RGB} color specification to \opt{rgb}. It essentially
just divides each component by 255.

\begin{cd}
\mfc{gray($g$)}%
\index{gray@\mfc{gray($g$)}}
\end{cd}

Converts a numeric $g$ (a gray level) to the corresponding multiple of
\mfc{(1,1,1)}.

\begin{cd}
\mfc{named(\meta{name})},
\mfc{rgb($r$,$g$,$b$)}%
\index{named@\mfc{named(\meta{name})}}%
\index{rgb@rgb($r$,$g$,$b$)}
\end{cd}

These are essentially no-ops. However; \mfc{rgb} will truncate the
arguments to the 0--1 range,  an unknown \meta{name} is converted to
\mfc{black}, and an unknown numeric argument is set to 0.

\medskip
As an example of the use of these functions, one could conceivable
write:
\begin{ex}
    \cs{drawcolor}\marg{0.5*RGB(255,0,0)+0.5*cmyk(1,0,0,0)}
\end{ex}
to have all curves drawn in a color halfway between red and cyan (which
turns out to be the same as \gbc{gray(0.5)}).

\subsubsection{Color Models.}\label{colormodels}

When the optional \meta{model} is specified in the color setting
commands, it determines the format of the color specification:

\medskip
\halign{\quad#\hfil\quad&#\hfil\cr
{\sl Model:}& {\sl Specification:}\cr
\opt{rgb}&  Three numbers in the range 0 to 1 separated by commas.\cr
\opt{RGB}&  Three numbers in the range 0 to 255 separated by commas.\cr
\opt{cmyk}& Four numbers in the range 0 to 1 separated by commas.\cr
\opt{gray}& One number in the range 0 to 1, with 1 indicating
                  white, 0 black.\cr
\opt{named}& A \MP{} color variable name either predefined by
                   \mfp{} or by the user.\cr}

\medskip
\Mfp{} translates
\begin{ex}
  \cs{fillcolor}\oarg{cmyk}\marg{1,.3,0,.2}
\end{ex}
into the equivalent of
\begin{ex}
  \cs{fillcolor}\marg{cmyk(1,.3,0,.2)}.
\end{ex}
Note that when the optional model is specified, the color
specification must not be enclosed in parentheses. Note also that each
model name is the name of a color function described in the previous
subsection. That is how the models are implemented internally.


\subsubsection{Defining a Color Name.}\label{colorname}

\begin{cd}
\cs{mfpdefinecolor}\marg{\meta{name}}\marg{\meta{model}}\marg{\meta{colorspec}}%
\index{mfpdefinecolor@\cs{mfpdefinecolor}}
\end{cd}

This defines a color variable \meta{name} for later use, either in the
commands \cs{drawcolor}, etc., or in the optional parameters to
\cs{draw}, etc. The name can be used alone or in the \opt{named} model.
The mandatory \meta{model} and \meta{colorspec} are as above.

\medskip
A final caution, the colors of an \mfp{} figure are stored in the
\file{.mp} output file, and are not related to colors used or defined by
the \LaTeX{} \prog{color} package. In particular a color defined only by
\LaTeX's \cs{definecolor} command will remain unknown to \mfp.
Conversely, \LaTeX{} commands will not recognize any color defined only
by \cs{mfpdefinecolor}.

\subsubsection{Color in \MF}

\CMF{} was never meant to understand colors, but it certainly can be
taught the difference between black and white and, to a limited extent,
various grays. Starting with version 0.7, \mfp{} will no longer generate
an error when a color-changing command is used under the \opt{metafont}
option. Instead, when possible, the variables that represent colors in
\MP{} will be converted to a numeric value between 0 and 1 in \MF. When
possible (for example, when a region is filled) the numeric will be
interpreted as a gray level and shading (see subsection~\ref{filling})
will be used to approximate the gray. In other cases (drawing or dashing
of curves, placing of points or symbols, filling with a pattern of hatch
lines) the number will be interpreted as black or white: a value less
than 1 will cause the figure to be rendered (in black), while a value
equal to 1 (white) will cause pixels corresponding to the figure to be
erased.

This is still somewhat experimental and depends on adhering to certain
restrictions. \CMF's syntax does not recognize a triple of numbers as
any sort of data structure, but it does allow \emph{commands} to have
any number of parameters in parentheses. So colors must be specified
using the color commands such as \gbc{rgb(1,1,0)} or color names such as
\gbc{yellow}, and never as a bare triple. Also, as currently written,
the color names defined in \file{dvipsnam.mp} are not defined in \MF.
With these provisions the same \mfp{} code can often produce either gray
scale \MF{} pictures or \MP{} color pictures depending only on the
\opt{metapost} option.

The commands \cs{shade} and \cs{gfill}\oarg{gray(.75)} (see
subsection~\ref{filling} for their meaning) will produce a similar shade
of gray, but there is a difference. The first simply adds small dots on
top of whatever is already drawn. The second, however, tries to simulate
the \MP{} effect, which is to cover up whatever is previously drawn.
Therefore, it first zeros all affected pixels before adding the dots to
simulate gray. In particular, \cs{gfill}\oarg{white} should have the
same effect as \cs{gclear}.


\subsection{Shape-Modifier Macros.}\label{modifier}

Some \mfp{} macros operate as \emph{shape-modifier} macros---for
example, if you want to put an arrowhead on a line segment, you could
write: \cs{arrow}\cs{lines}\marg{(0,0),(1,0)}. These are always prefixed
to some figure drawing command, and apply only to the next following
figure macro (which can be rather far removed) provided that only other
prefix commands intervene. This is a rather long section, but even more
modification prefixes are documented in subsection~\ref{transformation}.

For the purposes of these macros, a distinction must be made in the
figure macros between `open' and `closed' paths. A path that merely
returns to its starting point is \emph{not} automatically closed; such a
path is open, and must be explicitly closed, for example by \cs{lclosed}
(see below). The (already) closed paths are those that have
`\texttt{closed}' in their name plus: \cs{rect}, \cs{circle},
\cs{ellipse}, \cs{sector}, \cs{cyclic}, \cs{polygon}, \cs{plrregion},
\cs{chartbar}, \cs{piewedge}, \cs{tlabelrect}, \cs{tlabeloval},
\cs{tlabelellipse}, \cs{tlabelcircle} and \cs{btwnfcn} (below).

\subsubsection{Closure of Paths.}\label{closure}

\begin{cd}
\cs{lclosed}$\ldots$%
\index{lclosed@\cs{lclosed}}
\end{cd}

Makes each open path into a closed path by adding a line segment between
the endpoints of the path.

\begin{cd}
\cs{bclosed}\oarg{\meta{tens}}$\ldots$
\index{bclosed@\cs{bclosed}}%
\end{cd}

This macro is similar to \cs{lclosed}, except that it closes an open
path smoothly by drawing a B\'ezier curve. A B\'ezier is \MF's natural
way of connecting points into a curve, and \cs{bclosed} is the simplest
and most efficient closure next to \cs{lclosed}. Moreover it usually
gives a reasonably aesthetic result. Sometimes, however, one might wish
a tighter connection. If that is the case, use the optional argument
with a value of the tension \meta{tens} greater than $1$, the default.
The command \cs{settension} (see subsection~\ref{curves}) can be used to
change the default.

\begin{cd}
\cs{sclosed}\oarg{\meta{tens}}$\ldots$%
\index{sclosed@\cs{sclosed}}
\end{cd}

This closes the curve by mimicking the definition of the \cs{curve}
command. That command tries to force the curve to pass through the $n$th
point in a direction parallel to the line from point $(n-1)$ to point
$(n+1)$. In order to close a curve in this way, the direction at the two
endpoints often has to be changed, and this changes the shape of the
first and last segments of the curve. Use \cs{bclosed} if you don't wish
this to happen. However, \cs{sclosed}\cs{curve} produces the same result
as \cs{cyclic} given the same points and tension valuse. The optional
tension argument is as in the \cs{bclosed} command.


\subsubsection{Reversal, Connection and Subpaths.}\label{reversal}

\begin{cd}
\cs{reverse}$\ldots$%
\index{reverse@\cs{reverse}}
\end{cd}

Turns a path around, reversing its sense. This will affect both
the direction of arrows (e.g. bi-directional arrows can be coded with
\cs{arrow}\cs{reverse}\cs{arrow}$\ldots$, where the first \cs{arrow}
modifier applies to the \emph{reversed} path), and the order of
endpoints for a \cs{connect}$\ldots$\cs{endconnect} environment (below).


\begin{cd}
\cs{connect} $\ldots$
\cs{endconnect}%
\index{connect@\cs{connect}}
\index{endconnect@\cs{endconnect}}
\end{cd}

This pair of macros, acting as an environment, adds line segments from
the trailing endpoint of one path to the leading endpoint of the
next path, in the given order. The result is a connected, \emph{open}
path.

\emph{Note}: In \LaTeX, this pair of macros can be used in the form of a
\LaTeX-style environment called \env{connect} ---as in
\cs{begin}\marg{connect}$\ldots$\cs{end}\marg{connect}.

\begin{cd}
\cs{partpath}\marg{\meta{frac1},\meta{frac2}}\dots\\
\cs{subpath}\marg{\meta{num1},\meta{num2}}\dots%
\index{partpath@\cs{partpath}}%
\index{subpath@\cs{subpath}}
\end{cd}

Both produce a part of the following path. In \cs{partpath} the
parameters \meta{frac1} and \meta{frac2} should be numbers between 0 and
1. The path produced travels the same course as the path that follows,
but starts at the point that is \meta{frac1} of the original length
along it, and ends at the point \meta{frac2} of its original length. If
\meta{frac1} is greater than \meta{frac2}, the sense of the path is
reversed. In \cs{subpath}, the two numbers should be between 0 and the
number of B\'ezier segments in the path. This is mainly for experienced
\MF ers and provides an \mfp{} interface to \MF's
`\mfc{subpath}' operation.

As an example of \cs{partpath}, one can put an arrowhead (see next
subsection) in the middle of a path with something like the following.

\begin{ex}
\cs{arrow}\cs{partpath}\marg{0,.5}\cs{draw}\dots
\end{ex}


\subsubsection{Arrows.}\label{arrows}

\begin{cd}
\cs{arrow}\oarg{l\meta{headlen}}\oarg{r\meta{rotate}}%
    \oarg{b\meta{backset}}\oarg{c\meta{color}}$\ldots$%
\index{arrow@\cs{arrow}}
\end{cd}

Draws an arrowhead at the endpoint of the open path (or at the last key
point of the closed path) that follows. The optional parameter
\meta{headlen} determines the length of the arrowhead.  The default is
the value of the \TeX{} dimension \cs{headlen}, initially \dim{3pt}. The
optional parameter \meta{rotate} allows the arrowhead to be rotated
anticlockwise around its point an angle of \meta{rotate} degrees. The
default is 0. The optional parameter \meta{backset} allows the arrowhead
to be `set back' from its original point, thus allowing e.g. double
arrowheads. This parameter is in the form of a \TeX{} dimension---its
default value is \dim{0pt}. If an arrowhead is both rotated and set
back, the rotation affects the direction in which the arrowhead is set
back. The optional \meta{color} defaults to \gbc{headcolor}. The
optional parameters may appear in any order, but the indicated key
character for each parameter must always appear.


\subsection{Rendering macros}\label{rendering}

\subsubsection{Drawing.}\label{drawing}

When \mfp{} is loaded, the initial way in which figures are drawn
is with a solid outline. That is, \cs{lines}\marg{(1,0),(1,1),(0,0)}
will draw two solid lines connecting the points. When the macros in this
section are used, any previously established default (see
subsection~\ref{default} below) is overridden.

\begin{cd}
\cs{draw}\oarg{\meta{color}}$\ldots$%
\index{draw@\cs{draw}}
\end{cd}

Draws the subsequent path using a solid outline. For an example: to both
draw a curve and hatch its interior, \cs{draw}\cs{hatch} must be used.
The default for \meta{color} is \gbc{drawcolor}.

To save repetition, the color used for the following commands is also
\gbc{drawcolor}: \cs{dashed}, \cs{dotted}, \cs{plot}, \cs{plotnodes},
and \cs{gendashed},

\begin{cd}
\cs{dashed}\oarg{\meta{length},\meta{space}}$\ldots$%
\index{dashed@\cs{dashed}}
\end{cd}

Draws dashed segments along the path specified in the next command. The
default length of the dashes is the value of the \TeX{} dimension
\cs{dashlen}, initially \dim{4pt}. The default space between the dashes
is the value of the \TeX{} dimension \cs{dashspace}, initially
\dim{4pt}. The dashes and the spaces between may be increased or
decreased by as much as ${1\over n}$ of their value, where $n$ is the
number of spaces appearing in the curve, in order to have the proper
dashes at the ends. The dashes at the ends are half of \cs{dashlen}
long.

\begin{cd}
\cs{dotted}\oarg{\meta{size},\meta{space}}$\ldots$%
\index{dotted@\cs{dotted}}
\end{cd}

Draws dots along the specified path. The default size of the dots is the
value of the \TeX{} dimension \cs{dotsize}, initially \dim{0.5pt}. The
default space between the dots is the value of the \TeX{} dimension
\cs{dotspace}, initially \dim{3pt}. The size of the spaces may be
adjusted as in \cs{dashed}.

\begin{cd}
\cs{plot}\oarg{\meta{size},\meta{space}}\marg{\meta{symbol}}$\ldots$%
\index{plot@\cs{plot}}
\end{cd}

Similar to \cs{dotted} except copies of  \meta{symbol} are drawn along
the path. Possible symbols are those listed under \cs{plotsymbol} in
subsection~\ref{points}. The default \meta{size} is \cs{pointsize} and
the default \meta{space} is \cs{symbolspace}, initially \dim{5pt}.

\begin{cd}
\cs{plotnodes}\oarg{\meta{size}}\marg{\meta{symbol}}$\ldots$%
\index{plotnodes@\cs{plotnodes}}
\end{cd}

This places a symbol (same possibilities as in \cs{plotsymbol}, see
subsection~\ref{points}) at each node of the path that follows. A node
is one of the points through which \MF{} draws its curve.  If one of the
macros \cs{polyline}\marg{$\ldots$} or \cs{curve}\marg{$\ldots$}
follows, each of the points listed is a node. In the \cs{datafile}
command (below), each of the data points in the file is. In the function
macros (below) the points corresponding to \meta{min}, \meta{max} and
each step in between are nodes. The optional \meta{size} defaults to
\cs{pointsize}. If the command \cs{clearsymbols} has been issued then
the interiors of the open symbols are erased. The effect of something
like the following is rather nice:

\begin{verbatim}
  \clearsymbols
  \plotnodes{Circle}\draw\polyline{...}
\end{verbatim}
This will first draw the polyline with solid lines, and then the points
listed will be plotted as open circles with the portion of the lines
inside the circles erased. One sees a series of open circles connected
one to the next by line segments


\begin{cd}
\cs{dashpattern}\marg{\meta{name}}%
    \marg{\meta{len1},\meta{len2},$\ldots$,\meta{len2k}}%
\index{dashpattern@\cs{dashpattern}}
\end{cd}

For more general dash patterns than \cs{dashed} and \cs{dotted} provide,
there is a generalized dashing command. One must first establish a named
dashing pattern with this command. \meta{name} can be any sequence of
letters and underscores. Try to make it distinctive to avoid undoing
some internal variable. \meta{len1} through \meta{len2k} are an even
number of lengths. The odd ones determine the lengths of dashes, the
even ones the lengths of spaces. A dash of length \texttt{0pt} means a
dot. An alternating dot-dash pattern can be specified with

\begin{ex}
    \cs{dashpattern}\marg{dotdash}\marg{0pt,4pt,3pt,4pt}.
\end{ex}
\emph{Note}: Since pens have some thickness, dashes look a little
longer, and spaces a little shorter, than the numbers suggest. If one
wants dashes and space with the same length, one needs to take the size
desired and increase the spaces by the thickness of the drawing pen
(normally \dim{0.5pt}) and decrease the dashes by the same amount.

If \cs{dashpattern} is used with an odd number of entries, a space of
length \dim{0pt} is appended. This makes the last dash in one copy of
the pattern abut the first dash in the next copy.

\begin{cd}
\cs{gendashed}\marg{\meta{name}}$\ldots$%
\index{gendashed@\cs{gendashed}}
\end{cd}

Once a dashing pattern name has been defined, it can be used in this
command to draw the curve that follows it. Using a name not previously
defined will cause the curve to be drawn with a solid line, and generate
a \MF{} warning, but \TeX{} will not complain. If all the dimensions in
a dash pattern are 0, \cs{gendashed} responds by drawing a solid curve.
The same is true if the pattern has only one entry.


\subsubsection{Shading, Filling, Erasing, Clipping,
Hatching.}\label{filling}

These macros can all be used to fill (or unfill) the interior of closed
paths, even if the paths cross themselves. Filling an open curve is
technically an error, but the \MF{} code responds by drawing the path
and not doing any filling. These macros replace the default rendering:
when they are used the outline will not be drawn unless an explicit
prefix to do so is present.

\begin{cd}
\cs{gfill}\oarg{\meta{color}}$\ldots$%
\index{gfill@\cs{gfill}}
\end{cd}

Fills in the subsequent closed path. Under \MP{} it fills with
\meta{color}, which defaults to
\index{fillcolor@\gbc{fillcolor}}\gbc{fillcolor}. Under \MF{} it
approximates the color with a shade of gray, clears the interior, and
then fills with a pattern of black and white pixels simulating gray.

\begin{cd}
\cs{gclear}$\ldots$%
\index{gclear@\cs{gclear}}
\end{cd}

Erases everything \emph{inside} the subsequent closed path (except text
labels under some circumstances, see section~\ref{mplabels} and
\ref{overlaylabels}). Under \MP{} it actually fills with the
predefined color named \mfc{background}. Since \mfc{background} is normally
white, and so are most actual backgrounds, this is usually
indistinguishable from clearing.

\begin{cd}
\cs{gclip}$\ldots$%
\index{gclip@\cs{gclip}}
\end{cd}

Erases everything \emph{outside} the subsequent closed path from the
picture (except text labels under some circumstances, see
section~\ref{mplabels} and \ref{overlaylabels}).

\begin{cd}
\cs{shade}\oarg{\meta{shadesp}}$\ldots$%
\index{shade@\cs{shade}}
\end{cd}

Shades the interior of the subsequent closed path with dots. The
diameter of the dots is the \MF{} variable \mfc{shadewd}, set by the
macro \cs{shadewd}\marg{\meta{size}}. Normally this is \dim{0.5pt}. The
optional argument specifies the spacing between (the centers of) the
dots, which defaults to the \TeX{} dimension \cs{shadespace}, initially
\dim{1pt}. If \cs{shadespace} is less than \mfc{shadewd}, the closed
path is filled with black, as if with \cs{gfill}. Under \MP{} this macro
actually fills the path's interior with a shade of gray. The shade to
use is computed based on \cs{shadespace} and \mfc{shadewd}. The default
values of these parameters correspond to a gray level of 75\% of white.%
    \footnote{If \cs{shadewd} is $w$ and \cs{shadespace} is $s$, then
    the level of gray is $1 - (w/s)^2$, where $0$ denotes black and $1$
    white.} %
The \MF{} version attempts to optimize the dots to the pixel grid
corresponding to the printers resolution (to avoid generating dither
lines). Because this involves rounding, it will happen that values of
\cs{shadespace} that are relatively close and at the same time close to
\mfc{shadewd} produce exactly the same shade. Most of the time, however,
values of \cs{shadespace} that differ by at least 20\% will produce
different patterns. The actual behavior for particular values of the
parameters and particular printer resolutions cannot be predicted, and
we even make no guarantee it will not change from one version of \mfp{}
to another.

\begin{cd}
\cs{polkadot}\oarg{\meta{space}}$\ldots$%
\index{polkadot@\cs{polkadot}}
\end{cd}

Fills the interior of a closed path with large dots. This is almost what
\cs{shade} does, but there are several differences. \cs{shade} is
intended solely to simulate a gray fill in \MF{} where the only color is
black. So it is optimized for small dots aligned to the pixel grid (in
\MF). In \MP{} all it does is fill with gray and is intended merely for
compatibility. The macro \cs{polkadot} is intended for large dots in any
color, and so it optimizes spacing (a nice hexagonal array) and makes no
attempt to align at the pixel level. The \meta{space} defaults to the
\TeX{} dimension \cs{polkadotspace}, initially \dim{10pt}. The diameter
of the dots is the value of the \MF{} variable \mfc{polkadotwd}, which
can be set with \cs{polkadotwd}\marg{\meta{size}}, and is initially
\dim{5pt}. The dots are colored with
\index{fillcolor@\gbc{fillcolor}}\gbc{fillcolor}. In \MF, nonblack
values of \gbc{fillcolor} will produce shaded dots.

\begin{cd}
\cs{thatch}\oarg{\meta{hatchsp},\meta{angle}}\oarg{\meta{color}}$\ldots$%
\index{thatch@\cs{thatch}}
\end{cd}

Fills a closed path with equally spaced parallel lines at the specified
angle. The thickness of the lines is set by the macro \cs{hatchwd}. In
the optional argument, \meta{hatchsp} specifies the space between lines,
which defaults to the \TeX{} dimension \cs{hatchspace}, initially
\dim{3pt}. The \meta{angle} defaults to 0. The \meta{color} defaults to
\gbc{hatchcolor}. If \cs{hatchspace} is less than the line thickness,
the closed path is filled with \meta{color}, as if with \cs{gfill}. If
the first optional argument appears, both parts must be present,
separated by a comma. For the color argument to be present, the other
optional argument must also be present. However, if one wishes only to
override the default color one can use an empty first optional argument
(completely empty, no spaces).

\begin{cd}
\cs{lhatch}\oarg{\meta{hatchsp}}\oarg{\meta{color}}$\ldots$%
\index{lhatch@\cs{lhatch}}
\end{cd}

Draws lines shading in the subsequent closed path in a left-oblique
hatched (upper left to lower right) pattern. It is exactly the same as
\cs{thatch}\oarg{\meta{hatchsp},-45}\oarg{\meta{color}}$\ldots$

\begin{cd}
\cs{rhatch}\oarg{\meta{hatchsp}}\oarg{\meta{color}}$\ldots$%
\index{rhatch@\cs{rhatch}}
\end{cd}

Draws lines shading in the subsequent closed path in a right-oblique
hatched (lower left to upper right) pattern. It is exactly the same as
\cs{thatch}\oarg{\meta{hatchsp},45}\oarg{\meta{color}}$\ldots$

\begin{cd}
\cs{hatch}\oarg{\meta{hatchsp}}\oarg{\meta{color}}$\ldots$\\
\cs{xhatch}\oarg{\meta{hatchsp}}\oarg{\meta{color}}$\ldots$%
\index{hatch@\cs{hatch}}%
\index{xhatch@\cs{xhatch}}
\end{cd}

Draws lines shading in the subsequent closed path in a cross-hatched
pattern. It is exactly the same as \cs{rhatch} followed by \cs{lhatch}
using the same \meta{hatchsp} and \meta{color}.

Hatching should normally be used very sparingly, or never if
alternatives are available (color, shading). Hatching at two different
angles is, however, almost the only way to fill in two regions that
\emph{automatically} shows the overlapping region.


\subsubsection{Changing the Default Rendering.}\label{default}

\emph{Rendering} is the process of converting a geometric description
into a drawing.  In \MF, this means producing a bitmap (\MF{} stores
these in \mfc{picture} variables), either by stroking (drawing) a path
using a particular pen), or by filling a closed path. In \MP{} it means
producing a \PS{} description of strokes with pens, and fills

\begin{cd}
\cs{setrender}\marg{\meta{\TeX{} commands}}%
\index{setrender@\cs{setrender}}
\end{cd}

Initially, \mfp{} uses the \cs{draw} command (stroking) as the default
operation when a figure is to be rendered.  However, this can be changed
to any combination of \mfp{} rendering commands and/or other \TeX{}
commands, by using the \cs{setrender} command.  This redefinition is
local inside an \env{mfpic} environment, so it can be enclosed in braces
to restrict its range. Outside an \env{mfpic} environment it is a global
redefinition.

For example, after \cs{setrender}\marg{\cs{dashed}\cs{shade}} the
command \cs{circle}\marg{(0,0),1} produces a shaded circle with a dashed
outline. Any explicit rendering prefix overrides this default.

\subsubsection{Examples.}\label{examples}

It may be instructive, for the purpose of understanding the syntax of
\emph{shape-modifier and rendering prefixes}, to consider two examples:
\begin{ex}
    \cs{draw}\cs{shade}\cs{lclosed}\cs{lines}\marg{...}
\end{ex}
which shades inside a polygon and draws its outline; and
\begin{ex}
    \cs{shade}\cs{lclosed}\cs{draw}\cs{lines}\marg{...}
\end{ex}
which draws all of the outline \emph{except} the line segment supplied
by \cs{lclosed}, then shades the interior. Thus, in the first case the
path is defined (by \cs{lines}) then closed, then the resulting closed
path is shaded, then drawn; while in the second case the order is:
defined, drawn, closed, shaded. In particular, what is drawn is the path
not yet closed.


\subsection{Functions and Plotting.}\label{functions}

In the following macros, expressions like $f(\mathtt{x})$, $g(\mathtt{t})$
stand for any legal \MF{} expression, in which the only unknown
variables are those indicated (\texttt{x} in the first case, and \texttt{t} in
the second).

\subsubsection{Defining Functions}\label{defining}

\begin{cd}
\cs{fdef}\marg{\meta{fcn}}\marg{\meta{param1},\meta{param2},$\ldots$}%
    \marg{\meta{mf-expr}}%
\index{fdef@\cs{fdef}}
\end{cd}

Defines a \MF{} function \meta{fcn} of the parameters \meta{param1},
\meta{param2}, $\ldots$, by the \MF{} expression \meta{mf-expr} in which
the only free parameters are those named.  The return type of the
function is the same as the type of the expression. What is allowed for
the function name \meta{fcn} is more restrictive than \MF's rule for
variable names. Roughly speaking, it should consist of letters and
underscore characters only. (In particular, for those that know what
this means, the name should have no suffixes.) Try to make the names
distinctive to avoid redefining internal \MF{} commands.

The expression \meta{mf-expr} is passed directly into the corresponding
\MF{} macro and interpreted there, so \MF's rules for algebraic
expressions apply. If \cs{fdef} occurs inside an \env{mfpic}
environment, it is local to that environment, otherwise it is available
to all subsequent \env{mfpic} environments.

As an example, after \cs{fdef}\marg{myfcn}\marg{s,t}\marg{s*t-t}, any
place below where a \MF{} expression is required, you can use
\mfc{myfcn(2,3)} to mean \mfc{2*3-3} and \mfc{myfcn(x,x)} to mean
\mfc{x*x-x}.

Operations available include \mfc{+}, \mfc{-}, \mfc{*}, \mfc{/}, and
\mfc{**} (\mfc{x**y}$=x^y$), with \mfc{(} and \mfc{)} for grouping.
Functions already available include the standard \MF{} functions
\mfc{round}, \mfc{floor}, \mfc{ceiling}, \mfc{abs}, \mfc{sqrt},
\mfc{sind}, \mfc{cosd}, \mfc{mlog}, and \mfc{mexp}. Note that in \MF{}
the operations \mfc{*} and \mfc{**} have the same level of precedence,
so \mfc{x*y**z} means $(xy)^z$. Use parentheses liberally!

(\textit{Notes:} The \MF{} trigonometric functions \mfc{sind} and
\mfc{cosd} take arguments in degrees; \mfc{mlog(x)}$=256\ln x$, and
\mfc{mexp} is its inverse.) You can also define the function \meta{fcn}
by cases, using the \MF{} conditional expression
\begin{ex}
    \mfc{if~\meta{boolean}:~\meta{expr}~elseif
    \meta{boolean}:~$\ldots$~else:~\meta{expr}~fi}.
\end{ex}
Relations available for the \meta{boolean} part of the expression
include \mfc{=}, \mfc{<}, \mfc{>}, \mfc{<=}, \mfc{<>} and \mfc{>=}.

Complicated functions can be defined by a compound expression, which is
a series of \MF{} statements, followed by an expression, all enclosed in
the commands \mfc{begingroup} and \mfc{endgroup}. The \cs{fdef}
command automatically supplies the grouping around the definition so
the user need not type them if the entire \meta{mf-expr} is one such
compound expression. \CMF{} functions can call \MF{} functions,
even recursively.

Many common functions have been predefined in \file{grafbase}. These
include all the usual trig functions \mfc{tand}, \mfc{cotd}, \mfc{secd},
\mfc{cscd}, which take angles in degrees, plus variants \mfc{sin},
\mfc{cos}, \mfc{tan}, \mfc{cot}, \mfc{sec}, and \mfc{csc}, which take
angles in radians. Some inverse trig functions are also available, the
following produce angles in degrees: \mfc{asin}, \mfc{acos}, and
\mfc{atan}, and the following in radians: \mfc{invsin}, \mfc{invcos},
\mfc{invtan}. The exponential and hyperbolic functions: \mfc{exp},
\mfc{sinh}, \mfc{cosh}, \mfc{tanh}, and their inverses \mfc{ln} (or
\mfc{log}), \mfc{asinh}, \mfc{acosh}, and \mfc{atanh} are also defined.

\subsubsection{Plotting Functions}\label{plotting}

The plotting macros take two or more arguments. They have an optional
first argument, \meta{spec}, which determines whether a function is
drawn smooth (as a \MF{} B\'ezier curve), or polygonal (as line
segments)---if \meta{spec} is \texttt{p}, the function will be
polygonal. Otherwise the \meta{spec} should be \texttt{s}, followed by
an optional positive number no smaller than 0.75. In this case the
function will be smooth with a tension equal to the number. See the
\cs{curve} command (subsection~\ref{curves}) for an explanation of
tension. The default \meta{spec} depends on the purpose of the macro.

One compulsory argument contains three values \meta{min}, \meta{max} and
\meta{step} separated by commas.  The independent variable of a function
starts at the value \meta{min} and steps by \meta{step} until reaching
\meta{max}. If \meta{max}${}-{}$\meta{min} is not a whole number of
steps, then round$((\meta{max}-\meta{min})/\meta{step})$ equal steps are
used. One may have to experiment with the size of \meta{step}, since
\MF{} merely connects the points corresponding to these steps with what
\emph{it} considers to be a smooth curve. Smaller \meta{step} gives
better accuracy, but too small may cause the curve to exceed \MF's
capacity or slow down its processing. Increasing the tension may help
keep the curve in line, but at the expense of reduced smoothness.

There are one or more subsequent arguments, each of which is a \MF{}
function or expression as described above.

\begin{cd}
\cs{function}\oarg{\meta{spec}}\marg{\meta{$x_{\mathrm{min}}$},%
    \meta{$x_{\mathrm{max}}$},\meta{$\Delta x$}}%
    \marg{$f(\mathtt{x})$}%
\index{function@\cs{function}}
\end{cd}

Plots $f(\mathtt{x})$, a \MF{} numeric function or expression of one
numeric argument, which must be denoted by a literal \texttt{x}. The
default \meta{spec} is \texttt{s}. For example
\begin{ex}
\cs{function}\marg{0,pi,pi/10}\marg{sin x}
\end{ex}
draws the graph of $\sin x$ between 0 and $\pi$.

\begin{cd}
\cs{parafcn}\oarg{\meta{spec}}\marg{\meta{$t_{\mathrm{min}}$},%
    \meta{$t_{\mathrm{max}}$},\meta{$\Delta t$}}%
    \marg{\meta{pfcn}}%
\index{parafcn@\cs{parafcn}}
\end{cd}

Plots the parametric path determined by \meta{pfcn}, where \meta{pfcn}
is a \MF{} function or expression of one numeric argument \texttt{t},
returning a \MF{} \emph{pair}. Or a pair of numeric expressions
$(x(\mathtt{t}),y(\mathtt{t}))$ enclosed in parentheses and separated by
a comma. The default \meta{spec} is \texttt{s}. For example
\begin{ex}
\cs{parafcn}\marg{0,1,.1}\marg{(2t, t + t*t)}
\end{ex}
plots a smooth parabola from $(0,0)$ to $(2,2)$.

\begin{cd}
\cs{plrfcn}\oarg{\meta{spec}}\marg{\meta{$\theta_{\mathrm{min}}$},%
    \meta{$\theta_{\mathrm{max}}$},\meta{$\Delta\theta$}}%
    \marg{$f(\mathtt{t})$}%
\index{plrfcn@\cs{plrfcn}}
\end{cd}

Plots the polar function determined by $r=f(\theta)$, where $f$ is a
\MF{} numeric function or expression of one numeric argument, and
$\theta$ varies from \meta{$\theta_{\mathrm{min}}$} to
\meta{$\theta_{\mathrm{max}}$} in steps of \meta{$\Delta\theta$}. Each
$\theta$ value is interpreted as an angle measured in \emph{degrees}. In
the expression $f(\mathtt{t})$, the unknown \texttt{t} stands for
$\theta$. The default \meta{spec} is \texttt{s}. For example
\begin{ex}
\cs{plrfcn}\marg{0,90,5}\marg{sind (2t)}
\end{ex}
draws one loop of a 4-petal rosette. If one needs radian measures, use
something like the following.
\begin{ex}
\cs{plrfcn}\marg{0,pi*radian,pi*radian/18}\marg{sin (2t/radian)}
\end{ex}


\begin{cd}
\cs{btwnfcn}\oarg{\meta{spec}}\marg{\meta{$x_{\mathrm{min}}$},\meta{$x_{\mathrm{max}}$},\meta{$\Delta x$}}%
    \marg{$f(\mathtt{x})$}\marg{$g(\mathtt{x})$}%
\index{btwnfcn@\cs{btwnfcn}}
\end{cd}

Draws the region between the two functions $f(x)$ and $g(x)$, these
being numeric functions of one numeric argument \texttt{x}. The region is
bounded also by the vertical lines at \meta{$x_{\mathrm{min}}$} and \meta{$x_{\mathrm{max}}$}.
Unlike the previous function macros, the default \meta{spec} is
\texttt{p}---this macro is intended to be used for shading between drawn
functions, a task for which smoothness is usually unnecessary.
For example
\begin{ex}
\cs{shade}\cs{btwnfcn}\marg{0,180,5}\marg{0}\marg{sind x}
\end{ex}
shades the area between first crest of a sine wave and the x-axis.

Note: the effect of \cs{btwnfcn} could also be accomplished with
\begin{ex}
  \cs{lclosed}\cs{connect}\\
    \cs{function}\marg{\meta{$x_{\mathrm{min}}$},%
    \meta{$x_{\mathrm{max}}$},\meta{$\Delta x$}}\marg{$f(\mathtt{x})$}\\
    \cs{reverse}\cs{function}\marg{\meta{$x_{\mathrm{min}}$},%
    \meta{$x_{\mathrm{max}}$},\meta{$\Delta x$}}\marg{$g(\mathtt{x})$}\\
  \cs{endconnect}
\end{ex}

\begin{cd}
\cs{plrregion}\oarg{\meta{spec}}%
    \marg{\meta{$\theta_{\mathrm{min}}$},\meta{$\theta_{\mathrm{max}}$},%
    \meta{$\Delta\theta$}}\marg{$f(\mathtt{t})$}%
\index{plrregion@\cs{plrregion}}
\end{cd}

Plots the polar region determined by $r=f(\theta)$, where $f$ is a \MF{}
numeric function of one numeric argument \texttt{t}.  The $\theta$
values are angles (measured in \emph{degrees}), varying from
\meta{$\theta_{\mathrm{min}}$} to \meta{$\theta_{\mathrm{max}}$} in
steps of \meta{$\Delta\theta$}. In the expression $f(\mathtt{t})$, the
\texttt{t} stands for $\theta$. The region is also bounded by the angles
\meta{$\theta_{\mathrm{min}}$} and \meta{$\theta_{\mathrm{max}}$}, i.e.
by the line segments joining the origin to the endpoints of the
function. The default \meta{spec} is \texttt{p} ---this macro is
intended to be used for shading a region with the boundary drawn, a task
for which smoothness is usually unnecessary. For example
\begin{ex}
\cs{shade}\cs{plrregion}\marg{0,90,5}\marg{sind (2t)}
\end{ex}
shades one loop of the 4-petal rosette.


\subsubsection{Plotting external data files}\label{external}

\begin{cd}
\cs{datafile}\oarg{\meta{spec}}\marg{\meta{file}}\\
\cs{smoothdata}\oarg{\meta{tension}}\\
\cs{unsmoothdata}%
\index{datafile@\cs{datafile}}%
\index{smoothdata@\cs{smoothdata}}%
\index{unsmoothdata@\cs{unsmoothdata}}
\end{cd}

\cs{datafile} defines a curve connecting the points listed in the file
\meta{file}. (The context makes it clear whether this meaning of
\cs{datafile} or that of subsection~\ref{list} is meant.) The
\meta{spec} may be \texttt{p} to produce a polygonal path, or \texttt{s}
followed by a tension value (as in \cs{curve}) to produce a smooth path.
If no \meta{spec} is given, the default is initially \texttt{p}, but
\cs{smoothdata} may be used to change this. Thus, after the command
\cs{smoothdata}\oarg{\meta{tension}} the default \meta{spec} is changed
to \texttt{s\meta{tension}}. If the tension parameter is not supplied it
defaults to \mfc{1.0} (or the value set by the \cs{settension} command
if one has been used).

The command \cs{unsmoothdata} restores the default \meta{spec} to
\texttt{p}.

By default, each non-blank line in the file is assumed to contain at
least two numbers, separated by whitespace (blanks or tabs). The first
two numbers on each line are assumed to represent the $x$- and
$y$-coordinates of a point. Initial blank lines in the file are ignored,
as are comments. The comment character in the data file is assumed to be
\texttt{\%}, but it can be reset using \cs{mfpdatacomment} (below). Any
blank line other than at the start of the file causes the curve to
terminate. The \cs{datafile} command may be preceded by any of the
prefix commands, so that, for example, a closed curve could be formed
with \cs{lclosed}\cs{datafile}\marg{data.dat}.

The \index{datafile@\cs{datafile}}\cs{datafile} command has another use,
independent of the above description. We saw in subsection~\ref{list}
that any \mfp{} command (other than one that prints text labels) that
takes as its last argument a list of points (or numerical values)
separated by commas, can have that list replaced with a reference to an
external data file. For example, if a file \file{ptlist.dat} contains
two or more numerical values per line separated by whitespace, then one
can draw a dot at each of the points corresponding to the first pair of
numbers on each line with the following.
\begin{ex}
    \cs{point}\cs{datafile}\marg{ptlist.dat}
\end{ex}
In fact there is no essential difference between `\cs{datafile}\oarg{p}'
and `\cs{polyline}\cs{datafile}', and no difference between
`\cs{datafile}\oarg{s}' and `\cs{curve}\cs{datafile}'.

Here is the full list of \mfp{} macros that allow this usage of
\cs{datafile}\index{datafile@\cs{datafile}}:

    \begin{raggedright}
\begin{itemize}
\item Numeric data: \cs{piechart}, \cs{barchart}, \cs{numericarray}, and
    all the axis marks commands.
\item Point or vector data: \cs{point}, \cs{plotsymbol}, \cs{polyline},
    \cs{polygon}, \cs{fcncurve}, \cs{curve}, \cs{cyclic}, \cs{turtle},
    \cs{qspline}, \cs{closedqspline}, \cs{cspline}, \cs{closedcspline},
    \cs{mfbezier}, \cs{closedmfbezier}, \cs{qbeziers},
    \cs{closedqbeziers}, and \cs{pairarray}.
\end{itemize}

    \end{raggedright}

\begin{cd}
\cs{mfpdatacomment}\cs{}\meta{char}%
\index{mfpdatacomment@\cs{mfpdatacomment}}
\end{cd}

Changes \meta{char} to a comment character and changes the usual \TeX{}
comment character \texttt{\%} to an ordinary character \emph{while reading a
datafile for drawing}.

\begin{cd}
\cs{using}\marg{\meta{in-pattern}}\marg{\meta{out-pattern}}%
\index{using@\cs{using}}
\end{cd}

Used to change the assumptions about the format of the data file. For
example, if there are four numbers on each line separated by commas, to
plot the third against the second (in that order) you can say
\cs{using}\marg{\#1,\#2,\#3,\#4}\marg{(\#3,\#2)}. This means the
following: Everything on a line up to the first comma is assigned to
parameter \texttt{\#1}, everything from there up to the second comma is
assigned to parameter \texttt{\#2}, etc. Everything from the third comma
to the end of line is assigned to \texttt{\#4}. When the line is
processed by \TeX{} a \MF{} pair is produced representing a point on the
curve. \CMF{} pair expressions can be used in the output portion of
\cs{using}. For example \cs{using}\marg{\#1,\#2,\#3}\marg{(\#2,\#1)/10}
or even \cs{using}\marg{\#1 \#2 \#3}\marg{polar(\#1,\#2)} if the data
are polar coordinates. The default assumptions of the \cs{datafile}
command (i.e., space separated numbers, the first two determining each
point) correspond to the setting
\begin{ex}
\cs{using}\marg{\#1 \#2 \#3}\marg{(\#1,\#2)}
\end{ex}
The \cs{using} command cannot normally be used in the replacement text
of another command. Or rather, it can be so used, but then each
\texttt{\#} has to be doubled. If a \cs{using} declaration occurs in an
\env{mfpic} environment it is local to that environment. Otherwise it
affects all subsequent ones.

\begin{cd}
\cs{sequence}\index{sequence@\cs{sequence}}
\index{sequence@\cs{sequence}}
\end{cd}

As a special case, you can plot any number against its sequence
position, with something like
\cs{using}\marg{\#1 \#2}\marg{(\cs{sequence},\#1)}. Here, the macro
\cs{sequence} will take on the values \texttt{1}, \texttt{2}, etc. as
lines are read from the file.

\begin{cd}
\cs{usingpairdefault}\\
\cs{usingnumericdefault}%
\index{usingpairdefault@\cs{usingpairdefault}}%
\index{usingnumericdefault@\cs{usingnumericdefault}}
\end{cd}

The command \cs{usingpairdefault} restores the above default for pair
data. The command \cs{usingnumericdefault} is the equivalent of
\cs{using}\marg{\#1 \#2}\marg{\#1}.

Note that the default value of \cs{using} appears to reference three
arguments. If there are only two numbers on a line separated by
whitespace, this will still work because of \TeX's argument matching
rules. \TeX's file reading mechanism normally converts the EOL to a
space, but there are exceptions so \mfp{} internally adds a space at
the end of each line read in to be on the safe side. Then the default
definition of \cs{using} reads everything up to the first space as
\texttt{\#1} (whitespace is normally compressed to a single space by
\TeX's reading mechanism), then everything to the second space (the one
added at the end of the line, perhaps) is \texttt{\#2}, then everything
to the EOL is \texttt{\#3}. This might assign an empty argument to
\texttt{\#3}, but it is discarded anyway.

If the numerical data contain percentages with explicit \texttt{\%} signs,
then choose another comment character with \cs{mfpdatacomment}. This
will change \texttt{\%} to an ordinary character \emph{in the data file}.
However, in your \cs{using} command it would still be read as a comment.
The following example shows how to overcome this:
\begin{verbatim}
  \makepercentother
  \using{#1% #2 #3}{(#1/100,#2)}
  \makepercentcomment
\end{verbatim}


Here\index{makepercentother@\cs{makepercentother}}%
\index{makepercentcomment@\cs{makepercentcomment}}
is an analysis of the meaning of this example: everything in a line, up
to the first percent followed by a space is assigned to parameter
\texttt{\#1}, everything from there to the next space is assigned to
\texttt{\#2} and the rest of the line (which may be empty) is
\texttt{\#3}. On the output side in the above example, the percentage is
divided by 100 to convert it to a fraction, and plotted against the
second parameter. Note: normal comments should not be used between
\cs{makepercentother} and \cs{makepercentcomment}, for obvious reasons.

\begin{cd}
    \cs{plotdata}\oarg{\meta{spec}}\marg{\meta{file}}%
    \index{plotdata@\cs{plotdata}}
\end{cd}

This plots several curves from a single file. The \meta{spec} and the
command \cs{smoothdata} have the same effect on each curve as in the
\cs{datafile} command. The data for each curve is a succession of
nonblank lines separated from the data for the next curve by a single
blank line. A \emph{pair} of successive blank lines is treated as the
end of the data. No prefix macros are permitted in front of
\cs{plotdata}.

Each successive curve in the data file is drawn differently. By default,
the first is drawn as a solid line the next dashed, the third dotted,
etc., through a total of six different line types. A \cs{gendashed}
command is used with predefined dash patterns named \mfc{dashtype0}
through \mfc{dashtype5}. This behavior can be changed with:

\begin{cd}
\cs{coloredlines}\\
\cs{pointedlines}\\
\cs{datapointsonly}\\
\cs{dashedlines}%
\index{coloredlines@\cs{coloredlines}}%
\index{pointedlines@\cs{pointedlines}}%
\index{datapointsonly@\cs{datapointsonly}}%
\index{dashedlines@\cs{dashedlines}}
\end{cd}

The command \cs{coloredlines} changes to cycling through eight different
colors starting with black (hey, black is a color too). This has an
effect only for \MP. The sole exception to the general rule that all
curves are drawn in \gbc{drawcolor} is the \cs{plotdata} command after
\cs{coloredlines} has been issued. The command \cs{pointedlines} causes
\cs{plotdata} to use \cs{plot} commands, cycling through nine symbols.
The command \cs{datapointsonly} causes \cs{plotdata} to use
\cs{plotnodes}\marg{\meta{symbol}} commands to plot the data points
only. (See the Appendix for more details.) The command \cs{dashedlines}
restores the default. If, for some reason, you do not like the default
starting line style (say you want to start with a color other than
black), you can use one of the following commands.

\begin{cd}
\cs{mfplinetype}\marg{\meta{num}}, or\\
\cs{mfplinestyle}\marg{\meta{num}}%
\index{mfplinetype@\cs{mfplinetype}}%
\index{mfplinestyle@\cs{mfplinestyle}}
\end{cd}

Here \meta{num} is a non-negative number, less than the number of
different drawing types available. The four previous commands reset the
number to 0, so if you use one of them, issue \cs{mfplinetype}
\emph{after} it. The different line styles are numbered starting from
$0$. If two or more \cs{plotdata} commands are used in the same
\env{mfpic} environment, the numbering in each continues where the one
before left off (unless you issue one of the commands above in between).
\cs{mfplinestyle} means the same as \cs{mfplinetype}, and is included
for compatibility. See the Appendix to find out what dash pattern,
color or symbol corresponds to each number by default. The commands
below can be used to change the default dashess,  colors, or symbols.

\begin{cd}
\cs{reconfigureplot}\marg{dashes}\marg{\meta{pat$_1$},\dots,\meta{pat$_n$}}\\
\cs{reconfigureplot}\marg{colors}\marg{\meta{clr$_1$},\dots,\meta{clr$_n$}}\\
\cs{reconfigureplot}\marg{symbols}\marg{\meta{symb$_1$},\dots,\meta{symb$_n$}}%
\index{reconfigureplot@\cs{reconfigureplot}}
\end{cd}

The first argument of \cs{reconfigureplot} is the rendering method to
change: \texttt{dashes}, \texttt{colors}, or \texttt{symbols}. The
second argument is a list of dash patterns, colors, or symbols. The dash
patterns should be names of patterns defined through the use of
\cs{dashpattern}. The colors can be any color names already known to
\MP, or defined through \cs{mfpdefinecolor}. The symbols can be any of
those listed with the \cs{plotsymbol} command (see
subsection~\ref{points}), or any known \MF{} path variable. The colors
can also be \MP{} expressions of type color, and the symbols can be
expressions of type path. Within a \env{mfpic} environment, the changes
made are local to that environment. Outside, they affect all subsequent
environments.

\begin{cd}
\cs{defaultplot}\marg{dashes}\\
\cs{defaultplot}\marg{colors}\\
\cs{defaultplot}\marg{symbols}
\index{defaultplot@\cs{defaultplot}}
\end{cd}

The command \cs{defaultplot} restores the built-in defaults for the
indicated method of rendering in \cs{plotdata}.

The commands \cs{using}, \cs{mfpdatacomment} and \cs{sequence} have the
same meaning here (for \cs{plotdata}) as they do for \cs{datafile}
(above). The sequence numbering for \cs{sequence} starts over with each
new curve.

\subsection{Labels and Captions.}\label{labels}

\subsubsection{Setting Text.}\label{text}

If option \opt{metafont} is in effect macros \cs{tlabel}, \cs{tlabels},
\cs{axislabels} and \cs{tcaption} do not affect the \MF{} file
(\file{\meta{file}.mf}) at all, but are added to the picture by \TeX. If
\opt{metapost} is in effect but \opt{mplabels} is not, they do not
affect the \MP{} file. In these cases, if these macros are the only
changes or additions to your document, there is no need to repeat the
processing with \MF{} or \MP{} nor the reprocessing with \TeX{} in order
to complete your \TeX{} document.

\begin{cd}
\cs{tlabel}\oarg{\meta{just}}\parg{\meta{x},\meta{y}}\marg{\meta{labeltext}}\\
\cs{tlabel}\oarg{\meta{just}}\marg{\meta{pair-list}}\marg{\meta{label text}}\\
\cs{tlabels}\marg{\meta{params$_1$} \meta{params$_2$} $\ldots$}%
\index{tlabel@\cs{tlabel}}\index{tlabels@\cs{tlabels}}
\end{cd}

Places \TeX{} labels on the graph. (Not to be confused with \LaTeX's
\cs{label} command.) The special form \cs{tlabels} (note the plural)
essentially just applies \cs{tlabel} to each set of parameters listed in
its argument. That is, each \meta{params$_k$} is a valid set of
parameters for a \cs{tlabel} command. These can be separated by spaces,
newlines, or nothing at all. They should \emph{not} be separated by
blank lines.

The last required parameter is ordinary \TeX{} text. The pair
\parg{\meta{x},\meta{y}} gives the coordinates of a point in the graph
where the text will be placed. It may optionally be enclosed in braces.
In fact, the second syntax may be used if \opt{mplabels} is in effect,
where \meta{pair-list} is any expression recognized as a pair by \MP, or
a comma-separated list of such pairs.

The optional parameter \oarg{\meta{just}} specifies the
\emph{justification}, the relative placement of the label with respect
to the point \parg{\meta{x},\meta{y}}. It is a two-character sequence
where the first character is one of \texttt{t} (top), \texttt{c} (center),
\texttt{b} (bottom), or \texttt{B} (Baseline), to specify vertical placement,
and the second character is one of \texttt{l} (left), \texttt{c} (center), or
\texttt{r} (right), to specify horizontal placement. These letters specify
what part of the \emph{text} is to be placed at the given point, so
\texttt{r} puts the right end of the text there---which means the text will be
left of the point. The default justification is \oarg{Bl}.

When \opt{mplabels} is in effect, the two characters may optionally be
followed by a number, specifying an angle in degrees to rotate the text
about the point \parg{\meta{x},\meta{y}}. If the angle is supplied
without \opt{mplabels} it is ignored after a warning. If the angle is
absent, there is no rotation. Note that the rotation takes place after
the placement and uses the given point as the center of rotation. For
example, \oarg{cr} will place the text left of the point, while
\oarg{cr180} will rotate it around to the right side of the point (and
upsidedown, of course).

There should be no spaces before, between, or after the first two
characters. However the number, if present, is only required to be a
valid \MP{} numerical expression containing no bracket characters; as
such, it may contain some spaces (e.g., around operations as in
\texttt{45 + 30}).

A multiline \cs{tlabel} may be specified by explicit line breaks, which
are indicated by the \bbsl{} command or the \cs{cr} command. This is a
very rudimentary feature. By default it left justifies the lines and
causes \cs{tlabel} to redefine \bbsl. One can center a line by putting
\cs{hfil} as the first thing in the line, and right justify by putting
\cs{hfill} there (these are \TeX{} primitives). Redefining \bbsl{} can
interfere with \LaTeX's definition. For better control in \LaTeX{} use
\cs{shortstack} inside the label (or a \env{tabular} environment or some
other environment which always initializes \bbsl{} with its own
definition).

If the label goes beyond the bounds of the graph in any direction, the
space reserved for the graph is expanded to make room for it. (Note:
this behavior is very much different from that of the \LaTeX{}
\env{picture} environment.)

If the \opt{mplabels} option is in effect, \cs{tlabel} will write a
\mfc{btex $\ldots$ etex} group to the output file, allowing \MP{} to
arrange for typesetting the label. Normally, the label becomes part of
the picture, rather than being laid on top of it, and can be covered up
by any filling macros that follow, or clipped off by \cs{gclear} or
\cs{gclip}. However, under the \opt{overlaylabels} option (or after the
command \cs{overlaylabels}), labels are saved and added to the picture
at the very end. This may prevent some special effects, but it makes the
behavior of labels much more consistent through all the 12 permissable
settings of the options \opt{metapost}, \opt{mplabels}, \opt{clip}, and
\opt{truebbox}.

\begin{cd}
\cs{everytlabel}\marg{\meta{\TeX-code}}%
\index{everytlabel@\cs{everytlabel}}
\end{cd}

One problem with multi-line \cs{tlabel}s is that each line of their
contents constitutes a separate group. This makes it difficult to change
the \cs{baselineskip} (for example) inside a label. The command
\cs{everytlabel} saves it's contents in a token register and the code is
issued in each \cs{tlabel}, as the last thing before the actual line(s)
of text. Any switch you want to apply to every line can be supplied. For
example
\begin{ex}
    \cs{everytlabel}\marg{\cs{bf}\cs{baselineskip} 10pt}
\end{ex}
will make every line of every \cs{tlabel}'s text come out bold with 10
point baselines. The effect of \cs{everytlabel} is local to the
\env{mfpic} environment, if it is issued inside one. Note that the lines
of a tlabel are wrapped in a box, but the commands of \cs{everytlabel}
are outside all of them, so no actual text should be produced by these
commands.

Using \cs{tlabel} without an optional argument is equivalent to
specifying \oarg{Bl}. Use the following command to change this
behavior.

\begin{cd}
\cs{tlabeljustify}\marg{\meta{just}}%
\index{tlabeljustify@\cs{tlabeljustify}}
\end{cd}

After this command the placement of all subsequent labels without
optional argument will be as specified in this command. For example,
\cs{tlabeljustify}\marg{cr45} would cause all subsequent \cs{tlabel}
commands lacking an optional argument to be placed as if the argument
\oarg{cr45} were used in each. If \opt{mplabels} is not in effect at the
time of this command, the rotation part will be saved in case that
option is turned on later, but a warning message will be issued. Without
\opt{mplabels}, the rotation is ignored by \cs{tlabel} .

\begin{cd}
\cs{tlabeloffset}\marg{\meta{hlen}}\marg{\meta{vlen}}\\
\cs{tlabelsep}\marg{\meta{len}}%
\index{tlabeloffset@\cs{tlabeloffset}}%
\index{tlabelsep@\cs{tlabelsep}}
\end{cd}

The first command causes all subsequent \cs{tlabel} commands to shift
the label right by \meta{hlen} and up by \meta{vlen} (negative lengths
cause it to be shifted left and down, respectively).

The \cs{tlabelsep} command causes labels to be shifted by the given
amount in a direction that depends on the optional positioning
parameter. For example, if the first letter is \texttt{t} the label is
shifted down by the amount \meta{len} and if the second letter is
\texttt{l} it is also shifted right. In all cases it is shifted \emph{away} from
the point of placement (unless the dimension is negative). If \texttt{c} or
\texttt{B} is the first parameter, no vertical shift takes place, and if
\texttt{c} is the second, there is no horizontal shift. This is intended to
be used in cases where something has been drawn at that particular
point, in order to separate the text from the drawing, but the value is
also written to the output file for use by \cs{tlabelrect}
(subsection~\ref{surrounding}) and related
commands.

\begin{cd}
\cs{axislabels}\marg{\meta{axis}}\oarg{\meta{just}}%
    \marg{\marg{\meta{text$_1$}}\meta{$n_1$},%
    \marg{\meta{text$_2$}}\meta{$n_2$},$\ldots$}%
\index{axislabels@\cs{axislabels}}
\end{cd}

This command places the given \TeX{} text (\meta{text$_k$}) at the given
positions (\meta{$n_k$}) on the given axis, \meta{axis}, which must be a
single letter and one of \texttt{l}, \texttt{b}, \texttt{r}, \texttt{t},
\texttt{x}, or \texttt{y}. The text is placed as in \cs{tlabels}
(including the taking into account of \cs{tlabelsep} and
\cs{tlableoffset}), except that the default justification depends on the
axis (the settings of \cs{tlabeljustify} are ignored). In the case of
the border axes, the default is to place the label outside the axis and
centered. So, for example, for the bottom axis it is \oarg{tc}. The
defaults for the $x$- and $y$-axis are below and left, respectively. The
optional \meta{just} can be used to change this. For example, to place
the labels \emph{inside} the left border axis, use \oarg{cl}. If
\opt{mplabels} is in effect, rotations can be included in the
justification parameter. For example, to place the text strings
`first', `second' and `third' just below the positions 1, 2 and 3
on the $x$-axis, rotated so they read upwards at a 90 degree angle, one
can use \cs{axislabels}\marg{x}\oarg{cr90}\marg{\marg{first}1,
\marg{second}2, \marg{third}3}

\begin{cd}
\cs{plottext}\oarg{\meta{just}}\marg{\meta{text}}\marg{($x_0$,$y_0$),
 ($x_1$,$y_1$), $\ldots$}%
\index{plottext@\cs{plottext}}
\end{cd}

Similar in effect to \cs{point} and \cs{plotsymbol} (but without
requiring \MF), \cs{plottext} places a copy of \meta{text} at each of
the listed points. It simply issues multiple \cs{tlabel} commands with
the same text and optional parameter, but at the different points
listed. This is intended to plot a set of points with a single letter or
font symbol (instead of a \MF{} generated shape). Like \cs{axislabels},
this does not respond to the setting of \cs{tlabeljustify}. It has a
default setting of \oarg{cc} if the optional argument is omitted. The
points may be MetaPost pair expressions under \opt{mplabels}, but they
must \emph{not} be individually enclosed in braces. (This requirement is
new with version 0.7; prior to that pairs in braces didn't work reliably
anyway.) This command is actually unnecessary under \opt{mplabels} as
the plain \cs{tlabel} command can then be given a list of points. The
\cs{tlabel} command is more efficient, and \cs{plottext} is converted to
it internally.

\begin{cd}
\cs{mfpverbtex}\marg{\meta{\TeX-cmds}}%
\index{mfpverbtex@\cs{mfpverbtex}}
\end{cd}

This writes a \mfc{verbatimtex} block to the \file{.mp} file. It makes
sense only if the \opt{mplabels} option is used and so only for \MP. The
\meta{\TeX-cmds} in the argument are written to the \file{.mp} file,
preceded by the \MP{} command \mfc{verbatimtex} and followed by
\mfc{etex}. Line breaks within the \meta{\TeX-cmd} are preserved. The
\cs{mfpverbtex} command must come before any \cs{tlabel} that is to be
affected by it. Any settings common to all \env{mfpic} environments
should be in a \cs{mfpverbtex} command preceding all such environments.
It may be issued at any point after \mfp{} is loaded, and any number of
times. If it issued before \cs{opengraphsfile}, its contents are saved
and written by that command. Because of the way \MP{} handles
\mfc{verbatimtex} material, the effects cannot be constrained by any
grouping unless one places \TeX{} grouping commands within
\meta{\TeX-cmds}.

\begin{cd}
\cs{tcaption}\oarg{\meta{maxwd},\meta{linewd}}\marg{\meta{caption text}}%
\index{tcaption@\cs{tcaption}}
\end{cd}

Places a \TeX{} caption at the bottom of the graph. (Not to be confused
with \LaTeX's similar \cs{caption} command.) The macro will
automatically break lines which are too much wider than the graph---if
the \cs{tcaption} line exceeds \meta{maxwd} times the width of the
graph, then lines will be broken to form lines at most \meta{linewd}
times the width of the graph. The default settings for \meta{maxwd} and
\meta{linewd} are 1.2 and 1.0, respectively. \cs{tcaption} typesets its
argument twice (as does \LaTeX's \cs{caption}), the first time to test
its width, the second time for real. Therefore, the user is advised
\emph{not} to include any global assignments in the caption text.

If the \cs{tcaption} and graph have different widths, the two are
centered relative to each other. If the \cs{tcaption} takes multiple
lines, then the lines are both left- and right-justified (except for the
last line), but the first line is not indented. If the option
\opt{centeredcaptions} is in effect, each line of the caption will be
centered.

In a \cs{tcaption}, Explicit line breaks may be specified by using the
\bbsl{} command. The separation between the bottom of the picture and
the caption can be changed by increasing or decreasing the skip
\cs{mfpiccaptionskip}\index{mfpiccaptionskip@\cs{mfpiccaptionskip}}
(a `rubber' length in Lamport's terminology).

Many \mfp{} users find the \cs{tcaption} command too limiting (one
cannot, for example, place the caption to the side of the figure). It is
common to use some other method (such as \LaTeX's \cs{caption} command
in a \env{figure} environment). The dimensions \cs{mfpicheight} and
\cs{mfpicwidth} (see section~\ref{parameters}) might be a convenience
for plain \TeX{} users who want to roll their own caption macros.

\subsubsection{Curves surrounding text}\label{surrounding}


\begin{cd}
\cs{tlabelrect}\oarg{\meta{rad}}\oarg{\meta{just}}%
    \meta{pair}\marg{\meta{text}}\\
\cs{tlabelrect*...}%
\index{tlabelrect@\cs{tlabelrect}}
\end{cd}

This and the following two methods of surounding a bit of text with a
curve share some common characteristics which will be described here.
The commands all take an optional argument that can modify the shape of
the curve. After that come arguments exactly as for the \cs{tlabel}
command except that only a single point is permitted, not a list. (So
\meta{pair} is either of the form \parg{\meta{x},\meta{y}} or the same
enclosed in braces, or for \opt{mplabels} a pair expression in braces.)
After processing the surrounding curve, a \cs{tlabel} is applied to
those arguments unless a \texttt{*} is present. In order for the second
optional argument to be recognized as the second, the first optional
argument must also be present. An empty first optional argument is
permitted, causing the default value to be used. The default for the
justification parameter is \texttt{cc}, for compatibility with past
\mfp{} versions in which these commands all centered the figure around
the point and no justification parameter existed. This default can be
changed with the \cs{tlpathjustify} command below.

The plain rectangle version produces a frame separated from the text on
all sides by the amount defined with \cs{tlabelsep}. All other versions
produce the smallest described curve that contains this rectangle.

These commands may be preceded by prefix macros (see the sections
\ref{modifier}~and \ref{rendering}, above). They all have a
`\texttt{*}-form' which produces the curve but omits placing the text.
All have the effect of rendering the path \emph{before} placing any
text. For example, \cs{gclear}\cs{tlabelrect}\dots\ will clear the
rectangle and then place the following text in the cleared space.

The optional argument of \cs{tlabelrect}, \meta{rad}, is a dimension,
defaulting to \dim{0pt}, that produces rounded corners made from
quarter-circles of the given radius. If the corners are rounded, the
sides are expanded slightly so the resulting shape still encompasses the
rectangle mentioned above. There is one special case for the optional
argument \meta{rad}: if the keyword `\texttt{roundends}' is used instead
of a dimension, the radius will be chosen to make the nearest quarter
circles just meet, so the narrow side of the rectangle is a half circle.

\begin{cd}
\cs{tlabeloval}\oarg{\meta{mult}}\oarg{\meta{just}}%
    \meta{pair}\marg{\meta{text}}\\
\cs{tlabeloval*...}%
\index{tlabeloval@\cs{tlabeloval}}
\end{cd}

This is similar to \cs{tlabelrect}, except it draws an ellipse. The
ellipse is calculated to have the same ratio of width to height as the
rectangle mentioned above. The optional \meta{mult} is a multiplier that
increases or decreases this ratio. Values of \meta{mult} larger than 1
increase the width and decrease the height.

\begin{cd}
\cs{tlabelellipse}\oarg{\meta{ratio}}\oarg{\meta{just}}%
    \meta{pair}\marg{\meta{text}}\\
\cs{tlabelellipse*...}\\
\cs{tlabelcircle}\oarg{\meta{just}}\meta{pair}\marg{\meta{text}}\\
\cs{tlabelcircle*...}%
\index{tlabelellipse@\cs{tlabelellipse}}\index{tlabelcircle@\cs{tlabelcircle}}
\end{cd}

Draws the smallest ellipse centered at the point that encompasses the
rectangle defined above, and that has a ratio of width to height equal
to \meta{ratio} then places the text. The default ratio is $1$, which
produces a circle. We also provide the command \cs{tlabelcircle}, which
take only the \oarg{\meta{just}} optional argument. Internally, it just
processes any \texttt{*} and calls \cs{tlabelellipse} with parameter 1.

In the above \cs{tlabel...} curves, the optional parameter should be
positive. If it is zero, all the curves silently revert to
\cs{tlabelrect}. If it is negative, it is silently accepted. In the case
of \cs{tlabelrect} this causes the quarter-circles at the corners to be
indented rather than convex. In the other cases, there is no visible
effect, but in all cases the sense of the curve is reversed.

\begin{cd}
\cs{tlpathjustify}\marg{\meta{just}}
\index{tlpathjustify@\cs{tlpathjustify}}
\end{cd}

This can be used to change the default justification for \cs{tlabelrect}
and friends. The \meta{just} parameter is exactly as in
\cs{tlabeljustify} in subsection~\ref{text}.


\subsection{Saving and Reusing an \mfp{} Picture.}\label{saving}

These commands have been changed from versions prior to 0.3.14 in order
to behave more like the \LaTeX's \cs{savebox}, and also to allow the
reuse of an allocated box. Past files that use \cs{savepic} will have to
be edited to add \cs{newsavepic} commands that allocate the \TeX{}
boxes.

\begin{cd}
\cs{newsavepic}\marg{\meta{picname}}\\
\cs{savepic}\marg{\meta{picname}}\\
\cs{usepic}\marg{\meta{picname}}%
\index{newsavepic@\cs{newsavepic}}%
\index{savepic@\cs{savepic}}%
\index{usepic@\cs{usepic}}
\end{cd}

\cs{newsavepic} allocates a box (like \LaTeX's \cs{newsavebox}) in which
to save a picture. As in \cs{newsavebox}, \meta{picname} is a control
sequence. Example: \cs{newsavepic}\marg{\cs{foo}}.

\cs{savepic} saves the \emph{next} \cs{mfpic} picture in the named box,
which should have been previously allocated with \cs{newsavepic}. (This
command should not be used \emph{inside} an \env{mfpic} environment.)
The next picture will not be placed, but saved in the box for later use.
This is primarily intended as a convenience. One \emph{could} use
\begin{ex}
  \cs{savebox}\marg{\meta{picname}}\marg{\meta{entire \env{mfpic} environment}},
\end{ex}
but \cs{savepic} avoids having to place the \env{mfpic} environment in
braces, and avoids one extra level of \TeX{} grouping. It also avoids
reading the entire \env{mfpic} environment as a parameter, which would
nullify \mfp's efforts to preserve line breaks in parameters
written to the \MF{} output file. If you repeat \cs{savepic} with the
same \meta{picname}, the old contents are replaced with the next
picture.

\cs{usepic} copies the picture that had been saved in the named box.
This may be repeated as often as liked to create multiple copies of one
picture.


\subsection{Picture frames.}\label{frames}

When \TeX{} is run but before \MF{} or \MP{} has been run on the output
file, \mfp{} detects that the \file{.tfm} file is missing or that
the first \MP{} figure file \file{\meta{file}.1} is missing. In these
cases, the \env{mfpic} environment draws only a rectangular frame with
dimensions equal to the nominal size of the picture, containing the
figure name and number (and any \TeX{} labels). The command(s) used
internally to do this are made available to the user.

\begin{cd}
\cs{mfpframe}\oarg{\meta{fsep}}%
    \meta{ material-to-be-framed }%
\cs{endmfpframe}\\
\cs{mfpframed}\oarg{\meta{fsep}}\marg{\meta{material-to-be-framed}}%
\index{mfpframed@\cs{mfpframed}}%
\index{endmfpframe@\cs{endmfpframe}}%
\index{mfpframe@\cs{mfpframe}}
\end{cd}

These surround their contents with a rectangular frame consisting of
lines with thickness \cs{mfpframethickness} separated from the contents
by the \meta{fsep} if specified, otherwise by the value of the dimension
\cs{mfpframesep}. The default value of the \TeX{} dimensions
\cs{mfpframesep} and \cs{mfpframethickness} are \dim{2pt} and
\dim{0.4pt}, respectively. The \cs{mfpframe} $\ldots$ \cs{endmfpframe}
version is preferred around \env{mfpic} environments or verbatim
material since it avoids reading the enclosed material before
appropriate \cs{catcode} changes go into effect. In \LaTeX, one can also
use the \cs{begin}\marg{mfpframe} $\ldots$ \cs{end}\marg{mfpframe}
syntax.

An alternative way to frame \env{mfpic} pictures is to save them with
\cs{savepic} (see previous section) and issue a corresponding
\cs{usepic} command inside any framing environment/command of the user's
choice or devising.


\subsection{Affine Transforms.}\label{transforms}

Coordinate transformations that keep parallel lines in parallel are
called \emph{affine transforms}.  These include translation, rotation,
reflection, scaling and skewing (slanting). For the \MF{} coordinate
system only---that is, for paths, but not for \cs{tlabel}'s (let alone
\cs{tcaption}'s)---\mfp{} provides the ability to apply \MF{}
affine transforms.


\subsubsection{Affine Transforms of the \MF{} Coordinate
System.}\label{affine}

\begin{cd}
\cs{coords} $\ldots$
\cs{endcoords}%
\index{coords@\cs{coords}}%
\index{endcoords@\cs{endcoords}}
\end{cd}

All affine transforms are restricted to the innermost enclosing
\cs{coords}$\ldots$\cs{endcoords} pair.  If there is \emph{no} such
enclosure, then the transforms will apply to the rest of the \env{mfpic}
environment

\emph{Note}:  In \LaTeX, a \env{coords} environment may be used.

\medskip
Transforms provided by \mfp.

\medskip
\halign
{#\hfil&\quad#\hfil\cr
  \cs{rotate}\marg{\meta{$\theta$}}%
    \index{rotate@\cs{rotate}}%
    & Rotates around origin by \meta{$\theta$} degrees  \cr
  \cs{rotatearound}\marg{\meta{point}}\marg{\meta{$\theta$}}%
    \index{rotatearound@\cs{rotatearound}}%
    & Rotates around point \meta{point} by \meta{$\theta$} degrees  \cr
  \cs{turn}\oarg{\meta{point}}\marg{\meta{$\theta$}}%
    \index{turn@\cs{turn}}%
    & Rotates around point \meta{point} (origin is default) by
    \meta{$\theta$} \cr
  \cs{mirror}\marg{\meta{$p_1$}}\marg{\meta{$p_2$}}%
    \index{mirror@\cs{mirror}}%
    & Same as \cs{reflectabout}\cr
  \cs{reflectabout}\marg{\meta{$p_1$}}\marg{\meta{$p_1$}}%
    \index{reflectabout@\cs{reflectabout}}%
    & Reflect about the line \meta{$p_1$}\texttt{--}\meta{$p_2$}  \cr
  \cs{shift}\marg{\meta{pair}}%
    \index{shift@\cs{shift}}%
    & Shifts origin by the vector \meta{pair}  \cr
  \cs{scale}\marg{\meta{s}}%
    \index{scale@\cs{scale}}%
    & Scales uniformly by a factor of \meta{s}  \cr
  \cs{xscale}\marg{\meta{s}}%
    \index{xscale@\cs{xscale}}%
    & Scales only the X coordinates by a factor of \meta{s}  \cr
  \cs{yscale}\marg{\meta{s}}%
    \index{yscale@\cs{yscale}}%
    & Scales only the Y coordinates by a factor of \meta{s}  \cr
  \cs{zscale}\marg{\meta{pair}}%
    \index{zscale@\cs{zscale}}%
    & Scales uniformly by magnitude of \meta{pair}, and rotates by angle
        of \meta{pair}  \cr
  \cs{xslant}\marg{\meta{s}}%
    \index{xslant@\cs{xslant}}%
    & Skew in $X$ direction by the multiple \meta{s} of $Y$  \cr
  \cs{yslant}\marg{\meta{s}}%
    \index{yslant@\cs{yslant}}%
    & Skew in $Y$ direction by the multiple \meta{s} of $X$  \cr
  \cs{zslant}\marg{\meta{pair}}%
    \index{zslant@\cs{zslant}}%
    & See \mfc{zslanted} in \file{grafdoc.tex}  \cr
  \cs{boost}\marg{\meta{$\chi$}}%
    \index{boost@\cs{boost}}%
    & Special relativity boost by $\chi$, see \mfc{boost} in
        \file{grafdoc.tex}  \cr
  \cs{xyswap}%
    \index{xyswap@\cs{xyswap}}%
    & Exchanges the values of $x$ and $y$.  \cr}%

An arbitrary \MF{} transformation can be implemented with

\begin{cd}
\cs{applyT}\marg{\meta{transformer}}%
\index{applyT@\cs{applyT}}
\end{cd}

This is mainly for \MF{} hackers. This applies the \MF{}
\meta{transformer} to the current coordinate system. For example, the
\mfp{} \TeX{} macro \cs{zslant\#1} is implemented as
\cs{applyT}\marg{zslanted \#1} where the argument \mfc{\#1} is a \MF{}
pair, such as $(x,y)$. Any code that satisfies \MF's syntax for a
\meta{transformer} (see D.~E.~Knuth, ``The \MF book'') is permitted,
although no effort is made to correctly write \TeX{} special characters
nor to preserve linebreaks in the code.

When any of these commands is issued, the effect is to transform all
subsequent figures (within the enclosing \env{coords} or \env{mfpic}
environment). In particular, attention may need to be paid to whether
these transformations move (part of) the figure outside the space
allotted by the \cs{mfpic} command parameters.

A not-so-obvious point is that if several of these transformations are
applied in succession, then the most recent is applied first, so that
figures are transformed as if the transformations were applied in the
reverse order of their occurrence. This is similar to the application of
prefix macros (as well as application of transformations in mathematics:
$T_1 T_2 z$ usually means to apply $T_1$ to the result of $T_2 z$).


\subsubsection{Transformation of Paths.}\label{transformation}

In the previous section we discussed transformations of the \MF{}
coordinate system. Those macros affect the \emph{drawing} of paths and
other figures, but do not change the actual paths. We will explain the
distinction after introducing two macros for storing and reusing
figures.

\begin{cd}
\cs{store}\marg{\meta{path variable}}\marg{\meta{path}}\\
\cs{store}\marg{\meta{path variable}}\meta{path}%
\index{store@\cs{store}}
\end{cd}

This stores the following \meta{path} in the specified \MF{} \meta{path
variable}. Any valid \MF{} symbolic token will do, in particular, any
sequence of letters or underscores. You should be careful to make the
name distinctive to avoid overwriting the definition of some internal
variable. The stored path may later be used as a figure macro
using \cs{mfobj} (below). The \meta{path} may be any of the figure
macros (such as \cs{curve}\marg{(0,0),(1,0),(1,1)}) or the result of
modifying it. For example.

\begin{ex}
\cs{store}\marg{pth}\cs{lclosed}\cs{reverse}%
    \cs{curve}\marg{(0,0),(1,0),(1,1)})
\end{ex}

In fact, \cs{store} is a prefix macro that does nothing to the following
curve except store it. It acts as a rendering macro with a null
rendering, so the curve is not made visible unless other rendering
macros appear before or after it. It is special in that it is the only
prefix macro that allows the following path to be an argument, that is,
enclosed in braces. This is solely to support past \mfp{} versions in
which \cs{store} was \emph{not} defined as a prefix macro.

\begin{cd}
\cs{mfobj}\marg{\meta{path expression}}\\
\cs{mpobj}\marg{\meta{path expression}}%
\index{mfobj@\cs{mfobj}}\index{mpobj@\cs{mpobj}}
\end{cd}

The \meta{path expression} is a previously stored path variable, or a
valid \MF{} (or \MP) expression combining such variables and/or constant
paths. This allows the use of path variables or expressions as figure
macros, permitting all prefix operations, etc.. Here's some
oversimplified uses of \cs{store} and \cs{mfobj}:

\nobreak
\begin{verbatim}
\store{my_f}{\circle{...}}              % Store a circle.
\dotted\mfobj{my_f}                     % Now draw it dotted,
\hatch\mfobj{my_f}                      % and hatch its interior
% Store two curves:
\store{my_f}{\curve{...}}
\store{my_g}{\curve{...}}
% Store two combinations of them:
\store{my_h}{\mfobj{my_f--my_g--cycle}} % a MF path expression
\store{my_k}{%
  \lclosed\connect                      % a combination path created from
  \mfobj{my_f}\mfobj{my_g}              %   mfpic commands.
  \endconnect}
\dotted\mfobj{my_f}                     % Draw the first dotted,
\dotted\mfobj{my_g}                     % then the second.
\shade\mfobj{my_h}                      % Now shade one combination.
\hatch\mfobj{my_k}                      % and hatch the other
\end{verbatim}
The two forms \cs{mfobj} and \cs{mpobj} are absolutely equivalent.

It should be noted that every \mfp{} figure is implicitly stored in the
object \gbc{curpath}. So you can use \cs{mfobj}\marg{curpath} and get
the path defined by the most recent sequence of prefix macros and
figure.

Getting back to coordinate transforms, if one changes the coordinate
system and then stores and draws a curve, say by
\begin{verbatim}
  \coords
    \rotate{45 deg}
    \store{xx}{\rect{(0,0),(1,1)}}
    \dashed\mfobj{xx}
  \endcoords
\end{verbatim}
one will get a transformed picture, but the object \cs{mfobj}\marg{xx}
will contain the simple, unrotated rectangular path and drawing it later
(outside the \env{coords} environment) will prove that. This is because
the \texttt{coords} environment works at the drawing level, not at the
definition level. In oversimplified terms, \cs{dashed} invokes the
transformation, but not \cs{store}. More precisely, \mfp{} prefix macros
have an input and an output and a side effect. The input is the output
of whatever follows it, the output can be the same as the input (the
case for rendering prefixes) or modified version of that (the closure
prefixes). The side effect is the drawing (dashing, filling) of the path,
appending of an arrowhead, etc.. These side effects have to know where
to place their marks, so a computation is invoked that converts the
user's graph coordinates into \MF's drawing coordinates. The previous
transformation macros work by modifying the parameters used in this
computation.

The following transformation prefixes provide a means of actually
creating and storing a transformed path. In the terms just discussed,
their input is a path, their output is the transformed path, and they
have no side effects (other than invoking the default rendering if no
rendering prefix was previously provided).

\begin{cd}
\cs{rotatepath}\marg{(\meta{x},\meta{y}),\meta{$\theta$}}$\ldots$\\
\cs{shiftpath}\marg{(\meta{dx},\meta{dy})}$\ldots$\\
\cs{scalepath}\marg{(\meta{x},\meta{y}),\meta{s}}$\ldots$\\
\cs{xscalepath}\marg{\meta{x},\meta{s}}$\ldots$\\
\cs{yscalepath}\marg{\meta{y},\meta{s}}$\ldots$\\
\cs{slantpath}\marg{\meta{y},\meta{s}}$\ldots$\\
\cs{xslantpath}\marg{\meta{y},\meta{s}}$\ldots$\\
\cs{yslantpath}\marg{\meta{x},\meta{s}}$\ldots$\\
\cs{reflectpath}\marg{\meta{$p_1$},\meta{$p_2$}}$\ldots$\\
\cs{xyswappath}$\ldots$\\
\cs{transformpath}\marg{\meta{transformer}}$\ldots$
\index{rotatepath@\cs{rotatepath}}\index{shiftpath@\cs{shiftpath}}%
\index{scalepath@\cs{scalepath}}\index{xscalepath@\cs{xscalepath}}%
\index{yscalepath@\cs{yscalepath}}\index{slantpath@\cs{slantpath}}%
\index{xslantpath@\cs{xslantpath}}\index{yslantpath@\cs{yslantpath}}%
\index{reflectpath@\cs{reflectpath}}\index{xyswappath@\cs{xyswappath}}%
\index{transformpath@\cs{transformpath}}
\end{cd}

\cs{rotatepath} rotates the following path by \meta{$\theta$} degrees
about point \mfc{(\meta{x},\meta{y})}. After the commands:
\begin{ex}
  \cs{store}\marg{xx}\marg{\cs{rotatepath}\marg{(0,0), 45}%
    \cs{rect}\marg{(0,0),(1,1)}}
\end{ex}
the object \cs{mfobj}\marg{xx} contains an actual rotated rectangle, as
drawing it will prove. The above macro, and the five that follow are
extremely useful (and better than \env{coords} environments) if one
needs to draw a figure, together with many slightly different versions
of it.

\cs{shiftpath} shifts the following path by the horizontal amount
\meta{dx} and the vertical amount \meta{dy}.

\cs{scalepath} scales (magnifies or shrinks) the following path by the
factor \meta{s}, in such a way that the point \parg{\meta{x},\meta{y}}
is kept fixed. That is
\begin{ex}
  \cs{scalepath}\marg{(0,0),2}\cs{rect}\marg{(0,0),(1,1)}
\end{ex}
is essentially the same as \cs{rect}\marg{(0,0),(2,2)}, while
\begin{ex}
  \cs{scalepath}\marg{(1,1),2}\cs{rect}\marg{(0,0),(1,1)}
\end{ex}
is the same as \cs{rect}\marg{(-1,-1),(1,1)}. In both cases the
rectangle is doubled in size. In the first case the lower left corner
stays the same, while in the second case the the upper right corner
stays the same.

\cs{xscalepath} is similar to \cs{scalepath}, but only the $x$-direction
is scaled, and all points with first coordinate equal to \meta{x} remain
fixed. \cs{yscalepath} is similar, except the $y$-direction is affected.

\cs{slantpath} applies a slant transformation to the following path,
keeping points with second coordinate equal to \meta{y} fixed. That is,
a point $p$ on the path is moved right by an amount proportional to the
height of $p$ above the line $y={}$\meta{y}, with $s$ being the
proportionality factor. Vertical lines in the path will acquire a slope
of $1/s$, while horizontal lines stay horizontal.

\cs{xslantpath} is an alias for \cs{slantpath}

\cs{yslantpath} is similar to \cs{xslantpath}, but exchanges the roles
of $x$ and $y$ coordinates.

\cs{reflectpath} returns the mirror image of the following path, where
the line determined by the points \meta{$p_1$} and \meta{$p_2$} is the
mirror.

\cs{xyswappath} returns the path with the roles of $x$ and $y$
exchanged. This is similar in some respects to
\cs{reflectpath}\marg{(0,0),(1,1)}, and produces the same result if the
$x$ and $y$ scales of the picture are the same. However,
\cs{reflectpath} compensates for such different scales (so the path
shape remains the same), while \cs{xyswappath} does not (so that after a
swap, verticals become horizontal and horizontals become vertical). One
cannot have both when the scales are different.

For \MF{} or \MP{} power users, \cs{transformpath} can take any
`transformer' and transform the following path with it. Here, a
\emph{transformer} is anything that can follow a path  and create a new
path. Examples are \mfc{scaled}, \mfc{shifted (1,1)}, and \mfc{rotatedabout
(0,1)}.

All these prefixes change only the path that follows, not any rendering
of it that follows. For example:
\begin{ex}
  \cs{gfill}\cs{rotatepath}\marg{(0,0),90}\cs{dashed}%
    \cs{rect}\marg{(0,0),(1,1)}
\end{ex}
will not produce a rotated dashed rectangle. Rather the original
rectangle will be dashed, and the rotated rectangle will be filled.


\subsection{Parameters.}\label{parameters}

There are many parameters in \mfp{} which the user can modify to
obtain different effects, such as different arrowhead size or shape.
Most of these parameters have been described already in the context of
macros they modify, but they are all described together here.

Many of the parameters are stored by \TeX{} as dimensions, and so are
available even if there is no \MF{} file open; changes to them are not
subject to the usual \TeX{} rules of scope however: they are local to
\TeX{} groups only if set inside an \env{mfpic} environment otherwise
they are global. This is for consistency: other parameters are stored by
\MF{} (so the macros to change them will have no effect unless a \MF{}
file is open) and the changes are subject to \MF's rules of scope---to
the \mfp{} user, this means that changes inside the \cs{mfpic} $\ldots$
\cs{endmfpic} environment are local to that environment, but other
\TeX{} groupings have no effect on scope. Some commands (notably those
that set the axismargins and \cs{tlabel} parameters) change both \TeX{}
parameters and \MF{} parameters, and it is important to keep then
consistent.

\begin{cd}
\cs{mfpicunit}%
\index{mfpicunit@\cs{mfpicunit}}
\end{cd}

This \TeX{} dimension stores the basic unit length for \mfp{}
pictures---the $x$ and $y$ scales in the \cs{mfpic} macro are multiples
of this unit. The default value is \dim{1pt}.

\begin{cd}
\cs{pointsize}%
\index{pointsize@\cs{pointsize}}
\end{cd}

This \TeX{} dimension stores the diameter of the circle drawn by the
\cs{point} macro and the diameter of the symbols drawn by
\cs{plotsymbol} and by \cs{plot}. The default value is \dim{2pt}.

\begin{cd}
\cs{pointfilltrue} and \cs{pointfillfalse}%
\index{pointfilltrue@\cs{pointfilltrue}}%
\index{pointfillfalse@\cs{pointfillfalse}}
\end{cd}

This \TeX{} boolean switch determines whether the circle drawn by
\cs{point} will be filled or open (outline drawn, inside erased).
The default is \texttt{true}: filled. This value is local to any \TeX{}
group inside an \env{mfpic} environment. Outside such it is global.

\begin{cd}
\cs{pen}\marg{\meta{drawpensize}}\\
\cs{drawpen}\marg{\meta{drawpensize}}\\
\cs{penwd}\marg{\meta{drawpensize}}%
\index{pen@\cs{pen}}%
\index{drawpen@\cs{drawpen}}%
\index{penwd@\cs{penwd}}
\end{cd}

Establishes the width of the normal drawing pen. The default is
\dim{0.5pt}. This width is stored by \MF. The shading dots and hatching
pen are unaffected by this. There exist three aliases for this command,
the first two to maintain backward compatibility, the last one for
consistency with other dimension changing commands. Publishers generally
recommended authors to use at least a width of one-half point for
drawings submitted for publication.

\begin{cd}
\cs{shadewd}\marg{\meta{dotdiam}}%
\index{shadewd@\cs{shadewd}}
\end{cd}

Sets the diameter of the dots used in the shading macro. The drawing and
hatching pens are unaffected by this. The default is \dim{0.5pt}, and
the value is stored by \MF.

\begin{cd}
\cs{hatchwd}\marg{\meta{hatchpensize}}%
\index{hatchwd@\cs{hatchwd}}
\end{cd}

Sets the line thickness used in the hatching macros. The drawing pen and
shading dots are unaffected by this. The default is \dim{0.5pt}, and the
value is stored by \MF.

\begin{cd}
\cs{polkadotwd}\marg{\meta{polkadotdiam}}%
\index{polkadotwd@\cs{polkadotwd}}
\end{cd}

Sets the diameter of the dots used in the \cs{polkadot} macro. The
default is \dim{5pt}, and the value is stored by \MF.

\begin{cd}
\cs{headlen}%
\index{headlen@\cs{headlen}}
\end{cd}

This \TeX{} dimension stores the length of the arrowhead drawn by
the \cs{arrow} macro. The default value is \dim{3pt}.

\begin{cd}
\cs{axisheadlen}%
\index{axisheadlen@\cs{axisheadlen}}
\end{cd}

This \TeX{} dimension stores the length of the arrowhead drawn by the
\cs{axes}, \cs{xaxis} and \cs{yaxis} macros, and by the macros \cs{axis}
and \cs{doaxes} when applied to the parameters \texttt{x} and \texttt{y}.

\begin{cd}
\cs{sideheadlen}%
\index{sideheadlen@\cs{sideheadlen}}
\end{cd}

This \TeX{} dimension stores the length of the arrowhead drawn by the
\cs{axis} and \cs{doaxes} macros when applied to \texttt{l}, \texttt{b},
\texttt{r} or \texttt{t}. The default value is \dim{0pt}.

\begin{cd}
\cs{headshape}\marg{\meta{hdwdr}}\marg{\meta{hdten}}\marg{\meta{hfilled}}%
\index{headshape@\cs{headshape}}
\end{cd}

Establishes the shape of the arrowhead drawn by the \cs{arrow} and
\cs{axes} macros. The value of \meta{hdwdr} is the ratio of the width of
the arrowhead to its length; \meta{hdten} is the tension of the B\'ezier
curves; and \meta{hfilled} is a \MF{} boolean value indicating whether
the arrowheads are to be filled (if \mfc{true}) or open. The default
values are $1$, $1$, \mfc{false}, respectively. The \meta{hdwdr},
\meta{hdten} and \meta{hfilled} values are stored by \MF. Setting
\meta{hdten} to `\mfc{infinity}' will make the sides of the arrowheads
straight lines. These values are all stored by \MF.

\begin{cd}
\cs{dashlen}, \cs{dashspace}%
\index{dashlen@\cs{dashlen}}
\end{cd}

These \TeX{} dimensions store, respectively, the length of dashes and
the length of spaces between dashes, for lines drawn by the \cs{dashed}
macro. The \cs{dashed} macro may adjust the dashes and the spaces
between by as much as $1\over{n}$ of their value, where $n$ is the
number of spaces appearing in the curve, in order not to have partial
dashes at the ends. The default values are both \dim{4pt}. The dashes
will actually be longer (and the spaces shorter) by the thickness of the
pen used when they are drawn.

\begin{cd}
\cs{dashlineset},
\cs{dotlineset}%
\index{dashlineset@\cs{dashlineset}}%
\index{dotlineset@\cs{dotlineset}}
\end{cd}

These macros provide convenient standard settings for the \cs{dashlen}
and \cs{dashspace} dimensions. The macro \cs{dashlineset} sets both
values to \dim{4pt}; the macro \cs{dotlineset} sets \cs{dashlen} to
\dim{1pt} and \cs{dashspace} to \dim{2pt}.

\begin{cd}
\cs{hashlen}%
\index{hashlen@\cs{hashlen}}
\end{cd}

This \TeX{} dimension stores the length of the axis hash marks drawn by
the \cs{xmarks} and \cs{ymarks} macros. The default value is \dim{4pt}.

\begin{cd}
\cs{shadespace}%
\index{shadespace@\cs{shadespace}}
\end{cd}

This \TeX{} dimension establishes the spacing between dots drawn by the
\cs{shade} macro. The default value is \dim{1pt}.

\begin{cd}
\cs{darkershade},
\cs{lightershade}%
\index{darkershade@\cs{darkershade}}%
\index{lightershade@\cs{lightershade}}
\end{cd}

These macros both multiply the \cs{shadespace} dimension by constant
factors, $5/6=.833333$ and $6/5=1.2$ respectively, to provide convenient
standard settings for several levels of shading.

\begin{cd}
\cs{polkadotspace}%
\index{polkadotspace@\cs{polkadotspace}}
\end{cd}

This \TeX{} dimension establishes the spacing between the centers of the
dots used in the macro \cs{polkadot}. The default is \dim{10pt}.

\begin{cd}
\cs{dotsize}, \index{dotspace@\cs{dotspace}}\cs{dotspace}%
\index{dotsize@\cs{dotsize}}
\end{cd}

These \TeX{} dimensions establishes the size and spacing between the
centers of the dots used in the \cs{dotted} macro. The defaults are
\dim{0.5pt} and \dim{3pt}.

\begin{cd}
\cs{symbolspace}%
\index{symbolspace@\cs{symbolspace}}
\end{cd}

Similar to \cs{dotspace}, this \TeX{} dimension establishes the space
between symbols placed by the macro
\cs{plot}\marg{\meta{symbol}}$\ldots\,$. Its default is \dim{5pt}.

\begin{cd}
\cs{hatchspace}%
\index{hatchspace@\cs{hatchspace}}
\end{cd}

This \TeX{} dimension establishes the spacing between lines drawn by the
\cs{hatch} macro. The default value is \dim{3pt}.

\begin{cd}
\cs{tlabelsep}\marg{\meta{separation}}%
\index{tlabelsep@\cs{tlabelsep}}
\end{cd}

This macro establishes the separation between a label and its nominal
position. It affects text written with any of the commands \cs{tlabel},
\cs{tlabels}, \cs{axislabels} or \cs{plottext}. It also sets the
separation between the text and the curve defined by the commands
\cs{tlabelrect}, \cs{tlabeloval} or \cs{tlabelellipse}. The default is
\dim{0pt}. The value is stored by both \TeX{} and \MF.

\begin{cd}
\cs{tlabeloffset}\marg{\meta{hlen}}\marg{\meta{vlen}}%
\index{tlabeloffset@\cs{tlabeloffset}}
\end{cd}

This macro establishes a uniform offset that applies to all labels. It
affects text written with any of the commands \cs{tlabel}, \cs{tlabels},
\cs{axislabels} or \cs{plottext}. The default is to have both horizontal
and vertical offsets of \dim{0pt}. The values are stored by both \TeX{}
and \MF.

\begin{cd}
\cs{mfpdataperline}%
\index{mfpdataperline@\cs{mfpdataperline}}
\end{cd}

When \mfp{} is reading data from files and writing it to the
output file, this macro stores the maximum number of points that will be
written on a single line in the output file. Its default is defined by
\cs{def}\cs{mfpdataperline}\marg{5}.

\begin{cd}
\cs{mfpicheight},
\cs{mfpicwidth}%
\index{mfpicheight@\cs{mfpicheight}}%
\index{mfpicwidth@\cs{mfpicwidth}}
\end{cd}

These \TeX{} dimensions store the height and width of the figure created
by the most recently completed \env{mfpic} environment. This might
perhaps be of interest to hackers or to aid in precise positioning of
the graphics. They are meant to be read-only: the \cs{endmfpic} command
globally sets them equal to the height and width of the picture. But
\mfp{} does not otherwise make any use of them.


\subsection{For Advanced Users.}\label{advanced}

\subsubsection{Power Users.}\label{power}


\begin{cd}
\cs{qspline}\marg{\meta{list}}\\
\cs{closedqspline}\marg{\meta{list}}\\
\cs{cspline}\marg{\meta{list}}\\
\cs{closedcspline}\marg{\meta{list}}\\
\index{qspline@\cs{qspline}}%
\index{closedqspline@\cs{closedqspline}}%
\index{cspline@\cs{cspline}}%
\index{closedcspline@\cs{closedcspline}}%
\end{cd}

These are alternate ways of defining curves. In each case, \meta{list}
is a comma separated list of points. These represent not the points the
curve passes through, but the \emph{control points}. The first two
produce quadratic B-splines and the last two produce cubic B-splines. If
you don't know what B-splines are, or don't know what control points
are, it is recommended you not use these commands.

\begin{cd}
\cs{cbclosed}$\ldots$\\
\cs{qbclosed}$\ldots$%
\index{cbclosed@\cs{cbclosed}}%
\index{qbclosed@\cs{qbclosed}}
\end{cd}

These are prefix macros for closing curves. The first closes with a
cubic B-spline, the second with a quadratic B-spline. They will close
any given curve, but the command \cs{cbclosed} is meant to close a cubic
B-spline (see above). That is, \cs{cbclosed}\cs{cspline} should produce
the same result as \cs{closedcspline} with the same argument. The
corresponding statements are true of \cs{qbclosed}: it is meant to close
a quadratic B-spline and \cs{qbclosed}\cs{qspline} should produce the
same result as \cs{closedqspline} with the same argument.

The power user, having noticed that \cs{curve} and \cs{cyclic} insert
some direction modifiers into the path created, may have decided that
there is no \mfp{} command to create a simple \MF{} default style path,
for example \mfc{(1,1)..(0,1)..(0,0)..cycle}. If so, he or she has forgotten
about \cs{mfobj}: the command
\begin{verbatim}
  \mfobj{(1,1)..(0,1)..(0,0)..cycle}
\end{verbatim}
will produce, in the \file{.mf} file, exactly this path, but surround it
with the \TeX{} wrapping needed to make \mfp's prefix macro system work.
However, the syntax of more complicated paths can be extremely lengthy,
so we offer this interface:

\begin{cd}
  \cs{mfbezier}\oarg{\meta{tens}}\marg{\meta{list}}\\
  \cs{closedmfbezier}\oarg{\meta{tens}}\marg{\meta{list}}%
\index{mfbezier@\cs{mfbezier}}
\index{closedmfbezier@\cs{closedmfbezier}}
\end{cd}

This connects the points in the list with the path join operator
\mfc{..tension \meta{tens}..}. If the tension option \oarg{\meta{tens}}
is omitted, the value set by \cs{settension} (initially 1) is used. One
can get a cyclic path by prepending \cs{bclosed} (with matching tension
option), but it will not produce the same result as \cs{closedmfbezier}.
These are cubic B\'ezier's (but you know that if you are a power user).
Quadratic B\'eziers (as in \LaTeX's picture environment) can be
obtained with the following:

\begin{cd}
  \cs{qbeziers}\oarg{\meta{tens}}\marg{\meta{list}}\\
  \cs{closedqbeziers}\oarg{\meta{tens}}\marg{\meta{list}}%
\index{qbeziers@\cs{qbeziers}}
\index{closedqbeziers@\cs{closedqbeziers}}
\end{cd}

Note the plural, to indicate that they will draw a series of quadratic
B\'eziers. In the \meta{list}, the first, third, fifth, etc., are the
points to connect, while the second, fourth, etc., are the control
points. The open version requires an ending point, and so needs an odd
number of points in the list. The closed version assumes the first point
is the ending, and so requires an even number in the list. The curve
will not automatically be smooth. That depends on the choice of the
control points.


\begin{cd}
\cs{mfsrc}\marg{\meta{metafont code}}\\
\cs{mfcmd}\marg{\meta{metafont code}}\\
\cs{mflist}\marg{\meta{metafont code}}%
\index{mfsrc@\cs{mfsrc}}%
\index{mfcmd@\cs{mfcmd}}%
\index{mflist@\cs{mflist}}%
\end{cd}

These all write the \meta{metafont code} directly to the \MF{} file,
using a \TeX{} \cs{write} command. Line breaks within \meta{metafont
code} are preserved.%
    \footnote{Under most circumstances, but not if the command (plus its
    argument) is part of another macro} %
Almost all the \mfp{} drawing macros invoke one of these. Because of the
way \TeX{} reads and processes macro arguments, not all drawing macros
preserve line breaks (nor do they all need to). However, the ones that
operate on long lists of pair or numeric data (for example, \cs{point},
\cs{curve}, etc.), do preserve line breaks in that data. The difference
in these is minor: \cs{mfsrc} writes its argument without change,
\cs{mfcmd} appends a semicolon (`\mfc{;}') to the code, while
\cs{mflist} surrounds its argument with parentheses and then appends a
semicolon.

Using these can have some rather bizarre consequences, though, so
it is not recommended to the unwary. It is, however, currently the
only way to make use of \MF's equation solving ability. Here's an
oversimplified example:

\begin{verbatim}
\mfpic[20]{-0.5}{1.5}{0}{1.5}
\mfsrc{z1=(0,0);
  z2-z3=(1,2);
  z2+2z3=(1,-1);}       % z2=(1,1), z3=(0,-1)
\arc[t]{z1,z2,z3}
\endmfpic
\end{verbatim}

Check out the sample \file{forfun.tex} for a more realistic example.

\begin{cd}
\cs{setmfvariable}\marg{\meta{type}}\marg{\meta{name}}\marg{\meta{value}}\\
\cs{setmpvariable}\marg{\meta{type}}\marg{\meta{name}}\marg{\meta{value}}%
\index{setmfvariable@\cs{setmfvariable}}
\index{setmpvariable@\cs{setmpvariable}}
\end{cd}

These formerly internal \mfp{} macros can be use to define symbolic
names for any \MF{} or \MP{} variable type. They are interchangeable;
you can use either one with or without the \opt{metapost} option.
As an example of their use, since dimensions are numeric data types in
\MF, the command
\begin{ex}
 \cs{setmfvariable}\marg{numeric}\verb${my_dim}$\marg{7pt}
\end{ex}
would set the \MF{} variable \verb$my_dim$ to the value \texttt{7pt}.
After that, \verb$my_dim$ can be used in any \emph{drawing} command
where a dimension is required:
\begin{ex}
  \cs{plotsymbol}\verb$[my_dim]$\marg{Triangle}\cs{rect}\marg{(0,0),(1,1)}
\end{ex}
will plot the rectangle with small triangles spaced \dim{7pt} apart.

You can define paths this way
(\cs{setmfvariable}\marg{path}\marg{X}\marg{(0,0)..(1,1)..(0,1)}), but
the \meta{value} has to be valid \MF{} path construction syntax,
\emph{not} something like \cs{rect}\marg{$\ldots$}. You need \cs{store}
if you want to set a variable to an \mfp{} path. However, defined either
way, they can be used in \cs{mfobj}.

A variable defined this way is local to the \env{mfpic} environment it
is contained in. It is in fact local to any \MF{} group. In \mfp, only
\cs{connect} {\dots} \cs{endconnect} and \cs{mfpic} {\dots}
\cs{endmfpic} create \MF{} groups in the graph file.

\begin{cd}
\cs{noship}\\%
\cs{stopshipping}\\%
\cs{resumeshipping}\\%
\index{noship@\cs{noship}}
\index{stopshipping@\cs{stopshipping}}
\index{resumeshipping@\cs{resumeshipping}}
\end{cd}

\cs{stopshipping} turns off character shipping (by \MF{} to the TFM and
GF files, or by \MP{} to appropriate \EPS{} output file) until
\cs{resumeshipping} occurs. If you want just one character not shipped,
just use \cs{noship} inside the mfpic environment. This is useful if all
one wishes to do in the current \env{mfpic} environment is to make
\emph{tiles} (see below).

\begin{cd}
\cs{patharr}\marg{\meta{pv}}$\ldots$\cs{endpatharr}%
\index{patharr@\cs{patharr}}\index{endpatharr@\cs{endpatharr}}
\end{cd}

This pair of macros, acting as an environment, accumulate all enclosing
paths, in order, into a path array named \meta{pv}. A path array is a
collection of paths with a common base name indexed by integers from 1
to the number of paths.  Any path in the array can be accessed by means
of \cs{mfobj}. For example, after
\begin{verbatim}
\patharr{pa}
  \rect{(0,0),(1,1)} \circle{(.5,.5), .5}
\endpatharr
\end{verbatim}
then \cs{mfobj}\marg{pa[1]} refers to the rectangle and
\cs{mfobj}\marg{pa[2]} refers to the circle. In case explicit numbers
are used, \MF{} allows \gbc{pa1} as an abbreviation for \gbc{pa[1]}.
However, if a numeric variable or some expression is used (e.g.,
\gbc{pa[n+1]}) the square brackets are required.

This command can only be used in an \env{mfpic} environment. The
definitions it makes are, however, global.

\emph{Note}: In \LaTeX, this pair of macros can be used in the form of a
\LaTeX-style environment called \env{patharr}---as in
\cs{begin}\marg{patharr}$\ldots$\cs{end}\marg{patharr}.

\begin{cd}
\cs{pairarray}\marg{\meta{var}}{\meta{list-of-points}}\\
\cs{numericarray}\marg{\meta{var}}{\meta{list-of-numbers}}%
\index{pairarray@\cs{pairarray}}%
\index{numericarray@\cs{numericarray}}
\end{cd}

These enable the simultaneous definition of pair and numeric variables.
For example, after
\begin{verbatim}
  \pairarray{X}{(0,1),(1,1),(0,0),(1,0)}
\end{verbatim}
the variables \mfc{X1}, \mfc{X2}, \mfc{X3}, and \mfc{X4} are equal to
the given points in that order. And then
\begin{verbatim}
  \polyline{X1,X2,X3,X4}
\end{verbatim}
will draw the lines connecting these four points. The index may
optionally be put in square brackets and may be separated from the name
by any number of spaces. If a numeric expression is used instead of an
explicit number, square brackets \emph{must} surround it: \gbc{X[1+1]},
\gbc{X[2]}, \gbc{X2} and \gbc{X 2} are all the same. The arrays are
defined locally if these commands occur in an \env{mfpic} environment,
global otherwise. In all arrays, the variable \gbc{X} itself (not
followed by any digit or brackets) is a number equal to the number of
elements in the array.

Array variables may be used only where the values are processed only by
\MF{} or \MP, they are unknown to \TeX. In particular, they cannot be
used in commands that position text unless \opt{mplabels} is in effect.

Several commands in \mfp{} define arrays of objects that can be used in
other commands. The main ones are \cs{piechart} and \cs{barchart}. These
arrays are always global. Using \cs{piechart} causes the following
arrays to become defined:
\begin{itemize}
  \item \gbc{piewedge}, a path array describing the wedges of the chart.
        The command \cs{piewdge}\marg{\meta{num}} (without optional
        argument) is almost exactly the same as
        \cs{mfobj}\marg{piewedge[\meta{num}]}.
  \item \gbc{pieangle}, a numeric array, the starting angle of each wedge.
  \item \gbc{piedirection}, a pair array, the unit vectors pointing in
        the directions of the centers of the wedges. If \cs{pieangle1}
        is 0 and \gbc{pieangle2} is 90 degrees, then \gbc{piedirection1}
        is $(\cos 45,\sin 45)$.
\end{itemize}

Using \cs{barchart} causes the following arrays to become defined. The
exact meaning depends on whether bars are horizontal or vertical. The
following describes horizontal bars; interchange the roles of $x$ and
$y$ if they are vertical:
\begin{itemize}
  \item \gbc{barstart}, the position on the $y$-axis of the leading edge
        of the bars.
  \item \gbc{barbegin}, the $x$-coordinate of the leftmost end of the
        bars.
  \item \gbc{barend}, the $x$-coordinate of the rightmost end of the
        bars.
  \item \gbc{chartbar}, the rectangular path of the bar; \gbc{chartbar1}
        is the rectangle with corners at \gbc{(barbegin1,barstart1)} and
        \gbc{(barend1,barstart+barwd)}, where \gbc{barwd} is the
        width (thickness) of the bar.
  \item \gbc{barlength}, the same as \gbc{barend}. This is for backward
        compatibility; the was name chosen at a time when all the bars
        had one side on an axis (i.e., \gbc{barbegin[n] = 0}).
\end{itemize}

\begin{cd}
\cs{tile}\marg{\meta{tilename},\meta{unit},\meta{wd},\meta{ht},\meta{clip}}\\
  \ $\ldots$\\
\cs{endtile}%
\index{tile@\cs{tile}}\index{endtile@\cs{endtile}}
\end{cd}

In this environment, all drawing commands contribute to a \emph{tile}. A
\emph{tile} is a rectangular picture which may be used to fill the
interior of closed paths.  The units of drawing are given by
\meta{unit}, which should be a dimension (like \dim{1pt} or \dim{2in}).
The tile's horizontal dimensions are $0$ to $\meta{wd}\cdot\meta{unit}$
and its vertical dimensions $0$ to $\meta{ht}\cdot\meta{unit}$, so
\meta{wd} and \meta{ht} should be pure numbers. If \meta{clip} is
\mfc{true} then all drawing is clipped to be within the tile's boundary.

By using this macro, you can design your own fill patterns (to use them,
see the \cs{tess} macro below), but please take some care with the
\ae sthetics! The \meta{tilename} is globally defined by this command.

\begin{cd}
\cs{tess}\marg{\meta{tilename}}$\ldots$%
\index{tess@\cs{tess}}
\end{cd}

Tile the interior of a closed path with a tessellation comprised of
copies of the \emph{tile} specified by \meta{tilename}.  There is no
default \meta{tilename}; you must make all your own tiles. Tiling an
open curve is technically an error, but the \MF{} code responds by
drawing the path and not doing any tiling.

Tiling large regions with complicated tiles can exceed the capacity of
some versions of \MP. There is less of a problem with \MF. This is not
because \MF{} has greater capacity, but because of the natural
difference between bitmaps and vector graphics.

In \MP, the tiles are copied with whatever color they are given when
they are defined. They can be multicolored.

\begin{cd}
\cs{cutoffafter}\marg{\meta{obj}}\dots\\
\cs{cutoffbefore}\marg{\meta{obj}}\dots\\
\cs{trimpath}\marg{\meta{dim$_1$},\meta{dim$_2$}}\dots\\
\cs{trimpath}\marg{\meta{dim$_1$}}\dots\\
\index{cutoffafter@\cs{cutoffafter}}%
\index{cutoffbefore@\cs{cutoffbefore}}%
\index{trimpath@\cs{trimpath}}%
\end{cd}

These are prefix macros. The first two take an `object' (a variable in
which a path was previously stored using \cs{store}) and uses it to trim
one end off the following path. \cs{cutoffbefore} cuts off the part of
the path before its first intersection with the object, while
\cs{cutoffafter} cuts off the part after the last intersection. If the
path does not intersect the object, nothing is cut off. If the object
and the path intersect in more than one point, as little as possible
(usually%
    \footnote{\MF's methods for finding the `first' point of
    intersection do not always find the actual first one.}) %
is cut off. This is completely reliably only when there is only one
point of intersection.

The \cs{trimpath} macro takes two dimensions separated by commas and
trims those lengths off the initial and terminal ends of the path. If
only one dimension is given, that is used at both ends. This macro is
essentially equivalent to applying \cs{cutoffafter} and then
\cs{cutoffbefore} where the objects are circles which have radii equal
to the given dimensions and which are centered at the endpoints of the
path. Consequently, if the path is shorter than either dimension, it
will not intersect either circle and nothing will be trimmed. Similarly,
if the result of \cs{cutoffafter} is shorter than the first dimension,
then \cs{cutoffbefore} will not trim any more off. The first two macros
can be used to create a curve that starts or ends right at another
figure without having to find the point where the two curves intersect.
The third one can be used on the result to produce a curve that stops
just short of the point of intersection.

\begin{cd}
\cs{mftitle}\marg{\meta{title}}%
\index{mftitle@\cs{mftitle}}
\end{cd}

Write the string \meta{title} to the \MF{} file, and use it as a \MF{}
message. (See \textit{The \MF{}book}, chapter 22, page 187, for two uses of
this.)

\begin{cd}
\cs{tmtitle}\marg{\meta{title}}%
\index{tmtitle@\cs{tmtitle}}
\end{cd}

Write the text \meta{title} to the \TeX{} document, and to the log file,
and use it implicitly in \cs{mftitle}. This macro forms a local group
around its argument.

\medskip

Since \TeX{} is limited to 256 dimension registers, and since dimensions
are so important to typesetting and drawing, it is common to use up all
256 when drawing packages are loaded. Therefore \mfp{} uses font
dimensions to store dimension values. The following is the command that
handles the allocation of these dimensions.

\begin{cd}
\cs{newfdim}\marg{\meta{fdim}}%
\index{newfdim@\cs{newfdim}}
\end{cd}

This create a new global font dimension named \meta{fdim}, which is a
\TeX{} control sequence (with backslash). It can be used almost like
an ordinary \TeX{} dimension.  One exception is that the \TeX{} commands
\cs{advance}, \cs{multiply} and \cs{divide} cannot be applied directly
to font dimensions (nor \LaTeX's \cs{addtolength}); however, the font
dimension can be copied to a temporary \TeX{} dimension register, which
can then be manipulated and copied back (using \cs{setlength} in \LaTeX,
if desired). Another exception is that all changes to a font dimension
are global in scope. Also beware that \cs{newfdim} uses font dimensions
from a single font, the \file{dummy} font, which most \TeX{} systems
ought to have. (You'll know if yours doesn't, because \mfp{} will fail
upon loading!) Also, implementations of \TeX{} differ in the number of
font dimensions allowed per font. Hopefully, \mfp{} won't exceed your
local \TeX's limit.

All of \mfp's basic dimension parameters are font dimensions. We have
lied slightly when we called them `\TeX{} dimensions'. We arrange for
them to be local to \env{mfpic} environments by saving their values at
the start and restoring them at the end.

\begin{cd}
\cs{setmfpicgraphic}\marg{\meta{filename}}%
\index{setmfpicgraphic@\cs{setmfpicgraphic}}
\end{cd}

This is the command that is invoked to place the graphic created. See
appendix~\ref{graphics} for a discussion of its use and its default
definition. It is a user-level macro so that it can be redefined in
unusual cases. It operates on the output of the following macro:

\begin{cd}
\cs{setfilename}\marg{\meta{file}}\marg{\meta{num}}%
\index{setfilename@\cs{setfilename}}
\end{cd}

\Mfp's figure inclusion code ultimately executes
\cs{setmfpicgraphic} on the result of applying \cs{setfilename} to two
arguments: the file name specified in the \cs{opengraphsfile} command
and the number of the current picture. Normally \cs{setfilename} just
puts them together with the `\texttt{.}' separator (because that is
usually the way \MP{} names its output), but this can be redefined if
the \MP{} output undergoes further processing or conversion to another
format in which the name is changed. Any redefinition of
\cs{setfilename} must come before \cs{opengraphsfile} because that
command tests for the existence of the first figure. After any
redefinition, \cs{setfilename} must be a macro with two arguments that
creates the actual filename from the above two parts. It should also be
completely expandable. See the appendices, subsection~\ref{graphics} for
further dicussion.

\begin{cd}
\cs{preparemfpicgraphic}\marg{\meta{filename}}%
\index{preparemfpicgraphic@\cs{preparemfpicgraphic}}
\end{cd}

This command is automatically invoked before \cs{setmfpicgraphic} to
make any preparations needed. The default definition is to do nothing
except when the \prog{graphics} package is used. That package provides
no clean way to determine the bounding box of the graphic after it is
included. Since \mfp{} needs this information, this command
redefines an internal command of the graphics package to make the data
available. If \cs{setmfpicgraphic} is redefined then this may also have
to be redefined.

\begin{cd}
\cs{getmfpicoffset}\marg{\meta{filename}}%
\index{getmfpicoffset@\cs{getmfpicoffset}}
\end{cd}

This command is automatically invoked after \cs{setmfpicgraphic} to
store the offset of the lower left corner of the figure in the macros
\cs{mfpicllx} and \cs{mfpiclly}. If \cs{setmfpicgraphic} is redefined
then this may also have to be redefined.

\begin{cd}
\cs{ifmfpmpost}%
\index{ifmfpmpost@\cs{ifmfpmpost}}
\end{cd}

Users wishing to write code that adjusts its behavior to the graph file
processor can use this to test which option is in effect. The macro
\cs{usemetapost} sets it true and \cs{usemetafont} sets it false. There
are no commands \cs{mfpmposttrue} nor \cs{mfpmpostfalse}, since the user
should not be changing the setting once it is set: a great deal of
\mfp{} internal code depends on them, and on keeping them consistent
with the \cs{opengraphsfile} commands reading of these booleans.

\begin{cd}
\cs{mfpicversion}
\index{mfpicversion@\cs{mfpicversion}}
\end{cd}

This expands to the current \mfp{} version multiplied by 100. At this
writing, it produces `\texttt{70}' because the version is 0.7. It
can be used to test for the current version:
\begin{verbatim}
  \ifx\mfpicversion\undefined \def\mfpicversion{0}\fi
  \ifnum\mfpicversion>70 ... \else ... \fi
\end{verbatim}
\cs{mfpicversion} was added in version 0.7.

\subsubsection{Hackers.}\label{hackers}

\Mfp{} employs a modified version of \LaTeX's \cs{@ifnextchar}
that not only skips over spaces when seeking the next character, but
also skips over \cs{relax} or tokens that have been \cs{let} equal to
it. This is because, in contexts where we try to preserve lines, we make
the end-of-line character active and set it equal to \cs{relax}. Since
it is hard to predict in what context a macro will be used, this gives
code like
\begin{ex}
  \cs{function}\\
  \oarg{s1.2}\marg{0,2,.1}\marg{ x**2 }
\end{ex}
the same behavior in both.%
    \footnote{Actually, because of a bug in previous versions, this was
    not true, but it is now. I hope.}
One consequence is that putting \cs{relax} to stop a command from seeing
a `\texttt{[}' as the start of an optional argument will not work for
\mfp{} commands. The same holds for the `\texttt{*}' in those few
commands that have a star-form, and also for other commands that look
ahead (\cs{tlabel} looks for a `\texttt{(}' starting off the location,
and macros that operate on lists of data look ahead for
`\cs{datafile}'). This is not a serious problem, because there is only
one command (\cs{smoothdata}) that takes an optional arguments but
doesn't have mandatory arguments after that. If a `\cs{relax}' appeared
after any other \mfp{} command, it would be taken as an argument and an
error would result. In any case, \cs{empty} will stop the looking ahead
if it should ever be necessary.

Most of \mfp's commands have arguments with parts delimited by commas
and parentheses. In most cases this is no problem because they are
written unchanged to the \file{.mf} and there they are parsed just fine.
Some commands' arguments, however, have to be parsed by both \TeX{} and
\MF. Examples are \cs{tlabel} (sometimes, under \opt{mplabels}), and
\cs{pointdef}. One might be tempted to use \MP{} expressions there and
that works fine as long as they do not contain commas or parentheses. In
such cases, they can sometimes be enclosed in braces to prevent \TeX{}
seeing these elements as delimiters, but sometimes these braces might
get written to the \file{.mf} (or \file{.mp}) output and cause a \MF{}
(\MP) error. In such cases the following work-around might be possible:

\begin{verbatim}
  \def\identity#1{#1}
  \pointdef{A}(\identity{angle (1,2)},3)
  \rect{(0,0),\A}
\end{verbatim}

The braces prevent \TeX's argument parsing from seeing the first comma
as a delimiter, but upon writing to the \file{.mf}, the \cs{identity}
commands are expanded and only the contents appear in the output. (\TeX{}
parses the argument to assign meanings to \cs{Ax} and \cs{Ay}.)


\clearpage

\def\sectionmark#1{\markright {\thesection\quad#1}}%
\def\subsectionmark#1{}
\def\subsubsectionmark#1{}
\thispagestyle{plain}
\section{Appendices}\label{appendices}

\subsection{Acknowledgements.}\label{acknowledgements}

Tom would like to thank all of the people at Dartmouth as well as out in
the network world for testing \mfp{} and sending him back
comments. He would particularly like to thank:

\medskip
Geoffrey Tobin %(G.Tobin@latrobe.edu.au)
for his many suggestions, especially about cleaning up the \MF{} code,
enforcing dimensions, fixing the dotted line computations, and speeding
up the shading routines (through this process, Geoffrey and Tom managed
to teach each other many of the subtleties of \MF), and for keeping
track of \mfp{} for nearly a year while Tom finished his thesis;

\medskip
Bryan Green %(bgreen@sanjuan.uvic.ca)
for his many suggestions, some of which (including his rewriting the
\cs{tcaption} macro) ultimately led to the current version's ability to
put graphs in-line or side-by-side; and

\medskip
Uwe Bonnes %(bon@lte.e-technik.uni-erlangen.de)
and Jarom\'\i r Kuben, % (vabo@muni.cz)
who worked out rewrites of \mfp{} during Tom's
working hiatus and who each contributed several valuable ideas.

\medskip
Some credit also belongs to Anthony Stark, % (ajs@merck.com)
whose work on a FIG to \MF{} converter has had a serious impact on the
development of many of \mfp's capabilities.

\medskip
Finally, Tom would like to thank Alan Vlach, the other \TeX{}nician at
Berry College, for helping him decide on the format of many of the
macros, and for helping with testing.

\medskip
Dan Luecking would like to echo Tom's thanks to all of the above,
especially Geoffrey Tobin and Jarom\'\i r Kuben. And to add the names
Taco Hoekwater, for comments, advice and suggestions, and Zaimi
Sami~Alex for suggestions.

But mostly, he'd like to thank Tom Leathrum for starting it all.

\subsection{Changes History.}\label{changes}

See the file \file{changes.txt} for a somewhat sporadic and rambling
history of changes to \mfp. See the file \file{readme.txt} for a
list of any known problems.

%\clearpage
\subsection{Summary of Options}\label{summary}

Unless otherwise stated, any of the command forms will be local to the
current \env{mfpic} environment if used inside. Otherwise it will affect
all later environments.

\medskip
\def\stack#1{\everycr{}\def\\{\cr}\halign{\strut##\hfil\cr#1\crcr}}
{\everycr{\noalign{\medskip}}
\halign to \hsize{\opt{#}\hfil\quad\tabskip0pt plus 1fil&
        \vtop{\stack{#}}\hfil\quad&
        \vtop{\parindent0pt \hsize.45\hsize \rightskip0pt plus1fil\relax
            \strut\ignorespaces#\strut}\tabskip0pt\cr
{\rmfamily\scshape Option}:& \textsc{Command form(s)}:& \omit\textsc{Restrictions}: \hfil\cr
\noalign{\smallskip\hrule\smallskip}
metapost&\cs{usemetapost}& Command must come before
    \cs{opengraphsfile}. Incompatible with \opt{metafont} option.   \cr
metafont&\cs{usemetafont}& The default. Command must come before
    \cs{opengraphsfile}. Incompatible with \opt{metapost} option.   \cr
mplabels&\cs{usemplabels},\\ \cs{nomplabels}& Requires
    \opt{metapost}. If command is used inside an \env{mfpic}
    environment, it should come before \cs{tlabel} commands to be
    affected.                                                       \cr
overlaylabels&\cs{overlaylabels},\\ \cs{nooverlaylabels}& Has no effect
    without \opt{metapost}.                                         \cr
truebbox& \cs{usetruebbox},\\ \cs{notruebbox}& Has no effect
    without \opt{metapost}.                                         \cr
clip& \cs{clipmfpic},\\ \cs{noclipmfpic}& No restrictions.          \cr
clearsymbols& \cs{clearsymbols},\\ \cs{noclearsymbols}& No restrictions.          \cr
centeredcaptions& \cs{usecenteredcaptions},\\ \cs{nocenteredcaptions}&
    No restrictions.                                                \cr
debug&\cs{mfpicdebugtrue},\\\cs{mfpicdebugfalse}& To turn on
    debugging while \file{mfpic.tex} is loading, issue
    \cs{def}\cs{mfpicdebug}\marg{true}.                             \cr
\vtop{\hbox{draft\strut}
      \hbox{final\strut}
      \hbox{nowrite\strut}}&\cs{mfpicdraft}\\
                            \cs{mfpicfinal}\\
                            \cs{mfpicnowrite}& Should not be used
                            together. Command forms should come before
                            \cs{opengraphsfile}\cr
}}

%\clearpage
\subsection{Plotting styles for \cs{plotdata}}\label{styles}

When \cs{plotdata} passes from one curve to the next, it increments a
counter and uses that counter to select a dash pattern, color, or symbol.
It uses predefined dash pattern names \mfc{dashtype0} through
\mfc{dashtype5}, or predefined color names \mfc{colortype0} through
\mfc{colortype7}, or predefined symbols \mfc{pointtype0} through
\mfc{pointtype8}. Here follows a description of each of these variables.
These variables must not be used in the second argument of
\cs{reconfigureplot}, whose purpose is to redefine these variables.

\medskip
Under \cs{dashedlines}, we have the following dash patterns:

\medskip
\indent\vbox{%
\halign{#\hfil\qquad&#\hfil\quad&#\hfil\strut\cr
\textsc{Name}&\textsc{Pattern}&\textsc{Meaning}\cr
\noalign{\smallskip\hrule\smallskip}
\mfc{dashtype0}&    \dim{0bp}                       & solid line   \cr
\mfc{dashtype1}&    \dim{3bp,4bp}                   & dashes       \cr
\mfc{dashtype2}&    \dim{0bp,4bp}                   & dots         \cr
\mfc{dashtype3}&    \dim{0bp,4bp,3bp,4bp}           & dot-dash     \cr
\mfc{dashtype4}&    \dim{0bp,4bp,3bp,4bp,0bp,4bp}   & dot-dash-dot \cr
\mfc{dashtype5}&    \dim{0bp,4bp,3bp,4bp,3bp,4bp}   & dot-dash-dash\cr
}}

\medskip
Under \cs{coloredlines}, we have the following colors. Except for
\mfc{black} and \mfc{red}, each color is altered as indicated. This is
an attempt to make the colors more equal in visibility against a white
background. (The success of this attempt varies greatly with the output
or display device.)

\medskip
\indent\vbox{%
\halign{#\hfil\qquad&#\hfil\quad&#\hfil\strut\cr
\textsc{Name}&\textsc{Color}&\textsc{(r,g,b)}\cr
\noalign{\smallskip\hrule\smallskip}
\mfc{colortype0}&   black  &  $(  0,  0,  0)$\cr
\mfc{colortype1}&   red    &  $(  1,  0,  0)$\cr
\mfc{colortype2}&   blue   &  $( .2, .2,  1)$\cr
\mfc{colortype3}&   orange &  $(.66,.34,  0)$\cr
\mfc{colortype4}&   green  &  $(  0, .8,  0)$\cr
\mfc{colortype5}&   magenta&  $(.85,  0,.85)$\cr
\mfc{colortype6}&   cyan   &  $(  0,.85,.85)$\cr
\mfc{colortype7}&   yellow &  $(.85,.85,  0)$\cr
}}

\medskip

Under \cs{pointedlines} and \cs{datapointsonly}, the following symbols
are used. Internally each is referred to by the numeric name, but they
are identical to the more descriptive name. Syntactically, all are \MF{}
path variables. (The order changed between versions 0.6 and 0.7.)

\medskip
\indent\vbox{%
\halign{#\hfil\qquad&#\hfil\strut\cr
\textsc{Name}&\textsc{Description}\cr
\noalign{\smallskip\hrule\smallskip}
\mfc{pointtype0}&   \mfc{Circle}       \cr
\mfc{pointtype1}&   \mfc{Cross}        \cr
\mfc{pointtype2}&   \mfc{SolidDiamond} \cr
\mfc{pointtype3}&   \mfc{Square}       \cr
\mfc{pointtype4}&   \mfc{Plus}         \cr
\mfc{pointtype5}&   \mfc{Triangle}     \cr
\mfc{pointtype6}&   \mfc{SolidCircle}  \cr
\mfc{pointtype7}&   \mfc{Star}         \cr
\mfc{pointtype8}&   \mfc{SolidTriangle}\cr
}}

\subsection{Special considerations when using \MF}\label{mfconsiderations}

The most important restriction in \MF{} is on the size of a picture.
Coordinates in \MF{} ultimately refer to pixel units in the font that is
output. These are required to be less than 4096, so an absolute limit on
the size of a picture is whatever length a row of 4096 pixels is. In
fonts prepared for a LaserJet4 (600 DPI), this means about 6.8 inches.
For a 1200 DPI pronter, the limit is about 3.4 inches.

A similar limit holds for numbers input, and the values of variables:
\MF{} will return an error for \mfc{sin 4096}. Intermediate values can
be greater (\mfc{sin (2*2048)} will cause no error), but final, stored
results are subject to the limit. An \mfp{} example that generated an
error recently was:
\begin{verbatim}
  \mfpicunit 1mm
  \mfpic[10]{-3}{7}{-3.5}{5}
    \function{-4.5,4,.1}{x*x}
  \endmfpic
\end{verbatim}
The problem was the value of $(-4.5)^2=20.25$ in pixel units (after
multiplying by the \cs{mfpic} scaling factor the \cs{mfpicunit} in
inches and the DPI value): $20.25\times10\times0.03937\times600 > 4783$.
The error did not occur at the point of creating the font, but merely at
the point of storing the path in an internal variable for manipulation
and drawing.


\subsection{Special considerations when using \MP}\label{mpconsiderations}

\subsubsection{Required support}

To use \mfp{} with \MP, the following support is needed (besides a
working \MP{} installation):

\medskip
\halign{#\hfil\quad&\vtop{\hsize 4.4 truein \raggedright \noindent
    \strut#\strut}\hfil\cr
Under plain\TeX           &The file \file{epsf.tex}\cr
Under \LaTeX209           &The file \file{epsf.tex} or \file{epsf.sty}\cr
Under \LaTeXe             &The package \prog{graphics} or \prog{graphicx}\cr
Under \pdfLaTeX{}         &The package \prog{graphics} or
                           \prog{graphicx} with option \opt{pdftex}\cr
Under plain \pdfTeX{}     &The files \file{supp-pdf.tex} and
                           \file{supp-mis.tex}\cr
In all cases              &The files \file{grafbase.mp} and
                           \file{dvipsnam.mp} plus, of course,
                           \file{mfpic.tex} (and \file{mfpic.sty} for
                           \LaTeX)\cr
}

\medskip
The files \file{grafbase.mp} and \file{dvipsnam.mp} should be in a
directory searched by \MP. The remaining files should be in directories
searched by the appropriate \TeX{} variant. If \MP{} cannot find the
file \file{grafbase.mp}, then by default it will try to input
\file{grafbase.mf}, which is generally futile (or fatal).

In case \pdfLaTeX{} is used, the graphics package is given the
\opt{pdftex} option. This option requires the file \file{pdftex.def}
which currently inputs the files \file{supp-pdf.tex} and
\file{supp-mis.tex}. The file \file{pdftex.def} is supplied with the
\prog{graphics} package. The other two are usually supplied with a
\pdfTeX{} distribution, and are definitely part of the \ConTeXt{}
distribution. Older versions had some bugs in connection with the
\prog{babel} package. One workaround was to load the \prog{graphics}
package and \mfp{} before \prog{babel}.

If the user loads one of the above required files or packages before the
\mfp{} macros are loaded then \mfp{} will not reload them.
If they have not been input, \mfp{} will load whichever one it
decides is required. In the \LaTeXe{} case, \mfp{} will load the
\prog{graphics} package. If the user wishes \prog{graphicx}, then that
package must be loaded before \mfp.

\subsubsection{\CMP{} is not \MF}

\PS{} is not a pixel oriented language and so neither is \MP. The model
for drawing objects is completely different between \MF{} and \MP, and
so one cannot always expect the same results. \CMP{} support in
\mfp{} was carefully written so that files successfully printed
with \mfp{} using \MF{} would be just as successfully printed
using \MP. Nevertheless, it frequently choke on files that make use of
the \cs{mfsrc} command for writing code directly to the \file{.mf} file.
While \file{grafbase.mp} is closely based on \file{grafbase.mf}, much of
the code had to be completely rewritten.

Pictures in \MP{} are stored as (possibly nested) sequences of objects,
where objects are things like points, paths, contours, other pictures,
etc. In \MF, pictures are stored as a grid of pixels. Pictures that are
relatively simple in one program might be very complex in the other and
even exceed memory allocated for their storage. Two examples are the
\cs{polkadot} and \cs{hatch} commands. When the polkadot space and size
are both too small, a \cs{polkadot}-ed region has been known to exceed
\MP{} capacity, while being well within \MF{} capacity. In \MP{} the
memory consumed by \cs{hatch} goes up in direct proportion to the linear
dimensions of the figure being hatched, while in \MF{} it goes up in
proportion to the area, and then the reverse can happen, with \MF's
capacity exeeded far sooner that \MP's.

In \MP{} it is important to note that each
prefix modifies the result of the entire following sequence. In essence
prefixes can be viewed as being applied in the opposite order to their
occurrence. Example:

\begin{ex}
    \cs{dashed}\cs{gfill}\cs{rect}\marg{(0,0),(1,1)}
\end{ex}
This adds the dashed outline to the filled rectangle. That is, first the
rectangle is defined, then it is filled, then the outline is drawn in
dashed lines. This makes a difference when colors other than black are
used. Drawing is done with the center of the virtual pen stroked down
the middle of the boundary, so half of its width falls inside the
rectangle. On the other hand, filling is done right up to the boundary.
In this example, the dashed lines are drawn on top of part of the fill.
In the reverse order, the fill would cover part of the outline.

\subsubsection{Graphic inclusion}\label{graphics}

It may be impossible to completely cater to all possible methods of
graphic inclusions with automatic tests. The macro that is invoked
to include the \PS{} graphic is \cs{setmfpicgraphic} and the user
may (carefully!) redefine this to suit special circumstances. Actually,
\mfp{} runs the following sequence:

\begin{cd}
\cs{preparemfpicgraphic}\marg{\meta{filename}}\\
\cs{setmfpicgraphic}\marg{\meta{filename}}\\
\cs{getmfpicoffset}\marg{\meta{filename}}%
\index{preparemfpicgraphic@\cs{preparemfpicgraphic}}%
\index{setmfpicgraphic@\cs{setmfpicgraphic}}%
\index{getmfpicoffset@\cs{getmfpicoffset}}
\end{cd}

The following are the default definitions for \cs{setmfpicgraphic}:

\medskip
\halign{#:\hfil&\quad#\hfil\cr
In plain \TeX&
\cs{def}\cs{setmfpicgraphic}\texttt{\#1}\marg{\cs{epsfbox}\marg{\#1}}\cr
In \LaTeX209&
\cs{def}\cs{setmfpicgraphic}\texttt{\#1}\marg{\cs{epsfbox}\marg{\#1}}\cr
In \LaTeXe&
\cs{def}\cs{setmfpicgraphic}\texttt{\#1}\marg{\cs{includegraphics}\marg{\#1}}\cr
In \pdfLaTeX&
\cs{def}\cs{setmfpicgraphic}\texttt{\#1}\marg{\cs{includegraphics}\marg{\#1}}\cr
In \pdfTeX&
\cs{def}\cs{setmfpicgraphic}\texttt{\#1}\marg{\cs{convertMPtoPDF}\marg{\#1}%
    \marg{1}\marg{1}}\cr
}
\medskip
Moreover, since \MP{} by default writes files with numeric extensions,
we add code to each figure, so that these graphics are correctly
recognized as \EPS{} or \prog{MPS}. For example, to the figure with
extension \file{.1}, we add the equivalent of one of the following
\begin{itemize}
\item[] \cs{DeclareGraphicsRule}\marg{.1}\marg{eps}\marg{.1}\marg{} in \LaTeXe.
\item[] \cs{DeclareGraphicsRule}\marg{.1}\marg{mps}\marg{.1}\marg{} in \pdfLaTeX.
\end{itemize}

After running the command \cs{setmfpicgraphic}, \mfp{} runs
\cs{getmfpicoffset} to store the lower left corner of the bounding box
of the figure in two macros \cs{mfpicllx} and \cs{mfpiclly}. All the
above versions of \cs{setmfpicgraphic} (except \cs{includegraphics})
make this information available; the definition of \cs{getmfpicoffset}
merely copies it into these two macros. What \mfp{} does in the
case of \cs{includegraphics} is to modify (locally) the definition of an
internal command of the graphics package so that it copies the
information to those macros, and then \cs{getmfpicoffset} does nothing.
This internal modification is accomplished by the macro
\cs{preparemfpicgraphic}. Changes to \cs{setmfpicgraphic} might require
changing either or both of \cs{preparemfpicgraphic} and
\cs{getmfpicoffset}. All three of these commands are fed the graphic's
file name as the only argument, although only \cs{setmfpicgraphic}
currently does anything with it.

One possible reason for wanting to redefine \cs{setmfpicgraphic} might
be to rescale all pictures. This is \emph{definitely not} a good idea
without the option \opt{mplabels} since the \mfp{} code for
placing labels and captions and reserving space for the picture relies
on the picture having the dimensions given by the arguments to the
\cs{mfpic} command. With \opt{mplabels} plus \opt{truebbox} it will
probably work, but (i)~it has \emph{not} been considered in writing the
\mfp{} code, (ii)~it will then scale all the text as well as the
figure, and (iii)~it will scale all line thickness, which should
normally be a design choice independent of the size of a picture. To
rescale all pictures, one need only change \cs{mfpicunit} and rerun
\TeX{} and \MP.

A better reason might be to allow the conversion of your \MP{} figures
to some other format. Then redefining \cs{setmfpicgraphic}
could enable including the appropriate file in the appropriate format.

The filename argument mentioned above is actually the result obtained by
running the macro \cs{setfilename}\index{setfilename@\cs{setfilename}}.
The command \cs{setfilename} gets two arguments: the name of the \MP{}
output file (set in the \cs{opengraphsfile} command) without extension,
and the number of the picture. The default definition of
\cs{setfilename} merely inserts a dot between the two arguments. That is
\cs{setfilename}\marg{fig}\marg{1} produces \file{fig.1}. You can
redefine this behavior also. Any changes to \cs{setfilename} must come
after the \mfp{} macros are input and before the
\cs{opengraphsfile} command. Any changes to \cs{setmfpicgraphic} must
come after the \mfp{} macros are input and before any \cs{mfpic}
commands, but it is best to place it before the \cs{opengraphsfile}
command.

As \mfp{} is currently written, \cs{setfilename} must be
\emph{completely expandable}, which means it should contain no
definitions, no assignments such as \cs{setcounter}, and no
calculations. To test whether a proposed definition is completely
expandable, put
\begin{ex}
\cs{message}\marg{\texttt{***}%
\cs{setfilename}\marg{file}\marg{1}\texttt{***}}
\end{ex}
after the definition in a \file{.tex} file and view the result on the
terminal or in the \file{.log} file. You should see only your expected
filename between the asterisks.


\subsection{\prog{Mfpic} and the rest of the world}

\subsubsection{The literature}

There are at least two places where \mfp{} has garnered more than a
cursory mention. The most up-to-date is a section in \textit{The
\LaTeX{} Graphics Companion} by Michel Goossens, Sebastian Rahtz and
Frank Mittelbach. It describes a version prior to the introduction of
\MP{} support, but it correctly describes a subset of its current
commands and abilities.

The other is \textit{\TeX{} Unbound} by Alan Hoenig, which contains a
chapter on \mfp. Unfortunately, it describes a version that was
replaced in 1996 with version 0.2.10.9.  The following summarizes the
differences between the description%
    \footnote{While I'm at it: \textit{\TeX{} Unbound} occasionally
    refers to \mfp{} using a logo-like formatting in which the `MF' is
    in a special font and the `I' is lowered. This `logo' may suggest
    a relationship between \mfp{} and \PiCTeX. There is no such
    relationship, and there is no official logo-like designation for
    \mfp.} %
found in Chapter 15 and \mfp{} versions 0.2.10.9 through the
current one:

\cs{wedge} is now renamed \cs{sector} to avoid conflict with the \TeX{}
command of the same name. The syntax is slightly different from that
given for \cs{wedge}:
\begin{ex}
  \cs{sector}\marg{(\meta{x},\meta{y}), \meta{radius}, \meta{angle1}, \meta{angle2}}
\end{ex}

The macro \cs{plr}\marg{(\meta{$r_0$},\meta{$\theta_0$}),%
(\meta{$r_1$},\meta{$\theta_1$}),$\ldots$} is used to convert polar
coordinate pairs to rectangular coordinates, so the commands
\cs{plrcurve}, \cs{plrcyclic}, \cs{plrlines} and \cs{plrpoint} were
dropped from \mfp. Now use
\begin{ex}
  \cs{curve}\marg{\cs{plr}\marg{(\meta{$r_0$},\meta{$\theta_0$}),%
    (\meta{$r_1$},\meta{$\theta_1$}),$\ldots$}}
\end{ex}
instead of
\begin{ex}
  \cs{plrcurve}\marg{(\meta{$r_0$},\meta{$\theta_0$}),%
    (\meta{$r_1$},\meta{$\theta_1$}),$\ldots$}
\end{ex}
and similarly for \cs{cyclic}, \cs{lines} and \cs{point} with respect to
\cs{plrcyclic}, \cs{plrlines} and \cs{plrpoint}.

\cs{fill} is now renamed \cs{gfill} to avoid conflict with the \LaTeX{}
command of the same name.

\cs{rotate},  which rotates a following figure about a point, is now
renamed \cs{rotatepath} to avoid confusion with a similar name for a
transformation (see below).

\cs{white} is now renamed \cs{gclear} because \cs{white} is too likely
to be chosen for, or confused with, a color command.

\smallskip
The following affine transform commands were changed from a third person
indicative form (which could be confused with a plural noun) to an
imperative form:

\medskip
\moveright\parindent
\vbox{%
  \halign{#\qquad\hfil&#\hfil\cr
    Old name:           & New name:\cr
    \cs{boosts}         & \cs{boost}\cr
    \cs{reflectsabout}  & \cs{reflectabout}\cr
    \cs{rotatesaround}  & \cs{rotatearound}\cr
    \cs{rotates}        & \cs{rotate}\cr
    \cs{scales}         & \cs{scale}\cr
    \cs{shifts}         & \cs{shift}\cr
    \cs{xscales}        & \cs{xscale}\cr
    \cs{xslants}        & \cs{xslant}\cr
    \cs{xyswaps}        & \cs{xyswap}\cr
    \cs{yscales}        & \cs{yscale}\cr
    \cs{yslants}        & \cs{yslant}\cr
    \cs{zscales}        & \cs{zscale}\cr
    \cs{zslants}        & \cs{zslant}\cr
  }%
}

\medskip
\cs{caption} and \cs{label} are now renamed \cs{tcaption} and
\cs{tlabel} to avoid conflict with the \LaTeX{} commands.

\cs{mfcmd} was renamed \cs{mfsrc} for clarity, and (in version 0.7) a
new \cs{mfcmd} was defined, which is pretty much the same except it appends
a semicolon to its argument.

\smallskip
There is a misprint: \cs{axisheadlin} should be \cs{axisheadlen}.

Finally, in the \LaTeX{} template on page 496: \mfp{} now supports
the \cs{usepackage} method of loading.

\subsubsection{Other programs}

There exists a program, \prog{fig2mfpic} that produces \mfp{} code as
output. The code produced (as of this writing) is somewhat old and
mostly incompatible with the description in this manual. Fortunately, it
is accompanied by the appropriate versions of files \file{mfpic.tex} and
\file{grafbase.mf}. Unfortunately, the names conflict with the current
filenames and so they should only be used in circumstances where no
substitution will occur, say in a local directory with the other sources
for the document being produced. Moreover, the documentation in this
manual may not apply to the code produced. However the information in
\textit{\TeX{} Unbound} may apply.

There exist a package, \prog{circuit\_macros}, that can produce a
variety of output formats, one of which is \mfp{} code. One writes a
file (don't ask me what it consists of) and apparently processes it with
\prog{m4} and then \prog{dpic} to produce the output. The \mfp{} code
produced appears to be compatible with the current \mfp.

\renewcommand\mfpindexheading{%
  \subsection{Index of commands, options and parameters by page}}
\let\oldcs\cs
\renewcommand{\cs}[1]{\leavevmode\mytt{\llap{\char`\\}#1}}

\InputIfFileExists{mfpman.ind}{}{\mfpindexheading}

\let\cs\oldcs

\columnseprule 0pt
\columnsep 35pt
\twocolumn[\subsection{List of commands by type}]
\parindent0pt
\parskip0pt plus .3pt\relax
\makeatletter
\let\item\@idxitem
\makeatother

\subsubsection{Figures}

  \item \cs{arc}
  \item \cs{axis}
  \item \cs{btwnfcn}
  \item \cs{chartbar}
  \item \cs{circle}
  \item \cs{closedcspline}
  \item \cs{closedmfbezier}
  \item \cs{closedqbeziers}
  \item \cs{closedqspline}
  \item \cs{cspline}
  \item \cs{curve}
  \item \cs{cyclic}
  \item \cs{datafile}
  \item \cs{ellipse}
  \item \cs{fcncurve}
  \item \cs{function}
  \item \cs{graphbar}
  \item \cs{histobar}
  \item \cs{lines}
  \item \cs{mfbezier}
  \item \cs{mfobj}
  \item \cs{parafcn}
  \item \cs{piewedge}
  \item \cs{plrfcn}
  \item \cs{plrregion}
  \item \cs{polygon}
  \item \cs{polyline}
  \item \cs{qbeziers}
  \item \cs{qspline}
  \item \cs{rect}
  \item \cs{regpolygon}
  \item \cs{sector}
  \item \cs{tlabelcircle}
  \item \cs{tlabelellipse}
  \item \cs{tlabeloval}
  \item \cs{tlabelrect}
  \item \cs{turtle}


\subsubsection{Figure modifiers}

  \item \cs{arrow}
  \item \cs{bclosed}
  \item \cs{cbclosed}
  \item \cs{connect}, \cs{endconnect}
  \item \cs{cutoffafter}
  \item \cs{cutoffbefore}
  \item \cs{lclosed}
  \item \cs{makesector}
  \item \cs{partpath}
  \item \cs{qbclosed}
  \item \cs{reflectpath}
  \item \cs{reverse}
  \item \cs{rotatepath}
  \item \cs{scalepath}
  \item \cs{sclosed}
  \item \cs{shiftpath}
  \item \cs{slantpath}
  \item \cs{subpath}
  \item \cs{transformpath}
  \item \cs{trimpath}
  \item \cs{xscalepath}
  \item \cs{xslantpath}
  \item \cs{xyswappath}
  \item \cs{yscalepath}
  \item \cs{yslantpath}


\subsubsection{Figure renderers}

  \item \cs{dashed}
  \item \cs{dotted}
  \item \cs{draw}
  \item \cs{gclear}
  \item \cs{gclip}
  \item \cs{gendashed}
  \item \cs{gfill}
  \item \cs{hatch}
  \item \cs{lhatch}
  \item \cs{plot}
  \item \cs{plotdata} (sort of)
  \item \cs{plotnodes}
  \item \cs{polkadot}
  \item \cs{rhatch}
  \item \cs{shade}
  \item \cs{tess}
  \item \cs{thatch}
  \item \cs{xhatch}

\subsubsection{Lengths}


  \item \cs{axisheadlen}
  \item \cs{dashlen}
  \item \cs{dotsize}
  \item \cs{dotspace}
  \item \cs{hashlen}
  \item \cs{hatchspace}
  \item \cs{headlen}
  \item \cs{mfpiccaptionskip}
  \item \cs{mfpicheight}
  \item \cs{mfpicunit}
  \item \cs{mfpicwidth}
  \item \cs{pointsize}
  \item \cs{polkadotspace}
  \item \cs{shadespace}
  \item \cs{sideheadlen}
  \item \cs{symbolspace}

\subsubsection{Coordinate transformation}

  \item \cs{applyT}
  \item \cs{boost}
  \item \cs{coords}, \cs{endcoords}
  \item \cs{mirror}
  \item \cs{reflectabout}
  \item \cs{rotate}
  \item \cs{rotatearound}
  \item \cs{scale}
  \item \cs{shift}
  \item \cs{turn}
  \item \cs{xscale}
  \item \cs{xslant}
  \item \cs{xyswap}
  \item \cs{yscale}
  \item \cs{yslant}
  \item \cs{zscale}
  \item \cs{zslant}

\subsubsection{Axes, grids, and marks}

  \item \cs{axes}
  \item \cs{axis}
  \item \cs{axismarks}
  \item \cs{bmarks}
  \item \cs{doaxes}
  \item \cs{grid}
  \item \cs{gridarcs}
  \item \cs{gridlines}
  \item \cs{gridpoints}
  \item \cs{gridrays}
  \item \cs{hgridlines}
  \item \cs{lattice}
  \item \cs{lmarks}
  \item \cs{plotsymbol}
  \item \cs{plrgrid}
  \item \cs{plrgridpoints}
  \item \cs{plrpatch}
  \item \cs{point}
  \item \cs{rmarks}
  \item \cs{tmarks}
  \item \cs{vgridlines}
  \item \cs{xaxis}
  \item \cs{xmarks}
  \item \cs{yaxis}
  \item \cs{ymarks}

\subsubsection{Setting options}

  \item \cs{clearsymbols}
  \item \cs{clipmfpic}
  \item \cs{mfpicdebugfalse}
  \item \cs{mfpicdebugtrue}
  \item \cs{mfpicdraft}
  \item \cs{mfpicfinal}
  \item \cs{mfpicnowrite}
  \item \cs{nocenteredcaptions}
  \item \cs{noclearsymbols}
  \item \cs{noclipmfpic}
  \item \cs{nomplabels}
  \item \cs{nooverlaylabels}
  \item \cs{noship}
  \item \cs{notruebbox}
  \item \cs{overlaylabels}
  \item \cs{resumeshipping}
  \item \cs{stopshipping}
  \item \cs{usecenteredcaptions}
  \item \cs{usemetafont}
  \item \cs{usemetapost}
  \item \cs{usemplabels}
  \item \cs{usetruebbox}

\subsubsection{Changing values}

  \item \cs{axismargin}
  \item \cs{darkershade}
  \item \cs{dashlineset}
  \item \cs{dashpattern}
  \item \cs{dotlineset}
  \item \cs{drawpen}
  \item \cs{hatchwd}
  \item \cs{headshape}
  \item \cs{lightershade}
  \item \cs{mfpicnumber}
  \item \cs{mfplinestyle}
  \item \cs{mfplinetype}
  \item \cs{pen}
  \item \cs{penwd}
  \item \cs{polkadotwd}
  \item \cs{setallaxismargins}
  \item \cs{setallbordermarks}
  \item \cs{setaxismargins}
  \item \cs{setaxismarks}
  \item \cs{setbordermarks}
  \item \cs{setmfvariable}
  \item \cs{setmpvariable}
  \item \cs{settension}
  \item \cs{setxmarks}
  \item \cs{setymarks}
  \item \cs{shadewd}

\subsubsection{Changing colors}

  \item \cs{backgroundcolor}
  \item \cs{drawcolor}
  \item \cs{fillcolor}
  \item \cs{hatchcolor}
  \item \cs{headcolor}
  \item \cs{mfpdefinecolor}
  \item \cs{pointcolor}
  \item \cs{tlabelcolor}

\subsubsection{Defining arrays}

  \item \cs{barchart}
  \item \cs{bargraph}
  \item \cs{histogram}
  \item \cs{numericarray}
  \item \cs{pairarray}
  \item \cs{patharr}, \cs{endpatharr}
  \item \cs{piechart}

\subsubsection{Changing behavior}

  \item \cs{clearsymbols}
  \item \cs{coloredlines}
  \item \cs{dashedlines}
  \item \cs{datapointsonly}
  \item \cs{defaultplot}
  \item \cs{everytlabel}
  \item \cs{makepercentcomment}
  \item \cs{makepercentother}
  \item \cs{mfpdatacomment}
  \item \cs{mfpdataperline}
  \item \cs{mfpverbtex}
  \item \cs{noclearsymbols}
  \item \cs{pointedlines}
  \item \cs{pointfillfalse}
  \item \cs{pointfilltrue}
  \item \cs{reconfigureplot}
  \item \cs{setrender}
  \item \cs{smoothdata}
  \item \cs{tlabeljustify}
  \item \cs{tlabeloffset}
  \item \cs{tlabelsep}
  \item \cs{tlpathjustify}
  \item \cs{unsmoothdata}
  \item \cs{using}
  \item \cs{usingnumericdefault}
  \item \cs{usingpairdefault}

\subsubsection{Files and environments}

  \item \cs{closegraphsfile}
  \item \cs{mfpframe},  \cs{endmfpframe}
  \item \cs{mfpic}, \cs{endmfpic}
  \item \cs{opengraphsfile}

\subsubsection{Text}

  \item \cs{axislabels}
  \item \cs{plottext}
  \item \cs{tcaption}
  \item \cs{tlabels}
  \item \cs{tlabel}

\subsubsection{Misc} \widowpenalty10000

  \item \cs{fdef}
  \item \cs{getmfpicoffset}
  \item \cs{ifmfpmpost}
  \item \cs{mfcmd}
  \item \cs{mflist}
  \item \cs{mfpframed}
  \item \cs{mfpicversion}
  \item \cs{mfpverbtex}
  \item \cs{mfsrc}
  \item \cs{mftitle}
  \item \cs{newfdim}
  \item \cs{newsavepic}
  \item \cs{plr}
  \item \cs{pointdef}
  \item \cs{preparemfpicgraphic}
  \item \cs{savepic}
  \item \cs{setmfpicgraphic}
  \item \cs{setfilename}
  \item \cs{sequence}
  \item \cs{store}
  \item \cs{tile}, \cs{endtile}
  \item \cs{tmtitle}
  \item \cs{usepic}


\end{document}

