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path: root/Master/texmf-dist/doc/metapost/mpman-ru/mpman-ru.tex
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% $Id: mpman.tex 513 2008-04-29 12:03:53Z stephanhennig $
% MetaPost manual, by John Hobby.  License at end.
% Russian translation, 2008/05/10
\listfiles
\RequirePackage{ifpdf}
\ifpdf
\ifnum\pdftexversion<140
\else
\pdfminorversion=5
\pdfobjcompresslevel=1% Use compressed object streams.
\fi
\RequirePackage{cmap}
\documentclass{article} % article is NOT the original style
%%\usepackage[nofancy]{svninfo}% Access VCS information.
%%\svnInfo $Id: mpman.tex 513 2008-04-29 12:03:53Z stephanhennig $
\newcommand*{\mpversion}{1.004}

%%\usepackage[T1]{fontenc}
%%\usepackage{lmodern}
%%\usepackage{textcomp}
\usepackage{mflogo}
\usepackage{makeidx}
\usepackage{fancyvrb}
\usepackage{ctabbing}
\RecustomVerbatimEnvironment
  {verbatim}{BVerbatim}{baseline=c}
\usepackage{graphicx}
\newcommand\qq{"} % quotation mark is active in Russian Babel!
\usepackage{amssymb}
\usepackage{cmap-cyr-vf}
\usepackage[LCYW]{fontenc}
\usepackage[koi8-r]{inputenc}
\usepackage[english,russian]{babel}
%%\usepackage[latin1]{inputenc}
\usepackage[textwidth=6in,textheight=8.65in]{geometry}
\usepackage{tocloft}
  \setlength\cftbeforesecskip{1.3ex plus 0.3ex minus 0.3ex}
\usepackage{ltxtable}


\def\ttindex#1{{\tt #1}\index{#1?\texttt{#1}}}
\def\ttt{\texttt}  % I get tired of typing this out

\def\ConTeXt{Con\TeX t}

\newcommand\descr[1]{{\langle\hbox{#1}\rangle}}
\newcommand\invisgap{\nobreak\hskip0pt\relax}
\newcommand\tdescr[1]{$\langle$\invisgap#1\invisgap$\rangle$}

\newcommand\pl{\dag}
\newcommand\bx{$*$}


\newcommand\mathcenter[1]{\vcenter{\hbox{#1}}}

\renewcommand{\topfraction}{.85}
\renewcommand{\bottomfraction}{.7}
\renewcommand{\textfraction}{.15}
\renewcommand{\floatpagefraction}{.5}
\renewcommand{\dbltopfraction}{.66}
\renewcommand{\dblfloatpagefraction}{.66}
\setcounter{topnumber}{9}
\setcounter{bottomnumber}{9}
\setcounter{totalnumber}{20}
\setcounter{dbltopnumber}{9}

\makeindex

\usepackage{multicol}
\usepackage[rgb,x11names]{xcolor}% Optimize for screen reading.
\usepackage{hyperxmp}
\usepackage{hyperref}
\hypersetup{
  pdftitle={A User's Manual for MetaPost (translated to Russian)},
%%  pdftitle={A User's Manual for MetaPost},
  pdfauthor={John D. Hobby and the MetaPost development team},
  pdfkeywords={MetaPost, PostScript, vector graphics language, MetaFont, TeX, Russian}
%%  pdfkeywords={MetaPost, PostScript, vector graphics language, MetaFont, TeX}
}
\hypersetup{
  pdfstartview={XYZ null null null},% Zoom factor is determined by viewer.
  colorlinks,
  linkcolor=RoyalBlue3,
  urlcolor=Chocolate4,
  citecolor=SpringGreen3
}
\usepackage[all]{hypcap}

\begin{document}
\VerbatimFootnotes
%%% Title page layout documentation is missing.
\begin{titlepage}
  \vbox to \textheight {%
    \vskip0pt
    \vfil
    \vfil
    \vfil
    \centerline{\resizebox{3.5in}{!}{\fontseries{b}\selectfont\MP}}
    \vskip10bp% actually 21bp (-11bp)
    \centerline{\includegraphics{manfig-ru-60.mps}}
    \vskip15bp% actually 21bp (-6bp)
    \centerline{%
      \resizebox{3.5in}{!}{%
        \scshape%
        \fontsize{28bp}{28bp}\selectfont
          \strut\lowercase{òõëï÷ïäóô÷ï ðïìøúï÷áôåìñ}%
%%        \strut\lowercase{A USER\kern-2bp\lower3bp\hbox{'}S MANUAL}%
      }%
    }
    \vskip-11bp
    \vfil
    \vfil
    \centerline{\large John D. Hobby}
    \vskip3bp
    \centerline{É ËÏÍÁÎÄÁ ÒÁÚÒÁÂÏÔËÉ MetaPost}
%%    \centerline{and the MetaPost development team}
    \vskip20.8bp% actually 31.8bp (-11bp)
    \centerline{\large ×ÅÒÓÉÑ ÄÏËÕÍÅÎÔÁ: \mpversion}
%%    \centerline{\large documented version: \mpversion}
    \vskip3bp
%%    \centerline{\svnToday}
    \vfil
    \vfil
    \vfil
  }
\end{titlepage}

\section*{ðÒÉÍÅÞÁÎÉÑ ÐÅÒÅ×ÏÄÞÉËÁ}

÷ ×ÅÒÓÉÉ 1.004 MetaPost 
ÒÕËÏ×ÏÄÓÔ×Ï ÐÏÌØÚÏ×ÁÔÅÌÑ ÄÌÑ ÐÁËÅÔÁ \texttt{boxes} ÂÙÌÏ ×ÙÎÅÓÅÎÏ × ÏÔÄÅÌØÎÙÊ ÄÏËÕÍÅÎÔ. 
÷ ÐÅÒÅ×ÏÄÅ ÜÔÏÇÏ ÒÁÚÄÅÌÅÎÉÑ ÎÅ ÐÒÏÉÚÏÛÌÏ, ÎÏ ÄÏÂÁ×ÌÅÎÉÑ Ë ÄÏËÕÍÅÎÔÁÃÉÉ ÂÙÌÉ ÕÞÔÅÎÙ. 
óÏÚÄÁÎÉÑ ÜÔÏÇÏ ÐÅÒÅ×ÏÄÁ ÂÙÌÏ ÂÙ ÎÅ×ÏÚÍÏÖÎÙÍ ÂÅÚ ïÌØÇÉ çÁÇÁÒËÉÎÏÊ. 

\begin{flushright}÷ÌÁÄÉÍÉÒ ìÉÄÏ×ÓËÉÊ, \url{litwr@yandex.ru}\end{flushright}
\thispagestyle{empty}
\newpage

\setlength{\columnsep}{2.5em}
\begin{multicols}{2}
\tableofcontents
\end{multicols}

\section{÷×ÅÄÅÎÉÅ}
%%\section{Introduction}
\label{intro}

MetaPost --- ÜÔÏ ÑÚÙË ÐÒÏÇÒÁÍÍÉÒÏ×ÁÎÉÑ, ÏÞÅÎØ ÐÏÈÏÖÉÊ ÎÁ \MF\footnote{\MF\
--- ÜÔÏ ÔÏÒÇÏ×ÁÑ ÍÁÒËÁ ËÏÍÐÁÎÉÉ Addison Wesley 
Publishing.}\index{metafont?\MF}~\cite{kn:c} ëÎÕÔÁ Ó ÔÅÍ ÉÓËÌÀÞÅÎÉÅÍ, ÞÔÏ 
ÏÎ ÐÒÏÉÚ×ÏÄÉÔ PostScript-ÐÒÏÇÒÁÍÍÙ ×ÍÅÓÔÏ ÒÁÓÔÒÏ×ÙÈ ËÁÒÔÉÎÏË. 
%%MetaPost is a programming language much like Knuth's \MF\footnote{\MF\
%%is a trademark of Addison Wesley Publishing
%%company.}\index{metafont?\MF}~\cite{kn:c} except that it outputs
%%PostScript programs instead of bitmaps.  
úÁÉÍÓÔ×Ï×ÁÎÉÑ ÉÚ \MF --- ÜÔÏ ÂÁÚÏ×ÙÅ ÓÒÅÄÓÔ×Á ÄÌÑ ÓÏÚÄÁÎÉÑ É 
ÍÁÎÉÐÕÌÉÒÏ×ÁÎÉÑ ËÁÒÔÉÎËÁÍÉ.
%%Borrowed from \MF\ are the
%%basic tools for creating and manipulating pictures. 
ïÎÉ ×ËÌÀÞÁÀÔ ÞÉÓÌÁ, ËÏÏÒÄÉÎÁÔÎÙÅ ÐÁÒÙ, ËÕÂÉÞÅÓËÉÅ ÓÐÌÁÊÎÙ, ÁÆÆÉÎÎÙÅ 
ÔÒÁÎÓÆÏÒÍÁÃÉÉ, ÔÅËÓÔÏ×ÙÅ ÓÔÒÏËÉ É ÂÕÌÅ×Ù ×ÅÌÉÞÉÎÙ.
%%These include
%%numbers, coordinate pairs, cubic splines, affine transformations, text
%%strings, and boolean quantities.  
äÏÐÏÌÎÉÔÅÌØÎÙÅ ÓÒÅÄÓÔ×Á ÄÅÌÁÀÔ ×ÏÚÍÏÖÎÙÍÉ ÓÏÅÄÉÎÅÎÉÅ ÔÅËÓÔÁ É ÇÒÁÆÉËÉ É 
ÄÏÓÔÕÐ Ë ÓÐÅÃÉÁÌØÎÙÍ ×ÏÚÍÏÖÎÏÓÔÑÍ PostScript\footnote{PostScript --- 
ÜÔÏ ÔÏÒÇÏ×ÁÑ ÍÁÒËÁ Adobe Systems.}\index{PostScript} ÔÁËÉÍ ËÁË 
×ÙÒÅÚËÁ, ÚÁÔÅÎÅÎÉÅ, ÐÕÎËÔÉÒÎÙÅ ÌÉÎÉÉ.
%%Additional features facilitate
%%integrating text and graphics and accessing special features of
%%PostScript\footnote{PostScript is a trademark of Adobe Systems
%%Inc.}\index{PostScript} such as clipping, shading, and dashed lines.
äÒÕÇÏÅ Ó×ÏÊÓÔ×Ï, ÚÁÉÍÓÔ×Ï×ÁÎÎÏÅ Õ \MF, --- ÜÔÏ ÓÐÏÓÏÂÎÏÓÔØ ÒÅÛÁÔØ 
ÚÁÄÁÎÎÙÅ ÎÅÑ×ÎÏ ÌÉÎÅÊÎÙÅ ÕÒÁ×ÎÅÎÉÑ, ÞÔÏ ÐÏÚ×ÏÌÑÅÔ ÐÉÓÁÔØ ÍÎÏÇÉÅ 
ÐÒÏÇÒÁÍÍÙ × ÚÎÁÞÉÔÅÌØÎÏÊ ÍÅÒÅ × ÄÅËÌÁÒÁÔÉ×ÎÏÍ ÓÔÉÌÅ.
%%Another feature borrowed from \MF\ is the ability to solve linear
%%equations that are given implicitly, thus allowing many programs to be
%%written in a largely declarative style. 
íÏÝØ É ÇÉÂËÏÓÔØ MetaPost ÄÏÓÔÉÇÁÀÔÓÑ ÐÏÓÔÒÏÅÎÉÅÍ ÓÌÏÖÎÙÈ ÏÐÅÒÁÃÉÊ 
ÉÚ ÂÏÌÅÅ ÐÒÏÓÔÙÈ. 
%%By building complex operations
%%from simpler ones, MetaPost achieves both power and flexibility.

MetaPost ÏÓÏÂÅÎÎÏ ÈÏÒÏÛÏ ÐÒÉÓÐÏÓÏÂÌÅÎ ÄÌÑ ÇÅÎÅÒÁÃÉÉ ËÁÒÔÉÎÏË ÄÌÑ 
ÔÅÈÎÉÞÅÓËÉÈ ÄÏËÕÍÅÎÔÏ×, ÇÄÅ ÎÅËÏÔÏÒÙÅ Ó×ÏÊÓÔ×Á ÒÉÓÕÎËÁ ÍÏÇÕÔ 
ËÏÎÔÒÏÌÉÒÏ×ÁÔØÓÑ ÍÁÔÅÍÁÔÉÞÅÓËÉÍÉ ÉÌÉ ÇÅÏÍÅÔÒÉÞÅÓËÉÍÉ ÏÇÒÁÎÉÞÅÎÉÑÍÉ, 
ËÏÔÏÒÙÅ ÎÁÉÌÕÞÛÉÍ ÏÂÒÁÚÏÍ ×ÙÒÁÖÁÀÔÓÑ × ÓÉÍ×ÏÌØÎÏÊ ÆÏÒÍÅ.
%%MetaPost is particularly well-suited to generating figures for technical
%%documents where some aspects of a picture may be controlled by
%%mathematical or geometrical constraints that are best expressed
%%symbolically.  
äÒÕÇÉÍÉ ÓÌÏ×ÁÍÉ, MetaPost ÎÅ ÚÁÎÉÍÁÅÔ ÍÅÓÔÏ ÓÒÅÄÓÔ× ÄÌÑ ÒÕÞÎÏÇÏ 
ÒÉÓÏ×ÁÎÉÑ ÉÌÉ ÄÁÖÅ ÉÎÔÅÒÁËÔÉ×ÎÙÈ ÇÒÁÆÉÞÅÓËÉÈ ÒÅÄÁËÔÏÒÏ×.
%%In other words, MetaPost is not meant to take the place
%%of a freehand drawing tool or even an interactive graphics editor.  
üÔÏ ÎÁÓÔÏÑÝÉÊ ÑÚÙË ÐÒÏÇÒÁÍÍÉÒÏ×ÁÎÉÑ ÄÌÑ ÇÅÎÅÒÁÃÉÉ ÇÒÁÆÉËÉ É, ÏÓÏÂÅÎÎÏ, 
ÉÌÌÀÓÔÒÁÃÉÊ ÄÌÑ ÄÏËÕÍÅÎÔÏ× \TeX\footnote{\TeX\ --- ÜÔÏ ÔÏÒÇÏ×ÁÑ ÍÁÒËÁ American 
Mathematical Society.}\index{TeX?\TeX} É troff\index{troff}.
%%It 
%%is really a programming language for generating graphics, especially
%%figures for \TeX\footnote{\TeX\ is a trademark of the American
%%Mathematical Society.}\index{TeX?\TeX} and troff\index{troff} documents.

äÌÑ ÉÓÐÏÌØÚÏ×ÁÎÉÑ MetaPost ×Ù ÄÏÌÖÎÙ ÐÒÉÇÏÔÏ×ÉÔØ ×ÈÏÄÎÏÊ ÆÁÊÌ 
Ó Metapost-ËÏÄÏÍ É ÚÁÔÅÍ ×ÙÚ×ÁÔØ ÓÁÍ MetaPost ÐÒÉ ÐÏÍÏÝÉ, ËÁË ÐÒÁ×ÉÌÏ, 
ËÏÍÁÎÄÙ × ÆÏÒÍÅ \index{mpost?\texttt{mpost}}
$$ {\tt mpost}\, \descr{ÉÍÑ ÆÁÊÌÁ} $$
%%To use MetaPost, you prepare an input file containing MetaPost code and
%%then invoke MetaPost, usually by giving a command of the
%%form\index{mpost?\texttt{mpost}}
%%$$ {\tt mpost}\, \descr{filename} $$
óÉÎÔÁËÓÉÓ É ÉÍÑ ÐÒÏÇÒÁÍÍÙ Ñ×ÌÑÀÔÓÑ ÓÉÓÔÅÍÏ-ÚÁ×ÉÓÉÍÙÍÉ, ÉÎÏÇÄÁ ÏÎÁ 
ÚÏ×ÅÔÓÑ \texttt{mp}.
%%The syntax and program name itself are system-dependent; sometimes it is
%%named \texttt{mp}.  
÷ÈÏÄÎÙÅ ÆÁÊÌÙ ÄÌÑ MetaPost\index{ÆÁÊÌÙ!××ÏÄ} ÏÂÙÞÎÏ ÉÍÅÀÔ ÉÍÅÎÁ, 
ÚÁËÁÎÞÉ×ÁÀÝÉÅÓÑ ÎÁ ``{\tt .mp}'', É ÜÔÁ ÞÁÓÔØ ÉÍÅÎÉ ÍÏÖÅÔ ÏÐÕÓËÁÔØÓÑ ÐÒÉ 
×ÙÚÏ×Å MetaPost.
%%MetaPost input
%%files\index{files!input} normally have names ending ``{\tt .mp}'' but
%%this part of the name can be omitted when invoking MetaPost.  
îÁÐÒÉÍÅÒ, ÄÌÑ ×ÈÏÄÎÏÇÏ ÆÁÊÌÁ {\tt foo.mp}
$$ \hbox{\tt mpost foo} $$
×ÙÚÏ×ÅÔ MetaPost É ÐÒÏÉÚ×ÅÄÅÔ ×ÙÈÏÄÎÙÅ ÆÁÊÌÙ Ó ÉÍÅÎÁÍÉ ÔÉÐÁ {\tt foo.1}
É {\tt foo.2}.
%%For an
%%input file {\tt foo.mp}
%%$$ \hbox{\tt mpost foo} $$
%%invokes MetaPost and produces output files with names like {\tt foo.1}
%%and {\tt foo.2}. 
÷ÓÅ ÓÏÏÂÝÅÎÉÑ, ÐÏÑ×ÌÑÀÝÉÅÓÑ ÎÁ ÔÅÒÍÉÎÁÌÅ, ÓÏÂÉÒÁÀÔÓÑ × 
ÆÁÊÌ-ÄÕÂÌÉËÁÔ\index{ÆÁÊÌÙ!ÄÕÂÌÉËÁÔ}\index{ÆÁÊÌ-ÄÕÂÌÉËÁÔ} Ó ÉÍÅÎÅÍ
{\tt foo.log}.
%%Any terminal I/O is summarized in a
%%transcript\index{files!transcript}\index{transcript file} file called
%%{\tt foo.log}.  
ôÕÄÁ ×ËÌÀÞÁÀÔÓÑ ÓÏÏÂÝÅÎÉÑ Ï ÏÛÉÂËÁÈ É ×ÓÅ ËÏÍÁÎÄÙ MetaPost, ××ÅÄÅÎÎÙÅ 
ÉÎÔÅÒÁËÔÉ×ÎÏ.\footnote{úÎÁË {\tt *}\index{*?\texttt{*}} ÉÓÐÏÌØÚÕÅÔÓÑ
ÄÌÑ ÐÒÉÇÌÁÛÅÎÉÑ Ë ÉÎÔÅÒÁËÔÉ×ÎÏÍÕ ××ÏÄÕ É ÚÎÁË {\tt **}\index{**?\texttt{**}} 
ÐÏËÁÚÙ×ÁÅÔ, ÞÔÏ ÏÖÉÄÁÅÔÓÑ ÉÍÑ ×ÈÏÄÎÏÇÏ ÆÁÊÌÁ. äÉÁÌÏÇÁ ÍÏÖÎÏ ÉÚÂÅÖÁÔØ 
×ÙÚÏ×ÏÍ MetaPost Ó ÆÁÊÌÏÍ, ËÏÔÏÒÙÊ ÚÁËÁÎÞÉ×ÁÅÔÓÑ ËÏÍÁÎÄÏÊ {\tt
end}\index{end?\texttt{end}}.}
%%This includes error messages and any MetaPost commands
%%entered interactively.\footnote{A {\tt *}\index{*?\texttt{*}} prompt is
%%used for interactive input and a {\tt **}\index{**?\texttt{**}} prompt
%%indicates that an input file name is expected.  This can be avoided by
%%invoking MetaPost on a file that ends with an {\tt
%%end}\index{end?\texttt{end}} command.} 

\label{Dmpversion}æÁÊÌ-ÄÕÂÌÉËÁÔ ÎÁÞÉÎÁÅÔÓÑ Ó ÚÁÇÏÌÏ×ÏÞÎÏÊ ÓÔÒÏËÉ, 
ÉÄÅÎÔÉÆÉÃÉÒÕÀÝÅÊ ÉÓÐÏÌØÚÕÅÍÕÀ ×ÁÍÉ ×ÅÒÓÉÀ MetaPost.
%%\label{Dmpversion}The transcript file starts with a banner line that
%%identifies the version of MetaPost you are using.  
÷Ù ÍÏÖÅÔÅ ÔÁËÖÅ ÏÐÒÅÄÅÌÉÔØ ÔÅËÕÝÕÀ ×ÅÒÓÉÀ ÉÚ ÐÒÏÇÒÁÍÍÙ MetaPost ÞÅÒÅÚ 
ÓÔÒÏËÏ×ÕÀ ËÏÎÓÔÁÎÔÕ \texttt{mpversion} (ÜÔÏ ÓÔÁÌÏ ×ÏÚÍÏÖÎÙÍ Ó ×ÅÒÓÉÉ 0.9).
%%You can also determine
%%the current version from within a MetaPost program via the
%%\texttt{mpversion} predefined constant string (this was introduced in
%%version 0.9). 
îÁÐÒÉÍÅÒ,
%%For instance:
$$\begin{verbatim}
if known mpversion:
  message "mp = " & mpversion;
  if scantokens(mpversion) < 1: message "ðÏÄÄÅÒÖËÁ Ã×ÅÔÏ× CMYK ÎÅÄÏÓÔÕÐÎÁ!" fi
fi
\end{verbatim}
$$
ÐÅÞÁÔÁÅÔ
%%prints
$$\begin{verbatim}[commandchars=\\\{\}]
mp = \mpversion
\end{verbatim}
$$
ëÏÍÁÎÄÁ {\tt scantokens} ÏÐÉÓÁÎÁ ÎÁ Ó.~\pageref{Dscantokens} É 
ÍÏÖÅÔ ÂÙÔØ ÕÐÏÔÒÅÂÌÅÎÁ ÄÌÑ ËÏÎ×ÅÒÔÉÒÏ×ÁÎÉÑ ÓÔÒÏË × ÞÉÓÌÁ.
\index{ëÏÍÍÅÎÔÁÒÉÊ Creator × ×Ù×ÏÄÅ PostScript}%
%%The {\tt scantokens} command is described on p.~\pageref{Dscantokens}
%%and can be utilized to convert strings to numbers.
%%\index{Creator comment in PostScript output}%
îÏÍÅÒ ×ÅÒÓÉÉ ÔÁËÖÅ ×ËÌÀÞÁÅÔÓÑ × ËÏÍÍÅÎÔÁÒÉÊ \texttt{Creator} × 
Postscript-×Ù×ÏÄÅ. 
%%The version number is also included in the \texttt{Creator} comment in
%%the PostScript output.

üÔÏÔ ÄÏËÕÍÅÎÔ ÐÒÅÄÓÔÁ×ÌÑÅÔ ÑÚÙË MetaPost, ÎÁÞÉÎÁÑ Ó ÐÒÏÓÔÅÊÛÉÈ ÄÌÑ 
ÉÓÐÏÌØÚÏ×ÁÎÉÑ É ÎÁÉÂÏÌÅÅ ×ÁÖÎÙÈ ÄÌÑ ÐÒÏÓÔÙÈ ÐÒÉÌÏÖÅÎÉÊ Ó×ÏÊÓÔ×. 
%%This document introduces the MetaPost language, beginning with the
%%features that are easiest to use and most important for simple
%%applications.
þÔÅÎÉÅ ÒÕËÏ×ÏÄÓÔ×Á ÎÅ ÔÒÅÂÕÅÔ ÚÎÁÎÉÑ \MF\ ÉÌÉ ÄÏÓÔÕÐÁ Ë {\sl The \MF book}, 
ÎÏ ÏÂÅ ×ÏÚÍÏÖÎÏÓÔÉ ÂÕÄÕÔ ÐÏÌÅÚÎÙÍÉ. 
%%Reading the manual does not require knowledge of \MF\ or
%%access to {\sl The \MF book}, but both are beneficial.
ðÅÒ×ÙÅ ÎÅÓËÏÌØËÏ ÒÁÚÄÅÌÏ× ÏÐÉÓÙ×ÁÀÔ ÑÚÙË ÔÁËÉÍ, ËÁËÉÍ ÏÎ ËÁÖÅÔÓÑ 
ÐÏÌØÚÏ×ÁÔÅÌÀ-ÎÏ×ÉÞËÕ Ó ËÌÀÞÅ×ÙÍÉ ÐÁÒÁÍÅÔÒÁÍÉ, ÚÁÆÉËÓÉÒÏ×ÁÎÎÙÍÉ ÎÁ 
ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÈ ÚÎÁÞÅÎÉÑÈ.
%%The first few sections describe the language as it
%%appears to the novice user with key parameters at their default values.
îÅËÏÔÏÒÙÅ Ó×ÏÊÓÔ×Á, ÏÐÒÅÄÅÌÑÅÍÙÅ × ÜÔÉÈ ÒÁÚÄÅÌÁÈ, --- ÞÁÓÔØ ÍÁËÒÏÐÁËÅÔÁ 
Ó ÉÍÅÎÅÍ Plain.
%%Some features described in these sections are part of a predefined macro
%%package called Plain. 
óÌÅÄÕÀÝÉÅ ÒÁÚÄÅÌÙ ÏÈ×ÁÔÙ×ÁÀÔ ×ÅÓØ ÑÚÙË É ÏÔÌÉÞÁÀÔ ÐÒÉÍÉÔÉ×Ù ÏÔ ÍÁËÒÏÓÏ× 
ÉÚ Á×ÔÏÍÁÔÉÞÅÓËÉ ÚÁÇÒÕÖÁÅÍÏÇÏ ÍÁËÒÏÐÁËÅÔÁ Plain\index{ÍÁËÒÏÓÙ Plain}.
%%Later sections summarize the complete language
%%and distinguish between primitives and preloaded macros from the Plain
%%macro package\index{Plain macros}. 
÷ÓÌÅÄÓÔ×ÉÅ ÔÏÇÏ, ÞÔÏ ÂÏÌØÛÁÑ ÞÁÓÔØ ÑÚÙËÁ ÉÄÅÎÔÉÞÎÁ \MF\ ëÎÕÔÁ, ÐÒÉÌÏÖÅÎÉÅ 
ÄÁÅÔ ÄÅÔÁÌØÎÏÅ ÓÒÁ×ÎÅÎÉÅ ÔÁËÉÍ ÏÂÒÁÚÏÍ, ÞÔÏ ÏÐÙÔÎÙÅ ÐÏÌØÚÏ×ÁÔÅÌÉ ÓÍÏÇÕÔ 
ÕÚÎÁÔØ ÂÏÌØÛÅ Ï MetaPost, ÞÉÔÁÑ {\sl The \MF book\/} \cite{kn:c}. 
%%Since much of the language is
%%identical to Knuth's \MF, the appendix gives a detailed comparison so
%%that advanced users can learn more about MetaPost by reading {\sl The
%%\MF book\/} \cite{kn:c}.

äÏËÕÍÅÎÔÁÃÉÑ Ë MetaPost ÄÏÐÏÌÎÑÅÔÓÑ ``Drawing Boxes with MetaPost'' --- 
ÒÕËÏ×ÏÄÓÔ×ÏÍ Ë ÐÁËÅÔÕ \texttt{graph}, ÉÚÎÁÞÁÌØÎÏ ÒÁÚÒÁÂÏÔÁÎÎÏÍÕ 
äÖÏÎÏÍ~ä. èÏÂÂÉ.
%%MetaPost documentation is completed by ``Drawing Boxes with MetaPost''
%%and ``Drawing Graphs with MetaPost''---the manuals of the \texttt{boxes}
%%and \texttt{graph} packages originally developed by John~D. Hobby.

äÏÍÁÛÎÑÑ ÓÔÒÁÎÉÃÁ MetaPost --- \url{http://tug.org/metapost}.  
%%The MetaPost home page is \url{http://tug.org/metapost}.
ïÎÁ ÓÏÄÅÒÖÉÔ ÓÓÙÌËÉ ÎÁ ÍÎÏÇÏ ÄÏÐÏÌÎÉÔÅÌØÎÏÊ ÉÎÆÏÒÍÁÃÉÉ, ×ËÌÀÞÁÑ ÍÎÏÖÅÓÔ×Ï 
ÓÔÁÔÅÊ, ËÏÔÏÒÙÅ ÎÁÐÉÓÁÎÙ Ï MetaPost. 
%%It has links
%%to much additional information, including many articles that have been
%%written about MetaPost.  
ðÒÉ ÐÏÉÓËÅ ÐÏÄÓËÁÚËÉ ÐÏÐÒÏÂÕÊÔÅ ÒÁÓÓÙÌËÕ ÎÁ \url{metapost@tug.org}; ×Ù 
ÍÏÖÅÔÅ ÐÏÄÐÉÓÁÔØÓÑ ÔÕÄÁ ÎÁ \url{http://tug.org/mailman/listinfo/metapost}.
%%For general help, try the
%%\url{metapost@tug.org} mailing list; you can subscribe to this list at
%%\url{http://tug.org/mailman/listinfo/metapost}.

ôÅËÕÝÁÑ ÒÁÚÒÁÂÏÔËÁ ÒÁÚÍÅÝÅÎÁ ÎÁ  \url{https://foundry.supelec.fr/projects/metapost/}; ÐÏÓÅÔÉÔÅ ÜÔÏÔ 
ÓÁÊÔ ÄÌÑ ËÏÎÔÁËÔÏ× Ó ÞÌÅÎÁÍÉ ÔÅËÕÝÅÊ ËÏÍÁÎÄÙ ÒÁÚÒÁÂÏÔÞÉËÏ×, ÚÁÇÒÕÚËÉ 
ÉÓÈÏÄÎÉËÏ× É ÍÎÏÇÏÇÏ ÄÒÕÇÏÇÏ.
%%The development is currently hosted at
%%\url{https://foundry.supelec.fr/projects/metapost/}; visit this site
%%for the current development team members, sources, and much else.

ðÏÖÁÌÕÊÓÔÁ, ÓÏÏÂÝÁÊÔÅ Ï ÏÛÉÂËÁÈ É ÔÒÅÂÕÅÍÙÈ ÕÌÕÞÛÅÎÉÑÈ × ÓÐÉÓÏË ÎÁ 
\url{metapost@tug.org} ÉÌÉ ÞÅÒÅÚ ÁÄÒÅÓÁ, ÐÒÉ×ÅÄÅÎÎÙÅ ×ÙÛÅ. 
%%Please report bugs and request enhancements either on the
%%\url{metapost@tug.org} list, or through the address given above.
ðÏÖÁÌÕÊÓÔÁ, ÎÅ ÐÏÓÙÌÁÊÔÅ ÂÏÌØÛÅ ÏÔÞÅÔÙ ÎÁÐÒÑÍÕÀ Dr.\ Hobby.
%%(Please do not send reports directly to Dr.\ Hobby any more.)

\section{âÁÚÏ×ÙÅ ËÏÍÁÎÄÙ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ}
%%\section{Basic Drawing Statements}
\label{basic}

ðÒÏÓÔÅÊÛÉÅ ËÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ --- ÄÌÑ ÇÅÎÅÒÁÃÉÉ ÐÒÑÍÙÈ ÌÉÎÉÊ.
%The simplest drawing statements are the ones that generate straight lines.
ôÁËÉÍ ÏÂÒÁÚÏÍ\index{draw?\texttt{draw}}\index{-{}-?\texttt{-{}-}},
%%Thus\index{draw?\texttt{draw}}\index{-{}-?\texttt{-{}-}}
$$ \hbox{\verb|draw (20,20)--(0,0)|} $$
ÒÉÓÕÅÔ\index{draw?\texttt{draw}} ÄÉÁÇÏÎÁÌØÎÕÀ ÌÉÎÉÀ É 
%%draws\index{draw?\texttt{draw}} a diagonal line and
$$ \hbox{\verb|draw (20,20)--(0,0)--(0,30)--(30,0)--(0,0)|} $$
ÒÉÓÕÅÔ ÌÏÍÁÎÕÀ ÌÉÎÉÀ, ÐÏÄÏÂÎÕÀ ÜÔÏÊ:
%%draws a polygonal line like this:
$$ \includegraphics{manfig-ru-1} $$

\label{Ddrawdot}MetaPost ÔÁËÖÅ ÉÍÅÅÔ ËÏÍÁÎÄÕ \ttt{drawdot} ÄÌÑ ÐÅÞÁÔÉ 
ÏÄÎÏÊ ÔÏÞËÉ, ÎÁÐÒÉÍÅÒ, \ttt{drawdot(30,0)}. 
%%\label{Ddrawdot}MetaPost also has a \ttt{drawdot} command to print a
%%single point, as in \ttt{drawdot(30,0)}. 

þÔÏ ÏÚÎÁÞÁÅÔÓÑ ËÏÏÒÄÉÎÁÔÁÍÉ ÐÏÄÏÂÎÙÍÉ \verb|(30,0)|? 
%%What is meant by coordinates like \verb|(30,0)|?  
MetaPost ÉÓÐÏÌØÚÕÅÔ ÔÕ ÖÅ ÓÁÍÕÀ ÔÉÐÏ×ÕÀ ÓÉÓÔÅÍÕ ËÏÏÒÄÉÎÁÔ, ÞÔÏ É 
PostScript\index{PostScript!ÓÉÓÔÅÍÁ ËÏÏÒÄÉÎÁÔ}.
%%MetaPost uses the same
%%default coordinate system that PostScript\index{PostScript!coordinate
%%system} does. 
üÔÏ ÚÎÁÞÉÔ, ÞÔÏ \verb|(30,0)| --- ÜÔÏ 30 ÅÄÉÎÉà ×ÐÒÁ×Ï ÏÔ ÎÁÞÁÌÁ 
ËÏÏÒÄÉÎÁÔ, ÇÄÅ ÅÄÉÎÉÃÁ --- ÜÔÏ $1\over72$ ÄÀÊÍÁ.
%%This
%%means that \verb|(30,0)| is 30 units to the right of the origin, where a
%%unit is $1\over72$ of an inch.  
íÙ ÂÕÄÅÍ ÓÓÙÌÁÔØÓÑ ÎÁ ÜÔÕ ÅÄÉÎÉÃÕ ÉÚÍÅÒÅÎÉÑ ÐÏ-ÕÍÏÌÞÁÎÉÀ ËÁË ÎÁ 
{\sl PostScript-ÐÕÎËÔ}\index{PostScript!ÐÕÎËÔ}\index{ÐÕÎËÔ!PostScript} 
ÄÌÑ ÏÔÌÉÞÅÎÉÑ ÅÇÏ ÏÔ ÓÔÁÎÄÁÒÔÎÏÇÏ ÄÌÑ ÐÒÉÎÔÅÒÏ× 
ÐÕÎËÔÁ\index{ÐÕÎËÔ!ÐÒÉÎÔÅÒÁ}, ËÏÔÏÒÙÊ ÒÁ×ÅÎ $1\over72.27$ ÄÀÊÍÁ.
%We shall refer to this default unit as a
%{\sl PostScript point\/}\index{PostScript!point}\index{point!PostScript}
%to distinguish it from the standard printer's
%point\index{point!printer's} which is $1\over72.27$ inches.

MetaPost ÉÓÐÏÌØÚÕÅÔ ÔÅ ÖÅ ÉÍÅÎÁ ÄÌÑ ÅÄÉÎÉÃ ÉÚÍÅÒÅÎÉÑ, ÞÔÏ É \TeX\ É \MF.
%%MetaPost uses the same names for units of measure that \TeX\ and \MF\
%%do.  
ôÁËÉÍ ÏÂÒÁÚÏÍ, \verb|bp|\index{bp?\texttt{bp}}\label{Dbp} ÓÓÙÌÁÅÔÓÑ ÎÁ PostScript-ÐÕÎËÔÙ (``ÂÏÌØÛÉÅ ÐÕÎËÔÙ''), Á  \verb|pt|\index{pt?\texttt{pt}}\label{Dpt} --- ÎÁ ÐÕÎËÔÙ ÐÒÉÎÔÅÒÁ.
%%Thus \verb|bp|\index{bp?\texttt{bp}}\label{Dbp} refers to
%%PostScript points (``big points'') and
%%\verb|pt|\index{pt?\texttt{pt}}\label{Dpt} refers to printer's points.
äÒÕÇÉÅ ÅÄÉÎÉÃÙ ÉÚÍÅÒÅÎÉÑ ×ËÌÀÞÁÀÔ
\verb|in|\index{in?\texttt{in}}\label{Din} ÄÌÑ ÄÀÊÍÏ×,
\verb|cm|\index{cm?\texttt{cm}}\label{Dcm} ÄÌÑ ÓÁÎÔÉÍÅÔÒÏ× É  \verb|mm|\index{mm?\texttt{mm}}\label{Dmm} ÄÌÑ ÍÉÌÌÉÍÅÔÒÏ×. 
%%Other units of measure include
%%\verb|in|\index{in?\texttt{in}}\label{Din} for inches,
%%\verb|cm|\index{cm?\texttt{cm}}\label{Dcm} for centimeters, and
%%\verb|mm|\index{mm?\texttt{mm}}\label{Dmm} for millimeters.  
îÁÐÒÉÍÅÒ,
%%For example,
$$ \hbox{\verb|(2cm,2cm)--(0,0)--(0,3cm)--(3cm,0)--(0,0)|} $$
ÇÅÎÅÒÉÒÕÅÔ ÂÏÌØÛÉÊ ×ÁÒÉÁÎÔ ÄÉÁÇÒÁÍÍÙ ×ÙÛÅ.
%%generates a larger version of the above diagram. 
âÕÄÅÔ ×ÅÒÎÏ ÓËÁÚÁÔØ \verb|0| ×ÍÅÓÔÏ \verb|0cm|, ÐÏÔÏÍÕ ÞÔÏ {\tt cm} 
× ÄÅÊÓÔ×ÉÔÅÌØÎÏÓÔÉ ÔÏÌØËÏ ÍÎÏÖÉÔÅÌØ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÑ É {\tt 0cm} ÔÏÌØËÏ 
ÕÍÎÏÖÁÅÔ ÜÔÏÔ ÍÎÏÖÉÔÅÌØ ÎÁ ÎÏÌØ.
%%It is OK to say
%%\verb|0| instead \verb|0cm| because {\tt cm} is really just a conversion
%%factor and {\tt 0cm} just multiplies the conversion factor by zero.
(MetaPost ÐÏÎÉÍÁÅÔ ËÏÎÓÔÒÕËÃÉÉ ÐÏÄÏÂÎÙÅ 
{\tt 2cm}\index{ÕÍÎÏÖÅÎÉÅ, ÎÅÑ×ÎÏÅ} ËÁË ÓÏËÒÁÝÅÎÉÅ ÄÌÑ \verb|2*cm|).
%%(MetaPost understands constructions like {\tt
%%2cm}\index{multiplication, implicit} as shorthand for \verb|2*cm|).

õÄÏÂÎÏ ××ÅÓÔÉ Ó×ÏÊ ÓÏÂÓÔ×ÅÎÎÙÊ ÍÁÓÛÔÁÂÉÒÕÀÝÉÊ ÍÎÏÖÉÔÅÌØ, ÓËÁÖÅÍ $u$.
%%It is convenient to introduce your own scale factor, say $u$.  
úÁÔÅÍ ×Ù ÍÏÖÅÔÅ ÏÐÒÅÄÅÌÉÔØ ËÏÏÒÄÉÎÁÔÙ ÏÔÎÏÓÉÔÅÌØÎÏ $u$ É ÐÏÚÖÅ ÒÅÛÁÔØ, 
ÈÏÔÉÔÅ ÌÉ ×Ù ÎÁÞÁÔØ Ó \verb|u=1cm| ÉÌÉ \verb|u=0.5cm|.
%%Then you
%%can define coordinates in terms of $u$ and decide later whether you want
%%to begin with \verb|u=1cm| or \verb|u=0.5cm|.  
üÔÏ ÄÁÓÔ ×ÁÍ ËÏÎÔÒÏÌØ ÎÁÄ ÔÅÍ, ÞÔÏ ÍÁÓÛÔÁÂÉÒÕÅÍÏ É ÎÁÄ ÔÅÍ, ÞÔÏ ÎÅÔ, Ô.~Ë. 
ÉÚÍÅÎÅÎÉÅ $u$ ÎÅ ÐÏ×ÌÉÑÅÔ ÎÁ ÔÁËÉÅ Ó×ÏÊÓÔ×Á ËÁË ÔÏÌÝÉÎÁ ÌÉÎÉÊ. 
%%This gives you control
%%over what gets scaled and what does not so that changing $u$ will not
%%affect features such as line widths.

åÓÔØ ÍÎÏÇÏ ÐÕÔÅÊ ÉÚÍÅÎÑÔØ ×ÉÄ ÌÉÎÉÉ Ó×ÅÒÈ ÐÒÏÓÔÏÇÏ 
ÉÚÍÅÎÅÎÉÑ ÅÅ ÔÏÌÝÉÎÙ, ÏÄÎÁËÏ ÍÅÈÁÎÉÚÍÙ ÕÐÒÁ×ÌÅÎÉÑ ÛÉÒÉÎÏÊ ××ÏÄÑÔ 
ÍÎÏÇÏ ÏÂÝÉÈ ÐÏÎÑÔÉÊ, ËÏÔÏÒÙt ÎÁÍ ÐÏËÁ ÅÝÅ ÎÅ ÎÕÖÎÙ.
%%There are many ways to affect the appearance of a line besides just
%%changing its width, so the width-control mechanisms allow a lot of
%%generality that we do not need yet. 
óÏÏÔ×ÅÔÓÔ×ÕÀÝÉÅ ËÏÍÁÎÄÙ ÍÏÇÕÔ ÓÔÒÁÎÎÏ ×ÙÇÌÑÄÅÔØ, ÎÁÐÒÉÍÅÒ, 
ËÏÍÁÎÄÁ\index{pickup?\texttt{pickup}}\index{pencircle?\texttt{pencircle}}% 
\index{scaled?\texttt{scaled}}
%%This leads to the strange looking
%%statement\index{pickup?\texttt{pickup}}\index{pencircle?\texttt{pencircle}}%
%%\index{scaled?\texttt{scaled}}
$$ \hbox{\verb|pickup pencircle scaled 4pt|} $$
ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ ÔÏÌÝÉÎÕ ÌÉÎÉÉ × 4 ÐÕÎËÔÁ ÄÌÑ ÐÏÓÌÅÄÕÀÝÅÊ ËÏÍÁÎÄÙ \verb|draw|.
%%for setting the line width for subsequent \verb|draw| statements to 4 points.
(üÔÏ ÐÒÉÍÅÒÎÏ × 8 ÒÁÚ ÂÏÌØÛÅ ÓÔÁÎÄÁÒÔÎÏÊ ÔÏÌÝÉÎÙ ÌÉÎÉÉ).
%%(This is about eight times the default line width).

ó ÔÁËÏÊ ÂÏÌØÛÏÊ ÔÏÌÝÉÎÏÊ ÄÁÖÅ ÌÉÎÉÑ ÄÌÉÎÙ ÎÏÌØ ×ÙÇÌÑÄÉÔ ËÁË ÂÏÌØÛÁÑ ÖÉÒÎÁÑ 
ÔÏÞËÁ\index{ÔÏÞËÉ}. 
%%With such a wide line width, even a line of zero length comes out as a big bold
%%dot\index{dots}. 
íÙ ÍÏÖÅÍ ÜÔÏ ÉÓÐÏÌØÚÏ×ÁÔØ ÄÌÑ ÓÏÚÄÁÎÉÑ ÒÅÛÅÔËÉ ÉÚ ÖÉÒÎÙÈ ÔÏÞÅË, ÉÍÅÑ ÏÄÎÕ 
ËÏÍÁÎÄÕ \verb|drawdot| ÄÌÑ ËÁÖÄÏÇÏ ÕÚÌÁ ÒÅÛÅÔËÉ.
%%We can use this to make a grid of bold dots by having one
%%\verb|drawdot| statement for each grid point. 
ôÁËÁÑ ÐÏ×ÔÏÒÑÀÝÁÑÓÑ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ËÏÍÁÎÄ \verb|draw| ÚÁÐÉÓÙ×ÁÅÔÓÑ 
ÎÁÉÌÕÞÛÉÍ ÏÂÒÁÚÏÍ ËÁË ÐÁÒÁ ×ÌÏÖÅÎÎÙÈ ÃÉËÌÏ×:\index{ÃÉËÌÙ}%
\index{for?\texttt{for}}\index{endfor?\texttt{endfor}}
%%Such a repetitive sequence of \verb|draw| statements is
%%best written as a pair of nested loops:\index{loops}%
%%\index{for?\texttt{for}}\index{endfor?\texttt{endfor}}
$$\begin{verbatim}
for i=0 upto 2:
  for j=0 upto 2:  drawdot (i*u,j*u);  endfor
endfor
\end{verbatim}
$$
÷ÎÅÛÎÉÊ ÃÉËÌ ÉÓÐÏÌÎÑÅÔÓÑ ÄÌÑ $i=0,1,2$, Á ×ÎÕÔÒÅÎÎÉÊ --- ÄÌÑ $j=0,1,2$.
%%The outer loop runs for $i=0,1,2$ and the inner loop runs for $j=0,1,2$.
òÅÚÕÌØÔÁÔ --- ÒÅÛÅÔËÁ ÔÒÉ ÎÁ ÔÒÉ ÉÚ ÖÉÒÎÙÈ ÔÏÞÅË, ËÁË ÐÏËÁÚÁÎÏ ÎÁ 
ÒÉÓ.~\ref{fig1}.
%%The result is a three-by-three grid of bold dots as shown in Figure~\ref{fig1}.
üÔÏÔ ÒÉÓÕÎÏË ×ËÌÀÞÁÅÔ ÔÁËÖÅ ÂÏÌØÛÉÊ ×ÁÒÉÁÎÔ ÌÏÍÁÎÏÊ ÌÉÎÉÉ, ËÏÔÏÒÕÀ ÍÙ 
×ÉÄÅÌÉ ÒÁÎØÛÅ.
%%The figure also includes a larger version of the polygonal line diagram that we
%%saw before.

\begin{figure}[htp]
$$ \begin{verbatim}
beginfig(2);
u=1cm;
draw (2u,2u)--(0,0)--(0,3u)--(3u,0)--(0,0);
pickup pencircle scaled 4pt;
for i=0 upto 2:
  for j=0 upto 2:  drawdot (i*u,j*u);  endfor
endfor
endfig;
\end{verbatim}
\quad \mathcenter{\includegraphics{manfig-ru-2}}
$$
\caption{ëÏÍÁÎÄÙ MetaPost É ÒÅÚÕÌØÔÉÒÕÀÝÉÊ ×Ù×ÏÄ}
%%\caption{MetaPost commands and the resulting output}
\label{fig1}
\end{figure}

úÁÍÅÔØÔÅ, ÞÔÏ ÐÒÏÇÒÁÍÍÁ ÎÁ ÒÉÓ.~\ref{fig1} ÎÁÞÉÎÁÅÔÓÑ Ó 
\verb|beginfig(2)|\index{beginfig?\texttt{beginfig}} É ÚÁËÁÎÞÉ×ÁÅÔÓÑ Ó
\verb|endfig|\index{endfig?\texttt{endfig}}.
%%Note that the program in Figure~\ref{fig1} starts with
%%\verb|beginfig(2)|\index{beginfig?\texttt{beginfig}} and ends with
%%\verb|endfig|\index{endfig?\texttt{endfig}}.  
üÔÉ ÍÁËÒÏÓÙ, ×ÙÐÏÌÎÑÀÝÉÅ ÁÄÍÉÎÉÓÔÒÁÔÉ×ÎÙÅ ÆÕÎËÃÉÉ, ÇÁÒÁÎÔÉÒÕÀÔ, ÞÔÏ 
ÒÅÚÕÌØÔÁÔÙ ×ÓÅÈ ËÏÍÁÎÄ \verb|draw| ÓÏÂÉÒÁÀÔÓÑ ×ÍÅÓÔÅ É ÔÒÁÎÓÌÉÒÕÀÔÓÑ × 
PostScript.
%%These are macros that
%%perform various administrative functions and ensure that the results of
%%all the \verb|draw| statements get packaged up and translated into
%%PostScript. 
÷ÈÏÄÎÏÊ ÆÁÊÌ ÄÌÑ MetaPost ÏÂÙÞÎÏ ÓÏÄÅÒÖÉÔ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÐÁÒ
\verb|beginfig| É \verb|endfig| Ó ËÏÍÁÎÄÏÊ {\tt end}\index{end?\texttt{end}} 
ÐÏÓÌÅ ÐÏÓÌÅÄÎÅÊ ÐÁÒÙ. 
%%A MetaPost input file normally contains a sequence of
%%\verb|beginfig|, \verb|endfig| pairs with an {\tt
%%end}\index{end?\texttt{end}} statement after the last one.  
åÓÌÉ ÜÔÏÔ ÆÁÊÌ ÉÍÅÎÏ×ÁÎ {\tt fig.mp}, ÔÏ ×Ù×ÏÄ ÏÔ ËÏÍÁÎÄ \verb|draw| 
ÍÅÖÄÕ \verb|beginfig(1)| É ÓÌÅÄÕÀÝÅÊ \verb|endfig| ÐÉÛÅÔÓÑ × ÆÁÊÌ 
{\tt fig.1}\index{ÆÁÊÌÙ!×Ù×ÏÄ}.
%%If this file
%%is named {\tt fig.mp}, the output from \verb|draw| statements between
%%\verb|beginfig(1)| and the next \verb|endfig| is written in a file {\tt
%%fig.1}\index{files!output}. 
äÒÕÇÉÍÉ ÓÌÏ×ÁÍÉ, ÞÉÓÌÏ×ÏÊ ÁÒÇÕÍÅÎÔ × ÍÁËÒÏÓÅ \verb|beginfig| ÏÐÒÅÄÅÌÑÅÔ 
ÉÍÑ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÇÏ ×ÙÈÏÄÎÏÇÏ ÆÁÊÌÁ.
%%In other words, the numeric argument to the
%%\verb|beginfig| macro determines the name of the corresponding output
%%file.

þÔÏ ÄÅÌÁÔØ ÓÏ ×ÓÅÍÉ ÜÔÉÍÉ PostScript-ÆÁÊÌÁÍÉ?
%%What does one do with all the PostScript files? 
ïÎÉ ÍÏÇÕÔ ÂÙÔØ ×ËÌÀÞÅÎÙ ËÁË ÒÉÓÕÎËÉ × ÄÏËÕÍÅÎÔÙ \TeX\index{TeX?\TeX} ÉÌÉ 
troff\index{troff}, ÅÓÌÉ ×Ù ÉÍÅÅÔÅ ÄÒÁÊ×ÅÒ, ËÏÔÏÒÙÊ ÍÏÖÅÔ ÒÁÂÏÔÁÔØ Ó 
PostScript-ËÁÒÔÉÎËÁÍÉ. 
%%They can be included as
%%figures in a \TeX\index{TeX?\TeX} or troff\index{troff} document if you
%%have an output driver that can handle encapsulated PostScript figures.
ïÎÉ ÔÁËÖÅ ÍÏÇÕÔ ÂÙÔØ ÐÒÅÄ×ÁÒÉÔÅÌØÎÏ ÐÒÏÓÍÏÔÒÅÎÙ ÄÏ ÉÈ ×ËÌÀÞÅÎÉÑ × ÄÏËÕÍÅÎÔ 
Ó ÔÙÓÑÞÅÊ ÓÔÒÁÎÉÃ.
%%They can also be previewed before they are included in a thousand pages
%%document.  
óÌÅÄÕÀÝÉÅ ÒÁÚÄÅÌÙ ÄÁÀÔ ÂÏÌØÛÅ ÉÎÆÏÒÍÁÃÉÉ.
%%The next sections give some more information.

\section{õÐÒÁ×ÌÅÎÉÅ ×Ù×ÏÄÏÍ MetaPost}
%%\section{Handling MetaPost output}
\label{Dmpoutput}

÷ÚÁÉÍÏÄÅÊÓÔ×ÉÅ ÍÅÖÄÕ \TeX\ É MetaPost ÍÏÖÅÔ ÂÙÔØ Ä×ÏÑËÉÍ.
%%There can be a two-fold interaction between \TeX\ and MetaPost. 
ó ÏÄÎÏÊ ÓÔÏÒÏÎÙ, ÇÒÁÆÉËÁ MetaPost ÍÏÖÅÔ ÉÍÐÏÒÔÉÒÏ×ÁÔØÓÑ × ÄÏËÕÍÅÎÔÙ, 
ÎÁÂÉÒÁÅÍÙÅ \TeX\ É ÅÇÏ ÄÒÕÚØÑÍÉ. 
%%On one
%%hand, MetaPost graphics can be imported into documents typeset by \TeX\
%%and friends. 
ó ÄÒÕÇÏÊ ÓÔÏÒÏÎÙ, MetaPost ÍÏÖÅÔ ÐÏÒÕÞÉÔØ ÎÁÂÏÒ ÔÅËÓÔÏ×ÙÈ ÜÌÅÍÅÎÔÏ× \TeX, 
\LaTeX\ ÉÌÉ \emph{troff}, ÎÁÐÒÉÍÅÒ, ÔÅËÓÔÏ×ÙÈ ÍÅÔÏË ÉÌÉ ÍÁÔÅÍÁÔÉÞÅÓËÉÈ 
ÆÏÒÍÕÌ × ÇÒÁÆÉËÅ.
%%On the other hand, MetaPost can delegate typesetting
%%textual elements to \TeX, \LaTeX\ or \emph{troff}, e.g., text labels or
%%mathematical formulas in a graphic. 
ôÁËÉÍ ÓÐÏÓÏÂÏÍ ÇÒÁÆÉËÁ MetaPost ÍÏÖÅÔ ÌÅÇËÏ ÐÒÉÎÑÔØ ÓÔÉÌØ ÄÏËÕÍÅÎÔÁ 
(ÛÒÉÆÔ, ÒÁÚÍÅÒ ÛÒÉÆÔÁ É Ô.~Ð.) É ÓÏÏÔ×ÅÔÓÔ×Ï×ÁÔØ ËÁÞÅÓÔ×Õ ÅÇÏ ÎÁÂÏÒÁ 
(ÉÓÐÏÌØÚÏ×ÁÔØ ËÅÒÎÉÎÇ, ÌÉÇÁÔÕÒÙ É Ô.~Ð.).
%%That way, MetaPost graphics can
%%easily adopt the style of a document (type, type size, etc.) and fit its
%%typesetting quality (use kerning, ligatures, etc.) 
üÔÏ ÄÅÌÁÅÔ MetaPost ÉÄÅÁÌØÎÙÍ ÉÎÓÔÒÕÍÅÎÔÏÍ ÄÌÑ ÐÒÉÇÏÔÏ×ÌÅÎÉÑ ×ÙÓÏËÏËÁÞÅÓÔ×ÅÎÎÏÊ 
ÇÒÁÆÉËÉ ÄÌÑ ÄÏËÕÍÅÎÔÏ× \TeX\ ÉÌÉ \emph{troff}.
%%This makes MetaPost
%%an ideal tool for preparing high-quality graphics for \TeX\ or
%%\emph{troff} documents.

üÔÏÔ ÒÁÚÄÅÌ ÏÔÎÏÓÉÔÓÑ Ë ÐÅÒ×ÏÊ ÓÔÏÒÏÎÅ ×ÚÁÉÍÏÄÅÊÓÔ×ÉÑ \TeX--MetaPost: 
ÉÍÐÏÒÔÕ ÇÒÁÆÉËÉ MetaPost × \TeX\ É ÅÇÏ ÄÒÕÚÅÊ.
%%This section deals with the first aspect of \TeX--MetaPost interaction,
%%the import of MetaPost graphics into \TeX\ and friends. 
îÁÂÏÒ ÔÅËÓÔÏ× × MetaPost ÏÂÓÕÖÄÁÅÔÓÑ × ÒÁÚÄÅÌÅ~\ref{text}.
%%Typesetting
%%text in MetaPost is discussed in section~\ref{text}.

\subsection{ðÒÅÄ×ÁÒÉÔÅÌØÎÙÊ ÐÒÏÓÍÏÔÒ ÇÒÁÆÉËÉ MetaPost}
%%\subsection{Previewing MetaPost graphics}

\label{Dpreview}
\index{ÐÒÅÄÐÒÏÓÍÏÔÒ}
%%\index{previewing}

÷Ù×ÏÄ MetaPost --- ÜÔÏ ×ÁÒÉÁÎÔ PostScript, ÎÁÚÙ×ÁÅÍÙÊ Encapsulated
PostScript\index{PostScript!ÓÔÒÕËÔÕÒÎÙÊ} (EPSF\index{EPSF}).
%%The output of MetaPost is a variant of PostScript, called Encapsulated
%%PostScript\index{PostScript!structured} (EPSF\index{EPSF}).  
çÒÁÆÉËÁ MetaPost ÍÏÖÅÔ, ÓÌÅÄÏ×ÁÔÅÌØÎÏ, ÂÙÔØ ÐÒÏÓÍÏÔÒÅÎÁ × ÌÀÂÏÍ 
PostScript-ÐÒÏÓÍÏÔÒÝÉËÅ, ÎÁÐÒÉÍÅÒ, GSview\index{GSview}.
%%MetaPost 
%%graphics can therefore be previewed with any decent PostScript viewer,
%%e.\,g., GSview\index{GSview}.

óÉÔÕÁÃÉÑ ÓÔÁÎÏ×ÉÔÓÑ ÔÏÌØËÏ ÎÅÍÎÏÇÏ ÓÌÏÖÎÅÅ, ËÏÇÄÁ ×Ù×ÏÄ MetaPost ÓÏÄÅÒÖÉÔ 
ÔÅËÓÔ.
%%The situation becomes only a little bit fussy when MetaPost output
%%contains text. 
ïÂÙÞÎÏ MetaPost ÎÅ ÐÒÏÉÚ×ÏÄÉÔ ÓÁÍÏÄÏÓÔÁÔÏÞÎÙÅ EPS-ÆÁÊÌÙ, ÎÁÐÒÉÍÅÒ, 
ÛÒÉÆÔÙ É ÔÁÂÌÉÃÙ ËÏÄÉÒÏ×ÏË ÎÅ ÐÏÍÅÝÁÀÔÓÑ × ×Ù×ÏÄ. 
%%By default, MetaPost doesn't produce self-contained EPS
%%files, e.\,g., font resources and encoding vectors are not stored in
%%the output.  
ðÏÜÔÏÍÕ ×Ù×ÏÄ MetaPost, ÓÏÄÅÒÖÁÝÉÊ ÔÅËÓÔ, ÍÏÖÅÔ ÂÙÔØ ÐÏËÁÚÁÎ Ó ÎÅ×ÅÒÎÙÍÉ 
ÛÒÉÆÔÁÍÉ, ÎÅ×ÅÒÎÙÍÉ ÓÉÍ×ÏÌÁÍÉ ÉÌÉ ×ÏÏÂÝÅ ÂÅÚ ÔÅËÓÔÁ × 
PostScript-ÐÒÏÓÍÏÔÒÝÉËÅ.
%%For that reason MetaPost output containing text may be
%%rendered with wrong fonts, wrong glyphs or with no text at all in a
%%PostScript viewer.  
äÏÌÇÏÅ ×ÒÅÍÑ, ÎÁÉÂÏÌÅÅ ÎÁÄÅÖÎÙÊ ÐÕÔØ ÄÌÑ ÐÒÏÓÍÏÔÒÁ ÂÙÌ × ÐÏÄÇÏÔÏ×ËÅ 
ÔÅÓÔ-ÄÏËÕÍÅÎÔÁ, ×ËÌÀÞÁÀÝÅÇÏ ×ÓÅ ËÁÒÔÉÎËÉ MetaPost, ÏÂÒÁÂÏÔËÅ ÅÇÏ ÌÉÂÏ
\TeX, ÌÉÂÏ \LaTeX, ÚÁÔÅÍ \ttindex{dvips} É ÐÏËÁÚÕ ÒÅÚÕÌØÔÉÒÕÀÝÅÇÏ
\ttt{ps}-ÆÁÊÌÁ × PostScript-ÐÒÏÓÍÏÔÒÝÉËÅ.\footnote{èÏÔÑ ÅÓÔØ É 
ÁÌØÔÅÒÎÁÔÉ×Ù: \ttindex{mpstoeps} --- ÜÔÏ Perl-ÓÃÅÎÁÒÉÊ, ËÏÔÏÒÙÊ 
Á×ÔÏÍÁÔÉÚÉÒÕÅÔ ÐÒÏÃÅÓÓ, ÏÂÏÚÎÁÞÅÎÎÙÊ ×ÙÛÅ, Á 
\ttindex{mptopdf} --- ÜÔÏ ÄÒÕÇÏÅ ÓÒÅÄÓÔ×Ï, ËÏÔÏÒÏÅ ËÏÎ×ÅÒÔÉÒÕÅÔ 
MetaPost-ÆÁÊÌÙ × PDF.}
%%For a long time, the most reliable way for
%%previewing was to prepare a test document that includes all MetaPost
%%figures, process that with \TeX\ or \LaTeX\ and \ttindex{dvips} and
%%display the resulting \ttt{ps} file in a PostScript
%%viewer.\footnote{There are alternatives, though. \ttindex{mpstoeps} is
%%a Perl script that automates the process outlined above.
%%\ttindex{mptopdf} is another tools that converts MetaPost files to
%%PDF.}

ïÄÎÁËÏ, Ó ×ÅÒÓÉÉ 1.000 MetaPost ÓÉÔÕÁÃÉÑ ÉÚÍÅÎÉÌÁÓØ. ó ÜÔÏÊ ×ÅÒÓÉÉ 
MetaPost ÓÐÏÓÏÂÅÎ ÐÒÏÉÚ×ÏÄÉÔØ ÓÁÍÏÄÏÓÔÁÔÏÞÎÙÅ ÆÁÊÌÙ EPS, ËÏÔÏÒÙÅ 
ÍÏÇÕÔ ÂÙÔØ ÄÏÓÔÏ×ÅÒÎÏ ÐÒÏÓÍÏÔÒÅÎÙ × ÎÅÚÁ×ÉÓÉÍÏÓÔÉ ÏÔ ÔÏÇÏ, ÅÓÔØ ÌÉ × ÎÉÈ 
ÔÅËÓÔ ÉÌÉ ÎÅÔ.
%%However, with MetaPost version~1.000 the situation changed.  Since that
%%version MetaPost is able to produce self-contained EPS files, that can
%%reliably be previewed, may they contain text or not. 
îÏ×ÙÅ ×ÏÚÍÏÖÎÏÓÔÉ ÍÏÇÕÔ ÂÙÔØ ×ËÌÀÞÅÎÙ ÕÓÔÁÎÏ×ËÏÊ ×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ 
MetaPost \ttt{prologues}\index{prologues?\texttt{prologues}} ×~3. 
%%The
%%new behaviour can be triggered by setting MetaPost's internal variable
%%\ttt{prologues}\index{prologues?\texttt{prologues}} to~3.  
óÍÏÔÒÉ ÒÁÚÄÅÌ~\ref{Dbtex} ÄÌÑ ÂÏÌØÛÅÊ ÉÎÆÏÒÍÁÃÉÉ Ï \ttt{prologues}.
%%See
%%section~\ref{Dbtex} for more information on \ttt{prologues}.

\subsection{éÓÐÏÌØÚÏ×ÁÎÉÅ ÇÒÁÆÉËÉ MetaPost × \TeX, \LaTeX, pdf\LaTeX, pdf\TeX, Con\TeX{}t É troff}
%\subsection{Using MetaPost graphics in \TeX, \LaTeX, pdf\LaTeX, pdf\TeX, Con\TeX{}t and troff}
\label{Dteximport}
\index{TeX?\TeX!ÉÍÐÏÒÔ ÆÁÊÌÏ× MetaPost}
\index{LaTeX?\LaTeX!ÉÍÐÏÒÔ ÆÁÊÌÏ× MetaPost}
\index{pdfLaTeX?pdf\LaTeX!ÉÍÐÏÒÔ ÆÁÊÌÏ× MetaPost}
\index{pdfTeX?pdf\TeX!ÉÍÐÏÒÔ ÆÁÊÌÏ× MetaPost}
\index{ConTeXt?Con\TeX t!ÉÍÐÏÒÔ ÆÁÊÌÏ× MetaPost}
\index{troff!ÉÍÐÏÒÔ ÆÁÊÌÏ× MetaPost}
%%\index{TeX?\TeX!importing MetaPost files}
%%\index{LaTeX?\LaTeX!importing MetaPost files}
%%\index{pdfLaTeX?pdf\LaTeX!importing MetaPost files}
%%\index{pdfTeX?pdf\TeX!importing MetaPost files}
%%\index{ConTeXt?Con\TeX t!importing MetaPost files}
%%\index{troff!importing MetaPost files}

ôÏ ËÁË ÒÉÓÕÎËÉ MetaPost ÍÏÇÕÔ ÂÙÔØ ÉÎÔÅÇÒÉÒÏ×ÁÎÙ Ó ÄÏËÕÍÅÎÔÁÍÉ, 
ÐÏÄÇÏÔÏ×ÌÅÎÎÙÍÉ × \TeX\ É ÒÏÄÓÔ×ÅÎÎÙÈ \TeX\ ÐÒÏÇÒÁÍÍÁÈ, ÚÁ×ÉÓÉÔ ÏÔ 
ÆÏÒÍÁÔÁ ÄÏËÕÍÅÎÔÏ× É ÄÒÁÊ×ÅÒÁ ×Ù×ÏÄÁ.
%%How MetaPost figures can be integrated into documents prepared with
%%\TeX\ and friends depends on the exact format and output driver.
òÉÓ.~\ref{fig0} ÐÏËÁÚÙ×ÁÅÔ ÐÒÏÃÅÓÓ ÒÁÂÏÔÙ ÄÌÑ plain \TeX, \LaTeX\ É 
Ó×ÏÂÏÄÎÏ ÄÏÓÔÕÐÎÏÊ ÐÒÏÇÒÁÍÍÙ \ttindex{dvips}\footnote{éÓÈÏÄÎÉËÉ ÎÁ C ÄÌÑ 
\ttt{dvips} ÎÁÈÏÄÑÔÓÑ ×ÍÅÓÔÅ Ó web2c \TeX-ÄÉÓÔÒÉÂÕÔÉ×ÏÍ.  ðÏÄÏÂÎÙÅ 
ÐÒÏÇÒÁÍÍÙ ÄÏÓÔÕÐÎÙ É × ÄÒÕÇÉÈ ÍÅÓÔÁÈ.}.
%%Figure~\ref{fig0} shows the workflow for plain \TeX, \LaTeX\ and the
%%freely available program \ttindex{dvips}.\footnote{The C source for
%%\ttt{dvips} comes with the web2c \TeX\ distribution.  Similar programs
%%are available from other sources.} 
óÈÏÖÁÑ ÐÒÏÃÅÄÕÒÁ ÒÁÂÏÔÁÅÔ Ó troff: ÐÒÏÃÅÓÓÏÒ ×Ù×ÏÄÁ \ttt{grops} ×ËÌÀÞÁÅÔ  ÒÉÓÕÎËÉ ÎÁ PostScript, ËÏÇÄÁ ÏÎÉ ÚÁÐÒÁÛÉ×ÁÀÔÓÑ ÞÅÒÅÚ ËÏÍÁÎÄÕ troff
\ttt{\string\X}. 
%%A similar procedure works with
%%troff: the \ttt{grops} output processor includes PostScript figures when
%%they are requested via troff's \ttt{\string\X} command. 
ó ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ PDF Ó \TeX\ É \LaTeX\ ÓÉÔÕÁÃÉÑ ÎÅÓËÏÌØËÏ ÉÎÁÑ.
%%For the PDF
%%flavour of \TeX\ and \LaTeX\ the situation is a little bit different.
óÌÅÄÕÀÝÉÅ ÁÂÚÁÃÙ ÄÁÀÔ ËÒÁÔËÕÀ ÉÎÆÏÒÍÁÃÉÀ ÐÏ ÎÅËÏÔÏÒÙÍ ÐÏÐÕÌÑÒÎÙÍ 
\TeX-ÆÏÒÍÁÔÁÍ É ÄÒÁÊ×ÅÒÁÍ ×Ù×ÏÄÁ.
%%The next paragraphs give brief information on some popular \TeX\ formats
%%and output drivers.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-0} $$
\caption[äÉÁÇÒÁÍÍÁ ÏÂÒÁÂÏÔËÉ ÄÌÑ ÄÏËÕÍÅÎÔÁ Ó ÒÉÓÕÎËÁÍÉ MetaPost]
        {äÉÁÇÒÁÍÍÁ ÏÂÒÁÂÏÔËÉ ÄÌÑ \TeX-ÄÏËÕÍÅÎÔÁ Ó ÒÉÓÕÎËÁÍÉ × MetaPost}
%%\caption[A diagram of the processing for a document with MetaPost figures]
%%        {A diagram of the processing for a \TeX\ document with figures
%%        in MetaPost}
\label{fig0}
\end{figure}

\paragraph{\TeX}
ðÏÌØÚÏ×ÁÔÅÌÉ \TeX\ ÍÏÇÕÔ ÉÍÐÏÒÔÉÒÏ×ÁÔØ ÇÒÁÆÉËÕ, ÚÁÇÒÕÚÉ× ÓÎÁÞÁÌÁ ÐÁËÅÔ 
\ttt{epsf}\index{epsf.tex?\texttt{epsf.tex}} ÞÅÒÅÚ \verb+\input epsf+ É
ÚÁÔÅÍ ××ÅÄÑ ËÏÍÁÎÄÕ 
$$ \verb+\epsfbox{+\descr{ÉÍÑ ÆÁÊÌÁ}\verb+}+ $$%
\index{epsfbox?\texttt{\string\epsfbox}}
ÄÌÑ ÚÁÇÒÕÚËÉ EPS-ÆÁÊÌÁ, ÎÁÐÒÉÍÅÒ, \verb+\epsfbox{fig.1}+.
%%\TeX\ users can import EPS graphics by first loading package
%%\ttt{epsf}\index{epsf.tex?\texttt{epsf.tex}} via \verb+\input epsf+ and
%%then issuing the command
%%$$ \verb+\epsfbox{+\descr{filename}\verb+}+ $$%
%%\index{epsfbox?\texttt{\string\epsfbox}}
%%to load an EPS file, e.\,g., \verb+\epsfbox{fig.1}+.

\paragraph{\LaTeX}
äÌÑ ÄÏËÕÍÅÎÔÏ× \LaTeX\ ÐÒÏÃÅÄÕÒÁ ÐÏÈÏÖÁÑ:  ÐÅÒ×ÙÊ ÐÁËÅÔ 
\ttindex{graphicx} ÄÏÌÖÅÎ ÂÙÔØ ÚÁÇÒÕÖÅÎ ÒÁÚÍÅÝÅÎÉÅÍ 
\verb+\usepackage{graphicx}+ × ÐÒÅÁÍÂÕÌÕ ÄÏËÕÍÅÎÔÁ É ÚÁÔÅÍ 
EPS-ÆÁÊÌÙ ÍÏÇÕÔ ÂÙÔØ ÚÁÇÒÕÖÅÎÙ ÞÅÒÅÚ 
$$ \verb+\includegraphics{+\descr{ÉÍÑ ÆÁÊÌÁ}\verb+}+, $$%
\index{includegraphics?\texttt{\string\includegraphics}}%
ÎÁÐÒÉÍÅÒ, \verb+\includegraphics{fig.1}+.
%%For \LaTeX\ documents the procedure is similar:  first package
%%\ttindex{graphicx} has to be loaded by putting
%%\verb+\usepackage{graphicx}+ into the document preamble and then EPS
%%files can be loaded via
%%$$ \verb+\includegraphics{+\descr{filename}\verb+}+ $$%
%%e.\,g., \verb+\includegraphics{fig.1}+.

ëÁË ÍÏÖÎÏ ÚÁÍÅÔÉÔØ ÎÁ ÒÉÓ.~\ref{fig0} ÇÒÁÆÉÞÅÓËÉÅ ÆÁÊÌÙ ÎÉËÏÇÄÁ ÎÅ 
×ËÌÀÞÁÀÔÓÑ ÐÒÉ ÉÓÐÏÌÎÅÎÉÉ \TeX\index{TeX?\TeX!ÉÍÐÏÒÔ ÆÁÊÌÏ× MetaPost} ÉÌÉ 
\LaTeX\index{LaTeX?\LaTeX!ÉÍÐÏÒÔ ÆÁÊÌÏ× MetaPost}.
%%As can be seen in figure~\ref{fig0} graphic files are never included in a
%%\TeX\index{TeX?\TeX!importing MetaPost files} or
%%\LaTeX\index{LaTeX?\LaTeX!importing MetaPost files} run.
÷ÍÅÓÔÏ ÜÔÏÇÏ \TeX\ É \LaTeX\ ÔÏÌØËÏ ÞÉÔÁÀÔ ÉÎÆÏÒÍÁÃÉÀ Ï ÏÈ×ÁÔÙ×ÁÀÝÉÈ 
ÒÁÍËÁÈ ÉÚ PostScript-ÆÁÊÌÁ, ÒÅÚÅÒ×ÉÒÕÑ ÓÔÏÌØËÏ ÍÅÓÔÁ ÎÁ ÓÔÒÁÎÉÃÅ, ÓËÏÌØËÏ 
ÚÁÎÉÍÁÅÔ ÇÒÁÆÉËÁ É ÚÁÐÉÓÙ×ÁÑ ÓÓÙÌËÕ ÎÁ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ÆÁÊÌ × 
\ttt{dvi}-×Ù×ÏÄÅ. 
%%Instead,
%%\TeX\ and \LaTeX\ only read bounding box information off the PostScript
%%file, reserve as much space on a page as the graphic
%%occupies and write a reference to the corresponding file into the
%%\ttt{dvi} output. 
çÒÁÆÉÞÅÓËÉÊ ÆÁÊÌ ×ËÌÀÞÁÅÔÓÑ ÔÏÌØËÏ ÐÒÉ ÐÏÓÌÅÄÕÀÝÅÍ ÉÓÐÏÌÎÅÎÉÉ ÄÒÁÊ×ÅÒÁ 
×Ù×ÏÄÁ, ËÏÔÏÒÙÊ ÍÏÖÅÔ ÏÂÒÁÂÁÔÙ×ÁÔØ PostScript-ÆÁÊÌÙ, 
ÎÁÐÒÉÍÅÒ, \ttindex{dvips}.
%%The graphic file is only included in the subsequent
%%run of an output driver, that can handle PostScript files, e.\,g.,
%%\ttindex{dvips}.

\paragraph{pdf\LaTeX}
ðÒÉÌÏÖÅÎÉÅ pdf\LaTeX, ËÏÇÄÁ ÉÓÐÏÌÎÑÅÔÓÑ × ÒÅÖÉÍÅ PDF, Ñ×ÌÑÅÔÓÑ ÓÒÁÚÕ É 
\LaTeX-ÉÎÔÅÒÐÒÅÔÁÔÏÒÏÍ, É ÄÒÁÊ×ÅÒÏÍ ×Ù×ÏÄÁ ÄÌÑ ÄÏËÕÍÅÎÔÁ × PDF-ÆÏÒÍÁÔ.
%%The application pdf\LaTeX, when run in PDF mode, is both, a
%%\LaTeX\ interpreter and an output driver for the PDF document format.
ðÏÜÔÏÍÕ ÇÒÁÆÉÞÅÓËÉÅ ÆÁÊÌÙ ×ËÌÀÞÁÀÔÓÑ ×Ï ×ÒÅÍÑ ÉÓÐÏÌÎÅÎÉÑ pdf\LaTeX, ÚÁ 
ÏÄÉÎ ÐÒÏÈÏÄ.
%%For that reason graphic files are included in a single
%%pdf\LaTeX\ run. 
÷ ÏÔÌÉÞÉÅ ÏÔ \ttt{dvips}, pdf\LaTeX\ ÎÅ ÍÏÖÅÔ ÏÂÒÁÂÁÔÙ×ÁÔØ ÏÂÙÞÎÙÅ 
PostScript-ÆÁÊÌÙ  --- ÏÎ ÍÏÖÅÔ ÒÁÂÏÔÁÔØ ÔÏÌØËÏ Ó ÔÁË ÎÁÚÙ×ÁÅÍÙÍÉ ÏÞÉÝÅÎÎÙÍÉ 
EPS\index{PostScript!ÏÞÉÝÅÎÎÙÊ}-ÆÁÊÌÁÍÉ, ËÏÔÏÒÙÅ ÍÏÇÕÔ ÉÓÐÏÌØÚÏ×ÁÔØ ÔÏÌØËÏ 
ÏÇÒÁÎÉÞÅÎÎÏÅ ÍÎÏÖÅÓÔ×Ï ×ÏÚÍÏÖÎÏÓÔÅÊ ÑÚÙËÁ PostScript.
%%In contrast to \ttt{dvips}, pdf\LaTeX\ can't process
%%general PostScript files, but only so-called purified
%%EPS\index{PostScript!purified} files, which may only use a restricted
%%set of PostScript language features. 
ë ÓÞÁÓÔØÀ, ×Ù×ÏÄ MetaPost --- ÜÔÏ É \emph{ÅÓÔØ} ÏÞÉÝÅÎÎÙÊ EPS, ÔÁË ÞÔÏ ÔÕÔ 
ÎÁÍ ÐÏ×ÅÚÌÏ. 
%%Fortunately, MetaPost output
%%\emph{is} purified EPS, so we are in luck. 
éÚ ÔÏÇÏ, ÞÔÏ \ttt{mps}\index{ÆÁÊÌÙ!mps?\texttt{mps}} --- ÜÔÏ 
ÔÉÐÏ×ÏÅ ÒÁÓÛÉÒÅÎÉÅ pdf\LaTeX\ ÄÌÑ ÏÞÉÝÅÎÎÙÈ EPS-ÆÁÊÌÏ×, Á ×Ù×ÏÄ 
MetaPost ÏÂÙÞÎÏ ÉÍÅÅÔ ÒÁÓÛÉÒÅÎÉÑ-ÞÉÓÌÁ, ÍÙ ÄÏÌÖÎÙ  
%%Since
%%pdf\LaTeX's default extension for purified EPS files is
%%\ttt{mps}\index{files!mps?\texttt{mps}}, but MetaPost output by
%%default has a number as extensions, we either have to
\begin{itemize}
\item ÓËÁÚÁÔØ pdf\LaTeX\ ÏÂÒÁÂÁÔÙ×ÁÔØ ÚÁÎÕÍÅÒÏ×ÁÎÎÙÅ ÆÁÊÌÙ MetaPost 
ÓÏÇÌÁÓÎÏ ÐÒÁ×ÉÌÁÍ ÄÌÑ ÆÁÊÌÏ× \ttt{mps} ÉÌÉ
%%\item tell pdf\LaTeX\ to handle MetaPost's numbered files according to
%%\ttt{mps} file rules, or
\item ÉÚÍÅÎÉÔØ ÒÁÓÛÉÒÅÎÉÅ ÆÁÊÌÁ ×Ù×ÏÄÁ MetaPost ÎÁ \ttt{mps}.
%%\item change the file extension of MetaPost output to \ttt{mps}.
\end{itemize}

ðÒÉ ÐÅÒ×ÏÍ ÐÏÄÈÏÄÅ ÍÙ ÄÏÌÖÎÙ ÄÏÂÁ×ÉÔØ ÓÔÒÏËÕ
%%For the conventional first approach we have to add the line
$$ \verb+\DeclareGraphicsRule{*}{mps}{*}{}+ $$%
\index{DeclareGraphicsRule?\texttt{\string\DeclareGraphicsRule}}%
Ë ÐÒÅÁÍÂÕÌÅ ÄÏËÕÍÅÎÔÁ ÐÏÓÌÅ ÚÁÇÒÕÚËÉ ÐÁËÅÔÁ \ttt{graphicx}.
%%to the document preamble after loading package \ttt{graphicx}. 
üÔÁ ÄÅËÌÁÒÁÃÉÑ ÓËÁÖÅÔ pdf\LaTeX\ ÚÁÇÒÕÖÁÔØ \emph{×ÓÅ} ÆÁÊÌÙ Ó 
ÎÅÉÚ×ÅÓÔÎÙÍ ÒÁÓÛÉÒÅÎÉÅÍ ËÁË \ttt{mps}-ÆÁÊÌÙ.
%%That
%%declaration tells pdf\LaTeX\ to load \emph{all} files with unknown file
%%extensions as \ttt{mps} files. 
óÍ. ÄÏËÕÍÅÎÔÁÃÉÀ ÐÏ ÐÁËÅÔÁÍ \ttt{graphicx} É \ttt{graphics} ÄÌÑ 
ÄÏÐÏÌÎÉÔÅÌØÎÏÊ ÉÎÆÏÒÍÁÃÉÉ.
%%Refer to the documentation of the
%%\ttt{graphicx} and \ttt{graphics} packages for more details.

ó ×ÅÒÓÉÉ MetaPost 1.000 ÒÅËÏÍÅÎÄÏ×ÁÎ ×ÔÏÒÏÊ ÐÏÄÈÏÄ.\footnote{äÌÑ ÏÂÒÁÂÏÔËÉ 
ÒÁÓÛÉÒÅÎÉÊ MetaPost-ÆÁÊÌÏ× ÐÒÅÄÐÏÌÏÖÉÔÅÌØÎÏ ÂÏÌÅÅ ÅÓÔÅÓÔ×ÅÎÎÏ ×ÍÅÓÔÏ 
\LaTeX-ÉÓÈÏÄÎÉËÏ× ÉÓÐÏÌØÚÏ×ÁÔØ ÉÓÈÏÄÎÉËÉ MetaPost.
ôÅÍ ÂÏÌÅÅ, ÞÔÏ ÕÓÔÁÎÏ×ËÁ ÒÁÓÛÉÒÅÎÉÑ MetaPost-ÆÁÊÌÁ × \ttt{mps} ÐÒÅÄÏÈÒÁÎÑÅÔ 
ÏÔ ÚÁÇÒÑÚÎÅÎÉÑ ÉÚÂÙÔËÏÍ ÒÁÓÛÉÒÅÎÉÊ --- ×ÁÍ ÂÕÄÅÔ ÎÕÖÎÏ ÚÁÒÅÇÉÓÔÒÉÒÏ×ÁÔØ ÔÏÌØËÏ 
ÏÄÎÏ ÒÁÓÛÉÒÅÎÉÅ ÄÌÑ ×ÁÛÅÇÏ PostScript-ÐÒÏÓÍÏÔÒÝÉËÁ --- \ttt{.mps}, ×ÍÅÓÔÏ \ttt{.0}, \ttt{.1}, 
\ttt{.2} É Ô.~Ä.}
%%Since MetaPost version~1.000 the second approach is
%%recommended.\footnote{For handling MetaPost file extensions in MetaPost
%%source files seems to be the more natural place than \LaTeX\ sources.
%%Moreover, setting the MetaPost file extension to \ttt{mps} prevents from
%%file extension pollution and you only have to register one new extension
%%with your PostScript viewer, \ttt{.mps}, instead of \ttt{.0}, \ttt{.1},
%%\ttt{.2}, etc.} 
ðÒÉÍÉÔÉ× MetaPost \verb+filenametemplate+ ÍÏÖÅÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎ ÄÌÑ 
ÕÓÔÁÎÏ×ËÉ ÒÁÓÛÉÒÅÎÉÑ ÆÁÊÌÁ ×Ù×ÏÄÁ MetaPost × \ttt{mps} (ÓÍ. 
ÒÁÚÄÅÌ~\ref{Dfilenametemplate})
%%The MetaPost primitive \verb+filenametemplate+ can be
%%used to set the file extension of MetaPost output to \ttt{mps} (see
%%section~\ref{Dfilenametemplate}). 
ðÏÜÔÏÍÕ ÄÅËÌÁÒÁÃÉÑ \verb+\DeclareGraphicsRule+ ÚÄÅÓØ ÎÅ ÎÕÖÎÁ.
%%Hence, no \verb+\DeclareGraphicsRule+
%%declaration is needed. 
âÏÌÅÅ ÔÏÇÏ, ÒÁÓÛÉÒÅÎÉÅ ÍÏÖÅÔ ÏÐÕÓËÁÔØÓÑ × ËÏÍÁÎÄÅ \verb+\includegraphics+.
%%Moreover, the file extension can then be omitted
%%in the \verb+\includegraphics+ command.

\paragraph{\LaTeX\ É pdf\LaTeX}
åÓÌÉ ×Ù ÈÏÔÉÔÅ ÓÏÈÒÁÎÉÔØ ÇÉÂËÏÓÔØ É ×ÏÚÍÏÖÎÏÓÔØ ËÏÍÐÉÌÉÒÏ×ÁÔØ ËÁË \LaTeX, 
ÔÁË É pdf\LaTeX, ÔÏ ÎÕÖÎÏ ÐÏÚÁÂÏÔÉÔØÓÑ Ï ÎÅËÏÔÏÒÙÈ ×ÅÝÁÈ.
%%If you want to keep flexible and be able to compile your documents with
%%both, \LaTeX\ and pdf\LaTeX, there are some things to take care of. 
óÔÁÎÄÁÒÔÎÁÑ ÄÅËÌÁÒÁÃÉÑ \verb+\DeclareGraphicsRule+ ÍÏÖÅÔ ÂÙÔØ ÁËÔÉ×ÉÒÏ×ÁÎÁ 
ÔÏÌØËÏ, ÅÓÌÉ pdf\LaTeX\ ÉÓÐÏÌÎÑÅÔÓÑ × PDF-ÒÅÖÉÍÅ.
%%If
%%you're using the conventional \verb+\DeclareGraphicsRule+ declaration,
%%that may only be activated if pdf\LaTeX\ runs in PDF mode. 
ðÏÜÔÏÍÕ ÕÎÉ×ÅÒÓÁÌØÎÁÑ ÄÅËÌÁÒÁÃÉÑ ÄÏÌÖÎÁ ×ÙÇÌÑÄÅÔØ ÐÏÄÏÂÎÏ ÜÔÏÊ:
%%A fully-featured declaration should therefore look like this:

$$
\begin{verbatim}
\usepackage{graphicx}
\usepackage{ifpdf}
\ifpdf
  \DeclareGraphicsRule{*}{mps}{*}{}
\fi
\end{verbatim}
$$

åÓÌÉ ×Ù ÉÓÐÏÌØÚÕÅÔÅ ÍÅÔÏÄ \ttt{filenametemplate}, ÔÏ ÒÁÓÛÉÒÅÎÉÅ ÆÁÊÌÁ 
\ttt{mps} ÎÅ ÓÌÅÄÕÅÔ ÏÐÕÓËÁÔØ × ËÏÍÁÎÄÅ \verb+\includegraphics+, Ô.~Ë. 
\ttt{mps} --- ÜÔÏ ÎÅ ÞÁÓÔØ ÉÍÅÎÉ \LaTeX-ÆÁÊÌÁ, ÚÁÐÏÌÎÑÅÍÁÑ ÐÏ-ÕÍÏÌÞÁÎÉÀ.
%%If you're using the \ttt{filenametemplate} method the \ttt{mps} file
%%extension should not be omitted in \verb+\includegraphics+ commands,
%%since \ttt{mps} is not part of \LaTeX's file name completion scheme, by
%%default. 
åÓÌÉ ÒÁÓÛÉÒÅÎÉÅ \ttt{mps} ÐÒÉÓÕÔÓÔ×ÕÅÔ, ÔÏ \LaTeX\ ÏÂÒÁÂÁÔÙ×ÁÅÔ ÜÔÉ 
ÆÁÊÌÙ ËÁË \ttt{eps}-ÆÁÊÌÙ, ÞÔÏ ÏÞÅ×ÉÄÎÏ Ñ×ÌÑÅÔÓÑ ËÏÒÒÅËÔÎÙÍ. 
%%If the \ttt{mps} extension is present, \LaTeX\ handles those
%%files as \ttt{eps} files, which is obviously correct. 
äÌÑ ÄÏÐÏÌÎÉÔÅÌØÎÏÊ ÉÎÆÏÒÍÁÃÉÉ ÓÍ. ÏÐÉÓÁÎÉÅ \verb+\DeclareGraphicsExtensions+%
\index{DeclareGraphicsExtensions?\texttt{\string\DeclareGraphicsExtensions}}
É \verb+\DeclareGraphicsRule+ × ÄÏËÕÍÅÎÔÁÃÉÉ ÐÁËÅÔÏ× \ttt{graphicx} É 
\ttt{graphics}.
%%For more
%%information see the description of \verb+\DeclareGraphicsExtensions+%
%%\index{DeclareGraphicsExtensions?\texttt{\string\DeclareGraphicsExtensions}}
%%and \verb+\DeclareGraphicsRule+ in the documentation of packages
%%\ttt{graphicx} and \ttt{graphics}.

\paragraph{pdf\TeX}
ðÏÌØÚÏ×ÁÔÅÌÉ plain pdf\TeX\ ÄÏÌÖÎÙ ÏÚÎÁËÏÍÉÔØÓÑ Ó ÏÔÄÅÌØÎÏÊ ÐÒÏÇÒÁÍÍÏÊ  
\ttindex{mptopdf}, ËÏÔÏÒÕÀ ÍÏÖÎÏ ÎÁÊÔÉ ×
\url{http://context.aanhet.net/mptopdf.htm}.
%%Users of plain pdf\TeX\ should refer to the standalone macros of the
%%\ttindex{mptopdf} bundle, that can be found at
%%\url{http://context.aanhet.net/mptopdf.htm}.

\paragraph{Con\TeX t}
÷ Con\TeX t\index{ConTeXt?Con\TeX t} ÐÏÄÄÅÒÖËÁ MetaPost ÉÎÔÅÇÒÉÒÏ×ÁÎÁ × 
ÑÄÒÏ. 
%%In Con\TeX t\index{ConTeXt?Con\TeX t} support of MetaPost is integrated
%%in the kernel. 
ïÔÄÅÌØÎÏ ÏÔ ×ÓÔÒÏÅÎÎÏÊ ÇÒÁÆÉËÉ (ÓÍ. ÒÕËÏ×ÏÄÓÔ×Ï ÐÏ MetaFun\index{MetaFun}) 
ÍÏÖÎÏ ÔÁËÖÅ ×ÓÔÒÁÉ×ÁÔØ ÇÒÁÆÉËÕ ÉÚ×ÎÅ ËÏÍÁÎÄÏÊ
\verb+\externalfigure+%
\index{externalfigure?\texttt{\string\externalfigure}}.
%%Apart from inline graphics (see MetaFun\index{MetaFun}
%%manual), one can embed graphics explictely with the
%%\verb+\externalfigure+%
%%\index{externalfigure?\texttt{\string\externalfigure}} command.
úÁÎÕÍÅÒÏ×ÁÎÎÙÅ ÆÁÊÌÙ ÒÁÓÐÏÚÎÁÀÔÓÑ Á×ÔÏÍÁÔÉÞÅÓËÉ, ËÁË ÇÒÁÆÉËÁ Ó 
\ttt{mps}-ÒÁÓÛÉÒÅÎÉÅÍ. 
%%Numbered graphics are recognized automatically, as are graphics with the
%%\ttt{mps} suffix. 
óÐÅÃÉÁÌØÎÙÅ Ó×ÏÊÓÔ×Á, ÔÁËÉÅ ËÁË ÚÁÔÅÎÅÎÉÅ, ÐÒÏÚÒÁÞÎÏÓÔØ, ×ËÌÀÞÅÎÉÅ ÒÉÓÕÎËÏ×, 
Ã×ÅÔÏ×ÏÅ ÐÒÏÓÔÒÁÎÓÔ×Ï É ÐÏÄÏÂÎÙÅ ÏÂÒÁÂÁÔÙ×ÁÀÔÓÑ Á×ÔÏÍÁÔÉÞÅÓËÉ.
%%Special features like shading, transparency, image
%%inclusion, color spaces and such are handled automatically. 
ðÒÁËÔÉÞÅÓËÉ ÐÏÌØÚÏ×ÁÔÅÌÉ Con\TeX t ÂÕÄÕÔ ×ÅÒÏÑÔÎÏ ÏÐÒÅÄÅÌÑÔØ ÇÒÁÆÉËÕ 
MetaPost × ÄÏËÕÍÅÎÔÅ-ÉÓÈÏÄÎÉËÅ, ËÏÔÏÒÙÊ ÉÓÐÏÌØÚÕÅÔ ÎÅËÏÔÏÒÙÅ ÎÏ×ÛÅÓÔ×Á, 
ÎÁÐÒÉÍÅÒ, ÂÏÌÅÅ ÅÓÔÅÓÔ×ÅÎÎÙÊ ÉÎÔÅÒÆÅÊÓ ÓÏ Ó×ÏÊÓÔ×ÁÍÉ ÄÏËÕÍÅÎÔÁ, ÐÏÄÄÅÒÖËÁ 
ÛÒÉÆÔÏ× É Á×ÔÏÍÁÔÉÞÅÓËÁÑ ÏÂÒÁÂÏÔËÁ.
%%In practice
%%Con\TeX t users will probably define MetaPost graphics in the document
%%source which has some advantages, like a more natural interfacing with
%%document properties, font support, and automatic processing.  
ðÏÄÄÅÒÖËÁ ×ËÌÀÞÅÎÉÊ MetaPost ÐÒÅÄÓÔÁ×ÌÅÎÁ × ×ÅÒÓÉÑÈ MkII É MkIV, ÎÏ 
ÉÓÐÏÌØÚÕÅÍÙÅ ÍÅÔÏÄÙ ÓÌÅÇËÁ ÒÁÚÌÉÞÁÀÔÓÑ.
%%Support
%%for MetaPost inclusion is present in the versions MkII as well as MkIV,
%%but the used methods are slightly different. 
âÕÄÕÝÉÅ ×ÅÒÓÉÉ MkIV ÂÕÄÕÔ ÐÏÄÄÅÒÖÉ×ÁÔØ ÄÁÖÅ ÂÏÌÅÅ ÔÅÓÎÕÀ ÉÎÔÅÇÒÁÃÉÀ.
%%Future versions of MkIV
%%will support an even more tight integration.

\paragraph{troff}
ôÁËÖÅ ×ÏÚÍÏÖÎÏ ×ËÌÀÞÁÔØ ×Ù×ÏÄ MetaPost × GNU 
\emph{troff}-ÄÏËÕÍÅÎÔ. 
%%It is also possible to include MetaPost output in a GNU \emph{troff}
%%document.
íÁËÒÏÐÁËÅÔ \ttt{-mpspic}\index{mpspic?\texttt{-mpspic}} ÏÐÒÅÄÅÌÑÅÔ ËÏÍÁÎÄÕ  \verb|.PSPIC|\index{PSPIC?\texttt{.PSPIC}}, ËÏÔÏÒÁÑ ×ËÌÀÞÁÅÔ EPS-ÆÁÊÌ. 
%%The \ttt{-mpspic}\index{mpspic?\texttt{-mpspic}} macro
%%package defines a command \verb|.PSPIC|\index{PSPIC?\texttt{.PSPIC}}
%%that includes an encapsulated PostScript file. 
îÁÐÒÉÍÅÒ, ËÏÍÁÎÄÁ \emph{troff}
%%For instance, the \emph{troff} command
$$ \hbox{\verb|.PSPIC fig.1|} $$
×ËÌÀÞÁÅÔ \ttt{fig.1}, ÉÓÐÏÌØÚÕÑ ÚÁÄÁÎÎÙÅ × ÆÁÊÌÅ ÏÈ×ÁÔÙ×ÁÀÝÅÊ ÒÁÍËÏÊ ÅÓÔÅÓÔ×ÅÎÎÙÅ ×ÙÓÏÔÕ É ÛÉÒÉÎÕ ÏÂÒÁÚÁ. 
%%includes \ttt{fig.1}, using the natural height and width of the
%%image as given in the file's bounding box.

\subsection{ûÁÂÌÏÎÙ ÉÍÅÎ ÆÁÊÌÏ×}
%%\subsection{File name templates}
\suppressfloats[t]

MetaPost ÐÏÄÄÅÒÖÉ×ÁÅÔ ÛÁÂÌÏÎÙ ÄÌÑ ×ÙÈÏÄÎÙÈ ÆÁÊÌÏ×.
%%MetaPost has support for output file name templates. 
üÔÉ ÛÁÂÌÏÎÙ ÉÓÐÏÌØÚÕÀÔ ÓÔÉÌØ \ttt{printf} escape-ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔÅÊ 
É ÐÅÒÅÓÞÉÔÙ×ÁÀÔÓÑ ÐÅÒÅÄ ÔÅÍ, ËÁË ÒÉÓÕÎÏË ÚÁÐÉÓÙ×ÁÅÔÓÑ ÎÁ ÄÉÓË
%%These templates
%%use \ttt{printf}-style escape sequences and are re-evaluated before
%%each figure is written to disk. 

úÄÅÓØ ÉÓÐÏÌØÚÕÅÔÓÑ ËÏÍÁÎÄÁ \ttt{filenametemplate}%
\index{filenametemplate?\texttt{filenametemplate}}\label{Dfilenametemplate},
ËÏÔÏÒÁÑ ×ÏÓÐÒÉÎÉÍÁÅÔ ÓÔÒÏËÕ-ÁÒÇÕÍÅÎÔ.
%%The command to use is \ttt{filenametemplate}%
%%\index{filenametemplate?\texttt{filenametemplate}}\label{Dfilenametemplate},
%%and it accepts a string as argument. 
åÅ ÎÅÓÌÏÖÎÙÊ ÓÉÎÔÁËÓÉÓ:
%%The syntax is as simple as:

\begin{center}\begin{tabular}{l}
\verb|filenametemplate "%j-%3c.mps";|\\
\verb|beginfig(1);|\\
\verb|   draw p;|\\
\verb|endfig;|
\end{tabular}\end{center}

åÓÌÉ ÉÓÈÏÄÎÙÊ ÆÁÊÌ ÓÏÈÒÁÎÑÌÓÑ ËÁË \ttt{fig.mp}, ÔÏ ÂÕÄÅÔ ÓÏÚÄÁÎ ×ÙÈÏÄÎÏÊ ÆÁÊÌ 
\ttt{fig-001.mps} ×ÍÅÓÔÏ \ttt{fig.1}. 
%%If the file is saved as \ttt{fig.mp}, then this will create the output
%%file \ttt{fig-001.mps} instead of \ttt{fig.1}. 
íÁÌÅÎØËÏÅ ÍÎÏÖÅÓÔ×Ï ×ÏÚÍÏÖÎÙÈ escape-ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔÅÊ ÓÍ. × 
ÔÁÂÌÉÃÅ~\ref{tab:fntmpl}. 
%%A small set of escape
%%sequences are possible, see table~\ref{tab:fntmpl} for details.

\def\d{$\langle$0-9$\rangle$}

\begin{table}
\centering
\begin{tabular}{|>{\ttfamily}l|l|}
\hline
\multicolumn1{|c|}{Escape-ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ} & \multicolumn1{c|}{óÍÙÓÌ}\\\hline
%%\multicolumn1{|c|}{Escape sequence} & \multicolumn1{c|}{Meaning}\\\hline
\%\%    & úÎÁË ÐÒÏÃÅÎÔÁ \\
%%\%\%    & A percent sign \\
\%\,j     & éÍÑ ÔÅËÕÝÅÊ ÒÁÂÏÔÙ\\
%%\%\,j     & The current jobname\\
\%\d  c & úÎÁÞÅÎÉÅ {\tt charcode}\\
%%\%\d  c & The charcode value\\
\%\d  y & ôÅËÕÝÉÊ ÇÏÄ\\
%%\%\d  y & The current year\\
\%\d  m & îÏÍÅÒ ÍÅÓÑÃÁ\\
%%\%\d  m & The numeric month\\
\%\d  d & äÅÎØ ÍÅÓÑÃÁ\\
%%\%\d  d & The day of the month\\
\%\d  H & þÁÓ\\
%%\%\d  H & The hour\\
\%\d  M &  íÉÎÕÔÁ\\
%%\%\d  M &  The minute\\
\hline
\end{tabular}
\caption{òÁÚÒÅÛÅÎÎÙÅ escape-ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔÉ ÄÌÑ \ttt{filenametemplate}}
%%\caption{Allowed escape sequences for \ttt{filenametemplate}}
\label{tab:fntmpl}
\end{table}

ðÒÉÍÉÔÉ× \ttt{filenametemplate} ÍÏÖÅÔ ÂÙÔØ ÔÁËÖÅ ÐÏÌÅÚÎÙÍ ÄÌÑ ÉÍÅÎÏ×ÁÎÉÑ 
ÇÒÁÆÉÞÅÓËÉÈ ÆÁÊÌÏ× ÉÎÄÉ×ÉÄÕÁÌØÎÏ É ÅÝÅ ÄÌÑ ÈÒÁÎÅÎÉÑ ×ÓÅÈ 
MetaPost-ÉÓÈÏÄÎÉËÏ× × ÏÄÎÏÍ ÆÁÊÌÅ.
%%The \ttt{filenametemplate} primitive can also be helpful for naming
%%graphic files individually, yet keeping all MetaPost sources in one file.
îÁÐÒÉÍÅÒ, ÓÏÂÅÒÅÍ ÉÓÈÏÄÎÉËÉ ÒÁÚÎÙÈ ÄÉÁÇÒÁÍÍ × ÏÄÉÎ ÆÁÊÌ \ttt{fig.mp} 
%%E.\,g., collecting different diagram sources in a file \ttt{fig.mp}
$$
\begin{verbatim}
filenametemplate "fig-quality.mps";
beginfig(1);
  ...
endfig;

filenametemplate "fig-cost-vs-productivity.mps";
beginfig(2);
  ...
endfig;
\end{verbatim}
$$
--- ÍÏÖÅÔ ÏËÁÚÁÔØÓÑ ÐÒÏÝÅ ×ÓÐÏÍÎÉÔØ ÐÒÁ×ÉÌØÎÏÅ ÉÍÑ ÄÉÁÇÒÁÍÍÙ × ÄÏËÕÍÅÎÔÅ 
\TeX, ÞÅÍ ÎÕÍÅÒÏ×ÁÎÎÏÅ ÉÍÑ ÆÁÊÌÁ.
%%it might be easier to recall the correct diagram names in a 
%%\TeX\ document than with numbered file names.  
úÁÍÅÔØÔÅ, ÞÔÏ ÁÒÇÕÍÅÎÔ \ttt{beginfig} ÎÅ ÉÓÐÏÌØÚÕÅÔÓÑ ÐÒÉ ÏÔÓÕÔÓÔ×ÉÉ 
ÏÂÒÁÚÃÁ \ttt{\%c} × ÓÔÒÏËÅ ÛÁÂÌÏÎÁ ÉÍÅÎÉ ÆÁÊÌÁ.
%%Note, the argument to
%%\ttt{beginfig} is not relevant as long as there's no \ttt{\%c} pattern
%%in the file name template string.

äÌÑ ÏÂÅÓÐÅÞÅÎÉÑ ÓÏ×ÍÅÓÔÉÍÏÓÔÉ ÓÏ ÓÔÁÒÙÍÉ ÆÁÊÌÁÍÉ ÎÁÞÁÌØÎÏÅ ÚÎÁÞÅÎÉÅ 
\ttt{filenametemplate} ÕÓÔÁÎÁ×ÌÉ×ÁÅÔÓÑ × \verb|%j.%c|.
%%To ensure compatibility with older files, the default value of
%%\ttt{filenametemplate} is \verb|%j.%c|.
åÓÌÉ ×Ù ÐÒÉÓ×ÏÉÔÅ ÐÕÓÔÕÀ ÓÔÒÏËÕ, ÔÏ ÜÔÏ ÂÕÄÅÔ ÏÚÎÁÞÁÔØ ×ÏÚ×ÒÁÔ Ë 
ÎÁÞÁÌØÎÏÍÕ ÚÎÁÞÅÎÉÀ.
%%If you assign an empty string, it will revert to that default.

\section{ëÒÉ×ÙÅ}
%%\section{Curves}
\label{curves}

MetaPost ÓÏ×ÅÒÛÅÎÎÏ ÓÞÁÓÔÌÉ× ÐÒÉ ÒÉÓÏ×ÁÎÉÉ ËÁË ËÒÉ×ÙÈ, ÔÁË É ÐÒÑÍÙÈ ÌÉÎÉÊ.
%%MetaPost is perfectly happy to draw curved lines as well as straight ones.
ëÏÍÁÎÄÁ \verb|draw| Ó ÒÁÚÄÅÌÅÎÎÙÍÉ 
\verb|..|\index{..?\texttt{..}} ÁÒÇÕÍÅÎÔÁÍÉ-ÔÏÞËÁÍÉ ÒÉÓÕÅÔ ÐÌÁ×ÎÕÀ 
ËÒÉ×ÕÀ ÞÅÒÅÚ ÜÔÉ ÔÏÞËÉ.
%%A \verb|draw| statement with the points separated by
%%\verb|..|\index{..?\texttt{..}} draws a smooth curve through the points.
îÁÐÒÉÍÅÒ, ÐÏÓÍÏÔÒÉÔÅ ÎÁ ÒÅÚÕÌØÔÁÔ 
%%For example consider the result of
$$ \hbox{\verb|draw z0..z1..z2..z3..z4|} $$
ÐÏÓÌÅ ÏÐÒÅÄÅÌÅÎÉÑ ÐÑÔÉ ÔÏÞÅË ÔÁËÉÍ ÏÂÒÁÚÏÍ:
%%after defining five points as follows:
$$\begin{verbatim}
z0 = (0,0);    z1 = (60,40);
z2 = (40,90);  z3 = (10,70);
z4 = (30,50);
\end{verbatim}
$$
òÉÓ.~\ref{fig2} ÐÏËÁÚÙ×ÁÅÔ ËÒÉ×ÕÀ ÞÅÒÅÚ ÔÏÞËÉ, ÐÏÍÅÞÅÎÎÙÅ ÏÔ \verb|z0| 
ÄÏ \verb|z4|
%%Figure~\ref{fig2} shows the curve with points \verb|z0| through \verb|z4|
%%labeled.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-3}
$$
\caption[ëÒÉ×ÁÑ ÞÅÒÅÚ ÔÏÞËÉ 0, 1, 2, 3 É 4]
	{òÅÚÕÌØÔÁÔ {\tt draw z0..z1..z2..z3..z4}}
%%\caption[A curve through points 0, 1, 2, 3, and 4]
%        {The result of {\tt draw z0..z1..z2..z3..z4}}
\label{fig2}
\end{figure}

åÓÔØ ÍÎÏÇÏ ÄÒÕÇÉÈ ÓÐÏÓÏÂÏ× ÎÁÒÉÓÏ×ÁÔØ ÐÕÔØ ÞÅÒÅÚ ÔÅ ÖÅ ÓÁÍÙÅ ÐÑÔØ ÔÏÞÅË.
%%There are many other ways to draw a curved path through the same five
%%points. 
äÌÑ ÐÏÌÕÞÅÎÉÑ ÇÌÁÄËÏÊ ÚÁÍËÎÕÔÏÊ ËÒÉ×ÏÊ ÓÏÅÄÉÎÉÔÅ \verb|z4| Ó ÎÁÞÁÌÏÍ
ÄÏÂÁ×ÌÅÎÉÅÍ \verb|..cycle|\index{cycle?\texttt{cycle}} Ë ËÏÍÁÎÄÅ 
\verb|draw| ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig3}a. 
%%To make a smooth closed curve, connect \verb|z4| back to the
%%beginning by appending \verb|..cycle|\index{cycle?\texttt{cycle}} to the
%%\verb|draw| statement as shown in Figure~\ref{fig3}a. 
ôÁËÖÅ ×ÏÚÍÏÖÎÏ × ÏÄÎÏÊ ËÏÍÁÎÄÅ \verb|draw| ÓÍÅÛÉ×ÁÔØ ËÒÉ×ÙÅ É ÐÒÑÍÙÅ 
ÌÉÎÉÉ ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig3}b.  
%%It is also
%%possible in a single \verb|draw| statement to mix curves and straight
%%lines as shown in Figure~\ref{fig3}b. 
ðÒÏÓÔÏ ÉÓÐÏÌØÚÕÊÔÅ \verb|--| ÔÁÍ, ÇÄÅ ×Ù ÈÏÔÉÔÅ ÐÒÑÍÙÅ ÌÉÎÉÉ, É \verb|..| 
ÔÁÍ, ÇÄÅ ×Ù ÈÏÔÉÔÅ ËÒÉ×ÙÅ.
%%Just use \verb|--| where you want
%%straight lines and \verb|..| where you want curves. 
ôÁËÉÍ ÏÂÒÁÚÏÍ,
%%Thus
$$ \hbox{\verb|draw z0..z1..z2..z3--z4--cycle|} $$
ÐÒÏÉÚ×ÅÄÅÔ ËÒÉ×ÕÀ ÞÅÒÅÚ ÔÏÞËÉ 0,~1, 2 É~3, ÚÁÔÅÍ ÌÏÍÁÎÕÀ ÌÉÎÉÀ ÉÚ ÔÏÞËÉ~3 
× ÔÏÞËÕ~4 É ÏÂÒÁÔÎÏ × ÔÏÞËÕ~0.
%%produces a curve through points 0,~1, 2, and~3, then a polygonal line from
%%point~3 to point~4 and back to point~0. 
òÅÚÕÌØÔÁÔ ÂÕÄÅÔ ÔÏÞÎÏ ÔÁËÉÍ ÖÅ ËÁË ÐÏÓÌÅ Ä×ÕÈ ËÏÍÁÎÄ ÒÉÓÏ×ÁÎÉÑ
%%The result is essentially the same
%%as having two draw statements
\begin{eqnarray*}
  \hbox{\verb|draw z0..z1..z2..z3|}\\
\noalign{\hbox{É}}
%%\noalign{\hbox{and}}
  \hbox{\verb|draw z3--z4--z0|}
\end{eqnarray*}

\begin{figure}[htp]
$$ {\includegraphics{manfig-ru-104} \atop (a)}
  \qquad {\includegraphics{manfig-ru-204} \atop (b)}
$$
\caption[úÁÍËÎÕÔÁÑ ËÒÉ×ÁÑ ÞÅÒÅÚ ÐÑÔØ ÔÏÞÅË]
        {(a)~òÅÚÕÌØÔÁÔ {\tt draw z0..\linebreak[0]z1..\linebreak[0]%
        z2..\linebreak[0]z3..\linebreak[0]z4..\linebreak[0]cycle};
        (b)~òÅÚÕÌØÔÁÔ {\tt draw z0..\linebreak[0]z1..\linebreak[0]%
        z2..\linebreak[0]z3--\linebreak[0]z4--\linebreak[0]cycle}.}
%%\caption[Closed curves through five points]
%%        {(a)~The result of {\tt draw z0..\linebreak[0]z1..\linebreak[0]%
%%        z2..\linebreak[0]z3..\linebreak[0]z4..\linebreak[0]cycle};
%%        (b)~the result of {\tt draw z0..\linebreak[0]z1..\linebreak[0]%
%%        z2..\linebreak[0]z3--\linebreak[0]z4--\linebreak[0]cycle}.}
\label{fig3}
\end{figure}

\subsection{ëÕÂÉÞÅÓËÉÅ ËÒÉ×ÙÅ âÅÚØÅ}
%%\subsection{B\'ezier Cubic Curves}

ëÏÇÄÁ MetaPost ÐÒÏÓÑÔ ÎÁÒÉÓÏ×ÁÔØ ÇÌÁÄËÕÀ ËÒÉ×ÕÀ ÞÅÒÅÚ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ 
ÔÏÞÅË, ÏÎ ËÏÎÓÔÒÕÉÒÕÅÔ ËÕÓÏÞÎÕÀ ËÕÂÉÞÅÓËÕÀ ËÒÉ×ÕÀ Ó ÎÅÐÒÅÒÙ×ÎÙÍ ÕËÌÏÎÏÍ É 
Ó ÐÒÉÂÌÉÚÉÔÅÌØÎÏ ÎÅÐÒÅÒÙ×ÎÏÊ ËÒÉ×ÉÚÎÏÊ\index{ËÒÉ×ÉÚÎÁ}.
%%When MetaPost is asked to draw a smooth curve through a sequence of
%%points, it constructs a piecewise cubic curve with continuous slope and
%%approximately continuous curvature\index{curvature}. 
üÔÏ ÚÎÁÞÉÔ, ÞÔÏ ÓÐÅÃÉÆÉËÁÃÉÑ ÐÕÔÉ ÔÁËÁÑ ËÁË
%%This means that a
%%path specification such as
$$ \hbox{\verb|z0..z1..z2..z3..z4..z5|} $$
ÄÁÅÔ × ÒÅÚÕÌØÔÁÔÅ ËÒÉ×ÕÀ, ÞÔÏ ÍÏÖÅÔ ÂÙÔØ ÏÐÒÅÄÅÌÅÎÁ 
ÐÁÒÁÍÅÔÒÉÞÅÓËÉ\index{ÐÁÒÁÍÅÔÒÉÚÁÃÉÑ} ËÁË $(X(t),Y(t))$ ÄÌÑ 
$0\leqslant t\leqslant5$, ÇÄÅ $X(t)$ É $Y(t)$ --- ËÕÓÏÞÎÙÅ ËÕÂÉÞÅÓËÉÅ ÆÕÎËÃÉÉ. 
%%results in a curve that can be defined parametrically\index{parameterization}
%%as $(X(t),Y(t))$ for
%%$0\le t\le5$, where $X(t)$ and $Y(t)$ are piecewise cubic functions.
ôÁËÉÍ ÏÂÒÁÚÏÍ ÓÕÝÅÓÔ×ÕÀÔ ÒÁÚÌÉÞÎÙÅ ÐÁÒÙ ËÕÂÉÞÅÓËÉÈ ÆÕÎËÃÉÊ ÄÌÑ ËÁÖÄÏÇÏ ÏÇÒÁÎÉÞÅÎÎÏÇÏ 
ÃÅÌÙÍÉ ÞÉÓÌÁÍÉ ÉÎÔÅÒ×ÁÌÁ ÄÌÑ $t$.
%%That is,
%%there is a different pair of cubic functions for each integer-bounded
%%$t$-interval.
åÓÌÉ ${\tt z0}=(x_0,y_0)$, ${\tt z1}=(x_1,y_1)$,
${\tt z2}=(x_2,y_2)$, \ldots, ÔÏ MetaPost ×ÙÂÉÒÁÅÔ 
ËÏÎÔÒÏÌØÎÙÅ\index{ÕÐÒÁ×ÌÑÀÝÉÅ ÔÏÞËÉ} ÔÏÞËÉ âÅÚØÅ
%%If ${\tt z0}=(x_0,y_0)$, ${\tt z1}=(x_1,y_1)$,
%%${\tt z2}=(x_2,y_2)$, \ldots, MetaPost selects
%%B\'ezier control\index{control points} points
$(x_0^+,y_0^+)$, $(x_1^-,y_1^-)$, $(x_1^+,y_1^+)$, \ldots, 
ÇÄÅ
%%where
\begin{eqnarray*}
  X(t+i) &=& (1-t)^3x_i + 3t(1-t)^2x_i^+ + 3t^2(1-t)x_{i+1}^- + t^3x_{i+1},\\
  Y(t+i) &=& (1-t)^3y_i + 3t(1-t)^2y_i^+ + 3t^2(1-t)y_{i+1}^- + t^3y_{i+1}
\end{eqnarray*}
ÄÌÑ 
%%for 
$0\le t\le1$. 
ôÏÞÎÙÅ ÐÒÁ×ÉÌÁ ÄÌÑ ×ÙÂÏÒÁ ËÏÎÔÒÏÌØÎÙÈ ÔÏÞÅË âÅÚØÅ ÐÒÉ×ÅÄÅÎÙ × \cite{ho:splin} 
É × {\sl \MF book\/}~\cite{kn:c}.
%%The precise rules for choosing the B\'ezier control points
%%are described in \cite{ho:splin} and in {\sl The \MF book\/}~\cite{kn:c}.

äÌÑ ÔÏÇÏ, ÞÔÏÂÙ ÐÕÔØ ÉÍÅÌ ÎÅÐÒÅÒÙ×ÎÙÊ ÕËÌÏÎ × $(x_i,y_i)$ ×ÈÏÄÑÝÅÅ É 
ÉÓÈÏÄÑÝÅÅ ÎÁÐÒÁ×ÌÅÎÉÑ × $(X(i),Y(i))$ ÄÏÌÖÎÙ ÓÏÏÔ×ÅÔÓÔ×Ï×ÁÔØ.
%%In order for the path to have a continuous slope at $(x_i,y_i)$, the incoming
%%and outgoing directions at $(X(i),Y(i))$ must match. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, ×ÅËÔÏÒÁ
%%Thus the vectors
$$ (x_i-x_i^-,\,y_i-y_i^-) \qquad 
\hbox{É}
%%\hbox{and}
   \qquad (x_i^+-x_i,\,y_i^+-y_i)
$$
ÄÏÌÖÎÙ ÉÍÅÔØ ÏÄÉÎÁËÏ×ÏÅ ÎÁÐÒÁ×ÌÅÎÉÅ, Ô.~Å. $(x_i,y_i)$ ÄÏÌÖÎÁ ÂÙÔØ ÎÁ 
ÏÔÒÅÚËÅ ÌÉÎÉÉ ÍÅÖÄÕ $(x_i^-,y_i^-)$ É $(x_i^+,y_i^+)$.
%%must have the same direction; i.e., $(x_i,y_i)$ must be on the line segment
%%between $(x_i^-,y_i^-)$ and $(x_i^+,y_i^+)$. 
üÔÁ ÓÉÔÕÁÃÉÑ ÉÌÌÀÓÔÒÉÒÕÅÔÓÑ ÎÁ ÒÉÓ.~\ref{fig4}, ÇÄÅ ËÏÎÔÒÏÌØÎÙÅ ÔÏÞËÉ âÅÚØÅ, 
×ÙÂÉÒÁÅÍÙÅ MetaPost, ÓÏÅÄÉÎÅÎÙ ÐÕÎËÔÉÒÎÙÍÉ ÌÉÎÉÑÍÉ.
%%This situation is illustrated
%%in Figure~\ref{fig4} where the B\'ezier control points selected by MetaPost
%%are connected by dashed lines. 
äÌÑ ÔÅÈ, ËÔÏ ÚÎÁËÏÍ Ó ÉÎÔÅÒÅÓÎÙÍÉ Ó×ÏÊÓÔ×ÁÍÉ ÔÁËÏÊ ËÏÎÓÔÒÕËÃÉÉ, MetaPost 
ÐÏÚ×ÏÌÑÅÔ ÓÐÅÃÉÆÉÃÉÒÏ×ÁÔØ ËÏÎÔÒÏÌØÎÙÅ ÔÏÞËÉ ÎÁÐÒÑÍÕÀ × ÓÌÅÄÕÀÝÅÍ 
ÆÏÒÍÁÔÅ: \index{controls?\texttt{controls}}
%%For those who are familiar with the interesting
%%properties of this construction, MetaPost allows the control points to be
%%specified directly in the following format:\index{controls?\texttt{controls}}
$$ \begin{verbatim}
draw (0,0)..controls (26.8,-1.8) and (51.4,14.6)
 ..(60,40)..controls (67.1,61.0) and (59.8,84.6)
 ..(40,90)..controls (25.4,94.0) and (10.5,84.5)
 ..(10,70)..controls ( 9.6,58.8) and (18.8,49.6)
 ..(30,50);
\end{verbatim}
$$

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-5}
$$
\caption[ëÒÉ×ÁÑ É ÕÐÒÁ×ÌÑÀÝÁÑ ÌÏÍÁÎÁÑ]
	{òÅÚÕÌØÔÁÔ {\tt draw z0..z1..z2..z3..z4} Ó Á×ÔÏÍÁÔÉÞÅÓËÉ 
        ×ÙÂÉÒÁÅÍÏÊ ÕÐÒÁ×ÌÑÀÝÅÊ ÌÏÍÁÎÏÊ âÅÚØÅ, ÉÌÌÀÓÔÒÉÒÕÅÍÏÊ 
        ÐÕÎËÔÉÒÎÙÍÉ ÌÉÎÉÑÍÉ.}
%%\caption[A curve and the control polygon]
%%        {The result of {\tt draw z0..z1..z2..z3..z4} with the
%%        automatically-selected B\'ezier control polygon illustrated by dashed
%%        lines.}
\label{fig4}
\end{figure}

\subsection{óÐÅÃÉÆÉËÁÃÉÑ ÎÁÐÒÁ×ÌÅÎÉÑ, ÎÁÐÒÑÖÅÎÉÑ É ÉÚÇÉÂÁ}
%%\subsection{Specifying Direction, Tension, and Curl}
\label{tenscurl}

MetaPost ÏÂÅÓÐÅÞÉ×ÁÅÔ ÍÎÏÇÏ ÓÐÏÓÏÂÏ× ÕÐÒÁ×ÌÅÎÉÑ ÐÏ×ÅÄÅÎÉÅÍ ÐÕÔÉ ËÒÉ×ÏÊ 
ÂÅÚ ÄÅÊÓÔ×ÉÔÅÌØÎÏÇÏ ÕËÁÚÁÎÉÑ ËÏÎÔÒÏÌØÎÙÈ ÔÏÞÅË.
%%MetaPost provides many ways of controlling the behavior of a curved path
%%without actually specifying the control points. 
îÁÐÒÉÍÅÒ, ÎÅËÏÔÏÒÙÅ ÔÏÞËÉ ÎÁ ÐÕÔÉ ÍÏÇÕÔ ÂÙÔØ ×ÙÂÒÁÎÙ ËÁË ×ÅÒÔÉËÁÌØÎÙÊ ÉÌÉ 
ÇÏÒÉÚÏÎÔÁÌØÎÙÊ ÜËÓÔÒÅÍÕÍÙ.
%%For instance, some
%%points on the path may be selected as vertical or horizontal extrema.
åÓÌÉ \verb|z1| ÓÌÅÄÕÅÔ ÂÙÔØ ÇÏÒÉÚÏÎÔÁÌØÎÙÍ ÜËÓÔÒÅÍÕÍÏÍ, Á \verb|z2| --- 
×ÅÒÔÉËÁÌØÎÙÍ, ÔÏ ×Ù ÍÏÖÅÔÅ ÕËÁÚÁÔØ, ÞÔÏ $(X(t),Y(t))$ ÄÏÌÖÎÁ ÉÄÔÉ ××ÅÒÈ
× \verb|z1| É ×ÌÅ×Ï × \verb|z2|:
%%If \verb|z1| is to be a horizontal extreme and \verb|z2| is to be a
%%vertical extreme, you can specify that $(X(t),Y(t))$ should go upward at
%%\verb|z1| and to the left at \verb|z2|:
$$ \hbox{\verb|draw z0..z1{up}..z2{left}..z3..z4;|} $$
ëÁÒÔÉÎËÁ-ÒÅÚÕÌØÔÁÔ, ÐÏËÁÚÁÎÎÁÑ ÎÁ ÒÉÓ.~\ref{fig5}, ÉÍÅÅÔ ÖÅÌÁÅÍÙÅ 
×ÅÒÔÉËÁÌØÎÏÅ É ÇÏÒÉÚÏÎÔÁÌØÎÏÅ ÎÁÐÒÁ×ÌÅÎÉÑ × \verb|z1| É \verb|z2|, ÎÏ 
ÏÎÁ ÎÅ ×ÙÇÌÑÄÉÔ ÔÁËÏÊ ÐÌÁ×ÎÏÊ, ËÁË ËÒÉ×ÁÑ ÎÁ ÒÉÓ.~\ref{fig2}. 
%%The resulting shown in Figure~\ref{fig5} has the desired vertical and
%%horizontal directions at \verb|z1| and \verb|z2|, but it does not look
%%as smooth as the curve in Figure~\ref{fig2}. 
üÔÏ ÏÂÕÓÌÏ×ÌÅÎÏ ÂÏÌØÛÉÍ ÒÁÚÒÙ×ÏÍ × ×ÅÌÉÞÉÎÅ ËÒÉ×ÉÚÎÙ \index{ËÒÉ×ÉÚÎÁ} 
× \verb|z1|.
%%The reason is the large
%%discontinuity in curvature\index{curvature} at \verb|z1|.  
åÓÌÉ Ñ×ÎÏ ÎÅ ÕËÁÚÁÔØ ÎÁÐÒÁ×ÌÅÎÉÅ × \verb|z1|, ÔÏ MetaPost-ÉÎÔÅÒÐÒÅÔÁÔÏÒ 
×ÙÂÅÒÅÔ ÎÁÐÒÁ×ÌÅÎÉÅ ÔÁËÉÍ, ÞÔÏÂÙ ËÒÉ×ÉÚÎÁ ÎÁÄ \verb|z1| ÂÙÌÁ ÐÏÞÔÉ 
ÔÁËÏÊ ÖÅ ËÁË É ËÒÉ×ÉÚÎÁ ÐÏÄ ÜÔÏÊ ÔÏÞËÏÊ.
%%If it were
%%not for the specified direction at \verb|z1|, the MetaPost interpreter
%%would have chosen a direction designed to make the curvature above
%%\verb|z1| almost the same as the curvature below that point.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-6}
$$
\caption[ëÒÉ×ÁÑ É ÕÐÒÁ×ÌÑÀÝÁÑ ÌÏÍÁÎÁÑ]
	{òÅÚÕÌØÔÁÔ {\tt draw z0..z1\char`\{up\char`\}..z2\char`\{left\char`\}%
        ..z3..z4}.}
%%\caption[A curve and the control polygon]
%%        {The result of {\tt draw z0..z1\char`\{up\char`\}..z2\char`\{left\char`\}%
%%        ..z3..z4}.}
\label{fig5}
\end{figure}

ëÁË ÍÏÖÅÔ ×ÙÂÏÒ ÎÁÐÒÁ×ÌÅÎÉÊ × ÄÁÎÎÙÈ ÔÏÞËÁÈ ÎÁ ËÒÉ×ÏÊ ÏÐÒÅÄÅÌÑÔØ ÂÕÄÅÔ ÌÉ 
ËÒÉ×ÉÚÎÁ ÎÅÐÒÅÒÙ×ÎÏÊ?
%%How can the choice of directions at given points on a curve determine whether
%%the curvature will be continuous? 
ïÔ×ÅÔ × ÔÏÍ, ÞÔÏ ËÒÉ×ÙÅ, ÉÓÐÏÌØÚÕÅÍÙÅ × MetaPost, ÐÒÉÛÌÉ ÉÚ ÓÅÍÅÊÓÔ×Á, ÇÄÅ 
ÐÕÔØ ÏÐÒÅÄÅÌÑÅÔÓÑ Ó×ÏÉÍÉ ËÏÎÃÁÍÉ É ÎÁÐÒÁ×ÌÅÎÉÑÍÉ ÔÁÍ.
%%The reason is that curves used in MetaPost
%%come from a family where a path is determined by its endpoints and the
%%directions there. 
òÉÓÕÎËÉ \ref{fig6} É~\ref{fig7} ÄÁÀÔ ÈÏÒÏÛÕÀ ÉÄÅÀ Ï ÔÏÍ, ÎÁ ÞÔÏ ÐÏÈÏÖÅ 
ÜÔÏ ÓÅÍÅÊÓÔ×Ï ËÒÉ×ÙÈ.
%%Figures \ref{fig6} and~\ref{fig7} give a good idea of what
%%this family of curves is like.

\begin{figure}[htp]
$$ \mathcenter{\includegraphics{manfig-ru-7}} \quad
\begin{verbatim}
beginfig(7)
for a=0 upto 9:
  draw (0,0){dir 45}..{dir -10a}(6cm,0);
endfor
endfig;
\end{verbatim}
$$
\caption{óÅÍÅÊÓÔ×Ï ËÒÉ×ÙÈ É ÉÎÓÔÒÕËÃÉÉ MetaPost ÄÌÑ ÅÇÏ ÇÅÎÅÒÁÃÉÉ}
%%\caption{A curve family and the MetaPost instructions for generating it}
\label{fig6}
\end{figure}

\begin{figure}[htp]
$$ \mathcenter{\includegraphics{manfig-ru-8}} \quad
\begin{verbatim}
beginfig(8)
for a=0 upto 7:
  draw (0,0){dir 45}..{dir 10a}(6cm,0);
endfor
endfig;
\end{verbatim}
$$
\caption{äÒÕÇÏÅ ÓÅÍÅÊÓÔ×Ï ËÒÉ×ÙÈ Ó ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÍÉ ÉÎÓÔÒÕËÃÉÑÍÉ MetaPost}
%%\caption{Another curve family with the corresponding MetaPost instructions}
\label{fig7}
\end{figure}

òÉÓÕÎËÉ \ref{fig6} É~\ref{fig7} ÉÌÌÀÓÔÒÉÒÕÀÔ ÎÏ×ÙÅ ×ÏÚÍÏÖÎÏÓÔÉ MetaPost.  
%%Figures \ref{fig6} and~\ref{fig7} illustrate a few new MetaPost
%%features. 
ðÅÒ×ÁÑ --- ÜÔÏ ÏÐÅÒÁÔÏÒ {\tt dir}\index{dir?\texttt{dir}}\label{Ddirop}, 
ËÏÔÏÒÙÊ ÐÏ ÕÇÌÕ × ÇÒÁÄÕÓÁÈ ÇÅÎÅÒÉÒÕÅÔ ÅÄÉÎÉÞÎÙÊ ×ÅËÔÏÒ × ÜÔÏÍ ÎÁÐÒÁ×ÌÅÎÉÉ.  
%%The first is the {\tt
%%dir}\index{dir?\texttt{dir}}\label{Ddirop} operator that takes an angle
%%in degrees and generates a unit vector in that direction. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, \verb|dir 0| ÜË×É×ÁÌÅÎÔÅÎ {\tt
right}\index{right?\texttt{right}}\label{Dright} É \verb|dir 90| 
ÜË×É×ÁÌÅÎÔÅÎ {\tt up}\index{up?\texttt{up}}\label{Dup}. 
%%Thus \verb|dir 0| is equivalent to {\tt
%%right}\index{right?\texttt{right}}\label{Dright} and \verb|dir 90| is
%%equivalent to {\tt up}\index{up?\texttt{up}}\label{Dup}. 
åÓÔØ ÔÁËÖÅ ÇÏÔÏ×ÙÅ ×ÅËÔÏÒÁ ÎÁÐÒÁ×ÌÅÎÉÊ {\tt left}\index{left?\texttt{left}}\label{Dleft} É  {\tt
down}\index{down?\texttt{down}}\label{Ddown} ÄÌÑ {\tt dir 180} É {\tt
dir 270}.
%%There are also predefined direction vectors {\tt
%%left}\index{left?\texttt{left}}\label{Dleft} and {\tt
%%down}\index{down?\texttt{down}}\label{Ddown} for {\tt dir 180} and {\tt
%%dir 270}.

÷ÅËÔÏÒÁ ÎÁÐÒÁ×ÌÅÎÉÊ, ÚÁÄÁÎÎÙÅ × \verb|{}|, ÍÏÇÕÔ ÂÙÔØ ÌÀÂÏÊ ÄÌÉÎÙ É ÏÎÉ 
ÍÏÇÕÔ ËÁË ×ÈÏÄÉÔØ × ÔÏÞËÕ, ÔÁË É ×ÙÈÏÄÉÔØ ÉÚ ÎÅÅ.
%%The direction
%%vectors given in \verb|{}| can be of any length, and they can come before a
%%point as well as after one. 
÷ÏÚÍÏÖÎÏ ÄÁÖÅ × ÓÐÅÃÉÆÉËÁÃÉÉ ÐÕÔÉ ÉÍÅÔØ ÏÂÁ ÎÁÐÒÁ×ÌÅÎÉÑ ÄÌÑ ÏÄÎÏÊ ÔÏÞËÉ, ÄÏ É 
ÐÏÓÌÅ.
%%It is even possible for a path specification
%%to have directions given before and after a point. 
îÁÐÒÉÍÅÒ, ÕÞÁÓÔÏË ÓÐÅÃÉÆÉËÁÃÉÉ ÐÕÔÉ
%%For example a path specification containing
$$ \hbox{\verb|..{dir 60}(10,0){up}..|} $$
ÐÒÏÉÚ×ÅÄÅÔ ËÒÉ×ÕÀ Ó ÕÇÌÏÍ × $(10,0)$.
%%produces a curve with a corner at $(10,0)$.

úÁÍÅÔØÔÅ, ÞÔÏ ÎÅËÏÔÏÒÙÅ ËÒÉ×ÙÅ ÎÁ ÒÉÓ.~\ref{fig6} ÉÍÅÀÔ 
ÔÏÞËÉ ÐÅÒÅÇÉÂÁ\index{ÐÅÒÅÇÉÂÙ}.
%%Note that some of the curves in Figure~\ref{fig6} have points of
%%inflection\index{inflections}. 
üÔÏ ÎÅÏÂÈÏÄÉÍÏ ÐÒÉ ÓÏÚÄÁÎÉÉ ÇÌÁÄËÏÊ ËÒÉ×ÏÊ × ÓÉÔÕÁÃÉÉ ÐÏÄÏÂÎÏÊ 
ÒÉÓ.~\ref{fig3}a, ÎÏ ÜÔÏ ×ÅÒÏÑÔÎÏ ÎÅÖÅÌÁÔÅÌØÎÏ ÐÒÉ ÒÁÂÏÔÅ Ó 
×ÅÒÔÉËÁÌØÎÙÍÉ É ÇÏÒÉÚÏÎÔÁÌØÎÙÍÉ ÔÏÞËÁÍÉ ÜËÓÔÒÅÍÕÍÁ ËÁË ÐÏËÁÚÁÎÏ 
ÎÁ ÒÉÓ.~\ref{fig8}a.
%%This is necessary in order to produce
%%smooth curves in situations like Figure~\ref{fig3}a, but it is probably
%%not desirable when dealing with vertical and horizontal extreme points
%%as in Figure~\ref{fig8}a. 
åÓÌÉ \verb|z1| ÎÕÖÎÏ ÓÄÅÌÁÔØ ÎÁÉ×ÙÓÛÅÊ ÔÏÞËÏÊ ÎÁ ËÒÉ×ÏÊ, ÔÏ 
ÜÔÏ ÍÏÖÎÏ ÐÏÌÕÞÉÔØ, ÉÓÐÏÌØÚÕÑ 
\verb|...|\index{...?\texttt{...}} ×ÍÅÓÔÏ \verb|..| × 
ÓÐÅÃÉÆÉËÁÃÉÉ ÐÕÔÉ ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig8}b.
%%If \verb|z1| is supposed to be the topmost
%%point on the curve, this can be achieved by using
%%\verb|...|\index{...?\texttt{...}}  instead of \verb|..| in the path
%%specification as shown in Figure~\ref{fig8}b. 
úÎÁÞÅÎÉÅ \verb|...| --- ÜÔÏ ``×ÙÂÒÁÔØ Ó×ÏÂÏÄÎÙÊ ÏÔ ÐÅÒÅÇÉÂÏ× ÐÕÔØ ÍÅÖÄÕ 
ÜÔÉÍÉ ÔÏÞËÁÍÉ, ÅÓÌÉ ÎÁÐÒÁ×ÌÅÎÉÑ × ËÏÎÃÏ×ÙÈ ÔÏÞËÁÈ ÄÁÀÔ ÔÁËÕÀ ×ÏÚÍÏÖÎÏÓÔØ''. 
%%The meaning of \verb|...|
%%is ``choose an inflection-free path between these points unless the
%%endpoint directions make this impossible.'' 
îÁ ÒÉÓ.~\ref{fig6} ×ÏÚÍÏÖÎÏ ÉÚÂÁ×ÉÔØÓÑ ÏÔ ÐÅÒÅÇÉÂÏ×, Á ÎÁ ÒÉÓ.~\ref{fig7} ÎÅÔ.  
%%(It would be possible to
%%avoid inflections in Figure~\ref{fig6}, but not in Figure~\ref{fig7}).

\begin{figure}[htp]
$$ {\mathcenter{\includegraphics{manfig-ru-109}} \atop
    \hbox{\verb|draw z0{up}..z1{right}..z2{down}|}}
  \quad
   {\mathcenter{\includegraphics{manfig-ru-209}} \atop
    \hbox{\verb|draw z0{up}...z1{right}...z2{down}|}}
$$
\caption{ä×Å ËÏÍÁÎÄÙ {\tt draw} É ËÒÉ×ÁÑ-ÒÅÚÕÌØÔÁÔ.}
%%\caption{Two {\tt draw} statements and the resulting curves.}
\label{fig8}
\end{figure}

äÒÕÇÏÊ ÓÐÏÓÏ ÕÐÒÁ×ÌÑÔØ ÎÅÐÏÄÈÏÄÑÝÉÍ ÐÕÔÅÍ × Õ×ÅÌÉÞÅÎÉÉ ÐÁÒÁÍÅÔÒÁ 
"ÎÁÐÒÑÖÅÎÉÅ"\index{ÎÁÐÒÑÖÅÎÉÅ}.
%%Another way to control a misbehaving path is to increase the
%%``tension''\index{tension} parameter. 
éÓÐÏÌØÚÏ×ÁÎÉÅ \verb|..| × ÓÐÅÃÉÆÉËÁÃÉÉ ÐÕÔÉ ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ ÐÁÒÁÍÅÔÒ 
ÎÁÐÒÑÖÅÎÉÑ × ÔÉÐÏ×ÏÅ ÚÎÁÞÅÎÉÅ 1.
%%Using \verb|..| in a path
%%specification sets the tension parameter to the default value~1.  
åÓÌÉ ÜÔÏ ÄÅÌÁÅÔ ÎÅËÏÔÏÒÕÀ ÞÁÓÔØ ÐÕÔÉ ÓÌÉÛËÏÍ ÄÉËÏÊ, ÔÏ ÍÙ ÍÏÖÅÍ 
×ÙÂÏÒÏÞÎÏ Õ×ÅÌÉÞÉÔØ ÎÁÐÒÑÖÅÎÉÅ.
%%If this makes some part of a path a little too wild, we can selectively
%%increase the tension. 
åÓÌÉ ÒÉÓ.~\ref{fig9}a ÒÁÓÓÍÁÔÒÉ×ÁÅÔÓÑ ËÁË ``ÓÌÉÛËÏÍ ÄÉËÉÊ'',
ÔÏ ËÏÍÁÎÄÁ {\tt draw} × ÓÌÅÄÕÀÝÅÊ ÆÏÒÍÅ Õ×ÅÌÉÞÉÔ ÎÁÐÒÑÖÅÎÉÅ ÍÅÖÄÕ 
{\tt z1} É {\tt z2}:
%%If Figure~\ref{fig9}a is considered ``too wild,''
%%a {\tt draw} statement of the following form increases the tension
%%between {\tt z1} and {\tt z2}:
$$ \hbox{\verb|draw z0..z1..tension 1.3..z2..z3|} $$
üÔÏ ÐÒÏÉÚ×ÅÄÅÔ ÒÉÓ.~\ref{fig9}b.
%%This produces Figure~\ref{fig9}b. 
äÌÑ ÁÓÉÍÍÅÔÒÉÞÎÏÇÏ ÜÆÆÅËÔÁ ÐÏÄÏÂÎÏÇÏ ÒÉÓ.~\ref{fig9}c, ËÏÍÁÎÄÁ \verb|draw| 
ÐÏÌÕÞÁÅÔ ×ÉÄ
%%For an asymmetrical effect like
%%Figure~\ref{fig9}c, the \verb|draw| statement becomes
$$ \hbox{\verb|draw z0..z1..tension 1.5 and 1..z2..z3|} $$
ðÁÒÁÍÅÔÒ ÎÁÐÒÑÖÅÎÉÑ ÍÏÖÅÔ ÂÙÔØ ÍÅÎØÛÉÍ ÅÄÉÎÉÃÙ, ÎÏ ÏÎ ÄÏÌÖÅÎ ÂÙÔØ ÎÅ 
ÍÅÎÅÅ $3\over4$.
%%The tension parameter can be less than one, but it must be at least $3\over4$.

\begin{figure}[htp]
$$ {\mathcenter{\includegraphics{manfig-ru-110}} \atop (a)}
  \quad
   {\mathcenter{\includegraphics{manfig-ru-210}} \atop (b)}
  \quad
   {\mathcenter{\includegraphics{manfig-ru-310}} \atop (c)}
$$
\caption[üÆÆÅËÔ ÉÚÍÅÎÅÎÉÑ ÐÁÒÁÍÅÔÒÁ ÎÁÐÒÑÖÅÎÉÑ]
        {òÅÚÕÌØÔÁÔÙ {\tt draw z0..z1..tension} $\alpha$ {\tt É} $\beta$
        {\tt ..z2..z3} ÄÌÑ ÒÁÚÎÙÈ $\alpha$ É $\beta$:
%%\caption[Effects of changing the tension parameter]
%%        {Results of {\tt draw z0..z1..tension} $\alpha$ {\tt and} $\beta$
%%        {\tt ..z2..z3} for various  $\alpha$ and $\beta$:
        (a)~$\alpha=\beta=1$; (b)~$\alpha=\beta=1.3$;
        (c)~$\alpha=1.5$, $\beta=1$.}
\label{fig9}
\end{figure}

ðÕÔÉ MetaPost ÉÍÅÀÔ ÔÁËÖÅ ÐÁÒÁÍÅÔÒ, ÎÁÚÙ×ÁÅÍÙÊ 
``ÉÚÇÉÂ''\index{curl?\texttt{curl}}, ËÏÔÏÒÙÊ ×ÌÉÑÅÔ ÎÁ ËÏÎÃÙ ÐÕÔÅÊ.
%%MetaPost paths also have a parameter called
%%``curl''\index{curl?\texttt{curl}} that affects the ends of a path.  
ðÒÉ ÏÔÓÕÔÓÔ×ÉÉ ÓÐÅÃÉÆÉËÁÃÉÊ ÎÁÐÒÁ×ÌÅÎÉÑ ÐÅÒ×ÙÊ É ÐÏÓÌÅÄÎÉÊ ÏÔÒÅÚËÉ 
ÎÅÃÉËÌÉÞÅÓËÏÇÏ ÐÕÔÉ --- ÜÔÏ ÐÒÉÂÌÉÚÉÔÅÌØÎÏ ÄÕÇÉ ÏËÒÕÖÎÏÓÔÉ, ËÁË × ÓÌÕÞÁÅ 
$c=1$ ÎÁ ÒÉÓ.~\ref{fig10}.
%%In
%%the absence of any direction specifications, the first and last segments
%%of a non-cyclic path are approximately circular arcs as in the $c=1$
%%case of Figure~\ref{fig10}. 
äÌÑ ÉÓÐÏÌØÚÏ×ÁÎÉÑ ÄÒÕÇÏÇÏ ÚÎÁÞÅÎÉÑ ÄÌÑ ÐÁÒÁÍÅÔÒÁ ÉÚÇÉÂÁ ÕËÁÖÉÔÅ 
\verb|{curl c}| ÄÌÑ ÎÅËÏÔÏÒÏÇÏ ÚÎÁÞÅÎÉÑ $c$.
%%To use a different value for the curl
%%parameter, specify \verb|{curl c}| for some other value of $c$.  
ôÁËÉÍ ÏÂÒÁÚÏÍ,
%%Thus
$$ \hbox{\verb|draw z0{curl c}..z1..{curl c}z2|} $$
ÕÓÔÁÎÏ×ÉÔ ÐÁÒÁÍÅÔÒ ÉÚÇÉÂÁ ÄÌÑ \verb|z0| É \verb|z2|.
%%sets the curl parameter for \verb|z0| and \verb|z2|. 
íÁÌÅÎØËÉÅ ÚÎÁÞÅÎÉÑ ÐÁÒÁÍÅÔÒÁ ÉÚÇÉÂÁ ÕÍÅÎØÛÁÀÔ ËÒÉ×ÉÚÎÕ\index{ËÒÉ×ÉÚÎÁ} 
× ÕËÁÚÁÎÎÙÈ ËÏÎÃÏ×ÙÈ ÔÏÞËÁÈ ÐÕÔÉ, Á ÂÏÌØÛÉÅ ÚÎÁÞÅÎÉÑ Õ×ÅÌÉÞÉ×ÁÀÔ ËÒÉ×ÉÚÎÕ 
ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig10}. 
%%Small values of
%%the curl parameter reduce the curvature\index{curvature} at the
%%indicated path endpoints, while large values increase the curvature as
%%shown in Figure~\ref{fig10}. 
÷ ÞÁÓÔÎÏÓÔÉ, ÚÎÁÞÅÎÉÅ ÉÚÇÉÂÁ ÎÏÌØ ÄÅÌÁÅÔ ËÒÉ×ÉÚÎÕ ÎÕÌÅ×ÏÊ.
%%In particular, a curl value of zero makes
%%the curvature approach zero.

\begin{figure}[htp]
$$ {\mathcenter{\includegraphics{manfig-ru-111}} \atop c=0}
  \qquad
   {\mathcenter{\includegraphics{manfig-ru-211}} \atop c=1}
  \qquad
   {\mathcenter{\includegraphics{manfig-ru-311}} \atop c=2}
  \qquad
   {\mathcenter{\includegraphics{manfig-ru-411}} \atop c=\infty}
$$
\caption[üÆÆÅËÔ ÉÚÍÅÎÅÎÉÑ ÐÁÒÁÍÅÔÒÁ ÉÚÇÉÂÁ]
        {òÅÚÕÌØÔÁÔÙ {\tt draw z0\char`\{curl c\char`\}..z1..%
        \char`\{curl c\char`\}z2} ÄÌÑ ÒÁÚÎÙÈ ÚÎÁÞÅÎÉÊ
        ÐÁÒÁÍÅÔÒÁ ÉÚÇÉÂÁ~$c$.}
%%\caption[Effects of changing the curl parameter]
%%        {Results of {\tt draw z0\char`\{curl c\char`\}..z1..%
%%        \char`\{curl c\char`\}z2} for various values
%%        of the curl parameter~$c$.}
\label{fig10}
\end{figure}

\subsection{ðÏÌÎÙÊ ÓÉÎÔÁËÓÉÓ ÐÕÔÉ}
%%\subsection{Summary of Path Syntax}

åÓÔØ ÅÝÅ ÎÅÓËÏÌØËÏ ÄÒÕÇÉÈ Ó×ÏÊÓÔ× ÓÉÎÔÁËÓÉÓÁ ÐÕÔÉ MetaPost, ÎÏ ÏÎÉ 
ÏÔÎÏÓÉÔÅÌØÎÏ ÎÅ×ÁÖÎÙ.
%%There are a few other features of MetaPost path syntax, but they are
%%relatively unimportant. 
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ \MF\ ÉÓÐÏÌØÚÕÅÔ ÔÁËÏÊ ÖÅ ÓÉÎÔÁËÓÉÓ ÐÕÔÉ, ÚÁÉÎÔÅÒÅÓÏ×ÁÎÎÙÍ 
ÞÉÔÁÔÅÌÑÍ ÓÔÏÉÔ ÐÏÓÍÏÔÒÅÔØ \cite[ÒÁÚÄÅÌ 14]{kn:c}.
%%Since \MF\ uses the same path syntax,
%%interested readers can refer to \cite[chapter 14]{kn:c}.  
ó×ÏÄËÁ ÓÉÎÔÁËÓÉÓÁ ÐÕÔÉ ÎÁ ÒÉÓ.~\ref{sypath} ×ËÌÀÞÁÅÔ ×ÓÅ, 
ÏÂÓÕÖÄÁÅÍÏÅ ÄÏ ÓÉÈ ÐÏÒ, ×ËÌÀÞÁÑ ËÏÎÓÔÒÕËÃÉÉ \verb|--| É \verb|...|, 
ËÏÔÏÒÙÅ \cite{kn:c} ÐÏËÁÚÙ×ÁÅÔ ËÁË ÍÁËÒÏÓÙ, Á ÎÅ ÐÒÉÍÉÔÉ×Ù.
%%The summary of
%%path syntax in Figure~\ref{sypath} includes everything discussed so far
%%including the \verb|--| and \verb|...| constructions which \cite{kn:c}
%%shows to be macros rather than primitives.  
îÅÓËÏÌØËÏ ËÏÍÍÅÎÔÁÒÉÅ× ÐÏ ÓÅÍÁÎÔÉËÅ ÐÒÉ×ÅÄÅÎÙ ÚÄÅÓØ: ÅÓÌÉ ÎÅÐÕÓÔÏÊ 
$\descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ}$ ÓÔÏÉÔ ÐÅÒÅÄ $\descr{ÕÚÌÏÍ ÐÕÔÉ}$, ÎÏ 
ÎÅ ÐÏÓÌÅ, ÉÌÉ ÎÁÏÂÏÒÏÔ, ÔÏ ÕËÁÚÁÎÎÏÅ ÎÁÐÒÁ×ÌÅÎÉÅ (ÉÌÉ ×ÅÌÉÞÉÎÁ ÉÚÇÉÂÁ) 
ÐÒÉÌÁÇÁÅÔÓÑ ËÁË Ë ×ÈÏÄÑÝÉÍ, ÔÁË É Ë ×ÙÈÏÄÑÝÉÍ ÏÔÒÅÚËÁÍ ÐÕÔÉ. 
%%A few comments on the
%%semantics are in order here: If there is a non-empty $\descr{direction
%%specifier}$ before a $\descr{path knot}$ but not after it, or vice
%%versa, the specified direction (or curl amount) applies to both the
%%incoming and outgoing path segments. 
ðÏÈÏÖÅÅ ÓÏÇÌÁÛÅÎÉÅ ÐÒÉÍÅÎÑÅÔÓÑ, ËÏÇÄÁ ÓÐÅÃÉÆÉËÁÔÏÒ $\descr{ÕÐÒÁ×ÌÅÎÉÑ}$ 
ÄÁÅÔ ÔÏÌØËÏ ÏÄÎÕ $\descr{ÐÅÒ×ÉÞÎÕÀ ÐÁÒÕ}$.  
%%A similar arrangement applies when
%%a $\descr{controls}$ specification gives only one $\descr{pair
%%primary}$.  
ôÁËÉÍ ÏÂÒÁÚÏÍ,
%%Thus
$$ \hbox{\verb|..controls (30,20)..|} $$
ÜË×É×ÁÌÅÎÔÎÏ
%%is equivalent to
$$ \hbox{\verb|...controls (30,20) and (30,20)..|} $$

\begin{figure}[htp]
\begin{ctabbing}
$\descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \rightarrow
        \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}$\\
\qquad \= ${}\mid \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ}$\\
\>       ${}\mid \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÓÏÅÄÉÎÉÔÅÌØ ÐÕÔÉ}$ \verb|cycle|\\
$\descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \rightarrow
        \descr{ÕÚÅÌ ÐÕÔÉ}$\\
\>      ${}\mid \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÓÏÅÄÉÎÉÔÅÌØ ÐÕÔÉ} \descr{ÕÚÅÌ ÐÕÔÉ}$\\
$\descr{ÓÏÅÄÉÎÉÔÅÌØ ÐÕÔÉ} \rightarrow
        \hbox{\verb|--|}$\\
\>      ${}\mid \descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ} \descr{ÂÁÚÏ×ÙÊ ÓÏÅÄÉÎÉÔÅÌØ ÐÕÔÉ}
                \descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ}$\\
$\descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ} \rightarrow
        \descr{ÐÕÓÔÏ}$\\
\>      ${}\mid {}$\verb|{curl| $\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\verb|}|\\
\>      ${}\mid {}$\verb|{|$\descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}$\verb|}|\\
\>      ${}\mid {}$\verb|{|$\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\verb|,|%
                $\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\verb|}|\\
$\descr{ÂÁÚÏ×ÙÊ ÓÏÅÄÉÎÉÔÅÌØ ÐÕÔÉ} \rightarrow
        \hbox{\verb|..|}
        \mid \hbox{\verb|...|}
        \mid \hbox{\verb|..|}\descr{ÎÁÐÒÑÖÅÎÉÅ}\hbox{\verb|..|}
        \mid \hbox{\verb|..|}\descr{ÕÐÒÁ×ÌÅÎÉÅ}\hbox{\verb|..|}$\\
$\descr{ÎÁÐÒÑÖÅÎÉÅ} \rightarrow
        \hbox{\verb|tension|}\descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
\>      ${}\mid \hbox{\verb|tension|}\descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}
                \hbox{\verb|and|}\descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
$\descr{ÕÐÒÁ×ÌÅÎÉÅ} \rightarrow
        \hbox{\verb|controls|}\descr{ÐÅÒ×ÉÞÎÁÑ ÐÁÒÁ}$\\
\>      ${}\mid \hbox{\verb|controls|}\descr{ÐÅÒ×ÉÞÎÁÑ ÐÁÒÁ}
                \hbox{\verb|and|}\descr{ÐÅÒ×ÉÞÎÁÑ ÐÁÒÁ}$
%%$\descr{path expression} \rightarrow
%%        \descr{path subexpression}$\\
%%\qquad \= ${}\mid \descr{path subexpression} \descr{direction specifier}$\\
%%\>       ${}\mid \descr{path subexpression} \descr{path join}$ \verb|cycle|\\
%%$\descr{path subexpression} \rightarrow
%%        \descr{path knot}$\\
%%\>      ${}\mid \descr{path expression} \descr{path join} \descr{path knot}$\\
%%$\descr{path join} \rightarrow
%%        \hbox{\verb|--|}$\\
%%\>      ${}\mid \descr{direction specifier} \descr{basic path join}
%%                \descr{direction specifier}$\\
%%$\descr{direction specifier} \rightarrow
%%        \descr{empty}$\\
%%\>      ${}\mid {}$\verb|{curl| $\descr{numeric expression}$\verb|}|\\
%%\>      ${}\mid {}$\verb|{|$\descr{pair expression}$\verb|}|\\
%%\>      ${}\mid {}$\verb|{|$\descr{numeric expression}$\verb|,|%
%%                $\descr{numeric expression}$\verb|}|\\
%%$\descr{basic path join} \rightarrow
%%        \hbox{\verb|..|}
%%        \mid \hbox{\verb|...|}
%%        \mid \hbox{\verb|..|}\descr{tension}\hbox{\verb|..|}
%%       \mid \hbox{\verb|..|}\descr{controls}\hbox{\verb|..|}$\\
%%$\descr{tension} \rightarrow
%%        \hbox{\verb|tension|}\descr{numeric primary}$\\
%%\>      ${}\mid \hbox{\verb|tension|}\descr{numeric primary}
%%                \hbox{\verb|and|}\descr{numeric primary}$\\
%%$\descr{controls} \rightarrow
%%        \hbox{\verb|controls|}\descr{pair primary}$\\
%%\>      ${}\mid \hbox{\verb|controls|}\descr{pair primary}
%%                \hbox{\verb|and|}\descr{pair primary}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ËÏÎÓÔÒÕËÃÉÉ ÐÕÔÉ}
%%\caption{The syntax for path construction}
\label{sypath}
\end{figure}

ðÁÒÁ ËÏÏÒÄÉÎÁÔ, ÐÏÄÏÂÎÁÑ \verb|(30,20)| ÉÌÉ ÐÅÒÅÍÅÎÎÏÊ \verb|z|, 
ÐÒÅÄÓÔÁ×ÌÑÀÝÅÊ ËÏÏÒÄÉÎÁÔÎÕÀ ÐÁÒÕ, --- ÜÔÏ ÔÏ, ÞÔÏ ÎÁ ÒÉÓ.~\ref{sypath} 
ÚÏ×ÅÔÓÑ $\descr{ÐÅÒ×ÉÞÎÏÊ ÐÁÒÏÊ}$.
%%A pair of coordinates like \verb|(30,20)| or a \verb|z| variable that
%%represents a coordinate pair is what Figure~\ref{sypath} calls a
%%$\descr{pair primary}$. 
ðÏÈÏÖÉÍ Ñ×ÌÑÅÔÓÑ $\descr{ÕÚÅÌ ÐÕÔÉ}$ ÚÁ ÉÓËÌÀÞÅÎÉÅÍ ÔÏÇÏ, ÞÔÏ ÏÎ ÍÏÖÅÔ
ÐÒÉÏÂÒÅÔÁÔØ ÄÒÕÇÉÅ ÆÏÒÍÙ, ÔÁËÉÅ ËÁË ×ÙÒÁÖÅÎÉÅ ÐÕÔÉ × ÓËÏÂËÁÈ.
%%A $\descr{path knot}$ is similar except that it
%%can take on other forms such as a path expression in parentheses.
ðÅÒ×ÉÞÎÏÓÔÉ É ×ÙÒÁÖÅÎÉÑ ÒÁÚÌÉÞÎÙÈ ÔÉÐÏ× ÂÕÄÕÔ ÏÂÓÕÖÄÁÔØÓÑ × ÐÏÌÎÏÍ ÏÂßÅÍÅ 
× ÒÁÚÄÅÌÅ~\ref{exprs}.
%%Primaries and expressions of various types will be discussed in full
%%generality in Section~\ref{exprs}.

\section{ìÉÎÅÊÎÙÅ ÕÒÁ×ÎÅÎÉÑ}
%%\section{Linear Equations}
\label{lin.eq}

÷ÁÖÎÙÍ Ó×ÏÊÓÔ×ÏÍ, ×ÚÑÔÙÍ ÉÚ \MF, Ñ×ÌÑÅÔÓÑ ×ÏÚÍÏÖÎÏÓÔØ ÒÅÛÁÔØ ÌÉÎÅÊÎÙÅ 
ÕÒÁ×ÎÅÎÉÑ, ×ÓÌÅÄÓÔ×ÉÅ ÜÔÏÇÏ ÐÒÏÇÒÁÍÍÙ ÍÏÇÕÔ ÐÉÓÁÔØÓÑ × ÞÁÓÔÉÞÎÏ 
ÄÅËÌÁÒÁÔÉ×ÎÏÊ ÍÁÎÅÒÅ. 
%%An important feature taken from \MF\ is the ability to solve linear
%%equations so that programs can be written in a partially declarative fashion.
îÁÐÒÉÍÅÒ, MetaPost-ÉÎÔÅÒÐÒÅÔÁÔÏÒ ÍÏÖÅÔ ÓÞÉÔÁÔØ
%%For example, the MetaPost interpreter can read
$$ \hbox{\verb|a+b=3; 2a=b+3;|} $$
É ×Ù×ÅÓÔÉ, ÞÔÏ $a=2$ É $b=1$.  
%%and deduce that $a=2$ and $b=1$.  
üÔÉ ÖÅ ×ÙÒÁÖÅÎÉÑ ÍÏÇÕÔ ÂÙÔØ ÚÁÐÉÓÁÎÙ ÓÌÅÇËÁ ÂÏÌÅÅ ËÏÍÐÁËÔÎÏ ÐÕÔÅÍ 
ÓÏÅÄÉÎÅÎÉÑ ÉÈ ×ÍÅÓÔÅ ÎÅÓËÏÌØËÉÍÉ ÚÎÁËÁÍÉ ÒÁ×ÅÎÓÔ×Á:
%%The same equations can be written
%%slightly more compactly by stringing them together with multiple equal
%%signs:
$$ \hbox{\verb|a+b = 2a-b = 3;|} $$
ëÁËÉÍ ÂÙ ÓÐÏÓÏÂÏÍ ×Ù ÎÅ ÚÁÄÁ×ÁÌÉ ÕÒÁ×ÎÅÎÉÑ, ×Ù ÍÏÖÅÔÅ ÚÁÔÅÍ ÄÁÔØ 
ËÏÍÁÎÄÕ\index{show?\texttt{show}}
%%Whichever way you give the equations, you can then give the
%%command\index{show?\texttt{show}}
$$ \hbox{\tt show a,b;} $$
ÄÌÑ ÐÒÏÓÍÏÔÒÁ ÚÎÁÞÅÎÉÊ {\tt a} É {\tt b}.
%%to see the values of {\tt a} and {\tt b}.  
MetaPost ÏÔ×ÅÔÉÔ, ÎÁÐÅÞÁÔÁ×
%%MetaPost responds by typing
$$\begin{verbatim}
>> 2
>> 1
\end{verbatim}
$$

úÁÍÅÔØÔÅ, ÞÔÏ {\tt =}\index{=?\texttt{=}} ÎÅ Ñ×ÌÑÅÔÓÑ ÏÐÅÒÁÔÏÒÏÍ ÐÒÉÓ×ÁÉ×ÁÎÉÑ; 
ÏÎ ÐÒÏÓÔÏ ÏÂßÑ×ÌÑÅÔ, ÞÔÏ ÌÅ×ÁÑ ÞÁÓÔØ ÒÁ×ÎÁ ÐÒÁ×ÏÊ.
%%Note that {\tt =}\index{=?\texttt{=}} is not an assignment operator; it
%%simply declares that the left-hand side equals the right-hand side.
ôÁËÉÍ ÏÂÒÁÚÏÍ, {\tt a=a+1} ÐÒÉ×ÅÄÅÔ Ë ÓÏÏÂÝÅÎÉÀ Ï ÏÛÉÂËÅ, ÖÁÌÕÀÝÅÍÕÓÑ 
ÎÁ ``ÐÒÏÔÉ×ÏÒÅÞÉ×ÏÅ ÕÒÁ×ÎÅÎÉÅ\index{Inconsistent equation?\texttt{Inconsistent 
equation}}''.
%%Thus {\tt a=a+1} produces an error message complaining about an
%%``inconsistent equation\index{Inconsistent equation?\texttt{Inconsistent
%%equation}}.'' 
óÐÏÓÏ Õ×ÅÌÉÞÅÎÉÑ ÚÎÁÞÅÎÉÑ {\tt a} --- × ÉÓÐÏÌØÚÏ×ÁÎÉÉ ÏÐÅÒÁÔÏÒÁ 
ÐÒÉÓ×ÁÉ×ÁÎÉÑ\index{ÐÒÉÓ×ÁÉ×ÁÎÉÅ} {\tt :=}\index{:=?\texttt{:=}} ËÁË × 
ÐÒÉÍÅÒÅ:
%%The way to increase the value of {\tt a} is to use the
%%assignment\index{assignment} operator {\tt :=}\index{:=?\texttt{:=}} as
%%follows:
$$ \hbox{\tt a:=a+1;} $$
äÒÕÇÉÍÉ ÓÌÏ×ÁÍÉ, {\tt :=} ÄÌÑ ÉÚÍÅÎÅÎÉÑ ÓÕÝÅÓÔ×ÕÀÝÉÈ ÚÎÁÞÅÎÉÊ, Á 
{\tt =} ÄÌÑ ÚÁÄÁÎÉÑ ÌÉÎÅÊÎÙÈ ÕÒÁ×ÎÅÎÉÊ ÄÌÑ ÒÅÛÅÎÉÑ.
%%In other words, {\tt :=} is for changing existing values while {\tt =} is for
%%giving linear equations to solve.

îÅÔ ÏÇÒÁÎÉÞÅÎÉÊ ÎÁ ÓÍÅÛÉ×ÁÎÉÅ ÕÒÁ×ÎÅÎÉÊ É ÏÐÅÒÁÃÉÊ ÐÒÉÓ×ÁÉ×ÁÎÉÑ, ÎÁÐÒÉÍÅÒ, 
%%There is no restriction against mixing equations and assignment
%%operations as in the following example:
$$ \hbox{\tt a = 2; b = a; a := 3; c = a;} $$
ðÏÓÌÅ ÐÅÒ×ÙÈ Ä×ÕÈ ÕÒÁ×ÎÅÎÉÊ, ÕÓÔÁÎÁ×ÌÉ×ÁÀÝÉÈ {\tt a} É~{\tt b} ÒÁ×ÎÙÍÉ 2, 
ÏÐÅÒÁÃÉÑ ÐÒÉÓ×ÁÉ×ÁÎÉÑ ÉÚÍÅÎÉÔ {\tt a} ÎÁ~3 ÂÅÚ ×ÌÉÑÎÉÑ ÎÁ {\tt b}.
%%After the first two equations set {\tt a} and~{\tt b} equal to 2, the
%%assignment operation changes {\tt a} to~3 without affecting {\tt b}.
ïËÏÎÞÁÔÅÌØÎÏÅ ÚÎÁÞÅÎÉÅ {\tt c} --- 3, Ô.~Ë. ÏÎÏ ÐÒÉÒÁ×ÎÑÅÔÓÑ ÎÏ×ÏÍÕ 
ÚÎÁÞÅÎÉÀ {\tt a}.
%%The final value of {\tt c} is 3 since it is equated to the new value of
%%{\tt a}. 
÷ ÏÂÝÅÍ, ÏÐÅÒÁÃÉÑ ÐÒÉÓ×ÁÉ×ÁÎÉÑ ÉÎÔÅÒÐÒÅÔÉÒÕÅÔÓÑ ÓÎÁÞÁÌÁ ×ÙÞÉÓÌÅÎÉÅÍ ÎÏ×ÏÇÏ 
ÚÎÁÞÅÎÉÑ É ÚÁÔÅÍ ÕÎÉÞÔÏÖÅÎÉÅÍ ÓÔÁÒÏÇÏ ÚÎÁÞÅÎÉÑ ÉÚ ×ÓÅÈ ÓÕÝÅÓÔ×ÕÀÝÉÈ ÕÒÁ×ÎÅÎÉÊ 
ÐÅÒÅÄ ÓÏÂÓÔ×ÅÎÎÏ ÐÒÉÓ×ÁÉ×ÁÎÉÅÍ.
%%In general, an assignment operation is interpreted by first
%%computing the new value, then eliminating the old value from all
%%existing equations before actually assigning the new value.

\subsection{õÒÁ×ÎÅÎÉÑ É ËÏÏÒÄÉÎÁÔÎÙÅ ÐÁÒÙ}
%%\subsection{Equations and Coordinate Pairs}

MetaPost ÍÏÖÅÔ ÔÁËÖÅ ÒÅÛÁÔØ ÌÉÎÅÊÎÙÅ ÕÒÁ×ÎÅÎÉÑ, ÓÏÄÅÒÖÁÝÉÅ ËÏÏÒÄÉÎÁÔÎÙÅ ÐÁÒÙ.
%%MetaPost can also solve linear equations involving coordinate pairs.  
íÙ ÕÖÅ ×ÉÄÅÌÉ ÍÎÏÇÏ ÔÒÉ×ÉÁÌØÎÙÈ ÐÒÉÍÅÒÏ× ÜÔÏÇÏ × ÆÏÒÍÅ ÕÒÁ×ÎÅÎÉÊ, ÐÏÄÏÂÎÙÈ
%%We have
%%already seen many trivial examples of this in the form of equations like
$$ \hbox{\verb|z1=(0,.2in)|} $$
ëÁÖÄÁÑ ÓÔÏÒÏÎÁ ÕÒÁ×ÎÅÎÉÑ ÄÏÌÖÎÁ ÂÙÔØ ÓÆÏÒÍÉÒÏ×ÁÎÁ ÓÌÏÖÅÎÉÅÍ ÉÌÉ ×ÙÞÉÔÁÎÉÅÍ 
ËÏÏÒÄÉÎÁÔÎÙÈ ÐÁÒ É ÕÍÎÏÖÅÎÉÅÍ ÉÌÉ ÄÅÌÅÎÉÅÍ ÉÈ ÎÁ ÉÚ×ÅÓÔÎÙÅ ÞÉÓÌÏ×ÙÅ 
ËÏÌÉÞÅÓÔ×Á.
%%Each side of the equation must be formed by adding or subtracting
%%coordinate pairs and multiplying or dividing them by known numeric
%%quantities.  
äÒÕÇÉÅ ÓÐÏÓÏÂÙ ÉÍÅÎÏ×ÁÎÉÑ ÐÁÒ ÚÎÁÞÅÎÉÊ ÐÅÒÅÍÅÎÎÙÈ ÂÕÄÕÔ ÏÂÓÕÖÄÁÔØÓÑ ÐÏÚÖÅ, 
Á ÐÏËÁ ÒÁÓÓÍÏÔÒÉÍ ÉÍÅÎÏ×ÁÎÉÅ ×ÉÄÁ 
${\tt z}\descr{ÞÉÓÌÏ}$\index{z convention?{\tt z}-ÓÏÇÌÁÛÅÎÉÅ}, ËÏÔÏÒÏÅ ×ÅÓØÍÁ 
ÕÄÏÂÎÏ, ÐÏÔÏÍÕ ÞÔÏ ÏÎÏ --- ÓÏËÒÁÝÅÎÉÅ ÄÌÑ
$$ \hbox{\tt (x}\descr{ÞÉÓÌÏ} \hbox{\tt, y}\descr{ÞÉÓÌÏ}\hbox{\tt)} $$
%%Other ways of naming pair-valued variables will be
%%discussed later, but the ${\tt z}\descr{number}$\index{z convention?{\tt
%%z} convention} is convenient because it is an abbreviation for
%%$$ \hbox{\tt (x}\descr{number} \hbox{\tt, y}\descr{number}\hbox{\tt)} $$
üÔÏ ÄÅÌÁÅÔ ×ÏÚÍÏÖÎÙÍ ÄÁ×ÁÔØ ÚÎÁÞÅÎÉÑ ÐÅÒÅÍÅÎÎÙÍ \verb|z| ÚÁÄÁÎÉÅÍ 
ÕÒÁ×ÎÅÎÉÊ ÄÌÑ ÉÈ ËÏÏÒÄÉÎÁÔ.
%%This makes it possible to give values to \verb|z| variables by giving
%%equations involving their coordinates. 
îÁÐÒÉÍÅÒ, ÔÏÞËÉ {\tt z1}, {\tt z2}, {\tt z3}, É~{\tt z6} ÎÁ ÒÉÓ.~\ref{fig12} 
ÂÙÌÉ ÉÎÉÃÉÁÌÉÚÉÒÏ×ÁÎÙ ÓÌÅÄÕÀÝÉÍÉ ÕÒÁ×ÎÅÎÉÑÍÉ:
%%For instance, points {\tt z1},
%%{\tt z2}, {\tt z3}, and~{\tt z6} in Figure~\ref{fig12} were initialized
%%via the following equations:
\begin{eqnarray*}
  &&\hbox{\verb|z1=-z2=(.2in,0);|} \\
  &&\hbox{\verb|x3=-x6=.3in;|} \\
  &&\hbox{\verb|x3+y3=x6+y6=1.1in;|}
\end{eqnarray*}
÷ ÔÏÞÎÏÓÔÉ ÔÅ ÖÅ ÓÁÍÙÅ ÔÏÞËÉ ÍÏÇÌÉ ÂÙÔØ ÐÏÌÕÞÅÎÙ ÐÒÑÍÏÊ ÕÓÔÁÎÏ×ËÏÊ ÉÈ ÚÎÁÞÅÎÉÊ:
%%Exactly the same points could be obtained by setting their values directly:
$$ \begin{verbatim}
z1=(.2in,0);    z2=(-.2in,0);
z3=(.3in,.8in); z6=(-.3in,1.4in);
\end{verbatim}
$$

ðÏÓÌÅ ÞÔÅÎÉÑ ÕÒÁ×ÎÅÎÉÊ MetaPost-ÉÎÔÅÒÐÒÅÔÁÔÏÒ ÚÎÁÅÔ ÚÎÁÞÅÎÉÑ 
{\tt z1}, {\tt z2}, {\tt z3} É~{\tt z6}.
%%After reading the equations, the MetaPost interpreter knows the values
%%of {\tt z1}, {\tt z2}, {\tt z3}, and~{\tt z6}.  
óÌÅÄÕÀÝÉÊ ÛÁÇ × ËÏÎÓÔÒÕÉÒÏ×ÁÎÉÉ ÒÉÓ.~\ref{fig12} --- ÜÔÏ ÏÐÒÅÄÅÌÅÎÉÅ ÔÏÞÅË 
{\tt z4} É {\tt z5}, ÏÄÉÎÁËÏ×Ï ÕÄÁÌÅÎÎÙÈ ÏÔ {\tt z3} É {\tt z6} É ÌÅÖÁÝÉÈ ÎÁ 
ÏÄÎÏÊ ÌÉÎÉÉ Ó ÎÉÍÉ.
%%The next step in the
%%construction of Figure~\ref{fig12} is to define points {\tt z4} and {\tt
%%z5} equally spaced along the line from {\tt z3} to {\tt z6}. 
ðÏÔÏÍÕ ËÁË ÜÔÁ ÏÐÅÒÁÃÉÑ ÐÏÑ×ÌÑÅÔÓÑ ÞÁÓÔÏ, MetaPost ÉÍÅÅÔ ÄÌÑ ÎÅÅ ÓÐÅÃÉÁÌØÎÙÊ 
ÓÉÎÔÁËÓÉÓ.
%%Since this
%%operation comes up often, MetaPost has a special syntax for it. 
õÓÒÅÄÎÑÀÝÁÑ ËÏÎÓÔÒÕËÃÉÑ\index{ÕÓÒÅÄÎÅÎÉÅ}\index{[]?\texttt{[]}!ÕÓÒÅÄÎÅÎÉÅ} 
%%This
%%mediation construction\index{mediation}\index{[]?\texttt{[]}!mediation}
$$ \hbox{\verb|z4=1/3[z3,z6]|} $$
ÏÚÎÁÞÁÅÔ, ÞÔÏ {\tt z4} ÐÒÏÛÌÁ $1\over3$ ÐÕÔÉ ÏÔ $z3$ ÄÏ $z6$, Ô.~Å.
%%means that {\tt z4} is $1\over3$ of the way from $z3$ to $z6$; i.e.,
$$ {\tt z4}={\tt z3}+{1\over3}({\tt z6}-{\tt z3}). $$
óÈÏÖÁÑ ËÏÎÓÔÒÕËÃÉÑ 
%%Similarly
$$ \hbox{\verb|z5=2/3[z3,z6]|} $$
ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ {\tt z5} ÎÁ $2\over3$ ÐÕÔÉ ÏÔ $z3$ ÄÏ $z6$.
%%makes {\tt z5} $2\over3$ of the way from $z3$ to $z6$.

\begin{figure}[htp]
$$ \begin{verbatim}
beginfig(13);
z1=-z2=(.2in,0);
x3=-x6=.3in;
x3+y3=x6+y6=1.1in;
z4=1/3[z3,z6];
z5=2/3[z3,z6];
z20=whatever[z1,z3]=whatever[z2,z4];
z30=whatever[z1,z4]=whatever[z2,z5];
z40=whatever[z1,z5]=whatever[z2,z6];
draw z1--z20--z2--z30--z1--z40--z2;
pickup pencircle scaled 1pt;
draw z1--z2;
draw z3--z6;
endfig;
\end{verbatim}
\quad \mathcenter{\includegraphics{manfig-ru-13}}
$$
\caption[ëÏÄ MetaPost, ÉÓÐÏÌØÚÕÀÝÉÊ ÌÉÎÅÊÎÙÅ ÕÒÁ×ÎÅÎÉÑ, É ÒÉÓÕÎÏË]
        {ëÏÍÁÎÄÙ MetaPost É ÒÉÓÕÎÏË-ÒÅÚÕÌØÔÁÔ.  ñÒÌÙËÉ ÔÏÞÅË ÄÏÂÁ×ÌÅÎÙ
        Ë ÒÉÓÕÎËÕ ÄÌÑ ÑÓÎÏÓÔÉ.}
%%\caption[MetaPost code and figure using linear equations]
%%        {MetaPost commands and the resulting figure.  Point labels have been
%%        added to the figure for clarity.}
\label{fig12}
\end{figure}

õÓÒÅÄÎÅÎÉÅ ÍÏÖÅÔ ÂÙÔØ ÔÁËÖÅ ÉÓÐÏÌØÚÏ×ÁÎÏ ÄÌÑ ÔÏÇÏ, ÞÔÏÂÙ ÓËÁÚÁÔØ, ÞÔÏ 
ÎÅËÏÔÏÒÁÑ ÔÏÞËÁ ÎÁÈÏÄÉÔÓÑ × ÎÅÉÚ×ÅÓÔÎÏÊ ÐÏÚÉÃÉÉ ÎÁ ÐÒÑÍÏÊ ÍÅÖÄÕ Ä×ÕÍÑ 
ÉÚ×ÅÓÔÎÙÍÉ ÔÏÞËÁÍÉ.
%%Mediation can also be used to say that some point is at an unknown
%%position along the line between two known points.  
îÁÐÒÉÍÅÒ, ÍÙ ÍÏÖÅÍ ××ÅÓÔÉ ÎÏ×ÕÀ ÐÅÒÅÍÅÎÎÕÀ {\tt aa} É ÚÁÐÉÓÁÔØ ÞÔÏ-ÔÏ ×ÒÏÄÅ
%%For instance, we
%%could a introduce new variable {\tt aa} and write something like
$$ \hbox{\verb|z20=aa[z1,z3];|} $$
üÔÏ ÏÚÎÁÞÁÅÔ, ÞÔÏ {\tt z20} --- ÜÔÏ ÎÅÉÚ×ÅÓÔÎÏÅ ÏÔÎÏÛÅÎÉÅ {\tt aa} ÐÕÔÉ 
ÐÏ ÐÒÑÍÏÊ ÍÅÖÄÕ {\tt z1} É {\tt z3}.
%%This says that {\tt z20} is some unknown fraction {\tt aa} of the way
%%along the line between {\tt z1} and {\tt z3}. 
åÝÅ ÏÄÎÏÇÏ ÔÁËÏÇÏ ÏÔÎÏÛÅÎÉÑ ÄÌÑ ÄÒÕÇÏÊ ÌÉÎÉÉ ÄÏÓÔÁÔÏÞÎÏ ÄÌÑ ÆÉËÓÁÃÉÉ 
ÚÎÁÞÅÎÉÑ {\tt z20}.
%%Another such equation
%%involving a different line is sufficient to fix the value of {\tt z20}.
ïÐÉÓÁÎÉÅ ÔÏÇÏ, ÞÔÏ {\tt z20} ÐÅÒÅÓÅÞÅÎÉÅ ÐÒÑÍÙÈ {\tt z1}-{\tt z3}
É {\tt z2}-{\tt z4} ××ÏÄÉÔ ÅÝÅ ÏÄÎÕ ÐÅÒÅÍÅÎÎÕÀ {\tt ab} É ÕÓÔÁÎÁ×ÌÉ×ÁÅÔÓÑ 
%%To say that {\tt z20} is at the intersection of the {\tt z1}-{\tt z3}
%%line and the {\tt z2}-{\tt z4} line, introduce another variable {\tt ab}
%%and set
$$ \hbox{\verb|z20=ab[z2,z4];|} $$
üÔÏ ÐÏÚ×ÏÌÑÅÔ MetaPost ÎÁÊÔÉ {\tt x20}, {\tt y20}, {\tt aa} É {\tt ab}.
%%This allows MetaPost to solve for {\tt x20}, {\tt y20}, {\tt aa}, and {\tt ab}.

îÅÓËÏÌØËÏ ÓÌÏÖÎÏ×ÁÔÏ ÐÏÓÔÏÑÎÎÏ ÄÕÍÁÔØ Ï ÎÏ×ÙÈ ÉÍÅÎÁÈ, ÐÏÄÏÂÎÙÈ {\tt aa} É 
{\tt ab}.
%%It is a little painful to keep thinking up new names like {\tt aa} and
%%{\tt ab}. 
üÔÏÇÏ ÍÏÖÎÏ ÉÚÂÅÖÁÔØ, ÉÓÐÏÌØÚÕÑ ÓÐÅÃÉÁÌØÎÕÀ ×ÏÚÍÏÖÎÏÓÔØ, ÎÁÚÙ×ÁÅÍÕÀ 
{\tt whatever}\index{whatever?\texttt{whatever}}\label{Dwhatev}.
%%This can be avoided by using a special feature called {\tt
%%whatever}\index{whatever?\texttt{whatever}}\label{Dwhatev}.  
üÔÏÔ ÍÁËÒÏÓ ÇÅÎÅÒÉÒÕÅÔ ÎÏ×ÕÀ ÁÎÏÎÉÍÎÕÀ ÐÅÒÅÍÅÎÎÕÀ ËÁÖÄÙÊ ÒÁÚ, ËÏÇÄÁ ÏÎ 
ÐÏÑ×ÌÑÅÔÓÑ.
%%This macro
%%generates a new anonymous variable each time it appears.  
ôÁËÉÍ ÏÂÒÁÚÏÍ, ËÏÍÁÎÄÁ
%%Thus the statement
$$ \hbox{\verb|z20=whatever[z1,z3]=whatever[z2,z4]|} $$
ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ {\tt z20} ËÁË É ÒÁÎØÛÅ, ÎÏ ÏÎÁ ÉÓÐÏÌØÚÕÅÔ 
{\tt whatever} ÄÌÑ ÇÅÎÅÒÁÃÉÉ Ä×ÕÈ {\em ÒÁÚÌÉÞÎÙÈ\/} ÁÎÏÎÉÍÎÙÈ ÐÅÒÅÍÅÎÎÙÈ 
×ÍÅÓÔÏ {\tt aa} É {\tt ab}.
%%sets {\tt z20} as before, except it uses {\tt whatever} to generate two
%%{\em different\/} anonymous variables instead of {\tt aa} and {\tt ab}.
òÉÓ.~\ref{fig12} ÐÏËÁÚÙ×ÁÅÔ ËÁË ÕÓÔÁÎÁ×ÌÉ×ÁÀÔÓÑ {\tt z20}, {\tt z30} É
{\tt z40}.
%%This is how Figure~\ref{fig12} sets {\tt z20}, {\tt z30}, and
%%{\tt z40}.

\subsection{òÁÂÏÔÁ Ó ÎÅÉÚ×ÅÓÔÎÙÍÉ}
%%\subsection{Dealing with Unknowns}

õÒÁ×ÎÅÎÉÑ × ÓÉÓÔÅÍÅ ÔÁËÏÊ, ËÁË ÎÁ ÒÉÓ.~\ref{fig12}, ÍÏÇÕÔ ÂÙÔØ ÚÁÄÁÎÙ × ÌÀÂÏÍ 
ÐÏÒÑÄËÅ, ÎÏ ×ÓÅ ÕÒÁ×ÎÅÎÉÑ ÄÏÌÖÎÙ ÂÙÔØ ÌÉÎÅÊÎÙÍÉ É ×ÓÅ ÐÅÒÅÍÅÎÎÙÅ ÄÏÌÖÎÏ ÂÙÔØ 
×ÏÚÍÏÖÎÙÍ ×ÙÞÉÓÌÉÔØ ÔÏÇÄÁ, ËÏÇÄÁ ÏÎÉ ÐÏÎÁÄÏÂÑÔÓÑ.
%%A system of equations such as those used in Figure~\ref{fig12} can be given in
%%any order as long as all the equations are linear and all the variables can
%%be determined before they are needed. 
üÔÏ ÚÎÁÞÉÔ, ÞÔÏ ÕÒÁ×ÎÅÎÉÑ 
%%This means that the equations
\begin{eqnarray*}
 && \hbox{\verb|z1=-z2=(.2in,0);|}\\
 && \hbox{\verb|x3=-x6=.3in;|}\\
 && \hbox{\verb|x3+y3=x6+y6=1.1in;|}\\
 && \hbox{\verb|z4=1/3[z3,z6];|}\\
 && \hbox{\verb|z5=2/3[z3,z6];|}
\end{eqnarray*}
ÄÏÓÔÁÔÏÞÎÙ ÄÌÑ ÏÐÒÅÄÅÌÅÎÉÑ {\tt z1} É ÏÓÔÁÌØÎÙÈ ÄÏ {\tt z6} É ÐÏÒÑÄÏË 
ÕÒÁ×ÎÅÎÉÊ ÎÅ ×ÁÖÅÎ.
%%suffice to determine {\tt z1} through {\tt z6}, no matter what order the
%%equations are given in. 
ó ÄÒÕÇÏÊ ÓÔÏÒÏÎÙ 
%%On the other hand
$$ \hbox{\verb|z20=whatever[z1,z3]|} $$
ÂÕÄÅÔ ÐÒÁ×ÉÌØÎÏ ÔÏÌØËÏ × ÓÌÕÞÁÅ, ËÏÇÄÁ ÉÚ×ÅÓÔÎÏÅ ÚÎÁÞÅÎÉÅ ÂÙÌÏ ÐÒÅÄ×ÁÒÉÔÅÌØÎÏ 
ÕËÁÚÁÎÏ ÄÌÑ ÒÁÚÎÏÓÔÉ ${\tt z3}-{\tt z1}$, ÐÏÔÏÍÕ ÞÔÏ ÜÔÏ ÕÒÁ×ÎÅÎÉÅ 
ÜË×É×ÁÌÅÎÔÎÏ\index{ÕÓÒÅÄÎÅÎÉÅ}
%%is legal only when a known value has previously been specified for the difference
%%${\tt z3}-{\tt z1}$, because the equation is equivalent
%%to\index{mediation}
$$ \hbox{\verb|z20 = z1 + whatever*(z3-z1)|} $$
É ÔÒÅÂÏ×ÁÎÉÑ ÌÉÎÅÊÎÏÓÔÉ ÎÅ ÐÏÚ×ÏÌÑÀÔ ÕÍÎÏÖÁÔØ ÎÅÉÚ×ÅÓÔÎÙÅ ËÏÍÐÏÎÅÎÔÙ 
${\tt z3}-{\tt z1}$ ÎÁ ÁÎÏÎÉÍÎÙÊ ÎÅÉÚ×ÅÓÔÎÙÊ ÒÅÚÕÌØÔÁÔ 
{\tt whatever}.
%%and the linearity requirement disallows multiplying unknown components
%%of ${\tt z3}-{\tt z1}$ by the anonymous unknown result of {\tt
%%whatever}.  
ïÂÝÅÅ ÐÒÁ×ÉÌÏ × ÔÏÍ, ÞÔÏ ×Ù ÎÅ ÍÏÖÅÔÅ ÕÍÎÏÖÁÔØ Ä×Á ÎÅÉÚ×ÅÓÔÎÙÈ ËÏÌÉÞÅÓÔ×Á, 
ÄÅÌÉÔØ ÎÁ ÎÅÉÚ×ÅÓÔÎÏÅ ËÏÌÉÞÅÓÔ×Ï ÉÌÉ ÉÓÐÏÌØÚÏ×ÁÔØ ÎÅÉÚ×ÅÓÔÎÏÅ ËÏÌÉÞÅÓÔ×Ï × 
ËÏÍÁÎÄÅ {\tt draw}. 
%%The general rule is that you cannot multiply two unknown
%%quantities or divide by an unknown quantity, nor can an unknown quantity
%%be used in a {\tt draw} statement. 
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÒÁÚÒÅÛÅÎÙ ÔÏÌØËÏ ÌÉÎÅÊÎÙÅ ÕÒÁ×ÎÅÎÉÑ, MetaPost-ÉÎÔÅÒÐÒÅÔÁÔÏÒ 
ÍÏÖÅÔ ÌÅÇËÏ ÒÅÛÁÔØ ÕÒÁ×ÎÅÎÉÑ É ÈÒÁÎÉÔØ ÉÎÆÏÒÍÁÃÉÀ Ï ÔÏÍ, ËÁËÉÅ ×ÅÌÉÞÉÎÙ 
ÉÚ×ÅÓÔÎÙ. 
%%Since only linear equations are
%%allowed, the MetaPost interpreter can easily solve the equations and
%%keep track of what values are known.

îÁÉÂÏÌÅÅ ÅÓÔÅÓÔ×ÅÎÎÙÊ ÓÐÏÓÏ ÇÁÒÁÎÔÉÒÏ×ÁÔØ, ÞÔÏ MetaPost ÓÍÏÖÅÔ ×ÏÓÐÒÉÎÑÔØ 
×ÙÒÁÖÅÎÉÅ ÔÉÐÁ 
%%The most natural way to ensure that MetaPost can handle an expression like
$$ \hbox{\verb|whatever[z1,z3]|} $$
× ÇÁÒÁÎÔÉÉ, ÞÔÏ {\tt z1} É {\tt z3} ÉÚ×ÅÓÔÎÙ.
%%is to ensure that {\tt z1} and {\tt z3} are both known.  
ïÄÎÁËÏ ÜÔÏÇÏ × ÄÅÊÓÔ×ÉÔÅÌØÎÏÓÔÉ ÎÅ ÔÒÅÂÕÅÔÓÑ, Ô.~Ë. MetaPost ÓÍÏÖÅÔ ×Ù×ÅÓÔÉ 
ÚÎÁÞÅÎÉÅ ÄÌÑ ${\tt z3}-{\tt z1}$, ÎÅ ÚÎÁÑ ÐÒÅÄ×ÁÒÉÔÅÌØÎÏ {\tt z1} É {\tt z3}.
%%However this is not
%%actually required since MetaPost may be able to deduce a known value for
%%${\tt z3}-{\tt z1}$ before either of {\tt z1} and {\tt z3} are known.
îÁÐÒÉÍÅÒ, MetaPost ×ÏÓÐÒÉÎÉÍÁÅÔ ÐÒÁ×ÉÌØÎÙÍÉ ÕÒÁ×ÎÅÎÉÑ
%%For instance, MetaPost will accept the equations
$$ \hbox{\verb|z3=z1+(.1in,.6in);  z20=whatever[z1,z3];|} $$
É ÐÒÉ ÜÔÏÍ ÎÅ ÂÕÄÅÔ ÓÐÏÓÏÂÅÎ ÏÐÒÅÄÅÌÉÔØ ÌÀÂÕÀ ÉÚ ËÏÍÐÏÎÅÎÔ {\tt z1},
{\tt z3} ÉÌÉ {\tt z20}.
%%but it will not be able to determine any of the components of {\tt z1},
%%{\tt z3}, or {\tt z20}.

üÔÉ ÕÒÁ×ÎÅÎÉÑ ÄÁÀÔ ÞÁÓÔÉÞÎÕÀ ÉÎÆÏÒÍÁÃÉÀ Ï {\tt z1}, {\tt z3} É {\tt z20}.
%%These equations do give partial information about {\tt z1}, {\tt z3},
%%and {\tt z20}. 
èÏÒÏÛÉÊ ÓÐÏÓÏ ÐÏÎÑÔØ ÜÔÏ × ÒÁÓÓÍÏÔÒÅÎÉÉ ÄÒÕÇÏÇÏ ÕÒÁ×ÎÅÎÉÑ 
%%A good way to see this is to give another equation such as
$$ \hbox{\verb|x20-x1=(y20-y1)/6;|} $$
ïÎÏ ÐÒÏÉÚ×ÅÄÅÔ ÓÏÏÂÝÅÎÉÅ Ï ÏÛÉÂËÅ ``{\tt ! Redundant
equation}''\index{Redundant equation?\texttt{Redundant
equation}}\footnote{éÚÂÙÔÏÞÎÏÅ ÕÒÁ×ÎÅÎÉÅ}. 
%%This produces the error message ``{\tt ! Redundant
%%equation}\index{Redundant equation?\texttt{Redundant equation}}.''
MetaPost ÓÞÉÔÁÅÔ, ÞÔÏ ×Ù ÐÙÔÁÅÔÅÓØ ÓÏÏÂÝÁÔØ ÅÍÕ ÞÔÏ-ÔÏ ÎÏ×ÏÅ É ÐÏÜÔÏÍÕ 
ÏÎ ÏÂÙÞÎÏ ÐÒÅÄÕÐÒÅÖÄÁÅÔ ÐÒÉ ÚÁÄÁÎÉÉ ÉÚÂÙÔÏÞÎÏÇÏ ÕÒÁ×ÎÅÎÉÑ.
%%MetaPost assumes that you are trying to tell it something new, so it
%%will usually warn you when you give a redundant equation. 
îÏ×ÏÅ ÕÒÁ×ÎÅÎÉÅ ×ÉÄÁ
%%If the new equation had been
$$ \hbox{\verb|(x20-x1)-(y20-y1)/6=1in;|} $$
ÐÒÏÉÚ×ÅÄÅÔ ÓÏÏÂÝÅÎÉÅ Ï ÏÛÉÂËÅ\index{Inconsistent equation?\texttt{Inconsistent equation}}\footnote{ðÒÏÔÉ×ÏÒÅÞÉ×ÏÅ ÕÒÁ×ÎÅÎÉÅ 
(ÏÔËÌÏÎÅÎÉÅ ÎÁ 71.99979).}
%%the error message would have been\index{Inconsistent
%%equation?\texttt{Inconsistent equation}}
$$ \hbox{\verb|! Inconsistent equation (off by 71.99979).|} $$
üÔÏ ÓÏÏÂÝÅÎÉÅ ÏÂ ÏÛÉÂËÅ ÉÌÌÀÓÔÒÉÒÕÅÔ ÏÛÉÂËÕ ÏËÒÕÇÌÅÎÉÑ\index{ÏÛÉÂËÁ ÏËÒÕÇÌÅÎÉÑ} 
× ÍÅÈÁÎÉÚÍÅ MetaPost ÄÌÑ ÒÅÛÅÎÉÑ ÌÉÎÅÊÎÙÈ ÕÒÁ×ÎÅÎÉÊ.
%%This error message illustrates
%%roundoff\index{roundoff error} error in MetaPost's linear equation solving
%%mechanism. 
ïÛÉÂËÁ ÏËÒÕÇÌÅÎÉÑ --- ÜÔÏ ÏÂÙÞÎÏ ÎÅÓÅÒØÅÚÎÁÑ ÐÒÏÂÌÅÍÁ, ÎÏ ÏÎÁ ÍÏÖÅÔ ×ÙÚ×ÁÔØ 
ÚÁÔÒÕÄÎÅÎÉÅ ÐÒÉ ÐÏÐÙÔËÅ ÎÁÊÔÉ ÐÅÒÅÓÅÞÅÎÉÅ Ä×ÕÈ ÐÏÞÔÉ ÐÁÒÁÌÌÅÌØÎÙÈ ÐÒÑÍÙÈ.
%%Roundoff error
%%is normally not a serious problem. but it is likely to cause trouble if you are
%%trying to do something like find the intersection of two lines that are almost
%%parallel.

\section{÷ÙÒÁÖÅÎÉÑ}
%%\section{Expressions}
\label{exprs}

îÁÓÔÁÌÏ ×ÒÅÍÑ ÄÌÑ ÂÏÌÅÅ ÓÉÓÔÅÍÁÔÉÞÅÓËÏÇÏ ÏÂÚÏÒÁ ÑÚÙËÁ MetaPost.
%%It is now time for a more systematic view of the MetaPost language. 
íÙ ×ÉÄÅÌÉ ÞÉÓÌÏ×ÙÅ ËÏÌÉÞÅÓÔ×Á É ËÏÏÒÄÉÎÁÔÎÙÅ ÐÁÒÙ É ÔÏ, ÞÔÏ ÉÈ ÍÏÖÎÏ 
ÓÏÅÄÉÎÑÔØ ÄÌÑ ÕËÁÚÁÎÉÑ ÐÕÔÉ ÄÌÑ ËÏÍÁÎÄ {\tt draw}.
%%We
%%have seen that there are numeric quantities and coordinate pairs, and
%%that these can be combined to specify paths for {\tt draw} statements.
íÙ ÔÁËÖÅ ×ÉÄÅÌÉ, ËÁË ÐÅÒÅÍÅÎÎÙÅ ÍÏÇÕÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎÙ × ÌÉÎÅÊÎÙÈ ÕÒÁ×ÎÅÎÉÑÈ, 
ÎÏ ÎÅ ÏÂÓÕÖÄÁÌÉ ×ÓÅÈ ÏÐÅÒÁÃÉÊ É ÔÉÐÏ× ÄÁÎÎÙÈ, ÞÔÏ ÍÏÇÕÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎÙ × 
ÕÒÁ×ÎÅÎÉÑÈ. 
%%We have also seen how variables can be used in linear equations, but we
%%have not discussed all the operations and data types that can be used in
%%equations.

éÓÐÏÌØÚÏ×ÁÎÉÅ ËÏÍÁÎÄÙ \index{show?\texttt{show}}\label{Dshow}
$$ {\tt show}\, \descr{×ÙÒÁÖÅÎÉÅ} $$
ÄÌÑ ÐÅÞÁÔÉ ÓÉÍ×ÏÌØÎÏÇÏ ÐÒÅÄÓÔÁ×ÌÅÎÉÑ ÚÎÁÞÅÎÉÑ ÌÀÂÏÇÏ ×ÙÒÁÖÅÎÉÑ ÄÅÌÁÅÔ 
×ÏÚÍÏÖÎÙÍ ÜËÓÐÅÒÉÍÅÎÔÙ Ó ×ÙÒÁÖÅÎÉÑÍÉ ÌÀÂÙÈ ÔÉÐÏ× ÄÁÎÎÙÈ, ×ÓÔÒÅÞÁÀÝÉÈÓÑ ÄÁÌÅÅ.
%%It is possible to experiment with expressions involving any of the data types
%%mentioned below by using the statement\index{show?\texttt{show}}\label{Dshow}
%%$$ {\tt show}\, \descr{expression} $$
%%to ask MetaPost to print a symbolic representation of the value of each
%%expression. 
éÚ×ÅÓÔÎÙÅ ÞÉÓÌÏ×ÙÅ ÚÎÁÞÅÎÉÑ ÐÅÞÁÔÁÀÔÓÑ × ÏÔÄÅÌØÎÙÈ ÓÔÒÏËÁÈ, 
ÐÒÅÄ×ÁÒÑÅÍÙÅ ``{\tt >>} ''.
%%For known numeric values, each is printed on a new line
%%preceded by ``{\tt >>} ''. 
äÒÕÇÉÅ ÔÉÐÙ ÒÅÚÕÌØÔÁÔÁ ÒÁÓÞÅÔÁ ÐÅÞÁÔÁÀÔÓÑ ÐÏÈÏÖÉÍ ÏÂÒÁÚÏÍ, ÚÁ 
ÉÓËÌÀÞÅÎÉÅÍ ÔÏÇÏ, ÞÔÏ ÓÌÏÖÎÙÅ ÚÎÁÞÅÎÉÑ ÉÎÏÇÄÁ ÎÅ ÒÁÓÐÅÞÁÔÙ×ÁÀÔÓÑ ÎÁ ÕÓÔÒÏÊÓÔ×Å 
×Ù×ÏÄÁ.
%%Other types of result are printed similarly,
%%except that complicated values are sometimes not printed on standard
%%output. 
ðÏÓÌÅÄÎÅÅ ÐÒÏÉÚ×ÏÄÉÔ ÓÓÙÌËÕ ÎÁ 
ÆÁÊÌ-ÄÕÂÌÉËÁÔ\index{ÆÁÊÌÙ!ÄÕÂÌÉËÁÔ}, ËÏÔÏÒÁÑ ×ÙÇÌÑÄÉÔ ÐÒÉÍÅÒÎÏ 
ÔÁË\footnote{ËÁÒÔÉÎËÁ (ÓÍ. ÆÁÊÌ-ÄÕÂÌÉËÁÔ)}
%%This produces a reference to the transcript
%%file\index{files!transcript} that looks like this:
$$ \hbox{\tt >> picture (see the transcript file)} $$
åÓÌÉ ×Ù ÚÁÈÏÔÉÔÅ ÒÁÓÐÅÞÁÔËÉ ÎÁ ÔÅÒÍÉÎÁÌÅ ÐÏÌÎÙÈ ÒÅÚÕÌØÔÁÔÏ× ËÏÍÁÎÄÙ 
{\tt show}, ÔÏ ÎÁÚÎÁÞØÔÅ ÐÏÌÏÖÉÔÅÌØÎÏÅ ÚÎÁÞÅÎÉÅ ×ÎÕÔÒÅÎÎÅÊ\index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ} ÐÅÒÅÍÅÎÎÏÊ\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} {\tt
tracingonline}\index{tracingonline?\texttt{tracingonline}}\label{Dtonline}.
%%If you want to the full results of {\tt show} statements to be printed
%%on your terminal, assign a positive value to the internal\index{internal
%%variables} variable\index{variables!internal} {\tt
%%tracingonline}\index{tracingonline?\texttt{tracingonline}}\label{Dtonline}.

\subsection{ôÉÐÙ ÄÁÎÎÙÈ}
%%\subsection{Data Types}

MetaPost × ÄÅÊÓÔ×ÉÔÅÌØÎÏÓÔÉ ÉÍÅÅÔ ÄÅÓÑÔØ ÔÉÐÏ× ÄÁÎÎÙÈ\index{ÔÉÐÙ}: ÞÉÓÌÏ×ÏÊ, 
ÄÌÑ ÐÁÒ, ÄÌÑ ÐÕÔÅÊ, ÔÒÁÎÓÆÏÒÍÁÃÉÉ, Ã×ÅÔÁ (rgb-Ã×ÅÔÁ), cmyk-Ã×ÅÔÁ, ÓÔÒÏËÏ×ÙÊ, 
ÌÏÇÉÞÅÓËÉÊ, ÄÌÑ ËÁÒÔÉÎÏË É ÔÉÐ ÐÅÒÁ. 
%%MetaPost actually has ten basic data types\index{types}: numeric,
%%pair, path, transform, (rgb)color, cmykcolor, string, boolean, picture, and
%%pen. 
äÁ×ÁÊÔÅ ÒÁÓÓÍÁÔÒÉ×ÁÔØ ÉÈ ÐÏ-ÏÄÎÏÍÕ, ÎÁÞÉÎÁÑ Ó ÞÉÓÌÏ×ÏÇÏ ÔÉÐÁ.
%%Let us consider these one at a time beginning with the numeric
%%type.

þÉÓÌÏ×ÙÅ (numeric)\index{ÞÉÓÌÏ×ÏÊ ÔÉÐ} ËÏÌÉÞÅÓÔ×Á ÐÒÅÄÓÔÁ×ÌÑÀÔÓÑ × MetaPost Ó ÆÉËÓÉÒÏ×ÁÎÎÏÊ 
ÄÅÓÑÔÉÞÎÏÊ ÔÏÞËÏÊ\index{ÁÒÉÆÍÅÔÉËÁ} ËÁË ÃÅÌÙÅ, ÕÍÎÏÖÅÎÎÙÅ ÎÁ $1\over65536$.
%%Numeric\index{numeric type} quantities in MetaPost are represented in fixed
%%point arithmetic\index{arithmetic} as
%%integer multiples of $1\over65536$. 
ïÎÉ ÄÏÌÖÎÙ ÏÂÙÞÎÏ ÉÍÅÔØ ÍÏÄÕÌØ, ÍÅÎØÛÉÊ 4096, ÎÏ ÐÒÏÍÅÖÕÔÏÞÎÙÅ ÒÅÚÕÌØÔÁÔÙ ÍÏÇÕÔ 
ÂÙÔØ × ×ÏÓÅÍØ ÒÁÚ ÂÏÌØÛÅ.
%%They must normally have absolute values
%%less than 4096 but intermediate results can be eight times larger.
üÔÏ ÎÅ ÄÏÌÖÎÏ ÂÙÔØ ÐÒÏÂÌÅÍÏÊ ÄÌÑ ÒÁÓÓÔÏÑÎÉÊ ÉÌÉ ÚÎÁÞÅÎÉÊ ËÏÏÒÄÉÎÁÔ, Ô.~Ë. 4096 
PostScript-ÐÕÎËÔÏ× ÓÏÓÔÁ×ÌÑÀÔ ÂÏÌÅÅ 1.4 ÍÅÔÒÁ.
%%This should not be a problem for distances or coordinate values since 4096
%%PostScript points is more than 1.4~meters. 
åÓÌÉ ×ÁÍ ÎÕÖÎÏ ÒÁÂÏÔÁÔØ Ó ÞÉÓÌÁÍÉ ÒÁÚÍÅÒÁ 4096 É ÂÏÌÅÅ, ÔÏ ÕÓÔÁÎÏ×ËÁ ×ÎÕÔÒÅÎÎÅÊ 
ÐÅÒÅÍÅÎÎÏÊ {\tt warningcheck}\index{warningcheck?\texttt{warningcheck}}\label{Dwarncheck} × 
ÎÏÌØ ÐÏÄÁ×ÉÔ ÐÒÅÄÕÐÒÅÖÄÁÀÝÉÅ ÓÏÏÂÝÅÎÉÑ Ï ÂÏÌØÛÉÈ ÞÉÓÌÏ×ÙÈ ËÏÌÉÞÅÓÔ×ÁÈ.
%%If you need to work with numbers
%%of magnitude 4096 or more, setting the internal variable
%%{\tt warningcheck}\index{warningcheck}\label{Dwarncheck} to zero
%%suppresses the warning messages about large numeric quantities.

ôÉÐ pair (ÐÁÒÙ) \index{ÔÉÐ-ÐÁÒÁ} ÐÒÅÄÓÔÁ×ÌÑÅÔÓÑ ËÁË ÐÁÒÁ ÞÉÓÌÏ×ÙÈ ËÏÌÉÞÅÓÔ×.
%%The pair\index{pair type} type is represented as a pair of numeric
%%quantities. 
íÙ ×ÉÄÅÌÉ, ÞÔÏ ÐÁÒÙ ÉÓÐÏÌØÚÕÀÔÓÑ ÄÌÑ ÚÁÄÁÎÉÑ ËÏÏÒÄÉÎÁÔ × ËÏÍÁÎÄÅ {\tt draw}.
%%We have seen that pairs are used to give coordinates in
%%{\tt draw} statements. 
ðÁÒÙ ÍÏÖÎÏ ÓËÌÁÄÙ×ÁÔØ, ×ÙÞÉÔÁÔØ, ÉÓÐÏÌØÚÏ×ÁÔØ × ×ÙÒÁÖÅÎÉÑÈ ÕÓÒÅÄÎÅÎÉÑ, ÕÍÎÏÖÁÔØ É 
ÄÅÌÉÔØ ÎÁ ÞÉÓÌÁ.
%%Pairs can be added, subtracted, used in
%%mediation expressions, or multiplied or divided by numerics.

ôÉÐ ÐÕÔÅÊ (path)\index{ÔÉÐ-ÐÕÔØ} ÕÖÅ ÏÂÓÕÖÄÁÌÓÑ × ËÏÎÔÅËÓÔÅ ËÏÍÁÎÄÙ {\tt draw}, ÎÏ 
ÜÔÏ ÏÂÓÕÖÄÅÎÉÅ ÏÂÏÛÌÏ ÓÔÏÒÏÎÏÊ ÔÏ, ÞÔÏ ÐÕÔÉ ×ÁÖÎÙÅ ÏÔÄÅÌØÎÙÅ ÏÂßÅËÔÙ, ËÏÔÏÒÙÅ 
ÍÏÖÎÏ ÓÏÈÒÁÎÑÔØ É ÉÚÍÅÎÑÔØ. 
%%Paths\index{path type} have already been discussed in the context of {\tt draw}
%%statements, but
%%that discussion did not mention that paths are first-class objects that can be
%%stored and manipulated. 
ðÕÔØ ÐÒÅÄÓÔÁ×ÌÑÅÔ ÐÒÑÍÕÀ ÌÉÎÉÀ ÉÌÉ ËÒÉ×ÕÀ, ÏÐÒÅÄÅÌÑÅÍÙÅ ÐÁÒÁÍÅÔÒÉÞÅÓËÉ.
%%A path represents a straight or curved line that is
%%defined parametrically.

äÒÕÇÏÊ ÔÉÐ ÄÁÎÎÙÈ ÐÒÅÄÓÔÁ×ÌÑÅÔ ÐÒÏÉÚ×ÏÌØÎÕÀ ÁÆÆÉÎÎÕÀ 
ÔÒÁÎÓÆÏÒÍÁÃÉÀ (transform)\index{ÔÉÐ-ÔÒÁÎÓÆÏÒÍÁÃÉÑ}. 
%%Another data type represents an arbitrary affine
%%transformation\index{transform type}. 
{\em ôÒÁÎÓÆÏÒÍÁÃÉÑ} ÍÏÖÅÔ ÂÙÔØ ÌÀÂÏÊ ËÏÍÂÉÎÁÃÉÅÊ ×ÒÁÝÅÎÉÊ, ÍÁÓÛÔÁÂÉÒÏ×ÁÎÉÊ, 
ÎÁËÌÏÎÏ× É ÓÄ×ÉÇÏ×.
%%A {\em transform\/} can be any
%%combination of rotating, scaling, slanting, and shifting. 
åÓÌÉ ${\tt
p}=(p_x,p_y)$ --- ÜÔÏ ÐÁÒÁ É {\tt T} --- ÜÔÏ 
ÔÒÁÎÓÆÏÒÍÁÃÉÑ,\index{transformed?\texttt{transformed}} ÔÏ
$$ \hbox{\tt p transformed T} $$
%%If ${\tt
%%p}=(p_x,p_y)$ is a pair and {\tt T} is a
%%transform,\index{transformed?\texttt{transformed}}
%%$$ \hbox{\tt p transformed T} $$
--- ÜÔÏ ÐÁÒÁ ×ÉÄÁ
%%is a pair of the form
$$ (t_x+t_{xx}p_x+t_{xy}p_y, t_y+t_{yx}p_x+t_{yy}p_y), $$
ÇÄÅ 6 ÞÉÓÌÏ×ÙÈ ËÏÌÉÞÅÓÔ× $(t_x,t_y,t_{xx},t_{xy},t_{yx},t_{yy})$ 
ÏÐÒÅÄÅÌÑÀÔ {\tt T}.
%%where the six numeric quantities $(t_x,t_y,t_{xx},t_{xy},t_{yx},t_{yy})$
%%determine {\tt T}. 
ôÒÁÎÓÆÏÒÍÁÃÉÉ ÍÏÇÕÔ ÂÙÔØ ÐÒÉÍÅÎÉÍÙ Ë ÐÕÔÑÍ, ÒÉÓÕÎËÁÍ, ÐÅÒØÑÍ É ÔÒÁÎÓÆÏÒÍÁÃÉÑÍ. 
%%Transforms can also be applied to paths, pictures, pens,
%%and transforms.

ôÉÐ Ã×ÅÔÁ (color)\index{ÔÉÐ-Ã×ÅÔ} ÐÏÄÏÂÅÎ ÔÉÐÕ ÐÁÒÙ, ÎÏ ÏÎ ÉÍÅÅÔ ÔÒÉ ËÏÍÐÏÎÅÎÔÙ 
×ÍÅÓÔÏ Ä×ÕÈ É ËÁÖÄÁÑ ËÏÍÐÏÎÅÎÔÁ ÏÂÙÞÎÏ ÎÁÈÏÄÉÔÓÑ × ÄÉÁÐÁÚÏÎÅ ÏÔ 0 ÄÏ 1.
%%The color\index{color type} type is like the pair type, except
%%that it has three components instead of two and each component is
%%normally between 0 and 1. 
ðÏÄÏÂÎÏ ÐÁÒÁÍ, Ã×ÅÔÁ ÍÏÇÕÔ ÓËÌÁÄÙ×ÁÔØÓÑ, ×ÙÞÉÔÁÔØÓÑ, ÉÓÐÏÌØÚÏ×ÁÔØÓÑ × ×ÙÒÁÖÅÎÉÑ ÕÓÒÅÄÎÅÎÉÑ, ÕÍÎÏÖÁÔØÓÑ É ÄÅÌÉÔØÓÑ ÎÁ ÞÉÓÌÁ.
%%Like pairs, colors can be added,
%%subtracted, used in mediation expressions, or multiplied or divided
%%by numerics. 
ã×ÅÔÁ ÍÏÇÕÔ ÚÁÄÁ×ÁÔØÓÑ ÐÒÉ ÐÏÍÏÝÉ ËÏÎÓÔÁÎÔ \ttindex{black}\label{Dblack}, \ttindex{white}\label{Dwhite},
\ttindex{red}\label{Dred}, \ttindex{green}\label{Dgreen},
\ttindex{blue}\label{Dblue} ÉÌÉ Ñ×ÎÏ ÚÁÄÁÎÎÙÍÉ ËÒÁÓÎÏÊ, ÚÅÌÅÎÏÊ É ÓÉÎÅÊ 
ËÏÍÐÏÎÅÎÔÁÍÉ.
%%Colors can be specified in terms of the predefined
%%constants \ttindex{black}\label{Dblack}, \ttindex{white}\label{Dwhite},
%%\ttindex{red}\label{Dred}, \ttindex{green}\label{Dgreen},
%%\ttindex{blue}\label{Dblue}, or the red, green, and
%%blue components can be given explicitly. 
þÅÒÎÙÊ --- ÜÔÏ {\tt (0,0,0)} É ÂÅÌÙÊ --- ÜÔÏ {\tt (1,1,1)}.  
%%Black is {\tt (0,0,0)} and
%%white is {\tt (1,1,1)}. 
õÒÏ×ÅÎØ ÓÅÒÏÇÏ, ÔÁËÏÊ ËÁË {\tt (.4,.4,.4)}, ÍÏÖÎÏ ÔÁËÖÅ ÚÁÄÁÔØ ËÁË 
{\tt 0.4white}. 
%%A level of gray such as {\tt (.4,.4,.4)} can also be
%%specified as {\tt 0.4white}. 
èÏÔÑ Ã×ÅÔÏ×ÏÊ ÐÅÒÅÍÅÎÎÏÊ ÍÏÖÅÔ ÂÙÔØ ÌÀÂÁÑ ÕÐÏÒÑÄÏÞÅÎÎÁÑ ÔÒÏÊËÁ, ÐÒÉ 
ÄÏÂÁ×ÌÅÎÉÉ ÏÂßÅËÔÁ Ë ËÁÒÔÉÎËÅ MetaPost ÐÒÅÏÂÒÁÚÕÅÔ ÅÅ Ã×ÅÔÁ ÏÂÒÅÚËÏÊ 
ËÁÖÄÏÊ Ã×ÅÔÏ×ÏÊ ËÏÍÐÏÎÅÎÔÙ ÄÏ ÄÉÁÐÁÚÏÎÁ ÏÔ 0 ÄÏ 1.
%%Although color typed variables may be
%%any ordered triplet, when adding an object to a picture, MetaPost will
%%convert its color by clipping each component between 0 and 1. 
îÁÐÒÉÍÅÒ, MetaPost ÂÕÄÅÔ ×Ù×ÏÄÉÔØ Ã×ÅÔ (1,2,3) ËÁË (1,1,1).
%%For
%%example, MetaPost will output the color (1,2,3) as (1,1,1).
MetaPost ÒÅÛÁÅÔ ÌÉÎÅÊÎÙÅ ÕÒÁ×ÎÅÎÉÑ Ó Ã×ÅÔÁÍÉ ÔÁËÉÍ ÖÅ ÏÂÒÁÚÏÍ ËÁË É Ó ÐÁÒÁÍÉ. 
%%MetaPost solves linear equations involving
%%colors the same way it does for pairs. 
ôÉÐ `rgbcolor' (rgb-Ã×ÅÔ) --- ÜÔÏ ÓÉÎÏÎÉÍ ÔÉÐÁ `color' (Ã×ÅÔ).
%%The type `rgbcolor' is an alias of.
%%type `color'. 

ôÉÐ cmykcolor\index{ÔÉÐ-cmyk-Ã×ÅÔ} (cmyk-Ã×ÅÔÁ) ÐÏÄÏÂÅÎ ÔÉÐÕ color, ÎÏ 
ÉÍÅÅÔ ÞÅÔÙÒÅ ËÏÍÐÏÎÅÎÔÙ ×ÍÅÓÔÏ ÔÒÅÈ.
%%The cmykcolor\index{cmykcolor type} type is similar to the color
%%type except that it has four components instead of three. 
üÔÏÔ ÔÉÐ ÉÓÐÏÌØÚÕÅÔÓÑ ÄÌÑ ÚÁÄÁÎÉÑ Ã×ÅÔÏ× ÉÈ ÚÅÌÅÎÏÇÏÌÕÂÏÊ (cyan), 
ÐÕÒÐÕÒÎÏËÒÁÓÎÏÊ (magenta), ÖÅÌÔÏÊ É ÞÅÒÎÏÊ ËÏÍÐÏÎÅÎÔÁÍÉ.
%%This type is used to
%%specify colors by their cyan, magenta, yellow, and black components explicitly.
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ cmyk-Ã×ÅÔ ÉÓÐÏÌØÚÕÅÔ ËÒÁÓËÉ ×ÍÅÓÔÏ Ó×ÅÔÏ×ÙÈ ÌÕÞÅÊ, ÂÅÌÙÊ 
Ã×ÅÔ ÂÕÄÅÔ ×ÙÒÁÖÁÔØÓÑ ËÁË {\tt (0,0,0,0)} É ÞÅÒÎÙÊ ËÁË {\tt (0,0,0,1)}.
%%Because CMYK colors deal with pigments instead of light rays, the color
%%black would be expressed as {\tt (1,1,1,1)} and white as {\tt (0,0,0,0)}.
ôÅÏÒÅÔÉÞÅÓËÉ Ã×ÅÔÁ {\tt ($c$,$m$,$y$,1)} É {\tt (1,1,1,$k$)} ÄÏÌÖÎÙ ÄÁ×ÁÔØ ÞÅÒÎÙÊ 
ÄÌÑ ÌÀÂÙÈ ÚÎÁÞÅÎÉÊ $c$, $m$, $y$ É~$k$.
%%In theory, the colors
%%{\tt ($c$,$m$,$y$,1)} and {\tt (1,1,1,$k$)} should result in black for
%%any values of $c$, $m$, $y$ and~$k$, too. 
îÁ ÐÒÁËÔÉËÅ ÜÔÏÇÏ ÉÚÂÅÇÁÀÔ, Ô.~Ë. ÜÔÏ ÔÒÁÔÉÔ Ã×ÅÔÎÙÅ ÞÅÒÎÉÌÁ É ÍÏÖÅÔ ÐÒÉ×ÏÄÉÔØ Ë 
ÎÅÕÄÏ×ÌÅÔ×ÏÒÉÔÅÌØÎÙÍ ÒÅÚÕÌØÔÁÔÁÍ.
%%But in practice, this is
%%avoided since it is a waste of colored ink and can lead to
%%unsatisfactory results.

óÔÒÏËÉ (string)\index{ÓÔÒÏËÏ×ÙÊ ÔÉÐ} ÐÒÅÄÓÔÁ×ÌÑÀÔ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÓÉÍ×ÏÌÏ×.
%%A string\index{string type} represents a sequence of characters.
óÔÒÏËÏ×ÙÅ ËÏÎÓÔÁÎÔÙ\index{ÓÔÒÏËÏ×ÙÅ ËÏÎÓÔÁÎÔÙ} ÚÁÄÁÀÔÓÑ × Ä×ÏÊÎÙÈ ËÁ×ÙÞËÁÈ
\hbox{\verb|"ÐÏÄÏÂÎÏ ÜÔÏÊ"|}.
%%String constants\index{string constants} are given
%%in double quotes \hbox{\verb|"like this"|}.  
óÔÒÏËÏ×ÙÅ ËÏÎÓÔÁÎÔÙ ÎÅ ÍÏÇÕÔ ÓÏÄÅÒÖÁÔØ Ä×ÏÊÎÙÈ ËÁ×ÙÞÅË ÉÌÉ ÐÅÒÅÈÏÄÏ× ÎÁ ÎÏ×ÕÀ 
ÓÔÒÏËÕ, ÎÏ ÅÓÔØ ÓÐÏÓÏ ËÏÎÓÔÒÕÉÒÏ×ÁÔØ ÓÔÒÏËÉ, ÓÏÄÅÒÖÁÝÉÅ ÌÀÂÕÀ 
ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ×ÏÓØÍÉÂÉÔÎÙÈ ÚÎÁËÏ×.
%%String constants cannot contain
%%double quotes or newlines, but there is a way to construct a string containing
%%any sequence of eight-bit characters.

\label{Dscantokens}
ðÒÅÏÂÒÁÚÏ×ÁÎÉÅ ÓÔÒÏË × ÄÒÕÇÉÅ ÔÉÐÙ, ÏÂÙÞÎÏ ÞÉÓÌÏ×ÙÅ, ×ÏÚÍÏÖÎÏ ÐÒÉÍÉÔÉ×ÏÍ 
{\tt scantokens}\index{scantokens?\texttt{scantokens}}:
\begin{center}\texttt{n := scantokens(}\textit{ÓÔÒÏËÁ}\texttt{);}\end{center}
%%Conversion from strings to other types, notably numeric, can be accomplished by
%%the {\tt scantokens}\index{scantokens?\texttt{scantokens}} primitive:
%%\begin{center}\texttt{n := scantokens(}\textit{str}\texttt{);}\end{center}
âÏÌÅÅ ÁÂÓÔÒÁËÔÎÏ, \texttt{scantokens} ÒÁÚÂÉÒÁÅÔ ÓÔÒÏËÕ ÎÁ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ 
ÚÎÁËÏ×, ÔÁËÖÅ ËÁË MetaPost ÓÞÉÔÙ×ÁÌ ÂÙ ÉÈ ÐÒÉ ××ÏÄÅ.
%%More generally, \texttt{scantokens} parses a string into a token
%%sequence, as if MetaPost had read it as input.

ìÏÇÉÞÅÓËÉÊ\index{ÌÏÇÉÞÅÓËÉÊ ÔÉÐ} ÔÉÐ (boolean) ÉÍÅÅÔ ËÏÎÓÔÁÎÔÙ {\tt
true}\index{true?\texttt{true}}\label{Dtrue} É {\tt
false}\index{false?\texttt{false}}\label{Dfalse} É ÏÐÅÒÁÔÏÒÙ {\tt
and}\index{and?\texttt{and}}\label{Dand}, {\tt
or}\index{or?\texttt{or}}\label{Dor}, {\tt
not}\index{not?\texttt{not}}\label{Dnot}.
%%The boolean\index{boolean type} type has the constants {\tt
%%true}\index{true?\texttt{true}}\label{Dtrue} and {\tt
%%false}\index{false}\label{Dfalse} and the operators {\tt
%%and}\index{and?\texttt{and}}\label{Dand}, {\tt
%%or}\index{or?\texttt{or}}\label{Dor}, {\tt
%%not}\index{not?\texttt{not}}\label{Dnot}. 
ïÔÎÏÛÅÎÉÑ \verb|=| É \verb|<>|\index{<>?\texttt{<>}}\label{Dcmpar} 
ÐÒÏ×ÅÒÑÀÔ ÏÂßÅËÔÙ ÌÀÂÙÈ ÔÉÐÏ× ÎÁ ÒÁ×ÅÎÓÔ×Ï É ÎÅÒÁ×ÅÎÓÔ×Ï\index{ÎÅÒÁ×ÅÎÓÔ×Ï}.
%%The relations \verb|=| and
%%\verb|<>|\index{<>?\texttt{<>}}\label{Dcmpar} test objects of any type
%%for equality and inequality\index{inequality}.
ïÔÎÏÛÅÎÉÑ ÓÒÁ×ÎÅÎÉÑ \index{ÓÒÁ×ÎÅÎÉÅ} \verb|<|\index{<?\texttt{<}},
\verb|<=|\index{<=?\texttt{<=}}, \verb|>|\index{>?\texttt{>}} É 
\verb|>=|\index{>=?\texttt{>=}} ÏÐÒÅÄÅÌÑÀÔÓÑ ÓÌÏ×ÁÒÎÏ ÄÌÑ ÓÔÒÏË É 
ÏÂÙÞÎÙÍ ÓÐÏÓÏÂÏÍ ÄÌÑ ÞÉÓÅÌ.
%%Comparison\index{comparison} relations \verb|<|\index{<?\texttt{<}},
%%\verb|<=|\index{<=?\texttt{<=}}, \verb|>|\index{>?\texttt{>}}, and
%%\verb|>=|\index{>=?\texttt{>=}} are defined lexicographically for
%%strings and in the obvious way for numerics. 
ïÔÎÏÛÅÎÉÑ ÐÏÒÑÄËÁ ÏÐÒÅÄÅÌÅÎÙ ÔÁËÖÅ É ÄÌÑ ÌÏÇÉÞÅÓËÉÈ ×ÅÌÉÞÉÎ, ÐÁÒ, Ã×ÅÔÏ× É 
ÔÒÁÎÓÆÏÒÍÁÃÉÊ, ÎÏ ÐÒÁ×ÉÌÁ ÉÈ ÓÒÁ×ÎÅÎÉÑ ÎÅ ÓÔÏÉÔ ÏÂÓÕÖÄÁÔØ ÚÄÅÓØ.
%%Ordering relations are
%%also defined for booleans, pairs, colors, and transforms, but the
%%comparison rules are not worth discussing here.

ôÉÐ ÄÁÎÎÙÈ picture\index{ÔÉÐ-ÒÉÓÕÎÏË} (ÒÉÓÕÎÏË) --- ÜÔÏ × ÔÏÞÎÏÓÔÉ ÔÏ, ÞÔÏ 
ÐÏÄÒÁÚÕÍÅ×ÁÅÔÓÑ ÅÇÏ ÉÍÅÎÅÍ.
%%The picture\index{picture type} data type is just what the name implies.
÷ÓÅ, ÞÔÏ ÍÏÖÎÏ ÎÁÒÉÓÏ×ÁÔØ × MetaPost, ÍÏÖÎÏ ÓÏÈÒÁÎÉÔØ × ÐÅÒÅÍÅÎÎÏÊ-ËÁÒÔÉÎËÅ.
%%Anything that can be drawn in MetaPost can be stored in a picture
%%variable.  
æÁËÔÉÞÅÓËÉ ËÏÍÁÎÄÁ {\tt draw}\index{draw?\texttt{draw}} ÓÏÈÒÁÎÑÅÔ Ó×ÏÉ 
ÒÅÚÕÌØÔÁÔÙ × ÏÓÏÂÏÊ ÐÅÒÅÍÅÎÎÏÊ-ËÁÒÔÉÎËÅ, ÎÁÚÙ×ÁÅÍÏÊ {\tt
currentpicture}\index{currentpicture?\texttt{currentpicture}}. 
%%In fact, the {\tt draw}\index{draw?\texttt{draw}} statement
%%actually stores its results in a special picture variable called {\tt
%%currentpicture}\index{currentpicture?\texttt{currentpicture}}. 
ëÁÒÔÉÎËÉ ÍÏÇÕÔ ÂÙÔØ ÄÏÂÁ×ÌÅÎÙ Ë ÄÒÕÇÉÍ ËÁÒÔÉÎËÁÍ É ÉÈ ÍÏÖÎÏ ÔÒÁÎÓÆÏÒÍÉÒÏ×ÁÔØ.
%%Pictures
%%can be added to other pictures and operated on by transforms.

îÁËÏÎÅÃ, ÔÉÐ ÄÁÎÎÙÈ, ÎÁÚÙ×ÁÅÍÙÊ pen\index{ÔÉÐ-ÐÅÒÏ} (ÐÅÒÏ).
%%Finally, there is a data type called a pen\index{pen type}. 
çÌÁ×ÎÁÑ ÆÕÎËÃÉÑ ÐÅÒØÅ× × MetaPost × ÏÐÒÅÄÅÌÅÎÉÉ ÔÏÌÝÉÎÙ ÌÉÎÉÉ, ÎÏ ÉÈ 
ÔÁËÖÅ ÍÏÖÎÏ ÉÓÐÏÌØÚÏ×ÁÔØ ÄÌÑ ÄÏÓÔÉÖÅÎÉÑ ËÁÌÌÉÇÒÁÆÉÞÅÓËÉÈ ÜÆÆÅËÔÏ×.
%%The main
%%function of pens in MetaPost is to determine line thickness, but they
%%can also be used to achieve calligraphic effects.  
ëÏÍÁÎÄÁ\index{pickup?\texttt{pickup}}\label{Dpickup}
$$ {\tt pickup\ }\descr{×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ} $$
ÏÂÕÓÌÏ×ÉÔ ÉÓÐÏÌØÚÏ×ÁÎÉÅ ÚÁÄÁÎÎÏÇÏ ÐÅÒÁ × ÐÏÓÌÅÄÕÀÝÉÈ ËÏÍÁÎÄÁÈ {\tt draw}.
%%The statement\index{pickup?\texttt{pickup}}\label{Dpickup}
%%$$ {\tt pickup\ }\descr{pen expression} $$
%%causes the given pen to be used in subsequent {\tt draw} statements.

ïÂÙÞÎÏ ×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ ÉÍÅÅÔ ÆÏÒÍÕ
$$ {\tt pencircle\ scaled\ }\descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}. $$
%%Normally, the pen expression is of the form
%%$$ {\tt pencircle\ scaled\ }\descr{numeric primary}. $$
ïÎÏ ÏÐÒÅÄÅÌÑÅÔ ËÒÕÇÏ×ÏÅ ÐÅÒÏ, ÐÒÏÉÚ×ÏÄÑÝÅÅ ÌÉÎÉÉ ÐÏÓÔÏÑÎÎÏÊ ÔÏÌÝÉÎÙ.
%%This defines a circular pen that produces lines of constant thickness.
åÓÌÉ ÖÅÌÁÔÅÌØÎÙ ËÁÌÌÉÇÒÁÆÉÞÅÓËÉÅ ÜÆÆÅËÔÙ, ÔÏ ×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ ÍÏÖÅÔ ÂÙÔØ 
ÐÒÉÓÐÏÓÏÂÌÅÎÏ ÄÌÑ ÚÁÄÁÎÉÑ ÜÌÌÉÐÔÉÞÅÓËÏÇÏ ÉÌÉ ÍÎÏÇÏÕÇÏÌØÎÏÇÏ ÐÅÒÁ.
%%If calligraphic effects are desired, the pen expression can be adjusted to give
%%an elliptical pen or a polygonal pen.

\subsection{ïÐÅÒÁÔÏÒÙ}
%%\subsection{Operators}

åÓÔØ ÍÎÏÇÏ ÒÁÚÎÙÈ ÓÐÏÓÏÂÏ× ÓÄÅÌÁÔØ ×ÙÒÁÖÅÎÉÑ ÄÅÓÑÔÉ ÂÁÚÏ×ÙÈ ÔÉÐÏ×, ÎÏ 
ÂÏÌØÛÉÎÓÔ×Ï ÏÐÅÒÁÃÉÊ ÍÏÖÎÏ ÓÏÐÏÓÔÁ×ÉÔØ ÓÒÁ×ÎÉÔÅÌØÎÏ ÐÒÏÓÔÏÍÕ 
ÓÉÎÔÁËÓÉÓÕ Ó ÞÅÔÙÒØÍÑ ÕÒÏ×ÎÑÍÉ ÐÒÉÏÒÉÔÅÔÁ ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{syexpr}.
%%There are many different ways to make expressions of the ten basic
%%types, but most of the operations fit into a fairly simple syntax with
%%four levels of precedence as shown in Figure~\ref{syexpr}. 
åÓÔØ ÐÅÒ×ÉÞÎÏÓÔÉ\index{ÐÅÒ×ÉÞÎÏÓÔØ?\tdescr{ÐÅÒ×ÉÞÎÏÓÔØ}},
×ÔÏÒÉÞÎÏÓÔÉ\index{×ÔÏÒÉÞÎÏÓÔØ?\tdescr{×ÔÏÒÉÞÎÏÓÔØ}},
ÔÒÅÔÉÞÎÏÓÔÉ\index{ÔÒÅÔÉÞÎÏÓÔØ?\tdescr{ÔÒÅÔÉÞÎÏÓÔØ}} É 
×ÙÒÁÖÅÎÉÑ\index{×ÙÒÁÖÅÎÉÅ?\tdescr{×ÙÒÁÖÅÎÉÅ}} ËÁÖÄÏÇÏ ÉÚ ÂÁÚÏ×ÙÈ ÔÉÐÏ×, 
ÐÏÜÔÏÍÕ ÓÉÎÔÁËÓÉÞÅÓËÉÅ ÐÒÁ×ÉÌÁ ÍÏÇÕÔ ÕÔÏÞÎÑÔØÓÑ ÄÌÑ ÒÁÂÏÔÙ Ó ÔÁËÉÍÉ 
ÓÕÝÎÏÓÔÑÍÉ ËÁË \tdescr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}, \tdescr{ÌÏÇÉÞÅÓËÁÑ ÔÒÅÔÉÞÎÏÓÔØ} 
É Ô.~Ä.
%%There are
%%primaries\index{primary?\tdescr{primary}},
%%secondaries\index{secondary?\tdescr{secondary}},
%%tertiaries\index{tertiary?\tdescr{tertiary}}, and
%%expressions\index{expression?\tdescr{expression}} of each of the basic
%%types, so the syntax rules could be specialized to deal with items such
%%as \tdescr{numeric primary}, \tdescr{boolean tertiary}, etc. 
üÔÏ ÐÏÚ×ÏÌÑÅÔ ÔÉÐÕ ÒÅÚÕÌØÔÁÔÁ ÏÐÅÒÁÃÉÉ ÚÁ×ÉÓÅÔØ ÏÔ ×ÙÂÏÒÁ ÏÐÅÒÁÔÏÒÁ É ÔÉÐÏ× 
ÏÐÅÒÁÎÄÏ×.
%%This
%%allows the result type for an operation to depend on the choice of
%%operator and the types of its operands. 
îÁÐÒÉÍÅÒ, ÏÔÎÏÛÅÎÉÅ {\tt <} --- ÜÔÏ \tdescr{ÔÒÅÔÉÞÎÁÑ ÂÉÎÁÒÎÏÓÔØ}, ËÏÔÏÒÕÀ 
ÍÏÖÎÏ ÐÒÉÍÅÎÉÔØ Ë \tdescr{ÞÉÓÌÏ×ÏÍÕ ×ÙÒÁÖÅÎÉÀ} É Ë \tdescr{ÞÉÓÌÏ×ÏÊ ÔÒÅÔÉÞÎÏÓÔÉ} 
ÄÌÑ ÐÏÌÕÞÅÎÉÑ \tdescr{ÌÏÇÉÞÅÓËÏÇÏ ×ÙÒÁÖÅÎÉÑ}.
%%For example, the {\tt <}
%%relation is a \tdescr{tertiary binary} that can be applied to a
%%\tdescr{numeric expression} and a \tdescr{numeric tertiary} to give a
%%\tdescr{boolean expression}. 
üÔÏÔ ÖÅ ÏÐÅÒÁÔÏÒ ÍÏÖÅÔ ÄÏÐÕÓËÁÔØ ÄÒÕÇÉÅ ÔÉÐÙ ÏÐÅÒÁÎÄÏ× ÔÁËÉÅ ËÁË 
\tdescr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} É \tdescr{ÓÔÒÏËÏ×ÁÑ ÔÒÅÔÉÞÎÏÓÔØ}, ÎÏ 
ÒÅÚÕÌØÔÁÔÏÍ × ÓÌÕÞÁÅ ÎÅÓÏ×ÐÁÄÅÎÉÑ ÔÉÐÏ× ÏÐÅÒÁÎÄÏ× ÂÕÄÅÔ ÓÏÏÂÝÅÎÉÅ Ï 
ÏÛÉÂËÅ.
%%The same operator can accept other operand
%%types such as \tdescr{string expression} and \tdescr{string tertiary},
%%but an error message results if the operand types do not match.

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÐÅÒ×ÉÞÎÏÓÔØ} \rightarrow \descr{ÐÅÒÅÍÅÎÎÁÑ}$\\
%%$\tt \descr{primary} \rightarrow \descr{variable}$\\
$\tt \qquad \;|\; \hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; \hbox{\tt (}\descr{expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; \descr{ÏÐÅÒÁÔÏÒ 0-ÕÒÏ×ÎÑ}$\\
%%$\tt \qquad \;|\; \descr{nullary op}$\\
$\tt \qquad \;|\; \descr{of-ÏÐÅÒÁÔÏÒ} \descr{×ÙÒÁÖÅÎÉÅ}
        of \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{of operator} \descr{expression}
%%        of \descr{primary}$\\
$\tt \qquad \;|\; \descr{ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{unary op} \descr{primary}$\\
$\tt \descr{×ÔÏÒÉÞÎÏÓÔØ} \rightarrow \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \descr{secondary} \rightarrow \descr{primary}$\\
$\tt \qquad \;|\; \descr{×ÔÏÒÉÞÎÏÓÔØ} \descr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎ. ÏÐ-Ò} \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{secondary} \descr{primary binop} \descr{primary}$\\
$\tt \descr{ÔÒÅÔÉÞÎÏÓÔØ} \rightarrow \descr{×ÔÏÒÉÞÎÏÓÔØ}$\\
%%$\tt \descr{tertiary} \rightarrow \descr{secondary}$\\
$\tt \qquad \;|\; \descr{ÔÒÅÔÉÞÎÏÓÔØ} \descr{×ÔÏÒÉÞÎÙÊ ÂÉÎ. ÏÐ-Ò}
        \descr{×ÔÏÒÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{tertiary} \descr{secondary binop}
%%        \descr{secondary}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ} \rightarrow \descr{ÔÒÅÔÉÞÎÏÓÔØ}$\\
%%$\tt \descr{expression} \rightarrow \descr{tertiary}$\\
$\tt \qquad \;|\; \descr{×ÙÒÁÖÅÎÉÅ} \descr{ÔÒÅÔÉÞÎÙÊ ÂÉÎ. ÏÐ-Ò}
        \descr{ÔÒÅÔÉÞÎÏÓÔØ}$
%%$\tt \qquad \;|\; \descr{expression} \descr{tertiary binop}
%%        \descr{tertiary}$
\end{ctabbing}
\caption{ïÂÝÉÅ ÓÉÎÔÁËÓÉÞÅÓËÉÅ ÐÒÁ×ÉÌÁ ÄÌÑ ×ÙÒÁÖÅÎÉÊ}
%%\caption{The overall syntax rules for expressions}
\index{ÕÎÁÒÎÙÊ op?\tdescr{ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}} \index{ÏÐÅÒÁÔÏÒ 0?\tdescr{ÏÐÅÒÁÔÏÒ 0-ÕÒÏ×ÎÑ}}
\index{ÐÅÒ×ÉÞÎÙÊ binop?\tdescr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}
\index{×ÔÏÒÉÞÎÙÊ binop?\tdescr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}
\index{ÔÒÅÔÉÞÎÙÊ binop?\tdescr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}
%%\index{unary op?\tdescr{unary op}} \index{nullary op?\tdescr{nullary op}}
%%\index{primary binop?\tdescr{primary binop}}
%%\index{secondary binop?\tdescr{secondary binop}}
%%\index{tertiary binop?\tdescr{tertiary binop}}
\label{syexpr}
\end{figure}

ïÐÅÒÁÔÏÒÙ ÕÍÎÏÖÅÎÉÑ É ÄÅÌÅÎÉÑ, {\tt *}\label{Dmldiv} É~{\tt
/}, --- ÐÒÉÍÅÒÙ ÔÏÇÏ, ÞÔÏ ÎÁ ÒÉÓ.~\ref{syexpr} ÚÏ×ÅÔÓÑ \tdescr{ÐÅÒ×ÉÞÎÙÍ 
ÂÉÎÁÒÎÙÍ ÏÐÅÒÁÔÏÒÏÍ}.
%%The multiplication and division operators {\tt *}\label{Dmldiv} and~{\tt
%%/} are examples of what Figure~\ref{syexpr} calls a \tdescr{primary
%%binop}. 
ëÁÖÄÙÊ ÉÚ ÎÉÈ ÍÏÖÅÔ ÄÏÐÕÓËÁÔØ Ä×Á ÞÉÓÌÏ×ÙÈ ÏÐÅÒÁÎÄÁ ÉÌÉ ÏÄÉÎ ÞÉÓÌÏ×ÏÊ 
ÏÐÅÒÁÎÄ É ÏÄÉÎ ÔÉÐÁ ÐÁÒÁ ÉÌÉ Ã×ÅÔ.
%%Each can accept two numeric operands or one numeric operand and
%%one operand of type pair or color. 
ïÐÅÒÁÔÏÒ ×ÏÚ×ÅÄÅÎÉÑ × ÓÔÅÐÅÎØ \verb|**|\index{**?\texttt{**}}\index{ÓÔÅÐÅÎØ}\label{Dpow} 
--- ÜÔÏ \tdescr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}, ËÏÔÏÒÙÊ ÔÒÅÂÕÅÔ Ä×Á ÞÉÓÌÏ×ÙÈ ÏÐÅÒÁÎÄÁ.
%%The exponentiation operator
%%\verb|**|\index{**?\texttt{**}}\index{exponentiation}\label{Dpow} is a
%%\tdescr{primary binop} that requires two numeric operands. 
òÁÚÍÅÝÅÎÉÅ ÅÇÏ ÎÁ ÔÏÍ ÖÅ ÕÒÏ×ÎÅ ÐÒÉÏÒÉÔÅÔÁ, ÞÔÏ É ÕÍÎÏÖÅÎÉÅ É ÄÅÌÅÎÉÅ, ÉÍÅÅÔ 
ÎÅÐÒÉÑÔÎÏÅ ÐÏÓÌÅÄÓÔ×ÉÅ × ÔÏÍ, ÞÔÏ \verb|3*a**2| ÚÎÁÞÉÔ $(3a)^2$, Á ÎÅ 
$3(a^2)$\index{ÎÅÒÅÇÕÌÑÒÎÏÓÔÉ ÒÁÚÂÏÒÁ}.
%%Placing this
%%at the same level of precedence as multiplication and division has the
%%unfortunate consequence that \verb|3*a**2| means $(3a)^2$, not
%%$3(a^2)$\index{parsing irregularities}. 
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÕÎÁÒÎÙÊ ÍÉÎÕÓ\label{Dneg} ÏÔÎÏÓÉÔÓÑ Ë ÐÅÒ×ÉÞÎÏÍÕ ÕÒÏ×ÎÀ, ÏÎ ÔÁËÖÅ 
ÐÒÉ×ÏÄÉÔ Ë ÎÅÕÄÏÂÏÞÉÔÁÅÍÏÓÔÉ ÔÉÐÁ \verb|-a**2|, ÏÚÎÁÞÁÀÝÅÊ $(-a)^2$.
%%Since unary
%%negation\label{Dneg} applies at the primary level, it also turns out
%%that \verb|-a**2| means $(-a)^2$. 
ë ÓÞÁÓÔØÀ, ×ÙÞÉÔÁÎÉÅ ÉÍÅÅÔ ÍÅÎØÛÉÊ ÐÒÉÏÒÉÔÅÔ É \verb|a-b**2| 
ÏÚÎÁÞÁÅÔ $a-(b^2)$ ×ÍÅÓÔÏ $(a-b)^2$
%%Fortunately, subtraction has lower
%%precedence so that \verb|a-b**2| does mean $a-(b^2)$ instead of
%%$(a-b)^2$.

äÒÕÇÉÍ \tdescr{ÐÅÒ×ÉÞÎÙÍ ÂÉÎÁÒÎÙÍ ÏÐÅÒÁÔÏÒÏÍ} Ñ×ÌÑÅÔÓÑ ÏÐÅÒÁÔÏÒ {\tt
dotprod}\index{dotprod?\texttt{dotprod}}\label{Ddprod}, ×ÙÞÉÓÌÑÀÝÉÊ 
ÓËÁÌÑÒÎÏÅ ÐÒÏÉÚ×ÅÄÅÎÉÅ Ä×ÕÈ ÐÁÒ. 
%%Another \tdescr{primary binop} is the {\tt
%%dotprod}\index{dotprod?\texttt{dotprod}}\label{Ddprod} operator that
%%computes the vector dot product of two pairs.  
îÁÐÒÉÍÅÒ, {\tt z1 dotprod z2} ÜË×É×ÁÌÅÎÔÎÏ {\tt x1*x2 + y1*y2}.
%%For example, {\tt z1
%%dotprod z2} is equivalent to {\tt x1*y1 + x2*y2}.

áÄÄÉÔÉ×ÎÙÅ ÏÐÅÒÁÔÏÒÙ {\tt -} É {\tt +}\label{Dadd} --- 
\tdescr{×ÔÏÒÉÞÎÙÅ ÂÉÎÁÒÎÙÅ ÏÐÅÒÁÔÏÒÙ}, ÐÒÉÍÅÎÉÍÙÅ Ë ÞÉÓÌÁÍ, ÐÁÒÁÍ ÉÌÉ 
Ã×ÅÔÁÍ É ÐÒÏÉÚ×ÏÄÑÝÉÅ ÒÅÚÕÌØÔÁÔÙ ÔÏÇÏ ÖÅ ÔÉÐÁ.
%%The additive operators {\tt +} and {\tt -}\label{Dadd} are
%%\tdescr{secondary binops} that operate on numerics, pairs, or colors and
%%produce results of the same type.  
äÒÕÇÉÅ ÏÐÅÒÁÔÏÒÙ, ÞÔÏ ÐÏÐÁÄÁÀÔ × ÜÔÕ ËÁÔÅÇÏÒÉÀ --- ÜÔÏ ``ðÉÆÁÇÏÒÏ×Ï 
ÓÌÏÖÅÎÉÅ'' \verb|++|\index{++?\texttt{++}}\label{Dpyadd} É ``ðÉÆÁÇÏÒÏ×Ï 
×ÙÞÉÔÁÎÉÅ'' \verb|+-+|\index{+-+?\texttt{+-+}}\label{Dpysub}:
\verb|a++b| ÚÎÁÞÉÔ $\sqrt{a^2+b^2}$ É \verb|a+-+b| ÚÎÁÞÉÔ
$\sqrt{a^2-b^2}$. 
%%Other operators that fall in this
%%category are ``Pythagorean addition''
%%\verb|++|\index{++?\texttt{++}}\label{Dpyadd} and ``Pythagorean
%%subtraction'' \verb|+-+|\index{+-+?\texttt{+-+}}\label{Dpysub}:
%%\verb|a++b| means $\sqrt{a^2+b^2}$ and \verb|a+-+b| means
%%$\sqrt{a^2-b^2}$. 
åÓÔØ ÅÝÅ ÓÌÉÛËÏÍ ÍÎÏÇÏ ÄÒÕÇÉÈ ÏÐÅÒÁÔÏÒÏ× ÄÌÑ ÐÅÒÅÞÉÓÌÅÎÉÑ ÚÄÅÓØ, ÎÏ 
ÏÄÎÉ ÉÚ ÓÁÍÙÈ ×ÁÖÎÙÈ --- ÜÔÏ ÌÏÇÉÞÅÓËÉÅ ÏÐÅÒÁÔÏÒÙ {\tt
and}\index{and?\texttt{and}} É {\tt or}\index{or?\texttt{or}}.
%%There are too many other operators to list here, but
%%some of the most important are the boolean operators {\tt
%%and}\index{and?\texttt{and}} and {\tt or}\index{or?\texttt{or}}.  
ïÐÅÒÁÔÏÒ {\tt and} --- ÜÔÏ \tdescr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} É ÏÐÅÒÁÔÏÒ 
{\tt or} --- ÜÔÏ \tdescr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}.
%%The
%%{\tt and} operator is a \tdescr{primary binop} and the {\tt or} operator
%%is a \tdescr{secondary binop}.

âÁÚÏ×ÙÅ ÏÐÅÒÁÃÉÉ ÓÏ ÓÔÒÏËÁÍÉ --- ÜÔÏ ÓËÌÅÊËÁ\index{ÓËÌÅÊËÁ}, 
×ÙÄÅÌÅÎÉÅ ÐÏÄÓÔÒÏËÉ É ×ÙÞÉÓÌÅÎÉÅ ÄÌÉÎÙ ÓÔÒÏËÉ.
%%e basic operations on strings are concatenation\index{concatenation},
%%substring construction and calculating the length of a string.
óËÌÅÊËÁ ÒÅÁÌÉÚÕÅÔÓÑ \tdescr{ÔÒÅÔÉÞÎÙÍ ÂÉÎÁÒÎÙÍ 
ÏÐÅÒÁÔÏÒÏÍ} \verb|&|\index{&?\texttt{\&}}\label{Damp}, ÎÁÐÒÉÍÅÒ,
%%The \tdescr{tertiary binop} \verb|&|\index{&?\texttt{\&}}\label{Damp}
%%implements concatenation; e.g.,
$$ \hbox{\verb|"abc" & "de"|} $$
ÐÒÏÉÚ×ÏÄÉÔ ÓÔÒÏËÕ \verb|"abcde"|.
%%produces the string \verb|"abcde"|. 
ïÐÅÒÁÔÏÒ {\tt
length}\index{length?\texttt{length}}\label{DlengthString} ×ÏÚ×ÒÁÝÁÅÔ 
ÞÉÓÌÏ ÓÉÍ×ÏÌÏ× × ÓÔÒÏËÅ, ÅÓÌÉ ÁÒÇÕÍÅÎÔÏÍ Ñ×ÌÑÅÔÓÑ \tdescr{ÓÔÒÏËÏ×ÁÑ 
ÐÅÒ×ÉÞÎÏÓÔØ}, ÎÁÐÒÉÍÅÒ,
%%The {\tt
%%length}\index{length?\texttt{length}}\label{DlengthString} operator
%%returns the number of characters in a string if the argument is a
%%\tdescr{string primary}; e.g.,
$$ \hbox{\verb|length "abcde"|} $$
×ÏÚ×ÒÁÝÁÅÔ \verb|5|.
%%returns \verb|5|. 
äÒÕÇÏÅ ÐÒÉÍÅÎÅÎÉÅ ÏÐÅÒÁÔÏÒÁ {\tt length} ÏÂÓÕÖÄÁÅÔÓÑ ÎÁ 
ÓÔÒ.\ \pageref{Dlength}.
%%Another application of the {\tt length} operator is
%%discussed on p.\ \pageref{Dlength}.  
äÌÑ ×ÙÄÅÌÅÎÉÑ ÐÏÄÓÔÒÏËÉ \tdescr{of-ÏÐÅÒÁÔÏÒ} 
{\tt substring}\index{substring
of?\texttt{substring of}}\label{Dsubstr} ÉÓÐÏÌØÚÕÅÔÓÑ ÔÁËÉÍ ÏÂÒÁÚÏÍ:
$$ {\tt substring}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ} \,{\tt of}\, \descr{ÓÔÒÏËÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ} $$
%%For substring construction, the
%%\tdescr{of operator} {\tt substring}\index{substring
%%of?\texttt{substring of}}\label{Dsubstr} is used like this:
%%$$ {\tt substring}\, \descr{pair expression} \,{\tt of}\, \descr{string primary} $$
þÁÓÔØ ÓÔÒÏËÉ ÄÌÑ ×ÙÄÅÌÅÎÉÅ ÏÐÒÅÄÅÌÑÅÔÓÑ \tdescr{×ÙÒÁÖÅÎÉÅÍ-ÐÁÒÏÊ}. 
%%The \tdescr{pair expression} determines what part of the string to
%%select. 
ðÏÚÉÃÉÉ × ÓÔÒÏËÅ ÎÕÍÅÒÕÀÔÓÑ\index{ÉÎÄÅËÓÁÃÉÑ} ÔÁË, ÞÔÏ ÃÅÌÙÅ ÐÏÚÉÃÉÉ 
ÐÏÐÁÄÁÀÔ {\em ÍÅÖÄÕ\/} ÓÉÍ×ÏÌÁÍÉ.
%%For this purpose, the string is indexed\index{indexing} so that
%%integer positions fall {\em between\/} characters. 
ðÒÅÄÓÔÁ×ÉÍ ÓÔÒÏËÕ, ÎÁÐÉÓÁÎÎÕÀ ÎÁ ËÕÓÏÞËÅ ÂÕÍÁÇÅ × ËÌÅÔËÕ ÔÁË, ÞÔÏ ÐÅÒ×ÙÊ 
ÓÉÍ×ÏÌ ÚÁÊÍÅÔ $x$-ËÏÏÒÄÉÎÁÔÙ ÍÅÖÄÕ ÎÕÌÅÍ É ÅÄÉÎÉÃÅÊ, Á ÓÌÅÄÕÀÝÉÊ ÓÉÍ×ÏÌ 
ÐÏËÒÏÅÔ ËÏÏÒÄÉÎÁÔÙ × ÄÉÁÐÁÚÏÎÅ $1\leqslant x\leqslant2$, É Ô.~Ä.
%%Pretend the string
%%is written on a piece of graph paper so that the first character
%%occupies $x$~coordinates between zero and one and the next character
%%covers the range $1\le x\le2$, etc.  
ðÏÜÔÏÍÕ ÓÔÒÏËÕ \verb|"abcde"| ÓÌÅÄÕÅÔ ÐÒÅÄÓÔÁ×ÌÑÔØ × ×ÉÄÅ 
%%Thus the string \verb|"abcde"|
%%should be thought of like this
$$ \includegraphics{manfig-ru-14} $$
É {\tt substring (2,4) of {\qq}abcde{\qq}} ÂÕÄÅÔ {\tt {\qq}cd{\qq}}.
%%and {\tt substring (2,4) of {\qq}abcde{\qq}} is {\tt {\qq}cd{\qq}}. 
üÔÏ ×ÙÇÌÑÄÉÔ ÎÅÓËÏÌØËÏ ÕÓÌÏÖÎÅÎÏ, ÎÏ ÉÍÅÅÔ ÃÅÌØÀ ÉÚÂÅÖÁÔØ ÎÁÄÏÅÄÁÀÝÉÈ 
ÏÛÉÂÏË ``ÎÁ ÅÄÉÎÉÃÕ''.
%%This takes a little
%%getting used to but it tends to avoid annoying ``off by one'' errors.

îÅËÏÔÏÒÙÅ ÏÐÅÒÁÔÏÒÙ ÎÅ ÂÅÒÕÔ ÁÒÇÕÍÅÎÔÏ× ×ÏÏÂÝÅ.
%%Some operators take no arguments at all. 
ðÒÉÍÅÒ ÔÏÇÏ, ÞÔÏ ÎÁ ÒÉÓ.~\ref{syexpr} ÚÏ×ÅÔÓÑ \tdescr{ÏÐÅÒÁÔÏÒÏÍ 0-ÕÒÏ×ÎÑ}, --- 
ÜÔÏ {\tt 
nullpicture}\index{nullpicture?\texttt{nullpicture}}\label{Dnlpic}, 
ËÏÔÏÒÙÊ ×ÏÚ×ÒÁÝÁÅÔ ÓÏ×ÅÒÛÅÎÎÏ ÐÕÓÔÕÀ ËÁÒÔÉÎËÕ.
%%An example of what
%%Figure~\ref{syexpr} calls a \tdescr{nullary op} is {\tt
%%nullpicture}\index{nullpicture?\texttt{nullpicture}}\label{Dnlpic} which
%%returns a completely blank picture.

âÁÚÏ×ÙÊ ÓÉÎÔÁËÓÉÓ ÎÁ ÒÉÓ.~\ref{syexpr} ÐÏËÒÙ×ÁÅÔ ÔÏÌØËÏ ÔÅ ÁÓÐÅËÔÙ 
ÓÉÎÔÁËÓÉÓÁ ×ÙÒÁÖÅÎÉÊ, ËÏÔÏÒÙÅ Ñ×ÌÑÀÔÓÑ ÎÅÚÁ×ÉÓÉÍÙÍÉ ÏÔ ÔÉÐÁ.
%%The basic syntax in Figure~\ref{syexpr} only covers aspects of the
%%expression syntax that are relatively type-independent. 
îÁÐÒÉÍÅÒ, ÎÅÐÒÏÓÔÏÊ ÓÉÎÔÁËÓÉÓ ÐÕÔÉ ÎÁ ÒÉÓ.~\ref{sypath}, ÄÁÅÔ 
ÁÌØÔÅÒÎÁÔÉ×ÎÙÅ ÐÒÁ×ÉÌÁ ÄÌÑ ËÏÎÓÔÒÕÉÒÏ×ÁÎÉÑ \tdescr{×ÙÒÁÖÅÎÉÑ-ÐÕÔÉ}.
%%For instance,
%%the complicated path syntax given in Figure~\ref{sypath} gives
%%alternative rules for constructing a \tdescr{path expression}. 
äÏÐÏÌÎÉÔÅÌØÎÏÅ ÐÒÁ×ÉÌÏ\index{ÕÚÅÌ ÐÕÔÉ?\tdescr{ÕÚÅÌ ÐÕÔÉ}}
$$ \descr{ÕÚÅÌ ÐÕÔÉ} \rightarrow \descr{ÔÒÅÔÉÞÎÁÑ ÐÁÒÁ} \;|\; \descr{ÔÒÅÔÉÞÎÙÊ ÐÕÔØ}
$$
ÏÂßÑÓÎÑÅÔ ÚÎÁÞÅÎÉÅ \tdescr{ÕÚÌÁ ÐÕÔÉ} ÎÁ ÒÉÓ.~\ref{sypath}. 
%%An
%%additional rule\index{path knot?\tdescr{path knot}}
%%$$ \descr{path knot} \rightarrow \descr{pair tertiary} \;|\; \descr{path tertiary}
%%$$
%%explains the meaning of \tdescr{path knot} in Figure~\ref{sypath}. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, ×ÙÒÁÖÅÎÉÅ-ÐÕÔØ 
%%This means
%%that the path expression
$$ \hbox{\verb|z1+(1,1){right}..z2|} $$
ÎÅ ÎÕÖÄÁÅÔÓÑ × ÓËÏÂËÁÈ ×ÏËÒÕÇ {\tt z1+(1,1)}.
%%does not need parentheses around {\tt z1+(1,1)}.

\subsection{äÒÏÂÉ, ÕÓÒÅÄÎÅÎÉÑ É ÕÎÁÒÎÙÅ ÏÐÅÒÁÔÏÒÙ}
%%\subsection{Fractions, Mediation, and Unary Operators}

÷ÙÒÁÖÅÎÉÑ ÕÓÒÅÄÎÅÎÉÑ\index{ÕÓÒÅÄÎÅÎÉÅ} ÏÔÓÕÔÓÔ×ÕÀÔ × ÓÉÎÔÁËÓÉÓÅ ÂÁÚÏ×ÏÇÏ 
×ÙÒÁÖÅÎÉÑ ÎÁ ÒÉÓ.~\ref{syexpr}.
%%Mediation\index{mediation} expressions do not appear in the basic expression
%%syntax of Figure~\ref{syexpr}. 
÷ÙÒÁÖÅÎÉÑ ÕÓÒÅÄÎÅÎÉÑ ÒÁÚÂÉÒÁÀÔÓÑ ÎÁ \tdescr{ÐÅÒ×ÉÞÎÏÍ} ÕÒÏ×ÎÅ, ÔÁË ÞÔÏ 
ÏÂÝÅÅ ÐÒÁ×ÉÌÏ ÄÌÑ ÉÈ ËÏÎÓÔÒÕÉÒÏ×ÁÎÉÑ ÓÌÅÄÕÀÝÅÅ
$$ \descr{ÐÅÒ×ÉÞÎÏÓÔØ} \rightarrow
     \descr{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ} \hbox{\tt [} \descr{×ÙÒÁÖÅÎÉÅ}
        \hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ} \hbox{\tt ]},
$$
ÇÄÅ ËÁÖÄÏÅ \tdescr{×ÙÒÁÖÅÎÉÅ} ÍÏÖÅÔ ÂÙÔØ ÔÉÐÁ ÞÉÓÌÏ, ÐÁÒÁ ÉÌÉ Ã×ÅÔ.
%%Mediation expressions are parsed at the
%%\tdescr{primary} level, so the general rule for constructing them is
%%$$ \descr{primary} \rightarrow
%%     \descr{numeric atom} \hbox{\tt [} \descr{expression}
%%        \hbox{\tt ,} \descr{expression} \hbox{\tt ]}
%%$$
%%where each \tdescr{expression} can be of type numeric, pair, or color.
\tdescr{þÉÓÌÏ×ÏÊ ÁÔÏÍ}\index{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ?\tdescr{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ}} × 
×ÙÒÁÖÅÎÉÉ ÕÓÒÅÄÎÅÎÉÑ ÉÍÅÅÔ ÏÞÅÎØ ÐÒÏÓÔÏÊ ÔÉÐ \tdescr{ÞÉÓÌÏ×ÏÊ ÐÅÒ×ÉÞÎÏÓÔÉ}, 
ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{synprim}. 
%%The \tdescr{numeric atom}\index{numeric atom?\tdescr{numeric atom}} in a
%%mediation expression is an extra simple type of \tdescr{numeric primary}
%%as shown in Figure~\ref{synprim}. 
úÎÁÞÅÎÉÅÍ ×ÓÅÇÏ ÜÔÏÇÏ Ñ×ÌÑÅÔÓÑ ÔÏ, ÞÔÏ ÐÅÒ×ÙÊ ÐÁÒÁÍÅÔÒ × ×ÙÒÁÖÅÎÉÉ 
ÕÓÒÅÄÎÅÎÉÑ ÔÒÅÂÕÅÔ ÚÁËÌÀÞÅÎÉÑ × ÓËÏÂËÉ, ÅÓÌÉ ÏÎ × ÔÏÞÎÏÓÔÉ ÎÅ ÐÅÒÅÍÅÎÎÁÑ, 
ÎÅ ÐÏÌÏÖÉÔÅÌØÎÏÅ ÞÉÓÌÏ ÉÌÉ ÎÅ ÐÏÌÏÖÉÔÅÌØÎÁÑ ÄÒÏÂØ.
%%The meaning of all this is that the
%%initial parameter in a mediation expression needs to be parenthesized
%%when it is not just a variable, a positive number, or a positive
%%fraction. 
îÁÐÒÉÍÅÒ,\index{ÎÅÒÅÇÕÌÑÒÎÏÓÔÉ ÒÁÚÂÏÒÁ}
$$ \hbox{\tt -1[a,b]} \quad {\rm É}\quad \hbox{\tt (-1)[a,b]} $$
ÏÞÅÎØ ÒÁÚÌÉÞÎÙ:  ÐÅÒ×ÏÅ --- ÜÔÏ $-b$, Ô.~Ë. ÏÎÏ ÜË×É×ÁÌÅÎÔÎÏ 
{\tt -(1[a,b])}; ×ÔÏÒÏÅ --- ÜÔÏ $a-(b-a)$ ÉÌÉ $2a-b$.
%%For example,\index{parsing irregularities}
%%$$ \hbox{\tt -1[a,b]} \quad {\rm and}\quad \hbox{\tt (-1)[a,b]} $$
%%are very different:  the former is $-b$ since it is equivalent to
%%{\tt -(1[a,b])}; the latter is $a-(b-a)$ or $2a-b$.

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ} \rightarrow \descr{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ}$\\
%%$\tt \descr{numeric primary} \rightarrow \descr{numeric atom}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ}\hbox{\tt [}
  \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ]}$\\
%%$\tt \qquad \;|\; \descr{numeric atom}\hbox{\tt [}
%%  \descr{numeric expression}\hbox{\tt ,}\descr{numeric expression}\hbox{\tt ]}$\\
$\tt \qquad \;|\; \descr{of-ÏÐÅÒÁÔÏÒ} \descr{×ÙÒÁÖÅÎÉÅ} of \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{of operator} \descr{expression} of \descr{primary}$\\
$\tt \qquad \;|\; \descr{ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{unary op} \descr{primary}$\\
$\tt \descr{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ} \rightarrow \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ}$\\
%%$\tt \descr{numeric atom} \rightarrow \descr{numeric variable}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ ÉÌÉ ÄÒÏÂØ}$\\
%%$\tt \qquad \;|\; \descr{number or fraction}$\\
$\tt \qquad \;|\; \hbox{\tt (}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; \hbox{\tt (}\descr{numeric expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ×ÏÊ ÏÐÅÒÁÔÏÒ 0-ÕÒÏ×ÎÑ}$\\
%%$\tt \qquad \;|\; \descr{numeric nullary op}$\\
$\tt \descr{ÞÉÓÌÏ ÉÌÉ ÄÒÏÂØ} \rightarrow \descr{ÞÉÓÌÏ}
  \hbox{\tt /}\descr{ÞÉÓÌÏ}$\\
%%$\tt \descr{number or fraction} \rightarrow \descr{number}
%%  \hbox{\tt /}\descr{number}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ, ÚÁ ËÏÔÏÒÙÍ ÎÅÔ 
  `$\hbox{\tt /}\descr{ÞÉÓÌÁ}$'}$
%%$\tt \qquad \;|\; \descr{number not followed by
%%  `$\hbox{\tt /}\descr{number}$'}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÞÅÓËÉÅ ÐÒÁ×ÉÌÁ ÄÌÑ ÞÉÓÌÏ×ÙÈ ÐÅÒ×ÉÞÎÏÓÔÅÊ}
%%\caption{Syntax rules for numeric primaries}
\label{synprim}
\end{figure}

úÁÍÅÔÎÙÍ Ó×ÏÊÓÔ×ÏÍ ÓÉÎÔÁËÓÉÞÅÓËÉÈ ÐÒÁ×ÉÌ ÎÁ ÒÉÓ.~\ref{synprim} 
Ñ×ÌÑÅÔÓÑ ÔÏ, ÞÔÏ ÏÐÅÒÁÔÏÒ {\tt /}\index{ÄÒÏÂÉ} Ó×ÑÚÙ×ÁÅÔ ÂÏÌÅÅ ËÒÅÐËÏ, 
ËÏÇÄÁ ÅÇÏ ÏÐÅÒÁÎÄÙ  Ñ×ÌÑÀÔÓÑ ÞÉÓÌÁÍÉ.
%%A noteworthy feature of the syntax rules in Figure~\ref{synprim} is that
%%the {\tt /}\index{fractions} operator binds most tightly when its
%%operands are numbers. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, {\tt 2/3} --- ÜÔÏ \tdescr{ÞÉÓÌÏ×ÏÊ 
ÁÔÏÍ}\index{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ?\tdescr{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ}}\index{ÎÅÒÅÇÕÌÑÒÎÏÓÔÉ 
ÒÁÚÂÏÒÁ}, Á {\tt (1+1)/3} --- ÜÔÏ ÔÏÌØËÏ \tdescr{ÞÉÓÌÏ×ÁÑ 
×ÔÏÒÉÞÎÏÓÔØ}. 
%%Thus {\tt 2/3} is a \tdescr{numeric
%%atom}\index{numeric atom?\tdescr{numeric atom}}\index{parsing
%%irregularities} while {\tt (1+1)/3} is only a \tdescr{numeric
%%secondary}. 
ðÒÉÍÅÎÅÎÉÅ \tdescr{ÕÎÁÒÎÏÇÏ ÏÐÅÒÁÔÏÒÁ}, ÔÁËÏÇÏ ËÁË {\tt
sqrt}\index{sqrt?\texttt{sqrt}}\label{Dsqrt}, ÄÅÌÁÅÔ ÒÁÚÎÉÃÕ ÏÞÅ×ÉÄÎÏÊ:
$$ \hbox{\tt sqrt 2/3} $$
ÚÎÁÞÉÔ $\sqrt{2\over3}$, Á 
$$ \hbox{\tt sqrt(1+1)/3} $$
ÚÎÁÞÉÔ $\sqrt 2/3$.
%%Applying a \tdescr{primary binop} such as {\tt
%%sqrt}\index{sqrt?\texttt{sqrt}}\label{Dsqrt} makes the difference clear:
%%$$ \hbox{\tt sqrt 2/3} $$
%%means $\sqrt{2\over3}$ while
%%$$ \hbox{\tt sqrt(1+1)/3} $$
%%means $\sqrt 2/3$. 
ïÐÅÒÁÔÏÒÙ, ÔÁËÉÅ ËÁË {\tt sqrt}, ÍÏÇÕÔ ÂÙÔØ ÚÁÐÉÓÁÎÙ × ÓÔÁÎÄÁÒÔÎÏÊ 
ÆÕÎËÃÉÏÎÁÌØÎÏÊ ÎÏÔÁÃÉÉ, ÎÏ ÞÁÓÔÏ ÎÅÔ ÎÕÖÄÙ ÂÒÁÔØ ÁÒÇÕÍÅÎÔ × ÓËÏÂËÉ.
%%Operators such as {\tt sqrt} can be written in
%%standard functional notation, but it is often unnecessary to
%%parenthesize the argument. 
üÔÏ ×ÅÒÎÏ ÄÌÑ ÌÀÂÏÊ ÆÕÎËÃÉÉ, ÞÔÏ ÒÁÚÂÉÒÁÅÔÓÑ ËÁË \tdescr{ÕÎÁÒÎÁÑ ÏÐÅÒÁÃÉÑ}.
%%This applies to any function that is parsed
%%as a \tdescr{primary binop}. 
îÁÐÒÉÍÅÒ, É {\tt abs(x)}\index{abs?\texttt{abs}}\label{Dabs}, É {\tt abs x} 
×ÙÞÉÓÌÑÀÔ ÍÏÄÕÌØ {\tt x}.
%%For instance {\tt
%%abs(x)}\index{abs?\texttt{abs}}\label{Dabs} and {\tt abs x} both compute
%%the absolute value of {\tt x}. 
üÔÏ ÖÅ ×ÅÒÎÏ ÄÌÑ ÆÕÎËÃÉÊ {\tt round}\index{round?\texttt{round}}\label{Dround}, 
{\tt floor}\index{floor?\texttt{floor}}\label{Dfloor}, 
{\tt ceiling}\index{ceiling?\texttt{ceiling}}\label{Dceil}, 
{\tt sind}\index{sind?\texttt{sind}}\label{Dsind} É 
{\tt cosd}\index{cosd?\texttt{cosd}}\label{Dcosd}. 
%%The same holds for the {\tt
%%round}\index{round?\texttt{round}}\label{Dround}, {\tt
%%floor}\index{floor?\texttt{floor}}\label{Dfloor}, {\tt
%%ceiling}\index{ceiling?\texttt{ceiling}}\label{Dceil}, {\tt
%%sind}\index{sind?\texttt{sind}}\label{Dsind}, and {\tt
%%cosd}\index{cosd?\texttt{cosd}}\label{Dcosd} functions. 
ä×Å ÐÏÓÌÅÄÎÉÅ ÉÚ ÎÉÈ ×ÙÞÉÓÌÑÀÔ ÔÒÉÇÏÎÏÍÅÔÒÉÞÅÓËÉÅ ÆÕÎËÃÉÉ ÏÔ ÕÇÌÁ 
× ÇÒÁÄÕÓÁÈ.
%%The last two of
%%these compute trigonometric functions of angles in degrees.

îÅ ×ÓÅ ÕÎÁÒÎÙÅ ÏÐÅÒÁÔÏÒÙ ÂÅÒÕÔ ÞÉÓÌÏ×ÙÅ ÁÒÇÕÍÅÎÔÙ É ×ÏÚ×ÒÁÝÁÀÔ ÞÉÓÌÏ×ÙÅ 
ÒÅÚÕÌØÔÁÔÙ. 
%%Not all unary operators take numeric arguments and return numeric
%%results. 
îÁÐÒÉÍÅÒ, ÏÐÅÒÁÔÏÒ {\tt abs}\index{abs?\texttt{abs}} ÍÏÖÎÏ ÐÒÉÍÅÎÑÔØ 
Ë ÐÁÒÅ ÄÌÑ ×ÙÞÉÓÌÅÎÉÑ ÄÌÉÎÙ ×ÅËÔÏÒÁ.
%%For instance, the {\tt abs}\index{abs?\texttt{abs}} operator
%%can be applied to a pair to compute the Euclidean length of a vector.
ðÒÉÍÅÎÅÎÉÅ ÏÐÅÒÁÔÏÒÁ {\tt 
unitvector}\index{unitvector?\texttt{unitvector}}\label{Duvec} 
Ë ÐÁÒÅ ÐÒÏÉÚ×ÏÄÉÔ ÏÐÑÔØ ÐÁÒÕ, ÚÁÄÁÀÝÕÀ ×ÅËÔÏÒ Ó ÔÅÍ ÖÅ ÎÁÐÒÁ×ÌÅÎÉÅÍ É 
ÄÌÉÎÏÊ~1. 
%%Applying the {\tt
%%unitvector}\index{unitvector?\texttt{unitvector}}\label{Duvec} operator
%%to a pair produces the same pair rescaled so that its Euclidean length
%%is~1.
ïÐÅÒÁÔÏÒ {\tt decimal}\index{decimal?\texttt{decimal}}\label{Ddecop} 
ÂÅÒÅÔ ÞÉÓÌÏ É ×ÏÚ×ÒÁÝÁÅÔ ÅÇÏ ÓÔÒÏËÏ×ÏÅ ÐÒÅÄÓÔÁ×ÌÅÎÉÅ.
%%The {\tt decimal}\index{decimal?\texttt{decimal}}\label{Ddecop}
%%operator takes a number and returns the string representation. 
ïÐÅÒÁÔÏÒ {\tt angle}\index{angle?\texttt{angle}}\label{Dangle} ÂÅÒÅÔ ÐÁÒÕ 
É ×ÙÞÉÓÌÑÅÔ ÁÒËÔÁÎÇÅÎÓ ÏÔÎÏÛÅÎÉÑ ÅÅ ËÏÍÐÏÎÅÎÔ, Ô.~Å. {\tt angle} --- ÜÔÏ 
ÏÐÅÒÁÔÏÒ, ÏÂÒÁÔÎÙÊ {\tt dir}, ÞÔÏ ÏÂÓÕÖÄÁÅÔÓÑ × ÒÁÚÄÅÌÅ~\ref{tenscurl}. 
%%The {\tt angle}\index{angle?\texttt{angle}}\label{Dangle} operator takes a pair
%%and computes the two-argument arctangent; i.e., {\tt angle} is the
%%inverse of the {\tt dir} operator that was discussed in
%%Section~\ref{tenscurl}. 
åÓÔØ ÔÁËÖÅ ÏÐÅÒÁÔÏÒ {\tt cycle}\index{cycle?\texttt{cycle}}\label{Dcycop}, ÞÔÏ 
ÂÅÒÅÔ \tdescr{ÐÅÒ×ÉÞÎÙÊ ÐÕÔØ} É ×ÏÚ×ÒÁÝÁÅÔ ÌÏÇÉÞÅÓËÉÊ ÒÅÚÕÌØÔÁÔ, ÐÏËÁÚÙ×ÁÀÝÉÊ 
Ñ×ÌÑÅÔÓÑ ÌÉ ÜÔÏÔ ÐÕÔØ ÚÁÍËÎÕÔÏÊ ËÒÉ×ÏÊ.
%%There is also an operator {\tt
%%cycle}\index{cycle?\texttt{cycle}}\label{Dcycop} that takes a
%%\tdescr{path primary} and returns a boolean result indicating whether
%%the path is a closed curve.

óÕÝÅÓÔ×ÕÅÔ ÃÅÌÙÊ ËÌÁÓÓ ÄÒÕÇÉÈ ÏÐÅÒÁÔÏÒÏ× ÄÌÑ ËÌÁÓÓÉÆÉËÁÃÉÉ ×ÙÒÁÖÅÎÉÊ Ó 
ÌÏÇÉÞÅÓËÉÍ ÒÅÚÕÌØÔÁÔÏÍ.
%%There is a whole class of other operators that classify expressions and
%%return boolean results. 
éÍÑ ÔÉÐÁ, ÔÁËÏÅ ËÁË {\tt
pair}\index{pair?\texttt{pair}}, ÍÏÖÅÔ ÐÒÉÍÅÎÑÔØÓÑ Ë ÌÀÂÏÍÕ ÔÉÐÕ 
\tdescr{ÐÅÒ×ÉÞÎÏÓÔÉ} É ×ÏÚ×ÒÁÝÁÔØ ÌÏÇÉÞÅÓËÉÊ ÒÅÚÕÌØÔÁÔ, ÐÏËÁÚÙ×ÁÀÝÉÊ 
Ñ×ÌÑÅÔÓÑ ÌÉ ÁÒÇÕÍÅÎÔ ÐÁÒÏÊ\label{Dpairop}. 
%%A type name such as {\tt
%%pair}\index{pair?\texttt{pair}} can operate on any type of
%%\tdescr{primary} and return a boolean result indicating whether the
%%argument is a {\tt pair}\label{Dpairop}. 
áÎÁÌÏÇÉÞÎÏ, ËÁÖÄÏÅ ÉÍÑ ÉÚ ÓÌÅÄÕÀÝÉÈ ÄÁÌÅÅ ÍÏÖÎÏ ÉÓÐÏÌØÚÏ×ÁÔØ ËÁË ÕÎÁÒÎÙÊ 
ÏÐÅÒÁÔÏÒ: 
{\tt numeric}\index{numeric?\texttt{numeric}}\label{Dnumop}, 
{\tt boolean}\index{boolean?\texttt{boolean}}\label{Dboolop}, 
{\tt cmykcolor}\index{cmykcolor?\texttt{cmykcolor}}\label{Dccolrop}, 
{\tt color}\index{color?\texttt{color}}\label{Dcolrop}, 
{\tt string}\index{string?\texttt{string}}\label{Dstrgop}, 
{\tt transform}\index{transform?\texttt{transform}}\label{Dtrnfop}, 
{\tt path}\index{path?\texttt{path}}\label{Dpathop}, 
{\tt pen}\index{pen?\texttt{pen}}\label{Dpenop}, 
{\tt picture}\index{picture?\texttt{picture}}\label{Dpictop} É 
{\tt rgbcolor}\index{rgbcolor?\texttt{rgbcolor}}\label{Drcolrop}.
%%Similarly, each of the
%%following can be used as a unary operator: 
%%{\tt numeric}\index{numeric?\texttt{numeric}}\label{Dnumop}, 
%%{\tt boolean}\index{boolean?\texttt{boolean}}\label{Dboolop}, 
%%{\tt cmykcolor}\index{cmykcolor?\texttt{cmykcolor}}\label{Dccolrop}, 
%%{\tt color}\index{color?\texttt{color}}\label{Dcolrop}, 
%%{\tt string}\index{string?\texttt{string}}\label{Dstrgop}, 
%%{\tt transform}\index{transform?\texttt{transform}}\label{Dtrnfop}, 
%%{\tt path}\index{path?\texttt{path}}\label{Dpathop}, 
%%{\tt pen}\index{pen?\texttt{pen}}\label{Dpenop}, 
%%{\tt picture}\index{picture?\texttt{picture}}\label{Dpictop}, and
%%{\tt rgbcolor}\index{rgbcolor?\texttt{rgbcolor}}\label{Drcolrop}.
ëÒÏÍÅ ÐÒÏ×ÅÒËÉ ÔÉÐÁ \tdescr{ÐÅÒ×ÉÞÎÏÓÔÉ}, ×Ù ÍÏÖÅÔÅ ÉÓÐÏÌØÚÏ×ÁÔØ ÏÐÅÒÁÔÏÒÙ 
{\tt known}\index{known?\texttt{known}}\label{Dknown} É {\tt
unknown}\index{unknown?\texttt{unknown}}\label{Dunknwn} ÄÌÑ ÐÒÏ×ÅÒËÉ, 
ÉÍÅÅÔ ÌÉ ÏÎÁ ËÏÎËÒÅÔÎÏÅ ÚÎÁÞÅÎÉÅ.
%%Besides just
%%testing the type of a \tdescr{primary}, you can use the {\tt
%%known}\index{known?\texttt{known}}\label{Dknown} and {\tt
%%unknown}\index{unknown?\texttt{unknown}}\label{Dunknwn} operators to
%%test if it has a completely known value.

äÁÖÅ ÞÉÓÌÁ ÍÏÇÕÔ ×ÅÓÔÉ ÓÅÂÑ ËÁË ÏÐÅÒÁÔÏÒ × ÎÅËÏÔÏÒÙÈ ËÏÎÔÅËÓÔÁÈ.
%%Even a number can behave like an operator in some contexts. 
üÔÏ ÓÓÙÌËÁ ÎÁ ÔÒÀË, ÞÔÏ ÐÏÚ×ÏÌÑÅÔ {\tt 3x}\index{ÕÍÎÏÖÅÎÉÅ, ÎÅÑ×ÎÏÅ} É 
{\tt 3cm} ËÁË ÁÌØÔÅÒÎÁÔÉ×Ù ÄÌÑ {\tt 3*x} É {\tt 3*cm}.
%%This refers
%%to the trick that allows {\tt 3x}\index{multiplication, implicit} and
%%{\tt 3cm} as alternatives to {\tt 3*x} and {\tt 3*cm}. 
ðÒÁ×ÉÌÏ × ÔÏÍ, ÞÔÏ \tdescr{ÞÉÓÌÏ ÉÌÉ ÄÒÏÂØ}, ÚÁ ËÏÔÏÒÙÍÉ ÎÅÔ {\tt +}, {\tt -} 
ÉÌÉ ÄÒÕÇÏÇÏ \tdescr{ÞÉÓÌÁ ÉÌÉ ÄÒÏÂÉ}, ÍÏÖÅÔ ÓÌÕÖÉÔØ ËÁË \tdescr{ÐÅÒ×ÉÞÎÙÊ 
ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}. 
%%The rule is that
%%a \tdescr{number or fraction} that is not followed by {\tt +}, {\tt -},
%%or another \tdescr{number or fraction} can serve as a \tdescr{primary
%%binop}. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, {\tt 2/3x}\index{ÎÅÒÅÇÕÌÑÒÎÏÓÔÉ ÒÁÚÂÏÒÁ} --- ÜÔÏ Ä×Å ÔÒÅÔÉ ÏÔ 
{\tt x}, ÎÏ {\tt (2)/3x} --- ÜÔÏ $2\over3x$, Á {\tt 3 3} --- ÜÔÏ ÏÛÉÂËÁ.
%%Thus {\tt 2/3x}\index{parsing irregularities} is two thirds of
%%{\tt x} but {\tt (2)/3x} is $2\over3x$ and {\tt 3 3} is illegal.

åÓÔØ ÔÁËÖÅ ÏÐÅÒÁÔÏÒÙ ÄÌÑ ÉÚ×ÌÅÞÅÎÉÑ ÞÉÓÌÏ×ÙÈ ÐÏÌÅÊ ÉÚ ÐÁÒ, Ã×ÅÔÏ×, 
cmyk-Ã×ÅÔÏ× É ÄÁÖÅ ÔÒÁÎÓÆÏÒÍÁÃÉÊ.
%%There are also operators for extracting numeric subfields from pairs,
%%colors, cmykcolors, and even transforms. 
åÓÌÉ {\tt p} --- ÜÔÏ \tdescr{ÐÅÒ×ÉÞÎÁÑ 
ÐÁÒÁ}, ÔÏ {\tt xpart p}\index{xpart?\texttt{xpart}}\label{Dxprt} É
{\tt ypart p}\index{ypart?\texttt{ypart}}\label{Dyprt} ÉÚ×ÌÅËÁÀÔ ÅÅ ËÏÍÐÏÎÅÎÔÙ 
ÔÁË, ÞÔÏ 
$$ \hbox{\tt (xpart p, ypart p)} $$ ÜË×É×ÁÌÅÎÔÎÏ {\tt p}, ÄÁÖÅ ÅÓÌÉ 
{\tt p} --- ÎÅÉÚ×ÅÓÔÎÁÑ ÐÁÒÁ, ÉÓÐÏÌØÚÕÅÍÁÑ × ÌÉÎÅÊÎÏÍ ÕÒÁ×ÎÅÎÉÉ.
%%If {\tt p} is a \tdescr{pair
%%primary}, {\tt xpart p}\index{xpart?\texttt{xpart}}\label{Dxprt} and
%%{\tt ypart p}\index{ypart?\texttt{ypart}}\label{Dyprt} extract its components so that
%%$$ \hbox{\tt (xpart p, ypart p)} $$ is equivalent to~{\tt p} even if
%%{\tt p} is an unknown pair that is being used in a linear equation.
áÎÁÌÏÇÉÞÎÏ, Ã×ÅÔ {\tt c} ÜË×É×ÁÌÅÎÔÅÎ\index{redpart?\texttt{redpart}}%
\index{greenpart?\texttt{greenpart}}%
\index{bluepart?\texttt{bluepart}}\label{Drgbprt}
$$ \hbox{\tt (redpart c, greenpart c, bluepart c)}. $$
%%Similarly, a color {\tt c} is equivalent
%%to\index{redpart?\texttt{redpart}}%
%%\index{greenpart?\texttt{greenpart}}%
%%\index{bluepart?\texttt{bluepart}}\label{Drgbprt}
%%$$ \hbox{\tt (redpart c, greenpart c, bluepart c)} $$.
äÌÑ cmyk-Ã×ÅÔÁ {\tt c} ÅÇÏ ÜË×É×ÁÌÅÎÔ\index{cyanpart?\texttt{cyanpart}}%
\index{magentapart?\texttt{magentapart}}%
\index{yellowpart?\texttt{yellowpart}}%
\index{blackpart?\texttt{blackpart}}\label{Dcmykprt}
$$ \hbox{\tt (cyanpart c, magentapart c, yellowpart c, blackpart c)}, $$ 
Á ÄÌÑ ÏÔÔÅÎËÁ ÓÅÒÏÇÏ {\tt c} ÅÓÔØ ÔÏÌØËÏ ÏÄÉÎ ËÏÍÐÏÎÅÎÔ 
\index{greypart?\texttt{greypart}}\label{Dgreyprt}%
$$ \hbox{\tt greypart c}. $$
%%For a cmykcolor {\tt c},  the parts are:\index{cyanpart?\texttt{cyanpart}}%
%%\index{magentapart?\texttt{magentapart}}%
%%\index{yellowpart?\texttt{yellowpart}}%
%%\index{blackpart?\texttt{blackpart}}\label{Dcmykprt}
%%$$ \hbox{\tt (cyanpart c, magentapart c, yellowpart c, blackpart c)} $$ 
%%and for a greyscale color {\tt c}, there is only one component%
%%\index{greypart?\texttt{greypart}}\label{Dgreyprt}%
%%$$ \hbox{\tt greypart c}. $$
÷ÓÅ ÏÐÅÒÁÔÏÒÙ ËÏÍÐÏÎÅÎÔ Ã×ÅÔÁ ÏÂÓÕÖÄÁÀÔÓÑ ÂÏÌÅÅ ÐÏÄÒÏÂÎÏ × 
ÒÁÚÄÅÌÅ~\ref{piccomp}. 
%%All color component operators are discussed in more detail in
%%section~\ref{piccomp}. 
óÐÅÃÉÆÉËÁÔÏÒÙ ÞÁÓÔÅÊ ÔÒÁÎÓÆÏÒÍÁÃÉÊ ÏÂÓÕÖÄÁÀÔÓÑ × ÒÁÚÄÅÌÅ~\ref{transsec}.
%%The part specifiers for transforms are discussed
%%in section~\ref{transsec}.

\section{ðÅÒÅÍÅÎÎÙÅ}
%%\section{Variables}
\label{vars}
MetaPost ÐÏÚ×ÏÌÑÅÔ ÓÏÓÔÁ×ÎÙÅ ÉÍÅÎÁ ÐÅÒÅÍÅÎÎÙÈ, ÔÁËÉÅ ËÁË {\tt z.a}, {\tt x2r}, 
{\tt y2r} É {\tt z2r}, ÇÄÅ {\tt z2r} ÏÚÎÁÞÁÅÔ {\tt (x2r,y2r)}, Á 
{\tt z.a} --- {\tt (x.a,y.a)}.
%%MetaPost allows compound variable names such as {x.a}, {\tt x2r}, {\tt y2r},
%%and {\tt z2r}, where {\tt z2r} means {\tt (x2r,y2r)} and {\tt z.a} means
%%{\tt (x.a,y.a)}. 
æÁËÔÉÞÅÓËÉ ÓÕÝÅÓÔ×ÕÅÔ ÛÉÒÏËÉÊ ËÌÁÓÓ ÓÕÆÆÉËÓÏ×, ÎÁÐÒÉÍÅÒ, 
{\tt z}\tdescr{ÓÕÆÆÉËÓ}\index{ÓÕÆÆÉËÓ?\tdescr{ÓÕÆÆÉËÓ}}, ÏÚÎÁÞÁÀÝÉÊ 
$$ (x\descr{ÓÕÆÆÉËÓ},\, y\descr{ÓÕÆÆÉËÓ}). $$
%%In fact there is a broad class of suffixes such that
%%{\tt z}\tdescr{suffix}\index{suffix?\tdescr{suffix}} means
%%$$ (x\descr{suffix},\, y\descr{suffix}). $$
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ \tdescr{ÓÕÆÆÉËÓ} ÓÏÓÔÁ×ÌÑÅÔÓÑ ÉÚ ÚÎÁËÏ×, ÂÕÄÅÔ ÎÁÉÌÕÞÛÉÍ 
ÎÁÞÁÔØ Ó ÎÅÓËÏÌØËÉÈ ÓÌÏ× Ï ÚÎÁËÁÈ.
%%Since a \tdescr{suffix} is composed of tokens, it is best to begin with a few
%%comments about tokens.

\subsection{úÎÁËÉ}
%%\subsection{Tokens}

÷ÈÏÄÎÏÊ ÆÁÊÌ MetaPost ÒÁÓÓÍÁÔÒÉ×ÁÅÔÓÑ ËÁË ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÞÉÓÅÌ, 
ÓÔÒÏËÏ×ÙÈ ËÏÎÓÔÁÎÔ É ÓÉÍ×ÏÌØÎÙÈ ÚÎÁËÏ×\index{ÚÎÁËÉ}\index{ÚÎÁËÉ!ÓÉÍ×ÏÌÉÞÅÓËÉÅ}. 
%%A MetaPost input file is treated as a sequence of numbers, string
%%constants, and symbolic tokens\index{tokens}\index{tokens!symbolic}. 
þÉÓÌÏ ÓÏÓÔÏÉÔ ÉÚ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔÉ ÃÉÆÒ É ÍÏÖÅÔ ÓÏÄÅÒÖÁÔØ ÄÅÓÑÔÉÞÎÕÀ ÔÏÞËÕ.
%%A
%%number consists of a sequence of digits possibly containing a decimal
%%point. 
ôÅÈÎÉÞÅÓËÉ ÚÎÁË ÍÉÎÕÓ ×ÎÁÞÁÌÅ ÏÔÒÉÃÁÔÅÌØÎÏÇÏ ÞÉÓÌÁ --- ÜÔÏ ÏÔÄÅÌØÎÙÊ ÚÎÁË.
%%Technically, the minus sign in front of a negative number is a
%%separate token. 
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ MetaPost ÉÓÐÏÌØÚÕÅÔ ÁÒÉÆÍÅÔÉËÕ\index{ÁÒÉÆÍÅÔÉËÁ} Ó 
ÆÉËÓÉÒÏ×ÁÎÎÏÊ ÔÏÞËÏÊ, ÏÎ ÎÅ ÐÏÎÉÍÁÅÔ ÜËÓÐÏÎÅÎÃÉÁÌØÎÏÊ ÎÏÔÁÃÉÉ, ÔÁËÏÊ ËÁË
{\tt 6.02E23}. 
%%Since MetaPost uses fixed point
%%arithmetic\index{arithmetic}, it does not understand exponential
%%notation such as {\tt 6.02E23}. 
MetaPost ÂÕÄÅÔ ÉÎÔÅÒÐÒÅÔÉÒÏ×ÁÔØ ÜÔÏ ËÁË ÞÉÓÌÏ 6.02, ÚÁ ËÏÔÏÒÙÍ ÓÌÅÄÕÅÔ 
ÓÉÍ×ÏÌØÎÙÊ ÚÎÁË {\tt E}, ÚÁ ËÏÔÏÒÙÍ ÉÄÅÔ ÞÉÓÌÏ~23.
%%MetaPost would interpret this as the
%%number 6.02, followed by the symbolic token {\tt E}, followed by the
%%number~23.

÷ÓÅ ÍÅÖÄÕ ÐÁÒÏÊ Ä×ÏÊÎÙÈ ËÁ×ÙÞÅË, {\tt \qq}, Ñ×ÌÑÅÔÓÑ ÓÔÒÏËÏ×ÏÊ 
ËÏÎÓÔÁÎÔÏÊ\index{ÓÔÒÏËÏ×ÙÅ ËÏÎÓÔÁÎÔÙ}. 
%%Anything between a pair of double quotes {\tt \qq} is a
%%string constant\index{string constants}. 
óÔÒÏËÏ×ÏÊ ËÏÎÓÔÁÎÔÅ ÎÅÌØÚÑ ÎÁÞÉÎÁÔØÓÑ ÎÁ ÏÄÎÏÊ ÓÔÒÏËÅ É ÚÁËÁÎÞÉ×ÁÔØÓÑ ÎÁ 
ÄÒÕÇÏÊ.
%%It is
%%illegal for a string constant to start on one line and end on a later line.
óÔÒÏËÏ×ÁÑ ËÏÎÓÔÁÎÔÁ ÎÅ ÍÏÖÅÔ ÔÁËÖÅ ÓÏÄÅÒÖÁÔØ Ä×ÏÊÎÙÈ ËÁ×ÙÞÅË, {\tt \qq}, É 
ÞÅÇÏ-ÎÉÂÕÄØ ÅÝÅ, ÏÔÌÉÞÎÏÇÏ ÏÔ ÐÅÞÁÔÎÙÈ ÓÉÍ×ÏÌÏ× ASCII.
%%Nor can a string constant contain double quotes {\tt \qq} or anything other than
%%printable ASCII characters.

÷ÓÅ × ÓÔÒÏËÅ ××ÏÄÁ, ÏÔÌÉÞÎÏÅ ÏÔ ÞÉÓÅÌ É ÓÉÍ×ÏÌØÎÙÈ ËÏÎÓÔÁÎÔ, ÒÁÚÂÉ×ÁÅÔÓÑ ÎÁ 
ÓÉÍ×ÏÌØÎÙÅ ÚÎÁËÉ\index{ÚÎÁËÉ!ÓÉÍ×ÏÌÉÞÅÓËÉÅ}.
%%Everything in a line of input other than numbers and string constants is broken
%%into symbolic tokens\index{tokens!symbolic}. 
óÉÍ×ÏÌØÎÙÊ ÚÎÁË --- ÜÔÏ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÏÄÎÏÇÏ ÉÌÉ ÂÏÌÅÅ ÓÈÏÖÉÈ ÓÉÍ×ÏÌÏ×, 
ÇÄÅ ÓÉÍ×ÏÌÙ ``ÓÈÏÖÉ'', ÅÓÌÉ ÏÎÉ ×ÓÔÒÅÞÁÀÔÓÑ ÎÁ ÏÄÎÏÊ ÓÔÒÏËÅ ÔÁÂÌÉÃÙ~\ref{classes}.
%%A symbolic token is a sequence of
%%one or more similar characters, where characters are ``similar'' if they occur
%%on the same row of Table~\ref{classes}.

\begin{table}
$$\begin{tabular}{c}
\verb|ABCDEFGHIJKLMNOPQRSTUVWXYZ_abcdefghijklmnopqrstuvwxyz|\\
{\tt :<=>|}\\
\verb|#&@$|\\
\verb|/*\|\\
{\tt +-}\\
{\tt !?}\\
{\tt '`}\\
\verb|^~|\\
\verb|{}|\\
{\tt [}\\
{\tt ]}\\
\end{tabular}
$$
\caption{ëÌÁÓÓÙ ÓÉÍ×ÏÌÏ× ÄÌÑ ÒÁÚÂÉÅÎÉÑ ÎÁ ÚÎÁËÉ}
%%\caption{Character classes for tokenization}
\label{classes}
\end{table}

ôÁËÉÍ ÏÂÒÁÚÏÍ, \verb|A_alpha| É {\tt +-+} --- ÜÔÏ ÏÔÄÅÌØÎÙÅ ÓÉÍ×ÏÌÉÞÅÓËÉÅ 
ÚÎÁËÉ, {\tt !=} ÉÎÔÅÒÐÒÅÔÉÒÕÅÔÓÑ ËÁË Ä×Á ÚÎÁËÁ, Á {\tt x34} --- ÜÔÏ 
ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË, ÚÁ ËÏÔÏÒÙÍ ÓÌÅÄÕÅÔ ÞÉÓÌÏ.
%%Thus \verb|A_alpha| and {\tt +-+} are symbolic tokens but {\tt !=} is
%%interpreted as two tokens and {\tt x34} is a symbolic token followed by
%%a number. 
÷ÓÌÅÄÓÔ×ÉÅ ÔÏÇÏ, ÞÔÏ Ë×ÁÄÒÁÔÎÙÅ ÓËÏÂËÉ ÐÒÉ×ÅÄÅÎÙ ÎÁ ÏÔÄÅÌØÎÙÈ ÓÔÒÏËÁÈ, 
ÓÉÍ×ÏÌÉÞÅÓËÉÍÉ ÚÎÁËÁÍÉ, ×ËÌÀÞÁÀÝÉÍÉ ÉÈ, Ñ×ÌÑÀÔÓÑ ÔÏÌØËÏ {\tt [}, {\tt
[[}, {\tt [[[}, ... É {\tt ]}, {\tt ]]}, ...
%%Since the brackets {\tt [} and {\tt ]} are listed on lines by
%%themselves, the only symbolic tokens involving them are {\tt [}, {\tt
%%[[}, {\tt [[[}, etc.\ and {\tt ]}, {\tt ]]}, etc.

îÅËÏÔÏÒÙÅ ÓÉÍ×ÏÌÙ ÎÅ ÐÒÉ×ÅÄÅÎÙ × ÔÁÂÌÉÃÅ~\ref{classes}, ÐÏÔÏÍÕ ÞÔÏ ÏÎÉ 
ÔÒÅÂÕÀÔ ÓÐÅÃÉÁÌØÎÏÇÏ ÏÂÒÁÝÅÎÉÑ.
%%Some characters are not listed in Table~\ref{classes} because they need
%%special treatment. 
þÅÔÙÒÅ ÓÉÍ×ÏÌÁ {\tt ,;()} Ñ×ÌÑÀÔÓÑ ``ÏÄÉÎÏÞËÁÍÉ'': ÚÁÐÑÔÁÑ, ÔÏÞËÁ Ó ÚÁÐÑÔÏÊ ÉÌÉ 
ÓËÏÂËÁ --- ÜÔÏ ÏÔÄÅÌØÎÙÊ ÚÎÁË, ÄÁÖÅ ÅÓÌÉ ÏÄÉÎÁËÏ×ÙÅ ÉÚ ÎÉÈ ÉÄÕÔ ÐÏÄÒÑÄ.
%%The four characters {\tt ,;()} are ``loners'': each
%%comma, semicolon, or parenthesis is a separate token
%%even when they occur consecutively. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, {\tt (())} --- ÜÔÏ ÞÅÔÙÒÅ ÚÎÁËÁ, Á ÎÅ ÏÄÉÎ ÉÌÉ Ä×Á.
%%Thus {\tt (())} is four tokens, not
%%one or two. 
úÎÁË ÐÒÏÃÅÎÔÁ Ñ×ÌÑÅÔÓÑ ×ÅÓØÍÁ ÓÐÅÃÉÁÌØÎÙÍ, ÐÏÔÏÍÕ ÞÔÏ ÏÎ ××ÏÄÉÔ 
ËÏÍÍÅÎÔÁÒÉÉ\index{ËÏÍÍÅÎÔÁÒÉÉ}. 
%%The percent sign is very special because it introduces
%%comments\index{comments}. 
úÎÁË ÐÒÏÃÅÎÔÁ É ×ÓÅ ÐÏÓÌÅ ÎÅÇÏ ÄÏ ËÏÎÃÁ ÓÔÒÏËÉ ÉÇÎÏÒÉÒÕÅÔÓÑ.
%%The percent sign and everything after it up
%%to the end of the line are ignored.

äÒÕÇÉÍ ÓÐÅÃÉÁÌØÎÙÍ ÓÉÍ×ÏÌÏÍ Ñ×ÌÑÅÔÓÑ ÔÏÞËÁ.
%%Another special character is the period. 
ä×Å É ÂÏÌÅÅ ÔÏÞÅË ×ÍÅÓÔÅ ÆÏÒÍÉÒÕÀÔ ÓÉÍ×ÏÌØÎÙÊ ÚÎÁË, ÎÏ ÏÔÄÅÌØÎÁÑ ÔÏÞËÁ 
ÉÇÎÏÒÉÒÕÅÔÓÑ, Á ÔÏÞËÁ, ÐÅÒÅÄ ËÏÔÏÒÏÊ ÉÌÉ ÚÁ ËÏÔÏÒÏÊ ÉÄÕÔ ÃÉÆÒÙ, Ñ×ÌÑÅÔÓÑ 
ÞÁÓÔØÀ ÞÉÓÌÁ.
%%Two or more periods
%%together form a symbolic token, but a single period is ignored, and a period
%%preceded or followed by digits is part of a number 
ôÁËÉÍ ÏÂÒÁÚÏÍ, {\tt ..} É {\tt ...} --- ÜÔÏ ÓÉÍ×ÏÌØÎÙÅ ÚÎÁËÉ, Á {\tt a.b} --- ÜÔÏ 
ÐÒÏÓÔÏ Ä×Á ÚÎÁËÁ {\tt a} É {\tt b}. 
%%Thus {\tt ..}
%%and {\tt ...} are symbolic tokens while {\tt a.b} is just two tokens {\tt a}
%%and {\tt b}. 
ðÒÉÎÑÔÏ ÉÓÐÏÌØÚÏ×ÁÔØ ÔÏÞËÕ ÔÁËÉÍ ÏÂÒÁÚÏÍ ÄÌÑ ÒÁÚÄÅÌÅÎÉÑ ÚÎÁËÏ×, ËÏÇÄÁ ÉÍÑ  
ÐÅÒÅÍÅÎÎÏÊ ÉÍÅÅÔ ÄÌÉÎÕ ÂÏÌÅÅ ÏÄÎÏÇÏ ÚÎÁËÁ.
%%It conventional to use periods to separate tokens in this fashion
%%when naming a variable that is more than one token long.

\subsection{äÅËÌÁÒÁÃÉÉ ÐÅÒÅÍÅÎÎÙÈ}
%%\subsection{Variable Declarations}
\label{vardecl}

éÍÑ ÐÅÒÅÍÅÎÎÏÊ --- ÜÔÏ ÌÉÂÏ ÓÉÍ×ÏÌØÎÙÊ ÚÎÁË, ÌÉÂÏ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ 
ÓÉÍ×ÏÌØÎÙÈ ÚÎÁËÏ×.
%%A variable name is a symbolic token or a sequence of symbolic tokens.
âÏÌØÛÉÎÓÔ×Ï ÓÉÍ×ÏÌØÎÙÈ ÚÎÁËÏ× Ñ×ÌÑÀÔÓÑ ÐÒÁ×ÉÌØÎÙÍÉ ÉÍÅÎÁÍÉ ÐÅÒÅÍÅÎÎÙÈ, ÎÏ 
ÞÔÏ ÕÇÏÄÎÏ Ó ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÍ ÚÎÁÞÅÎÉÅÍ ÐÏÄÏÂÎÏ {\tt draw}, {\tt +} ÉÌÉ {\tt ..} 
ÎÅÄÏÐÕÓÔÉÍÏ, ÎÁÐÒÉÍÅÒ, ÉÍÅÎÁ ÐÅÒÅÍÅÎÎÙÈ ÎÅ ÍÏÇÕÔ ÂÙÔØ ÍÁËÒÏÓÁÍÉ ÉÌÉ 
ÐÒÉÍÉÔÉ×ÁÍÉ MetaPost. 
%%Most symbolic tokens are legitimate variable names, but anything with a
%%predefined meaning like {\tt draw}, {\tt +}, or {\tt ..} is disallowed;
%%i.e., variable names cannot be macros or MetaPost primitives. 
üÔÏ ×ÔÏÒÏÓÔÅÐÅÎÎÏÅ ÏÇÒÁÎÉÞÅÎÉÅ ÄÏÐÕÓËÁÅÔ ÛÉÒÏËÉÊ ËÌÁÓÓ ÉÍÅÎ ÐÅÒÅÍÅÎÎÙÈ: 
{\tt alpha}, \verb|==>|, \verb|@&#$&| É \verb|~~| --- ×ÓÅ ÏÎÉ ÌÅÇÉÔÉÍÎÙÅ 
ÉÍÅÎÁ ÐÅÒÅÍÅÎÎÙÈ.
%%This
%%minor restriction allows an amazingly broad class of variable names:
%%{\tt alpha}, \verb|==>|, \verb|@&#$&|, and \verb|~~| are all legitimate
%%variable names. 
óÉÍ×ÏÌØÎÙÅ ÚÎÁËÉ ÂÅÚ ÓÐÅÃÉÁÌØÎÏÇÏ ÚÎÁÞÅÎÉÑ ÎÁÚÙ×ÁÀÔÓÑ ÜÔÉËÅÔËÁÍÉ  
({\em tags}\index{ÜÔÉËÅÔËÉ}).
%%Such symbolic tokens without special meanings are
%%called {\em tags}\index{tags}.

éÍÑ ÐÅÒÅÍÅÎÎÏÊ ÍÏÖÅÔ ÂÙÔØ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØÀ ÜÔÉËÅÔÏË, ÐÏÄÏÂÎÏÊ 
{\tt f.bot} ÉÌÉ {\tt f.top}.
%%A variable name can be a sequence of tags like {\tt f.bot} or {\tt
%%f.top}. 
üÔÁ ÉÄÅÑ ÓÌÕÖÉÔ ÄÌÑ ÓÏÚÄÁÎÉÑ ÎÅËÏÔÏÒÙÈ ×ÏÚÍÏÖÎÏÓÔÅÊ ÚÁÐÉÓÅÊ ðÁÓËÁÌÑ 
ÉÌÉ ÓÔÒÕËÔÕÒ óÉ.
%%The idea is to provide some of the functionality of Pascal
%%records or C structures. 
ôÁËÖÅ ×ÏÚÍÏÖÎÏ ÓÉÍÕÌÉÒÏ×ÁÔØ ÍÁÓÓÉ×Ù ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ ÉÍÅÎ ÐÅÒÅÍÅÎÎÙÈ, 
ÓÏÄÅÒÖÁÝÉÈ ÞÉÓÌÁ É ÓÉÍ×ÏÌØÎÙÅ ÚÎÁËÉ.
%%It is also possible to simulate arrays by
%%using variable names that contain numbers as well as symbolic tokens. 
îÁÐÒÉÍÅÒ, ÉÍÑ ÐÅÒÅÍÅÎÎÏÊ {\tt x2r} ÓÏÓÔÏÉÔ ÉÚ ÜÔÉËÅÔËÉ {\tt x}, 
ÞÉÓÌÁ 2 É ÜÔÉËÅÔËÉ~{\tt r}.
%%For example, the variable name {\tt x2r} consists of the tag {\tt x},
%%the number 2, and the tag~{\tt r}.  
íÏÇÕÔ ÂÙÔØ ÔÁËÖÅ ÐÅÒÅÍÅÎÎÙÅ, ÉÍÅÎÏ×ÁÎÎÙÅ {\tt x3r} É ÄÁÖÅ {\tt x3.14r}.
%%There can also be variables named {\tt x3r} and even {\tt x3.14r}. 
üÔÉ ÐÅÒÅÍÅÎÎÙÅ ÍÏÖÎÏ ÒÁÓÓÍÁÔÒÉ×ÁÔØ ËÁË ÍÁÓÓÉ×\index{ÍÁÓÓÉ×Ù} ÞÅÒÅÚ ËÏÎÓÔÒÕËÃÉÉ, 
ÐÏÄÏÂÎÙÅ {\tt x[i]r}, ÇÄÅ {\tt i} ÉÍÅÅÔ ÐÏÄÈÏÄÑÝÅÅ ÞÉÓÌÏ×ÏÅ ÚÎÁÞÅÎÉÅ. 
%%These variables can be treated as an
%%array\index{arrays} via constructions like {\tt x[i]r}, where {\tt i}
%%has an appropriate numeric value. 
óÕÍÍÁÒÎÙÊ ÏÂÚÏÒ ÓÉÎÔÁËÓÉÓÁ ÄÌÑ ÉÍÅÎ ÐÅÒÅÍÅÎÎÙÈ ÐÏËÁÚÁÎ ÎÁ ÒÉÓ.~\ref{syvar}.
%%The overall syntax for variable names is shown in Figure~\ref{syvar}.

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÐÅÒÅÍÅÎÎÁÑ} \rightarrow \descr{ÜÔÉËÅÔËÁ}\descr{ÓÕÆÆÉËÓ}$\\
%%$\tt \descr{variable} \rightarrow \descr{tag}\descr{suffix}$\\
$\tt \descr{ÓÕÆÆÉËÓ} \rightarrow \descr{ÐÕÓÔÏ} \;|\;
        \descr{ÓÕÆÆÉËÓ}\descr{ÉÎÄÅËÓ} \;|\; \descr{ÓÕÆÆÉËÓ}\descr{ÜÔÉËÅÔËÁ}$\\
%%$\tt \descr{suffix} \rightarrow \descr{empty} \;|\;
%%        \descr{suffix}\descr{subscript} \;|\; \descr{suffix}\descr{tag}$\\
$\tt \descr{ÉÎÄÅËÓ} \rightarrow \descr{ÞÉÓÌÏ} \;|\;
        \hbox{\tt [}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ]}$
%%$\tt \descr{subscript} \rightarrow \descr{number} \;|\;
%%        \hbox{\tt [}\descr{numeric expression}\hbox{\tt ]}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÉÍÅÎ ÐÅÒÅÍÅÎÎÙÈ.}
%%\caption{The syntax for variable names.}
\index{ÓÕÆÆÉËÓ?\tdescr{ÓÕÆÆÉËÓ}}\index{ÉÎÄÅËÓ?\tdescr{ÉÎÄÅËÓ}}
%%\index{suffix?\tdescr{suffix}}\index{subscript?\tdescr{subscript}}
\label{syvar}
\end{figure}

ðÅÒÅÍÅÎÎÙÅ, ÐÏÄÏÂÎÙÅ {\tt x2} É {\tt y2}, ÏÂÙÞÎÏ ÉÍÅÀÔ ÞÉÓÌÏ×ÏÅ ÚÎÁÞÅÎÉÅ, 
ÐÏÜÔÏÍÕ ÍÙ ÍÏÖÅÍ ÉÓÐÏÌØÚÏ×ÁÔØ ÆÁËÔ, ÞÔÏ {\tt z}\tdescr{ÓÕÆÆÉËÓ} --- ÜÔÏ 
ÓÏËÒÁÝÅÎÉÅ ÄÌÑ\index{z convention?{\tt z}-ÓÏÇÌÁÛÅÎÉÅ}\label{Dzconv}
$$ (x\descr{ÓÕÆÆÉËÓ},\, y\descr{ÓÕÆÆÉËÓ}), $$
ÄÌÑ ÇÅÎÅÒÁÃÉÉ ÐÁÒ-ÚÎÁÞÅÎÉÊ, ËÏÇÄÁ ÎÕÖÎÏ.
%%Variables like {\tt x2} and {\tt y2} take on numeric values by default, so we
%%can use the fact that {\tt z}\tdescr{suffix} is an abbreviation for\index{z %%convention?{\tt z} convention}\label{Dzconv}
%%$$ (x\descr{suffix},\, y\descr{suffix}) $$
%%to generate pair-valued variables when needed. 
ó ÄÒÕÇÏÊ ÓÔÏÒÏÎÙ, ÍÁËÒÏÓ {\tt beginfig}\index{beginfig?\texttt{beginfig}} 
ÕÎÉÞÔÏÖÁÅÔ ×ÓÅ ÓÕÝÅÓÔ×ÕÀÝÉÅ ÄÏ ÅÇÏ ÉÓÐÏÌÎÅÎÉÑ ÐÅÒÅÍÅÎÎÙÅ, ÎÁÞÉÎÁÀÝÉÅÓÑ Ó 
ÜÔÉËÅÔÏË {\tt x} ÉÌÉ {\tt y}, ÔÁË ÞÔÏ ÂÌÏËÉ {\tt beginfig} \ldots\ {\tt endfig} 
ÎÅ ×ÚÁÉÍÏÄÅÊÓÔ×ÕÀÔ ÄÒÕÇ Ó ÄÒÕÇÏÍ ÐÒÉ ÉÓÐÏÌØÚÏ×ÁÎÉÉ ÔÁËÏÊ ÓÈÅÍÙ ÉÍÅÎÏ×ÁÎÉÑ.
%%It turns out that the
%%{\tt beginfig}\index{beginfig?\texttt{beginfig}} macro wipes out
%%pre-existing values variables that begin with the tags {\tt x} or {\tt
%%y} so that {\tt beginfig} \ldots\ {\tt endfig} blocks do not interfere
%%with each other when this naming scheme is used. 
äÒÕÇÉÍÉ ÓÌÏ×ÁÍÉ, ÐÅÒÅÍÅÎÎÙÅ, ÎÁÞÉÎÁÀÝÉÅÓÑ Ó {\tt x}, {\tt y}, {\tt z}, 
ÌÏËÁÌØÎÙ\index{ÐÅÒÅÍÅÎÎÙÅ!ÌÏËÁÌØÎÙÅ}\index{ÌÏËÁÌØÎÏÓÔØ} × ÔÏÊ ËÁÒÔÉÎËÅ, ÇÄÅ ÏÎÉ 
ÉÓÐÏÌØÚÕÀÔÓÑ.
%%In other words,
%%variables that start with {\tt x}, {\tt y}, {\tt z} are
%%local\index{variables!local}\index{locality} to the figure they are used
%%in. 
ïÂÝÉÊ ÍÅÈÁÎÉÚÍ ÄÌÑ ÓÏÚÄÁÎÉÑ ÌÏËÁÌØÎÙÈ ÐÅÒÅÍÅÎÎÙÈ ÂÕÄÅÔ ÏÂÓÕÖÄÁÔØÓÑ 
× ÒÁÚÄÅÌÅ~\ref{grsec}.
%%General mechanisms for making variables local will be discussed in
%%Section~\ref{grsec}.

ïÂßÑ×ÌÅÎÉÑ ÔÉÐÁ\index{ÄÅËÌÁÒÁÃÉÉ}\index{ÄÅËÌÁÒÁÃÉÉ ÔÉÐÁ} 
ÄÅÌÁÅÔ ×ÏÚÍÏÖÎÙÍ ÉÓÐÏÌØÚÏ×ÁÎÉÅ ÐÏÞÔÉ ÌÀÂÏÊ ÓÈÅÍÙ ÉÍÅÎÏ×ÁÎÉÑ ÐÒÉ 
ÕÄÁÌÅÎÉÉ ×ÓÅÈ ÐÒÅÄÛÅÓÔ×ÕÀÝÉÈ ÚÎÁÞÅÎÉÊ, ÞÔÏ ÍÏÇÕÔ ×ÙÚ×ÁÔØ 
×ÚÁÉÍÏÄÅÊÓÔ×ÉÅ.
%%Type declarations\index{declarations}\index{type declarations}
%%make it possible to use almost any naming scheme while still
%%wiping out any previous value that might cause interference. 
îÁÐÒÉÍÅÒ, ÄÅËÌÁÒÁÃÉÑ 
$$ \hbox{\tt pair pp, a.b;} $$
ÄÅÌÁÅÔ {\tt pp} É {\tt a.b} ÎÅÉÚ×ÅÓÔÎÙÍÉ ÐÁÒÁÍÉ.
%%For example, the declaration
%%$$ \hbox{\tt pair pp, a.b;} $$
%%makes {\tt pp} and {\tt a.b} unknown pairs. 
ôÁËÁÑ ÄÅËÌÁÒÁÃÉÑ ÎÅ Ñ×ÌÑÅÔÓÑ ÓÔÒÏÇÏ ÌÏËÁÌØÎÏÊ, Ô.~Ë. {\tt pp} É {\tt a.b} 
ÎÅ ×ÏÓÓÔÁÎÁ×ÌÉ×ÁÀÔ Á×ÔÏÍÁÔÉÞÅÓËÉ Ó×ÏÉ ÐÒÅÄÛÅÓÔ×ÕÀÝÉÅ ÚÎÁÞÅÎÉÑ × ËÏÎÃÅ 
ÔÅËÕÝÅÇÏ ÒÉÓÕÎËÁ.
%%Such a declaration is not
%%strictly local since {\tt pp} and {\tt a.b} are not automatically
%%restored to their previous values at the end of the current figure. 
ïÎÉ ÏÐÑÔØ ÓÔÁÎÏ×ÑÔÓÑ ÎÅÉÚ×ÅÓÔÎÙÍÉ ÐÁÒÁÍÉ ÐÒÉ ÐÏ×ÔÏÒÅÎÉÉ ÜÔÏÊ ÄÅËÌÁÒÁÃÉÉ.
%%Of
%%course, they are restored to unknown pairs if the declaration is
%%repeated.

äÅËÌÁÒÁÃÉÉ ÒÁÂÏÔÁÀÔ ÏÄÉÎÁËÏ×ÙÍ ÏÂÒÁÚÏÍ ÄÌÑ ÌÀÂÏÇÏ ÄÒÕÇÏÇÏ ÉÚ ÏÓÔÁ×ÛÉÈÓÑ 
ÄÅ×ÑÔÉ ÔÉÐÏ×:  ÞÉÓÌÏ×ÏÇÏ, ÐÕÔÅ×ÏÇÏ, ÔÒÁÎÓÆÏÒÍÁÃÉÏÎÎÏÇÏ, Ã×ÅÔÏ×ÏÇÏ, 
cmyk-Ã×ÅÔÏ×ÏÇÏ, ÓÔÒÏËÏ×ÏÇÏ, ÌÏÇÉÞÅÓËÏÇÏ, ÒÉÓÕÎÏÞÎÏÇÏ É ÐÅÒØÅ×ÏÇÏ.
%%Declarations work the same way for any of the other eight types:
%%numeric, path, transform, color, string, boolean, picture, and pen. 
åÄÉÎÓÔ×ÅÎÎÏÅ ÏÇÒÁÎÉÞÅÎÉÅ × ÔÏÍ, ÞÔÏ ×Ù ÎÅ ÍÏÖÅÔÅ ÚÁÄÁÔØ ÔÏÞÎÙÊ ÞÉÓÌÏ×ÏÊ 
ÉÎÄÅËÓ × ÄÅËÌÁÒÁÃÉÉ ÐÅÒÅÍÅÎÎÏÊ.
%%The
%%only restriction is that you cannot give explicit numeric subscripts in
%%a variable declaration. 
îÅ ÐÉÛÉÔÅ ÏÛÉÂÏÞÎÙÈ ÄÅËÌÁÒÁÃÉÊ ÔÉÐÁ
$$ \hbox{\tt numeric q1, q2, q3;} $$
ÉÓÐÏÌØÚÕÊÔÅ ÏÂÏÂÝÅÎÎÙÊ ÓÉÍ×ÏÌ ÉÎÄÅËÓÁ\index{ÉÎÄÅËÓ!ÏÂÏÂÝÅÎÎÙÊ} 
{\tt []}\index{ÍÁÓÓÉ×Ù}\index{[]?\texttt{[]}!ÍÁÓÓÉ×}
×ÍÅÓÔÏ ÞÉÓÅÌ ÄÌÑ ÏÂßÑ×ÌÅÎÉÑ ×ÓÅÇÏ ÍÁÓÓÉ×Á:
$$ \hbox{\tt numeric q[];} $$
%%Do not give the illegal declaration
%%$$ \hbox{\tt numeric q1, q2, q3;} $$
%%use the generic subscript\index{subscript!generic} symbol
%%{\tt []}\index{arrays}\index{[]?\texttt{[]}!array}
%%instead, to declare the whole array:
%%$$ \hbox{\tt numeric q[];} $$
÷Ù ÍÏÖÅÔÅ ÔÁËÖÅ ÏÐÒÅÄÅÌÉÔØ ``ÍÎÏÇÏÒÁÚÍÅÒÎÙÅ'' 
ÍÁÓÓÉ×Ù\index{ÍÁÓÓÉ×Ù!ÍÎÏÇÏÍÅÒÎÙÅ}.
%%You can also declare ``multidimensional'' arrays\index{arrays!multidimensional}.
ðÏÓÌÅ ÄÅËÌÁÒÁÃÉÉ 
$$ \hbox{\tt path p[]q[], pq[][];} $$
{\tt p2q3} É {\tt pq1.4 5} --- ÜÔÏ Ä×Á ÐÕÔÉ.
%%After the declaration
%%$$ \hbox{\tt path p[]q[], pq[][];} $$
%%{\tt p2q3} and {\tt pq1.4 5} are both paths.

÷ÎÕÔÒÅÎÎÉÅ\index{×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} ÐÅÒÅÍÅÎÎÙÅ, 
ÐÏÄÏÂÎÙÅ {\tt tracingonline}, ÎÅ ÍÏÇÕÔ ÂÙÔØ ÏÂßÑ×ÌÅÎÙ ÎÏÒÍÁÌØÎÙÍ ÏÂÒÁÚÏÍ.
%%Internal\index{internal variables}\index{variables!internal} variables
%%like {\tt tracingonline} cannot be declared in the normal fashion. 
÷ÓÅ ×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ, ÏÂÓÕÖÄÁÅÍÙÅ × ÜÔÏÍ ÒÕËÏ×ÏÄÓÔ×Å ÉÍÅÀÔ ÚÎÁÞÅÎÉÑ 
ÉÚÎÁÞÁÌØÎÏ É ÎÉËÁË ÎÅ ÍÏÇÕÔ ÂÙÔØ ÄÅËÌÁÒÉÒÏ×ÁÎÙ ÓÎÏ×Á, ÎÏ ÅÓÔØ ÓÐÏÓÏ 
ÏÂßÑ×ÉÔØ, ÞÔÏ ÎÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ ÄÏÌÖÎÁ ×ÅÓÔÉ ÓÅÂÑ ÐÏÄÏÂÎÏ ×ÎÕÔÒÅÎÎÅÊ.
%%All
%%the internal variables discussed in this manual are predefined and do
%%not have to be declared at all, but there is a way to declare that a
%%variable should behave like a newly-created internal variable. 
üÔÏ ÄÅËÌÁÒÁÃÉÑ {\tt
newinternal}\index{newinternal?\texttt{newinternal}}\label{Dnewint}, 
ÚÁ ËÏÔÏÒÏÊ ÓÌÅÄÕÅÔ ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×.
%%The
%%declaration is {\tt
%%newinternal}\index{newinternal?\texttt{newinternal}}\label{Dnewint}
%%followed by a list of symbolic tokens. 
îÁÐÒÉÍÅÒ,
$$ \hbox{\tt newinternal a, b, c;} $$
ÏÂÕÓÌÏ×ÉÔ ÐÏ×ÅÄÅÎÉÅ {\tt a}, {\tt b} É {\tt c}, ËÁË É Õ ×ÎÕÔÒÅÎÎÉÈ ÐÅÒÅÍÅÎÎÙÈ.
%%For example,
%%$$ \hbox{\tt newinternal a, b, c;} $$
%%causes {\tt a}, {\tt b}, and {\tt c} to behave like internal variables.
ôÁËÉÅ ÐÅÒÅÍÅÎÎÙÅ ×ÓÅÇÄÁ ÉÍÅÀÔ ÉÚ×ÅÓÔÎÙÅ ÞÉÓÌÏ×ÙÅ ÚÎÁÞÅÎÉÑ É ÜÔÉ ÚÎÁÞÅÎÉÑ 
ÍÏÇÕÔ ÂÙÔØ ÉÚÍÅÎÅÎÙ ÔÏÌØËÏ ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ ÏÐÅÒÁÔÏÒÁ 
ÐÒÉÓ×ÁÉ×ÁÎÉÑ\index{ÐÒÉÓ×ÁÉ×ÁÎÉÅ} {\tt:=}\index{:=?\texttt{:=}}. 
%%Such variables always have known numeric values, and these values can
%%only be changed by using the assignment\index{assignment} operator
%%{\tt:=}\index{:=?\texttt{:=}}. 
÷ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ ÉÎÉÃÉÁÌÉÚÉÒÕÀÔÓÑ ÎÕÌÅÍ É, ËÒÏÍÅ ÔÏÇÏ, ÍÁËÒÏÐÁËÅÔ 
Plain\index{ÍÁËÒÏÓÙ Plain} ÄÁÅÔ ÎÅËÏÔÏÒÙÍ ÉÚ ÎÉÈ ÎÅÎÕÌÅ×ÙÅ ÚÎÁÞÅÎÉÑ. 
%%Internal variables are initially zero
%%except that the Plain\index{Plain macros} macro package gives some of
%%them nonzero initial values. 
(íÁËÒÏÓÙ Plain ÏÂÙÞÎÏ ÚÁÇÒÕÖÁÀÔÓÑ Á×ÔÏÍÁÔÉÞÅÓËÉ × ÎÁÞÁÌÅ ÒÁÂÏÔÙ ËÁË 
ÏÐÉÓÁÎÏ × ÒÁÚÄÅÌÅ~\ref{intro}.)
%%(The Plain macros are normally preloaded
%%automatically as explained in Section~\ref{intro}.)

\section{éÎÔÅÇÒÁÃÉÑ ÔÅËÓÔÁ É ÇÒÁÆÉËÉ}
%%\section{Integrating Text and Graphics}
\label{text}

MetaPost ÉÍÅÅÔ ÎÅÓËÏÌØËÏ ×ÏÚÍÏÖÎÏÓÔÅÊ ÄÌÑ ×ËÌÀÞÅÎÉÑ ÍÅÔÏË É ÐÒÏÞÅÇÏ 
ÔÅËÓÔÁ\index{ÔÅËÓÔ É ÇÒÁÆÉËÁ} × ÇÅÎÅÒÉÒÕÅÍÙÅ ÉÍ ÒÉÓÕÎËÉ. 
%%MetaPost has a number of features for including labels and other
%%text\index{text and graphics} in the figures it generates. 
ðÒÏÓÔÅÊÛÉÊ ÓÐÏÓÏ ÓÄÅÌÁÔØ ÜÔÏ × ÉÓÐÏÌØÚÏ×ÁÎÉÉ ËÏÍÁÎÄÙ {\tt
label}\index{label?\texttt{label}}\label{Dlabel}\index{label
suffix?\tdescr{ÓÕÆÆÉËÓ ÍÅÔËÉ}} 
$$ {\tt label}\descr{ÓÕÆÆÉËÓ ÍÅÔËÉ} \hbox{\tt (}
        \descr{×ÙÒÁÖÅÎÉÅ-ÓÔÒÏËÁ ÉÌÉ ËÁÒÔÉÎËÁ} \hbox{\tt,}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}
        \hbox{\tt );}
$$
%%The simplest
%%way to do this is to use the {\tt
%%label}\index{label?\texttt{label}}\label{Dlabel} statement\index{label
%%suffix?\tdescr{label suffix}}
%%$$ {\tt label}\descr{label suffix} \hbox{\tt (}
%%        \descr{string or picture expression} \hbox{\tt,}\, \descr{pair expression}
%%        \hbox{\tt );}
%%$$
\tdescr{÷ÙÒÁÖÅÎÉÅ-ÓÔÒÏËÁ ÉÌÉ ËÁÒÔÉÎËÁ} ÚÁÄÁÅÔ ÍÅÔËÕ, Á 
\tdescr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ} ÐÏÚÉÃÉÀ ÄÌÑ ÎÅÅ. 
%%The \tdescr{string or picture expression} gives the label and the
%%\tdescr{pair expression} says where to put it. 
\tdescr{óÕÆÆÉËÓ ÍÅÔËÉ} ÍÏÖÅÔ ÂÙÔØ \tdescr{ÐÕÓÔÙÍ}, ÞÔÏ ÂÕÄÅÔ ÏÚÎÁÞÁÔØ 
ÃÅÎÔÒÉÒÏ×ÁÔØ ÍÅÔËÕ ÎÁ ÚÁÄÁÎÎÙÈ ËÏÏÒÄÉÎÁÔÁÈ.
%%The \tdescr{label
%%suffix} can be \tdescr{empty} in which case the label is just centered
%%on the given coordinates. 
åÓÌÉ ×Ù ÒÁÚÍÅÞÁÅÔÅ ÎÅËÏÔÏÒÙÅ ÕÞÁÓÔËÉ ÄÉÁÇÒÁÍÍÙ, ÔÏ ×ÁÍ ×ÅÒÏÑÔÎÏ ÐÏÎÁÄÏÂÉÔÓÑ 
ÓÌÅÇËÁ ÓÍÅÓÔÉÔØ ÍÅÔËÕ, ÞÔÏÂÙ ÉÚÂÅÖÁÔØ ÎÁËÌÁÄËÉ.
%%If you are labeling some feature of a diagram
%%you probably want to offset the label slightly to avoid overlapping.
üÔÏ ÉÌÌÀÓÔÒÉÒÕÅÔÓÑ ÎÁ ÒÉÓ.~\ref{fig16}, ÇÄÅ ÍÅÔËÁ {\tt \qq{a}\qq} 
ÒÁÚÍÅÝÁÅÔÓÑ ÎÁÄ ÓÅÒÅÄÉÎÏÊ ÕËÁÚÙ×ÁÅÍÏÊ ÌÉÎÉÉ, Á ÍÅÔËÁ {\tt \qq{b}\qq} --- 
ÓÌÅ×Á ÏÔ ÓÅÒÅÄÉÎÙ Ó×ÏÅÊ ÌÉÎÉÉ.
%%This is illustrated in Figure~\ref{fig16} where the {\tt \qq{a}\qq} label is
%%placed above the midpoint of the line it refers to and the {\tt \qq{b}\qq}
%%label is to the left of the midpoint of its line. 
üÔÏ ÄÏÓÔÉÇÁÅÔÓÑ ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ {\tt label.top}\index{top?\texttt{top}} ÄÌÑ 
ÍÅÔËÉ {\tt \qq{a}\qq} É {\tt label.lft}\index{lft?\texttt{lft}} ÄÌÑ
ÍÅÔËÉ {\tt \qq{b}\qq}, ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓÕÎËÅ.
%%This is achieved by
%%using {\tt label.top}\index{top?\texttt{top}} for the {\tt \qq{a}\qq} label
%%and {\tt label.lft}\index{lft?\texttt{lft}} for the {\tt \qq{b}\qq} label as
%%shown in the figure. 
\tdescr{óÕÆÆÉËÓ ÍÅÔËÉ} ÕËÁÚÙ×ÁÅÔ ÐÏÚÉÃÉÀ ÍÅÔËÉ ÏÔÎÏÓÉÔÅÌØÎÏ ÚÁÄÁÎÎÙÈ 
ËÏÏÒÄÉÎÁÔ.
%%The \tdescr{label suffix} specifies the position
%%of the label relative to the specified coordinates. 
ðÏÌÎÏÅ ÍÎÏÖÅÓÔ×Ï ×ÏÚÍÏÖÎÏÓÔÅÊ --- ÜÔÏ\index{rt?\texttt{rt}}\index{bot?\texttt{bot}}%
\index{ulft?\texttt{ulft}}\index{urt?\texttt{urt}}\index{llft?\texttt{llft}}\index{lrt?\texttt{lrt}}
$$ {\tt \descr{ÓÕÆÆÉËÓ ÍÅÔËÉ} \rightarrow
   \descr{ÐÕÓÔÏ} \;|\; lft \;|\; rt \;|\; top \;|\; bot \;|\;
   ulft \;|\;urt \;|\; llft \;|\; lrt},
$$
ÇÄÅ {\tt lft} É {\tt rt} ÏÚÎÁÞÁÀÔ ×ÌÅ×Ï É ×ÐÒÁ×Ï, Á {\tt llft}, {\tt
ulft} É Ô.~Ð. ÚÎÁÞÁÔ ×ÎÉÚ É ×ÌÅ×Ï, ××ÅÒÈ É ×ÌÅ×Ï É Ô.~Ð. 
%%The complete set of
%%possibilities is\index{rt?\texttt{rt}}\index{bot?\texttt{bot}}%
%%\index{ulft?\texttt{ulft}}\index{urt?\texttt{urt}}\index{llft?\texttt{llft}}\index{lrt?\t%%exttt{lrt}}
%%$$ \tt \descr{label suffix} \rightarrow
%%   \descr{empty} \;|\; lft \;|\; rt \;|\; top \;|\; bot \;|\;
%%   ulft \;|\;urt \;|\; llft \;|\; lrt
%%$$
%%where {\tt lft} and {\tt rt} mean left and right and {\tt llft}, {\tt
%%ulft}, etc.\ mean lower left, upper left, etc. 
äÅÊÓÔ×ÉÔÅÌØÎÏÅ ÒÁÓÓÔÏÑÎÉÅ, ÎÁ ËÏÔÏÒÏÅ ÂÕÄÅÔ ÓÍÅÝÅÎÁ ÍÅÔËÁ × ÚÁÄÁÎÎÏÍ 
ÎÁÐÒÁ×ÌÅÎÉÉ, ÏÐÒÅÄÅÌÑÅÔÓÑ ×ÎÕÔÒÅÎÎÅÊ 
ÐÅÒÅÍÅÎÎÏÊ \index{×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ}
{\tt
labeloffset}\index{labeloffset?\texttt{labeloffset}}\label{Dlaboff}.
%%The actual amount by
%%which the label is offset in whatever direction is determined by the
%%internal variable\index{internal variables}\index{variables!internal}
%%{\tt
%%labeloffset}\index{labeloffset?\texttt{labeloffset}}\label{Dlaboff}.

\begin{figure}[htp]
$$
\begin{verbatim}
beginfig(17);
a=.7in; b=.5in;
z0=(0,0);
z1=-z3=(a,0);
z2=-z4=(0,b);
draw z1..z2..z3..z4..cycle;
draw z1--z0--z2;
label.top("a", .5[z0,z1]);
label.lft("b", .5[z0,z2]);
dotlabel.bot("(0,0)", z0);
endfig;
\end{verbatim}
\qquad \mathcenter{\includegraphics{manfig-ru-17}}
$$
\caption{ëÏÄ MetaPost É ÒÅÚÕÌØÔÁÔ ×Ù×ÏÄÁ}
%%\caption{MetaPost code and the resulting output}
\label{fig16}
\end{figure}

òÉÓ.\ref{fig16} ÔÁËÖÅ ÉÌÌÀÓÔÒÉÒÕÅÔ ËÏÍÁÎÄÕ {\tt dotlabel}\index{dotlabel?\texttt{dotlabel}}\label{Ddotlab}.
%%Figure~\ref{fig16} also illustrates the
%%{\tt dotlabel}\index{dotlabel?\texttt{dotlabel}}\label{Ddotlab}
%%statement. 
ïÎÁ × ÔÏÞÎÏÓÔÉ ÔÁËÁÑ ÖÅ ËÁË ËÏÍÁÎÄÁ {\tt label}, ÚÁ ËÏÔÏÒÏÊ ÓÌÅÄÕÅÔ 
ËÏÍÁÎÄÁ ÒÉÓÏ×ÁÎÉÑ ÔÏÞËÉ × ÚÁÄÁÎÎÙÈ ËÏÏÒÄÉÎÁÔÁÈ.
%%This is effectively
%%like a {\tt label} statement followed by a statement drawing a dot at
%%the indicated coordinates. 
îÁÐÒÉÍÅÒ, 
$$ \hbox{\tt dotlabel.bot(\qq(0,0)\qq, z0)} $$
ÐÏÍÅÝÁÅÔ ÔÏÞËÕ × {\tt z0} É ÚÁÔÅÍ ÒÁÚÍÅÝÁÅÔ ÍÅÔËÕ ``(0,0)'' ÔÏÞÎÏ ÐÏÄ ÔÏÞËÏÊ.
%%For example
%%$$ \hbox{\tt dotlabel.bot("(0,0)", z0)} $$
%%places a dot at {\tt z0} and then puts the label ``(0,0)'' just below the dot.

äÒÕÇÏÊ ÁÌØÔÅÒÎÁÔÉ×ÏÊ Ñ×ÌÑÅÔÓÑ ÍÁËÒÏÓ {\tt thelabel}\index{thelabel?\texttt{thelabel}}\label{Dthelab}. 
%%Another alternative is the macro
%%{\tt thelabel}\index{thelabel?\texttt{thelabel}}\label{Dthelab}. 
ïÎ ÉÍÅÅÔ ÔÁËÏÊ ÖÅ ÓÉÎÔÁËÓÉÓ, ÞÔÏ É ËÏÍÁÎÄÙ {\tt label} É {\tt dotlabel}, ÎÏ 
ÏÎ ×ÏÚ×ÒÁÝÁÅÔ ÒÅÚÕÌØÔÁÔ ËÁË \tdescr{ÐÅÒ×ÉÞÎÙÊ ÒÉÓÕÎÏË} ×ÍÅÓÔÏ ÅÇÏ 
ÄÅÊÓÔ×ÉÔÅÌØÎÏÇÏ ÉÚÏÂÒÁÖÅÎÉÑ.
%%This has
%%the same syntax as the {\tt label} and {\tt dotlabel} statements except that it
%%returns the label as a \tdescr{picture primary} instead of actually drawing it.
ôÁËÉÍ ÏÂÒÁÚÏÍ, 
$$ \hbox{\tt label.bot(\qq(0,0)\qq, z0)} $$
ÜË×É×ÁÌÅÎÔÎÏ
$$ \hbox{\tt draw thelabel.bot(\qq(0,0)\qq, z0)} $$
%%Thus
%%$$ \hbox{\tt label.bot("(0,0)", z0)} $$
%%is equivalent to
%%$$ \hbox{\tt draw thelabel.bot("(0,0)", z0)} $$

äÌÑ ÐÒÏÓÔÙÈ ÓÌÕÞÁÅ× ÒÁÚÍÅÞÅÎÎÙÈ ÒÉÓÕÎËÏ×, ×ÁÍ ÍÏÖÅÔ ÏÂÙÞÎÏ ÂÙÔØ ÄÏÓÔÁÔÏÞÎÏ 
{\tt label} É {\tt dotlabel}.
%%For simple applications of labeled figures, you can normally get by with
%%just {\tt label} and {\tt dotlabel}. 
äÏÐÏÌÎÉÔÅÌØÎÏ ×Ù ÍÏÖÅÔÅ ÉÓÐÏÌØÚÏ×ÁÔØ ËÏÒÏÔËÕÀ ÆÏÒÍÕ ËÏÍÁÎÄÙ {\tt dotlabel}, 
ÞÔÏ ÓÜËÏÎÏÍÉÔ ÍÎÏÇÏ ×ÒÅÍÅÎÉ, ËÏÇÄÁ ×Ù ÉÍÅÅÔÅ ÍÎÏÇÏ ÔÏÞÅË {\tt z0}, {\tt z1}, 
{\tt z.a}, {\tt z.b}, É Ô.~Ð. É ÈÏÔÉÔÅ ÉÓÐÏÌØÚÏ×ÁÔØ ÓÕÆÆÉËÓÙ {\tt z} ËÁË ÍÅÔËÉ. 
%%In fact, you may be able to use a
%%short form of the {\tt dotlabel} statement that saves a lot of typing
%%when you have many points {\tt z0}, {\tt z1}, {\tt z.a}, {\tt z.b},
%%etc.\ and you want to use the {\tt z} suffixes as labels. 
ëÏÍÁÎÄÁ \index{dotlabels?\texttt{dotlabels}}\label{Ddotlbs}
$$ \hbox{\tt dotlabels.rt(0, 1, a);} $$
ÜË×É×ÁÌÅÎÔÎÁ 
$$ \hbox{\tt dotlabel.rt(\qq0\qq,z0); dotlabel.rt(\qq1\qq,z1); dotlabel.rt({\qq}a{\qq},z.a);} $$
%%The statement\index{dotlabels?\texttt{dotlabels}}\label{Ddotlbs}
%%$$ \hbox{\tt dotlabels.rt(0, 1, a);} $$
%%is equivalent to
%%$$ \hbox{\tt dotlabel.rt("0",z0); dotlabel.rt("1",z1); dotlabel.rt("a",z.a);} $$
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÁÒÇÕÍÅÎÔ {\tt dotlabels} --- ÜÔÏ ÓÐÉÓÏË ÓÕÆÆÉËÓÏ× ÄÌÑ 
ÐÅÒÅÍÅÎÎÙÈ {\tt z}, Á \tdescr{ÓÕÆÆÉËÓ ÍÅÔËÉ}, ÚÁÄÁ×ÁÅÍÙÊ Ó {\tt dotlabels}, 
ÉÓÐÏÌØÚÕÅÔÓÑ ÄÌÑ ÐÏÚÉÃÉÏÎÉÒÏ×ÁÎÉÑ ×ÓÅÈ ÍÅÔÏË.
%%Thus the argument to {\tt dotlabels} is a list of suffixes for which {\tt z}
%%variables are known, and the \tdescr{label suffix} given with {\tt dotlabels}
%%is used to position all the labels.

åÓÔØ ÅÝÅ ËÏÍÁÎÄÁ {\tt
labels}\index{labels?\texttt{labels}}\label{Dlabels}, ÁÎÁÌÏÇÉÞÎÁÑ 
{\tt dotlabels}, ÎÏ ÅÅ ÉÓÐÏÌØÚÏ×ÁÎÉÅ ÎÅ ÒÅËÏÍÅÎÄÕÅÔÓÑ, Ô.~Ë. ÏÎÁ ÓÏÚÄÁÅÔ 
ÐÒÏÂÌÅÍÙ ÓÏ×ÍÅÓÔÉÍÏÓÔÉ Ó \MF\index{metafont?\MF}. 
%%There is also a {\tt
%%labels}\index{labels?\texttt{labels}}\label{Dlabels} statement that is
%%analogous to {\tt dotlabels} but its use is discouraged because it
%%presents compatibility problems with \MF\index{metafont?\MF}. 
îÅËÏÔÏÒÙÅ ×ÅÒÓÉÉ ÓÔÁÎÄÁÒÔÎÏÇÏ ÍÁËÒÏÐÁËÅÔÁ Plain\index{ÍÁËÒÏÓÙ Plain} ÏÐÒÅÄÅÌÑÀÔ 
{\tt labels} ËÁË ÓÉÎÏÎÉÍ {\tt dotlabels}.
%%Some
%%versions of the preloaded Plain\index{Plain macros} macro package define
%%{\tt labels} to be synonymous with {\tt dotlabels}.

äÌÑ ËÏÍÁÎÄ ÒÁÚÍÅÔËÉ, ÔÁËÉÈ ËÁË {\tt label} É {\tt dotlabel}, ÉÓÐÏÌØÚÕÀÝÉÈ 
ÓÔÒÏËÏ×ÙÅ ×ÙÒÁÖÅÎÉÑ ÄÌÑ ÔÅËÓÔÁ ÍÅÔÏË, ÓÔÒÏËÉ ÐÅÞÁÔÁÀÔÓÑ × ÓÔÁÎÄÁÒÔÎÏÍ 
ÛÒÉÆÔÅ, ÏÐÒÅÄÅÌÑÅÍÏÍ ÓÔÒÏËÏ×ÏÊ ÐÅÒÅÍÅÎÎÏÊ {\tt
defaultfont}\index{defaultfont?\texttt{defaultfont}}\label{Ddffont}.
%%For labeling statements such as {\tt label} and {\tt dotlabel} that use
%%a string expression for the label text, the string gets typeset in a
%%default font as determined by the string variable {\tt
%%defaultfont}\index{defaultfont?\texttt{defaultfont}}\label{Ddffont}.
îÁÞÁÌØÎÏÅ ÚÎÁÞÅÎÉÅ {\tt defaultfont} --- ÜÔÏ  ÏÂÙÞÎÏ {\tt \qq{cmr10}\qq},
ÎÏ ÏÎÏ ÍÏÖÅÔ ÂÙÔØ ÉÚÍÅÎÅÎÏ ÎÁ ÄÒÕÇÏÅ ÉÍÑ ÛÒÉÆÔÁ ÐÒÉÓ×ÁÉ×ÁÎÉÅÍ, ÎÁÐÒÉÍÅÒ, 
$$ \hbox{\tt defaultfont:=\qq{ptmr8r}\qq}, $$
\ttt{ptmr8r} --- ÜÔÏ ÔÉÐÉÞÎÙÊ ÓÐÏÓÏÂ ÓÏÓÌÁÔØÓÑ ÎÁ ÛÒÉÆÔ Times-Roman × \TeX.
%%The initial value of {\tt defaultfont} is likely to be {\tt \qq{cmr10}\qq},
%%but it can be changed to a different font name by giving an assignment
%%such as
%%$$ \hbox{\tt defaultfont:=\qq{ptmr8r}\qq} $$
%%\ttt{ptmr8r} is a typical way to refer to the Times-Roman font in \TeX.
%%The discussion of font names on p.\ \pageref{fontname} explains further.

åÓÔØ ÅÝÅ ÞÉÓÌÏ×ÏÅ ËÏÌÉÞÅÓÔ×Ï, ÎÁÚÙ×ÁÅÍÏÅ {\tt defaultscale}\index{defaultscale?\texttt{defaultscale}}\label{Ddfscale}, 
ÏÐÒÅÄÅÌÑÀÝÅÅ ÒÁÚÍÅÒ ÛÒÉÆÔÁ.
%%There is also a numeric quantity called
%%{\tt defaultscale}\index{defaultscale?\texttt{defaultscale}}\label{Ddfscale}
%%that determines the type size.
ðÏËÁ {\tt default\-scale} ÒÁ×ÎÏ 1, ×Ù ÐÏÌÕÞÁÅÔÅ ``ÎÏÒÍÁÌØÎÙÊ ÒÁÚÍÅÒ'', 
ËÏÔÏÒÙÊ ÏÂÙÞÎÏ ÒÁ×ÅÎ 10 ÐÕÎËÔÁÍ, ÎÏ ÜÔÏ ÍÏÖÎÏ ÉÚÍÅÎÉÔØ.
%%When {\tt default\-scale} is 1, you get the ``normal size'' which is
%%usually 10 point, but this can also be changed. 
îÁÐÒÉÍÅÒ, 
$$ \hbox{\tt defaultscale := 1.2} $$
ÄÅÌÁÅÔ ÍÅÔËÉ ÎÁ Ä×ÁÄÃÁÔØ ÐÒÏÃÅÎÔÏ× ÂÏÌØÛÅ.
%%For instance
%%$$ \hbox{\tt defaultscale := 1.2} $$
%%makes labels come out twenty percent larger. 
åÓÌÉ ×ÁÍ ÎÅÉÚ×ÅÓÔÅÎ ÎÏÒÍÁÌØÎÙÊ ÒÁÚÍÅÒ É ×Ù ÈÏÔÉÔÅ ÂÙÔØ Õ×ÅÒÅÎÎÙÍÉ × 
ËÏÎËÒÅÔÎÏÍ ÒÁÚÍÅÒÅ ÛÒÉÆÔÁ, ÓËÁÖÅÍ 12 ÐÕÎËÔÏ×, ×Ù ÍÏÖÅÔÅ ÉÓÐÏÌØÚÏ×ÁÔØ 
ÏÐÅÒÁÔÏÒ {\tt fontsize}\index{fontsize?\texttt{fontsize}}\label{Dfntsiz} 
ÄÌÑ ÏÐÒÅÄÅÌÅÎÉÑ ÎÏÒÍÁÌØÎÏÇÏ ÒÁÚÍÅÒÁ, ÎÁÐÒÉÍÅÒ,
$$ \hbox{\tt defaultscale := 12pt/fontsize defaultfont;} $$
%%If you do not know the
%%normal size and you want to be sure the text comes out at some specific
%%size, say 12 points, you can use the {\tt
%%fontsize}\index{fontsize?\texttt{fontsize}}\label{Dfntsiz} operator to
%%determine the normal size: e.g.,
%%$$ \hbox{\tt defaultscale := 12pt/fontsize defaultfont;} $$

\label{fontname}
ëÏÇÄÁ ×Ù ÍÅÎÑÅÔÅ {\tt defaultfont}, ÔÏ ÉÍÑ ÎÏ×ÏÇÏ ÛÒÉÆÔÁ ÄÏÌÖÎÏ ÂÙÔØ 
ÞÅÍ-ÔÏ, ÞÔÏ \TeX\ ÓÍÏÖÅÔ ÐÏÎÑÔØ, Ô.~Ë. MetaPost ÐÏÌÕÞÁÅÔ ÉÎÆÏÒÍÁÃÉÀ Ï 
×ÙÓÏÔÅ É ÛÉÒÉÎÅ ÞÔÅÎÉÅÍ 
{\tt tfm}\index{tfm file?{\tt tfm}-ÆÁÊÌ}\index{ÆÁÊÌÙ!tfm?{\tt tfm}}-ÆÁÊÌÁ.
%%When you change {\tt defaultfont}, the new font name should be something
%%that \TeX\ would understand since MetaPost gets height and width
%%information by reading a {\tt tfm}\index{tfm file?{\tt tfm}
%%file}\index{files!tfm?{\tt tfm}} file. 
(üÔÏ ÏÂßÑÓÎÑÅÔÓÑ × {\sl The \TeX book\/} \cite{kn:a}.)
%%(This is explained in {\sl The \TeX book\/} \cite{kn:a}.) 
äÏÌÖÎÏ ÂÙÔØ ×ÏÚÍÏÖÎÏ ÉÓÐÏÌØÚÏ×ÁÔØ ×ÓÔÒÏÅÎÎÙÅ ÛÒÉÆÔÙ 
PostScript\index{PostScript!ÛÒÉÆÔÙ}, ÎÏ ÉÈ ÉÍÅÎÁ ÚÁ×ÉÓÑÔ ÏÔ ÓÉÓÔÅÍÙ.
%%It should be possible to use built-in
%%PostScript\index{PostScript!fonts} fonts, but the names for
%%them are system-dependent. 
îÅËÏÔÏÒÙÅ ÔÉÐÉÞÎÙÅ ÉÍÅÎÁ ÛÒÉÆÔÏ× --- ÜÔÏ {\tt ptmr8r} ÄÌÑ 
Times-Roman\index{Times-Roman}, \ttt{pplr8r} ÄÌÑ Palatino\index{Palatino} 
É \ttt{phvr} ÄÌÑ Helvetica\index{Helvetica}. 
%%Some typical ones are {\tt ptmr8r} for
%%Times-Roman\index{Times-Roman}, \ttt{pplr8r} for Palatino\index{Palatino},
%%and \ttt{phvr} for Helvetica\index{Helvetica}. 
äÏËÕÍÅÎÔ Fontname, ÄÏÓÔÕÐÎÙÊ × 
\url{http://tug.org/fontname}, ÓÏÄÅÒÖÉÔ ÍÎÏÇÏ ÉÎÆÏÒÍÁÃÉÉ Ï ÉÍÅÎÁÈ ÛÒÉÆÔÏ× 
É \TeX. 
%%The Fontname document,
%%available at \url{http://tug.org/fontname}, has much more information
%%about font names and \TeX. 
\TeX\index{TeX?\TeX!ÛÒÉÆÔÙ}-ÛÒÉÆÔ, ÔÁËÏÊ ËÁË {\tt cmr10}, Ñ×ÌÑÅÔÓÑ ÎÅÍÎÏÇÏ 
ÏÐÁÓÎÙÍ, ÐÏÔÏÍÕ ÞÔÏ ÏÎ ÎÅ ÉÍÅÅÔ ÓÉÍ×ÏÌÁ ÐÒÏÂÅÌ É ÎÅËÏÔÏÒÙÈ ÄÒÕÇÉÈ ÓÉÍ×ÏÌÏ× 
ASCII.
%%A \TeX\index{TeX?\TeX!fonts} font such
%%as {\tt cmr10} is a little dangerous because it does not have a space
%%character or certain ASCII symbols.

MetaPost ÎÅ ÉÓÐÏÌØÚÕÅÔ ÉÎÆÏÒÍÁÃÉÀ Ï ÌÉÇÁÔÕÒÁÈ\index{ÌÉÇÁÔÕÒÙ} É 
ËÅÒÎÉÎÇÁÈ\index{ËÅÒÎÉÎÇ}, ÞÔÏ ÓÏÄÅÒÖÉÔÓÑ × ÛÒÉÆÔÁÈ \TeX.
%%MetaPost does not use the ligatures\index{ligatures} and
%%kerning\index{kerning} information that comes with a \TeX\ font.
âÏÌÅÅ ÔÏÇÏ, ÓÁÍ MetaPost ÎÅ ÍÏÖÅÔ ÉÎÔÅÒÐÒÅÔÉÒÏ×ÁÔØ ×ÉÒÔÕÁÌØÎÙÅ ÛÒÉÆÔÙ.
%%Further, MetaPost itself does not interpret virtual fonts.

\subsection{îÁÂÏÒ ×ÁÛÉÈ ÍÅÔÏË}
%%\subsection{Typesetting Your Labels}

\label{Dbtex}
\index{ÍÅÔËÉ, ÎÁÂÏÒ}
%%\index{labels, typesetting}

\TeX\index{TeX?\TeX} ÍÏÖÅÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎ ÄÌÑ ÆÏÒÍÁÔÉÒÏ×ÁÎÉÑ ÓÌÏÖÎÙÈ ÍÅÔÏË.
%%\TeX\index{TeX?\TeX} may be used to format complex labels.
åÓÌÉ ×Ù ÎÁÐÉÛÉÔÅ \index{btex?\texttt{btex}}\index{etex?\texttt{etex}}
$$ {\tt btex}\, \descr{ËÏÍÁÎÄÙ ÐÅÞÁÔÉ}\, {\tt etex} $$
×Ï ×ÈÏÄÎÏÍ ÆÁÊÌÅ MetaPost, ÔÏ \tdescr{ËÏÍÁÎÄÙ ÐÅÞÁÔÉ} ÂÕÄÕÔ ÏÂÒÁÂÏÔÁÎÙ 
\TeX\ É ÔÒÁÎÓÌÉÒÏ×ÁÎÙ × ×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÕ, ÔÏÞÎÅÅ × \tdescr{ÐÅÒ×ÉÞÎÙÊ  
ÒÉÓÕÎÏË}, ÞÔÏ ÓÍÏÖÅÔ ÉÓÐÏÌØÚÏ×ÁÔØÓÑ × ËÏÍÁÎÄÅ {\tt label} ÉÌÉ {\tt dotlabel}. 
%%If you say\index{btex?\texttt{btex}}\index{etex?\texttt{etex}}
%%$$ {\tt btex}\, \descr{typesetting commands}\, {\tt etex} $$
%%in a MetaPost input file, the \tdescr{typesetting commands} get processed by
%%\TeX\ and translated into a picture expression
%%(actually a \tdescr{picture primary}) that can be used in a {\tt label}
%%or {\tt dotlabel} statement. 
ðÒÏÂÅÌÙ ÐÏÓÌÅ {\tt btex} ÉÌÉ ÐÅÒÅÄ {\tt etex} ÉÇÎÏÒÉÒÕÀÔÓÑ.
%%Any spaces after {\tt btex} or before {\tt etex} are ignored. 
îÁÐÒÉÍÅÒ, ËÏÍÁÎÄÁ 
$$ \hbox{\verb|label.lrt(btex $\sqrt x$ etex, (3,sqrt 3)*u)|} $$
ÎÁ ÒÉÓ.~\ref{fig17} ÐÏÍÅÓÔÉÔ ÍÅÔËÕ $\sqrt x$ ÓÎÉÚÕ É ×ÐÒÁ×Ï ÏÔ 
ÔÏÞËÉ {\tt (3,sqrt 3)*u}.
%%For instance, the statement
%%$$ \hbox{\verb|label.lrt(btex $\sqrt x$ etex, (3,sqrt 3)*u)|} $$
%%in Figure~\ref{fig17} places the label $\sqrt x$ at the lower right of the
%%point {\tt (3,sqrt 3)*u}.

\begin{figure}[htp]
$$
\begin{verbatim}
beginfig(18);
numeric u;
u = 1cm;
draw (0,2u)--(0,0)--(4u,0);
pickup pencircle scaled 1pt;
draw (0,0){up}
  for i=1 upto 8: ..(i/2,sqrt(i/2))*u  endfor;
label.lrt(btex $\sqrt x$ etex, (3,sqrt 3)*u);
label.bot(btex $x$ etex, (2u,0));
label.lft(btex $y$ etex, (0,u));
endfig;
\end{verbatim}
\qquad \mathcenter{\includegraphics{manfig-ru-18}}
$$
\caption{ðÒÏÉÚ×ÏÌØÎÙÊ \TeX\ × ËÁÞÅÓÔ×Å ÍÅÔËÉ}
%%\caption{Arbitrary \TeX\ as labels}
\label{fig17}
\end{figure}

òÉÓ.~\ref{fig18} ÉÌÌÀÓÔÒÉÒÕÅÔ ÎÅËÏÔÏÒÙÅ ÂÏÌÅÅ ÓÌÏÖÎÙÅ ×ÅÝÉ, ÞÔÏ ÍÏÖÎÏ 
ÓÄÅÌÁÔØ Ó ÍÅÔËÁÍÉ.
%%Figure~\ref{fig18} illustrates some of the more complicated things that can
%%be done with labels. 
÷ÓÌÅÄÓÔ×ÉÅ ÔÏÇÏ, ÞÔÏ ÒÅÚÕÌØÔÁÔÏÍ {\tt btex} \ldots {\tt etex} Ñ×ÌÑÅÔÓÑ 
ËÁÒÔÉÎËÁ, ÉÍ ÍÏÖÎÏ ÏÐÅÒÉÒÏ×ÁÔØ ËÁË ËÁÒÔÉÎËÏÊ.
%%Since the result of {\tt btex} \ldots {\tt etex} is
%%a picture, it can be operated on like a picture. 
÷ ÞÁÓÔÎÏÓÔÉ, Ë ËÁÒÔÉÎËÁÍ ×ÏÚÍÏÖÎÏ ÐÒÉÍÅÎÑÔØ ÔÒÁÎÓÆÏÒÍÁÃÉÉ.
%%In particular, it is possible
%%to apply transformations to pictures. 
íÙ ÐÏËÁ ÎÅ ÏÂÓÕÖÄÁÌÉ ÓÉÎÔÁËÓÉÓ ÄÌÑ ÜÔÏÇÏ, ÎÏ \tdescr{ÒÉÓÕÎÏË-×ÔÏÒÉÞÎÏÓÔØ}
ÍÏÖÅÔ ÂÙÔØ \index{×ÒÁÝÁÅÍÙÊ ÔÅËÓÔ}\index{rotated?\texttt{rotated}}
$$ \descr{ÒÉÓÕÎÏË-×ÔÏÒÉÞÎÏÓÔØ}\, {\tt rotated}\, \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ} $$
%%We have not discussed the syntax for
%%this yet, but a \tdescr{picture secondary}
%%can be\index{rotated text}\index{rotated?\texttt{rotated}}
%%$$ \descr{picture secondary}\, {\tt rotated}\, \descr{numeric primary} $$
üÔÏ ÉÓÐÏÌØÚÕÅÔÓÑ ÎÁ ÒÉÓ.~\ref{fig18} ÄÌÑ ×ÒÁÝÅÎÉÑ ÍÅÔËÉ ``$y$ axis'' ÔÁË, 
ÞÔÏ ÏÎÁ ÒÁÓÐÏÌÁÇÁÅÔÓÑ ÐÏ-×ÅÒÔÉËÁÌÉ.
%%This is used in Figure~\ref{fig18} to rotate the label ``$y$ axis'' so that
%%it runs vertically.

\begin{figure}[htp]
$$
\begin{verbatim}
beginfig(19);
numeric ux, uy;
120ux=1.2in; 4uy=2.4in;
draw (0,4uy)--(0,0)--(120ux,0);
pickup pencircle scaled 1pt;
draw (0,uy){right}
  for ix=1 upto 8:
    ..(15ix*ux, uy*2/(1+cosd 15ix))
  endfor;
label.bot(btex $x$ axis etex, (60ux,0));
label.lft(btex $y$ axis etex rotated 90,
          (0,2uy));
label.lft(
  btex $\displaystyle y={2\over1+\cos x}$ etex,
  (120ux, 4uy));
endfig;
\end{verbatim}
\qquad \mathcenter{\includegraphics{manfig-ru-19}}
$$
\caption{íÁÔÅÍÁÔÉÞÅÓËÉÅ ÍÅÔËÉ \TeX\ É ÍÅÔËÉ, ×ÒÁÝÁÅÍÙÅ MetaPost}
%%\caption{\TeX\ labels with display math, and rotated by MetaPost}
\label{fig18}
\end{figure}

äÒÕÇÏÊ ÓÌÏÖÎÏÓÔØÀ ÎÁ ÒÉÓ.~\ref{fig18} Ñ×ÌÑÅÔÓÑ ÉÓÐÏÌØÚÏ×ÁÎÉÅ ÕÒÁ×ÎÅÎÉÑ
$$y={2\over 1+\cos x}$$
ËÁË ÍÅÔËÉ.
%%Another complication in Figure~\ref{fig18} is the use of the displayed equation
%%$$y={2\over 1+\cos x}$$
%%as a label. 
âÕÄÅÔ ÂÏÌÅÅ ÅÓÔÅÓÔ×ÅÎÎÏ ÚÁËÏÄÉÒÏ×ÁÔØ ÜÔÕ ÍÅÔËÕ ËÁË 
$$ \hbox{\verb|$$y={2\over 1+\cos x}$$|}, $$
ÎÏ ÜÔÏ ÎÅ ÓÒÁÂÏÔÁÅÔ, ÐÏÔÏÍÕ ÞÔÏ \TeX\ ÎÁÂÉÒÁÅÔ ÍÅÔËÉ × 
``ÇÏÒÉÚÏÎÔÁÌØÎÏÍ ÒÅÖÉÍÅ''.
%%It would be more natural to code this as
%%$$ \hbox{\verb|$$y={2\over 1+\cos x}$$|} $$
%%but this would not work because
%%\TeX\ typesets the labels in ``horizontal mode.''

äÌÑ ÐÅÞÁÔÉ \emph{ÐÅÒÅÍÅÎÎÏÇÏ} ÔÅËÓÔÁ, ËÁË ÍÅÔËÉ, ÉÓÐÏÌØÚÕÊÔÅ 
ÐÏÌÅÚÎÏÅ ÓÒÅÄÓÔ×Ï \texttt{TEX}, ÏÐÉÓÁÎÎÏÅ ÎÁ ÓÔÒ.\ \pageref{dTEX}.
%%For a way to typeset \emph{variable} text as labels, see the
%%\texttt{TEX} utility routine described on p.\ \pageref{dTEX}.

äÁÌÅÅ Ï ÔÏÍ, ËÁË \TeX-ÔÅËÓÔ ÔÒÁÎÓÌÉÒÕÅÔÓÑ × ÆÏÒÍÕ, ÐÏÎÑÔÎÕÀ MetaPost: 
ÐÒÏÃÅÓÓÏÒ MetaPost ÐÒÏÐÕÓËÁÅÔ ÂÌÏË {\tt
btex}\index{btex?\texttt{btex}} \ldots\ {\tt
etex}\index{etex?\texttt{etex}}, ÐÏÌÁÇÁÑÓØ ÎÁ ÐÒÅÐÒÏÃÅÓÓÏÒ, 
ËÏÔÏÒÙÊ ÄÏÌÖÅÎ ÐÅÒÅ×ÅÓÔÉ ÜÔÏÔ ÂÌÏË × ËÏÍÁÎÄÙ ÎÉÚËÏÇÏ ÕÒÏ×ÎÑ MetaPost. 
%%Here is how \TeX\ material gets translated into a form MetaPost
%%understands: The MetaPost processor skips over {\tt
%%btex}\index{btex?\texttt{btex}} \ldots\ {\tt
%%etex}\index{etex?\texttt{etex}} blocks and depends on a preprocessor to
%%translate them into low level MetaPost commands. 
åÓÌÉ {\tt fig.mp} --- ÜÔÏ ÇÌÁ×ÎÙÊ ÆÁÊÌ, ÔÏ ÔÒÁÎÓÌÉÒÏ×ÁÎÎÙÊ \TeX-ÔÅËÓÔ 
ÐÏÍÅÝÁÅÔÓÑ × ÆÁÊÌ Ó ÉÍÅÎÅÍ {\tt fig.mpx}\index{ÆÁÊÌÙ!mpx?{\tt mpx}}.
%%If the main file is
%%{\tt fig.mp}, the translated \TeX\ material is placed in a file named
%%{\tt fig.mpx}\index{files!mpx?{\tt mpx}}. 
üÔÏ ÏÂÙÞÎÏ ÄÅÌÁÅÔÓÑ ÎÅÚÁÍÅÔÎÏ ÄÌÑ ÐÏÌØÚÏ×ÁÔÅÌÑ, ÎÏ ×ÙÚÙ×ÁÅÔ ÏÛÉÂËÕ, ÅÓÌÉ 
ÏÄÉÎ ÉÚ ÂÌÏËÏ× {\tt btex} $\ldots$ {\tt etex} ÓÏÄÅÒÖÉÔ ÏÛÉÂÏÞÎÕÀ ËÏÍÁÎÄÕ 
\TeX\index{TeX?\TeX!ÏÛÉÂËÉ}.
%%This is normally done
%%silently without any user intervention but it could fail if one of the
%%{\tt btex} $\ldots$ {\tt etex} blocks contains an erroneous
%%\TeX\index{TeX?\TeX!errors} command. 
ðÏÓÌÅ ÏÛÉÂËÉ, ÏÛÉÂÏÞÎÙÊ ÔÅËÓÔ \TeX\ ÓÏÈÒÁÎÑÅÔÓÑ × ÆÁÊÌÅ 
{\tt mpxerr.tex}\index{mpxerr.tex?\texttt{mpxerr.tex}} É ÓÏÏÂÝÅÎÉÑ ÏÂ ÏÛÉÂËÁÈ 
ÐÏÑ×ÌÑÀÔÓÑ × {\tt
mpxerr.log}\index{mpxerr.log?\texttt{mpxerr.log}}.
%%Then the erroneous \TeX\ input is
%%saved in the file {\tt mpxerr.tex}\index{mpxerr.tex?\texttt{mpxerr.tex}}
%%and the error messages appear in {\tt
%%mpxerr.log}\index{mpxerr.log?\texttt{mpxerr.log}}.

ðÒÅÐÒÏÃÅÓÓÏÒ ÄÌÑ ÍÅÔÏË \TeX\ {\it ÐÏÎÉÍÁÅÔ\/} ×ÉÒÔÕÁÌØÎÙÅ ÛÒÉÆÔÙ, Ô.~Å. ×Ù 
ÍÏÖÅÔÅ ÉÓÐÏÌØÚÏ×ÁÔØ ËÏÍÁÎÄÙ ×ÁÛÅÇÏ ÏÂÙÞÎÏÇÏ \TeX\ ÄÌÑ ÐÅÒÅËÌÀÞÅÎÉÑ ÛÒÉÆÔÏ× 
×ÎÕÔÒÉ ÍÅÔËÉ.
%%The preprocessor for \TeX\ labels {\it does\/} understand virtual
%%fonts, so you can use your normal \TeX\ font switching commands inside
%%the label.

\label{Dverbatimtex}
ïÐÒÅÄÅÌÅÎÉÑ ÍÁËÒÏÓÏ× \TeX\ ÉÌÉ ÌÀÂÙÅ ÄÒÕÇÉÅ ×ÓÐÏÍÏÇÁÔÅÌØÎÙÅ ËÏÍÁÎÄÙ \TeX\ 
ÍÏÇÕÔ ÚÁËÌÀÞÁÔØÓÑ × ÂÌÏË {\tt verbatimtex}\index{verbatimtex?\texttt{verbatimtex}}
\ldots\ {\tt etex}\index{etex?\texttt{etex}}. 
%%\TeX\ macro definitions or any other auxiliary \TeX\ commands can be
%%enclosed in a {\tt verbatimtex}\index{verbatimtex?\texttt{verbatimtex}}
%%\ldots\ {\tt etex}\index{etex?\texttt{etex}} block. 
òÁÚÎÉÃÁ ÍÅÖÄÕ {\tt btex} É {\tt verbatimtex} × ÔÏÍ, ÞÔÏ ÐÅÒ×ÙÊ ÇÅÎÅÒÉÒÕÅÔ 
×ÙÒÁÖÅÎÉÅ-ÒÉÓÕÎÏË, Á ×ÔÏÒÏÊ ÔÏÌØËÏ ÄÏÂÁ×ÌÑÅÔ ÄÁÎÎÙÅ ÄÌÑ ÏÂÒÁÂÏÔËÉ \TeX.
%%The difference
%%between {\tt btex} and {\tt verbatimtex} is that the former generates a
%%picture expression while the latter only adds material for \TeX\ to
%%process. 
îÁÐÒÉÍÅÒ, ÅÓÌÉ ×Ù ÈÏÔÉÔÅ, ÉÓÐÏÌØÚÕÑ \TeX, ÎÁÐÅÞÁÔÁÔØ ÍÅÔËÉ, ÉÓÐÏÌØÚÕÑ ÍÁËÒÏÓÙ ÉÚ 
{\tt mymac.tex}, ÔÏ ×ÁÛ ×ÈÏÄÎÏÊ ÆÁÊÌ ÄÌÑ MetaPost ÂÕÄÅÔ ×ÙÇÌÑÄÅÔØ ÐÏÄÏÂÎÏ ÞÅÍÕ-ÔÏ 
ÔÁËÏÍÕ:
%%For instance, if you want \TeX\ to typeset labels using macros
%%defined in {\tt mymac.tex}, your MetaPost input file would look
%%something like this:
\begin{eqnarray*}
&& \verb|verbatimtex \input mymac etex|\\
&& \verb|beginfig(1);|\\
&& \qquad \dots\\
&& \verb|label(btex|\, \descr{\TeX-ÔÅËÓÔ, ÉÓÐÏÌØÚÕÀÝÉÊ \hbox{\tt mymac.tex}}\,
       \verb|etex, | \descr{ÎÅËÏÔÏÒÙÅ ËÏÏÒÄÉÎÁÔÙ} \hbox{\tt );}\\
%%&& \verb|label(btex|\, \descr{\TeX\ material using \hbox{\tt mymac.tex}}\,
%%        \verb|etex, | \descr{some coordinates} \hbox{\tt );}\\
&& \qquad \dots
\end{eqnarray*}

\label{Dtroffmode}
äÌÑ Unix\footnote{Unix --- ÜÔÏ ÚÁÒÅÇÉÓÔÒÉÒÏ×ÁÎÎÁÑ ÔÏÒÇÏ×ÁÑ ÍÁÒËÁ Unix Systems
Laboratories.}\index{Unix} É ÄÒÕÇÉÈ ÏÓÎÏ×ÁÎÎÙÈ ÎÁ Web2C ÓÉÓÔÅÍ 
ÏÐÃÉÑ MetaPost {\tt -troff} ÓËÁÖÅÔ ÐÒÅÐÒÏÃÅÓÓÏÒÕ, ÞÔÏ ÂÌÏËÉ {\tt btex}
$\ldots$ {\tt etex} É {\tt verbatimtex} $\ldots$ {\tt etex} 
ÐÒÅÄÓÔÁ×ÌÅÎÙ × troff\index{troff} ×ÍÅÓÔÏ \TeX. 
%%On Unix\footnote{Unix is a registered trademark of Unix Systems
%%Laboratories.}\index{Unix\regmark} and other Web2C-based systems, the
%%option {\tt -troff} to MetaPost tells the preprocessor that {\tt btex}
%%$\ldots$ {\tt etex} and {\tt verbatimtex} $\ldots$ {\tt etex} blocks
%%are in troff\index{troff} instead of \TeX. 
ëÏÇÄÁ ÉÓÐÏÌØÚÕÅÔÓÑ ÜÔÁ ÏÐÃÉÑ, MetaPost ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ ×ÎÕÔÒÅÎÎÀÀ ÐÅÒÅÍÅÎÎÕÀ 
\ttindex{troffmode} ×~1\index{prologues?\texttt{prologues}}.
%%When using this option,
%%MetaPost sets the internal variable
%%\ttindex{troffmode} to~1\index{prologues?\texttt{prologues}}.

\label{Dprologues}
õÓÔÁÎÏ×ËÁ \ttt{prologues} ÍÏÖÅÔ ÂÙÔØ ÐÏÌÅÚÎÁ ÔÁËÖÅ É Ó \TeX, Á ÎÅ ÔÏÌØËÏ 
ÄÌÑ troff.
%%Setting \ttt{prologues} can be useful with \TeX, too, not just troff.
äÁÌÅÅ ÐÒÉ×ÏÄÑÔÓÑ ÎÅËÏÔÏÒÙÅ ÒÁÚßÑÓÎÅÎÉÑ:
%%Here is some explanation:

\begin{itemize}
\item ëÏÇÄÁ \ttt{prologues} ÒÁ×ÎÏ 0, ÞÔÏ ÕÓÔÁÎÁ×ÌÉ×ÁÅÔÓÑ ÐÏ-ÕÍÏÌÞÁÎÉÀ, 
×ÙÈÏÄÎÙÅ ÆÁÊÌÙ MetaPost ÎÅ ÓÏÄÅÒÖÁÔ ÉÓÐÏÌØÚÕÅÍÙÈ ÛÒÉÆÔÏ×.
%%\item When \ttt{prologues} is 0, which is the default, the MetaPost
%%output files do not have embedded fonts. 
ûÒÉÆÔÙ × ÒÅÚÕÌØÔÁÔÅ-×Ù×ÏÄÅ ÂÕÄÕÔ ×ÅÒÏÑÔÎÏ Courier\index{Courier} ÉÌÉ 
Times-Roman\index{Times-Roman}.
%%Fonts in the resulting
%%output will probably render as Courier\index{Courier} or %%Times-Roman\index{Times-Roman}.

\item ëÏÇÄÁ \ttt{prologues} ÒÁ×ÎÏ 1, ×Ù×ÏÄ MetaPost ÏÂßÑ×ÌÑÅÔÓÑ 
``ÓÔÒÕËÔÕÒÉÒÏ×ÁÎÎÙÍ PostScript''\index{PostScript!ÓÔÒÕËÔÕÒÎÙÊ} (EPSF\index{EPSF}), 
ÎÏ ÜÔÏ ÎÅ ×ÐÏÌÎÅ ×ÅÒÎÏ.
%%\item When \ttt{prologues} is 1, the MetaPost output claims to be
%%``structured PostScript''\index{PostScript!structured} (EPSF\index{EPSF}),
%%but it is not completely conformant. 
üÔÏÔ ×ÁÒÉÁÎÔ ÐÏÄÄÅÒÖÉ×ÁÅÔÓÑ ÄÌÑ ÏÂÒÁÔÎÏÊ ÓÏ×ÍÅÓÔÉÍÏÓÔÉ ÓÏ ÓÔÁÒÙÍÉ 
troff-ÄÏËÕÍÅÎÔÁÍÉ, ÎÏ ÅÇÏ ÉÓÐÏÌØÚÏ×ÁÎÉÅ ËÁË ÕÓÔÁÒÅ×ÛÅÇÏ ÎÅ ÒÅËÏÍÅÎÄÕÅÔÓÑ.
%%This variant is kept for backward
%%compatibility with old (troff) documents, but its use is deprecated. 
éÚ ÉÓÔÏÒÉÞÅÓËÉÈ ÓÏÏÂÒÁÖÅÎÉÊ, MetaPost ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ \ttt{prologues} ×~1, 
ËÏÇÄÁ ÏÐÃÉÑ {\tt -troff} ÐÒÉ×ÏÄÉÔÓÑ × ËÏÍÁÎÄÎÏÊ ÓÔÒÏËÅ.
%%For historical reasons, MetaPost sets \ttt{prologues} to~1 when the {\tt
%%-troff} option is given on the command line.

\item ëÏÇÄÁ \ttt{prologues} ÒÁ×ÎÏ 2, ×Ù×ÏÄ MetaPost --- ÜÔÏ EPSF, × ËÏÔÏÒÏÍ 
ÐÒÅÄÐÏÌÁÇÁÅÔÓÑ, ÞÔÏ ÔÅËÓÔ ÎÁÂÒÁÎ PostScript\index{PostScript!ÛÒÉÆÔÙ}-ÛÒÉÆÔÁÍÉ, 
ÐÒÅÄÏÓÔÁ×ÌÑÅÍÙÍÉ ``ÓÒÅÄÏÊ'', ÔÁËÏÊ ËÁË ÐÒÏÓÍÏÔÒÝÉË ÄÏËÕÍÅÎÔÁ ÉÌÉ ×ÓÔÒÏÅÎÎÏÅ 
ÐÒÉÌÏÖÅÎÉÅ, ÉÓÐÏÌØÚÕÀÝÉÅ ÜÔÏÔ ×Ù×ÏÄ.
%%\item When \ttt{prologues} is 2, the MetaPost output is EPSF and assumes
%%that the text comes from PostScript\index{PostScript!fonts} fonts
%%provided by the ``environment'', such as the document viewer or
%%embedded application using the output. 
MetaPost ÂÕÄÅÔ ÐÙÔÁÔØÓÑ ÕÓÔÁÎÏ×ÉÔØ ËÏÄÉÒÏ×ËÕ ÛÒÉÆÔÁ ÐÒÁ×ÉÌØÎÏ, ÏÓÎÏ×Ù×ÁÑÓØ 
ÎÁ ËÏÍÁÎÄÁÈ \ttt{fontmapfile} É \ttt{fontmapline}.
%%MetaPost will attempt to
%%set up the font encodings correctly, based on \ttt{fontmapfile} and
%%\ttt{fontmapline} commands.

\item ëÏÇÄÁ \ttt{prologues} ÒÁ×ÎÏ 3, ×Ù×ÏÄ MetaPost ÂÕÄÅÔ EPSF, ÓÏÄÅÒÖÁÝÉÊ 
ÛÒÉÆÔÙ PostScript (ÉÌÉ ÐÏÄÍÎÏÖÅÓÔ×Á ÛÒÉÆÔÏ×),  ÉÓÐÏÌØÚÕÅÍÙÅ ÎÁ ÏÓÎÏ×Å ËÏÍÁÎÄ 
\ttt{fontmapfile} É \ttt{fontmapline}. 
%%\item When \ttt{prologues} is 3, the MetaPost output will be EPSF but
%%will contain the PostScript font(s) (or a subset) used based on the
%%\ttt{fontmapfile} and \ttt{fontmapline} commands. 
üÔÏ ÚÎÁÞÅÎÉÅ ÐÏÌÅÚÎÏ ÄÌÑ ÇÅÎÅÒÁÃÉÉ ÓÁÍÏÄÏÓÔÁÔÏÞÎÏÊ PostScript-ÇÒÁÆÉËÉ.
%%This value is useful
%%for generating stand-alone PostScript graphics.
\end{itemize}

óÔÏÉÔ ÏÔÍÅÔÉÔØ, ÞÔÏ ÓÔÁÎÄÁÒÔÎÏÅ ÚÎÁÞÅÎÉÅ \ttt{prologues:=0} ÄÏÓÔÁÔÏÞÎÏ ÄÌÑ 
ÇÒÁÆÉËÉ, ×ËÌÀÞÁÅÍÏÊ × ÄÏËÕÍÅÎÔÙ \TeX.
%%It is worth noting that the default value \ttt{prologues:=0} is sufficient
%%for graphics included in \TeX-based documents. 
ðÅÒÅÍÅÎÎÁÑ \ttt{prologues} ÔÁËÖÅ ÎÅ ÎÕÖÎÁ ÐÒÉ ÏÂÒÁÂÏÔËÅ MetaPost-ÆÁÊÌÏ× 
ÞÅÒÅÚ ÕÔÉÌÉÔÕ \ttindex{mptopdf} (ÉÚ ÄÉÓÔÒÉÂÕÔÉ×Á \ConTeXt), ÐÏÔÏÍÕ ÞÔÏ 
PDF-ÆÁÊÌÙ ÅÓÔÅÓÔ×ÅÎÎÏ ÓÁÍÏÄÏÓÔÁÔÏÞÎÙ.  
%%Also, the \ttt{prologues} variable is irrelevant
%%when processing MetaPost files through the \ttindex{mptopdf} utility
%%(part of the \ConTeXt\ distribution), because PDF files are, by nature,
%%stand-alone. 
âÏÌÅÅ ÔÏÇÏ, ÚÎÁÞÅÎÉÅ \ttt{prologues} ÎÅ ÉÍÅÅÔ ÜÆÆÅËÔÁ ÎÁ ÛÒÉÆÔÙ \MF\ × 
×ÁÛÉÈ MetaPost-ÆÁÊÌÁÈ, Ô.~Å. MetaPost ÎÉËÏÇÄÁ ÎÅ ×ÓÔÒÁÉ×ÁÅÔ ÔÁËÉÅ ÛÒÉÆÔÙ 
× Ó×ÏÊ ×Ù×ÏÄ.
%%Moreover, the value of \ttt{prologues} has no effect on
%%\MF\ fonts in your MetaPost files, i.\,e., MetaPost never embeds such
%%fonts. 
ôÏÌØËÏ ÄÒÁÊ×ÅÒÙ ×Ù×ÏÄÁ, ÎÁÐÒÉÍÅÒ, \ttt{dvips} ÉÌÉ pdf\LaTeX, ÍÏÇÕÔ ×ÓÔÒÏÉÔØ 
ÔÁËÉÅ ÛÒÉÆÔÙ.
%%Only output drivers, e.\,g., \ttt{dvips} or pdf\LaTeX\ will
%%handle those.

äÅÔÁÌÉ ÔÏÇÏ, ËÁË ×ËÌÀÞÁÔØ ÒÉÓÕÎËÉ PostScript × ÄÏËÕÍÅÎÔ, ÓÄÅÌÁÎÎÙÊ × 
\TeX\ ÉÌÉ troff, ÓÉÓÔÅÍÏ-ÚÁ×ÉÓÉÍÙ.
%%The details on how to include PostScript figures in a paper
%%done in \TeX\ or troff are system-dependent. 
ïÎÉ ÍÏÇÕÔ ÏÂÙÞÎÏ ÂÙÔØ ÎÁÊÄÅÎÙ × ÓÔÒÁÎÉÃÁÈ ÒÕËÏ×ÏÄÓÔ×Á (man pages) ÉÌÉ 
× ÄÒÕÇÏÊ ÓÅÔÅ×ÏÊ ÄÏËÕÍÅÎÔÁÃÉÉ, ÎÏ ÐÏÓÍÏÔÒÉÔÅ ÓÎÁÞÁÌÁ 
× ÒÁÚÄÅÌ~\ref{Dteximport} ÜÔÏÇÏ ÒÕËÏ×ÏÄÓÔ×Á ÄÌÑ ËÒÁÔËÉÈ ÉÎÓÔÒÕËÃÉÊ, 
ËÏÔÏÒÙÅ ×Ï ÍÎÏÇÉÈ ÓÌÕÞÁÑÈ ÏËÁÖÕÔÓÑ ÄÏÓÔÁÔÏÞÎÙÍÉ.
%%They can generally be found
%%in manual pages and other on-line documentation, but have a look at
%%section~\ref{Dteximport} of this manual for some brief instructions that
%%in many cases should work. 
òÕËÏ×ÏÄÓÔ×Ï ÄÌÑ ÛÉÒÏËÏ ÉÓÐÏÌØÚÕÅÍÏÊ ÐÒÏÇÒÁÍÍÙ Dvips ÎÁÈÏÄÉÔÓÑ × ÆÁÊÌÅ 
\ttt{dvips.texi}, ×ËÌÀÞÅÎÎÏÍ × ÂÏÌØÛÉÎÓÔ×Ï ÓÔÁÎÄÁÒÔÎÙÈ ÄÉÓÔÒÉÂÕÔÉ×Ï× É 
ÄÏÓÔÕÐÎÏÍ × ÓÅÔÉ × \url{http://tug.org/texinfohtml/dvips.html} É × ÄÒÕÇÉÈ 
ÍÅÓÔÁÈ, Á ÔÁËÖÅ × ÄÒÕÇÉÈ ÆÏÒÍÁÔÁÈ.
%%The manual for the
%%widely-used Dvips processor is in a file \ttt{dvips.texi}, included in
%%most distributions, and is available online at
%%\url{http://tug.org/texinfohtml/dvips.html}, among many other places and
%%formats.

\label{Dmakempx}
÷ ÓÉÓÔÅÍÁÈ, ÏÓÎÏ×ÁÎÎÙÈ ÎÁ Web2C, ÐÒÅÐÒÏÃÅÓÓÏÒ ÎÁÚÙ×ÁÅÔÓÑ 
\ttindex{makempx} --- ÏÎ ×ÙÚÙ×ÁÅÔ ÐÒÏÇÒÁÍÍÕ \ttindex{mpto}; 
ÄÏËÕÍÅÎÔÁÃÉÑ ÐÏ  Web2C ÏÐÉÓÙ×ÁÅÔ ÉÈ ÂÏÌÅÅ ÐÏÄÒÏÂÎÏ.
%%On Web2C-based systems, the preprocessor is named \ttindex{makempx},
%%which calls another utility \ttindex{mpto}; the Web2C documentation
%%describes them in more detail.  
ïÄÎÁËÏ, ÕÐÏÍÑÎÅÍ ÚÄÅÓØ ÏÄÎÏ Ó×ÏÊÓÔ×Ï: 
ÅÓÌÉ ÐÅÒÅÍÅÎÎÁÑ ÓÒÅÄÙ \ttindex{MPTEXPRE} ÓÏÄÅÒÖÉÔ ÉÍÑ ÓÕÝÅÓÔ×ÕÀÝÅÇÏ 
ÆÁÊÌÁ, ÔÏ {\tt makempx} ÂÕÄÅÔ ÐÏÍÅÝÁÔØ ÅÇÏ × ÎÁÞÁÌÏ ÐÒÉ ×Ù×ÏÄÅ.
%%We'll mention one feature here, though:
%%if the environment variable \ttindex{MPTEXPRE} is set to the name of an
%%existing file, {\tt makempx} will prepend it to the output. 
÷Ù ÍÏÖÅÔÅ ÜÔÏ ÉÓÐÏÌØÚÏ×ÁÔØ, ÎÁÐÒÉÍÅÒ, ÄÌÑ ×ËÌÀÞÅÎÉÑ ÐÒÅÁÍÂÕÌ \LaTeX. 
%%You can use
%%this to include \LaTeX\ preambles, for instance. 
íÁËÒÏÓ \ttt{TEX}, ÏÐÉÓÁÎÎÙÊ ÎÁ ÓÔÒ.~\pageref{dTEX}, ÏÂÅÓÐÅÞÉ×ÁÅÔ ÄÒÕÇÏÊ 
ÓÐÏÓÏ ÔÁËÏÇÏ ×ËÌÀÞÅÎÉÑ. 
%%The \ttt{TEX}
%%macro described on p.\ \pageref{dTEX} provides another way to handle this.

\subsection{æÁÊÌÙ-ËÁÒÔÙ ÛÒÉÆÔÏ×}
%%\subsection{Font map files}
\label{Sfontmapfile}\label{Sfontmapline}

åÓÌÉ \ttt{prologues} ÕÓÔÁÎÏ×ÌÅÎÏ ×~2, ÔÏ ÌÀÂÙÅ ÉÓÐÏÌØÚÕÅÍÙÅ × ×Ù×ÏÄÅ 
ÛÒÉÆÔÙ Á×ÔÏÍÁÔÉÞÅÓËÉ ÐÅÒÅËÏÄÉÒÕÀÔÓÑ ÓÏÇÌÁÓÎÏ ÔÁÂÌÉÃÅ, ÕËÁÚÁÎÎÏÊ × 
ÏÔÄÅÌØÎÏÊ ÚÁÐÉÓÉ ÛÒÉÆÔÏ×ÏÇÏ ÆÁÊÌÁ-ËÁÒÔÙ É ×ËÌÀÞÁÅÍÏÊ × ÆÁÊÌ ×Ù×ÏÄÁ.
%%If \ttt{prologues} is set to~2, any used fonts in the output file are
%%automatically re-encoded, and the encoding vector file specified in
%%the fontmap entry will be embedded in the output file. 
åÓÌÉ \ttt{prologues} ÕÓÔÁÎÏ×ÌÅÎÏ ×~3, ÔÏ MetaPost ÂÕÄÅÔ ÔÁËÖÅ ÐÙÔÁÔØÓÑ 
×ËÌÀÞÉÔØ ÉÓÐÏÌØÚÕÅÍÙÅ PostScript\index{PostScript!ÛÒÉÆÔÙ} ÛÒÉÆÔÙ ÉÌÉ ÉÈ 
ÐÏÄÍÎÏÖÅÓÔ×Á.
%%If \ttt{prologues} is set to~3, MetaPost will also attempt to include
%%(a subset of) the used PostScript\index{PostScript!fonts} fonts. 
þÔÏÂÙ ÜÔÏ ÒÁÂÏÔÁÌÏ, ÎÕÖÎÏ ÐÏÌÕÞÅÎÉÅ ÉÎÆÏÒÍÁÃÉÉ ÉÚ ÛÒÉÆÔÏ×ÏÇÏ 
ÆÁÊÌÁ-ËÁÒÔÙ. 
%For this to work, it needs to acquire font map information. 

ëÏÄ, ÏÓÎÏ×ÁÎÎÙÊ ÎÁ ÛÒÉÆÔÏ×ÏÊ ÂÉÂÌÉÏÔÅËÅ, ÉÓÐÏÌØÚÕÅÔÓÑ pdf\TeX. 
%%The code is based on the font library used by pdf\TeX. 
óÌÅÄÕÑ ÚÁ pdf\TeX, ÏÂÎÁÒÕÖÉ×ÁÅÍ Ä×Á ÎÏ×ÙÈ Ó×ÑÚÁÎÎÙÈ Ó ÔÅÍÏÊ ÐÒÉÍÉÔÉ×Á:
\ttindex{fontmapfile} É \ttindex{fontmapline}. 
%%Following in
%%the footsteps of pdf\TeX, there are two new associated primitives:
%%\ttindex{fontmapfile} and \ttindex{fontmapline}. 
äÁÌÅÅ ÓÌÅÄÕÅÔ ÐÒÏÓÔÏÊ ÐÒÉÍÅÒ, ÕËÁÚÙ×ÁÀÝÉÊ ÆÁÊÌ-ËÁÒÔÕ ÄÌÑ ÛÒÉÆÔÏ× 
Latin Modern × ËÏÄÉÒÏ×ËÅ YandY (\LaTeX\ LY1): 
%%Here is a simple
%%example, specifying the map file for Latin Modern fonts in YandY
%%(\LaTeX\ LY1) encoding:
\begin{center}\begin{tabular}{l}
\verb|prologues:=2;|\\
\verb|fontmapfile "texnansi-lm.map";|\\
\verb|beginfig(1);|\\
\verb|   draw "Hell|{\tt\'o, vil\'a}\verb|g" infont "texnansi-lmr10";|\\
%%\verb|   draw "Helló, világ" infont "texnansi-lmr10";|\\
\verb|endfig;|
\end{tabular}\end{center}

éÓÐÏÌØÚÕÑ \ttt{fontmapline}, ÍÏÖÎÏ ÕËÁÚÁÔØ ÉÎÆÏÒÍÁÃÉÀ Ï ÛÒÉÆÔÅ 
×ÎÕÔÒÉ ÒÉÓÕÎËÁ:
%%Using \ttt{fontmapline}, you can specify font mapping information
%%inside the figure:
\begin{center}\begin{tabular}{l}
\verb|prologues:=2;|\\
\verb|fontmapline "pplbo8r URWPalladioL-Bold  "&ditto&|\\
\verb|            ".167 SlantFont"&ditto&" <8r.enc <uplb8a.pfb";|\\
\verb|beginfig(1);|\\
\verb|   draw "Hello, world" infont "pplbo8r";|\\
\verb|endfig;|
\end{tabular}\end{center}
üÔÏ ÂÕÄÅÔ ÐÏÐÙÔËÁ ÐÅÒÅËÏÄÉÒÏ×ÁÔØ PostScript-ÛÒÉÆÔ 
URWPalladioL-Bold\index{URWPalladioL-Bold}\index{Palatino}, 
ÞÅÊ tfm-ÆÁÊÌ --- ÜÔÏ pplbo8r.tfm. 
%%This will attempt to reencode the PostScript font
%%URWPalladioL-Bold\index{URWPalladioL-Bold}\index{Palatino}
%%whose tfm file is pplbo8r.tfm. 
ëÏÄÉÒÏ×ËÁ ÏÐÒÅÄÅÌÑÅÔÓÑ × ÆÁÊÌÅ 8r.enc É ÂÕÄÅÔ ×ËÌÀÞÁÔÓÑ × ÆÁÊÌ ×Ù×ÏÄÁ. 
%%The encoding is found in the file
%%8r.enc, and will be included into the output file.

åÓÌÉ ÜÔÏÔ ÖÅ ÐÒÉÍÅÒ ÚÁÐÕÓËÁÔØ Ó \ttt{prologues:=3}, ÔÏ MetaPost ÂÕÄÅÔ 
×ËÌÀÞÁÔØ ÐÏÄÍÎÏÖÅÓÔ×Ï ÛÒÉÆÔÁ, ÞÔÏ ÒÁÓÐÏÌÏÖÅÎÏ × uplb8a.pfb, × ×Ù×ÏÄ.
%%If the same example was run with \ttt{prologues:=3}, MetaPost would
%%include a subset of the font that resides in uplb8a.pfb into the
%%output. 
÷ ÜÔÏÍ ÓÌÕÞÁÅ ÐÏÄÍÎÏÖÅÓÔ×Ï ÛÒÉÆÔÁ ÐÅÒÅÓÔÒÁÉ×ÁÅÔÓÑ ÔÁË, ÞÔÏ ÏÎÏ ÂÕÄÅÔ 
×ÅÒÎÏ ÚÁËÏÄÉÒÏ×ÁÎÏ ÎÁ ×ÎÕÔÒÅÎÎÅÍ ÕÒÏ×ÎÅ, ÐÏÜÔÏÍÕ 8r.enc ÎÅ ÂÕÄÅÔ 
×ËÌÀÞÁÔØÓÑ.
%%In this case, the subset of the font is reorganized so that it
%%has the correct encoding internally, 8r.enc will not be embedded also.

áÒÇÕÍÅÎÔ Ë ÏÂÅÉÍ ËÏÍÁÎÄÁÍ ÉÍÅÅÔ ÓÉÍ×ÏÌ ÏÐÃÉÏÎÁÌØÎÏÇÏ ÆÌÁÇÁ × ÓÁÍÏÍ 
ÎÁÞÁÌÅ. 
%%The argument to both commands has an optional flag character at the very
%%beginning. 
üÔÏÔ ÏÐÃÉÏÎÁÌØÎÙÊ ÆÌÁÇ ÉÍÅÅÔ ÔÏ ÖÅ ÓÁÍÏÅ ÚÎÁÞÅÎÉÅ ËÁË É × pdf\TeX: 
%%This optional flag has the same meaning as in pdf\TeX: 
$$\begin{tabular}{|c|l|} \hline
\multicolumn1{|c|}{ïÐÃÉÑ}&  \multicolumn1{c|}{úÎÁÞÅÎÉÅ}\\ \hline
%%\multicolumn1{|c|}{Option}&  \multicolumn1{c|}{Meaning}\\ \hline
    +    & ÒÁÓÛÉÒÉÔØ ÓÐÉÓÏË ÛÒÉÆÔÁ, ÉÇÎÏÒÉÒÕÑ ÐÏ×ÔÏÒÅÎÉÑ \\
%%    +    & extend the font list, but ignore duplicates \\
    =    & ÒÁÓÛÉÒÉÔØ ÓÐÉÓÏË ÛÒÉÆÔÁ, ÚÁÍÅÝÁÑ ÐÏ×ÔÏÒÅÎÉÑ \\
%%    =    & extend the font list, replacing duplicates \\
    $-$  & ÕÄÁÌÉÔØ ×ÓÅ ÐÏÄÈÏÄÑÝÉÅ ÛÒÉÆÔÙ ÉÚ ÓÐÉÓËÁ ÛÒÉÆÔÁ \\
%%    $-$  & remove all matching fonts from the font list \\
\hline
\end{tabular}
$$ 
âÅÚ ÏÐÃÉÊ ÔÅËÕÝÉÊ ÓÐÉÓÏË ÂÕÄÅÔ ÐÏÌÎÏÓÔØÀ ÚÁÍÅÝÅÎ.
%%Without any option, the current list will be completely replaced.  

åÓÌÉ \ttt{prologues} ÕÓÔÁÎÏ×ÌÅÎ × Ä×Á ÉÌÉ ÔÒÉ É ËÏÍÁÎÄÙ 
\ttt{fontmapfile} ÏÔÓÕÔÓÔ×ÕÀÔ, ÔÏ MetaPost ÂÕÄÅÔ ÐÙÔÁÔØÓÑ 
ÎÁÊÔÉ ÔÉÐÏ×ÏÊ ÆÁÊÌ-ËÁÒÔÕ, ÎÁÞÉÎÁÑ Ó {\tt mpost.map}.
%%If \ttt{prologues} is set to two or three, yet there are no
%%\ttt{fontmapfile} statements, MetaPost will attempt to locate a
%%default map file, with a preference to read {\tt mpost.map}. 
åÓÌÉ ÜÔÏ ÎÅ ÐÒÉ×ÅÄÅÔ Ë ÕÓÐÅÈÕ, ÔÏ ÏÎ ÂÕÄÅÔ ÔÁËÖÅ ÐÒÏÂÏ×ÁÔØ {\tt troff.map} 
ÉÌÉ {\tt pdftex.map}, × ÚÁ×ÉÓÉÍÏÓÔÉ ÏÔ ÐÒÉÓÕÔÓÔ×ÉÑ ÕÓÔÁÎÏ×ËÉ ÒÅÖÉÍÁ troff.
%%If that
%%fails, it will also attempt either {\tt troff.map} or {\tt
%%pdftex.map}, depending on whether or not troff mode is enabled. 
åÓÌÉ \ttt{prologues} ÕÓÔÁÎÏ×ÌÅÎÏ ×~1, ÔÏ MetaPost ÐÙÔÁÅÔÓÑ ÞÉÔÁÔØ ÆÁÊÌ Ó ÉÍÅÎÅÍ 
{\tt psfonts.map}, ÉÇÎÏÒÉÒÕÑ ÌÀÂÕÀ ËÏÍÁÎÄÕ {\tt fontmapfile}.
%%If
%%\ttt{prologues} is set to~1, MetaPost attempts to read a file called
%%{\tt psfonts.map}, regardless of any {\tt fontmapfile}
%%statement. 
ðÏ×ÔÏÒÉÍ, ÜÔÏ ÔÏÌØËÏ ÄÌÑ ÏÂÒÁÔÎÏÊ ÓÏ×ÍÅÓÔÉÍÏÓÔÉ.
%%Again, this is for backward compatibility only.

\subsection{ïÐÅÒÁÔÏÒ \texttt{infont}}
%%\subsection{The \texttt{infont} operator}
\label{Sinfont}

ëÁË Ó \TeX, ÔÁË É Ó troff ×ÓÀ ÒÅÁÌØÎÕÀ ÒÁÂÏÔÕ ÐÏ ÄÏÂÁ×ÌÅÎÉÀ ÔÅËÓÔÁ Ë 
ËÁÒÔÉÎËÅ ÄÅÌÁÅÔ ÐÒÉÍÉÔÉ×ÎÙÊ ÏÐÅÒÁÔÏÒ MetaPost Ó ÉÍÅÎÅÍ 
{\tt infont}\index{infont?\texttt{infont}}. 
%%Regardless of whether you use \TeX\ or troff, all the real work of
%%adding text to pictures is done by a MetaPost primitive operator called
%%{\tt infont}\index{infont?\texttt{infont}}. 
ïÎ --- \tdescr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ 
ÏÐÅÒÁÔÏÒ}\index{ÐÅÒ×ÉÞÎÙÊ binop?\tdescr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ 
ÏÐÅÒÁÔÏÒ}}, ÂÅÒÕÝÉÊ ÌÅ×ÙÍ ÁÒÇÕÍÅÎÔÏÍ \tdescr{ÓÔÒÏËÏ×ÕÀ ×ÔÏÒÉÞÎÏÓÔØ} 
É ÐÒÁ×ÙÍ --- \tdescr{ÓÔÒÏËÏ×ÕÀ ÐÅÒ×ÉÞÎÏÓÔØ}. 
%%It is a \tdescr{primary
%%binop}\index{primary binop?\tdescr{primary binop}} that takes a
%%\tdescr{string secondary} as its left argument and a \tdescr{string
%%primary} as its right argument. 
ìÅ×ÙÊ ÁÒÇÕÍÅÎÔ --- ÜÔÏ ÔÅËÓÔ, Á ÐÒÁ×ÙÊ --- ÉÍÑ ÛÒÉÆÔÁ.
%%The left argument is text, and the right argument is a font name.
òÅÚÕÌØÔÁÔ ÏÐÅÒÁÃÉÉ --- ÜÔÏ \tdescr{ÒÉÓÕÎÏË-×ÔÏÒÉÞÎÏÓÔØ}, ËÏÔÏÒÙÊ ÍÏÖÎÏ 
ÔÒÁÎÓÆÏÒÍÉÒÏ×ÁÔØ ÍÎÏÇÉÍÉ ÓÐÏÓÏÂÁÍÉ.
%%The result of the operation is a
%%\tdescr{picture secondary} that can then be transformed in various ways.
ïÄÎÁ ÉÚ ×ÏÚÍÏÖÎÏÓÔÅÊ --- ÜÔÏ Õ×ÅÌÉÞÅÎÉÅ × ÚÁÄÁÎÎÏÅ ÞÉÓÌÏ ÒÁÚ 
ÞÅÒÅÚ ÓÉÎÔÁËÓÉÓ\index{scaled?\texttt{scaled}}
$$ \descr{ÒÉÓÕÎÏË-×ÔÏÒÉÞÎÏÓÔØ}\, \hbox{\tt scaled}\, \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ} $$
%%One possibility is enlargement by a given factor via the
%%syntax\index{scaled?\texttt{scaled}}
%%$$ \descr{picture secondary}\, \hbox{\tt scaled}\, \descr{numeric primary} $$
ôÁËÉÍ ÏÂÒÁÚÏÍ, {\tt label(\qq text\qq,z0)} ÜË×É×ÁÌÅÎÔÎÏ 
$$ \hbox{\tt label({\qq}ÔÅËÓÔ{\qq} infont defaultfont scaled defaultscale, z0)} $$
%%Thus {\tt label("text",z0)} is equivalent to
%%$$ \hbox{\tt label("text" infont defaultfont scaled defaultscale, z0)} $$

åÓÌÉ ÉÓÐÏÌØÚÏ×ÁÔØ ÓÔÒÏËÏ×ÕÀ ËÏÎÓÔÁÎÔÕ ÄÌÑ ÌÅ×ÏÇÏ ÁÒÇÕÍÅÎÔÁ {\tt infont} ÏËÁÖÅÔÓÑ 
ÎÅÕÄÏÂÎÙÍ, ÔÏ ÍÏÖÎÏ ÉÓÐÏÌØÚÏ×ÁÔØ\index{char?\texttt{char}}\label{Dchar} 
$$ {\tt char}\, \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ} $$
ÄÌÑ ×ÙÂÏÒÁ ÓÉÍ×ÏÌÁ ÐÏ ÅÇÏ ÞÉÓÌÏ×ÏÊ ÐÏÚÉÃÉÉ × ÛÒÉÆÔÅ.
%%If it is not convenient to use a string constant for the left argument of
%%{\tt infont}, you can use\index{char?\texttt{char}}\label{Dchar}
%%$$ {\tt char}\, \descr{numeric primary} $$
%%to select a character based on its numeric position in the font.
ôÁËÉÍ ÏÂÒÁÚÏÍ, 
$$ \hbox{\tt char(n+64) infont \qq{ptmr8r}\qq} $$
--- ÜÔÏ ËÁÒÔÉÎËÁ, ÓÏÄÅÒÖÁÝÁÑ ÓÉÍ×ÏÌ {\tt n+64} ÛÒÉÆÔÁ \ttt{ptmr8r},
ËÏÔÏÒÙÊ ÏÂÙÞÎÏ ÉÓÐÏÌØÚÕÅÔÓÑ \TeX\ ÄÌÑ ÓÓÙÌËÉ ÎÁ Times-Roman. 
%%Thus
%%$$ \hbox{\tt char(n+64) infont \qq{ptmr8r}\qq} $$
%%is a picture containing character {\tt n+64} of the font \ttt{ptmr8r},
%%which is a typical \TeX\ way to refer to Times-Roman. 
óÍ. ÓÔÒ.\ \pageref{fontname} ÄÌÑ ÄÁÌØÎÅÊÛÅÇÏ ÏÂÓÕÖÄÅÎÉÑ.
%%See p.\ \pageref{fontname} for further discussion.

óÁÍ MetaPost ÎÅ ÐÅÒÅËÏÄÉÒÕÅÔ Ó×ÏÊ ××ÏÄ, Ô.~Å. ËÏÇÄÁ ×Ù 
ÉÓÐÏÌØÚÕÅÔÅ ÓÔÒÏËÕ {\tt infont} ÄÌÑ ÍÅÔÏË (×ÍÅÓÔÏ {\tt btex} \ldots\
{\tt etex}), ÓÔÒÏËÁ ÄÏÌÖÎÁ ÂÙÔØ ÚÁÄÁÎÁ × ËÏÄÉÒÏ×ËÅ ÛÒÉÆÔÁ.
%%Bare MetaPost does not do any kind of input reencoding, so when
%%you use {\tt infont} string for labels (instead of {\tt btex} \ldots\
%%{\tt etex}), the string has to be specified in the font encoding.

\subsection{éÚÍÅÒÅÎÉÅ ÔÅËÓÔÁ}
%%\subsection{Measuring Text}
\label{meas}

MetaPost ÄÅÌÁÅÔ ÄÏÓÔÕÐÎÙÍÉ ÆÉÚÉÞÅÓËÉÅ ÒÁÚÍÅÒÙ \index{ÒÁÚÍÅÒ} 
ËÁÒÔÉÎÏË, ÇÅÎÅÒÉÒÕÅÍÙÈ ÏÐÅÒÁÔÏÒÏÍ {\tt infont}. 
%%MetaPost makes readily available the physical dimensions\index{size} of
%%pictures generated by the {\tt infont} operator. 
õÎÁÒÎÙÅ ÏÐÅÒÁÔÏÒÙ {\tt
llcorner}\index{llcorner?\texttt{llcorner}}\label{Dcornop}, {\tt
lrcorner}\index{lrcorner?\texttt{lrcorner}}, {\tt
urcorner}\index{urcorner?\texttt{urcorner}}, {\tt
ulcorner}\index{ulcorner?\texttt{ulcorner}} É {\tt
center}\index{center?\texttt{center}}\label{Dcenter} Ó ÁÒÇÕÍÅÎÔÏÍ 
\tdescr{ÒÉÓÕÎÏË-ÐÅÒ×ÉÞÎÏÓÔØ} ×ÏÚ×ÒÁÝÁÀÔ ÕÇÌÙ Ó×ÏÅÊ ``ÏÈ×ÁÔÙ×ÁÀÝÅÊ ÒÁÍËÉ'', 
ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{bbox}. 
%%There are unary
%%operators {\tt
%%llcorner}\index{llcorner?\texttt{llcorner}}\label{Dcornop}, {\tt
%%lrcorner}\index{lrcorner?\texttt{lrcorner}}, {\tt
%%urcorner}\index{urcorner?\texttt{urcorner}}, {\tt
%%ulcorner}\index{ulcorner?\texttt{ulcorner}}, and {\tt
%%center}\index{center}\label{Dcenter} that take a \tdescr{picture
%%primary} and return the corners of its ``bounding box'' as illustrated
%%in Figure~\ref{bbox}. 
ïÐÅÒÁÔÏÒ {\tt center} ÔÁËÖÅ ÄÏÐÕÓËÁÅÔ ÏÐÅÒÁÎÄÙ 
\tdescr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ} É \tdescr{ÐÅÒÏ-ÐÅÒ×ÉÞÎÏÓÔØ}. 
%%The {\tt center} operator also accepts
%%\tdescr{path primary} and \tdescr{pen primary} operands. 
MetaPost ×ÅÒÓÉÉ 0.30 É ÎÏ×ÅÅ ÄÏÐÕÓËÁÅÔ ÄÌÑ {\tt llcorner}, {\tt lrcorner}, $\ldots$ 
×ÓÅ ÔÒÉ ÔÉÐÁ ÁÒÇÕÍÅÎÔÏ×.
%%In MetaPost
%%Version 0.30 and higher, {\tt llcorner}, {\tt lrcorner}, etc.  accept
%%all three argument types as well.

ïÇÒÁÎÉÞÅÎÉÑ ÎÁ ÔÉÐ ÁÒÇÕÍÅÎÔÁ ÄÌÑ corner-ÏÐÅÒÁÔÏÒÏ× ÎÅ ÏÞÅÎØ ×ÁÖÎÙ, 
ÐÏÔÏÍÕ ÞÔÏ ÉÈ ÇÌÁ×ÎÏÅ ÎÁÚÎÁÞÅÎÉÅ ÐÏÚ×ÏÌÉÔØ ËÏÍÁÎÄÁÍ {\tt label} É {\tt
dotlabel} ÃÅÎÔÒÉÒÏ×ÁÔØ Ó×ÏÊ ÔÅËÓÔ ÐÒÁ×ÉÌØÎÏ.
%%The argument type restrictions on the corner operators are not very
%%important because their main purpose is to allow {\tt label} and {\tt
%%dotlabel} statements to center their text properly. 
úÁÒÁÎÅÅ ÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ\index{bbox?\texttt{bbox}}\label{Dbbox}
$$ {\tt bbox}\, \descr{ÒÉÓÕÎÏË-ÐÅÒ×ÉÞÎÏÓÔØ} $$ 
ÎÁÈÏÄÉÔ ÐÒÑÍÏÕÇÏÌØÎÙÊ ÐÕÔØ, ÐÒÅÄÓÔÁ×ÌÑÀÝÉÊ ÏÈ×ÁÔÙ×ÁÀÝÕÀ ÒÁÍËÕ ÄÌÑ ÄÁÎÎÏÇÏ 
ÒÉÓÕÎËÁ.
%%The predefined
%%macro\index{bbox?\texttt{bbox}}\label{Dbbox}
%%$$ {\tt bbox}\, \descr{picture primary} $$
%%finds a rectangular path that represents the bounding box of a given picture. 
åÓÌÉ {\tt p} --- ÜÔÏ ËÁÒÔÉÎËÁ, ÔÏ {\tt bbox p} ÜË×É×ÁÌÅÎÔÎÏ 
$$\begin{verbatim}
(llcorner p-{}-lrcorner p-{}-urcorner p-{}-ulcorner p-{}-cycle), 
\end{verbatim}
$$
ÚÁ ÉÓËÌÀÞÅÎÉÅÍ ÔÏÇÏ, ÞÔÏ ÐÅÒ×ÏÅ ÄÏÐÕÓËÁÅÔ ÎÅÂÏÌØÛÏÊ ÐÒÏÍÅÖÕÔÏË ×ÏËÒÕÇ {\tt p} 
ËÁË ÕËÁÚÁÎÏ ×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ \index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} {\tt
bboxmargin}\index{bboxmargin?\texttt{bboxmargin}}\label{Dbbmargin}.
%%If {\tt p} is a picture, {\tt bbox p} is equivalent to
%%$$\begin{verbatim}
%%(llcorner p--lrcorner p--urcorner p--ulcorner p--cycle)}
%%\end{verbatim}
%%$$
%%except that it allows for a small amount of extra space around {\tt p}
%%as specified by the internal variable\index{internal
%%variables}\index{variables!internal} {\tt
%%bboxmargin}\index{bboxmargin?\texttt{bboxmargin}}\label{Dbbmargin}.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-20} $$
\caption{ïÈ×ÁÔÙ×ÁÀÝÁÑ ÒÁÍËÁ É ÅÅ ÕÇÌÏ×ÙÅ ÔÏÞËÉ.}
%%\caption{A bounding box and its corner points.}
\label{bbox}
\end{figure}

úÁÍÅÔØÔÅ, ÞÔÏ MetaPost ×ÙÞÉÓÌÑÅÔ ÏÈ×ÁÔÙ×ÁÀÝÕÀ ÒÁÍËÕ ÒÉÓÕÎËÁ {\tt
btex}\index{btex?\texttt{btex}} \ldots\ {\tt
etex}\index{etex?\texttt{etex}} ÔÅÍ ÖÅ ÓÐÏÓÏÂÏÍ, ÞÔÏ É \TeX\index{TeX?\TeX}. 
%%Note that MetaPost computes the bounding box of a {\tt
%%btex}\index{btex?\texttt{btex}} \ldots\ {\tt
%%etex}\index{etex?\texttt{etex}} picture just the way
%%\TeX\index{TeX?\TeX} does. 
üÔÏ ×ÐÏÌÎÅ ÅÓÔÅÓÔ×ÅÎÎÏ, ÎÏ ×Ï×ÌÅËÁÅÔ × ÒÁÓÓÍÏÔÒÅÎÉÅ ÆÁËÔÁ ÔÏÇÏ, ÞÔÏ 
\TeX\ ÉÍÅÅÔ Ó×ÏÊÓÔ×Á ÔÉÐÁ {\tt\string\strut}\index{strut?{\tt\string\strut}} É 
{\tt\string\rlap}\index{rlap?{\tt\string\rlap}}, ÞÔÏ ÐÏÚ×ÏÌÑÀÔ ÐÏÌØÚÏ×ÁÔÅÌÑÍ \TeX\ 
ÌÇÁÔØ Ï ÒÁÚÍÅÒÁÈ ÒÁÍËÉ.
%%This is quite natural, but it has certain
%%implications in view of the fact that \TeX\ has features like
%%{\tt\string\strut}\index{strut?{\tt\string\strut}} and
%%{\tt\string\rlap}\index{rlap?{\tt\string\rlap}} that allow \TeX\ users
%%to lie about the dimensions of a box.

ëÏÇÄÁ ËÏÍÁÎÄÙ \TeX, ÌÇÕÝÉÅ Ï ÒÁÚÍÅÒÁÈ ÒÁÍËÉ, ÔÒÁÎÓÌÉÒÕÀÔÓÑ × ÎÉÚËÏÕÒÏ×ÎÅ×ÙÊ 
ËÏÄ Meta\-Post, ËÏÍÁÎÄÁ {\tt
setbounds}\index{setbounds?\texttt{setbounds}}\label{Dsetbnd} 
ÌÖÅÔ:\index{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ?\tdescr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ}}
$$ {\tt setbounds}\, \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ}\, {\tt to}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}
$$
ÄÅÌÁÅÔ \tdescr{ÐÅÒÅÍÅÎÎÕÀ-ËÁÒÔÉÎËÕ} ÔÁËÏÊ, ËÁË ÅÓÌÉ ÂÙ ÅÅ ÏÈ×ÁÔÙ×ÁÀÝÁÑ 
ÒÁÍËÁ ÂÙÌÁ ÔÁËÏÊ ÖÅ ËÁË ÚÁÄÁÎÎÙÊ ÐÕÔØ. 
%%When \TeX\ commands that lie about the dimensions of a box are
%%translated in to low-level MetaPost code, a {\tt
%%setbounds}\index{setbounds?\texttt{setbounds}}\label{Dsetbnd} statement
%%does the lying:\index{picture variable?\tdescr{picture variable}}
%%$$ {\tt setbounds}\, \descr{picture variable}\, {\tt to}\, \descr{path expression}
%%$$
%%makes the \tdescr{picture variable} behave as if its bounding box were
%%the same as the given path. 
üÔÏÔ ÐÕÔØ ÄÏÌÖÅÎ ÂÙÔØ ÃÉËÌÉÞÅÓËÉÍ, Ô.~Å. ÚÁÍËÎÕÔÙÍ.
%%The path has to be a cycle, i.e., it must
%%be a closed path. 
äÌÑ ÐÏÌÕÞÅÎÉÑ ÎÁÓÔÏÑÝÅÊ ÏÈ×ÁÔÙ×ÁÀÝÅÊ ÒÁÍËÉ ÔÁËÏÊ ËÁÒÔÉÎËÉ ÐÒÉÓ×ÏÊÔÅ 
ÐÏÌÏÖÉÔÅÌØÎÏÅ ÚÎÁÞÅÎÉÅ ×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ\index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} {\tt
truecorners}\index{truecorners?\texttt{truecorners}}\label{Dtruecorn}:\footnote{ó×ÏÊÓÔ×Á 
{\tt setbounds} É {\tt truecorners} ÐÒÉÓÕÔÓÔ×ÕÀÔ ÔÏÌØËÏ × MetaPost ×ÅÒÓÉÉ 0.30 
É ÎÏ×ÅÅ.}, Ô.~Å.
$$ \hbox{\verb|show urcorner btex $\bullet$\rlap{ A} etex|} $$
ÐÒÏÉÚ×ÏÄÉÔ ``\verb|>> (4.9813,6.8078)|'', Á
$$ \hbox{\verb|truecorners:=1; show urcorner btex $\bullet$\rlap{ A} etex|} $$
ÐÒÏÉÚ×ÏÄÉÔ ``\verb|>> (15.7742,6.8078)|''.
%%To get the true bounding box of such a
%%picture, assign a positive value to the internal variable\index{internal
%%variables}\index{variables!internal} {\tt
%%truecorners}\index{truecorners?\texttt{truecorners}}\label{Dtruecorn}:\footnote{The
%%{\tt setbounds} and {\tt truecorners} features are only found in
%%MetaPost version 0.30 and higher.}  i.e.,
%%$$ \hbox{\verb|show urcorner btex $\bullet$\rlap{ A} etex|} $$
%%produces ``\verb|>> (4.9813,6.8078)|'' while
%%$$ \hbox{\verb|truecorners:=1; show urcorner btex $\bullet$\rlap{ A} etex|} $$
%%produces ``\verb|>> (15.7742,6.8078)|.''

\section{ðÒÏÄ×ÉÎÕÔÁÑ ÇÒÁÆÉËÁ}
%%\section{Advanced Graphics}
\label{adv.gr}

÷ÓÅ ÐÒÉÍÅÒÙ ÐÒÅÄÙÄÕÝÉÈ ÒÁÚÄÅÌÏ× ÂÙÌÉ ÐÒÏÓÔÙÍ ÒÉÓÏ×ÁÎÉÅÍ ÌÉÎÉÊ Ó ÄÏÂÁ×ÌÅÎÉÅÍ 
ÍÅÔÏË. 
%%All the examples in the previous sections have been simple line drawings
%%with labels added. 
üÔÏÔ ÒÁÚÄÅÌ ÏÐÉÓÙ×ÁÅÔ ÚÁÔÅÎÅÎÉÅ É ÓÒÅÄÓÔ×Á ÄÌÑ ÇÅÎÅÒÁÃÉÉ ÎÅ ÓÔÏÌØ ÐÒÏÓÔÙÈ 
ÌÉÎÉÊ.
%%This section describes shading and tools for
%%generating not-so-simple line drawings. 
úÁÔÅÎÅÎÉÅ ÄÅÌÁÅÔÓÑ ËÏÍÁÎÄÏÊ {\tt fill}\index{fill?\texttt{fill}}\label{Dfill}. 
%%Shading is done with the {\tt
%%fill}\index{fill?\texttt{fill}}\label{Dfill} statement. 
÷ Ó×ÏÅÊ ÐÒÏÓÔÅÊÛÅÊ ÆÏÒÍÅ ËÏÍÁÎÄÁ {\tt fill} ÔÒÅÂÕÅÔ \tdescr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}, 
ÚÁÄÁÀÝÅÅ ÇÒÁÎÉÃÕ ÒÅÇÉÏÎÁ ÄÌÑ ÚÁÐÏÌÎÅÎÉÑ.
%%In its simplest
%%form, the {\tt fill} statement requires a \tdescr{path expression} that
%%gives the boundary of the region to be filled. 
÷ ÓÉÎÔÁËÓÉÓÅ 
$$ {\tt fill}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} $$
ÁÒÇÕÍÅÎÔ ÄÏÌÖÅÎ ÂÙÔØ ÃÉËÌÉÞÅÓËÉÍ ÐÕÔÅÍ, Ô.~Å. ÐÕÔÅÍ, ËÏÔÏÒÙÊ ÏÐÉÓÙ×ÁÅÔÓÑ 
ÚÁÍËÎÕÔÏÊ ËÒÉ×ÏÊ ÞÅÒÅÚ {\tt ..cycle} ÉÌÉ {\tt -{}-cycle}. 
%%In the syntax
%%$$ {\tt fill}\, \descr{path expression} $$
%%the argument should be a cyclic path, i.e., a path that describes a
%%closed curve via the {\tt ..cycle} or {\tt --cycle} notation. 
îÁÐÒÉÍÅÒ, ËÏÍÁÎÄÁ {\tt fill} ÎÁ ÒÉÓ.~\ref{fig20} ÓÔÒÏÉÔ ÚÁÍËÎÕÔÙÊ 
ÐÕÔØ ÐÒÏÄÏÌÖÅÎÉÅÍ ÐÒÉÂÌÉÚÉÔÅÌØÎÏ ÐÏÌÕËÒÕÇÏ×ÏÇÏ ÐÕÔÉ~{\tt p}.
%%For
%%example, the {\tt fill} statement in Figure~\ref{fig20} builds a closed
%%path by extending the roughly semicircular path~{\tt p}. 
üÔÏÔ ÐÕÔØ ÉÍÅÅÔ ÏÒÉÅÎÔÁÃÉÀ ÐÒÏÔÉ× ÞÁÓÏ×ÏÊ ÓÔÒÅÌËÉ, ÎÏ ÜÔÏ ÎÅ ÉÍÅÅÔ ÚÎÁÞÅÎÉÅ, 
ÐÏÔÏÍÕ ÞÔÏ ËÏÍÁÎÄÁ {\tt fill} ÉÓÐÏÌØÚÕÅÔ ÐÒÁ×ÉÌÏ ``ÎÅÎÕÌÅ×ÏÇÏ ×ÅÒÔÑÝÅÇÏÓÑ 
ÞÉÓÌÁ''\index{×ÅÒÔÑÝÅÅÓÑ ÞÉÓÌÏ} (non-zero winding number) 
PostScript\index{PostScript}~\cite{ad:red2}.
%%This path has
%%a counter-clockwise orientation, but that does not matter because the
%%{\tt fill} statement uses PostScript's\index{PostScript} non-zero
%%winding\index{winding number} number rule~\cite{ad:red2}.

\begin{figure}[htp]
$$ \begin{verbatim}
beginfig(21);
path p;
p = (-1cm,0)..(0,-1cm)..(1cm,0);
fill p{up}..(0,0){-1,-2}..{up}cycle;
draw p..(0,1cm)..cycle;
endfig;
\end{verbatim}
\qquad \mathcenter{\includegraphics{manfig-ru-21}}
$$
\caption{MetaPost ËÏÄ É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ×Ù×ÏÄ.}
%%\caption{MetaPost code and the corresponding output.}
\label{fig20}
\end{figure}

ïÂÝÁÑ ËÏÍÁÎÄÁ\index{withcolor?\texttt{withcolor}}\label{Dwithcolor} {\tt fill} 
$$ {\tt fill}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\,
        {\tt withcolor}\, \descr{×ÙÒÁÖÅÎÉÅ-Ã×ÅÔ}
$$
ÕËÁÚÙ×ÁÅÔ ÕÒÏ×ÅÎØ ÓÅÒÏÇÏ ÉÌÉ (ÅÓÌÉ Õ ×ÁÓ ÅÓÔØ Ã×ÅÔÎÏÊ ÐÒÉÎÔÅÒ) ÎÅËÏÔÏÒÙÊ 
Ã×ÅÔ ÒÁÄÕÇÉ.
%%The general {\tt fill} statement\index{withcolor?\texttt{withcolor}}\label{Dwithcolor}
%%$$ {\tt fill}\, \descr{path expression}\,
%%        {\tt withcolor}\, \descr{color expression}
%%$$
%%specifies a shade of gray or (if you have a color printer) some
%%rainbow color. 
$\descr{÷ÙÒÁÖÅÎÉÅ-Ã×ÅÔ}$ ÍÏÖÅÔ ÉÍÅÔØ ÐÑÔØ ×ÏÚÍÏÖÎÙÈ ÚÎÁÞÅÎÉÊ, 
ÐÅÒÅ×ÏÄÉÍÙÈ Ë ÞÅÔÙÒÅÍ ×ÏÚÍÏÖÎÙÍ Ã×ÅÔÏ×ÙÍ ÍÏÄÅÌÑÍ: 
%%The $\descr{color expression}$ can have five possible
%%values, mapping to four possible color models:

$$
\begin{tabular}{ll}
äÅÊÓÔ×ÉÔÅÌØÎÙÊ ××ÏÄ                     & ðÅÒÅ×ÏÄÉÍÏÅ ÚÎÁÞÅÎÉÅ\\\hline
%%Actual input                          & Remapped meaning\\\hline
{\tt withcolor} $\descr{rgb-Ã×ÅÔ} c$  & withrgbcolor\index{withrgbcolor?\texttt{withrgbcolor}}\label{Dwithrgbcolor} $c$\\
%%{\tt withcolor} $\descr{rgbcolor} c$  & %%withrgbcolor\index{withrgbcolor?\texttt{withrgbcolor}}\label{Dwithrgbcolor} $c$\\
{\tt withcolor} $\descr{cmyk-Ã×ÅÔ} c$ & withcmykcolor\index{withrgbcolor?\texttt{withcmykcolor}}\label{Dwithcmykcolor} $c$\\
%%{\tt withcolor} $\descr{cmykcolor} c$ & %%withcmykcolor\index{withrgbcolor?\texttt{withcmykcolor}}\label{Dwithcmykcolor} $c$\\
{\tt withcolor} $\descr{ÞÉÓÌÏ} c$   & withgreyscale\index{withrgbcolor?\texttt{withgreyscale}}\label{Dwithgreyscale} $c$\\
%%{\tt withcolor} $\descr{numeric} c$   & %%withgreyscale\index{withrgbcolor?\texttt{withgreyscale}}\label{Dwithgreyscale}  $c$\\
{\tt withcolor} $\descr{ÌÏÖØ}$       & withoutcolor\index{withrgbcolor?\texttt{withoutcolor}}\label{Dwithoutcolor} \\
%%{\tt withcolor} $\descr{false}$       & %%withoutcolor\index{withrgbcolor?\texttt{withoutcolor}}\label{Dwithoutcolor} \\
{\tt withcolor} $\descr{ÉÓÔÉÎÁ}$        & $\descr{ÔÅËÕÝÁÑ ÔÉÐÏ×ÁÑ ÍÏÄÅÌØ Ã×ÅÔÁ}$\\
%%{\tt withcolor} $\descr{true}$        & $\descr{current default color model}$\\
\end{tabular}
$$

äÌÑ ÕËÁÚÁÎÎÙÈ ÍÏÄÅÌÅÊ Ã×ÅÔÁ ÅÓÔØ ÔÁËÖÅ
$$ {\tt fill}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\,
        {\tt withrgbcolor}\, \descr{×ÙÒÁÖÅÎÉÅ-rgb-Ã×ÅÔ}
$$
$$ {\tt fill}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\,
        {\tt withcmykcolor}\, \descr{×ÙÒÁÖÅÎÉÅ-cmyk-Ã×ÅÔ}
$$
$$ {\tt fill}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\,
        {\tt withgreyscale}\, \descr{ÞÉÓÌÏ}
$$
$$ {\tt fill}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\,
        {\tt withoutcolor}
$$
%%For the specific color models, there are also:
%%$$ {\tt fill}\, \descr{path expression}\,
%%        {\tt withrgbcolor}\, \descr{rgbcolor expression}
%%$$
%%$$ {\tt fill}\, \descr{path expression}\,
%%        {\tt withcmykcolor}\, \descr{cmykcolor expression}
%%$$
%%$$ {\tt fill}\, \descr{path expression}\,
%%        {\tt withgreyscale}\, \descr{numeric}
%%$$
%%$$ {\tt fill}\, \descr{path expression}\,
%%        {\tt withoutcolor}
%%$$

ïÂßÅËÔ-ÉÚÏÂÒÁÖÅÎÉÅ ÎÅ ÍÏÖÅÔ ÉÍÅÔØ ÂÏÌÅÅ ÏÄÎÏÊ Ã×ÅÔÏ×ÏÊ ÍÏÄÅÌÉ, ÐÏÓÌÅÄÎÅÅ 
ÕËÁÚÁÎÉÅ \ttt{withcolor}, \ttt{withrgbcolor}, \ttt{withcmykcolor},
\ttt{withgreyscale} ÉÌÉ \ttt{withoutcolor} ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ ÍÏÄÅÌØ Ã×ÅÔÁ 
ÄÌÑ ÌÀÂÏÇÏ ÏÔÄÅÌØÎÏÇÏ ÏÂßÅËÔÁ.
%%An image object cannot have more then one color model, the last
%%\ttt{withcolor}, \ttt{withrgbcolor}, \ttt{withcmykcolor},
%%\ttt{withgreyscale} or \ttt{withoutcolor} specification sets the color
%%model for any particular object.

íÏÄÅÌØ \ttt{withoutcolor} ÔÒÅÂÕÅÔ ÎÅÂÏÌØÛÉÈ ÒÁÚßÑÓÎÅÎÉÊ: ×ÙÂÏÒ ÜÔÏÊ 
ÍÏÄÅÌÉ ÏÚÎÁÞÁÅÔ, ÞÔÏ MetaPost ÎÅ ÂÕÄÅÔ ÐÉÓÁÔØ ËÏÍÁÎÄÕ ×ÙÂÏÒÁ Ã×ÅÔÁ 
× ×ÙÈÏÄÎÏÊ ÆÁÊÌ PostScript ÄÌÑ ÜÔÏÇÏ ÏÂßÅËÔÁ.
%%The model \ttt{withoutcolor} needs a bit more explanation: selecting
%%this model means that MetaPost will not write a color selection
%%statement to the PostScript output file for this object.

`ôÅËÕÝÁÑ ÔÉÐÏ×ÁÑ' ÍÏÄÅÌØ Ã×ÅÔÁ ÍÏÖÅÔ ÂÙÔØ ÕÓÔÁÎÏ×ÌÅÎÁ ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ 
×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ \ttindex{defaultcolormodel}. 
%%The `current default' color model can be set up using the internal
%%variable \ttindex{defaultcolormodel}. 
ôÁÂÌÉÃÁ~\ref{dfltcmod} ÐÅÒÅÞÉÓÌÑÅÔ ÅÅ ÄÏÐÕÓÔÉÍÙÅ ÚÎÁÞÅÎÉÑ. 
\begin{table}
\centering
\begin{tabular}{|c|l|}
\hline
úÎÁÞÅÎÉÅ & íÏÄÅÌØ Ã×ÅÔÁ\\\hline
1  & ÎÅÔ ÍÏÄÅÌÉ\\
3  & ÏÔÔÅÎËÉ ÓÅÒÏÇÏ\\
5  & rgb (ÐÏ-ÕÍÏÌÞÁÎÉÀ)\\
7  & cmyk\\
\hline
\end{tabular}
\caption{ðÏÄÄÅÒÖÉ×ÁÅÍÙÅ ÍÏÄÅÌÉ Ã×ÅÔÁ.}
\label{dfltcmod}
\end{table}
%%\begin{table}
%%\centering
%%\begin{tabular}{|Ó|l|}
%%\hline
%%Value & Color model\\\hline
%%1  & no model\\
%%3  & greyscale\\
%%5  & rgb (default)\\
%%7  & cmyk\\
%%\hline
%%\end{tabular}
%%\caption{Supported color models.}
%%\label{dfltcmod}
%%\end{table}

òÉÓ.~\ref{fig21} ÉÌÌÀÓÔÒÉÒÕÅÔ ÎÅÓËÏÌØËÏ ÐÒÉÍÅÎÅÎÉÊ ËÏÍÁÎÄÙ {\tt fill} ÄÌÑ 
ÚÁÐÏÌÎÅÎÉÑ ÏÂÌÁÓÔÅÊ ÏÔÔÅÎËÁÍÉ ÓÅÒÏÇÏ.
%%Figure~\ref{fig21} illustrates several applications of the fill command
%%to fill areas with shades of gray. 
ðÕÔÉ ×ËÌÀÞÁÀÔ ÐÅÒÅÓÅÞÅÎÉÑ ËÒÕÇÏ× {\tt a} É {\tt b} É ÐÕÔØ {\tt ab}, 
ÏÈ×ÁÔÙ×ÁÀÝÉÊ ÏÂÌÁÓÔØ ×ÎÕÔÒÉ ÏÂÏÉÈ ËÒÕÇÏ×. 
%%The paths involved are intersecting
%%circles {\tt a} and {\tt b} and a path {\tt ab} that bounds the region
%%inside both circles. 
ëÒÕÇÉ {\tt a} É {\tt b} ÐÒÏÉÓÈÏÄÑÔ ÏÔ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÏÇÏ ÐÕÔÉ {\tt
fullcircle}\index{fullcircle?\texttt{fullcircle}}\label{Dfcirc}, 
ÐÒÉÂÌÉÚÉÔÅÌØÎÏ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÇÏ ËÒÕÇÕ Ó ÅÄÉÎÉÞÎÙÍ ÄÉÁÍÅÔÒÏÍ É 
Ó ÃÅÎÔÒÏÍ × ÎÁÞÁÌÅ ËÏÏÒÄÉÎÁÔ. 
%%Circles {\tt a} and {\tt b} are derived from a
%%predefined path {\tt
%%fullcircle}\index{fullcircle?\texttt{fullcircle}}\label{Dfcirc} that
%%approximates a circle of unit diameter centered on the origin. 
åÓÔØ ÔÁËÖÅ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÐÕÔØ {\tt
halfcircle}\index{halfcircle?\texttt{halfcircle}}\label{Dhcirc} --- 
ÐÏÌÏ×ÉÎÁ {\tt fullcircle} ÎÁÄ ÏÓØÀ $x$. 
%%There is also a predefined path {\tt
%%halfcircle}\index{halfcircle?\texttt{halfcircle}}\label{Dhcirc} that is
%%the part of {\tt fullcircle} above the $x$ axis. 
ðÕÔØ~{\tt ab} ÚÁÔÅÍ ÉÎÉÃÉÁÌÉÚÉÒÕÅÔÓÑ, ÉÓÐÏÌØÚÕÑ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ 
{\tt buildcycle}, ËÏÔÏÒÙÊ ÂÕÄÅÔ ÏÂÓÕÖÄÁÔØÓÑ ×ÓËÏÒÅ.
%%Path~{\tt ab} is then
%%initialized using a predefined macro {\tt buildcycle} that will be
%%discussed shortly.

\begin{figure}[htp]
$$ \begin{verbatim}
beginfig(22);
path a, b, aa, ab;
a = fullcircle scaled 2cm;
b = a shifted (0,1cm);
aa = halfcircle scaled 2cm;
ab = buildcycle(aa, b);
picture pa, pb;
pa = thelabel(btex $A$ etex, (0,-.5cm));
pb = thelabel(btex $B$ etex, (0,1.5cm));
fill a withcolor .7white;
fill b withcolor .7white;
fill ab withcolor .4white;
unfill bbox pa;
draw pa;
unfill bbox pb;
draw pb;
label.lft(btex $U$ etex, (-1cm,.5cm));
draw bbox currentpicture;
endfig;
\end{verbatim}
\qquad \mathcenter{\includegraphics{manfig-ru-22}}
$$
\caption{MetaPost ËÏÄ É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ×Ù×ÏÄ.}
%%\caption{MetaPost code and the corresponding output.}
\index{fullcircle?\texttt{fullcircle}}\index{halfcircle?\texttt{halfcircle}}\index{buildcycle?\texttt{buildcycle}}
\label{fig21}
\end{figure}

úÁÐÏÌÎÅÎÉÅ ËÒÕÇÁ {\tt a} Ó×ÅÔÌÙÍ ÓÅÒÙÍ Ã×ÅÔÏÍ {\tt .7white} É ÚÁÔÅÍ ÔÁËÏÅ 
ÖÅ ÚÁÐÏÌÎÅÎÉÅ ËÒÕÇÁ {\tt b} Ä×ÁÖÄÙ ÚÁÐÏÌÎÑÅÔ ÏÂÌÁÓÔØ, ÇÄÅ ËÒÕÇÉ ÐÅÒÅÓÅËÁÀÔÓÑ. 
%%Filling circle {\tt a} with the light gray color {\tt .7white} and then
%%doing the same with circle {\tt b} doubly fills the region where the
%%disks overlap. 
åÓÔØ ÐÒÁ×ÉÌÏ, ÞÔÏ ËÁÖÄÁÑ ËÏÍÁÎÄÁ {\tt fill} ÐÒÉÓ×ÁÉ×ÁÅÔ ÄÁÎÎÙÊ Ã×ÅÔ 
×ÓÅÍ ÔÏÞËÁÍ ÐÏËÒÙ×ÁÅÍÏÇÏ ÒÅÇÉÏÎÁ, ÕÎÉÞÔÏÖÁÑ ×ÓÅ, ÞÔÏ ÔÁÍ ÂÙÌÏ, ×ËÌÀÞÁÑ 
ÌÉÎÉÉ, ÔÅËÓÔ É ÚÁÐÏÌÎÅÎÎÙÅ ÏÂÌÁÓÔÉ.
%%The rule is that each {\tt fill} statement assigns the
%%given color to all points in the region covered, wiping out whatever was
%%there previously including lines and text as well as filled regions.
ôÁËÉÍ ÏÂÒÁÚÏÍ, ×ÁÖÎÏ ÚÁÄÁ×ÁÔØ ËÏÍÁÎÄÙ {\tt fill} × ÐÒÁ×ÉÌØÎÏÍ ÐÏÒÑÄËÅ.
%%Thus it is important to give {\tt fill} commands in the right order. 
÷ ÐÒÉÍÅÒÅ ×ÙÛÅ ÐÅÒÅËÒÙ×ÁÅÍÁÑ ÏÂÌÁÓÔØ ÐÏÌÕÞÁÅÔ ÏÄÉÎÁËÏ×ÙÊ Ã×ÅÔ Ä×ÁÖÄÙ, 
ÏÓÔÁ×ÁÑÓØ Ó×ÅÔÌÏÓÅÒÏÊ ÐÏÓÌÅ ÐÅÒ×ÙÈ Ä×ÕÈ ËÏÍÁÎÄ {\tt fill}.
%%In the above example, the overlap region gets the same color twice, leaving
%%it light gray after the first two {\tt fill} statements. 
ôÒÅÔØÑ ËÏÍÁÎÄÁ {\tt fill} ÐÒÉÓ×ÁÉ×ÁÅÔ ÂÏÌÅÅ ÔÅÍÎÙÊ Ã×ÅÔ {\tt .4white} 
ÐÅÒÅËÒÙ×ÁÅÍÏÊ ÏÂÌÁÓÔÉ.
%%The third fill
%%statement assigns the darker color {\tt .4white} to the overlap region.

ðÏÓÌÅ ÜÔÏÇÏ ËÒÕÇÉ É ÉÈ ÐÅÒÅÓÅÞÅÎÉÅ ÐÏÌÕÞÁÀÔ Ó×ÏÉ ÏËÏÎÞÁÔÅÌØÎÙÅ Ã×ÅÔÁ, ÎÏ 
× ÎÉÈ ÎÅÔ ×ÙÒÅÚÏË ÄÌÑ ÍÅÔÏË. 
%%At this point the circles and the overlap region have their final colors
%%but there are no cutouts for the labels. 
÷ÙÒÅÚËÉ ÐÏÌÕÞÁÀÔÓÑ ËÏÍÁÎÄÁÍÉ {\tt 
unfill}\index{unfill?\texttt{unfill}}\label{Dunfill}, ËÏÔÏÒÙÅ 
ÂÙÓÔÒÏ ÕÎÉÞÔÏÖÁÀÔ\index{ÓÔÉÒÁÎÉÅ} ÏÂÌÁÓÔÉ, ÏÈ×ÁÔÙ×ÁÀÝÉÉ {\tt bbox
pa}\index{bbox?\texttt{bbox}} É {\tt bbox pb}. 
%%The cutouts are achieved by
%%the {\tt unfill}\index{unfill?\texttt{unfill}}\label{Dunfill} statements
%%that effectively erase\index{erasing} the regions bounded by {\tt bbox
%%pa}\index{bbox?\texttt{bbox}} and {\tt bbox pb}. 
âÏÌÅÅ ÔÏÞÎÏ, {\tt unfill} --- ÜÔÏ ÓÏËÒÁÝÅÎÉÅ ÚÁÐÏÌÎÅÎÉÑ Ó {\tt withcolor 
background}, ÇÄÅ {\tt background} ÏÂÙÞÎÏ ÒÁ×ÅÎ {\tt white}, ÞÔÏ ÐÏÄÈÏÄÉÔ 
ÐÒÉ ÐÅÞÁÔÉ ÎÁ ÂÅÌÏÊ ÂÕÍÁÇÅ.
%%More precisely, {\tt
%%unfill} is shorthand for filling {\tt withcolor background}, where {\tt
%%background} is normally equal to {\tt white} as is appropriate for
%%printing on white paper. 
åÓÌÉ ÎÅÏÂÈÏÄÉÍÏ, ÔÏ ×Ù ÍÏÖÅÔÅ ÐÒÉÓ×ÏÉÔØ ÎÏ×ÙÊ Ã×ÅÔ {\tt
background}\index{background?\texttt{background}}\label{Dbground}.
%%If necessary, you can assign a new color value to {\tt
%%background}\index{background?\texttt{background}}\label{Dbground}.

íÅÔËÉ ÄÏÌÖÎÙ ÂÙÔØ ÐÏÍÅÝÅÎÙ × ËÁÒÔÉÎËÉ {\tt pa} É {\tt pb} ÄÌÑ ×ÏÚÍÏÖÎÏÓÔÉ 
ÉÚÍÅÒÅÎÉÑ ÉÈ ÏÈ×ÁÔÙ×ÁÀÝÉÈ ÒÁÍÏË ÄÏ ÉÈ ÒÉÓÏ×ÁÎÉÑ.
%%The labels need to be stored in pictures {\tt pa} and {\tt pb} to allow
%%for measuring their bounding box before actually drawing them. 
íÁËÒÏÓ {\tt thelabel}\index{thelabel?\texttt{thelabel}} ÓÏÚÄÁÅÔ 
ÔÁËÉÅ ËÁÒÔÉÎËÉ É ÓÄ×ÉÇÁÅÔ ÉÈ × ÐÏÚÉÃÉÉ, ÇÄÅ ÏÎÉ ÇÏÔÏ×Ù ÄÌÑ ÒÉÓÏ×ÁÎÉÑ.
%%The macro {\tt thelabel}\index{thelabel?\texttt{thelabel}} creates such
%%pictures and shifts them into position so that they are ready to draw.
éÓÐÏÌØÚÏ×ÁÎÉÅ ÉÔÏÇÏ×ÙÈ ËÁÒÔÉÎÏË × ËÏÍÁÎÄÅ {\tt draw} × 
ÆÏÒÍÅ\index{draw?\texttt{draw}}
$$ {\tt draw}\, \descr{×ÙÒÁÖÅÎÉÅ-ÒÉÓÕÎÏË} $$
ÄÏÂÁ×ÌÑÅÔ ÉÈ Ë ÔÅËÕÝÅÊ ËÁÒÔÉÎËÅ {\tt 
currentpicture}\index{currentpicture?\texttt{currentpicture}} 
ÔÁË, ÞÔÏ ÏÎÉ ÐÅÒÅÚÁÐÉÓÙ×ÁÀÔ ÞÁÓÔØ ÔÏÇÏ, ÞÔÏ ÕÖÅ 
ÎÁÒÉÓÏ×ÁÎÏ.
%%Using the resulting pictures in {\tt draw} statements of the
%%form\index{draw?\texttt{draw}}
%%$$ {\tt draw}\, \descr{picture expression} $$
%%adds them to {\tt currentpicture}\index{currentpicture?\texttt{currentpicture}}
%%so that they overwrite a portion of what has
%%already been drawn. 
îÁ ÒÉÓ.~\ref{fig21} ÐÅÒÅÚÁÐÉÓÙ×ÁÀÔÓÑ ÓÁÍÉ ÂÅÌÙÅ ÐÒÑÍÏÕÇÏÌØÎÉËÉ, 
ÓÏÚÄÁÎÎÙÅ {\tt unfill}.
%%In Figure~\ref{fig21} just the white rectangles produced by
%%{\tt unfill} get overwritten.

\subsection{ðÏÓÔÒÏÅÎÉÅ ÃÉËÌÏ×}
%%\subsection{Building Cycles}
\label{buildcy}

ëÏÍÁÎÄÁ {\tt buildcycle}\index{buildcycle?\texttt{buildcycle}} 
ËÏÎÓÔÒÕÉÒÕÅÔ ÐÕÔÉ ÄÌÑ ÉÓÐÏÌØÚÏ×ÁÎÉÑ Ó ÍÁËÒÏÓÁÍÉ {\tt fill} ÉÌÉ {\tt unfill}.
%%The {\tt buildcycle}\index{buildcycle?\texttt{buildcycle}} command
%%constructs paths for use with the {\tt fill} or {\tt unfill} macros.
ëÏÇÄÁ ÚÁÄÁÀÔÓÑ Ä×Á ÉÌÉ ÂÏÌÅÅ ÐÕÔÅÊ, ÔÁËÉÈ ËÁË {\tt aa} É {\tt b}, 
ÍÁËÒÏÓ {\tt buildcycle} ÐÙÔÁÅÔÓÑ ÓÏÅÄÉÎÉÔØ ÉÈ ÞÁÓÔÉ ×ÍÅÓÔÅ, ÆÏÒÍÉÒÕÑ 
ÃÉËÌÉÞÅÓËÉÊ ÐÕÔØ. 
%%When given two or more paths such as {\tt aa} and {\tt b}, the {\tt
%%buildcycle} macro tries to piece them together so as to form a cyclic
%%path. 
÷ ÒÁÓÓÍÏÔÒÅÎÎÏÍ ÓÌÕÞÁÅ ÐÕÔØ {\tt aa} Ñ×ÌÑÅÔÓÑ ÐÏÌÕËÒÕÇÏÍ, ÎÁÞÉÎÁÀÝÉÍÓÑ 
ÓÐÒÁ×Á ÏÔ ÐÅÒÅÓÅÞÅÎÉÑ Ó ÐÕÔÅÍ {\tt b}, ÚÁÔÅÍ ÐÒÏÈÏÄÑÝÉÍ ÞÅÒÅÚ 
{\tt b} É ÚÁËÁÎÞÉ×ÁÀÝÉÍÓÑ ÓÎÁÒÕÖÉ ËÒÕÇÁ ÓÌÅ×Á, ËÁË ÐÏËÁÚÁÎÏ ÎÁ 
ÒÉÓ.~\ref{fig22}a.
%%In this case path {\tt aa} is a semicircle that starts just to
%%the right of the intersection with path {\tt b}, then passes through
%%{\tt b} and ends just outside the circle on the left as shown in
%%Figure~\ref{fig22}a.

òÉÓ.~\ref{fig22}b ÐÏËÁÚÙ×ÁÅÔ ËÁË {\tt buildcycle} ÆÏÒÍÉÒÕÅÔ ÚÁÍËÎÕÔÙÊ ÃÉËÌ 
ÉÚ ËÕÓËÏ× ÐÕÔÅÊ {\tt aa} É {\tt b}. 
%%Figure~\ref{fig22}b shows how {\tt buildcycle} forms a closed cycle from
%%the pieces of paths {\tt aa} and {\tt b}. 
íÁËÒÏÓ {\tt buildcycle} ÎÁÈÏÄÉÔ Ä×Á ÐÅÒÅÓÅÞÅÎÉÑ\index{ÐÅÒÅÓÅÞÅÎÉÑ},
ÐÏÍÅÞÅÎÎÙÅ 1 É 2 ÎÁ ÒÉÓ.~\ref{fig22}b. 
%%The {\tt buildcycle} macro
%%detects the two intersections\index{intersections} labeled 1 and 2 in
%%Figure~\ref{fig22}b. 
úÁÔÅÍ ÏÎ ËÏÎÓÔÒÕÉÒÕÅÔ ÃÉËÌÉÞÅÓËÉÊ ÐÕÔØ, ÐÏËÁÚÁÎÎÙÊ ×ÙÄÅÌÅÎÎÙÍ ÎÁ 
ÒÉÓÕÎËÅ, Ä×ÉÇÁÑÓØ ×ÄÏÌØ ÐÕÔÉ {\tt aa} ÏÔ ÐÅÒÅÓÅÞÅÎÉÑ~1 Ë ÐÅÒÅÓÅÞÅÎÉÀ~2 
É ÚÁÔÅÍ ÐÒÏÔÉ× ÞÁÓÏ×ÏÊ ÓÔÒÅÌËÉ ÐÏ ÐÕÔÉ {\tt b} ÏÂÒÁÔÎÏ Ë ÐÅÒÅÓÅÞÅÎÉÀ~1.
%%Then it constructs the cyclic path shown in bold
%%in the figure by going forward along path {\tt aa} from intersection~1
%%to intersection~2 and then forward around the counter-clockwise path
%%{\tt b} back to intersection~1. 
ëÁÖÅÔÓÑ ÏÞÅ×ÉÄÎÙÍ, ÞÔÏ {\tt buildcycle(a,b)} ÂÕÄÅÔ ÐÒÏÉÚ×ÏÄÉÔØ ÔÁËÏÊ ÖÅ 
ÒÅÚÕÌØÔÁÔ, ÎÏ ÏÓÎÏ×ÁÎÉÑ ÄÌÑ ÜÔÏÇÏ ÎÅÓËÏÌØËÏ ÐÕÔÁÎÎÙÅ.
%%It turns out that {\tt buildcycle(a,b)}
%%would have produced the same result, but the reasoning behind this is a
%%little confusing.

\begin{figure}[htp]
$$ {\includegraphics{manfig-ru-123} \atop (a)}
 \qquad {\includegraphics{manfig-ru-223} \atop (b)}
$$
\caption[äÅÍÏÎÓÔÒÁÃÉÑ ÐÏÓÔÒÏÅÎÉÑ ÃÉËÌÁ]
        {(a)~ðÏÌÕËÒÕÇÏ×ÏÊ ÐÕÔØ~{\tt aa}
        Ó ÐÕÎËÔÉÒÎÏÊ ÌÉÎÉÅÊ, ÏÔÍÅÞÁÀÝÅÊ ÐÕÔØ {\tt b}; (b)~ÐÕÔÉ~{\tt aa} É {\tt b}
        Ó ÞÁÓÔÑÍÉ, ×ÙÄÅÌÑÅÍÙÍÉ {\tt buildcycle} É ÐÏËÁÚÁÎÎÙÍÉ ÖÉÒÎÙÍÉ ÌÉÎÉÑÍÉ.}
%%\caption[A demonstration of cycle building]
%%        {(a)~The semicircular path~{\tt aa}
%%        with a dashed line marking path {\tt b}; (b)~paths~{\tt aa} and {\tt b}
%%        with the portions selected by {\tt buildcycle} shown by heavy lines.}
\label{fig22}
\end{figure}

ðÒÏÝÅ ×ÓÅÇÏ ÉÓÐÏÌØÚÏ×ÁÔØ ÍÁËÒÏÓ {\tt buildcycle} × ÓÉÔÕÁÃÉÑÈ, ÐÏÄÏÂÎÙÈ 
ÒÉÓ.~\ref{fig23}, ÇÄÅ ÅÓÔØ ÂÏÌÅÅ Ä×ÕÈ ÁÒÇÕÍÅÎÔÏ×-ÐÕÔÅÊ É ËÁÖÄÁÑ ÐÁÒÁ 
ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÙÈ ÐÕÔÅÊ ÉÍÅÅÔ ÕÎÉËÁÌØÎÏÅ ÐÅÒÅÓÅÞÅÎÉÅ.
%%It is a easier to use the {\tt buildcycle} macro in situations like
%%Figure~\ref{fig23} where there are more than two path arguments and each
%%pair of consecutive paths has a unique intersection. 
îÁÐÒÉÍÅÒ, ÐÒÑÍÁÑ~{\tt q0.5} É ËÒÉ×ÁÑ~{\tt p2} ÐÅÒÅÓÅËÁÀÔÓÑ ÔÏÌØËÏ 
× ÔÏÞËÅ~$P$; ËÒÉ×ÁÑ {\tt p2} É ÐÒÑÍÁÑ ~{\tt q1.5} --- ÔÏÌØËÏ × ÔÏÞËÅ~$Q$.
%%For instance, the
%%line~{\tt q0.5} and the curve~{\tt p2} intersect only at point~$P$; and
%%the curve {\tt p2} and the line~{\tt q1.5} intersect only at point~$Q$.
æÁËÔÉÞÅÓËÉ ËÁÖÄÁÑ ÉÚ ÔÏÞÅË $P$, $Q$, $R$, $S$ Ñ×ÌÑÅÔÓÑ ÕÎÉËÁÌØÎÙÍ 
ÐÅÒÅÓÅÞÅÎÉÅÍ É ÒÅÚÕÌØÔÁÔ\index{buildcycle?\texttt{buildcycle}} ËÏÍÁÎÄÙ 
$$ \hbox{\tt buildcycle(q0.5, p2, q1.5, p4)} $$
ÂÅÒÅÔ {\tt q0.5} ÏÔ $S$ ÄÏ~$P$, ÚÁÔÅÍ {\tt p2} ÏÔ $P$ ÄÏ~$Q$, ÚÁÔÅÍ 
{\tt q1.5} ÏÔ $Q$ ÄÏ~$R$ É, ÎÁËÏÎÅÃ, {\tt p4} ÏÔ $R$ ÏÂÒÁÔÎÏ ÄÏ~$S$.
%%In fact, each of the points $P$, $Q$, $R$, $S$ is a unique intersection,
%%and the result of\index{buildcycle?\texttt{buildcycle}}
%%$$ \hbox{\tt buildcycle(q0.5, p2, q1.5, p4)} $$
%%takes {\tt q0.5} from $S$ to~$P$, then {\tt p2} from $P$ to~$Q$, then
%%{\tt q1.5} from $Q$ to~$R$, and finally {\tt p4} from $R$ back to~$S$.
éÓÓÌÅÄÏ×ÁÎÉÅ ËÏÄÁ MetaPost ÄÌÑ ÒÉÓ.~\ref{fig23} ÏÔËÒÙ×ÁÅÔ, ÞÔÏ 
×Ù ÄÏÌÖÎÙ ÉÄÔÉ ÎÁÚÁÄ ×ÄÏÌØ {\tt p2} ÎÁ ÐÅÒÅÈÏÄÅ ÏÔ $P$ ÄÏ~$Q$.
%%An examination of the MetaPost code for Figure~\ref{fig23} reveals that
%%you have to go backwards along {\tt p2} in order to get from $P$ to~$Q$.
÷ÓÅ ÒÁÂÏÔÁÅÔ ×ÐÏÌÎÅ ÓÏ×ÅÒÛÅÎÎÏ ÄÏ ÔÅÈ ÐÏÒ, ÐÏËÁ ÔÏÞËÉ 
ÐÅÒÅÓÅÞÅÎÉÑ\index{ÐÅÒÅÓÅÞÅÎÉÅ} ÏÐÒÅÄÅÌÑÀÔÓÑ ÕÎÉËÁÌØÎÏ, ÎÏ ÍÏÖÅÔ ÏÂÕÓÌÏ×ÉÔØ 
ÎÅÏÖÉÄÁÎÎÙÅ ÒÅÚÕÌØÔÁÔÙ, ËÏÇÄÁ ÐÁÒÙ ÐÕÔÅÊ ÐÅÒÅÓÅËÁÀÔÓÑ ÂÏÌÅÅ ÏÄÎÏÇÏ ÒÁÚÁ.
%%This works perfectly well as long as the
%%intersection\index{intersection} points are uniquely defined but it can
%%cause unexpected results when pairs of paths intersect more than once.

\begin{figure}[htp]
$$ \begin{verbatim}
beginfig(24);
h=2in; w=2.7in;
path p[], q[], pp;
for i=2 upto 4: ii:=i**2;
  p[i] = (w/ii,h){1,-ii}...(w/i,h/i)...(w,h/ii){ii,-1};
endfor
q0.5 = (0,0)--(w,0.5h);
q1.5 = (0,0)--(w/1.5,h);
pp = buildcycle(q0.5, p2, q1.5, p4);
fill pp withcolor .7white;
z0=center pp;
picture lab; lab=thelabel(btex $f>0$ etex, z0);
unfill bbox lab; draw lab;
draw q0.5; draw p2; draw q1.5; draw p4;
dotlabel.top(btex $P$ etex, p2 intersectionpoint q0.5);
dotlabel.rt(btex $Q$ etex, p2 intersectionpoint q1.5);
dotlabel.lft(btex $R$ etex, p4 intersectionpoint q1.5);
dotlabel.bot(btex $S$ etex, p4 intersectionpoint q0.5);
endfig;
\end{verbatim}
\atop \mathcenter{\includegraphics{manfig-ru-24}}
$$
\caption{MetaPost-ËÏÄ É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ×Ù×ÏÄ.}
%%\caption{MetaPost code and the corresponding output.}
\label{fig23}
\end{figure}

ïÂÝÅÅ ÐÒÁ×ÉÌÏ ÄÌÑ ÍÁËÒÏÓÁ {\tt buildcycle}: 
$$ \hbox{\tt buildcycle(}p_1\hbox{\tt,}\, p_2\hbox{\tt,}\, 
        p_3\hbox{\tt,}\, \ldots \hbox{\tt,} p_k \hbox{\tt )}
$$
×ÙÂÉÒÁÅÔ ÐÅÒÅÓÅÞÅÎÉÅ ÍÅÖÄÕ ËÁÖÄÙÍ $p_i$ É $p_{i+1}$ ÔÁË, ÞÔÏÂÙ ÜÔÏ 
ÂÙÌÏ ËÁË ÍÏÖÎÏ ÄÁÌØÛÅ ÎÁ $p_i$ É ËÁË ÍÏÖÎÏ ÂÌÉÖÅ ÎÁ 
$p_{i+1}$\footnote{ðÅÒ×ÙÍ ÎÁÈÏÄÉÔÓÑ ÐÅÒÅÓÅÞÅÎÉÅ ÍÅÖÄÕ $p_k$ É $p_1$, 
ÚÁÔÅÍ $p_1$ É $p_2$, $\ldots$ (ÐÒÉÍ. ÐÅÒÅ×.)}.
%%The general rule for the {\tt buildcycle} macro is that
%%$$ \hbox{\tt buildcycle(}p_1\hbox{\tt,}\, p_2\hbox{\tt,}\, 
%%        p_3\hbox{\tt,}\, \ldots \hbox{\tt,} p_k \hbox{\tt )}
%%$$
%%chooses the intersection between each $p_i$ and $p_{i+1}$ to be as late
%%as possible on $p_i$ and as early as possible on $p_{i+1}$. 
îÅÔ ÐÒÏÓÔÏÇÏ ÐÒÁ×ÉÌÁ ÄÌÑ ÒÁÚÒÅÛÅÎÉÑ ËÏÎÆÌÉËÔÏ× ÍÅÖÄÕ ÜÔÉÍÉ Ä×ÕÍÑ ÃÅÌÑÍÉ, 
ÔÁË ÞÔÏ ×ÁÍ ÓÌÅÄÕÅÔ ÉÚÂÅÇÁÔØ ÓÌÕÞÁÅ×, ËÏÇÄÁ ÏÄÎÁ ÔÏÞËÁ ÐÅÒÅÓÅÞÅÎÉÑ ÓÌÕÞÁÅÔÓÑ 
ÄÁÌØÛÅ ÎÁ $p_i$ É ÄÒÕÇÁÑ ÔÏÞËÁ ÐÅÒÅÓÅÞÅÎÉÑ\index{ÐÅÒÅÓÅÞÅÎÉÅ} ÓÌÕÞÁÅÔÓÑ 
ÂÌÉÖÅ ÎÁ $p_{i+1}$.
%%There is no
%%simple rule for resolving conflicts between these two goals, so you
%%should avoid cases where one intersection point occurs later on $p_i$
%%and another intersection\index{intersection} point occurs earlier on
%%$p_{i+1}$.

õÓÔÁÎÏ×ËÁ ÎÁ ÓÁÍÙÅ ÄÁÌØÎÉÅ ÐÅÒÅÓÅÞÅÎÉÑ ÄÌÑ $p_i$ É ÓÁÍÙÅ ÂÌÉÖÎÉÅ ÄÌÑ 
$p_{i+1}$ ×ÅÄÅÔ Ë ÕÓÔÒÁÎÅÎÉÑ ÎÅÑÓÎÏÓÔÉ ÐÒÅÄÐÏÞÔÅÎÉÅÍ ÉÄÕÝÉÈ ×ÐÅÒÅÄÉ 
ÐÏÄÐÕÔÅÊ.
%%The preference for intersections as late as possible on $p_i$ and as
%%early as possible on $p_{i+1}$ leads to ambiguity resolution in favor of
%%forward-going subpaths. 
äÌÑ ÃÉËÌÉÞÅÓËÉÈ ÐÕÔÅÊ, ËÁË ÐÕÔØ~{\tt b} ÎÁ 
ÒÉÓ.~\ref{fig22}, ``ÂÌÉÚËÏ'' É ``ÄÁÌÅËÏ'' ÏÔÎÏÓÉÔÅÌØÎÙ ÐÏ ÏÔÎÏÛÅÎÉÀ 
Ë ÎÁÞÁÌØÎÏÊ/ËÏÎÅÞÎÏÊ ÔÏÞËÅ, ËÏÔÏÒÁÑ ÒÁÓÐÏÌÏÖÅÎÁ ÔÁÍ, ËÕÄÁ ×Ù ÐÏÐÁÄÁÅÔÅ 
ÏÂÒÁÔÎÏ, ÓËÁÚÁ× ``{\tt ..cycle}''.
%%For cyclic paths such as path~{\tt b} in
%%Figure~\ref{fig22} ``early'' and ``late'' are relative to a start/finish
%%point which is where you get back to when you say ``{\tt ..cycle}''.
äÌÑ ÐÕÔÉ~{\tt b} ÜÔÁ ÔÏÞËÁ ÕÓÔÁÎÁ×ÌÉ×ÁÅÔÓÑ ÎÁ ÓÁÍÕÀ ÐÒÁ×ÕÀ ÔÏÞËÕ ÎÁ ËÒÕÇÅ.
%%For the path~{\tt b}, this turns out to be the rightmost point on the
%%circle.

âÏÌÅÅ ÐÒÑÍÏÊ ÐÕÔØ ÄÌÑ ÒÁÂÏÔÙ Ó ÐÕÔÅ×ÙÍÉ ÐÅÒÅÓÅÞÅÎÉÑÍÉ × ÉÓÐÏÌØÚÏ×ÁÎÉÉ 
\tdescr{×ÔÏÒÉÞÎÏÇÏ ÂÉÎÁÒÎÏÇÏ 
ÏÐÅÒÁÔÏÒÁ}\index{×ÔÏÒÉÞÎÙÊ binop?\tdescr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}} 
{\tt 
intersection\-point}\index{intersectionpoint?\texttt{intersectionpoint}}\label{Disecpt},
ÎÁÈÏÄÑÝÅÇÏ ÔÏÞËÉ $P$, $Q$, $R$ É~$S$ ÎÁ ÒÉÓ.~\ref{fig23}.
%%A more direct way to deal with path intersections is via the
%%\tdescr{secondary binop}\index{secondary binop?\tdescr{secondary binop}}
%%{\tt
%%intersection\-point}\index{intersectionpoint?\texttt{intersectionpoint}}\label{Disecpt}
%%that finds the points $P$, $Q$, $R$, and~$S$ in Figure~\ref{fig23}.
üÔÏÔ ÍÁËÒÏÓ ÎÁÈÏÄÉÔ ÔÏÞËÕ, ÇÄÅ Ä×Á ÄÁÎÎÙÈ ÐÕÔÉ ÐÅÒÅÓÅËÁÀÔÓÑ.
%%This macro finds a point where two given paths intersect. 
åÓÌÉ ÓÕÝÅÓÔ×ÕÅÔ ÂÏÌÅÅ ÏÄÎÏÊ ÔÏÞËÉ ÐÅÒÅÓÅÞÅÎÉÑ, ÔÏ ÏÎ ×ÙÂÉÒÁÅÔ ÏÄÎÕ; ÅÓÌÉ 
ÔÏÞÅË ÐÅÒÅÓÅÞÅÎÉÑ ÎÅÔ, ÔÏ ÍÁËÒÏÓ ÇÅÎÅÒÉÒÕÅÔ ÓÏÏÂÝÅÎÉÅ ÏÂ ÏÛÉÂËÅ.
%%If there is
%%more than one intersection point, it just chooses one; if there is no
%%intersection, the macro generates an error message.

\subsection{ðÁÒÁÍÅÔÒÉÞÅÓËÁÑ ÒÁÂÏÔÁ Ó ÐÕÔÑÍÉ}
%%\subsection{Dealing with Paths Parametrically}

íÁËÒÏÓ {\tt
intersectionpoint}\index{intersectionpoint?\texttt{intersectionpoint}}
ÏÓÎÏ×ÁÎ ÎÁ ÐÒÉÍÉÔÉ×ÎÏÊ ÏÐÅÒÁÃÉÉ Ó ÉÍÅÎÅÍ {\tt
intersectiontimes}\index{intersectiontimes?\texttt{intersectiontimes}}\label{Disectt}.
%%The {\tt
%%intersectionpoint}\index{intersectionpoint?\texttt{intersectionpoint}}
%%macro is based on a primitive operation called {\tt
%%intersectiontimes}\index{intersectiontimes?\texttt{intersectiontimes}}\label{Disectt}.
üÔÏÔ \tdescr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} --- ÏÄÉÎ ÉÚ ÎÅÓËÏÌØËÉÈ ÏÐÅÒÁÔÏÒÏ×, 
ÒÁÂÏÔÁÀÝÉÈ Ó ÐÕÔÑÍÉ ÐÁÒÁÍÅÔÒÉÞÅÓËÉ. 
%%This \tdescr{secondary binop} is one of several operations that deal
%%with paths parametrically. 
ïÎ ÎÁÈÏÄÉÔ ÐÅÒÅÓÅÞÅÎÉÅ ÍÅÖÄÕ Ä×ÕÍÑ ÐÕÔÑÍÉ, ÚÁÄÁÎÉÅÍ ÐÁÒÁÍÅÔÒÁ ``×ÒÅÍÑ'' ÎÁ 
ËÁÖÄÏÍ ÉÚ ÐÕÔÅÊ.
%%It locates an intersection between two paths
%%by giving the ``time'' parameter on each path. 
üÔÏ ÓÓÙÌËÁ ÎÁ ÓÈÅÍÕ ÐÁÒÁÍÅÔÒÉÚÁÃÉÉ ÉÚ ÒÁÚÄÅÌÁ~\ref{curves}, ÏÐÒÅÄÅÌÑÀÝÅÇÏ 
ÐÕÔÉ ËÁË ËÕÓÏÞÎÙÅ ËÕÂÉÞÅÓËÉÅ ËÒÉ×ÙÅ $\bigl(X(t),Y(t)\bigr)$, ÇÄÅ ÄÉÁÐÁÚÏÎ $t$ 
ÏÔ ÎÕÌÑ ÄÏ ÞÉÓÌÁ ÏÔÒÅÚËÏ× ËÒÉ×ÏÊ.
%%This refers to the
%%parameterization scheme from Section~\ref{curves} that described paths
%%as piecewise cubic curves $\bigl(X(t),Y(t)\bigr)$ where $t$ ranges from
%%zero to the number of curve segments. 
äÒÕÇÉÍÉ ÓÌÏ×ÁÍÉ, ÐÕÔØ ÚÁÄÁÅÔÓÑ, ËÁË ÐÒÏÈÏÄÑÝÉÊ ÞÅÒÅÚ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ 
ÔÏÞÅË, ÇÄÅ $t=0$ × ÐÅÒ×ÏÊ ÔÏÞËÅ, $t=1$ × ÓÌÅÄÕÀÝÅÊ, $t=2$ × ÓÌÅÄÕÀÝÅÊ É Ô.~Ä.
%%In other words, when a path is
%%specified as passing through a sequence of points, where $t=0$ at the
%%first point, then $t=1$ at the next, and $t=2$ at the next, etc. 
òÅÚÕÌØÔÁÔÏÍ  
$$ \hbox{\tt a intersectiontimes b} $$
ÂÕÄÅÔ $(-1,-1)$, ÅÓÌÉ ÐÅÒÅÓÅÞÅÎÉÑ ÎÅÔ; × ÐÒÏÔÉ×ÎÏÍ ÓÌÕÞÁÅ, ×Ù ÐÏÌÕÞÉÔÅ 
ÐÁÒÕ $(t_a,t_b)$, ÇÄÅ $t_a$ --- ÜÔÏ ×ÒÅÍÑ ÎÁ ÐÕÔÉ {\tt a}, ËÏÇÄÁ ÏÎ 
ÐÅÒÅÓÅËÁÅÔ ÐÕÔØ~{\tt b}, É $t_b$ --- ÜÔÏ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÅ ×ÒÅÍÑ ÎÁ 
ÐÕÔÉ~{\tt b}.
%%The result of
%%$$ \hbox{\tt a intersectiontimes b} $$
%%is $(-1,-1)$ if there is no intersection; otherwise you get
%%a pair $(t_a,t_b)$, where $t_a$ is a time on path {\tt a} when it intersects
%%path~{\tt b}, and $t_b$ is the corresponding time on path~{\tt b}.
îÁÐÒÉÍÅÒ, ÐÒÅÄÐÏÌÏÖÉÍ, ÞÔÏ ÐÕÔØ~{\tt a} ÏÂÏÚÎÁÞÅÎ ÔÏÎËÏÊ ÌÉÎÉÅÊ ÎÁ 
ÒÉÓ.~\ref{fig24} É ÐÕÔØ~{\tt b} ÏÂÏÚÎÁÞÅÎ ÂÏÌÅÅ ÔÏÌÓÔÏÊ ÌÉÎÉÅÊ. 
%%For example, suppose path~{\tt a} is denoted by the thin line in
%%Figure~\ref{fig24} and path~{\tt b} is denoted by the thicker line. 
åÓÌÉ ÍÅÔËÉ ÐÏËÁÚÙ×ÁÀÔ ÚÎÁÞÅÎÉÑ ×ÒÅÍÅÎÉ ÎÁ ÐÕÔÑÈ, ÔÏ ÐÁÒÁ ÚÎÁÞÅÎÉÊ ×ÒÅÍÅÎÉ, 
×ÙÞÉÓÌÅÎÎÁÑ ×
$$ \hbox{\tt a intersectiontimes b} $$
ÄÏÌÖÎÁ ÂÙÔØ ÏÄÎÏÊ ÉÚ 
$$ (0.25,1.77),\ (0.75,1.40) {\rm ÉÌÉ}\ (2.58,0.24) $$
É ËÁËÁÑ ÉÚ ÔÒÅÈ ÂÕÄÅÔ ×ÙÂÒÁÎÁ ÚÁ×ÉÓÉÔ ÏÔ ÉÎÔÅÒÐÒÅÔÁÔÏÒÁ MetaPost.
%%If
%%the labels indicate time values on the paths, the pair of time values
%%computed by
%%$$ \hbox{\tt a intersectiontimes b} $$
%%must be one of
%%$$ (0.25,1.77),\ (0.75,1.40), {\rm or}\ (2.58,0.24), $$
%%depending on which of the three intersection points is chosen by the
%%MetaPost interpreter. 
ôÏÞÎÏÅ ÐÒÁ×ÉÌÏ ×ÙÂÏÒÁ ÉÚ ÍÎÏÇÉÈ ÔÏÞÅË ÐÅÒÅÓÅÞÅÎÉÑ ÎÅÓËÏÌØËÏ ÓÌÏÖÎÏ×ÁÔÏÅ, ÎÏ 
× ÄÁÎÎÏÍ ÐÒÉÍÅÒÅ ×Ù ÐÏÌÕÞÉÔÅ $(0.25,1.77)$.
%%The exact rules for choosing among multiple
%%intersection points are a little complicated, but it turns out that you
%%get the time values $(0.25,1.77)$ in this example. 
íÅÎØÛÉÅ ÚÎÁÞÅÎÉÑ ×ÒÅÍÅÎÉ ÐÒÅÄÐÏÞÔÉÔÅÌØÎÅÅ ÂÏÌØÛÉÈ, ÔÁË ÞÔÏ $(t_a,t_b)$ 
ÐÒÅÄÐÏÞÔÉÔÅÌØÎÅÅ, ÞÅÍ $(t'_a,t'_b)$ ÐÏËÁ $t_a<t'_a$ É $t_b<t'_b$. 
%%Smaller time values
%%are preferred over larger ones so that $(t_a,t_b)$ is preferred to
%%$(t'_a,t'_b)$ whenever $t_a<t'_a$ and $t_b<t'_b$. 
ëÏÇÄÁ ÎÅÔ ÐÒÏÓÔÏÇÏ ÓÐÏÓÏÂÁ ÍÉÎÉÍÉÚÉÒÏ×ÁÔØ ÏÂÅ ËÏÍÐÏÎÅÎÔÙ $t_a$ É $t_b$, 
$t_a$ ÐÏÌÕÞÁÅÔ ÂÏÌØÛÉÊ ÐÒÉÏÒÉÔÅÔ, ÎÏ ÐÒÁ×ÉÌÁ ÓÔÁÎÏ×ÑÔÓÑ ÂÏÌÅÅ ÓÌÏÖÎÙÍÉ, 
ËÏÇÄÁ ÍÅÖÄÕ $t_a$ É $t'_a$\index{ÐÅÒÅÓÅÞÅÎÉÅ} ÎÅÔ ÃÅÌÙÈ ÞÉÓÅÌ.
%%When no single
%%alternative minimizes both the $t_a$ and $t_b$ components the $t_a$
%%component tends to get priority, but the rules get more complicated when
%%there are no integers between $t_a$ and $t'_a$\index{intersection}.
(âÏÌØÛÅ ÄÅÔÁÌÅÊ ÓÍ. × {\sl The \MF book} \cite[Chapter 14]{kn:c}).
%%(For more details, see {\sl The \MF book} \cite[Chapter 14]{kn:c}).

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-25} $$
\caption{ä×Á ÐÅÒÅÓÅËÁÀÝÉÈÓÑ ÐÕÔÉ Ó ÏÔÍÅÔËÁÍÉ ÚÎÁÞÅÎÉÊ ×ÒÅÍÅÎÉ ÎÁ ËÁÖÄÏÍ.}
%%\caption{Two intersecting paths with time values marked on each path.}
\label{fig24}
\end{figure}

ïÐÅÒÁÔÏÒ {\tt intersectiontimes} ÂÏÌÅÅ ÇÉÂËÉÊ, ÞÅÍ {\tt
intersectionpoint}, ÐÏÔÏÍÕ ÞÔÏ ÓÕÝÅÓÔ×ÕÅÔ ÍÎÏÇÏ ×ÓÅÇÏ, ÞÔÏ ÍÏÖÎÏ ÓÄÅÌÁÔØ 
ÓÏ ÚÎÁÞÅÎÉÑÍÉ ×ÒÅÍÅÎÉ ÎÁ ÐÕÔÉ.
%%The {\tt intersectiontimes} operator is more flexible than {\tt
%%intersectionpoint} because there are a number of things that can be done
%%with time values on a path. 
ïÄÎÏ ÉÚ ÓÁÍÙÈ ×ÁÖÎÙÈ --- ÜÔÏ ÚÁÄÁÔØ ×ÏÐÒÏÓ: ``çÄÅ ÐÒÏÈÏÄÉÔ ÐÕÔØ {\tt p} ×Ï 
×ÒÅÍÑ {\tt t}?'' 
%%One of the most important is just to ask
%%``where is path {\tt p} at time {\tt t}?'' 
ëÏÎÓÔÒÕËÃÉÑ\index{point
of?\texttt{point of}}\label{Dpntof}
$$ {\tt point}\, \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\, {\tt of}\, \descr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ} $$ 
ÏÔ×ÅÞÁÅÔ ÎÁ ÜÔÏÔ ×ÏÐÒÏÓ.
%%The construction\index{point
%%of?\texttt{point of}}\label{Dpntof}
%%$$ {\tt point}\, \descr{numeric expression}\, {\tt of}\, \descr{path primary} $$
%%answers this question. 
åÓÌÉ \tdescr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} ÍÅÎØÛÅ ÎÕÌÑ ÉÌÉ ÂÏÌØÛÅ 
ÚÎÁÞÅÎÉÑ ×ÒÅÍÅÎÉ, ÐÒÉÓ×ÏÅÎÎÏÇÏ ÐÏÓÌÅÄÎÅÊ ÔÏÞËÅ ÎÁ ÐÕÔÉ, ÔÏ 
ËÏÎÓÔÒÕËÃÉÑ {\tt point of} ÏÂÙÞÎÏ ×ÏÚ×ÒÁÝÁÅÔ ÐÏÓÌÅÄÎÀÀ ÔÏÞËÕ ÐÕÔÉ.
%%If the \tdescr{numeric expression} is less than
%%zero or greater than the time value assigned to the last point on the
%%path, the {\tt point of} construction normally yields an endpoint of the
%%path. 
ðÏÜÔÏÍÕ ÐÒÉÎÑÔÏ ÉÓÐÏÌØÚÏ×ÁÔØ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÕÀ ËÏÎÓÔÁÎÔÕ {\tt
infinity}\index{infinity?\texttt{infinity}}\label{Dinf} (ÒÁ×ÎÕÀ 
4095.99998) ËÁË \tdescr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} × ËÏÎÓÔÒÕËÃÉÉ {\tt point of}, 
ËÏÇÄÁ ÉÍÅÅÍ ÄÅÌÏ Ó ËÏÎÃÏÍ ÐÕÔÉ.
%%Hence, it is common to use the predefined constant {\tt
%%infinity}\index{infinity?\texttt{infinity}}\label{Dinf} (equal to
%%4095.99998) as the \tdescr{numeric expression} in a {\tt point of}
%%construction when dealing with the end of a path.

ôÁËÏÅ ``ÂÅÓËÏÎÅÞÎÏÅ'' ÚÎÁÞÅÎÉÅ ×ÒÅÍÅÎÉ ÎÅ ÒÁÂÏÔÁÅÔ ÄÌÑ ÃÉËÌÉÞÅÓËÏÇÏ ÐÕÔÉ, 
Ô.~Ë. ÚÎÁÞÅÎÉÑ ×ÒÅÍÅÎÉ, ×ÙÈÏÄÑÝÉÅ ÚÁ ÎÏÒÍÁÌØÎÙÊ ÄÉÁÐÁÚÏÎ, ÍÏÇÕÔ × ÜÔÏÍ 
ÓÌÕÞÁÅ ÏÂÒÁÂÁÔÙ×ÁÔØÓÑ ÍÏÄÕÌØÎÏÊ ÁÒÉÆÍÅÔÉËÏÊ, Ô.~Å. ÄÌÑ ÃÉËÌÉÞÅÓËÏÇÏ ÐÕÔÉ~{\tt p} 
ÞÅÒÅÚ ÔÏÞËÉ $z_0$, $z_1$, $z_2$, \ldots, $z_{n-1}$ Ó ÏÂÙÞÎÙÍ 
ÄÉÁÐÁÚÏÎÏÍ ÐÁÒÁÍÅÔÒÏ× $0\leqslant t<n$, 
$$ \hbox{\tt point t of p} $$
ÍÏÖÅÔ ÂÙÔØ ×ÙÞÉÓÌÅÎÏ ÄÌÑ ÌÀÂÏÇÏ~$t$ ÐÒÅÄ×ÁÒÉÔÅÌØÎÙÍ ×ÚÑÔÉÅÍ $t$ ÐÏ ÍÏÄÕÌÀ~$n$. 
%%Such ``infinite'' time values do not work for a cyclic path, since time
%%values outside of the normal range can be handled by modular arithmetic
%%in that case; i.e., a cyclic path~{\tt p} through points $z_0$, $z_1$,
%%$z_2$, \ldots, $z_{n-1}$ has the normal parameter range $0\le t<n$, but
%%$$ \hbox{\tt point t of p} $$
%%can be computed for any~$t$ by first reducing $t$ modulo~$n$. 
åÓÌÉ ÍÏÄÕÌØ $n$ ÎÅÄÏÓÔÕÐÅÎ, ÔÏ\index{length?\texttt{length}}\label{Dlength}
$$ {\tt length}\, \descr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ} $$ 
ÄÁÅÔ ÃÅÌÏÅ ÚÎÁÞÅÎÉÅ ×ÅÒÈÎÅÇÏ ÐÒÅÄÅÌÁ ÎÏÒÍÁÌØÎÏÇÏ ÄÉÁÐÁÚÏÎÁ ÐÁÒÁÍÅÔÒÁ-×ÒÅÍÅÎÉ 
ÄÌÑ ÚÁÄÁÎÎÏÇÏ ÐÕÔÉ.
%%If the
%%modulus~$n$ is not readily
%%available,\index{length?\texttt{length}}\label{Dlength}
%%$$ {\tt length}\, \descr{path primary} $$
%%gives the integer value of the upper limit of the normal time parameter
%%range for the specified path.

MetaPost ÉÓÐÏÌØÚÕÅÔ ÔÁËÉÅ ÖÅ ÓÏÏÔ×ÅÔÓÔ×ÉÑ ÍÅÖÄÕ ÚÎÁÞÅÎÉÑÍÉ ×ÒÅÍÅÎÉ 
É ÔÏÞËÁÍÉ ÎÁ ÐÕÔÉ ÐÒÉ ×ÙÞÉÓÌÅÎÉÉ ÏÐÅÒÁÔÏÒÁ {\tt
subpath}\index{subpath?\texttt{subpath}}\label{Dsubpth}. 
%%MetaPost uses the same correspondence between time values and points on
%%a path to evaluate the {\tt
%%subpath}\index{subpath?\texttt{subpath}}\label{Dsubpth} operator. 
óÉÎÔÁËÓÉÓ ÜÔÏÇÏ ÏÐÅÒÁÔÏÒÁ 
$$ {\tt subpath}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\, {\tt of}\, \descr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ} $$
%%The syntax for this operator is
%%$$ {\tt subpath}\, \descr{pair expression}\, {\tt of}\, \descr{path primary} $$
åÓÌÉ ÚÎÁÞÅÎÉÅ \tdescr{×ÙÒÁÖÅÎÉÑ-ÐÁÒÙ} ÂÕÄÅÔ $(t_1,t_2)$ É 
\tdescr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ} --- ÜÔÏ $p$, ÔÏ ÒÅÚÕÌØÔÁÔ ÂÕÄÅÔ ÐÕÔÅÍ, ÞÔÏ 
ÓÌÅÄÕÅÔ ËÁË É $p$ ÏÔ {\tt point $t_1$ of $p$} ÄÏ {\tt point $t_2$ of $p$}. 
%%If the value of the \tdescr{pair expression} is $(t_1,t_2)$ and the
%%\tdescr{path primary} is $p$, the result is a path that follows $p$ from
%%{\tt point $t_1$ of $p$} to {\tt point $t_2$ of $p$}. 
åÓÌÉ $t_2<t_1$, ÔÏ ÐÏÄÐÕÔØ ÉÄÅÔ ÏÂÒÁÔÎÏ ×ÄÏÌØ~$p$.
%%If $t_2<t_1$, the subpath runs backwards along~$p$.

÷ÁÖÎÙÊ ÏÐÅÒÁÔÏÒ, ÏÓÎÏ×ÁÎÎÙÊ ÎÁ ÏÐÅÒÁÔÏÒÅ {\tt subpath}, --- ÜÔÏ 
\tdescr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}\index{ÔÒÅÔÉÞÎÙÊ binop?\tdescr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}
{\tt cutbefore}\index{cutbefore?\texttt{cutbefore}}\label{Dcutb}. 
%%An important operation based on the {\tt subpath} operator is the
%%\tdescr{tertiary binop}\index{tertiary binop?\tdescr{tertiary binop}}
%%{\tt cutbefore}\index{cutbefore?\texttt{cutbefore}}\label{Dcutb}. 
äÌÑ ÐÅÒÅÓÅËÁÀÝÉÈÓÑ ÐÕÔÅÊ $p_1$ É $p_2$,
$$ p_1\ {\tt cutbefore}\ p_2 $$
ÜË×É×ÁÌÅÎÔÎÏ 
$$ \hbox{\tt subpath (xpart($p_1$ intersectiontimes $p_2$), length $p_1$) of $p_1$}
$$
Ó ÔÅÍ ÉÓËÌÀÞÅÎÉÅÍ, ÞÔÏ ÏÎ ÔÁËÖÅ ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ ÐÅÒÅÍÅÎÎÕÀ-ÐÕÔØ {\tt
cuttings}\index{cuttings?\texttt{cuttings}}\label{Dcuttings} × ÞÁÓÔØ 
$p_1$, ÞÔÏ ÏÔÂÒÁÓÙ×ÁÅÔÓÑ. 
%%For intersecting paths $p_1$ and $p_2$,
%%$$ p_1\ {\tt cutbefore}\ p_2 $$
%%is equivalent to
%%$$ \hbox{\tt subpath (xpart($p_1$ intersectiontimes $p_2$), length $p_1$) of $p_1$}
%%$$
%%except that it also sets the path variable {\tt
%%cuttings}\index{cuttings?\texttt{cuttings}}\label{Dcuttings} to the
%%portion of $p_1$ that gets cut off. 
äÒÕÇÉÍÉ ÓÌÏ×ÁÍÉ, {\tt cutbefore} ×ÏÚ×ÒÁÝÁÅÔ Ó×ÏÊ ÐÅÒ×ÙÊ ÁÒÇÕÍÅÎÔ ÂÅÚ 
ÞÁÓÔÉ ÄÏ ÐÅÒÅÓÅÞÅÎÉÑ.
%%In other words, {\tt cutbefore}
%%returns its first argument with the part before the intersection cut
%%off. 
ðÒÉ ÍÎÏÖÅÓÔ×ÅÎÎÙÈ ÐÅÒÅÓÅÞÅÎÉÑÈ ÏÎ ÐÙÔÁÅÔÓÑ ÏÔÂÒÏÓÉÔØ ÎÁÉÍÅÎØÛÕÀ ÞÁÓÔØ.
%%With multiple intersections, it tries to cut off as little as
%%possible. 
åÓÌÉ ÐÕÔÉ ÎÅ ÐÅÒÅÓÅËÁÀÔÓÑ, ÔÏ {\tt cutbefore} ×ÏÚ×ÒÁÝÁÅÔ Ó×ÏÊ ÐÅÒ×ÙÊ 
ÁÒÇÕÍÅÎÔ.
%%If the paths do not intersect, {\tt cutbefore} returns its
%%first argument.

åÓÔØ ÔÁËÖÅ ÁÎÁÌÏÇÉÞÎÙÊ \tdescr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}\index{ÔÒÅÔÉÞÎÙÊ
binop?\tdescr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}, ÎÁÚÙ×ÁÅÍÙÊ {\tt
cutafter}\index{cutafter?\texttt{cutafter}}\label{Dcuta}, ËÏÔÏÒÙÊ ÒÁÂÏÔÁÅÔ 
ÐÒÉÍÅÎÅÎÉÅÍ {\tt cutbefore} Ó ÉÎ×ÅÒÔÉÒÏ×ÁÎÎÙÍ ×ÒÅÍÅÎÅÍ ×ÄÏÌØ Ó×ÏÅÇÏ ÐÅÒ×ÏÇÏ 
ÁÒÇÕÍÅÎÔÁ.
%%There is also an analogous \tdescr{tertiary binop}\index{tertiary
%%binop?\tdescr{tertiary binop}} called {\tt
%%cutafter}\index{cutafter?\texttt{cutafter}}\label{Dcuta} that works by
%%applying {\tt cutbefore} with time reversed along its first argument.
ôÁËÉÍ ÏÂÒÁÚÏÍ, 
$$ p_1\ {\tt cutafter}\ p_2 $$
ÐÙÔÁÅÔÓÑ ÏÔÒÅÚÁÔØ ÞÁÓÔØ $p_1$ ÐÏÓÌÅ ÐÏÓÌÅÄÎÅÇÏ ÐÅÒÅÓÅÞÅÎÉÑ Ó $p_2$.
%%Thus
%%$$ p_1\ {\tt cutafter}\ p_2 $$
%%tries to cut off the part of $p_1$ after its last intersection with $p_2$.

äÒÕÇÏÊ ÏÐÅÒÁÔÏÒ\index{direction of?\texttt{direction of}}\label{Ddirof}
$$ {\tt direction}\, \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\, {\tt of}\, \descr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ}
$$
ÎÁÈÏÄÉÔ ×ÅËÔÏÒ × ÎÁÐÒÁ×ÌÅÎÉÉ \tdescr{ÐÕÔÉ-ÐÅÒ×ÉÞÎÏÓÔÉ}. 
%%Another operator\index{direction of?\texttt{direction of}}\label{Ddirof}
%%$$ {\tt direction}\, \descr{numeric expression}\, {\tt of}\, \descr{path primary}
%%$$
%%finds a vector in the direction of the \tdescr{path primary}. 
ïÎ ÏÐÒÅÄÅÌÑÅÔÓÑ ÄÌÑ ÌÀÂÏÇÏ ×ÒÅÍÅÎÉ, ÐÏÄÏÂÎÏ ËÏÎÓÔÒÕËÃÉÉ {\tt point of}.
%%This is
%%defined for any time value analogously to the {\tt point of}
%%construction. 
÷ÅËÔÏÒ-ÒÅÚÕÌØÔÁÔ ÉÍÅÅÔ ÐÒÁ×ÉÌØÎÏÅ ÎÁÐÒÁ×ÌÅÎÉÅ É ÎÅÓËÏÌØËÏ ÐÒÏÉÚ×ÏÌØÎÏÊ ÒÁÚÍÅÒ.
%%The resulting direction vector has the correct
%%orientation and a somewhat arbitrary magnitude. 
óÏÅÄÉÎÅÎÉÅ ËÏÎÓÔÒÕËÃÉÊ {\tt point of} É {\tt direction of} ÄÁÅÔ ÕÒÁ×ÎÅÎÉÅ ÄÌÑ 
ÌÉÎÉÉ ÔÁÎÇÅÎÓÁ, ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig25}.
%%Combining {\tt point
%%of} and {\tt direction of} constructions yields the equation for a
%%tangent line as illustrated in Figure~\ref{fig25}.

\begin{figure}[htp]
$$ \begin{verbatim}
beginfig(26);
numeric scf, #, t[]; 
3.2scf = 2.4in;
path fun;
# = .1;  % Keep the function single-valued
fun = ((0,-1#)..(1,.5#){right}..(1.9,.2#){right}..{curl .1}(3.2,2#))
  yscaled(1/#) scaled scf;
x1 = 2.5scf;
for i=1 upto 2:
  (t[i],whatever) =
    fun intersectiontimes ((x[i],-infinity)--(x[i],infinity));
  z[i] = point t[i] of fun;
  z[i]-(x[i+1],0) = whatever*direction t[i] of fun;
  draw (x[i],0)--z[i]--(x[i+1],0);
  fill fullcircle scaled 3bp shifted z[i];
endfor
label.bot(btex $x_1$ etex, (x1,0));
label.bot(btex $x_2$ etex, (x2,0));
label.bot(btex $x_3$ etex, (x3,0));
draw (0,0)--(3.2scf,0);
pickup pencircle scaled 1pt;
draw fun;
endfig;
\end{verbatim}
\atop \includegraphics{manfig-ru-26}
$$
\caption{ëÏÄ MetaPost É ÒÉÓÕÎÏË-ÒÅÚÕÌØÔÁÔ}
%%\caption{MetaPost code and the resulting figure}
\label{fig25}
\end{figure}

åÓÌÉ ×Ù ÚÎÁÅÔÅ ÕËÌÏÎ É ×Ù ÈÏÔÉÔÅ ÎÁÊÔÉ ÔÏÞËÕ ÎÁ ËÒÉ×ÏÊ Ó ÔÁÎÇÅÎÓÏÍ, ÒÁ×ÎÙÍ 
ÜÔÏÍÕ ÕËÌÏÎÕ, ÔÏ ÎÕÖÅÎ ÏÐÅÒÁÔÏÒ {\tt directiontime}\index{directiontime
of?\texttt{directiontime of}}\label{Ddtimof} --- ÏÂÒÁÔÎÙÊ Ë 
{\tt direction of}.
%%If you know a slope and you want to find a point on a curve where the
%%tangent line has that slope, the {\tt directiontime}\index{directiontime
%%of?\texttt{directiontime of}}\label{Ddtimof} operator inverts the {\tt
%%direction of} operation. 
C ÄÁÎÎÙÍÉ ×ÅËÔÏÒÏÍ-ÕËÌÏÎÏÍ É ÐÕÔÅÍ 
$$ {\tt directiontime}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\, {\tt of}\,
  \descr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ}
$$
×ÏÚ×ÒÁÝÁÅÔ ÞÉÓÌÏ×ÏÅ ÚÎÁÞÅÎÉÅ, ÞÔÏ ÄÁÅÔ ÐÅÒ×ÏÅ ×ÒÅÍÑ~$t$, ËÏÇÄÁ ÐÕÔØ ÉÍÅÅÔ 
ÚÁÄÁÎÎÏÅ ÎÁÐÒÁ×ÌÅÎÉÅ. 
%%Given a direction vector and a path,
%%$$ {\tt directiontime}\, \descr{pair expression}\, {\tt of}\,
%%  \descr{path primary}
%%$$
%%returns a numeric value that gives the first time~$t$ when the path has
%%the indicated direction. 
(åÓÌÉ ÔÁËÏÇÏ ×ÒÅÍÅÎÉ ÎÅÔ, ÔÏ ÒÅÚÕÌØÔÁÔ ÂÕÄÅÔ $-1$.)
%%(If there is no such time, the result is
%%$-1$). 
îÁÐÒÉÍÅÒ, ÅÓÌÉ {\tt a} --- ÜÔÏ ÐÕÔØ, ÎÁÒÉÓÏ×ÁÎÎÙÊ ÔÏÎËÏÊ ËÒÉ×ÏÊ ÎÁ 
ÒÉÓ.~\ref{fig24}, ÔÏ {\tt directiontime (1,1) of a} ×ÏÚ×ÒÁÝÁÅÔ 0.2084.
%%For example, if {\tt a} is the path drawn as a thin curve in
%%Figure~\ref{fig24}, {\tt directiontime (1,1) of a} returns 0.2084.

åÓÔØ ÅÝÅ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ \index{directionpoint
of?\texttt{directionpoint of}}\label{Ddpntof}
$$ {\tt directionpoint}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\, {\tt of}\,
  \descr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ},
$$
ËÏÔÏÒÙÊ ÎÁÈÏÄÉÔ ÐÅÒ×ÕÀ ÔÏÞËÕ ÎÁ ÐÕÔÉ, ÇÄÅ ÅÓÔØ ÄÁÎÎÏÅ ÎÁÐÒÁ×ÌÅÎÉÅ. 
%%There is also an predefined macro \index{directionpoint
%%of?\texttt{directionpoint of}}\label{Ddpntof}
%%$$ {\tt directionpoint}\, \descr{pair expression}\, {\tt of}\,
%%  \descr{path primary}
%%$$
%%that finds the first point on a path where a given direction is achieved. 
íÁËÒÏÓ {\tt directionpoint} ÐÒÏÉÚ×ÏÄÉÔ ÓÏÏÂÝÅÎÉÅ Ï ÏÛÉÂËÅ, ÅÓÌÉ ÉÓËÏÍÏÅ 
ÎÁÐÒÁ×ÌÅÎÉÅ ÏÔÓÕÔÓÔ×ÕÅÔ ÎÁ ÐÕÔÉ.
%%The
%%{\tt directionpoint} macro produces an error message if the direction does not
%%occur on the path.

ïÐÅÒÁÔÏÒÙ {\tt
arclength}\index{arclength?\texttt{arclength}}\label{Darclng} É {\tt
arctime of}\index{arctime of?\texttt{arctime of}}\label{Darctim} ÏÔÎÏÓÑÔÓÑ 
Ë ``×ÒÅÍÅÎÉ'' ÎÁ ÐÕÔÉ ÂÏÌÅÅ ÚÎÁËÏÍÙÍ ÏÂÒÁÚÏÍ, ÉÓÐÏÌØÚÕÑ ÐÏÎÑÔÉÅ ÄÌÉÎÙ 
ÄÕÇÉ.\index{ÄÌÉÎÁ ÄÕÇÉ}\footnote{ïÐÅÒÁÔÏÒÙ {\tt arclength} É {\tt arctime}
ÄÏÓÔÕÐÎÙ ÔÏÌØËÏ × MetaPost ×ÅÒÓÉÉ 0.50 É ÎÏ×ÅÅ.} 
%%Operators {\tt
%%arclength}\index{arclength?\texttt{arclength}}\label{Darclng} and {\tt
%%arctime of}\index{arctime of?\texttt{arctime of}}\label{Darctim} relate
%%the ``time'' on a path to the more familiar concept of arc
%%length.\index{arc length}\footnote{The {\tt arclength} and {\tt arctime}
%%operators are only found in MetaPost version 0.50 and higher.} 
÷ÙÒÁÖÅÎÉÅ 
$$ \hbox{{\tt arclength} \tdescr{ÐÕÔØ-ÐÅÒ×ÉÞÎÏÓÔØ}} $$ 
×ÙÄÁÅÔ ÄÌÉÎÕ ÄÕÇÉ ÐÕÔÉ.
%%The expression
%%$$ \hbox{{\tt arclength} \tdescr{path primary}} $$
%%gives the arc length of a path. 
åÓÌÉ {\tt p} --- ÜÔÏ ÐÕÔØ É {\tt a} --- ÞÉÓÌÏ ÍÅÖÄÕ 0 É {\tt arclength p}, ÔÏ 
$$ \hbox{\tt arctime a of p} $$
ÄÁÅÔ ×ÒÅÍÑ~{\tt t}, ÔÁËÏÅ ÞÔÏ 
$$ \hbox{\tt arclength subpath (0,t) of p} = {\tt a}. $$
%%If {\tt p} is a path and {\tt a} is a number
%%between 0 and {\tt arclength p},
%%$$ \hbox{\tt arctime a of p} $$
%%gives the time~{\tt t} such that
%%$$ \hbox{\tt arclength subpath (0,t) of p} = {\tt a}. $$

\subsection{áÆÆÉÎÎÙÅ ÔÒÁÎÓÆÏÒÍÁÃÉÉ}
%%\subsection{Affine Transformations}
\label{transsec}
\index{ÔÉÐ-ÔÒÁÎÓÆÏÒÍÁÃÉÑ}
%%\index{transform type}

úÁÍÅÔØÔÅ, ÞÔÏ ÐÕÔØ {\tt fun} ÎÁ ÒÉÓ.~\ref{fig25} ÓÎÁÞÁÌÁ ËÏÎÓÔÒÕÉÒÕÅÔÓÑ ËÁË 
$$ \hbox{\verb|(0,-.1)..(1,.05){right}..(1.9,.02){right}..{curl .1}(3.2,.2)|} $$
É ÚÁÔÅÍ ÉÓÐÏÌØÚÕÀÔÓÑ ÏÐÅÒÁÔÏÒÙ {\tt yscaled}\index{yscaled?\texttt{yscaled}} 
É {\tt scaled}\index{scaled?\texttt{scaled}} ÄÌÑ ÎÁÓÔÒÏÊËÉ ÆÏÒÍÙ É ÒÁÚÍÅÒÁ 
ÐÕÔÉ. 
%%Note how path {\tt fun} in Figure~\ref{fig25} is first constructed as
%%$$ \hbox{\verb|(0,-.1)..(1,.05){right}..(1.9,.02){right}..{curl .1}(3.2,.2)|} $$
%%and then the {\tt yscaled}\index{yscaled?\texttt{yscaled}} and {\tt
%%scaled}\index{scaled?\texttt{scaled}} operators are used to adjust the
%%shape and size of the path. 
ëÁË ÐÏÄÓËÁÚÙ×ÁÅÔ ÎÁÚ×ÁÎÉÅ, ×ÙÒÁÖÅÎÉÅ Ó ``{\tt yscaled 10}'' ÕÍÎÏÖÁÅÔ 
ËÏÏÒÄÉÎÁÔÙ $y$ ÎÁ ÄÅÓÑÔØ ÔÁË, ÞÔÏ ËÁÖÄÁÑ ÔÏÞËÁ $(x,y)$ ÉÓÈÏÄÎÏÇÏ ÐÕÔÉ 
ÂÕÄÅÔ ÓÏÏÔ×ÅÔÓÔ×Ï×ÁÔØ ÔÏÞËÅ $(x,10y)$ ÎÁ ÔÒÁÎÓÆÏÒÍÉÒÏ×ÁÎÎÏÍ ÐÕÔÉ. 
%%As the name suggests, an expression
%%involving ``{\tt yscaled 10}'' multiplies $y$ coordinates by ten so that
%%every point $(x,y)$ on the original path corresponds to a point
%%$(x,10y)$ on the transformed path.

÷ÍÅÓÔÅ Ó {\tt scaled} É {\tt yscaled} ÓÕÝÅÓÔ×ÕÅÔ ÓÅÍØ ÏÐÅÒÁÔÏÒÏ× 
ÔÒÁÎÓÆÏÒÍÁÃÉÉ Ó ÁÒÇÕÍÅÎÔÏÍ ÞÉÓÌÏÍ ÉÌÉ ÐÁÒÏÊ :\index{shifted?\texttt{shifted}}%
\index{rotated?\texttt{rotated}}\index{slanted?\texttt{slanted}}\index{scaled?\texttt{scaled}}\index{xscaled?\texttt{xscaled}}%
\index{yscaled?\texttt{yscaled}}\index{zscaled?\texttt{zscaled}}\label{Dtranop}
%%Including {\tt scaled} and {\tt yscaled}, there are seven transformation
%%operators that take a numeric or pair
%%argument:\index{shifted?\texttt{shifted}}%
%%\index{rotated?\texttt{rotated}}\index{slanted?\texttt{slanted}}\index{scaled?\texttt{%%scaled}}\index{xscaled?\texttt{xscaled}}%
%%\index{yscaled?\texttt{yscaled}}\index{zscaled?\texttt{zscaled}}\label{Dtranop}
\begin{eqnarray*}
 (x,y){\tt\ shifted\ }(a,b)     &=& (x+a,\, y+b); \\
 (x,y){\tt\ rotated\ }\theta    &=& (x\cos\theta-y\sin\theta,\,
                                        x\sin\theta+y\cos\theta); \\
 (x,y){\tt\ slanted\ }a         &=& (x+ay,\, y); \\
 (x,y){\tt\ scaled\ }a          &=& (ax,\, ay); \\
 (x,y){\tt\ xscaled\ }a         &=& (ax,\, y); \\
 (x,y){\tt\ yscaled\ }a         &=& (x,\, ay); \\
 (x,y){\tt\ zscaled\ }(a,b)     &=& (ax-by,\, bx+ay).
\end{eqnarray*}
âÏÌØÛÉÎÓÔ×Ï ÜÔÉÈ ÏÐÅÒÁÔÏÒÏ× ÏÂßÑÓÎÑÀÔ ÓÁÍÉ ÓÅÂÑ, ÚÁ ÉÓËÌÀÞÅÎÉÅÍ 
{\tt zscaled}, Ï ËÏÔÏÒÏÍ ÍÏÖÎÏ ÄÕÍÁÔØ ËÁË Ï ÐÒÏÉÚ×ÅÄÅÎÉÉ ËÏÍÐÌÅËÓÎÙÈ ÞÉÓÅÌ.
%%Most of these operations are self-explanatory except for {\tt zscaled}
%%which can be thought of as multiplication of complex numbers. 
üÆÆÅËÔ {\tt zscaled} $(a,b)$ --- ÜÔÏ ÐÏ×ÏÒÏÔ É ÍÁÓÛÔÁÂÉÒÏ×ÁÎÉÅ ÔÁË, ÞÔÏ 
$(1,0)$ ÐÅÒÅÈÏÄÉÔ × $(a,b)$. 
%%The
%%effect of {\tt zscaled} $(a,b)$ is to rotate and scale so as to map
%%$(1,0)$ into $(a,b)$. 
üÆÆÅËÔ ÏÔ {\tt rotated}~$\theta$ ×Ï ×ÒÁÝÅÎÉÉ ÎÁ $\theta$ ÇÒÁÄÕÓÏ× ÐÒÏÔÉ× 
ÞÁÓÏ×ÏÊ ÓÔÒÅÌËÉ. 
%%The effect of {\tt rotated}~$\theta$ is rotate
%%$\theta$ degrees counter-clockwise.

ìÀÂÁÑ ËÏÍÂÉÎÁÃÉÑ ÓÄ×ÉÇÏ×, ×ÒÁÝÅÎÉÊ, ÎÁËÌÏÎÏ× É Ô.~Ð. --- ÜÔÏ ÁÆÆÉÎÎÁÑ 
ÔÒÁÎÓÆÏÒÍÁÃÉÑ, ÓÏ×ÏËÕÐÎÙÊ ÜÆÆÅËÔ ËÏÔÏÒÏÊ × ÔÒÁÎÓÆÏÒÍÁÃÉÉ ÌÀÂÏÊ ÐÁÒÙ 
$(x,y)$ × 
$$ (t_x+t_{xx}x+t_{xy}y,\, t_y+t_{yx}x+t_{yy}y), $$
ÄÌÑ ÎÅËÏÔÏÒÏÊ ÛÅÓÔÅÒËÉ $(t_x,t_y,t_{xx},t_{xy},t_{yx},t_{yy})$. 
%%Any combination of shifting, rotating, slanting, etc.\ is an affine
%%transformation, the net effect of which is to transform any pair $(x,y)$
%%into
%%$$ (t_x+t_{xx}x+t_{xy}y,\, t_y+t_{yx}x+t_{yy}y), $$
%%for some sextuple $(t_x,t_y,t_{xx},t_{xy},t_{yx},t_{yy})$. 
ðÏÓÌÅÄÎÑÑ ÉÎÆÏÒÍÁÃÉÑ ÍÏÖÅÔ ÂÙÔØ ÓÏÈÒÁÎÅÎÁ × ÐÅÒÅÍÅÎÎÏÊ ÔÉÐÁ ÔÒÁÎÓÆÏÒÍÁÃÉÑ, 
ÔÁË ÞÔÏ {\tt
transformed T}\index{transformed?\texttt{transformed}}\label{Dtrfrmd}
ÍÏÖÅÔ ÂÙÔØ ÜË×É×ÁÌÅÎÔÎÏ 
$$ \hbox{\tt xscaled -1 rotated 90 shifted (1,1)}, $$
ÅÓÌÉ {\tt T} --- ÜÔÏ ÐÅÒÅÍÅÎÎÁÑ-ÔÒÁÎÓÆÏÒÍÁÃÉÑ. 
%%This
%%information can be stored in a variable of type transform so that {\tt
%%transformed T}\index{transformed?\texttt{transformed}}\label{Dtrfrmd}
%%might be equivalent to
%%$$ \hbox{\tt xscaled -1 rotated 90 shifted (1,1)} $$
%%if {\tt T} is an appropriate transform variable. 
ôÒÁÎÓÆÏÒÍÁÃÉÑ~{\tt T} ÍÏÇÌÁ ÂÙÔØ ÉÎÉÃÉÁÌÉÚÉÒÏ×ÁÎÁ ×ÙÒÁÖÅÎÉÅÍ ÔÉÐÁ 
ÔÒÁÎÓÆÏÒÍÁÃÉÑ, ÎÁÐÒÉÍÅÒ, 
%%The transform~{\tt T} could then be initialized with an
%%expression of type transform as follows:
$$ \begin{verbatim}
transform T;
T = identity xscaled -1 rotated 90 shifted (1,1);
\end{verbatim}
$$
üÔÏÔ ÐÒÉÍÅÒ ÐÏËÁÚÙ×ÁÅÔ, ÞÔÏ ×ÙÒÁÖÅÎÉÑ-ÔÒÁÎÓÆÏÒÍÁÃÉÉ ÍÏÇÕÔ ÓÔÒÏÉÔØÓÑ 
ÐÒÉÍÅÎÅÎÉÅÍ ÔÒÁÎÓÆÏÒÍÁÃÉÏÎÎÙÈ ÏÐÅÒÁÔÏÒÏ× Ë ÄÒÕÇÉÍ ÔÒÁÎÓÆÏÒÍÁÃÉÑÍ. 
%%As this example indicates, transform expressions can be built up by
%%applying transformation operators to other transforms. 
óÔÁÎÄÁÒÔÎÁÑ ÔÒÁÎÓÆÏÒÍÁÃÉÑ {\tt
identity}\index{identity?\texttt{identity}}\label{Dident} --- ÜÔÏ ÐÏÌÅÚÎÁÑ 
ÏÔÐÒÁ×ÎÁÑ ÔÏÞËÁ ÄÌÑ ÜÔÏÇÏ ÐÒÏÃÅÓÓÁ. 
%%The predefined transformation {\tt
%%identity}\index{identity?\texttt{identity}}\label{Dident} is a useful
%%starting point for this process. 
÷ÓÅ ÍÏÖÎÏ ÐÒÏÉÌÌÀÓÔÒÉÒÏ×ÁÔØ ÐÅÒÅ×ÏÄÏÍ ÕÒÁ×ÎÅÎÉÑ ×ÙÛÅ ÎÁ ÅÓÔÅÓÔ×ÅÎÎÙÊ ÑÚÙË: 
``{\tt T} ÓÌÅÄÕÅÔ ÂÙÔØ ÔÒÁÎÓÆÏÒÍÁÃÉÅÊ, ÔÁËÏÊ ÖÅ ËÁË {\tt identity}, ÚÁÔÅÍ 
ÍÁÓÛÔÁÂÉÒÏ×ÁÎÎÏÊ ÐÏ ËÏÏÒÄÉÎÁÔÁÍ $x$ × $-1$ ÒÁÚ, ×ÒÁÝÅÎÎÏÊ ÎÁ 
$90^\circ$ É ÓÄ×ÉÎÕÔÏÊ ÎÁ $(1,1)$.''
%%This can be illustrated by
%%paraphrasing the above equation for {\tt T} into English: ``{\tt T}
%%should be the transform obtained by doing whatever {\tt identity}
%%does. 
%%Then scaling $x$~coordinates by $-1$, rotating $45^\circ$, and
%%shifting by $(1,1)$.'' 
üÔÏ ÒÁÂÏÔÁÅÔ, ÐÏÔÏÍÕ ÞÔÏ {\tt identity} --- ÔÏÖÄÅÓÔ×ÅÎÎÁÑ ÔÒÁÎÓÆÏÒÍÁÃÉÑ, 
ËÏÔÏÒÁÑ ÎÉÞÅÇÏ ÎÅ ÄÅÌÁÅÔ, Ô.~Å. {\tt transformed identity} --- ÜÔÏ ÐÕÓÔÏÊ 
ÏÐÅÒÁÔÏÒ.
%%This works because {\tt identity} is the
%%identity transformation which does nothing; i.e., {\tt transformed
%%identity} is a no-op.

óÉÎÔÁËÓÉÓ ÄÌÑ ×ÙÒÁÖÅÎÉÊ-ÔÒÁÎÓÆÏÒÍÁÃÉÊ É ÏÐÅÒÁÔÏÒÏ× ÔÒÁÎÓÆÏÒÍÁÃÉÉ ÄÁÅÔÓÑ ÎÁ 
ÒÉÓ.~\ref{sytrans}.
%%The syntax for transform expressions and transformation operators is given in
%%Figure~\ref{sytrans}. 
ïÎ ×ËÌÀÞÁÅÔ Ä×Å ÄÏÐÏÌÎÉÔÅÌØÎÙÅ ×ÏÚÍÏÖÎÏÓÔÉ ÄÌÑ 
\tdescr{ÔÒÁÎÓÆÏÒÍÁÃÉÉ}:\index{reflectedabout?\texttt{reflectedabout}}
$$ \hbox{\tt reflectedabout(}p, q\hbox{\tt )} $$
ÏÔÒÁÖÁÅÔ ÏÔÎÏÓÉÔÅÌØÎÏ ÐÒÑÍÏÊ, ÏÐÒÅÄÅÌÑÅÍÏÊ ÔÏÞËÁÍÉ $p$ É $q$ 
É\index{rotatedaround?\texttt{rotatedaround}}
$$ \hbox{\tt rotatedaround(}p,\theta\hbox{\tt )} $$
×ÒÁÝÁÅÔ ÎÁ $\theta$ ÇÒÁÄÕÓÏ× ÐÒÏÔÉ× ÞÁÓÏ×ÏÊ ÓÔÒÅÌËÉ ×ÏËÒÕÇ ÔÏÞËÉ $p$. 
%%It includes two more options for
%%\tdescr{transformer}:\index{reflectedabout?\texttt{reflectedabout}}
%%$$ \hbox{\tt reflectedabout(}p, q\hbox{\tt )} $$
%%reflects about the line defined by points $p$ and $q$;
%%and\index{rotatedaround?\texttt{rotatedaround}}
%%$$ \hbox{\tt rotatedaround(}p,\theta\hbox{\tt )} $$
%%rotates $\theta$ degrees counter-clockwise around point $p$. 
îÁÐÒÉÍÅÒ, ÕÒÁ×ÎÅÎÉÅÍ ÄÌÑ ÉÎÉÃÉÁÌÉÚÁÃÉÉ ÔÒÁÎÓÆÏÒÍÁÃÉÉ~{\tt T} ÍÏÖÅÔ ÂÙÔØ 
$$ \hbox{\tt T = identity reflectedabout((2,0), (0,2))}. $$
%%For example,
%%the equation for initializing transform~{\tt T} could have been
%%$$ \hbox{\tt T = identity reflectedabout((2,0), (0,2))}. $$

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{×ÔÏÒÉÞÎÁÑ ÐÁÒÁ} \rightarrow
        \descr{×ÔÏÒÉÞÎÁÑ ÐÁÒÁ} \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ}$\\
%%$\tt \descr{pair secondary} \rightarrow
%%        \descr{pair secondary} \descr{transformer}$\\
$\tt \descr{ÐÕÔØ-×ÔÏÒÉÞÎÏÓÔØ} \rightarrow
        \descr{ÐÕÔØ-×ÔÏÒÉÞÎÏÓÔØ} \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ}$\\
%%$\tt \descr{path secondary} \rightarrow
%%        \descr{path secondary} \descr{transformer}$\\
$\tt \descr{ÒÉÓÕÎÏË-×ÔÏÒÉÞÎÏÓÔØ} \rightarrow
        \descr{ÒÉÓÕÎÏË-×ÔÏÒÉÞÎÏÓÔØ} \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ}$\\
%%$\tt \descr{picture secondary} \rightarrow
%%        \descr{picture secondary} \descr{transformer}$\\
$\tt \descr{ÐÅÒÏ-×ÔÏÒÉÞÎÏÓÔØ} \rightarrow
        \descr{ÐÅÒÏ-×ÔÏÒÉÞÎÏÓÔØ} \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ}$\\
%%$\tt \descr{pen secondary} \rightarrow
%%        \descr{pen secondary} \descr{transformer}$\\
$\tt \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ-×ÔÏÒÉÞÎÏÓÔØ} \rightarrow
        \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ-×ÔÏÒÉÞÎÏÓÔØ} \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ}$\\[6pt]
%%$\tt \descr{transform secondary} \rightarrow
%%        \descr{transform secondary} \descr{transformer}$\\[6pt]
$\tt \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ} \rightarrow rotated \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \descr{transformer} \rightarrow rotated \descr{numeric primary}$\\
$\tt \qquad \;|\; scaled \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; scaled \descr{numeric primary}$\\
$\tt \qquad \;|\; shifted \descr{ÐÅÒ×ÉÞÎÁÑ ÐÁÒÁ}$\\
%%$\tt \qquad \;|\; shifted \descr{pair primary}$\\
$\tt \qquad \;|\; slanted \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; slanted \descr{numeric primary}$\\
$\tt \qquad \;|\; transformed \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ-ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; transformed \descr{transform primary}$\\
$\tt \qquad \;|\; xscaled \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; xscaled \descr{numeric primary}$\\
$\tt \qquad \;|\; yscaled \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; yscaled \descr{numeric primary}$\\
$\tt \qquad \;|\; zscaled \descr{ÐÅÒ×ÉÞÎÁÑ ÐÁÒÁ}$\\
%%$\tt \qquad \;|\; zscaled \descr{pair primary}$\\
$\tt \qquad \;|\; reflectedabout\hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}
        \hbox{\tt ,}\descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; reflectedabout\hbox{\tt (}\descr{pair expression}
%%        \hbox{\tt ,}\descr{pair expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; rotatedaround\hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}
        \hbox{\tt ,}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt )}$
%%$\tt \qquad \;|\; rotatedaround\hbox{\tt (}\descr{pair expression}
%%        \hbox{\tt ,}\descr{numeric expression}\hbox{\tt )}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÄÌÑ ÔÒÁÎÓÆÏÒÍÁÃÉÊ É ÒÏÄÓÔ×ÅÎÎÙÈ ÏÐÅÒÁÔÏÒÏ×}
%%\caption{The syntax for transforms and related operators}
\label{sytrans}
\end{figure}

åÓÔØ ÅÝÅ ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ Ó ÏÄÎÉÍ ÁÒÇÕÍÅÎÔÏÍ {\tt
inverse}\index{inverse?\texttt{inverse}}\label{Dinv}, ÎÁÈÏÄÑÝÉÊ 
ÏÂÒÁÔÎÕÀ ÔÒÁÎÓÆÏÒÍÁÃÉÀ, ÏÔÍÅÎÑÀÝÕÀ ÜÆÆÅËÔ 
ÔÒÁÎÓÆÏÒÍÁÃÉÉ-ÁÒÇÕÍÅÎÔÁ.
%%There is also a unary operator {\tt
%%inverse}\index{inverse?\texttt{inverse}}\label{Dinv} that takes a
%%transform and finds another transform that undoes the effect of the
%%first transform. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÅÓÌÉ 
$$ p = q{\tt\ transformed\ }T, $$
ÔÏ 
$$ q = p{\tt\ transformed\ inverse\ }T. $$
%%Thus if
%%$$ p = q{\tt\ transformed\ }T $$
%%then
%%$$ q = p{\tt\ transformed\ inverse\ }T. $$

îÅÌØÚÑ ÂÒÁÔØ {\tt inverse} ÄÌÑ ÎÅÉÚ×ÅÓÔÎÏÊ 
ÔÒÁÎÓÆÏÒÍÁÃÉÉ\index{ÔÒÁÎÓÆÏÒÍÁÃÉÑ!ÎÅÉÚ×ÅÓÔÎÁÑ}, ÎÏ ÍÙ ÕÖÅ ×ÉÄÅÌÉ, ÞÔÏ  
ÍÏÖÎÏ 
$$ \hbox{\tt T = } \descr{×ÙÒÁÖÅÎÉÅ-ÔÒÁÎÓÆÏÒÍÁÃÉÑ}, $$ 
ËÏÇÄÁ {\tt T} ÅÝÅ ÎÅ ÉÍÅÅÔ ÚÎÁÞÅÎÉÑ.
%%It is not legal to take the {\tt inverse} of an
%%unknown transform\index{transformation!unknown} but we
%%have already seen that you can say
%%$$ \hbox{\tt T = } \descr{transform expression} $$
%%when {\tt T} has not been given a value yet. 
ôÁËÖÅ ×ÏÚÍÏÖÎÏ ÐÒÉÍÅÎÑÔØ ÎÅÉÚ×ÅÓÔÎÕÀ ÔÒÁÎÓÆÏÒÍÁÃÉÀ Ë ÉÚ×ÅÓÔÎÏÊ ÐÁÒÅ ÉÌÉ 
ÔÒÁÎÓÆÏÒÍÁÃÉÉ É ÉÓÐÏÌØÚÏ×ÁÔØ ÒÅÚÕÌØÔÁÔ × ÌÉÎÅÊÎÏÍ ÕÒÁ×ÎÅÎÉÉ.
%%It is also possible to
%%apply an unknown transform to a known pair or transform and use the
%%result in a linear equation. 
ôÒÉ ÔÁËÉÈ ÕÒÁ×ÎÅÎÉÑ ÄÏÓÔÁÔÏÞÎÙ ÄÌÑ ÏÐÒÅÄÅÌÅÎÉÑ ÔÒÁÎÓÆÏÒÍÁÃÉÉ.
%%Three such equations are sufficient to determine a transform. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÕÒÁ×ÎÅÎÉÑ 
%%Thus the equations
$$ \begin{verbatim}
(0,1) transformed T' = (3,4);
(1,1) transformed T' = (7,1);
(1,0) transformed T' = (4,-3);
\end{verbatim}
$$
ÐÏÚ×ÏÌÑÀÔ MetaPost ÏÐÒÅÄÅÌÉÔØ, ÞÔÏ ÔÒÁÎÓÆÏÒÍÁÃÉÑ {\tt T'} --- ÜÔÏ 
ËÏÍÂÉÎÁÃÉÑ ×ÒÁÝÅÎÉÑ É ÍÁÓÛÔÁÂÉÒÏ×ÁÎÉÑ Ó 
%%allow MetaPost to determine that the transform {\tt T'} is a combination of
%%rotation and scaling with
$$\openup\jot
  \tabskip=0pt plus 1fil
  \halign to\displaywidth{\tabskip=0pt
        \hfil$\displaystyle{#}$& $\displaystyle{{}#}$\hfil \qquad&
        \hfil$\displaystyle{#}$& $\displaystyle{{}#}$\hfil
        \tabskip=0pt plus 1fil\cr
\noalign{\vskip-\jot}
 t_{xx}&=4,&    t_{yx}&=-3,\cr
 t_{yx}&=3,&    t_{yy}&=4,\cr
 t_x&=0,&       t_y&=0.\cr}
$$

õÒÁ×ÎÅÎÉÑ Ó ÎÅÉÚ×ÅÓÔÎÙÍÉ ÔÒÁÎÓÆÏÒÍÁÃÉÑÍÉ ÒÁÓÓÍÁÔÒÉ×ÁÀÔÓÑ ËÁË ÌÉÎÅÊÎÙÅ 
ÕÒÁ×ÎÅÎÉÑ Ó ÛÅÓÔØÀ ÐÁÒÁÍÅÔÒÁÍÉ, ÏÐÒÅÄÅÌÑÀÝÉÍÉ ÔÒÁÎÓÆÏÒÍÁÃÉÀ.
%%Equations involving an unknown transform are treated as linear equations
%%in the six parameters that define the transform. 
üÔÉ ÛÅÓÔØ ÐÁÒÁÍÅÔÒÏ× ÍÏÇÕÔ ÔÁËÖÅ ÉÍÅÎÏ×ÁÔØÓÑ ÎÁÐÒÑÍÕÀ 
ËÁË\index{xpart?\texttt{xpart}}\index{ypart?\texttt{ypart}}\index{xxpart?\texttt{xxpart}}%
\index{xypart?\texttt{xypart}}\index{yxpart?\texttt{yxpart}}\index{yypart?\texttt{yypart}}\label{Dtrprt}
$$ {\tt xpart\ T},\ {\tt ypart\ T},\ {\tt xxpart\ T},\ {\tt xypart\ T},\
        {\tt yxpart\ T},\ {\tt yypart\ T},
$$
ÇÄÅ {\tt T} --- ÜÔÏ ÔÒÁÎÓÆÏÒÍÁÃÉÑ.
%%These six parameters can also be referred to directly
%%as\index{xpart?\texttt{xpart}}\index{ypart?\texttt{ypart}}\index{xxpart?\texttt{xxpart%%}}%
%%\index{xypart?\texttt{xypart}}\index{yxpart?\texttt{yxpart}}\index{yypart?\texttt{yypa%%rt}}\label{Dtrprt}
%%$$ {\tt xpart\ T},\ {\tt ypart\ T},\ {\tt xxpart\ T},\ {\tt xypart\ T},\
%%        {\tt yxpart\ T},\ {\tt yypart\ T},
%%$$
%%where {\tt T} is a transform. 
îÁÐÒÉÍÅÒ, ÒÉÓ.~\ref{fig27} ÉÓÐÏÌØÚÕÅÔ ÕÒÁ×ÎÅÎÉÑ 
$$ \hbox{\tt xxpart T=yypart T;  yxpart T=-xypart T} $$
ÄÌÑ ÕËÁÚÁÎÉÑ, ÞÔÏ {\tt T} ÓÏÈÒÁÎÑÅÔ ÆÏÒÍÕ, Ô.~Å. Ñ×ÌÑÅÔÓÑ ËÏÍÂÉÎÁÃÉÅÊ 
×ÒÁÝÅÎÉÑ, ÓÄ×ÉÇÁ É ÓÏÈÒÁÎÑÀÝÅÇÏ ÆÏÒÍÕ ÍÁÓÛÔÁÂÉÒÏ×ÁÎÉÑ.
%%For instance, Figure~\ref{fig27} uses the
%%equations
%%$$ \hbox{\tt xxpart T=yypart T;  yxpart T=-xypart T} $$
%%to specify that {\tt T} is shape preserving; i.e., it is a combination of
%%rotating, shifting, and uniform scaling.

\begin{figure}[htp]
$$\begin{verbatim}
beginfig(28);
path p[];
p1 = fullcircle scaled .6in;
z1=(.75in,0)=-z3;
z2=directionpoint left of p1=-z4;
p2 = z1..z2..{curl1}z3..z4..{curl 1}cycle;
fill p2 withcolor .4[white,black];
unfill p1;
draw p1;
transform T;
z1 transformed T = z2;
z3 transformed T = z4;
xxpart T=yypart T;  yxpart T=-xypart T;
picture pic;
pic = currentpicture;
for i=1 upto 2:
  pic:=pic transformed T;
  draw pic;
endfor
dotlabels.top(1,2,3); dotlabels.bot(4);
endfig;
\end{verbatim}
\quad \mathcenter{\includegraphics{manfig-ru-28}}
$$
\caption{ëÏÄ MetaPost É ``ÆÒÁËÔÁÌØÎÁÑ'' ËÁÒÔÉÎËÁ-ÒÅÚÕÌØÔÁÔ}
%%\caption{MetaPost code and the resulting ``fractal'' figure}
\label{fig27}
\end{figure}

\subsection{ðÕÎËÔÉÒÎÙÅ ÌÉÎÉÉ}
%%\subsection{Dashed Lines}

ñÚÙË MetaPost ÐÒÅÄÏÓÔÁ×ÌÑÅÔ ÍÎÏÇÏ ÓÐÏÓÏÂÏ× ÉÚÍÅÎÑÔØ ÌÉÎÉÉ ÐÏÍÉÍÏ ÐÒÏÓÔÏÇÏ 
ÉÚÍÅÎÅÎÉÑ ÉÈ ÔÏÌÝÉÎÙ.
%%The MetaPost language provides many ways of changing the appearance of a
%%line besides just changing its width. 
ïÄÉÎ ÔÁËÏÊ ÓÐÏÓÏÂ × ÉÓÐÏÌØÚÏ×ÁÎÉÉ ÐÕÎËÔÉÒÎÙÈ ÌÉÎÉÊ, ËÁË ÓÄÅÌÁÎÏ ÎÁ 
ÒÉÓÕÎËÁÈ \ref{fig4} É~\ref{fig22}. 
%%One way is to use dashed lines as
%%was done in Figures \ref{fig4} and~\ref{fig22}. 
óÉÎÔÁËÓÉÓ ÄÌÑ ÜÔÏÇÏ\index{dashed?\texttt{dashed}}\label{Ddashed} --- 
$$ {\tt draw}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\, {\tt dashed}\, \descr{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ}, $$
ÇÄÅ \tdescr{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ}\index{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ?\tdescr{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ}} 
--- ÜÔÏ × ÄÅÊÓÔ×ÉÔÅÌØÎÏÓÔÉ ÓÐÅÃÉÁÌØÎÙÊ ÔÉÐ \tdescr{×ÙÒÁÖÅÎÉÑ-ËÁÒÔÉÎËÉ}.
%%The syntax for this
%%is\index{dashed?\texttt{dashed}}
%%$$ {\tt draw}\, \descr{path expression}\, {\tt dashed}\, \descr{dash pattern} $$
%%where a \tdescr{dash pattern}\index{dash pattern?\tdescr{dash pattern}}
%%is really a special type of \tdescr{picture expression}. 
åÓÔØ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ \tdescr{ÏÂÒÁÚÅà ÐÕÎËÔÉÒÁ}, ÎÁÚÙ×ÁÅÍÙÊ {\tt
evenly}\index{evenly?\texttt{evenly}}\label{Devenly}, ÄÅÌÁÀÝÉÊ 
ÔÉÒÅ ÄÌÉÎÏÊ 3 PostScript ÐÕÎËÔÁ, ÒÁÚÄÅÌÅÎÎÙÅ ÐÒÏÍÅÖÕÔËÁÍÉ ÔÁËÏÇÏ ÖÅ 
ÒÁÚÍÅÒÁ.
%%There is a predefined \tdescr{dash pattern} called {\tt
%%evenly}\index{evenly?\texttt{evenly}}\label{Devenly} that makes dashes 3
%%PostScript points long separated by gaps of the same size. 
äÒÕÇÏÊ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÏÂÒÁÚÅÃ, {\tt
withdots}\index{withdots?\texttt{withdots}}\label{Dwdots}, ÐÒÏÉÚ×ÏÄÉÔ 
ÔÏÞÅÞÎÕÀ ÌÉÎÉÀ Ó ÔÏÞËÏÊ ÎÁ ËÁÖÄÙÅ 5 PostScript ÐÕÎËÔÏ×.\footnote{{\tt
withdots} ÅÓÔØ ÔÏÌØËÏ × MetaPost ×ÅÒÓÉÉ 0.50 É ÎÏ×ÅÅ.} 
%%Another predefined dash pattern {\tt
%%withdots}\index{withdots?\texttt{withdots}}\label{Dwdots} produces
%%dotted lines with dots 5 PostScript points apart.\footnote{{\tt
%%withdots} is only found in MetaPost version 0.50 and higher.} 
äÌÑ ÂÏÌÅÅ ÒÁÚÒÑÖÅÎÎÙÈ ÔÏÞÅË É ÒÁÚÒÑÖÅÎÎÙÈ É ÕÄÌÉÎÅÎÎÙÈ ÔÉÒÅ 
\tdescr{ÏÂÒÁÚÅà ÐÕÎËÔÉÒÁ} ÍÏÖÅÔ ÂÙÔØ ÍÁÓÛÔÁÂÉÒÏ×ÁÎ\index{scaled?\texttt{scaled}} 
ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig28}.
%%For dots
%%further apart or longer dashes further apart, the \tdescr{dash pattern}
%%can be scaled\index{scaled?\texttt{scaled}} as shown in
%%Figure~\ref{fig28}.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-29} $$
\caption[ðÕÎËÔÉÒÎÙÅ ÌÉÎÉÉ É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÅ ÏÂÒÁÚÃÙ ÐÕÎËÔÉÒÁ]
        {ðÕÎËÔÉÒÎÙÅ ÌÉÎÉÉ, ÐÏÍÅÞÅÎÎÙÅ \tdescr{ÏÂÒÁÚÃÏÍ ÐÕÎËÔÉÒÁ}, ÉÓÐÏÌØÚÕÅÍÙÍ 
        ÄÌÑ ÉÈ ÓÏÚÄÁÎÉÑ.}
%%\caption[Dashed lines and the corresponding dash patters]
%%        {Dashed lines each labeled with the \tdescr{dash pattern} used to create
%%        it.}
\label{fig28}
\end{figure}

äÒÕÇÏÊ ÓÐÏÓÏÂ ÉÚÍÅÎÉÔØ ÏÂÒÁÚÅÃ ÌÉÎÉÉ × ÉÚÍÅÎÅÎÉÉ ÅÇÏ ÆÁÚÙ ÇÏÒÉÚÏÎÔÁÌØÎÙÍ 
ÓÄ×ÉÇÏÍ. 
%%Another way to change a dash pattern is to alter its phase by shifting
%%it horizontally. 
óÄ×ÉÇ ×ÐÒÁ×Ï Ä×ÉÇÁÅÔ ÏÂÒÁÚÅà ×ÐÅÒÅÄ ×ÄÏÌØ ÐÕÔÉ, Á ÓÄ×ÉÇ ×ÐÒÁ×Ï --- ÎÁÚÁÄ.
%%Shifting to the right makes the dashes move forward
%%along the path and shifting to the left moves them backward.
òÉÓ.~\ref{fig29} ÉÌÌÀÓÔÒÉÒÕÅÔ ÜÔÏÔ ÜÆÆÅËÔ.
%%Figure~\ref{fig29} illustrates this effect. 
ïÂÒÁÚÅà ÐÕÎËÔÉÒÁ ÍÏÖÎÏ ÐÒÅÄÓÔÁ×ÌÑÔØ ËÁË ÂÅÓËÏÎÅÞÎÏ ÐÏ×ÔÏÒÑÀÝÉÊÓÑ ÏÂÒÁÚÅÃ, 
ÒÁÓÐÒÅÄÅÌÅÎÎÙÊ ×ÄÏÌØ ÇÏÒÉÚÏÎÔÁÌØÎÏÊ ÌÉÎÉÉ, ÇÄÅ ÕÞÁÓÔÏË ÌÉÎÉÉ ÓÐÒÁ×Á ÏÔ 
ÏÓÉ $y$ ÒÁÚÍÅÝÁÅÔÓÑ ÎÁ ÐÕÔÉ, ÇÄÅ ÎÕÖÎÙ 
ÒÁÚÒÙ×Ù\index{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ?\tdescr{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ}}.
%%The dash pattern can be
%%thought of as an infinitely repeating pattern strung out along a
%%horizontal line where the portion of the line to the right of the
%%$y$~axis is laid out along the path to be dashed\index{dash
%%pattern?\tdescr{dash pattern}}.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-30} $$
\caption[ðÕÎËÔÉÒÎÙÅ ÌÉÎÉÉ É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÅ ÏÂÒÁÚÃÙ ÐÕÎËÔÉÒÁ]
        {ðÕÎËÔÉÒÎÙÅ ÌÉÎÉÉ É ËÏÍÁÎÄÙ MetaPost ÄÌÑ ÉÈ ÒÉÓÏ×ÁÎÉÑ, ÇÄÅ {\tt e4}
        ÓÓÙÌÁÅÔÓÑ ÎÁ ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ {\tt evenly scaled 4}.}
%%\caption[Dashed lines and the corresponding dash patters]
%%        {Dashed lines and the MetaPost statements for drawing them where {\tt e4}
%%        refers to the dash pattern {\tt evenly scaled 4}.}
\label{fig29}
\end{figure}

ëÏÇÄÁ ×Ù ÓÄ×ÉÇÁÅÔÅ ÏÂÒÁÚÅà ÐÕÎËÔÉÒÁ, ÔÁË ÞÔÏ ÏÓØ $y$ ÐÅÒÅÓÅËÁÅÔ ÓÅÒÅÄÉÎÕ, 
ÐÅÒ×ÏÅ ÔÉÒÅ ÕÒÅÚÁÅÔÓÑ. 
%%When you shift a dash pattern so that the $y$~axis crosses the middle of
%%a dash, the first dash gets truncated. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÌÉÎÉÑ Ó ÏÂÒÁÚÃÁÍÉ ÐÕÎËÔÉÒÁ {\tt e4} ÎÁÞÉÎÁÅÔÓÑ Ó ÔÉÒÅ ÄÌÉÎÏÊ 
12bp, ÚÁ ËÏÔÏÒÙÍ ÉÄÅÔ ÒÁÚÒÙ× 12bp, ÚÁ ËÏÔÏÒÙÍ --- ÄÒÕÇÏÅ 12bp ÔÉÒÅ É Ô.~Ä.;
{\tt e4 shifted (-6bp,0)} ÐÒÏÉÚ×ÏÄÉÔ 6bp ÔÉÒÅ, 12 bp ÐÒÏÍÅÖÕÔÏË, ÚÁÔÅÍ 12bp 
ÔÉÒÅ É Ô.~Ä. 
%%Thus the line with dash pattern
%%{\tt e4} starts with a dash of length 12bp followed by a 12bp gap and
%%another 12bp dash, etc., while {\tt e4 shifted (-6bp,0)} produces a 6bp
%%dash, a 12 bp gap, then a 12bp dash, etc. 
üÔÏÔ ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ ÍÏÖÅÔ ÂÙÔØ ÕËÁÚÁÎ ÂÏÌÅÅ ÐÒÑÍÏ ÞÅÒÅÚ ÆÕÎËÃÉÀ 
{\tt dashpattern}\index{dash
pattern?\texttt{dashpattern}}\label{Ddshpat}: 
$$ \hbox{\tt dashpattern(on 6bp  off 12bp  on 6bp)} $$
%%This dash pattern could be
%%specified more directly via the {\tt dashpattern}\index{dash
%%pattern?\texttt{dash pattern}}\label{Ddshpat} function:
%%$$ \hbox{\tt dashpattern(on 6bp  off 12bp  on 6bp)} $$
ðÒÉÍÅÒ ÏÚÎÁÞÁÅÔ ``ÎÁÒÉÓÕÊ ÐÅÒ×ÙÅ 6bp ÌÉÎÉÉ, ÚÁÔÅÍ ÐÒÏÐÕÓÔÉ ÓÌÅÄÕÀÝÉÅ 12bp, 
ÚÁÔÅÍ ÒÉÓÕÊ 6bp É ÐÏ×ÔÏÒÑÊ''.
%%This means ``draw the first 6bp of the line, then skip the next 12bp, then draw
%%another 6bp and repeat.'' 
åÓÌÉ ÜÔÁ ÌÉÎÉÑ Ó ÒÁÚÒÙ×ÁÍÉ ÉÍÅÅÔ ÄÌÉÎÕ ÂÏÌÅÅ 30bp, ÔÏ ÐÏÓÌÅÄÎÉÅ 6bp ÐÅÒ×ÏÊ ËÏÐÉÉ 
ÏÂÒÁÚÃÁ ÌÉÎÉÉ ÂÕÄÕÔ ÓÏÅÄÉÎÑÔØÓÑ Ó ÐÅÒ×ÙÍÉ 6bp ÓÌÅÄÕÀÝÅÊ ËÏÐÉÉ ÄÌÑ ÆÏÒÍÉÒÏ×ÁÎÉÑ 
ÔÉÒÅ ÄÌÉÎÏÊ 12bp.
%%If the line to be dashed is more than 30bp long, the
%%last 6bp of the first copy of the dash pattern will merge with the first 6bp of
%%the next copy to form a dash 12bp long. 
ïÂÝÉÊ ÓÉÎÔÁËÓÉÓ ÄÌÑ ÆÕÎËÃÉÉ {\tt dashpattern} ÐÏËÁÚÁÎ ÎÁ ÒÉÓ.~\ref{sydash}.
%%The general syntax for the
%%{\tt dashpattern} function is shown in Figure~\ref{sydash}.

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ} \rightarrow dashpattern
        \hbox{\tt (}\descr{ÓÐÉÓÏË ÅÓÔØ/ÎÅÔ}\hbox{\tt )}$\\
%%$\tt \descr{dash pattern} \rightarrow dashpattern
%%        \hbox{\tt (}\descr{on/off list}\hbox{\tt )}$\\
$\tt \descr{ÓÐÉÓÏË ÅÓÔØ/ÎÅÔ} \rightarrow
        \descr{ÓÐÉÓÏË ÅÓÔØ/ÎÅÔ}\descr{ÐÕÎËÔ ÅÓÔØ/ÎÅÔ} \;|\; \descr{ÐÕÎËÔ ÅÓÔØ/ÎÅÔ}$\\
%%$\tt \descr{on/off list} \rightarrow
%%        \descr{on/off list}\descr{on/off clause} \;|\; \descr{on/off clause}$\\
$\tt \descr{ÐÕÎËÔ ÅÓÔØ/ÎÅÔ} \rightarrow on \descr{ÞÉÓÌÏ×ÁÑ ÔÒÅÔÉÞÎÏÓÔØ}
        \;|\; off \descr{ÞÉÓÌÏ×ÁÑ ÔÒÅÔÉÞÎÏÓÔØ}$
%%$\tt \descr{on/off clause} \rightarrow on \descr{numeric tertiary}
%%        \;|\; off \descr{numeric tertiary}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÆÕÎËÃÉÉ {\tt dashpattern}}
%%\caption{The syntax for the {\tt dashpattern} function}
\label{sydash}
\end{figure}

éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÏÂÒÁÚÅà ÐÕÎËÔÉÒÁ × ÄÅÊÓÔ×ÉÔÅÌØÎÏÓÔÉ Ñ×ÌÑÅÔÓÑ ÏÓÏÂÙÍ ÔÉÐÏÍ 
ÒÉÓÕÎËÁ, ÆÕÎËÃÉÑ {\tt dashpattern} ×ÏÚ×ÒÁÝÁÅÔ ÒÉÓÕÎÏË.
%%Since a dash pattern is really just a special kind of picture, the {\tt
%%dashpattern} function returns a picture. 
îÅÔ ÎÅÏÂÈÏÄÉÍÏÓÔÉ ÚÎÁÔØ ÓÔÒÕËÔÕÒÕ ÔÁËÏÇÏ ÒÉÓÕÎËÁ, ÐÏÜÔÏÍÕ ÓÌÕÞÁÊÎÙÊ 
ÞÉÔÁÔÅÌØ ÂÕÄÅÔ ×ÅÒÏÑÔÎÏ ÈÏÔÅÔØ ÐÅÒÅÊÔÉ Ë ÒÁÚÄÅÌÕ~\ref{oopt}. 
%%It is not really necessary to
%%know the structure of such a picture, so the casual reader will probably
%%want to skip on to Section~\ref{oopt}. 
äÌÑ ÔÅÈ, ËÔÏ ÈÏÞÅÔ ÚÎÁÔØ, ÍÁÌÅÎØËÉÊ ÜËÓÐÅÒÉÍÅÎÔ ÐÏËÁÚÙ×ÁÅÔ, ÞÔÏ ÅÓÌÉ 
{\tt d} --- ÜÔÏ 
$$ \hbox{\tt dashpattern(on 6bp  off 12bp  on 6bp)}, $$
ÔÏ {\tt llcorner d} --- ÜÔÏ $(0,24)$ É {\tt urcorner d} --- $(24,24)$.
%%For those who want to know, a
%%little experimentation shows that if {\tt d} is
%%$$ \hbox{\tt dashpattern(on 6bp  off 12bp  on 6bp)}, $$
%%then {\tt llcorner d} is $(0,24)$ and {\tt urcorner d} is $(24,24)$.
ðÒÑÍÏÅ ÉÚÏÂÒÁÖÅÎÉÅ {\tt d} ÂÅÚ ÉÓÐÏÌØÚÏ×ÁÎÉÑ ÅÇÏ ËÁË ÏÂÒÁÚÃÁ 
ÐÒÏÉÚ×ÅÄÅÔ Ä×Á ÔÏÎËÉÈ ÇÏÒÉÚÏÎÔÁÌØÎÙÈ ÏÔÒÅÚËÁ ÐÒÑÍÏÊ, ÐÏÄÏÂÎÙÅ ÔÁËÉÍ:
%%Drawing {\tt d} directly without using it as a dash pattern produces two
%%thin horizontal line segments like this:
$$ \includegraphics{manfig-ru-31} $$
ìÉÎÉÉ × ÜÔÏÍ ÐÒÉÍÅÒÅ ÏÐÉÓÙ×ÁÌÉÓØ, ËÁË ÉÍÅÀÝÉÅ ÔÏÌÝÉÎÕ ÎÏÌØ, ÎÏ ÜÔÏ ÎÅ ÉÍÅÅÔ 
ÚÎÁÞÅÎÉÑ, ÐÏÔÏÍÕ ÞÔÏ ÔÏÌÝÉÎÁ ÌÉÎÉÉ ÉÇÎÏÒÉÒÕÅÔÓÑ, ËÏÇÄÁ ÒÉÓÕÎÏË ÉÓÐÏÌØÚÕÅÔÓÑ 
ËÁË ÏÂÒÁÚÅÃ ÌÉÎÉÉ.
%%The lines in this example are specified as having width zero, but this
%%does not matter because the line width is ignored when a picture is used
%%as a dash pattern.

ïÂÝÅÅ ÐÒÁ×ÉÌÏ ÉÎÔÅÒÐÒÅÔÁÃÉÉ ÒÉÓÕÎËÁ {\tt d}, ËÁË ÏÂÒÁÚÃÁ ÌÉÎÉÉ, × ÔÏÍ, 
ÞÔÏ ÏÔÒÅÚËÉ × {\tt d} ÐÒÏÅËÔÉÒÕÀÔÓÑ ÎÁ ÏÓØ $x$ É ÉÔÏÇÏ×ÙÊ ÏÂÒÁÚÅà 
ÐÏ×ÔÏÒÑÅÔÓÑ ÂÅÓËÏÎÅÞÎÏ × ÏÂÏÉÈ ÎÁÐÒÁ×ÌÅÎÉÑÈ ÐÏÍÅÝÅÎÉÅÍ ×ÐÌÏÔÎÕÀ ËÏÐÉÊ 
ÏÂÒÁÚÃÁ.
%%The general rule for interpreting a picture {\tt d} as a dash pattern is
%%that the line segments in {\tt d} are projected onto the $x$-axis and
%%the resulting pattern is replicated to infinity in both directions by
%%placing copies of the pattern end-to-end. 
îÁÓÔÏÑÝÉÅ ÄÌÉÎÙ ÐÏÌÕÞÁÀÔÓÑ, ÎÁÞÉÎÁÑ Ó $x=0$, Ä×ÉÖÅÎÉÅÍ × ÐÏÌÏÖÉÔÅÌØÎÏÍ 
ÎÁÐÒÁ×ÌÅÎÉÉ $x$.
%%The actual dash lengths are
%%obtained by starting at $x=0$ and scanning in the positive $x$
%%direction.

þÔÏÂÙ ÓÄÅÌÁÔØ ÉÄÅÀ ``ÐÏ×ÔÏÒÑÔØ ÂÅÓËÏÎÅÞÎÏ'' ÂÏÌÅÅ ÔÏÞÎÏÊ, ÕÓÔÁÎÏ×ÉÍ 
$P({\tt d})$ ÐÒÏÅËÃÉÅÊ {\tt d} ÎÁ ÏÓØ $x$ É ÐÕÓÔØ 
${\rm shift}(P({\tt d}),x)$ --- ÜÔÏ ÒÅÚÕÌØÔÁÔ ÓÄ×ÉÇÁ {\tt d} ÎÁ~$x$.
%%To make the idea of ``replicating to infinity'' more precise, let $P({\tt d})$
%%be the projection of {\tt d} onto the $x$~axis, and let
%%${\rm shift}(P({\tt d}),x)$ be the result of shifting {\tt d} by~$x$.
ïÂÒÁÚÅÃ, ÐÏÌÕÞÁÀÝÉÊÓÑ × ÒÅÚÕÌØÔÁÔÅ ÂÅÓËÏÎÅÞÎÏÇÏ ÐÏ×ÔÏÒÅÎÉÑ, --- ÜÔÏ 
$$ \bigcup_{\hbox{\scriptsize ÃÅÌÙÅ}\ n} {\rm shift}(P(d),\, n\cdot\ell(d)), $$
ÇÄÅ $\ell(d)$ ÉÚÍÅÒÑÅÔ ÄÌÉÎÕ $P(d)$. 
%%The pattern resulting from infinite replication is
%%$$ \bigcup_{{\rm integers}\ n} {\rm shift}(P(d),\, n\cdot\ell(d)), $$
%%where $\ell(d)$ measures the length of $P(d)$. 
îÁÉÂÏÌÅÅ ÏÇÒÁÎÉÞÉ×ÁÀÝÅÅ ÏÐÒÅÄÅÌÅÎÉÅ ÜÔÏÊ ÄÌÉÎÙ ÒÁ×ÎÏ  
$d_{\rm max}-d_{\rm min}$, ÇÄÅ $[d_{\rm min},d_{\rm max}]$
--- ÜÔÏ ÄÉÁÐÁÚÏÎ ËÏÏÒÄÉÎÁÔ $x$ × $P(d)$. 
%%The most restrictive possible
%%definition of this length is $d_{\rm max}-d_{\rm min}$,
%%where $[d_{\rm min},d_{\rm max}]$
%%is the range of $x$~coordinates in $P(d)$. 
æÁËÔÉÞÅÓËÉ MetaPost ÉÓÐÏÌØÚÕÅÔ 
$$ \max(\left|y_0({\tt d})\right|,\, d_{\rm max}-d_{\rm min}), $$
ÇÄÅ $y_0({\tt d})$ --- ÜÔÏ ËÏÏÒÄÉÎÁÔÁ $y$ ÓÏÄÅÒÖÉÍÏÇÏ {\tt d}.
%%In fact, MetaPost uses
%%$$ \max(\left|y_0({\tt d})\right|,\, d_{\rm max}-d_{\rm min}), $$
%%where $y_0({\tt d})$ is the $y$ coordinate of the contents of {\tt d}.
óÏÄÅÒÖÉÍÏÅ {\tt d} ÄÏÌÖÎÏ ÎÁÈÏÄÉÔØÓÑ ÎÁ ÇÏÒÉÚÏÎÔÁÌØÎÏÊ ÌÉÎÉÉ, ÎÏ ÅÓÌÉ 
ÜÔÏ ÎÅ ÔÁË, ÔÏ ÉÎÔÅÒÐÒÅÔÁÔÏÒ MetaPost ÐÒÏÓÔÏ ×ÏÚØÍÅÔ ËÏÏÒÄÉÎÁÔÕ $y$ ×ÎÕÔÒÉ 
{\tt d}\index{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ?\tdescr{ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ}}.
%%The contents of {\tt d} should lie on a horizontal line, but if they do
%%not, the MetaPost interpreter just picks a $y$~coordinate that occurs in
%%{\tt d}\index{dash pattern?\tdescr{dash pattern}}.

ëÁÒÔÉÎËÁ Ó ÏÂÒÁÚÃÏÍ ÐÕÎËÔÉÒÁ ÎÅ ÄÏÌÖÎÁ ÓÏÄÅÒÖÁÔØ ÔÅËÓÔÁ ÉÌÉ ÚÁÐÏÌÎÅÎÎÙÈ 
ÏÂÌÁÓÔÅÊ, ÎÏ ÏÎÁ ÍÏÖÅÔ ÓÏÄÅÒÖÁÔØ ÌÉÎÉÉ, ËÏÔÏÒÙÅ ÐÕÎËÔÉÒÎÙÅ.
%%A picture used as a dashed pattern must contain no text or filled
%%regions, but it can contain lines that are themselves dashed. 
üÔÏ ÄÁÅÔ ÍÁÌÅÎØËÉÅ É ÂÏÌØÛÉÅ ÒÁÚÒÙ×Ù ËÁË ÐÏËÁÚÁÎÏ ÎÁ 
ÒÉÓ.~\ref{fig32}.\index{ÏÂÒÁÚÅà ÐÕÎËÔÉÒÁ?\tdescr{ÏÂÒÁÚÅà ÐÕÎËÔÉÒÁ}!ÒÅËÕÒÓÉ×ÎÙÊ}
%%This can give small dashes inside of larger dashes as shown in
%%Figure~\ref{fig32}.\index{dash pattern?\tdescr{dash pattern}!recursive}

\begin{figure}[htp]
$$\begin{verbatim}
beginfig(32);
draw dashpattern(on 15bp off 15bp) dashed evenly;
picture p;
p=currentpicture;
currentpicture:=nullpicture;
draw fullcircle scaled 1cm xscaled 3 dashed p;
endfig;
\end{verbatim}
\quad \mathcenter{\includegraphics{manfig-ru-32}}
$$
\caption{ëÏÄ MetaPost ÄÌÑ ÏÂÒÁÚÃÁ ÐÕÎËÔÉÒÁ É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ×Ù×ÏÄ}
%%\caption{MetaPost code for dashed patterns and the corresponding output}
\label{fig32}
\end{figure}

\label{dashed-pens}
ïÂÒÁÚÃÙ ÐÕÎËÔÉÒÁ ÔÁËÖÅ ÐÒÅÄÎÁÚÎÁÞÅÎÙ ÄÌÑ ÉÓÐÏÌØÚÏ×ÁÎÉÑ Ó {\tt
pencircle} ÉÌÉ Ó ÏÔÓÕÔÓÔ×ÉÅÍ ÐÅÒÁ; {\tt pensquare} É ÄÒÕÇÉÈ ÓÌÏÖÎÙÈ 
ÐÅÒØÅ× ÓÌÅÄÕÅÔ ÉÚÂÅÇÁÔØ. 
%%Also, dashed patterns are intended to be used either with {\tt
%%pencircle} or no pen at all; {\tt pensquare} and other complex pens
%%should be avoided. 
ðÏÓÌÅÄÎÅÅ ÏÂÕÓÌÏ×ÌÅÎÏ ÔÅÍ, ÞÔÏ ×Ù×ÏÄ ÉÓÐÏÌØÚÕÅÔ ÐÒÉÍÉÔÉ× PostScript
{\tt setdash}, ËÏÔÏÒÙÊ ÎÅ ÏÞÅÎØ ÈÏÒÏÛÏ ×ÚÁÉÍÏÄÅÊÓÔ×ÕÅÔ Ó ÚÁÐÏÌÎÅÎÎÙÍÉ 
ÐÕÔÑÍÉ, ÓÏÚÄÁÎÎÙÍÉ ÍÎÏÇÏÕÇÏÌØÎÙÍÉ ÐÅÒØÑÍÉ. 
%%This is because the output uses the PostScript
%%primitive {\tt setdash}, which does not interact well with the filled
%%paths created by polygonal pens. 
óÍ. ÒÁÚÄÅÌ~\ref{sec.pens}, ÓÔÒ.~\pageref{sec.pens}.
%%See Section~\ref{sec.pens}, p.\ \pageref{sec.pens}.

%\newpage

\subsection{÷ËÌÀÞÅÎÉÅ PostScript}
%%\subsection{Local specials}

åÓÌÉ ×Ù ÈÏÔÉÔÅ ÄÏÂÁ×ÉÔØ ËÏÄ PostScript Ë Ó×ÏÉÍ ÏÂßÅËÔÁÍ, ÔÏ 
×Ù ÍÏÖÅÔÅ ÉÓÐÏÌØÚÏ×ÁÔØ 
$$
{\tt withprescript} \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}%
\index{withprescript?\texttt{withprescript}}\label{Dwithpre}
$$
É 
$$ 
{\tt withpostcript} \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}%
\index{withpostscript?\texttt{withpostscript}}\label{Dwithpost}
$$
%%If you want to attach a special bit of PostScript code, you can use 
%%$$
%%{\tt withprescript} \descr{string expression}
%%$$\index{withprescript?\texttt{withprescript}}\label{Dwithpre}%
%%and 
%%$$ 
%%{\tt withpostcript} \descr{string expression}
%%$$\index{withpostscript?\texttt{withpostscript}}\label{Dwithpost}%
óÔÒÏËÉ-ÒÅÚÕÌØÔÁÔÙ ÂÕÄÕÔ ÚÁÐÉÓÁÎÙ × ÆÁÊÌ ×Ù×ÏÄÁ ÓÏÏÔ×ÅÔÓÔ×ÅÎÎÏ ÐÅÒÅÄ ÉÌÉ 
ÐÏÓÌÅ ÔÅËÕÝÅÇÏ ÏÂßÅËÔÁ, ÎÁÞÉÎÁÑÓØ Ó ÎÏ×ÏÊ ÓÔÒÏËÉ ËÁÖÄÁÑ.
%%The strings will be written to the output file before and after the
%%current object, each beginning on their own line. 
ïÐÃÉÉ {\tt withprescript} ÉÌÉ {\tt withpostscript} ÍÏÖÎÏ ÕËÁÚÙ×ÁÔØ 
ÍÎÏÇÏËÒÁÔÎÏ.
%%You can specify
%%multiple {\tt withprescript} or {\tt withpostscript} options if you
%%like.

ëÏÇÄÁ ×Ù ÕËÁÚÙ×ÁÅÔÅ ÂÏÌÅÅ ÏÄÎÏÊ ÏÐÃÉÉ {\tt withprescript} ÉÌÉ {\tt 
withpostscript}, ÂÕÄØÔÅ ×ÎÉÍÁÔÅÌØÎÙ Ó ÆÁËÔÏÍ ÔÏÇÏ, ÞÔÏ ÜÔÉ ÓËÒÉÐÔÙ ÉÓÐÏÌØÚÕÀÔ 
×ÌÏÖÅÎÎÏÓÔØ: ÐÕÎËÔÙ {\tt withprescript} ÚÁÐÉÓÙ×ÁÀÔÓÑ × PostScript-ÆÁÊÌ 
ËÁË × ÓÔÅË, Á ÐÕÎËÔÙ {\tt withpostscript} ÚÁÐÉÓÙ×ÁÀÔÓÑ ËÁË × ÏÞÅÒÅÄØ.
%%When you specify more than one {\tt withprescript} or more than one {\tt
%%  withpostscript} option, be wary of the fact that the scripts use a
%%form of nesting: the {\tt withprescript} items are written to the
%%PostScript file in last in, first out order; whereas the {\tt
%%  withpostscript} items are written in first in, first out order.

\subsection{äÒÕÇÉÅ ÏÐÃÉÉ}
%%\subsection{Other Options}
\label{oopt}

÷Ù ÍÏÇÌÉ ÚÁÍÅÔÉÔØ, ÞÔÏ ÐÕÎËÔÉÒÎÙÅ ÌÉÎÉÉ, ÐÒÏÉÚ×ÏÄÉÍÙÅ 
{\tt dashed evenly}\index{evenly?\texttt{evenly}}, ÓÏÄÅÒÖÁÔ 
ÂÏÌØÛÅ ÞÅÒÎÏÇÏ, ÞÅÍ ÂÅÌÏÇÏ.
%%You might have noticed that the dashed lines produced by {\tt dashed
%%evenly}\index{evenly?\texttt{evenly}} appear to have more black than
%%white. 
üÔÏ ÉÚ-ÚÁ ÜÆÆÅËÔÁ ÐÁÒÁÍÅÔÒÁ {\tt
linecap}\index{linecap?\texttt{linecap}}\label{Dlinecap}, ËÏÔÏÒÙÊ 
ÕÐÒÁ×ÌÑÅÔ ÐÏÑ×ÌÅÎÉÅÍ ËÏÎÃÏ× ÌÉÎÉÊ É ËÏÎÃÏ× ÏÔÒÅÚËÏ×-ÔÉÒÅ.
%%This is an effect of the {\tt
%%linecap}\index{linecap?\texttt{linecap}}\label{Dlinecap} parameter that
%%controls the appearance of the ends of lines as well as the ends of
%%dashes. 
åÓÔØ ÔÁËÖÅ É ÄÒÕÇÉÅ ÓÐÏÓÏÂÙ ×ÌÉÑÔØ ÎÁ ÐÏÑ×ÌÅÎÉÅ ÔÏÇÏ, ÞÔÏ ÒÉÓÕÅÔÓÑ 
MetaPost.
%%There are also a number of other ways to affect the appearance
%%of things drawn with MetaPost.

ðÁÒÁÍÅÔÒ {\tt linecap} ÉÍÅÅÔ ÔÒÉ ÒÁÚÌÉÞÎÙÈ ÕÓÔÁÎÏ×ËÉ --- ÔÏÞÎÏ ÔÁËÉÅ ÖÅ, 
ËÁË É × PostScript.
%%The {\tt linecap} parameter has three different settings just as in
%%PostScript. 
Plain MetaPost ÄÁÅÔ ÜÔÏÊ ×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ\index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} ÔÉÐÏ×ÏÅ ÚÎÁÞÅÎÉÅ {\tt
rounded}\index{rounded?\texttt{rounded}}, ÞÔÏ ÏÚÎÁÞÁÅÔ ÒÉÓÏ×ÁÔØ 
ÏÔÒÅÚËÉ Ó ÚÁËÒÕÇÌÅÎÎÙÍÉ ËÏÎÃÁÍÉ, ÐÏÄÏÂÎÏ ÏÔÒÅÚËÕ ÏÔ 
{\tt z0} ÄÏ {\tt z3} ÎÁ ÒÉÓ.~\ref{fig33}. 
%%Plain MetaPost gives this internal variable\index{internal
%%variables}\index{variables!internal} the default value {\tt
%%rounded}\index{rounded?\texttt{rounded}} which causes line segments to
%%be drawn with rounded ends like the segment from {\tt z0} to {\tt z3} in
%%Figure~\ref{fig33}. 
õÓÔÁÎÏ×ËÁ ${\tt linecap}\mathrel{\hbox{\tt:=}}{\tt
butt}$\index{butt?\texttt{butt}}\label{Dbutt} ÏÂÒÅÚÁÅÔ ËÏÎÃÙ ÔÁË, ÞÔÏ 
ÔÉÒÅ, ÐÒÏÉÚ×ÏÄÉÍÙÅ {\tt dashed
evenly}\index{evenly?\texttt{evenly}}, ÉÍÅÀÔ ÄÌÉÎÕ 3bp, Á ÎÅ 3bp ÐÌÀÓ 
ÔÏÌÝÉÎÁ ÌÉÎÉÉ. 
%%Setting ${\tt linecap}\mathrel{\hbox{\tt:=}}{\tt
%%butt}$\index{butt?\texttt{butt}}\label{Dbutt} cuts the ends off flush so
%%that dashes produced by {\tt dashed
%%evenly}\index{evenly?\texttt{evenly}} have length 3bp, not 3bp plus the
%%line width. 
÷Ù ÔÁËÖÅ ÍÏÖÅÔÅ ÐÏÌÕÞÉÔØ ËÏÎÃÙ-Ë×ÁÄÒÁÔÙ, ×ÙÈÏÄÑÝÉÅ ÚÁ ÐÒÅÄÅÌÙ ÕËÁÚÁÎÎÙÈ 
ÔÏÞÅË-ËÏÎÃÏ×, ÕÓÔÁÎÏ×ËÏÊ ${\tt linecap}\mathrel{\hbox{\tt:=}}{\tt
squared}$\index{squared?\texttt{squared}}\label{Dsqred}, ËÁË ÜÔÏ ÓÄÅÌÁÎÏ 
ÎÁ ÌÉÎÉÉ ÏÔ {\tt z2} ÄÏ {\tt z5} × ÒÉÓ.~\ref{fig33}.
%%You can also get squared-off ends that extend past the
%%specified endpoints by setting ${\tt linecap}\mathrel{\hbox{\tt:=}}{\tt
%%squared}$\index{squared?\texttt{squared}}\label{Dsqred} as was done in
%%the line from {\tt z2} to {\tt z5} in Figure~\ref{fig33}.

\begin{figure}[htp]
$$\begin{verbatim}
beginfig(33);
for i=0 upto 2:
  z[i]=(0,40i); z[i+3]-z[i]=(100,30);
endfor
pickup pencircle scaled 18;
draw z0..z3 withcolor .8white;
linecap:=butt;
draw z1..z4 withcolor .8white;
linecap:=squared;
draw z2..z5 withcolor .8white;
dotlabels.top(0,1,2,3,4,5);
endfig; linecap:=rounded;
\end{verbatim}
\qquad
\mathcenter{\includegraphics{manfig-ru-33}}
$$
\caption{ëÏÄ MetaPost É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ×Ù×ÏÄ}
%%\caption{MetaPost code and the corresponding output}
\label{fig33}
\end{figure}

äÒÕÇÏÊ ÐÁÒÁÍÅÔÒ, ÚÁÉÍÓÔ×Ï×ÁÎÎÙÊ ÉÚ PostScript, ×ÌÉÑÅÔ ÎÁ ÓÐÏÓÏÂ, ËÏÔÏÒÙÍ 
ËÏÍÁÎÄÁ {\tt draw} ÒÉÓÕÅÔ ÕÇÌÙ\index{ÕÇÌÙ} ÎÁ ÉÚÏÂÒÁÖÁÅÍÏÍ ÐÕÔÉ.
%%Another parameter borrowed from PostScript affects the way a {\tt draw}
%%statement treats sharp corners\index{corners} in the path to be drawn.
ðÁÒÁÍÅÔÒ {\tt linejoin}\index{linejoin?\texttt{linejoin}}\label{Dlinejoin}
ÍÏÖÅÔ ÂÙÔØ {\tt
rounded}\index{rounded?\texttt{rounded}}\label{Drnded}, {\tt
beveled}\index{beveled?\texttt{beveled}}\label{Dbvled} ÉÌÉ {\tt
mitered}\index{mitered?\texttt{mitered}}\label{Dmitred}, ËÁË ÐÏËÁÚÁÎÏ 
ÎÁ ÒÉÓ.~\ref{fig34}. 
%%The {\tt linejoin}\index{linejoin?\texttt{linejoin}}\label{Dlinejoin}
%%parameter can be {\tt
%%rounded}\index{rounded?\texttt{rounded}}\label{Drnded}, {\tt
%%beveled}\index{beveled?\texttt{beveled}}\label{Dbvled}, or {\tt
%%mitered}\index{mitered?\texttt{mitered}}\label{Dmitred} as shown in
%%Figure~\ref{fig34}. 
óÔÁÎÄÁÒÔÎÏÅ ÚÎÁÞÅÎÉÅ ÄÌÑ plain MetaPost --- ÜÔÏ {\tt
rounded}, ÏÎÏ ÄÁÅÔ ÜÆÆÅËÔ ÒÉÓÏ×ÁÎÉÑ ËÒÕÇÌÙÍ ÐÅÒÏÍ.
%%The default value for plain MetaPost is {\tt
%%rounded} which gives the effect of drawing with a circular brush.

\begin{figure}[htp]
$$\begin{verbatim}
beginfig(34);
for i=0 upto 2:
  z[i]=(0,50i); z[i+3]-z[i]=(60,40);
  z[i+6]-z[i]=(120,0);
endfor
pickup pencircle scaled 24;
draw z0--z3--z6 withcolor .8white;
linejoin:=mitered;
draw z1..z4--z7 withcolor .8white;
linejoin:=beveled;
draw z2..z5--z8 withcolor .8white;
dotlabels.bot(0,1,2,3,4,5,6,7,8);
endfig; linejoin:=rounded;
\end{verbatim}
\qquad
\mathcenter{\includegraphics{manfig-ru-34}}
$$
\caption{ëÏÄ MetaPost É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ×Ù×ÏÄ}
%%\caption{MetaPost code and the corresponding output}
\label{fig34}
\end{figure}

ëÏÇÄÁ {\tt linejoin} ÒÁ×ÅÎ {\tt mitered}, ÕÇÌÙ ÉÚÏÂÒÁÖÁÀÔÓÑ Ó ÄÌÉÎÎÙÍ 
ÏÓÔÒÉÅÍ, ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig35}. 
%%When {\tt linejoin} is {\tt mitered}, sharp corners generate long
%%pointed features as shown in Figure~\ref{fig35}. 
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÜÔÏ ÍÏÖÅÔ ÂÙÔØ ÎÅÖÅÌÁÔÅÌØÎÙÍ, ÅÓÔØ ×ÎÕÔÒÅÎÎÑÑ 
ÐÅÒÅÍÅÎÎÁÑ\index{×ÎÕÔÒÅÎÎÉÅ
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} Ó ÉÍÅÎÅÍ {\tt
miterlimit}\index{miterlimit?\texttt{miterlimit}}\label{Dmiterlim}, 
ËÏÔÏÒÁÑ ÕÐÒÁ×ÌÑÅÔ ÐÅÒÅÈÏÄÏÍ ÏÔ ÏÓÔÒÏËÏÎÅÞÎÏÇÏ ÓÏÅÄÉÎÅÎÉÑ Ë ÓÒÅÚÁÎÎÏÍÕ 
ÓÏÅÄÉÎÅÎÉÀ. 
%%Since this might be
%%undesirable, there is an internal variable\index{internal
%%variables}\index{variables!internal} called {\tt
%%miterlimit}\index{miterlimit?\texttt{miterlimit}}\label{Dmiterlim} that
%%controls how extreme the situation can get before the mitered join is
%%replaced by a beveled join. 
äÌÑ Plain MetaPost {\tt miterlimit} ÉÍÅÅÔ ÓÔÁÎÄÁÒÔÎÏÅ ÚÎÁÞÅÎÉÅ 10.0 É 
ÓÏÅÄÉÎÅÎÉÅ ÌÉÎÉÊ ÏÂÒÁÝÁÅÔÓÑ Ë ÓÒÅÚÁÎÎÏÍÕ ÔÏÇÄÁ, ËÏÇÄÁ ÏÔÎÏÛÅÎÉÅ 
ÄÌÉÎÙ ÏÓÔÒÉÑ Ë ÔÏÌÝÉÎÅ ÌÉÎÉÉ ÄÏÓÔÉÇÁÅÔ ÜÔÏÇÏ ÚÎÁÞÅÎÉÑ.
%%For Plain MetaPost, {\tt miterlimit} has a
%%default value of 10.0 and line joins revert to beveled when the ratio of
%%miter length to line width reaches this value.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-35} $$
\caption{äÌÉÎÁ ÏÓÔÒÉÑ É ÔÏÌÝÉÎÁ ÌÉÎÉÉ, ÞØÅ ÏÔÎÏÛÅÎÉÅ ÏÇÒÁÎÉÞÉ×ÁÅÔÓÑ 
        {\tt miterlimit}.}
%%\caption{The miter length and line width whose ratio is limited by
%%        {\tt miterlimit}.}
\label{fig35}
\end{figure}

ðÁÒÁÍÅÔÒÙ {\tt linecap}, {\tt linejoin} É {\tt miterlimit} ÏÞÅÎØ 
×ÁÖÎÙ, ÐÏÔÏÍÕ ÞÔÏ ÏÎÉ ×ÌÉÑÀÔ É ÎÁ ÄÒÕÇÉÅ ÒÉÓÕÅÍÙÅ ÏÂßÅËÔÙ. 
%%The {\tt linecap}, {\tt linejoin}, and {\tt miterlimit} parameters are
%%especially important because they also affect things that get drawn
%%behind the scenes. 
îÁÐÒÉÍÅÒ, Plain MetaPost ÉÍÅÅÔ ËÏÍÁÎÄÕ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ 
ÓÔÒÅÌÏË\index{ÓÔÒÅÌËÉ} É ËÏÎÃÙ ÓÔÒÅÌÏË ÐÏÌÕÞÁÀÔÓÑ ÓÌÅÇËÁ ÓËÒÕÇÌÅÎÎÙÍÉ 
ÐÒÉ {\tt linejoin} ÒÁ×ÎÏÍ {\tt rounded}. 
%%For instance, Plain MetaPost has statements for
%%drawing arrows\index{arrows}, and the arrowheads are slightly rounded
%%when {\tt linejoin} is {\tt rounded}. 
üÆÆÅËÔ ÚÁ×ÉÓÉÔ ÏÔ ÔÏÌÝÉÎÙ ÌÉÎÉÉ É ÐÏÞÔÉ ÎÅÚÁÍÅÔÅÎ ÐÒÉ ÓÔÁÎÄÁÒÔÎÏÊ ÔÏÌÝÉÎÅ 
ÌÉÎÉÉ × 5bp, ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig36}.
%%The effect depends on the line
%%width and is quite subtle at the default line width of 0.5bp as shown in
%%Figure~\ref{fig36}.

\begin{figure}[htp]
$$\includegraphics{manfig-ru-36}$$
\caption{ôÒÉ ÓÐÏÓÏÂÁ ÒÉÓÏ×ÁÔØ ÓÔÒÅÌËÉ.}
%%\caption{Three ways of drawing arrows.}
\label{fig36}
\end{figure}

îÁÒÉÓÏ×ÁÎÎÙÅ ÓÔÒÅÌËÉ, ÐÏÄÏÂÎÙÅ ÔÅÍ, ÞÔÏ ÎÁ ÒÉÓ.~\ref{fig36}, --- ÜÔÏ ÐÒÏÓÔÏ 
ÒÅÚÕÌØÔÁÔ, ËÏÇÄÁ ×ÍÅÓÔÏ {\tt draw} \tdescr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} 
ÐÉÛÕÔ\index{drawarrow?\texttt{drawarrow}}\label{Ddrwarr}
$$ {\tt drawarrow}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}. $$
%%Drawing arrows like the ones in Figure~\ref{fig36} is simply a matter of
%%saying\index{drawarrow?\texttt{drawarrow}}\label{Ddrwarr}
%%$$ {\tt drawarrow}\, \descr{path expression} $$
%%instead of {\tt draw} \tdescr{path expression}. 
ðÏÓÌÅÄÎÅÅ ÒÉÓÕÅÔ ÐÕÔØ Ó ÎÁËÏÎÅÞÎÉËÏÍ ÓÔÒÅÌÙ × ÐÏÓÌÅÄÎÅÊ ÔÏÞËÅ ÐÕÔÉ.
%%This draws the given
%%path with an arrowhead at the last point on the path. 
åÓÌÉ ×Ù ÈÏÔÉÔÅ ÎÁËÏÎÅÞÎÉË ÓÔÒÅÌÙ × ÎÁÞÁÌÅ ÐÕÔÉ, ÔÏ ÐÒÏÓÔÏ ÉÓÐÏÌØÚÕÊÔÅ 
ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ {\tt
reverse}\index{reverse?\texttt{reverse}}\label{Drevrse}, ËÏÔÏÒÙÊ ÉÚ 
ÐÕÔÉ-ÁÒÇÕÍÅÎÔÁ ÄÅÌÁÅÔ ÏÂÒÁÔÎÙÊ ÐÕÔØ ÏÔÎÏÓÉÔÅÌØÎÏ ×ÒÅÍÅÎÉ, Ô.~Å. ÄÌÑ 
ÐÕÔÉ {\tt p} Ó {\tt length p}${}=n$,
$$ {\tt point\ } t {\tt\ of\ reverse\ p}
  \quad \hbox{\rm É} \quad
   {\tt point\ } n-t {\tt\ of\ p}
$$ --- ÓÉÎÏÎÉÍÙ.
%%If you want the
%%arrowhead at the beginning of the path, just use the unary operator {\tt
%%reverse}\index{reverse?\texttt{reverse}}\label{Drevrse} to take the
%%original path and make a new one with its time sense reversed; i.e., for
%%a path~{\tt p} with {\tt length p}${}=n$,
%%$$ {\tt point\ } t {\tt\ of\ reverse\ p}
%%  \quad {\rm and} \quad
%%   {\tt point\ } n-t {\tt\ of\ p}
%%$$ are synonymous.

ëÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig36}, ËÏÍÁÎÄÁ, ÎÁÞÉÎÁÀÝÁÑÓÑ Ó 
\index{drawdblarrow?\texttt{drawdblarrow}}%
\index{ÓÔÒÅÌËÉ!Ä×ÕÈËÏÎÅÞÎÙÅ}\label{Ddrwdar}
$$ {\tt drawdblarrow}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}, $$
ÒÉÓÕÅÔ ÎÁËÏÎÅÞÎÉËÉ ÓÔÒÅÌÏË × ÏÂÏÉÈ ËÏÎÃÁÈ ÐÕÔÉ. 
%%As shown in Figure~\ref{fig36}, a statement
%%beginning\index{drawdblarrow?\texttt{drawdblarrow}}%
%%\index{arrows!double-headed}\label{Ddrwdar}
%%$$ {\tt drawdblarrow}\, \descr{path expression} $$
%%draws a double-headed arrow. 
òÁÚÍÅÒ ÎÁËÏÎÅÞÎÉËÁ ÇÁÒÁÎÔÉÒÕÅÔÓÑ ÂÏÌØÛÉÍ, ÞÅÍ ÔÏÌÝÉÎÁ ÌÉÎÉÉ, ÎÏ 
×ÏÚÍÏÖÎÏ ÐÏÎÁÄÏÂÉÔÓÑ ÄÏÐÏÌÎÉÔÅÌØÎÁÑ ÎÁÓÔÒÏÊËÁ ÄÌÑ ÏÞÅÎØ ÔÏÌÓÔÙÈ ÌÉÎÉÊ.
%%The size of the arrowhead is guaranteed to
%%be larger than the line width, but it might need adjusting if the line
%%width is very great. 
üÔÏ ÄÅÌÁÅÔÓÑ ÐÒÉÓ×ÏÅÎÉÅÍ ÎÏ×ÏÇÏ ÚÎÁÞÅÎÉÑ ×ÎÕÔÒÅÎÎÅÊ 
ÐÅÒÅÍÅÎÎÏÊ\index{×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ}
{\tt ahlength}\index{ahlength?\texttt{ahlength}}\label{Dahlength}, 
ËÏÔÏÒÁÑ ÏÐÒÅÄÅÌÑÅÔ ÄÌÉÎÕ ÎÁËÏÎÅÞÎÉËÁ, ËÁË ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{fig37}.
%%This is done by assigning a new value to the
%%internal variable\index{internal variables}\index{variables!internal}
%%{\tt ahlength}\index{ahlength?\texttt{ahlength}}\label{Dahlength} that
%%determines arrowhead length as shown in Figure~\ref{fig37}. 
õ×ÅÌÉÞÅÎÉÅ {\tt ahlength} ÂÏÌÅÅ ÓÔÁÎÄÁÒÔÎÏÇÏ ÚÎÁÞÅÎÉÑ 4 PostScript-ÐÕÎËÔÁ 
ÄÏ 1.5 ÓÁÎÔÉÍÅÔÒÏ× ÐÒÏÉÚ×ÏÄÉÔ ÂÏÌØÛÏÊ ÎÁËÏÎÅÞÎÉË ÎÁ ÒÉÓ.~\ref{fig37}. 
%%Increasing
%%{\tt ahlength} from the default value of 4 PostScript points to 1.5
%%centimeters produces the large arrowhead in Figure~\ref{fig37}. 
åÓÔØ ÅÝÅ ÐÁÒÁÍÅÔÒ {\tt 
ahangle}\index{ahangle?\texttt{ahangle}}\label{Dahangle},
ËÏÎÔÒÏÌÉÒÕÀÝÉÊ ÕÇÏÌ ÎÁ ×ÅÒÈÕÛËÅ ÎÁËÏÎÅÞÎÉËÁ ÓÔÒÅÌËÉ.
%%There
%%is also an {\tt ahangle}\index{ahangle?\texttt{ahangle}}\label{Dahangle}
%%parameter that controls the angle at the tip of the arrowhead. 
ôÉÐÏ×ÏÅ ÚÎÁÞÅÎÉÅ ÜÔÏÇÏ ÕÇÌÁ --- 45 ÇÒÁÄÕÓÏ×, ÞÔÏ ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓÕÎËÅ.
%%The default value of this angle is 45 degrees as shown in the figure.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-37} $$
\caption[âÏÌØÛÏÊ ÎÁËÏÎÅÞÎÉË ÓÔÒÅÌËÉ Ó ÏÔÍÅÞÅÎÎÙÍÉ ËÌÀÞÅ×ÙÍÉ ÐÁÒÁÍÅÔÒÁÍÉ.]
        {âÏÌØÛÏÊ ÎÁËÏÎÅÞÎÉË ÓÔÒÅÌËÉ Ó ÏÔÍÅÞÅÎÎÙÍÉ ËÌÀÞÅ×ÙÍÉ ÐÁÒÁÍÅÔÒÁÍÉ É 
        Ó ×ÙÄÅÌÅÎÎÙÍÉ ÂÅÌÙÍÉ ÌÉÎÉÑÍÉ ÐÕÔÑÍÉ ÄÌÑ ÅÇÏ ÒÉÓÏ×ÁÎÉÑ.}
%%\caption[A large arrowhead with key parameters labeled.]
%%        {A large arrowhead with key parameters labeled and paths used to
%%        draw it marked with white lines.}
\label{fig37}
\end{figure}

îÁËÏÎÅÞÎÉË ÓÏÚÄÁÅÔÓÑ ÚÁÐÏÌÎÅÎÉÅÍ ÔÒÅÕÇÏÌØÎÏÊ ÏÂÌÁÓÔÉ, ×ÙÄÅÌÅÎÎÏÊ ÂÅÌÙÍ 
ÎÁ ÒÉÓ.~\ref{fig37}, É ÚÁÔÅÍ ÐÒÏÒÉÓÏ×ËÏÊ ×ÏËÒÕÇ ÎÅÅ ÔÅËÕÝÉÍ ÐÅÒÏÍ.
%%The arrowhead is created by filling the triangular region that is
%%outlined in white in Figure~\ref{fig37} and then drawing around it with
%%the currently picked up pen. 
üÔÁ ËÏÍÂÉÎÁÃÉÑ ÉÚ ÚÁÐÏÌÎÅÎÉÑ É ÒÉÓÏ×ÁÎÉÑ ÍÏÖÅÔ ÂÙÔØ ÏÂßÅÄÉÎÅÎÁ × 
ÏÄÎÕ ËÏÍÁÎÄÕ {\tt 
filldraw}\index{filldraw?\texttt{filldraw}}\label{Dfildrw}:
$$ {\tt filldraw}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\,
   \descr{ÏÐÃÉÏÎÁÌØÎÙÅ {\tt dashed}, {\tt withcolor} É {\tt withpen} ÐÕÎËÔÙ};
$$
%%This combination of filling and drawing
%%can be combined into a single {\tt filldraw}
%%statement\index{filldraw?\texttt{filldraw}}\label{Dfildrw}:
%%$$ {\tt filldraw}\, \descr{path expression}\,
%%   \descr{optional {\tt dashed} and {\tt withcolor} and {\tt withpen} clauses};
%%$$
\tdescr{÷ÙÒÁÖÅÎÉÅ-ÐÕÔØ} ÄÏÌÖÎÏ ÂÙÔØ ÚÁÍËÎÕÔÙÍ ÃÉËÌÏÍ, ÐÏÄÏÂÎÙÍ 
ÔÒÅÕÇÏÌØÎÏÍÕ ÐÕÔÉ ÎÁ ÒÉÓ.~\ref{fig37}. 
%%The \tdescr{path expression} should be a closed cycle like the
%%triangular path in Figure~\ref{fig37}. 
üÔÏÔ ÐÕÔØ ÎÅ ÓÌÅÄÕÅÔ ÓÍÅÛÉ×ÁÔØ Ó ÁÒÇÕÍÅÎÔÏÍ-ÐÕÔÅÍ Ë {\tt drawarrow}, 
ËÏÔÏÒÙÊ ÉÚÏÂÒÁÖÅÎ ÂÅÌÏÊ ÌÉÎÉÅÊ ÎÁ ÒÉÓÕÎËÅ.
%%This path should not be confused
%%with the path argument to {\tt drawarrow} which is indicated by a white
%%line in the figure.

âÅÌÙÅ ÌÉÎÉÉ, ÐÏÄÏÂÎÙÅ ÔÅÍ, ÞÔÏ ÎÁ ÒÉÓÕÎËÅ, ÍÏÇÕÔ ÓÏÚÄÁ×ÁÔØÓÑ ËÏÍÁÎÄÏÊ 
{\tt undraw}\index{undraw?\texttt{undraw}}\label{Dundraw}.
%%White lines like the ones in the figure can be created by an {\tt
%%undraw}\index{undraw?\texttt{undraw}}\label{Dundraw} statement. 
üÔÏ ÓÔÉÒÁÀÝÁÑ\index{ÓÔÉÒÁÎÉÅ} ×ÅÒÓÉÑ {\tt draw}, ËÏÔÏÒÁÑ ÉÓÐÏÌØÚÕÅÔ {\tt
withcolor background}\index{background?\texttt{background}} ÔÁË ÖÅ, ËÁË É 
ËÏÍÁÎÄÁ {\tt unfill}. 
%%This is
%%an erasing\index{erasing} version of {\tt draw} that draws {\tt
%%withcolor background}\index{background?\texttt{background}} just as the
%%{\tt unfill} statement does. 
åÓÔØ ÅÝÅ ËÏÍÁÎÄÁ {\tt
unfilldraw}\index{unfilldraw?\texttt{unfilldraw}}\label{Dunfdrw} 
ËÁË ÒÁÚ ÄÌÑ ÓÌÕÞÁÑ, ËÏÔÏÒÙÊ ÓÌÅÄÕÅÔ ÉÚ ÅÅ ÎÁÚ×ÁÎÉÑ.
%%There is also an {\tt
%%unfilldraw}\index{unfilldraw?\texttt{unfilldraw}}\label{Dunfdrw}
%%statement just in case someone finds a use for it.

ëÏÍÁÎÄÙ {\tt filldraw}, {\tt undraw}, {\tt unfilldraw} É ×ÓÅ ËÏÍÁÎÄÙ 
ÄÌÑ ÒÉÓÏ×ÁÎÉÑ ÓÔÒÅÌÏË ÐÏÄÏÂÎÙ ËÏÍÁÎÄÁÍ {\tt fill} É {\tt draw}
× ÔÏÍ, ÞÔÏ ÏÎÉ ÍÏÇÕÔ ÉÍÅÔØ ÏÐÃÉÉ {\tt dashed}\index{dashed?\texttt{dashed}},
{\tt withpen}\index{withpen?\texttt{withpen}} É {\tt
withcolor}\index{withcolor?\texttt{withcolor}}. 
%%The {\tt filldraw}, {\tt undraw} and {\tt unfilldraw} statements and all
%%the arrow drawing statements are like the {\tt fill} and {\tt draw}
%%statements in that they take {\tt dashed}\index{dashed?\texttt{dashed}},
%%{\tt withpen}\index{withpen?\texttt{withpen}}, and {\tt
%%withcolor}\index{withcolor?\texttt{withcolor}} options. 
ëÏÇÄÁ Õ ×ÁÓ ÉÍÅÅÔÓÑ ÍÎÏÇÏ ËÏÍÁÎÄ ÒÉÓÏ×ÁÎÉÑ, ÔÏ ÕÄÏÂÎÏ ÉÍÅÔØ ×ÏÚÍÏÖÎÏÓÔØ 
ÐÒÉÍÅÎÉÔØ ÏÐÃÉÀ, ÔÁËÕÀ ËÁË {\tt withcolor 0.8white}, ËÏ ×ÓÅÍ ÎÉÍ ÂÅÚ 
ÐÏ×ÔÏÒÅÎÉÑ ÅÅ ×ÓÑËÉÊ ÒÁÚ, ËÁË ÎÁ ÒÉÓÕÎËÁÈ \ref{fig33} É~\ref{fig34}.  
%%When you have a
%%lot of drawing statements it is nice to be able to apply an option such
%%as {\tt withcolor 0.8white} to all of them without having to type this
%%repeatedly as was done in Figures \ref{fig33} and~\ref{fig34}. 
ëÏÍÁÎÄÁ ÄÌÑ ÜÔÏÊ ÃÅÌÉ ÎÁÚÙ×ÁÅÔÓÑ\index{drawoptions?\texttt{drawoptions}}\label{Ddropts}
$$ \hbox{\tt drawoptions(} \descr{ÔÅËÓÔ} \hbox{\tt )},  $$
ÇÄÅ ÁÒÇÕÍÅÎÔ \tdescr{ÔÅËÓÔ} ÄÁÅÔ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÏÐÃÉÊ {\tt dashed}, 
{\tt withcolor} É {\tt withpen}, ËÏÔÏÒÙÅ ÐÒÉÍÅÎÑÀÔ Á×ÔÏÍÁÔÉÞÅÓËÉ ËÏ 
×ÓÅÍ ÒÉÓÕÀÝÉÍ ËÏÍÁÎÄÁÍ. 
%%The statement for this purpose
%%is\index{drawoptions?\texttt{drawoptions}}\label{Ddropts}
%%$$ \hbox{\tt drawoptions(} \descr{text} \hbox{\tt )}  $$
%%where the \tdescr{text} argument gives a sequence of {\tt dashed}, {\tt
%%withcolor}, and {\tt withpen} options to be applied automatically to all
%%drawing statements. 
åÓÌÉ ×Ù ÕËÁÖÉÔÅ
$$ \hbox{\tt drawoptions(withcolor .5[black,white])} $$ 
É ÚÁÔÅÍ ÚÁÈÏÔÉÔÅ ÎÁÒÉÓÏ×ÁÔØ ÞÅÒÎÕÀ ÌÉÎÉÀ, ÔÏ ×ÁÍ ÐÒÉÄÅÔÓÑ 
ÐÅÒÅÕÓÔÁÎÏ×ÉÔØ {\tt drawoptions} ÕËÁÚÁÎÉÅÍ
$$ {\tt draw}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\, {\tt withcolor\ black}. $$
%%If you specify
%%$$ \hbox{\tt drawoptions(withcolor .5[black,white])} $$
%%and then want to draw a black line, you can override the {\tt drawoptions}
%%by specifying
%%$$ {\tt draw}\, \descr{path expression}\, {\tt withcolor\ black} $$
äÌÑ ÏÔËÌÀÞÅÎÉÑ ×ÓÅÈ ÐÏÓÌÅÄÓÔ×ÉÊ {\tt drawoptions} ÐÒÏÓÔÏ ÉÓÐÏÌØÚÕÊÔÅ 
ÐÕÓÔÏÊ ÓÐÉÓÏË-ÁÒÇÕÍÅÎÔ:
$$ \hbox{\tt drawoptions()}. $$
%%To turn off {\tt drawoptions} all together, just give an empty list:
%%$$ \hbox{\tt drawoptions()} $$
(üÔÏ ÄÅÌÁÅÔÓÑ Á×ÔÏÍÁÔÉÞÅÓËÉ ÍÁËÒÏÓÏÍ {\tt
beginfig}\index{beginfig?\texttt{beginfig}}.)
%%(This is done automatically by the {\tt
%%beginfig}\index{beginfig?\texttt{beginfig}} macro).

éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÎÅ×ÅÒÎÙÅ ÏÐÃÉÉ ÉÇÎÏÒÉÒÕÀÔÓÑ, ÎÅ ÂÕÄÅÔ ×ÒÅÄÁ ÏÔ 
ËÏÍÁÎÄÙ, ÐÏÄÏÂÎÏÊ 
$$ \hbox{\tt drawoptions(dashed evenly)}, $$
ÚÁ ËÏÔÏÒÏÊ ÉÄÅÔ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ËÏÍÁÎÄ {\tt draw} É {\tt fill}.
%%Since irrelevant options are ignored, there is no harm in giving a statement
%%like
%%$$ \hbox{\tt drawoptions(dashed evenly)} $$
%%followed by a sequence of {\tt draw} and {\tt fill} commands. 
îÅ ÉÍÅÅÔ ÓÍÙÓÌÁ ÉÓÐÏÌØÚÏ×ÁÔØ ÏÂÒÁÚÅà ÌÉÎÉÉ ÐÒÉ ÚÁÌÉ×ËÅ, ÐÏÜÔÏÍÕ 
{\tt dashed evenly} ÉÇÎÏÒÉÒÕÅÔÓÑ ÄÌÑ ËÏÍÁÎÄ {\tt fill}. 
%%It does
%%not make sense to use a dash pattern when filling so the {\tt dashed
%%evenly} gets ignored for {\tt fill} statements. 
ïÞÅ×ÉÄÎÏ, ÞÔÏ 
$$ \hbox{\tt drawoptions(withpen } \descr{×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ} \hbox{\tt )} $$
×ÌÉÑÅÔ ÎÁ ËÏÍÁÎÄÙ {\tt fill} É {\tt draw}.
%%It turns out that
%%$$ \hbox{\tt drawoptions(withpen } \descr{pen expression} \hbox{\tt )} $$
%%does affect {\tt fill} statements as well as {\tt draw} statements.
æÁËÔÉÞÅÓËÉ ÓÕÝÅÓÔ×ÕÅÔ ÓÐÅÃÉÁÌØÎÁÑ ÐÅÒÅÍÅÎÎÁÑ-ÐÅÒÏ Ó ÉÍÅÎÅÍ 
{\tt currentpen}\index{currentpen?\texttt{currentpen}} ÔÁËÁÑ, ÞÔÏ 
{\tt fill} \ldots\ {\tt withpen currentpen} ÜË×É×ÁÌÅÎÔÎÏ 
ËÏÍÁÎÄÅ {\tt filldraw}.
%%In fact there is a special pen variable called
%%{\tt currentpen}\index{currentpen?\texttt{currentpen}} such that
%%{\tt fill} \ldots\ {\tt withpen currentpen} is equivalent to a {\tt filldraw}
%%statement.

ôÁË ÞÔÏ ÖÅ ÔÏÞÎÏ ÚÎÁÞÉÔ ÓËÁÚÁÔØ, ÞÔÏ ÏÐÃÉÉ ÒÉÓÏ×ÁÎÉÑ ×ÌÉÑÀÔ ÎÁ 
ËÏÍÁÎÄÙ ÔÏÇÄÁ, ËÏÇÄÁ ÜÔÏ ÉÍÅÅÔ ÓÍÙÓÌ?
%%Precisely what does it mean to say that drawing options affect those
%%statements where they make sense? 
ïÐÃÉÑ {\tt dashed} \tdescr{ÏÂÒÁÚÅà ÐÕÎËÔÉÒÁ} ×ÌÉÑÅÔ ÔÏÌØËÏ ÎÁ ËÏÍÁÎÄÙ 
$$ {\tt draw}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}, $$
Á ÐÏÑ×ÌÅÎÉÅ ÔÅËÓÔÁ × ÁÒÇÕÍÅÎÔÅ ÔÉÐÁ \tdescr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ} ÄÌÑ 
ËÏÍÁÎÄÙ 
$$ {\tt draw}\, \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ} $$
ÍÅÎÑÅÔÓÑ ÔÏÌØËÏ ÏÐÃÉÅÊ {\tt withcolor} \tdescr{×ÙÒÁÖÅÎÉÅ-Ã×ÅÔ}. 
%%The {\tt dashed} \tdescr{dash
%%pattern} option only affects
%%$$ {\tt draw}\, \descr{path expression} $$
%%statements, and text appearing in the \tdescr{picture expression} argument to
%%$$ {\tt draw}\, \descr{picture expression} $$
%%statement is only affected by the {\tt withcolor} \tdescr{color
%%expression} option. 
÷Ï ×ÓÅÈ ÄÒÕÇÉÈ ËÏÍÂÉÎÁÃÉÑÈ ËÏÍÁÎÄ É ÏÐÃÉÊ ÒÉÓÏ×ÁÎÉÑ ÅÓÔØ ÎÅËÏÔÏÒÙÊ 
ÜÆÆÅËÔ.
%%For all other combinations of drawing statements
%%and options, there is some effect. 
ïÐÃÉÑ, ÐÒÉÍÅÎÅÎÎÁÑ Ë ËÏÍÁÎÄÅ {\tt draw} \tdescr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ}, 
ÂÕÄÅÔ, ×ÏÏÂÝÅ ÇÏ×ÏÒÑ, ×ÌÉÑÔØ ÎÁ ÎÅËÏÔÏÒÙÅ ÞÁÓÔÉ ÒÉÓÕÎËÁ, ÎÏ ÎÅ ×ÓÅ.
%%An option applied to a {\tt draw}
%%\tdescr{picture expression} statement will in general affect some parts
%%of the picture but not others. 
îÁÐÒÉÍÅÒ, ÏÐÃÉÉ {\tt dashed} ÉÌÉ {\tt withpen} ÂÕÄÕÔ ×ÌÉÑÔØ ÎÁ ×ÓÅ ÌÉÎÉÉ, 
ÎÏ ÎÅ ÎÁ ÍÅÔËÉ.
%%For instance, a {\tt dashed} or {\tt
%%withpen} option will affect all the lines in the picture but none of the
%%labels.

\subsection{ðÅÒØÑ}
%%\subsection{Pens}
\label{sec.pens}

ðÒÅÄÙÄÕÝÉÅ ÒÁÚÄÅÌÙ ÄÁÌÉ ÍÎÏÖÅÓÔ×Ï ÐÒÉÍÅÒÏ× ÔÉÐÁ {\tt pickup}
\tdescr{×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ} É {\tt withpen} \tdescr{×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ}, ÎÏ 
ÎÅ ÂÙÌÏ ÐÒÉÍÅÒÏ×, ÏÔÌÉÞÎÙÈ ÏÔ 
$$ {\tt pencircle\ scaled}\, \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}, $$
ÞÔÏ ÓÏÚÄÁ×ÁÌÉ ÌÉÎÉÉ ÕËÁÚÁÎÎÏÊ ÔÏÌÝÉÎÙ. 
%%Previous sections have given numerous examples of {\tt pickup}
%%\tdescr{pen expression} and {\tt withpen} \tdescr{pen expression}, but
%%there have not been any examples of pen expressions other than
%%$$ {\tt pencircle\ scaled}\, \descr{numeric primary} $$
%%which produces lines of a specified width. 
äÌÑ ËÁÌÌÉÇÒÁÆÉÞÅÓËÉÈ ÜÆÆÅËÔÏ×, ÔÁËÉÈ ËÁË ÎÁ ÒÉÓ.~\ref{fig38}, ×Ù 
ÍÏÖÅÔÅ ÐÒÉÍÅÎÑÔØ ÌÀÂÙÅ ÔÒÁÎÓÆÏÒÍÁÃÉÏÎÎÙÅ ÏÐÅÒÁÔÏÒÙ, ÏÂÓÕÖÄÁÅÍÙÅ × 
ÒÁÚÄÅÌÅ~\ref{transsec}. 
%%For calligraphic effects
%%such in Figure~\ref{fig38}, you can apply any of the transformation
%%operators discussed in Section~\ref{transsec}. 
ïÔÐÒÁ×ÎÏÊ ÔÏÞËÏÊ ÄÌÑ ÔÁËÉÈ ÔÒÁÎÓÆÏÒÍÁÃÉÊ ÓÌÕÖÉÔ {\tt
pencircle}\index{pencircle?\texttt{pencircle}}\label{Dpncirc} --- 
ËÒÕÇ ÄÉÁÍÅÔÒÏÍ ÏÄÉÎ PostScript ÐÕÎËÔ. 
%%The starting point for
%%such transformations is {\tt
%%pencircle}\index{pencircle?\texttt{pencircle}}\label{Dpncirc}, a circle
%%one PostScript point in diameter. 
ðÏÜÔÏÍÕ ÁÆÆÉÎÎÙÅ ÔÒÁÎÓÆÏÒÍÁÃÉÉ ÐÒÏÉÚ×ÏÄÑÔ ËÒÕÇÏ×ÕÀ ÉÌÉ 
ÜÌÌÉÐÔÉÞÅÓËÕÀ\index{ÐÅÒØÑ!ÜÌÌÉÐÔÉÞÅÓËÉÅ} ÆÏÒÍÕ ÐÅÒÁ.
%%Thus affine transformations produce a
%%circular or elliptical\index{pens!elliptical} pen shape. 
ôÏÌÝÉÎÁ ÌÉÎÉÉ, ÒÉÓÕÅÍÏÊ ÐÅÒÏÍ, ÚÁ×ÉÓÉÔ ÏÔ ÔÏÇÏ, ÎÁÓËÏÌØËÏ ÐÅÒÐÅÎÄÉËÕÌÑÒÎÁ 
ÌÉÎÉÑ ÂÏÌØÛÅÊ ÏÓÉ ÜÌÌÉÐÓÁ.
%%The width of
%%lines drawn with the pen depends on how nearly perpendicular the line is
%%to the long axis of the ellipse.

\begin{figure}[htp]
$$\begin{verbatim}
beginfig(38);
pickup pencircle scaled .2in yscaled .08 rotated 30;
x0=x3=x4;
z1-z0 = .45in*dir 30;
z2-z3 = whatever*(z1-z0);
z6-z5 = whatever*(z1-z0);
z1-z6 = 1.2*(z3-z0);
rt x3 = lft x2;
x5 = .55[x4,x6];
y4 = y6;
lft x3 = bot y5 = 0;
top y2 = .9in;
draw z0--z1--z2--z3--z4--z5--z6 withcolor .7white;
dotlabels.top(0,1,2,3,4,5,6);
endfig;
\end{verbatim}
\quad \mathcenter{\includegraphics{manfig-ru-38}}
$$
\caption{ëÏÄ MetaPost É ``ËÁÌÌÉÇÒÁÆÉÞÅÓËÉÊ'' ÒÉÓÕÎÏË-ÒÅÚÕÌØÔÁÔ.}
%%\caption{MetaPost code and the resulting ``calligraphic'' figure.}
\label{fig38}\index{lft?\texttt{lft}}\index{bot?\texttt{bot}}\index{top?\texttt{top}}
\end{figure}

òÉÓ.~\ref{fig38} ÄÅÍÏÎÓÔÒÉÒÕÅÔ ÏÐÅÒÁÔÏÒÙ {\tt
lft}\index{lft?\texttt{lft}}\label{Dlft}, {\tt
rt}\index{rt?\texttt{rt}}\label{Drt}, {\tt
top}\index{top?\texttt{top}}\label{Dtop} É {\tt
bot}\index{bot?\texttt{bot}}\label{Dbot}, ÏÔ×ÅÞÁÀÝÉÅ ÎÁ ×ÏÐÒÏÓ: 
``åÓÌÉ ÔÅËÕÝÅÅ ÐÅÒÏ ÐÏÍÅÓÔÉÔØ × ÚÁÄÁÎÎÕÀ ÁÒÇÕÍÅÎÔÏÍ ÐÏÚÉÃÉÀ, ÔÏ ÇÄÅ 
ÂÕÄÕÔ ÎÁÈÏÄÉÔØÓÑ ÌÅ×ÙÊ, ÐÒÁ×ÙÊ, ×ÅÒÈÎÉÊ ÉÌÉ ÎÉÖÎÉÊ ËÒÁÊ?'' 
%%Figure~\ref{fig38} demonstrates operators {\tt
%%lft}\index{lft?\texttt{lft}}\label{Dlft}, {\tt
%%rt}\index{rt?\texttt{rt}}\label{Drt}, {\tt
%%top}\index{top?\texttt{top}}\label{Dtop}, and {\tt
%%bot}\index{bot?\texttt{bot}}\label{Dbot} that answer the question, ``If
%%the current pen is placed at the position given by the argument, where
%%will its left, right, top, or bottom edge be?'' 
îÁ ÜÔÏÍ ÒÉÓÕÎËÅ ÔÅËÕÝÅÅ ÐÅÒÏ Ñ×ÌÑÅÔÓÑ ÜÌÌÉÐÓÏÍ, ÚÁÄÁÎÎÙÍ ËÏÍÁÎÄÏÊ 
{\tt pickup}, É ÅÇÏ ÏÈ×ÁÔÙ×ÁÀÝÁÑ ÒÁÍËÁ ÒÁ×ÎÁ 0.1734 ÄÀÊÍÁ ÛÉÒÉÎÙ É 
0.101 ÄÀÊÍÁ ×ÙÓÏÔÙ, ÐÏÜÔÏÍÕ {\tt rt
x3} ÒÁ×ÎÏ ${\tt x3}+{\tt 0.0867in}$ É {\tt bot y5} ÒÁ×ÎÏ ${\tt y5}-{\tt
0.0505in}$. 
%%In this case the
%%current pen is the ellipse given in the {\tt pickup} statement and its
%%bounding box is 0.1734 inches wide and 0.1010 inches high, so {\tt rt
%%x3} is ${\tt x3}+{\tt 0.0867in}$ and {\tt bot y5} is ${\tt y5}-{\tt
%%0.0505in}$. 
ïÐÅÒÁÔÏÒÙ {\tt lft}, {\tt rt}, {\tt top} É {\tt bot} ÍÏÇÕÔ ÔÁËÖÅ ÉÍÅÔØ 
ÁÒÇÕÍÅÎÔ ÔÉÐÁ ÐÁÒÁ --- × ÜÔÏÍ ÓÌÕÞÁÅ ÏÎÉ ×ÙÞÉÓÌÑÀÔ ËÏÏÒÄÉÎÁÔÙ $x$
É~$y$ ÎÁÉÂÏÌÅÅ ÌÅ×ÏÊ, ÐÒÁ×ÏÊ, ×ÅÒÈÎÅÊ ÉÌÉ ÎÉÖÎÅÊ ÔÏÞËÉ ÆÏÒÍÙ ÐÅÒÁ.
%%The {\tt lft}, {\tt rt}, {\tt top}, and {\tt bot} operators
%%also accept arguments of type pair in which case they compute the $x$
%%and~$y$ coordinates of the leftmost, rightmost, topmost, or bottommost
%%point on the pen shape. 
îÁÐÒÉÍÅÒ, 
$$ {\tt rt}(x,y) = (x,y)+({\tt 0.0867in}, {\tt 0.0496in}) $$
ÄÌÑ ÐÅÒÁ ÎÁ ÒÉÓ.~\ref{fig38}. 
%%For example,
%%$$ {\tt rt}(x,y) = (x,y)+({\tt 0.0867in}, {\tt 0.0496in}) $$
%%for the pen in Figure~\ref{fig38}. 
úÁÍÅÔØÔÅ, ÞÔÏ {\tt
beginfig}\index{beginfig?\texttt{beginfig}} ÓÂÒÁÓÙ×ÁÅÔ ÔÅËÕÝÅÅ ÐÅÒÏ Ë 
ÓÔÁÎÄÁÒÔÎÏÍÕ ÚÎÁÞÅÎÉÀ 
$$ \hbox{\tt pencircle scaled 0.5bp} $$
× ÎÁÞÁÌÅ ËÁÖÄÏÊ ÆÉÇÕÒÙ.
%%Note that {\tt
%%beginfig}\index{beginfig?\texttt{beginfig}} resets the current pen to a
%%default value of
%%$$ \hbox{\tt pencircle scaled 0.5bp} $$
%%at the beginning of each figure. 
üÔÏ ÚÎÁÞÅÎÉÅ ÍÏÖÅÔ ÂÙÔØ ÔÁËÖÅ ×ÙÂÒÁÎÏ × ÌÀÂÏÅ ×ÒÅÍÑ ËÏÍÁÎÄÏÊ {\tt pickup
defaultpen}\index{defaultpen?\texttt{defaultpen}}\label{Ddefaultpen}.
%%This value can be reselected at any
%%time by giving the command {\tt pickup
%%defaultpen}\index{defaultpen?\texttt{defaultpen}}\label{Ddefaultpen}.

úÄÅÓØ ÍÏÇ ÂÙ ÂÙÔØ ËÏÎÅÃ ÉÓÔÏÒÉÉ Ï ÐÅÒØÑÈ, ÎÏ 
ÄÌÑ ÓÏ×ÍÅÓÔÉÍÏÓÔÉ Ó \MF\index{metafont?\MF}, MetaPost ÔÁËÖÅ ÄÏÐÕÓËÁÅÔ
ÍÎÏÇÏÕÇÏÌØÎÙÅ ÆÏÒÍÙ\index{ÐÅÒØÑ!ÍÎÏÇÏÕÇÏÌØÎÙÅ} ÐÅÒØÅ×.
%%This would be the end of the story on pens, except that for
%%compatibility with \MF\index{metafont?\MF}, MetaPost also allows pen
%%shapes to be polygonal\index{pens!polygonal}. 
åÓÔØ ÓÔÁÎÄÁÒÔÎÏÅ ÐÅÒÏ Ó ÉÍÅÎÅÍ 
{\tt pensquare}\index{pensquare?\texttt{pensquare}}\label{Dpnsqr}, 
ËÏÔÏÒÏÅ ÍÏÖÎÏ ÔÒÁÎÓÆÏÒÍÉÒÏ×ÁÔØ × ÐÅÒÏ × ÆÏÒÍÅ ÐÁÒÁÌÌÅÌÏÇÒÁÍÍÁ.
%%There is a predefined pen
%%called {\tt pensquare}\index{pensquare?\texttt{pensquare}}\label{Dpnsqr}
%%that can be transformed to yield pens shaped like parallelograms.
æÁËÔÉÞÅÓËÉ ÅÓÔØ ÄÁÖÅ ÏÐÅÒÁÔÏÒ, ÎÁÚÙ×ÁÅÍÙÊ {\tt
makepen}\index{makepen?\texttt{makepen}}\label{Dmkpen}, ÂÅÒÕÝÉÊ 
ÐÕÔØ × ÆÏÒÍÅ ×ÙÐÕËÌÏÇÏ ÍÎÏÇÏÕÇÏÌØÎÉËÁ É ÄÅÌÁÀÝÉÊ ÐÅÒÏ ÔÁËÏÊ ÖÅ ÆÏÒÍÙ 
É ÒÁÚÍÅÒÁ.
%%In fact, there is even an operator called {\tt
%%makepen}\index{makepen?\texttt{makepen}}\label{Dmkpen} that takes a
%%convex-polygon-shaped path and makes a pen that shape and size. 
åÓÌÉ ÐÕÔØ ÎÅ ÓÔÒÏÇÏ ×ÙÐÕËÌÙÊ ÉÌÉ ÍÎÏÇÏÕÇÏÌØÎÙÊ, ÔÏ ÏÐÅÒÁÔÏÒ 
{\tt makepen} ÂÕÄÅÔ ÓÐÒÑÍÌÑÔØ ËÒÁÑ É/ÉÌÉ ÓÂÒÁÓÙ×ÁÔØ ÎÅËÏÔÏÒÙÅ ×ÅÒÛÉÎÙ.
%%If the
%%path is not exactly convex or polygonal, the {\tt makepen} operator will
%%straighten the edges and/or drop some of the vertices. 
÷ ÞÁÓÔÎÏÓÔÉ, {\tt pensquare} ÜË×É×ÁÌÅÎÔÎÏ 
$$ \hbox{\tt makepen((-.5,-.5)-{}-(.5,-.5)-{}-(.5,.5)-{}-(-.5,.5)-{}-cycle)} $$
%%In particular, {\tt pensquare} is equivalent to
%%$$ \hbox{\tt makepen((-.5,-.5)--(.5,-.5)--(.5,.5)--(-.5,.5)--cycle)} $$
ëÏÍÁÎÄÙ {\tt pensquare} É {\tt makepen} ÎÅ ÄÏÌÖÎÙ ÉÓÐÏÌØÚÏ×ÁÔØÓÑ Ó 
ÏÂÒÁÚÃÁÍÉ ÐÕÎËÔÉÒÁ. 
%%{\tt pensquare} and {\tt makepen} should not be used with dash
%%patterns. 
óÍ. ËÏÎÅÃ ÒÁÚÄÅÌÁ~\ref{sec.pens}, ÓÔÒ. \pageref{dashed-pens}.
%%See the end of Section~\ref{sec.pens}, p.\ \pageref{dashed-pens}.

ïÂÒÁÔÎÙÍ Ë {\tt makepen} Ñ×ÌÑÅÔÓÑ ÏÐÅÒÁÔÏÒ {\tt
makepath}\index{makepath?\texttt{makepath}}\label{Dmkpath}, ËÏÔÏÒÙÊ 
ÂÅÒÅÔ \tdescr{ÐÅÒÏ-ÐÅÒ×ÉÞÎÏÓÔØ} É ×ÏÚ×ÒÁÝÁÅÔ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ÐÕÔØ.
%%The inverse of {\tt makepen} is the {\tt
%%makepath}\index{makepath?\texttt{makepath}}\label{Dmkpath} operator that
%%takes a \tdescr{pen primary} and returns the corresponding path. 
ðÏÜÔÏÍÕ {\tt makepath pencircle} ÐÒÏÉÚ×ÏÄÉÔ ËÒÕÇÏ×ÏÊ ÐÕÔØ, ÉÄÅÎÔÉÞÎÙÊ {\tt
fullcircle}\index{fullcircle?\texttt{fullcircle}}. 
%%Thus
%%{\tt makepath pencircle} produces a circular path identical to {\tt
%%fullcircle}\index{fullcircle?\texttt{fullcircle}}. 
üÔÏ ÔÁËÖÅ ÒÁÂÏÔÁÅÔ ÄÌÑ ÍÎÏÇÏÕÇÏÌØÎÏÇÏ ÐÅÒÁ, ÔÁË ÞÔÏ 
$$ {\tt makepath\ makepen}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} $$
ÂÕÄÅÔ ÂÒÁÔØ ÌÀÂÏÊ ÃÉËÌÉÞÅÓËÉÊ ÐÕÔØ É ÏÂÒÁÝÁÔØ ÅÇÏ × ×ÙÐÕËÌÙÊ 
ÍÎÏÇÏÕÇÏÌØÎÉË\index{×ÙÐÕËÌÙÅ ÍÎÏÇÏÕÇÏÌØÎÉËÉ}.
%%This also works for
%%a polygonal pen so that
%%$$ {\tt makepath\ makepen}\, \descr{path expression} $$
%%will take any cyclic path and turn it into a convex polygon\index{convex %%polygons}.

\subsection{÷ÙÒÅÚËÁ É ÎÉÚËÏÕÒÏ×ÎÅ×ÙÅ ËÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ}
%%\subsection{Clipping and Low-Level Drawing Commands}

ëÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ, ÔÁËÉÅ ËÁË {\tt draw}, {\tt fill}, {\tt filldraw} É 
{\tt unfill}, --- ÜÔÏ ÞÁÓÔÉ ÍÁËÒÏÐÁËÅÔÁ Plain\index{ÍÁËÒÏÓÙ Plain},  
ÏÐÒÅÄÅÌÅÎÎÙÅ ÞÅÒÅÚ ÂÏÌÅÅ ÐÒÉÍÉÔÉ×ÎÙÅ ËÏÍÁÎÄÙ.
%%Drawing statements such as {\tt draw}, {\tt fill}, {\tt filldraw}, and
%%{\tt unfill} are part of the Plain macro\index{Plain macros} package and
%%are defined in terms of more primitive statements. 
ïÓÎÏ×ÎÁÑ ÒÁÚÎÉÃÁ ÍÅÖÄÕ ËÏÍÁÎÄÁÍÉ ÒÉÓÏ×ÁÎÉÑ, ÒÁÓÓÍÏÔÒÅÎÎÙÍÉ × 
ÐÒÅÄÙÄÕÝÉÈ ÒÁÚÄÅÌÁÈ, É ÂÏÌÅÅ ÐÒÉÍÉÔÉ×ÎÙÍÉ × ÔÏÍ, ÞÔÏ ×ÓÅ ÐÒÉÍÉÔÉ×ÎÙÅ 
ËÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ ÔÒÅÂÕÀÔ ÕËÁÚÁÎÉÑ ÐÅÒÅÍÅÎÎÏÊ-ËÁÒÔÉÎËÉ ÄÌÑ ÈÒÁÎÅÎÉÑ 
ÒÅÚÕÌØÔÁÔÏ×.
%%The main difference
%%between the drawing statements discussed in previous sections and the
%%more primitive versions is that the primitive drawing statements all
%%require you to specify a picture variable to hold the results. 
äÌÑ ËÏÍÁÎÄ {\tt fill}, {\tt draw} É ÒÏÄÓÔ×ÅÎÎÙÈ ÉÍ, ÒÅÚÕÌØÔÁÔÙ ×ÓÅÇÄÁ 
ÎÁÐÒÁ×ÌÑÀÔÓÑ × ÐÅÒÅÍÅÎÎÕÀ-ËÁÒÔÉÎËÕ Ó ÉÍÅÎÅÍ {\tt
currentpicture}\index{currentpicture?\texttt{currentpicture}}\label{Dcurpic}.
%%For {\tt
%%fill}, {\tt draw}, and related statements, the results always go to a
%%picture variable called {\tt
%%currentpicture}\index{currentpicture?\texttt{currentpicture}}\label{Dcurpic}.
óÉÎÔÁËÓÉÓ ÄÌÑ ÐÒÉÍÉÔÉ×ÎÙÈ ËÏÍÁÎÄ ÒÉÓÏ×ÁÎÉÑ, ÐÏÚ×ÏÌÑÀÝÉÊ ÕËÁÚÙ×ÁÔØ 
ÐÅÒÅÍÅÎÎÕÀ-ËÁÒÔÉÎËÕ, ÐÏËÁÚÁÎ ÎÁ ÒÉÓ.~\ref{sydraw}. 
%%The syntax for the primitive drawing statements that allow you to
%%specify a picture variable is shown in Figure~\ref{sydraw}.

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ËÏÍÁÎÄÁ addto} \rightarrow$\\
%%$\tt \descr{addto command} \rightarrow$\\
$\tt \qquad addto \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ} also
        \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \qquad addto \descr{picture variable} also
%%        \descr{picture expression} \descr{option list}$\\
$\tt \qquad \;|\; addto \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ}
        contour \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \qquad \;|\; addto \descr{picture variable}
%%        contour \descr{path expression} \descr{option list}$\\
$\tt \qquad \;|\; addto \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ}
        doublepath \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \qquad \;|\; addto \descr{picture variable}
%%        doublepath \descr{path expression} \descr{option list}$\\
$\tt \descr{ÓÐÉÓÏË ÏÐÃÉÊ} \rightarrow \descr{ÐÕÓÔÏ} \;|\;
        \descr{ÏÐÃÉÑ ÒÉÓÏ×ÁÎÉÑ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \descr{option list} \rightarrow \descr{empty} \;|\;
%%        \descr{drawing option} \descr{option list}$\\
$\tt \descr{ÏÐÃÉÑ ÒÉÓÏ×ÁÎÉÑ} \rightarrow withcolor \descr{×ÙÒÁÖÅÎÉÅ-Ã×ÅÔ}$\\
%%$\tt \descr{drawing option} \rightarrow withcolor \descr{color expression}$\\
$\tt \qquad \;|\; withrgbcolor \descr{×ÙÒÁÖÅÎÉÅ-rgb-Ã×ÅÔ} \;|\;
        withcmykcolor \descr{×ÙÒÁÖÅÎÉÅ-cmyk-Ã×ÅÔ}$\\
%%$\tt \qquad \;|\; withrgbcolor \descr{rgbcolor expression} \;|\;
%%        withcmykcolor \descr{cmykcolor expression}$\\
$\tt \qquad \;|\; withgreyscale  \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} \;|\;
        withoutcolor$\\
%%$\tt \qquad \;|\; withgreyscale  \descr{numeric expression} \;|\;
%%        withoutcolor$\\
$\tt \qquad \;|\; withprescript  \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} \;|\;
        withpostscript \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; withprescript  \descr{string expression} \;|\;
%%        withpostscript \descr{string expression}$\\
$\tt \qquad \;|\; withpen \descr{×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ} \;|\;
        dashed \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ}$
%%$\tt \qquad \;|\; withpen \descr{pen expression} \;|\;
%%        dashed \descr{picture expression}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÄÌÑ ÐÒÉÍÉÔÉ×ÎÙÈ ËÏÍÁÎÄ ÒÉÓÏ×ÁÎÉÑ}
%%\caption{The syntax for primitive drawing statements}
\label{sydraw}
\index{ÓÐÉÓÏË ÏÐÃÉÊ?\tdescr{ÓÐÉÓÏË ÏÐÃÉÊ}}\index{addto also?\texttt{addto also}}\index{addto contour?\texttt{addto contour}}%
\index{addto doublepath?\texttt{addto doublepath}}\index{withcolor?\texttt{withcolor}}\index{withpen?\texttt{withpen}}%
\index{dashed?\texttt{dashed}}\index{ÏÐÃÉÉ ÒÉÓÏ×ÁÎÉÑ?\tdescr{ÏÐÃÉÉ ÒÉÓÏ×ÁÎÉÑ}}
\end{figure}

óÉÎÔÁËÓÉÓ ÄÌÑ ÐÒÉÍÉÔÉ×ÎÙÈ ËÏÍÁÎÄ ÒÉÓÏ×ÁÎÉÑ ÓÏ×ÍÅÓÔÉÍ Ó 
\MF\index{metafont?\MF}. 
%%The syntax for primitive drawing commands is compatible with
%%\MF\index{metafont?\MF}. 
ôÁÂÌÉÃÁ~\ref{draweqv} ÐÏËÁÚÙ×ÁÅÔ, ËÁË ÐÒÉÍÉÔÉ×ÎÙÅ 
ËÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ ÏÔÎÏÓÑÔÓÑ Ë ÚÎÁËÏÍÙÍ {\tt draw} É {\tt fill}. 
%%Table~\ref{draweqv} shows how the primitive
%%drawing statements relate to the familiar {\tt draw} and {\tt fill}
%%statements. 
ëÁÖÄÁÑ ËÏÍÁÎÄÁ × ÐÅÒ×ÏÊ ËÏÌÏÎËÅ ÔÁÂÌÉÃÙ ÍÏÖÅÔ ÚÁËÁÎÞÉ×ÁÔØÓÑ 
Ó×ÏÉÍ \tdescr{ÓÐÉÓËÏÍ ÏÐÃÉÊ}, ËÏÔÏÒÙÊ ÜË×É×ÁÌÅÎÔÅÎ ÄÏÂÁ×ÌÅÎÉÀ 
\tdescr{ÓÐÉÓËÁ ÏÐÃÉÊ} Ë ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÊ ÚÁÐÉÓÉ ×Ï ×ÔÏÒÏÊ ËÏÌÏÎËÅ.
%%Each of the statements in the first column of the table
%%could be ended with an \tdescr{option list} of its own, which is
%%equivalent to appending the \tdescr{option list} to the corresponding
%%entry in the second column of the table. 
îÁÐÒÉÍÅÒ,
$$ {\tt draw}\ p\ {\tt withpen\ pencircle} $$
ÜË×É×ÁÌÅÎÔÎÏ 
$$ {\tt addto\ currentpicture\ doublepath}\ p\
     {\tt withpen\ currentpen\ withpen\ pencircle},
$$
ÇÄÅ {\tt
currentpen}\index{currentpen?\texttt{currentpen}}\label{Dcurpen} --- 
ÜÔÏ ÓÐÅÃÉÁÌØÎÁÑ ÐÅÒÅÍÅÎÎÁÑ, × ËÏÔÏÒÏÊ ×ÓÅÇÄÁ ÈÒÁÎÉÔÓÑ ÔÅËÕÝÅÅ ÐÅÒÏ.
%%For example,
%%$$ {\tt draw%%}\ p\ {\tt withpen\ pencircle} $$
%%is equivalent to
%%$$ {\tt addto\ currentpicture\ doublepath}\ p\
%%     {\tt withpen\ currentpen\ withpen\ pencircle}
%%$$
%%where {\tt
%%currentpen}\index{currentpen?\texttt{currentpen}}\label{Dcurpen} is a
%%special pen variable that always holds the last pen picked up. 
÷ÔÏÒÁÑ ÏÐÃÉÑ {\tt withpen} ÂÅÚ ÛÕÍÁ ÏÔÍÅÎÑÅÔ {\tt withpen
currentpen} × ÒÁÓËÒÙÔÉÉ {\tt draw}.
%%The second {\tt withpen} option silently overrides the {\tt withpen
%%currentpen} from the expansion of {\tt draw}.

\begin{table}[htp]
$$\begin{tabular}{|l|l|}  \hline
\multicolumn1{|c|}{ËÏÍÁÎÄÁ}&  \multicolumn1{c|}{ÜË×É×ÁÌÅÎÔÎÙÊ ÐÒÉÍÉÔÉ×}\\ \hline
%%\multicolumn1{|c|}{statement}&  \multicolumn1{c|}{equivalent primitives}\\ \hline
{\tt draw} {\it pic}&   {\tt addto currentpicture also} {\it pic}\\
{\tt draw} $p$&         {\tt addto currentpicture doublepath} $p$
                        {\tt withpen} $q$\\
{\tt fill} $c$&         {\tt addto currentpicture contour} $c$\\
{\tt filldraw} $c$&     {\tt addto currentpicture contour} $c$ {\tt withpen} $q$\\
{\tt undraw} {\it pic}& {\tt addto currentpicture also} {\it pic}
                        {\tt withcolor} $b$\\
{\tt undraw} $p$&       {\tt addto currentpicture doublepath} $p$
                        {\tt withpen} $q$
                        {\tt withcolor} $b$\\
{\tt unfill} $c$&       {\tt addto currentpicture contour} $c$
                        {\tt withcolor} $b$\\
{\tt unfilldraw} $c$&   {\tt addto currentpicture contour} $c$ {\tt withpen} $q$
                        {\tt withcolor} $b$\\ \hline
\end{tabular}
$$
\caption[ëÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ É ÜË×É×ÁÌÅÎÔÎÙÅ ÐÒÉÍÉÔÉ×ÎÙÅ ËÏÍÁÎÄÙ] {ïÂÙÞÎÙÅ 
        ËÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ É ÜË×É×ÁÌÅÎÔÎÙÅ ×ÅÒÓÉÉ ÐÒÉÍÉÔÉ×Ï×, ÇÄÅ $q$
        ÚÎÁÞÉÔ {\tt currentpen}, $b$ --- {\tt background},
        $p$ --- ÌÀÂÏÊ ÐÕÔØ, $c$ --- ÃÉËÌÉÞÅÓËÉÊ ÐÕÔØ É {\it
        pic} --- \tdescr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ}.  úÁÍÅÔØÔÅ, ÞÔÏ 
        ÎÅÐÕÓÔÏÅ ÐÏÌÅ {\tt drawoptions} ÍÏÇÌÏ ÂÙ ÕÓÌÏÖÎÉÔØ ÚÁÐÉÓÉ ×Ï 
        ×ÔÏÒÏÊ ËÏÌÏÎËÅ.}
%%\caption[Drawing statements and equivalent primitive commands] {Common
%%        drawing statements and equivalent primitive versions, where $q$
%%        stands for {\tt currentpen}, $b$ stands for {\tt background},
%%        $p$ stands for any path, $c$ stands for a cyclic path, and {\it
%%        pic} stands for a \tdescr{picture expression}.  Note that
%%        nonempty {\tt drawoptions} would complicate the entries in the
%%        second column.}
\label{draweqv}
\index{drawoptions?\texttt{drawoptions}}
\end{table}

åÓÔØ ÅÝÅ Ä×Å ÐÒÉÍÉÔÉ×ÎÙÅ ÒÉÓÕÀÝÉÅ ËÏÍÁÎÄÙ, ÎÅÄÏÐÕÓËÁÀÝÉÅ ÎÉËÁËÉÈ ÏÐÃÉÊ 
ÒÉÓÏ×ÁÎÉÑ. 
%%There are two more primitive drawing commands that do not accept any
%%drawing options. 
ðÅÒ×ÁÑ --- ÜÔÏ {\tt setbounds}, ÏÂÓÕÖÄÁÅÍÁÑ × 
ÒÁÚÄÅÌÅ~\ref{meas}; ×ÔÏÒÁÑ --- ÜÔÏ {\tt clip}\index{clip?\texttt{clip}}\label{Dclip}:
$$ {\tt clip}\, \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ}\, {\tt to}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} $$
%%One is the {\tt setbounds} command that was discussed
%%in Section~\ref{meas}; the other is the {\tt clip}
%%command\index{clip?\texttt{clip}}\label{Dclip}:
%%$$ {\tt clip}\, \descr{picture variable}\, {\tt to}\, \descr{path expression} $$
ðÏ ÄÁÎÎÏÍÕ ÃÉËÌÉÞÅÓËÏÍÕ ÐÕÔÉ, ËÏÍÁÎÄÁ {\tt clip} ÏÂÒÅÚÁÅÔ ÓÏÄÅÒÖÉÍÏÅ 
\tdescr{ÐÅÒÅÍÅÎÎÏÊ-ËÁÒÔÉÎËÉ} ÔÁË, ÞÔÏ ÕÄÁÌÑÅÔÓÑ ×ÓÅ, ÞÔÏ ÏËÁÚÙ×ÁÅÔÓÑ ÓÎÁÒÕÖÉ 
ÃÉËÌÉÞÅÓËÏÇÏ ÐÕÔÉ.
%%Given a cyclic path, this statement trims the contents of the
%%\tdescr{picture variable} to eliminate everything outside of the cyclic path.
îÅÔ ``×ÙÓÏËÏÕÒÏ×ÎÅ×ÏÊ'' ×ÅÒÓÉÉ ÜÔÏÊ ËÏÍÁÎÄÙ, ÔÁË ÞÔÏ ×Ù ÄÏÌÖÎÙ ÉÓÐÏÌØÚÏ×ÁÔØ 
$$ {\tt clip\ currentpicture\ to}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}, $$
ÅÓÌÉ ×Ù ÈÏÔÉÔÅ ÏÂÒÅÚÁÔØ {\tt
currentpicture}\index{currentpicture?\texttt{currentpicture}}.
%%There is no ``high level'' version of this statement, so you have to use
%%$$ {\tt clip\ currentpicture\ to}\, \descr{path expression} $$
%%if you want to clip {\tt
%%currentpicture}\index{currentpicture?\texttt{currentpicture}}.
òÉÓ.~\ref{fig40} ÉÌÌÀÓÔÒÉÒÕÅÔ ÏÂÒÅÚËÕ.
%%Figure~\ref{fig40} illustrates clipping.

\begin{figure}[htp]
$$\begin{verbatim}
beginfig(40);
path p[];
p1 = (0,0){curl 0}..(5pt,-3pt)..{curl 0}(10pt,0);
p2 = p1..(p1 yscaled-1 shifted(10pt,0));
p0 = p2;
for i=1 upto 3:  p0:=p0.. p2 shifted (i*20pt,0);
  endfor
for j=0 upto 8:  draw p0 shifted (0,j*10pt);
  endfor
p3 = fullcircle shifted (.5,.5) scaled 72pt;
clip currentpicture to p3;
draw p3;
endfig;
\end{verbatim}
\qquad
\mathcenter{\includegraphics{manfig-ru-40}}
$$
\caption{ëÏÄ MetaPost É ×ÙÒÅÚÁÎÎÁÑ ËÁÒÔÉÎËÁ-ÒÅÚÕÌØÔÁÔ.}
%%\caption{MetaPost code and the resulting ``clipped'' figure.}
\label{fig40}
\end{figure}

÷ÓÅ ÐÒÉÍÉÔÉ×ÎÙÅ ÏÐÅÒÁÃÉÉ ÒÉÓÏ×ÁÎÉÑ ÂÙÌÉ ÂÙ ÂÅÓÐÏÌÅÚÎÙ ÂÅÚ ÐÏÓÌÅÄÎÅÊ 
ÏÐÅÒÁÃÉÉ Ó ÉÍÅÎÅÍ {\tt shipout}. 
%%All the primitive drawing operations would be useless without one last
%%operation called {\tt shipout}. 
ëÏÍÁÎÄÁ \index{shipout?\texttt{shipout}}\label{Dship}
$$ {\tt shipout}\, \descr{×ÙÒÁÖÅÎÉÅ-ÒÉÓÕÎÏË} $$
ÐÉÛÅÔ ËÁÒÔÉÎËÕ, ËÁË ÆÁÊÌ PostScript\index{PostScript}, ÞØÅ ÉÍÑ 
ÏÐÒÅÄÅÌÑÅÔÓÑ ÚÎÁÞÅÎÉÅÍ {\tt filenametemplate}\index{filenametemplate?\texttt{filenametemplate}}
(ÓÍ. ÒÁÚÄÅÌ~\ref{Dfilenametemplate}). 
%%The statement\index{shipout?\texttt{shipout}}\label{Dship}
%%$$ {\tt shipout}\, \descr{picture expression} $$
%%writes out a picture as a PostScript\index{PostScript} file whose
%%file name is determined by
%%{\tt filenametemplate}\index{filenametemplate?\texttt{filenametemplate}}
%%(see section~\ref{Dfilenametemplate}). 
ïÂÙÞÎÏ ÉÍÑ ÆÁÊÌÁ ÚÁËÁÎÞÉ×ÁÅÔÓÑ ÎÁ {\tt.}{\it nnn}, ÇÄÅ {\tt nnn} --- ÜÔÏ 
ÄÅÓÑÔÉÞÎÏÅ ÐÒÅÄÓÔÁ×ÌÅÎÉÅ ÚÎÁÞÅÎÉÑ ×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ\index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} {\tt
charcode}\index{charcode?\texttt{charcode}}\label{Dcharcode}. 
%%By default, the file name ends
%%{\tt.}{\it nnn}, where {\tt nnn} is the decimal representation
%%of the value of the internal variable\index{internal
%%variables}\index{variables!internal} {\tt
%%charcode}\index{charcode?\texttt{charcode}}\label{Dcharcode}. 
éÍÑ ``{\tt charcode}'' ÉÓÐÏÌØÚÕÅÔÓÑ ÄÌÑ ÓÏ×ÍÅÓÔÉÍÏÓÔÉ 
Ó \MF\index{metafont?\MF}.
%%(The name
%%``{\tt charcode}'' is for compatibility with \MF\index{metafont?\MF}.)
ëÁË ÐÒÁ×ÉÌÏ, {\tt beginfig}\index{beginfig?\texttt{beginfig}} ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ 
{\tt charcode}, Á {\tt endfig}\index{endfig?\texttt{endfig}} ×ÙÚÙ×ÁÅÔ {\tt
shipout}.
%%Normally, {\tt beginfig}\index{beginfig?\texttt{beginfig}} sets {\tt
%%charcode}, and {\tt endfig}\index{endfig?\texttt{endfig}} invokes {\tt
%%shipout}.

\subsection{îÁÐÒÁ×ÌÅÎÉÅ ×Ù×ÏÄÁ × ÐÅÒÅ\-ÍÅÎÎÕÀ-ËÁÒÔÉÎËÕ}
%%\subsection{Directing Output to a Picture Variable}

éÎÏÇÄÁ ÍÏÖÅÔ ÂÙÔØ ÖÅÌÁÔÅÌØÎÏ ÓÏÈÒÁÎÉÔØ ×Ù×ÏÄ ÒÉÓÕÀÝÉÈ ÏÐÅÒÁÃÉÊ É 
ÉÓÐÏÌØÚÏ×ÁÔØ ÅÇÏ ÐÏÔÏÍ.
%%Sometimes, it might be desirable to save the output of a drawing
%%operation and re-use them later. 
üÔÏ ÍÏÖÅÔ ÂÙÔØ ÌÅÇËÏ ÓÄÅÌÁÎÏ ÐÒÉÍÉÔÉ×ÁÍÉ MetaPost ÔÉÐÁ \ttt{addto}. 
%%This can easily be done with
%%MetaPost primitives like \ttt{addto}. 
ó ÄÒÕÇÏÊ ÓÔÏÒÏÎÙ, ÉÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ×ÙÓÏËÏÕÒÏ×ÎÅ×ÙÅ ËÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ, 
ÏÐÒÅÄÅÌÅÎÎÙÅ × ÍÁËÒÏÐÁËÅÔÅ Plain, ×ÓÅÇÄÁ ÐÉÛÕÔ × \ttt{currentpicture}\index{currentpicture?\texttt{currentpicture}},
ÓÏÈÒÁÎÅÎÉÅ ÉÈ ×Ù×ÏÄÁ ÔÒÅÂÕÅÔ ×ÒÅÍÅÎÎÏÇÏ ÓÏÈÒÁÎÅÎÉÑ \ttt{currentpicture},  
ÚÁÔÅÍ ÓÂÒÏÓÁ ÅÅ × \ttt{nullpicture}\index{nullpicture?\texttt{nullpicture}},
ÚÁÔÅÍ ÉÓÐÏÌÎÅÎÉÑ ÒÉÓÕÀÝÉÈ ÏÐÅÒÁÃÉÊ, ÚÁÔÅÍ ÚÁÐÉÓÉ ÚÎÁÞÅÎÉÑ \ttt{currentpicture} 
× ÎÏ×ÕÀ ÐÅÒÅÍÅÎÎÕÀ ÔÉÐÁ \ttt{picture} É, ÎÁËÏÎÅÃ, ×ÏÓÓÔÁÎÏ×ÌÅÎÉÑ 
\ttt{currentpicture} × ÉÓÈÏÄÎÏÅ ÓÏÓÔÏÑÎÉÅ. 
%%On the other hand, since the
%%higher-level drawing commands defined in the Plain macro package
%%always write to the
%%\ttt{currentpicture}\index{currentpicture?\texttt{currentpicture}},
%%saving their output required to temporarily save \ttt{currentpicture},
%%reset it to \ttt{nullpicture}\index{nullpicture?\texttt{nullpicture}},
%%execute the drawing operations, save the \ttt{currentpicture} to a
%%new \ttt{picture} variable and finally restore \ttt{currentpicture} to
%%the saved state. 
÷ MetaPost ×ÅÒÓÉÉ~0.60 ÎÏ×ÙÊ ÍÁËÒÏÓ 
$$ \hbox{\tt image( $\descr{ËÏÍÁÎÄÙ ÒÉÓÏ×ÁÎÉÑ}$ )} $$%
\index{image?\texttt{image}}\label{Dimage}%
××ÏÄÉÔÓÑ ÄÌÑ ÕÐÒÏÝÅÎÉÑ ÜÔÏÇÏ ÚÁÄÁÎÉÑ. 
%%In MetaPost version~0.60 a new macro
%%$$ \hbox{\tt image( $\descr{drawing commands}$ )} $$%
%%\index{image?\texttt{image}}\label{Dimage}%
%%was introduced that eases this task. 
ïÎ ×ÏÓÐÒÉÎÉÍÁÅÔ ËÁË ××ÏÄ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÐÒÏÉÚ×ÏÌØÎÙÈ ÏÐÅÒÁÃÉÊ 
ÒÉÓÏ×ÁÎÉÑ É ×ÏÚ×ÒÁÝÁÅÔ ÐÅÒÅÍÅÎÎÕÀ ÔÉÐÁ \ttt{picture}, ÓÏÄÅÒÖÁÝÕÀ 
ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ×Ù×ÏÄ, ÂÅÚ ×ÌÉÑÎÉÑ ÎÁ {\tt currentpicture}.
%%It takes as input a sequence of arbitrary
%%drawing operations and returns a \ttt{picture} variable containing the
%%corresponding output, without affecting {\tt currentpicture}.

îÁÐÒÉÍÅÒ, × ËÏÄÅ ÒÉÓ.~\ref{fig55} ÏÂßÅËÔ \ttt{wheel} ÏÐÒÅÄÅÌÑÅÔÓÑ 
ÓÏÈÒÁÎÅÎÉÅÍ ×Ù×ÏÄÁ Ä×ÕÈ ÏÐÅÒÁÃÉÊ \ttt{draw} (ÓÍ. ËÏÄ).
%%As an example, in the code of figure~\ref{fig55} an object \ttt{wheel} has
%%been defined that saves the output of two \ttt{draw} operations as follows:
\begin{figure}[b]
$$ \includegraphics{manfig-ru-55} $$
\caption{ëÏÐÉÒÏ×ÁÎÉÅ ÏÂßÅËÔÏ× ÏÐÅÒÁÔÏÒÏÍ \ttt{image}.}
%%\caption{Copying objects with the \ttt{image} operator.}
\label{fig55}
\end{figure}
$$\begin{verbatim}
picture wheel;
wheel := image(
  draw fullcircle scaled 2u xscaled .8 rotated 30;
  draw fullcircle scaled .15u xscaled .8 rotated 30;
);
\end{verbatim}
$$
ïÂßÅËÔ \ttt{wheel} ÐÏ×ÔÏÒÎÏ ÉÓÐÏÌØÚÕÅÔÓÑ × ÏÐÒÅÄÅÌÅÎÉÉ ÄÒÕÇÏÇÏ ÏÂßÅËÔÁ \ttt{car}.
%%This \ttt{wheel} object is re-used in the definition of another object \ttt{car}.
òÉÓ.~\ref{fig55} ÐÏËÁÚÙ×ÁÅÔ ÔÒÉ ÏÂßÅËÔÁ \ttt{car}, ÎÁÒÉÓÏ×ÁÎÎÙÅ Ó Ä×ÕÍÑ ÒÁÚÎÙÍÉ 
ÚÎÁÞÅÎÉÑÍÉ ÎÁËÌÏÎÁ.
%%Figure~\ref{fig55} shows three \ttt{car} objects drawn with two different slant
%%values.

\subsection{òÁÂÏÔÁ Ó ËÏÍÐÏÎÅÎÔÁÍÉ ÒÉÓÕÎËÁ}
%%\subsection{Inspecting the Components of a Picture}
\label{piccomp}

\mbox{}% Start paragraph here.
\index{setbounds?\texttt{setbounds}|(}%
\index{for within?\texttt{for within}|(}%
%
òÉÓÕÎËÉ MetaPost ÓÏÓÔÁ×ÌÑÀÔÓÑ ÉÚ ÎÁÒÉÓÏ×ÁÎÎÙÈ ÌÉÎÉÊ, ÚÁÐÏÌÎÅÎÎÙÈ 
ËÏÎÔÕÒÏ×, ÔÅËÓÔÏ×ÙÈ ÆÒÁÇÍÅÎÔÏ×, ÐÕÔÅÊ ÄÌÑ ×ÙÒÅÚËÉ\index{clip?\texttt{clip}} É 
ÐÕÔÅÊ {\tt setbounds}\index{setbounds?\texttt{setbounds}}. 
%%MetaPost pictures are composed of stroked lines, filled outlines, pieces
%%of typeset text, clipping paths\index{clip?\texttt{clip}}, and
%%{\tt setbounds}\index{setbounds?\texttt{setbounds}} paths. 
ðÕÔØ {\tt setbounds} ÄÁÅÔ ÉÓËÕÓÓÔ×ÅÎÎÕÀ ÏÈ×ÁÔÙ×ÁÀÝÕÀ ÒÁÍËÕ, ÎÕÖÎÕÀ ÄÌÑ  
×Ù×ÏÄÁ \TeX.
%%(A {\tt setbounds}
%%path gives an artificial bounding box as is needed for \TeX\ output.)
òÉÓÕÎÏË ÍÏÖÅÔ ÉÍÅÔØ ÍÎÏÇÏ ËÏÍÐÏÎÅÎÔ ËÁÖÄÏÇÏ ÔÉÐÁ.
%%A picture can have many components of each type. 
üÔÉ ËÏÍÐÏÎÅÎÔÙ ÄÏÓÔÕÐÎÙ ÞÅÒÅÚ ÉÔÅÒÁÃÉÀ × ÆÏÒÍÅ 
$$ {\tt for}\ \descr{ÓÉÍ×ÏÌØÎÙÊ ÚÎÁË}\ {\tt within}\
     \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ}\hbox{\tt:}\ \descr{ÔÅÌÏ ÃÉËÌÁ}\ {\tt endfor}
$$\index{for within?\texttt{for within}}\label{Dforwithin}%
%%They can be accessed via an iteration of the form
%%$$ {\tt for}\ \descr{symbolic token}\ {\tt within}\
%%     \descr{picture expression}\hbox{\tt:}\ \descr{loop text}\ {\tt endfor}
%%$$\index{for within?\texttt{for within}}\label{Dforwithin}%
\tdescr{ôÅÌÏ ÃÉËÌÁ} ÍÏÖÅÔ ÂÙÔØ ÞÅÍ-ÕÇÏÄÎÏ, ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÍ ÏÔÎÏÓÉÔÅÌØÎÏ 
{\tt for} É {\tt endfor}. 
%%The \tdescr{loop text} can be anything that is balanced with respect to
%%{\tt for} and {\tt endfor}. 
\tdescr{óÉÍ×ÏÌØÎÙÊ ÚÎÁË} --- ÜÔÏ ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ ÄÌÑ ÃÉËÌÁ, 
ÓËÁÎÉÒÕÀÝÁÑ ËÏÍÐÏÎÅÎÔÙ ÒÉÓÕÎËÁ × ÐÏÒÑÄËÅ ÉÈ ÒÉÓÏ×ÁÎÉÑ.
%%The \tdescr{symbolic token} is a loop variable that
%%scans the components of the picture in the order in which they were drawn. 
ëÏÍÐÏÎÅÎÔÁ ÄÌÑ ÐÕÔÉ ×ÙÒÅÚËÉ ÉÌÉ {\tt setbounds} ×ËÌÀÞÁÅÔ ×ÓÅ, Ë ÞÅÍÕ 
ÐÒÉÍÅÎÑÅÔÓÑ ÐÕÔØ.
%%The
%%component for a clipping or {\tt setbounds} path includes everything the path
%%applies to. 
ðÏÜÔÏÍÕ, ÅÓÌÉ ÏÄÉÎÏÞÎÙÊ ÐÕÔØ ×ÙÒÅÚËÉ ÉÌÉ {\tt setbounds} ÐÒÉÍÅÎÑÅÔÓÑ ËÏ
×ÓÅÍÕ × \tdescr{×ÙÒÁÖÅÎÉÉ-ËÁÒÔÉÎËÅ}, ÔÏ ×ÓÑ ËÁÒÔÉÎËÁ ÍÏÖÅÔ ÒÁÓÓÍÁÔÒÉ×ÁÔØÓÑ 
ËÁË ÏÄÎÁ ÂÏÌØÛÁÑ ËÏÍÐÏÎÅÎÔÁ.
%%Thus if a single clipping or {\tt setbounds} path applies to
%%everything in the \tdescr{picture expression}, the whole picture could be
%%thought of as one big component. 
äÌÑ ÔÏÇÏ, ÞÔÏÂÙ ÓÏÄÅÒÖÉÍÏÅ ÔÁËÏÊ ËÁÒÔÉÎËÉ ÂÙÌÏ ÄÏÓÔÕÐÎÙÍ, ÉÔÅÒÁÃÉÑ 
{\tt for}\ldots{\tt within} ÉÇÎÏÒÉÒÕÅÔ ÏÈ×ÁÔÙ×ÁÀÝÉÊ ÐÕÔØ ×ÙÒÅÚËÉ ÉÌÉ 
{\tt setbounds} × ÜÔÏÍ ÓÌÕÞÁÅ.
%%In order to make the contents of such a picture
%%accessible, the {\tt for}\ldots{\tt within} iteration ignores the enclosing
%%clipping or {\tt setbounds} path in this case.
þÉÓÌÏ ËÏÍÐÏÎÅÎÔ, ÎÁÈÏÄÉÍÙÈ ÉÔÅÒÁÃÉÅÊ {\tt for}\ldots {\tt within}, ×ÏÚ×ÒÁÝÁÅÔÓÑ 
$$ {\tt length}\ \descr{ÒÉÓÕÎÏË-ÐÅÒ×ÉÞÎÏÓÔØ}\index{length?\texttt{length}}\label{DlengthPicture}$$
%%The number of components
%%that a {\tt for}\ldots {\tt within} iteration would find is returned by
%%$$ {\tt length}\ \descr{picture primary}\index{length?\texttt{length}}\label{DlengthPicture}$$

\index{for within?\texttt{for within}|)}
\mbox{}% Start paragraph here.
\index{stroked?\texttt{stroked}|(}%
\index{filled?\texttt{filled}|(}%
\index{textual?\texttt{textual}|(}%
\index{clipped?\texttt{clipped}|(}%
\index{bounded?\texttt{bounded}|(}%
%
ëÁË ÔÏÌØËÏ ÉÔÅÒÁÃÉÑ {\tt for}\ldots{\tt within} ÎÁÈÏÄÉÔ ËÏÍÐÏÎÅÎÔ ËÁÒÔÉÎËÉ, 
ÓÒÁÚÕ ×ÏÚÎÉËÁÅÔ ÒÑÄ ÏÐÅÒÁÔÏÒÏ× ÄÌÑ ÅÇÏ ÉÄÅÎÔÉÆÉËÁÃÉÉ É ÐÏÌÕÞÅÎÉÑ 
ÏÔÎÏÓÑÝÅÊÓÑ Ë ÎÅÍÕ ÉÎÆÏÒÍÁÃÉÉ.
%%Once the {\tt for}\ldots{\tt within} iteration has found a picture component,
%%there are numerous operators for identifying it and extracting relevant
%%information. 
ïÐÅÒÁÔÏÒ 
$$ {\tt stroked}\ \descr{ÐÅÒ×ÉÞÎÏÅ ×ÙÒÁÖÅÎÉÅ} $$\index{stroked?\texttt{stroked}}\label{Dstroked}%
ÐÒÏ×ÅÒÑÅÔ, Ñ×ÌÑÅÔÓÑ ÌÉ ×ÙÒÁÖÅÎÉÅ ÉÚ×ÅÓÔÎÏÊ ËÁÒÔÉÎËÏÊ, ÞÅÊ ÐÅÒ×ÙÊ 
ËÏÍÐÏÎÅÎÔ --- ÜÔÏ ÉÚÏÂÒÁÖÅÎÎÁÑ ÌÉÎÉÑ.
%%The operator
%%$$ {\tt stroked}\ \descr{primary expression} %%$$\index{stroked?\texttt{stroked}}\label{Dstroked}%
%%tests whether the expression is a known picture whose first component is a
%%stroked line. 
áÎÁÌÏÇÉÞÎÙÍ ÏÂÒÁÚÏÍ, ÏÐÅÒÁÔÏÒÙ {\tt filled}\index{filled?\texttt{filled}}\label{Dfilled}
É {\tt textual}\index{textual?\texttt{textual}}\label{Dtextual} 
×ÏÚ×ÒÁÝÁÀÔ {\tt true}, ÅÓÌÉ ÐÅÒ×ÙÊ ËÏÍÐÏÎÅÎÔ --- ÜÔÏ 
ÓÏÏÔ×ÅÔÓÔ×ÅÎÎÏ ÚÁÐÏÌÎÅÎÎÙÊ ËÏÎÔÕÒ ÉÌÉ ÆÒÁÇÍÅÎÔ ÔÅËÓÔÁ.
%%Similarly, the {\tt filled}\index{filled?\texttt{filled}}\label{Dfilled}
%%and {\tt textual}\index{textual?\texttt{textual}}\label{Dtextual} operators
%%return {\tt true} if the first component is a filled outline or a piece of
%%typeset text. 
ïÐÅÒÁÔÏÒÙ {\tt clipped}\index{clipped?\texttt{clipped}}\label{Dclipped}
É {\tt bounded}\index{bounded?\texttt{bounded}}\label{Dbounded} 
ÐÒÏ×ÅÒÑÀÔ, Ñ×ÌÑÅÔÓÑ ÌÉ ÁÒÇÕÍÅÎÔ ËÁÒÔÉÎËÏÊ, ÎÁÞÉÎÁÀÝÅÊÓÑ Ó ÐÕÔÉ ×ÙÒÅÚËÉ 
ÉÌÉ {\tt setbounds}.
%%The {\tt clipped}\index{clipped?\texttt{clipped}}\label{Dclipped}
%%and {\tt bounded}\index{bounded?\texttt{bounded}}\label{Dbounded} operators
%%test whether the argument is a known picture that starts with a clipping
%%path or a {\tt setbounds} path. 
ïÎÉ ÂÕÄÕÔ ÉÓÔÉÎÎÙ, ÅÓÌÉ ÐÅÒ×ÁÑ ËÏÍÐÏÎÅÎÔÁ ×ÙÒÅÚÁÎÁ ÉÌÉ ÏÇÒÁÎÉÞÅÎÁ (ËÏÍÁÎÄÏÊ 
{\tt setbounds}) ÉÌÉ ÅÓÌÉ ×ÓÑ ËÁÒÔÉÎËÁ ÚÁËÌÀÞÅÎÁ × ÐÕÔØ ×ÙÒÅÚËÉ 
ÉÌÉ {\tt setbounds}.
%%This is true if the first component is
%%clipped or bounded or if the entire picture is enclosed in a clipping or
%%{\tt setbounds} path.

\mbox{}% Start paragraph here.
\index{pathpart?\texttt{pathpart}|(}%
\index{penpart?\texttt{penpart}|(}%
\index{dashpart?\texttt{dashpart}|(}%
%
åÓÔØ ÅÝÅ ÒÑÄ ÏÐÅÒÁÔÏÒÏ× ÉÚ×ÌÅÞÅÎÉÑ ÞÁÓÔÅÊ, ÐÒÉÍÅÎÑÅÍÙÈ Ë ÐÅÒ×ÏÊ 
ËÏÍÐÏÎÅÎÔÅ ÒÉÓÕÎËÁ.
%%There are also numerous part extraction operators that test the first component
%%of a picture. 
åÓÌÉ {\tt p} --- ÜÔÏ ËÁÒÔÉÎËÁ É {\tt stroked p} --- ÉÓÔÉÎÎÏ, ÔÏ
{\tt pathpart p}\index{pathpart?\texttt{pathpart}}\label{Dpathpart} --- ÜÔÏ 
ÐÕÔØ, ÏÐÉÓÙ×ÁÀÝÉÊ ÎÁÒÉÓÏ×ÁÎÎÕÀ ÌÉÎÉÀ, 
{\tt penpart p}\index{penpart?\texttt{penpart}}\label{Dpenpart} --- ÜÔÏ 
ÉÓÐÏÌØÚÏ×ÁÎÎÏÅ ÐÅÒÏ, {\tt dashpart p}\index{dashpart?\texttt{dashpart}}\label{Ddashpart} --- 
ÜÔÏ ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÁ.
%%If {\tt p} is a picture and {\tt stroked p} is true,
%%{\tt pathpart p}\index{pathpart?\texttt{pathpart}}\label{Dpathpart} is the
%%path describing the line that got stroked,
%%{\tt penpart p}\index{penpart?\texttt{penpart}}\label{Dpenpart} is the pen
%%that was used, {\tt dashpart p}\index{dashpart?\texttt{dashpart}}\label{Ddashpart}
%%is the dash pattern.
åÓÌÉ ÌÉÎÉÑ ÂÅÚ ÒÁÚÒÙ×Ï×, ÔÏ {\tt dashpart p} ×ÏÚ×ÒÁÝÁÅÔ ÐÕÓÔÕÀ ËÁÒÔÉÎËÕ.
%%If the line is not dashed, {\tt dashpart p} returns an empty picture.

ôÁËÉÅ ÖÅ ÏÐÅÒÁÔÏÒÙ ÄÌÑ ÉÚ×ÌÅÞÅÎÉÑ ÞÁÓÔÅÊ ÒÁÂÏÔÁÀÔ, ËÏÇÄÁ {\tt filled p} --- 
ÉÓÔÉÎÎÏ, ÚÁ ÉÓËÌÀÞÅÎÉÅÍ ÔÏÇÏ, ÞÔÏ {\tt dashpart p} ÎÅ ÉÍÅÅÔ ÓÍÙÌÁ × ÜÔÏÍ 
ÓÌÕÞÁÅ.
%%The same part extraction operators work when {\tt filled p} is true, except
%%that {\tt dashpart p} is not meaningful in that case. 

äÌÑ ÔÅËÓÔÏ×ÙÈ ÆÒÁÇÍÅÎÔÏ×, ËÏÇÄÁ {\tt textual p} --- ÉÓÔÉÎÎÏ,
{\tt textpart p}\index{textpart?\texttt{textpart}}\label{Dtextpart}
ÄÁÅÔ ÎÁÐÅÞÁÔÁÎÎÙÊ ÔÅËÓÔ,
{\tt fontpart p}\index{fontpart?\texttt{fontpart}}\label{Dfontpart}
--- ÉÓÐÏÌØÚÕÅÍÙÊ ÛÒÉÆÔ É {\tt xpart~p}\index{xpart?\texttt{xpart}}\index{ypart?\texttt{ypart}}\index{xxpart?\texttt{xxpart}}%
\index{xypart?\texttt{xypart}}\index{yxpart?\texttt{yxpart}}\index{yypart?\texttt{yypart}},
{\tt ypart~p}, {\tt xxpart~p}, {\tt xypart~p}, {\tt yxpart~p}, {\tt yypart~p}
ÐÏËÁÚÙ×ÁÀÔ, ËÁË ÔÅËÓÔ ÓÄ×ÉÇÁÌÓÑ, ×ÒÁÝÁÌÓÑ É ÍÁÓÛÔÁÂÉÒÏ×ÁÌÓÑ. 
%%For text components,
%%{\tt textual p} is true,
%%{\tt textpart p}\index{textpart?\texttt{textpart}}\label{Dtextpart}
%%gives the text that got typeset,
%%{\tt fontpart p}\index{fontpart?\texttt{fontpart}}\label{Dfontpart}
%%gives the font that was used, and {\tt %%xpart~p}\index{xpart?\texttt{xpart}}\index{ypart?\texttt{ypart}}\index{xxpart?\tex%%ttt{xxpart}}%
%%\index{xypart?\texttt{xypart}}\index{yxpart?\texttt{yxpart}}\index{yypart?\texttt{%%yypart}},
%%{\tt ypart~p}, {\tt xxpart~p}, {\tt xypart~p}, {\tt yxpart~p}, {\tt yypart~p}
%%tell how the text has been shifted, rotated, and scaled. 

îÁËÏÎÅÃ, ÄÌÑ ËÏÍÐÏÎÅÎÔ \ttt{stroked}, \ttt{filled} É \ttt{textual}  
ÍÏÖÎÏ ÐÏÌÕÞÉÔØ Ã×ÅÔ, ÓËÁÚÁ×
$$ {\tt colorpart}\
\descr{ËÏÍÐÏÎÅÎÔÁ}\index{colorpart?\texttt{colorpart}}\label{Dcolorpart}
$$
%%Finally, for \ttt{stroked}, \ttt{filled} and \ttt{textual} components
%%the color can be examined by saying
%%$$ {\tt colorpart}\
%%\descr{item}\index{colorpart?\texttt{colorpart}}\label{Dcolorpart}
%%$$
üÔÏ ×ÏÚ×ÒÁÝÁÅÔ Ã×ÅÔ ËÏÍÐÏÎÅÎÔÙ × ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÊ ÍÏÄÅÌÉ Ã×ÅÔÁ. 
%%This returns the color of a component in its respective color model.
íÏÄÅÌØ Ã×ÅÔÁ ËÏÍÐÏÎÅÎÔÙ ÍÏÖÅÔ ÂÙÔØ ÉÄÅÎÔÉÆÉÃÉÒÏ×ÁÎÁ ÏÐÅÒÁÔÏÒÏÍ 
\ttt{colormodel}\index{colormodel?\texttt{colormodel}}\label{Dcolormodel}
(ÓÍ. ÔÁÂÌÉÃÕ~\ref{dfltcmod} ÎÁ ÓÔÒ.~\pageref{dfltcmod}). 
%%The color model of a component can be identified by the
%%\ttt{colormodel}\index{colormodel?\texttt{colormodel}}\label{Dcolormodel}
%%operator (cf. Table~\ref{dfltcmod} on p.~\pageref{dfltcmod}).

äÌÑ ÂÏÌÅÅ ÄÅÔÁÌØÎÙÈ ÏÐÅÒÁÃÉÊ ÓÏ Ã×ÅÔÏÍ ÅÓÔØ ÏÐÅÒÁÔÏÒÙ ÄÌÑ ÉÚ×ÌÅÞÅÎÉÑ ÏÔÄÅÌØÎÙÈ  
ÓÏÓÔÁ×ÌÑÀÝÉÈ Ã×ÅÔÁ ÉÚ ËÏÍÐÏÎÅÎÔÙ ÒÉÓÕÎËÁ.
%%For more fine grained color operations there are operators to extract
%%single color components of an item.  
÷ ÚÁ×ÉÓÉÍÏÓÔÉ ÏÔ ÍÏÄÅÌÉ Ã×ÅÔÁ Ã×ÅÔ ËÏÍÐÏÎÅÎÔÙ ÒÉÓÕÎËÁ \ttt{p} --- ÜÔÏ 
$$ \hbox{\tt (cyanpart p, magentapart p, yellowpart p, blackpart p)} $$%
\index{cyanpart?\texttt{cyanpart}}\index{magentapart?\texttt{magentapart}}\index{yellowpart?\texttt{yellowpart}}\index{blackpart?\texttt{blackpart}}
ÉÌÉ 
$$ \hbox{\tt (redpart p, greenpart p, bluepart p)} $$%
\index{redpart?\texttt{redpart}}\index{greenpart?\texttt{greenpart}}\index{bluepart?\texttt{bluepart}}
ÉÌÉ 
$$ \hbox{\tt (greypart p)} $$%
\index{greypart?\texttt{greypart}}
ÉÌÉ 
$$ \hbox{\tt false}. $$
%%Depending on the color model the color of a picture component \ttt{p} is
%%$$ \hbox{\tt (cyanpart p, magentapart p, yellowpart p, blackpart p)} $$%
%%\index{cyanpart?\texttt{cyanpart}}\index{magentapart?\texttt{magentapart}}\index{yellowpart?\texttt{yellowpart}}\index{blackpart?\texttt{blackpart}}
%%or
%%$$ \hbox{\tt (redpart p, greenpart p, bluepart p)} $$%
%%\index{redpart?\texttt{redpart}}\index{greenpart?\texttt{greenpart}}\index{bluepart?\texttt{bluepart}}
%%or
%%$$ \hbox{\tt greypart p} $$%
%%\index{greypart?\texttt{greypart}}
%%or
%%$$ \hbox{\tt false}. $$

úÁÍÅÔØÔÅ, ÞÔÏ ÏÐÅÒÁÔÏÒÙ ÞÁÓÔÅÊ Ã×ÅÔÁ {\tt redpart}, {\tt cyanpart} É Ô.~Ð. 
ÄÏÌÖÎÙ ÓÏÏÔ×ÅÔÓÔ×Ï×ÁÔØ ÍÏÄÅÌÉ Ã×ÅÔÁ ËÏÍÐÏÎÅÎÔÁ ÒÉÓÕÎËÁ × ×ÏÐÒÏÓÅ.
%%Note, color part operators {\tt redpart}, {\tt cyanpart} etc. have to
%%match the color model of the picture component in question. 
ðÒÉÍÅÎÅÎÉÅ ÎÅÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÇÏ ÏÐÅÒÁÔÏÒÁ ÞÁÓÔÉ Ã×ÅÔÁ Ë ËÏÍÐÏÎÅÎÔÕ ËÁÒÔÉÎËÉ 
ÉÎÉÃÉÉÒÕÅÔ ÏÛÉÂËÕ É ×ÏÚ×ÒÁÝÁÅÔ ÞÁÓÔØ Ã×ÅÔÁ \ttindex{black} × ÚÁÐÒÏÛÅÎÎÏÊ 
ÍÏÄÅÌÉ Ã×ÅÔÁ.
%%Applying a non-matching color part
%%operator to a picture component triggers an error and returns 
%%a \ttindex{black} color part in the requested color model.
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÄÌÑ ËÏÄÁ
%%That is, for the code
$$\begin{verbatim}
picture pic;
pic := image(fill unitsquare scaled 1cm withcolor (0.3, 0.6, 0.9););
for item within pic:
  show greypart item;
  show cyanpart item;
  show blackpart item;
  show redpart item;
endfor
\end{verbatim}
$$
×Ù×ÏÄÏÍ ÂÕÄÅÔ (ÓÏÏÂÝÅÎÉÑ Ï ÏÛÉÂËÁÈ ÏÐÕÝÅÎÙ)
%%the output is (omitting the error messages)
$$\begin{verbatim}
>> 0
>> 0
>> 1
>> 0.3,
\end{verbatim}
$$
ÐÏÔÏÍÕ ÞÔÏ × ÍÏÄÅÌÉ ÏÔÔÅÎËÏ× ÓÅÒÏÇÏ ÞÅÒÎÙÊ --- ÜÔÏ {\tt 0}, Á × ÍÏÄÅÌÉ 
cmyk-Ã×ÅÔÏ× ÞÅÒÎÙÊ --- ÜÔÏ {\tt (0,0,0,1)}. 
%%since in grey scale color model black is {\tt 0} and in CMYK color model
%%black is {\tt (0, 0, 0, 1)}. 
äÌÑ ÐÏÄÏÛÅÄÛÅÊ ÍÏÄÅÌÉ rgb-Ã×ÅÔÁ ÂÙÌ ×ÏÚ×ÒÁÝÅÎ ×ÅÒÎÙÊ Ã×ÅÔÏ×ÏÊ ËÏÍÐÏÎÅÎÔ.
%%For the matching RGB color model the true
%%color component is returned.

ëÏÇÄÁ {\tt clipped p} ÉÌÉ {\tt bounded p} --- ÉÓÔÉÎÎÏ, ÔÏ {\tt pathpart p} 
ÄÁÅÔ ÐÕÔØ ×ÙÒÅÚËÉ ÉÌÉ {\tt setbounds}, Á ÄÒÕÇÉÅ ÏÐÅÒÁÔÏÒÙ ÉÚ×ÌÅÞÅÎÉÑ ÞÁÓÔÅÊ 
ÎÅ ÉÍÅÀÔ ÓÍÙÓÌÁ.
%%When {\tt clipped p} or {\tt bounded p} is true, {\tt pathpart p} gives the
%%clipping or {\tt setbounds} path and the other part extraction operators are
%%not meaningful. 
ôÁËÉÅ ÎÅ ÉÍÅÀÝÉÅ ÓÍÙÓÌÁ ÐÏÌÕÞÅÎÉÑ ÞÁÓÔÅÊ ÎÅ ÇÅÎÅÒÉÒÕÀÔ ÏÛÉÂÏË.
%%Such non-meaningful part extractions do not generate
%%errors.
ïÎÉ ×ÍÅÓÔÏ ÜÔÏÇÏ ×ÏÚ×ÒÁÝÁÀÔ (ËÏÍÐÏÎÅÎÔÙ) ÎÕÌÅ×ÙÅ ÚÎÁÞÅÎÉÑ ÉÌÉ ÞÅÒÎÙÊ Ã×ÅÔ: 
ÐÕÓÔÏÊ ÐÕÔØ {\tt (0,0)} ÄÌÑ {\tt pathpart}, 
{\tt nullpen}\index{nullpen?\texttt{nullpen}}\label{Dnlpen} ÄÌÑ {\tt penpart}, 
ÐÕÓÔÏÊ ÒÉÓÕÎÏË ÄÌÑ {\tt dashpart}, 
ÐÕÓÔÕÀ ÓÔÒÏËÕ ÄÌÑ {\tt textpart} ÉÌÉ {\tt fontpart}, 
0 ÄÌÑ {\tt colormodel}, {\tt greypart}, {\tt redpart}, {\tt greenpart}, 
{\tt bluepart}, {\tt cyanpart}, {\tt magentapart}, {\tt yellowpart}, 
ÏÄÉÎ ÄÌÑ {\tt blackpart} É ÞÅÒÎÙÊ × ÔÅËÕÝÅÊ ÔÉÐÏ×ÏÊ ÍÏÄÅÌÉ Ã×ÅÔÁ ÄÌÑ {\tt colorpart}.
%%Instead, they return null values or black color (components):
%%the trivial path {\tt (0,0)} for {\tt pathpart},
%%{\tt nullpen}\index{nullpen?\texttt{nullpen}}\label{Dnlpen} for {\tt penpart},
%%an empty picture for {\tt dashpart},
%%the null string for {\tt textpart} or {\tt fontpart},
%%zero for {\tt colormodel},
%%{\tt greypart},
%%{\tt redpart}, {\tt greenpart}, {\tt bluepart},
%%{\tt cyanpart}, {\tt magentapart}, {\tt yellowpart},
%%one for {\tt blackpart}, and
%%black in the current default color model for {\tt colorpart}.

ðÏÄ×ÅÄÅÍ ÉÔÏÇ ÄÉÓËÕÓÓÉÉ Ï ÎÅÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÈ ÏÐÅÒÁÔÏÒÁÈ ×ÙÄÅÌÅÎÉÑ ÞÁÓÔÅÊ.
%%To summarize the discussion of mismatching part operators:
\begin{enumerate}
\item ÷ÏÐÒÏÓ Ï ÂÅÓÓÍÙÓÌÅÎÎÙÈ ÞÁÓÔÑÈ ËÏÍÐÏÎÅÎÔÙ ÒÉÓÕÎËÁ, ÔÁËÉÈ ËÁË {\tt
  redpart} ÄÌÑ ÐÕÔÉ ×ÙÒÅÚËÉ, {\tt textpart} ÄÌÑ ÉÚÏÂÒÁÖÅÎÉÑ ÐÅÒÏÍ 
  ÉÌÉ {\tt pathpart} ÄÌÑ ÔÅËÓÔÁ, ÓÐÏËÏÊÎÏ ÐÒÉÎÉÍÁÅÔÓÑ É 
  ÏÔ×ÅÔÏÍ ÎÁ ÎÅÇÏ ÂÕÄÅÔ ÌÉÂÏ ÎÕÌÅ×ÏÅ ÚÎÁÞÅÎÉÅ, ÌÉÂÏ ÞÅÒÎÙÊ Ã×ÅÔ 
  (ËÏÍÐÏÎÅÎÔ).
%%\item Asking for non-meaningful parts of an item---such as the {\tt
%%    redpart} of a clipping path, the {\tt textpart} of a stroked item,
%%  or the {\tt pathpart} of a textual item---is silently accepted and
%%  returns a null value or a black color (component).
\item ðÒÉÍÅÎÅÎÉÅ ÏÐÅÒÁÔÏÒÁ Ã×ÅÔÏ×ÏÊ ÞÁÓÔÉ × ÎÅÐÒÁ×ÉÌØÎÏÊ ÍÏÄÅÌÉ Ã×ÅÔÁ Ë 
  Ã×ÅÔÎÏÍÕ ËÏÍÐÏÎÅÎÔÕ ×ÏÚ×ÒÁÝÁÅÔ ÞÅÒÎÙÊ ËÏÍÐÏÎÅÎÔ. âÏÌÅÅ ÔÏÇÏ, ÜÔÏ ÉÎÉÉÃÉÉÒÕÅÔ 
  ÏÛÉÂËÕ.
%%\item Applying a color part operator of the wrong color model to a
%%  coloured item returns a black color component.  Additionally, this
%%  triggers an error.
\end{enumerate}

\index{setbounds?\texttt{setbounds}|)}
\index{stroked?\texttt{stroked}|)}
\index{filled?\texttt{filled}|)}
\index{textual?\texttt{textual}|)}
\index{clipped?\texttt{clipped}|)}
\index{bounded?\texttt{bounded}|)}
\index{pathpart?\texttt{pathpart}|)}
\index{penpart?\texttt{penpart}|)}
\index{dashpart?\texttt{dashpart}|)}
\index{colormodel?\texttt{colormodel}|)}
\index{colorpart?\texttt{colorpart}|)}
\index{redpart?\texttt{redpart}|)}
\index{greenpart?\texttt{greenpart}|)}
\index{bluepart?\texttt{bluepart}|)}
\index{cyanpart?\texttt{cyanpart}|)}
\index{magentapart?\texttt{magentapart}|)}
\index{yellowpart?\texttt{yellowpart}|)}
\index{blackpart?\texttt{blackpart}|)}
\index{greypart?\texttt{greypart}|)}

\section{íÁËÒÏÓÙ}
%%\section{Macros}
\label{macros}

õÖÅ ÕÐÏÍÉÎÁÌÏÓØ, ÞÔÏ MetaPost ÉÍÅÅÔ ÍÎÏÖÅÓÔ×Ï Á×ÔÏÍÁÔÉÞÅÓËÉ 
×ËÌÀÞÁÅÍÙÈ ÍÁËÒÏÓÏ×, ÎÁÚÙ×ÁÅÍÏÅ ÍÁËÒÏÐÁËÅÔ Plain\index{ÍÁËÒÏÓÙ Plain}, É 
ÎÅËÏÔÏÒÙÅ ËÏÍÁÎÄÙ, ÒÁÓÓÍÏÔÒÅÎÎÙÅ × ÐÒÅÄÛÅÓÔ×ÕÀÝÉÈ ÒÁÚÄÅÌÁÈ, ÏÐÒÅÄÅÌÅÎÙ 
ËÁË ÍÁËÒÏÓÙ É ÎÅ Ñ×ÌÑÀÔÓÑ ×ÓÔÒÏÅÎÎÙÍÉ × MetaPost.
%%As alluded to earlier, MetaPost has a set of automatically included
%%macros called the Plain macro package\index{Plain macros}, and some of
%%the commands discussed in previous sections are defined as macros
%%instead of being built into MetaPost. 
ãÅÌØ ÜÔÏÇÏ ÒÁÚÄÅÌÁ ÏÂßÑÓÎÉÔØ, ËÁË ÐÉÓÁÔØ ÔÁËÉÅ ÍÁËÒÏÓÙ.
%%The purpose of this section is to
%%explain how to write such macros.

íÁËÒÏÓÙ ÂÅÚ ÁÒÇÕÍÅÎÔÏ× ÏÞÅÎØ ÐÒÏÓÔÙ.
%%Macros with no arguments are very simple.
ïÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ\index{ÔÅËÓÔ ÚÁÍÅÎÙ?\tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ}}%
\index{def?\texttt{def}}\index{enddef?\texttt{enddef}}
$$ {\tt def}\, \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}\, \hbox{\tt =}\,
     \descr{ÔÅËÓÔ ÚÁÍÅÎÙ}\, {\tt enddef}
$$
ÄÅÌÁÅÔ \tdescr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} ÓÏËÒÁÝÅÎÉÅÍ ÄÌÑ 
\tdescr{ÔÅËÓÔÁ ÚÁÍÅÎÙ}, ÇÄÅ \tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ} ÍÏÖÅÔ ÂÙÔØ, × ÓÕÝÎÏÓÔÉ, 
ÌÀÂÏÊ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØÀ ÚÎÁËÏ×. 
%%A macro definition\index{replacement text?\tdescr{replacement text}}%
%%\index{def?\texttt{def}}\index{enddef?\texttt{enddef}}
%%$$ {\tt def}\, \descr{symbolic token}\, \hbox{\tt =}\,
%%     \descr{replacement text}\, {\tt enddef}
%%$$
%%makes the \tdescr{symbolic token} an abbreviation for the
%%\tdescr{replacement text}, where the \tdescr{replacement text} can be
%%virtually any sequence of tokens. 
îÁÐÒÉÍÅÒ, ÍÁËÒÏÐÁËÅÔ Plain ÍÏÇ ÂÙ ÏÐÒÅÄÅÌÉÔØ ËÏÍÁÎÄÕ {\tt fill} ÐÒÉÍÅÒÎÏ 
ÔÁË\index{fill?\texttt{fill}}:
$$ \hbox{\tt def fill = addto currentpicture contour enddef} $$
%%For example, the Plain macro package
%%could almost define the {\tt fill} statement like
%%this\index{fill?\texttt{fill}}:
%%$$ \hbox{\tt def fill = addto currentpicture contour enddef} $$

íÁËÒÏÓÙ Ó ÁÒÇÕÍÅÎÔÁÍÉ ÐÏÈÏÖÉ, ÚÁ ÉÓËÌÀÞÅÎÉÅÍ ÔÏÇÏ, ÞÔÏ ÏÎÉ ÉÍÅÀÔ 
ÆÏÒÍÁÌØÎÙÅ ÐÁÒÁÍÅÔÒÙ, ËÏÔÏÒÙÅ ÇÏ×ÏÒÑÔ, ËÁË ÉÓÐÏÌØÚÏ×ÁÔØ ÁÒÇÕÍÅÎÔÙ × 
\tdescr{ÔÅËÓÔÅ ÚÁÍÅÎÙ}.
%%Macros with arguments are similar, except they have formal parameters
%%hat tell how to use the arguments in the \tdescr{replacement text}.
îÁÐÒÉÍÅÒ, ÍÁËÒÏÓ {\tt
rotatedaround}\index{rotatedaround?\texttt{rotatedaround}} ÏÐÒÅÄÅÌÑÅÔÓÑ 
ÐÒÉÍÅÒÎÏ ÔÁË:
$$\begin{verbatim}
def rotatedaround(expr z, d) =
  shifted -z rotated d shifted z enddef;
\end{verbatim}
$$
%%For example, the {\tt
%%rotatedaround}\index{rotatedaround?\texttt{rotatedaround}} macro is
%%defined like this:
%%$$\begin{verbatim}
%%def rotatedaround(expr z, d) =
%%  shifted -z rotated d shifted z enddef;
%%\end{verbatim}
%%$$
óÌÏ×Ï {\tt expr}\index{expr?\texttt{expr}} × ÜÔÏÍ ÏÐÒÅÄÅÌÅÎÉÉ ÚÎÁÞÉÔ, ÞÔÏ 
ÆÏÒÍÁÌØÎÙÅ ÐÁÒÁÍÅÔÒÙ {\tt z} É {\tt d} ÍÏÇÕÔ ÂÙÔØ ÐÒÏÉÚ×ÏÌØÎÙÍÉ ×ÙÒÁÖÅÎÉÑÍÉ.
%%The {\tt expr}\index{expr?\texttt{expr}} in this definition means that
%%formal parameters {\tt z} and {\tt d} can be arbitrary expressions.
üÔÉÍ ÐÁÒÁÍÅÔÒÁÍ ÓÌÅÄÕÅÔ ÓÏÏÔ×ÅÔÓÔ×Ï×ÁÔØ ×ÙÒÁÖÅÎÉÑÍ-ÐÁÒÁÍ, ÎÏ MetaPost ÎÅ 
ÐÒÏ×ÅÒÑÅÔ ÜÔÏÇÏ ÓÒÁÚÕ.
%%(They should be pair expressions but the MetaPost interpreter does not
%%immediately check for that.)

éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ MetaPost --- ÜÔÏ ÉÎÔÅÒÐÒÅÔÉÒÕÅÍÙÊ ÑÚÙË, ÍÁËÒÏÓÙ Ó 
ÁÒÇÕÍÅÎÔÁÍÉ ÏÞÅÎØ ÐÏÈÏÖÉ ÎÁ ÐÏÄÐÒÏÇÒÁÍÍÙ\index{ÐÏÄÐÒÏÇÒÁÍÍÙ}.
%%Since MetaPost is an interpreted language, macros with arguments are a
%%lot like subroutines\index{subroutines}. 
íÁËÒÏÓÙ MetaPost ÞÁÓÔÏ ÉÓÐÏÌØÚÕÀÔÓÑ ÐÏÄÏÂÎÏ ÐÏÄÐÒÏÇÒÁÍÍÁÍ, ÐÏÜÔÏÍÕ ÑÚÙË 
×ËÌÀÞÁÅÔ × ÓÅÂÑ ÐÒÏÇÒÁÍÍÎÙÅ ËÏÎÃÅÐÃÉÉ ÄÌÑ ÔÁËÏÇÏ ÉÓÐÏÌØÚÏ×ÁÎÉÑ.
%%MetaPost macros are often used
%%like subroutines, so the language includes programming concepts to
%%support this. 
üÔÉ ËÏÎÃÅÐÃÉÉ ×ËÌÀÞÁÀÔ ÌÏËÁÌØÎÙÅ ÐÅÒÅÍÅÎÎÙÅ, ÃÉËÌÙ É ÕÓÌÏ×ÎÙÅ ËÏÍÁÎÄÙ.
%%These concepts include local variables, loops, and
%%conditional statements.

\subsection{çÒÕÐÐÉÒÏ×ËÁ}
%%\subsection{Grouping}
\label{grsec}

çÒÕÐÐÉÒÏ×ËÁ × MetaPost ×ÅÓØÍÁ ×ÁÖÎÁ ÄÌÑ ÆÕÎËÃÉÊ\index{ÆÕÎËÃÉÉ} É 
ÌÏËÁÌØÎÙÈ\index{ÐÅÒÅÍÅÎÎÙÅ!ÌÏËÁÌØÎÙÅ}\index{ÌÏËÁÌØÎÏÓÔØ} ÐÅÒÅÍÅÎÎÙÈ.
%%Grouping in MetaPost is essential for functions\index{functions} and
%%local\index{variables!local}\index{locality} variables. 
âÁÚÏ×ÁÑ ÉÄÅÑ × ÔÏÍ, ÞÔÏ ÇÒÕÐÐÁ --- ÜÔÏ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ËÏÍÁÎÄ, 
×ÏÚÍÏÖÎÏ ÚÁ×ÅÒÛÁÀÝÁÑÓÑ ×ÙÒÁÖÅÎÉÅÍ, Ó ÏÂÅÓÐÅÞÅÎÉÅÍ ÔÏÇÏ, ÞÔÏ ÎÅËÏÔÏÒÙÅ 
ÓÉÍ×ÏÌØÎÙÅ ÚÎÁËÉ\index{ÚÎÁËÉ!ÓÉÍ×ÏÌÉÞÅÓËÉÅ} ÍÏÇÕÔ ×ÏÓÓÔÁÎÏ×ÉÔØ Ó×ÏÉ 
ÓÔÁÒÙÅ ÚÎÁÞÅÎÉÑ × ËÏÎÃÅ ÇÒÕÐÐÙ. 
%%The basic idea
%%is that a group is a sequence of statements possibly followed by an
%%expression with the provision that certain symbolic
%%tokens\index{tokens!symbolic} can have their old meanings restored at
%%the end of the group. 
åÓÌÉ ÇÒÕÐÐÁ ÚÁËÁÎÞÉ×ÁÅÔÓÑ ×ÙÒÁÖÅÎÉÅÍ, ÔÏ ÇÒÕÐÐÁ ×ÅÄÅÔ ÓÅÂÑ ÐÏÄÏÂÎÏ 
×ÙÚÏ×Õ ÆÕÎËÃÉÉ, ÞÔÏ ×ÏÚ×ÒÁÝÁÅÔ ÜÔÏ ×ÙÒÁÖÅÎÉÅ.
%%If the group ends with an expression, the group
%%behaves like a function call that returns that expression. 
÷ ÐÒÏÔÉ×ÎÏÍ ÓÌÕÞÁÅ, ÇÒÕÐÐÁ --- ÜÔÏ ÐÒÏÓÔÏ ÓÏÓÔÁ×ÎÁÑ 
ËÏÍÁÎÄÁ\index{ÂÌÏË}. 
%%Otherwise,
%%the group is just a compound statement\index{compound statement}. 
óÉÎÔÁËÓÉÓ ÄÌÑ ÇÒÕÐÐÙ\index{begingroup?\texttt{begingroup}}\index{endgroup?\texttt{endgroup}} 
--- 
$$ {\tt begingroup}\, \descr{ÓÐÉÓÏË ËÏÍÁÎÄ}\, {\tt endgroup} $$
ÉÌÉ
$$ {\tt begingroup}\, \descr{ÓÐÉÓÏË ËÏÍÁÎÄ}\, \descr{×ÙÒÁÖÅÎÉÅ}\, {\tt endgroup},
$$
ÇÄÅ \tdescr{ÓÐÉÓÏË ËÏÍÁÎÄ} --- ÜÔÏ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ËÏÍÁÎÄ, ÚÁ 
ËÁÖÄÏÊ ÉÚ ËÏÔÏÒÙÈ ÓÌÅÄÕÅÔ ÔÏÞËÁ Ó ÚÁÐÑÔÏÊ. 
%%The syntax for a group
%%is\index{begingroup?\texttt{begingroup}}\index{endgroup?\texttt{endgroup}}
%%$$ {\tt begingroup}\, \descr{statement list}\, {\tt endgroup} $$
%%or
%%$$ {\tt begingroup}\, \descr{statement list}\, \descr{expression}\, {\tt %%endgroup}
%%$$
%%where a \tdescr{statement list} is a sequence of statements each
%%followed by a semicolon. 
çÒÕÐÐÁ Ó \tdescr{×ÙÒÁÖÅÎÉÅÍ} ÐÏÓÌÅ 
\tdescr{ÓÐÉÓËÁ ËÏÍÁÎÄ} ×ÅÄÅÔ ÓÅÂÑ ËÁË \tdescr{ÐÅÒ×ÉÞÎÏÓÔØ} ÉÚ 
ÒÉÓ.~\ref{syexpr} ÉÌÉ ÐÏÄÏÂÎÏ \tdescr{ÞÉÓÌÏ×ÏÍÕ ÁÔÏÍÕ} ÉÚ 
ÒÉÓ.~\ref{synprim}.
%%A group with an \tdescr{expression} after the
%%\tdescr{statement list} behaves like a \tdescr{primary} in
%%Figure~\ref{syexpr} or like a \tdescr{numeric atom} in
%%Figure~\ref{synprim}.

éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ \tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ} ÄÌÑ ÍÁËÒÏÓÁ {\tt
beginfig}\index{beginfig?\texttt{beginfig}} ÎÁÞÉÎÁÅÔÓÑ Ó {\tt
begingroup}, Á \tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ} ÄÌÑ {\tt
endfig}\index{endfig?\texttt{endfig}} ÚÁËÁÎÞÉ×ÁÅÔÓÑ ÎÁ {\tt endgroup}, 
ËÁÖÄÁÑ ËÁÒÔÉÎËÁ ×ÈÏÄÎÏÇÏ ÆÁÊÌÁ MetaPost ×ÅÄÅÔ ÓÅÂÑ ËÁË ÇÒÕÐÐÁ. 
%%Since the \tdescr{replacement text} for the {\tt
%%beginfig}\index{beginfig?\texttt{beginfig}} macro starts with {\tt
%%begingroup} and the \tdescr{replacement text} for {\tt
%%endfig}\index{endfig?\texttt{endfig}} ends with {\tt endgroup}, each
%%figure in a MetaPost input file behaves like a group. 
üÔÏ ÐÏÚ×ÏÌÑÅÔ ËÁÒÔÉÎËÁÍ ÉÍÅÔØ ÌÏËÁÌØÎÙÅ ÐÅÒÅÍÅÎÎÙÅ.
%%This is what allows figures can have local variables. 
íÙ ÕÖÅ ×ÉÄÅÌÉ × ÒÁÚÄÅÌÅ~\ref{vardecl}, ÞÔÏ ÉÍÅÎÁ ÐÅÒÅÍÅÎÎÙÈ, 
ÎÁÞÉÎÁÀÝÉÅÓÑ Ó {\tt x} ÉÌÉ {\tt y} Ñ×ÌÑÀÔÓÑ ÌÏËÁÌØÎÙÍÉ × ÔÏÍ ÓÍÙÓÌÅ, 
ÞÔÏ ÏÎÉ ÓÞÉÔÁÀÔÓÑ ÎÅÉÚ×ÅÓÔÎÙÍÉ × ÎÁÞÁÌÅ ËÁÖÄÏÊ ËÁÒÔÉÎËÉ É ÉÈ ÚÎÁÞÅÎÉÑ 
ÚÁÂÙ×ÁÀÔÓÑ × ËÏÎÃÅ ËÁÖÄÏÊ ËÁÒÔÉÎËÉ. 
%%We have already seen in
%%Section~\ref{vardecl} that variable names beginning with {\tt x} or {\tt
%%y} are local in the sense that they have unknown values at the beginning
%%of each figure and these values are forgotten at the end of each figure.
óÌÅÄÕÀÝÉÊ ÐÒÉÍÅÒ ÉÌÌÀÓÔÒÉÒÕÅÔ ËÁË ÒÁÂÏÔÁÅÔ ÌÏËÁÌØÎÏÓÔØ.
%%The following example illustrates how locality works:
\begin{eqnarray*}
&& \hbox{\tt x23 = 3.1;}\\
&& \hbox{\tt beginfig(17);}\\
&& \qquad \vdots\\
&& \hbox{\tt y3a=1; x23=2;}\\
&& \qquad \vdots\\
&& \hbox{\tt endfig;}\\
&& \hbox{\tt show x23, y3a;}
\end{eqnarray*}
òÅÚÕÌØÔÁÔ ËÏÍÁÎÄÙ {\tt show}\index{show?\texttt{show}}
%%The result of the {\tt show}\index{show?\texttt{show}} command is
$$\begin{verbatim}
>> 3.1
>> y3a
\end{verbatim}
$$
ÐÏËÁÚÙ×ÁÅÔ, ÞÔÏ {\tt x23} ×ÏÚ×ÒÁÝÁÅÔÓÑ Ë Ó×ÏÅÍÕ ÐÒÅÖÎÅÍÕ ÚÎÁÞÅÎÉÀ {\tt 3.1}, 
Á {\tt y3a} ÓÏ×ÅÒÛÅÎÎÏ ÎÅÉÚ×ÅÓÔÎÏ, ËÁË ÏÎÏ É ÂÙÌÏ × {\tt beginfig(17)}.
%%indicating that {\tt x23} has returned to its former value of {\tt 3.1} and
%%{\tt y3a} is completely unknown as it was at {\tt beginfig(17)}.

ìÏËÁÌØÎÏÓÔØ ÐÅÒÅÍÅÎÎÙÈ {\tt x} É {\tt y} ÄÏÓÔÉÇÁÅÔÓÑ 
ËÏÍÁÎÄÏÊ\index{save?\texttt{save}}\label{Dsave}
$$ \hbox{\tt save x,y} $$
× \tdescr{ÔÅËÓÔÅ ÚÁÍÅÎÙ} ÄÌÑ {\tt
beginfig}\index{beginfig?\texttt{beginfig}}. 
%%The locality of {\tt x} and {\tt y} variables is achieved by the
%%statement\index{save?\texttt{save}}\label{Dsave}
%%$$ \hbox{\tt save x,y} $$
%%in the \tdescr{replacement text} for {\tt
%%beginfig}\index{beginfig?\texttt{beginfig}}. 
÷ ÏÂÝÅÍ, ÐÅÒÅÍÅÎÎÙÅ ÄÅÌÁÀÔÓÑ ÌÏËÁÌØÎÙÍÉ ËÏÍÁÎÄÏÊ 
$$ {\tt save}\, \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×}, $$
ÇÄÅ \tdescr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×} --- ÜÔÏ ÒÁÚÄÅÌÅÎÎÙÊ ÚÁÐÑÔÙÍÉ 
ÓÐÉÓÏË ÚÎÁËÏ×:\index{ÚÎÁËÉ!ÓÉÍ×ÏÌÉÞÅÓËÉÅ}
\begin{ctabbing}
$\tt \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×} \rightarrow \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}$\\
        $\tt \qquad \;|\; \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}\hbox{\tt ,}
        \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×}$
\end{ctabbing}
%%In general, variables are made local by the statement
%%$$ {\tt save}\, \descr{symbolic token list} $$
%%where \tdescr{symbolic token list} is a comma-separated list of
%%tokens:\index{tokens!symbolic}
%%\begin{ctabbing}
%%$\tt \descr{symbolic token list} \rightarrow \descr{symbolic token}$\\
%%        $\tt \qquad \;|\; \descr{symbolic token}\hbox{\tt ,}
%%        \descr{symbolic token list}$
%%\end{ctabbing}
÷ÓÅ ÐÅÒÅÍÅÎÎÙÅ, ÞØÉ ÉÍÅÎÁ ÎÁÞÉÎÁÀÔÓÑ Ó ÏÄÎÏÇÏ ÉÚ ÕËÁÚÁÎÎÙÈ ÓÉÍ×ÏÌÉÞÅÓËÉÈ 
ÚÎÁËÏ×, ÓÔÁÎÏ×ÑÔÓÑ ÎÅÉÚ×ÅÓÔÎÙÍÉ ÞÉÓÌÁÍÉ, Á ÉÈ ÐÒÅÖÎÉÅ ÚÎÁÞÅÎÉÑ ÓÏÈÒÁÎÑÀÔÓÑ 
ÄÌÑ ×ÏÓÓÔÁÎÏ×ÌÅÎÉÑ × ËÏÎÃÅ ÔÅËÕÝÅÊ ÇÒÕÐÐÙ.
%%All variables whose names begin with one of the specified symbolic
%%tokens become unknown numerics and their present values are saved for
%%restoration at the end of the current group. 
åÓÌÉ ËÏÍÁÎÄÁ {\tt save} ÉÓÐÏÌØÚÕÅÔÓÑ ×ÎÅ ÇÒÕÐÐÙ, ÔÏ ÚÎÁÞÅÎÉÑ ÐÏ-ÐÒÏÓÔÕ 
ÎÅ×ÏÓÓÔÁÎÏ×ÉÍÏ ÕÎÉÞÔÏÖÁÀÔÓÑ.
%%If the {\tt save}
%%statement is used outside of a group, the original values are simply
%%discarded.

çÌÁ×ÎÁÑ ÃÅÌØ ËÏÍÁÎÄÙ {\tt save} ÐÏÚ×ÏÌÉÔØ ÍÁËÒÏÓÁÍ ÉÓÐÏÌØÚÏ×ÁÔØ 
ÐÅÒÅÍÅÎÎÙÅ ÂÅÚ ×ÚÁÉÍÏÄÅÊÓÔ×ÉÑ Ó ÓÕÝÅÓÔ×ÕÀÝÉÍÉ ÐÅÒÅÍÅÎÎÙÍÉ ÉÌÉ ÐÅÒÅÍÅÎÎÙÍÉ 
× ÎÅÓËÏÌØËÉÈ ×ÙÚÏ×ÁÈ ÏÄÎÏÇÏ É ÔÏÇÏ ÖÅ ÍÁËÒÏÓÁ.
%%The main purpose of the {\tt save} statement is to allow macros to use
%%variables without interfering with existing variables or variables in
%%other calls to the same macro. 
îÁÐÒÉÍÅÒ, ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ {\tt
whatever}\index{whatever?\texttt{whatever}} ÉÍÅÅÔ ÔÁËÏÊ \tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ}
$$ \hbox{\tt begingroup save ?; ? endgroup} $$
%%For example, the predefined macro {\tt
%%whatever}\index{whatever?\texttt{whatever}} has the \tdescr{replacement text}
%%$$ \hbox{\tt begingroup save ?; ? endgroup} $$
ïÎ ×ÏÚ×ÒÁÝÁÅÔ ÎÅÉÚ×ÅÓÔÎÏÅ ÞÉÓÌÏ×ÏÅ ËÏÌÉÞÅÓÔ×Ï, ÎÏ ÏÎÏ ÎÅ ÚÏ×ÅÔÓÑ ÂÏÌØÛÅ 
ÚÎÁËÏÍ ×ÏÐÒÏÓÁ, ÐÏÔÏÍÕ ÞÔÏ ÜÔÏ ÉÍÑ ÂÙÌÏ ÌÏËÁÌØÎÙÍ × ÇÒÕÐÐÅ.
%%This returns an unknown numeric quantity, but it is no longer called
%%question mark since that name was local to the group. 
óÐÒÁÛÉ×ÁÑ ÉÍÑ ÞÅÒÅÚ {\tt show\index{show?\texttt{show}} whatever},
ÐÏÌÕÞÁÅÍ\index{CAPSULE?\texttt{CAPSULE}}
$$ \hbox{\tt >> \%CAPSULE}{\it nnnn}, $$
ÇÄÅ {\it nnnn} --- ÜÔÏ ÉÄÅÎÔÉÆÉËÁÃÉÏÎÎÙÊ ÎÏÍÅÒ, ×ÙÂÉÒÁÅÍÙÊ, ËÏÇÄÁ {\tt save} 
ÏÒÇÁÎÉÚÕÅÔ ÉÓÞÅÚÎÏ×ÅÎÉÅ ÉÍÅÎÉ ÚÎÁË ×ÏÐÒÏÓÁ.
%%Asking the name via {\tt show\index{show?\texttt{show}} whatever}
%%yields\index{CAPSULE?\texttt{CAPSULE}}
%%$$ \hbox{\tt >> \%CAPSULE}{\it nnnn} $$
%%where {\it nnnn} is an identification number that is chosen when {\tt save}
%%makes the name question mark disappear.

÷ÏÐÒÅËÉ ÕÎÉ×ÅÒÓÁÌØÎÏÓÔÉ, {\tt save} ÎÅ ÍÏÖÅÔ ÉÓÐÏÌØÚÏ×ÁÔØÓÑ 
ÄÌÑ ÌÏËÁÌØÎÏÇÏ ÉÚÍÅÎÅÎÉÑ ÌÀÂÏÊ ×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ\index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} MetaPost. 
%%In spite of the versatility of {\tt save}, it cannot be used to make
%%local changes to any of MetaPost's internal variables\index{internal
%%variables}\index{variables!internal}. 
ëÏÍÁÎÄÁ, ÔÁËÁÑ ËÁË 
$$ \hbox{\tt save linecap}, $$
ÐÒÉ×ÅÄÅÔ MetaPost Ë ×ÒÅÍÅÎÎÏÍÕ ÚÁÂÙ×ÁÎÉÀ ÓÐÅÃÉÁÌØÎÏÇÏ ÚÎÁÞÅÎÉÑ ÜÔÏÊ 
ÐÅÒÅÍÅÎÎÏÊ É ÓÄÅÌÁÅÔ ÅÅ ÏÂÙÞÎÏÊ ÎÅÉÚ×ÅÓÔÎÏÊ ÞÉÓÌÏ×ÏÊ ×ÅÌÉÞÉÎÏÊ.
%%A statement such as\index{linecap?\texttt{linecap}}
%%$$ \hbox{\tt save linecap} $$
%%would cause MetaPost to temporarily forget the special meaning of this
%%variable and just make it an unknown numeric. 
åÓÌÉ ×Ù ÈÏÔÉÔÅ ÎÁÒÉÓÏ×ÁÔØ ÏÄÎÕ ÐÕÎËÔÉÒÎÕÀ ÌÉÎÉÀ Ó {\tt linecap:=butt} É 
ÚÁÔÅÍ ×ÅÒÎÕÔØÓÑ ÎÁÚÁÄ Ë ÐÒÅÖÎÅÍÕ ÚÎÁÞÅÎÉÀ, ÔÏ ×Ù ÍÏÖÅÔÅ ÉÓÐÏÌØÚÏ×ÁÔØ 
ËÏÍÁÎÄÕ {\tt
interim}\index{interim?\texttt{interim}}\label{Dinterm} ËÁË 
× ÓÌÅÄÕÀÝÅÍ ÐÒÉÍÅÒÅ:
\begin{eqnarray*}
&& \hbox{\tt begingroup interim linecap:=butt;}\\
&& {\tt draw}\, \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\, \hbox{\tt dashed evenly; endgroup}
\end{eqnarray*}
%%If you want to draw one
%%dashed line with {\tt linecap:=butt} and then go back to the previous
%%value, you can use the {\tt
%%interim}\index{interim?\texttt{interim}}\label{Dinterm} statement as
%%follows:
%%\begin{eqnarray*}
%%&& \hbox{\tt begingroup interim linecap:=butt;}\\
%%&& {\tt draw}\, \descr{path expression}\, \hbox{\tt dashed evenly; endgroup}
%%\end{eqnarray*}
üÔÏ ÓÏÈÒÁÎÉÔ ÚÎÁÞÅÎÉÅ ×ÎÕÔÒÅÎÎÅÊ 
ÐÅÒÅÍÅÎÎÏÊ\index{×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} 
{\tt linecap}, ×ÒÅÍÅÎÎÏ ÄÁÓÔ ÅÊ ÎÏ×ÏÅ ÚÎÁÞÅÎÉÅ É ÜÔÏ ÎÅ ÐÒÉ×ÅÄÅÔ Ë 
ÚÁÂÙ×ÁÎÉÀ ÔÏÇÏ, ÞÔÏ {\tt linecap} --- ×ÎÕÔÒÅÎÎÑÑ ÐÅÒÅÍÅÎÎÁÑ.  
%%This saves the value of the
%%internal variable\index{internal variables}\index{variables!internal}
%%{\tt linecap} and temporarily
%%gives it a new value without forgetting that {\tt linecap} is an internal
%%variable. 
ïÂÝÉÊ ÓÉÎÔÁËÓÉÓ: 
$$ {\tt interim}\, \descr{×ÎÕÔÒÅÎÎÑÑ ÐÅÒÅÍÅÎÎÁÑ} \mathrel{\hbox{\tt:=}}
        \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}
$$
%%The general syntax is
%%$$ {\tt interim}\, \descr{internal variable} \mathrel{\hbox{\tt:=}}
%%        \descr{numeric expression}
%%$$

\subsection{ðÁÒÁÍÅÔÒÉÚÏ×ÁÎÎÙÅ ÍÁËÒÏÓÙ}
%%\subsection{Parameterized Macros}

âÁÚÏ×ÁÑ ÉÄÅÑ ÍÁËÒÏÓÏ× Ó ÐÁÒÁÍÅÔÒÁÍÉ × ÄÏÓÔÉÖÅÎÉÉ ÂÏÌØÛÅÊ ÇÉÂËÏÓÔÉ ÐÅÒÅÄÁÞÅÊ 
ÄÏÂÁ×ÏÞÎÏÊ ÉÎÆÏÒÍÁÃÉÉ × ÍÁËÒÏÓ.
%%The basic idea behind parameterized macros is to achieve greater flexibility by
%%allowing auxiliary information to be passed to a macro. 
íÙ ÕÖÅ ×ÉÄÅÌÉ, ÞÔÏ ÏÐÒÅÄÅÌÅÎÉÑ ÍÁËÒÏÓÏ× ÍÏÇÕÔ ÉÍÅÔØ ÆÏÒÍÁÌØÎÙÅ ÐÁÒÁÍÅÔÒÙ ÄÌÑ 
×ÙÒÁÖÅÎÉÊ, ÚÁÄÁ×ÁÅÍÙÈ ÐÒÉ ×ÙÚÏ×Å ÍÁËÒÏÓÁ. 
%%We have already seen
%%that macro definitions can have formal parameters that represent expressions
%%to be given when the macro is called. 
îÁÐÒÉÍÅÒ, ÏÐÒÅÄÅÌÅÎÉÅ 
$$ \hbox{\tt def rotatedaround(expr z, d) = } \descr{ÔÅËÓÔ ÚÁÍÅÎÙ}\,
   {\tt enddef}
$$
ÐÏÚ×ÏÌÑÅÔ MetaPost-ÉÎÔÅÒÐÒÅÔÁÔÏÒÕ ÐÏÎÉÍÁÔØ ×ÙÚÏ×Ù ÍÁËÒÏÓÁ × ÆÏÒÍÅ 
$$\tt rotatedaround\hbox{\tt (}
  \descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt )}
$$
%%For instance a definition such as
%%$$ \hbox{\tt def rotatedaround(expr z, d) = } \descr{replacement text}\,
%%   {\tt enddef}
%%$$
%%allows the MetaPost interpreter to understand macro calls of the form
%%$$\tt rotatedaround\hbox{\tt (}
%%  \descr{expression}\hbox{\tt ,} \descr{expression}\hbox{\tt )}
%%$$

ëÌÀÞÅ×ÏÅ ÓÌÏ×Ï {\tt expr}\index{expr?\texttt{expr}}\index{ÐÁÒÁÍÅÔÒ!expr}
× ÏÐÒÅÄÅÌÅÎÉÉ ÍÁËÒÏÓÁ ÚÎÁÞÉÔ, ÞÔÏ ÐÁÒÁÍÅÔÒÙ ÍÏÇÕÔ ÂÙÔØ ×ÙÒÁÖÅÎÉÑÍÉ ÌÀÂÏÇÏ 
ÔÉÐÁ.
%%The keyword {\tt expr}\index{expr?\texttt{expr}}\index{parameter!expr}
%%in the macro definition means that the parameters can be expressions of
%%any type. 
ëÏÇÄÁ ÏÐÒÅÄÅÌÅÎÉÅ ÕËÁÚÙ×ÁÅÔ {\tt (expr z, d)}, ÔÏ ÆÏÒÍÁÌØÎÙÅ 
ÐÁÒÁÍÅÔÒÙ {\tt z} É {\tt d} ×ÅÄÕÔ ÓÅÂÑ ÐÏÄÏÂÎÏ ÐÅÒÅÍÅÎÎÙÍ ÐÏÄÈÏÄÑÝÅÇÏ ÔÉÐÁ.
%%When the definition specifies {\tt (expr z, d)}, the formal
%%parameters {\tt z} and {\tt d} behave like variables of the appropriate
%%types. 
÷ÎÕÔÒÉ \tdescr{ÔÅËÓÔÁ ÚÁÍÅÎÙ} ÏÎÉ ÍÏÇÕÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎÙ × ×ÙÒÁÖÅÎÉÑÈ, 
ËÁË ÏÂÙÞÎÙÅ ÐÅÒÅÍÅÎÎÙÅ, ÎÏ ÏÎÉ ÎÅ ÍÏÇÕÔ ÐÏ×ÔÏÒÎÏ ÄÅËÌÁÒÉÒÏ×ÁÔØÓÑ ÉÌÉ 
ÐÏÌÕÞÁÔØ ÎÏ×ÙÅ ÚÎÁÞÅÎÉÑ.
%%Within the \tdescr{replacement text}, they can be used in
%%expressions just like variables, but they cannot be redeclared or
%%assigned to. 
îÅÔ ÏÇÒÁÎÉÞÅÎÉÊ ÎÁ ÎÅÉÚ×ÅÓÔÎÙÅ ÉÌÉ ÞÁÓÔÉÞÎÏ ÉÚ×ÅÓÔÎÙÅ ÁÒÇÕÍÅÎÔÙ.
%%There is no restriction against unknown or partially known
%%arguments. 
ðÏÜÔÏÍÕ ÏÐÒÅÄÅÌÅÎÉÅ\index{midpoint?\texttt{midpoint}}
$$ \hbox{\tt def midpoint(expr a, b) = (.5[a,b]) enddef} $$
ÐÒÅËÒÁÓÎÏ ÒÁÂÏÔÁÅÔ ÄÌÑ ÎÅÉÚ×ÅÓÔÎÙÈ {\tt a} É {\tt b}.
%%Thus the definition\index{midpoint?\texttt{midpoint}}
%%$$ \hbox{\tt def midpoint(expr a, b) = (.5[a,b]) enddef} $$
%%works perfectly well when {\tt a} and {\tt b} are unknown. 
õÒÁ×ÎÅÎÉÅ, ÔÁËÏÅ ËÁË
$$ \hbox{\tt midpoint(z1,z2) = (1,1)}, $$
ÍÏÖÅÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎÏ ÄÌÑ ÏÐÒÅÄÅÌÅÎÉÑ {\tt z1} É {\tt z2}.
%%An equation such as
%%$$ \hbox{\tt midpoint(z1,z2) = (1,1)} $$
%%could be used to help determine {\tt z1} and {\tt z2}.

úÁÍÅÔØÔÅ, ÞÔÏ ÏÐÒÅÄÅÌÅÎÉÅ ×ÙÛÅ ÄÌÑ {\tt midpoint} ÒÁÂÏÔÁÅÔ ÄÌÑ ÞÉÓÅÌ, 
ÐÁÒ ÉÌÉ Ã×ÅÔÏ× --- ÎÕÖÎÏ ÔÏÌØËÏ ÓÏ×ÐÁÄÅÎÉÅ ÔÉÐÏ× ÏÂÏÉÈ ÐÁÒÁÍÅÔÒÏ×.
%%Notice that the above definition for {\tt midpoint} works for numerics,
%%pairs, or colors as long as both parameters have the same type. 
åÓÌÉ ÚÁÞÅÍ-ÔÏ ÎÕÖÅÎ ÍÁËÒÏÓ {\tt
middlepoint}\index{middlepoint?\texttt{middlepoint}}, ÒÁÂÏÔÁÀÝÉÊ ÔÏÌØËÏ 
ÄÌÑ ÐÕÔÉ ÉÌÉ ÒÉÓÕÎËÁ, ÔÏ ÂÕÄÅÔ ÎÅÏÂÈÏÄÉÍÏ ×ÙÐÏÌÎÑÔØ 
ÐÒÏ×ÅÒËÕ {\tt if}\index{if?\texttt{if}} ÔÉÐÁ ÁÒÇÕÍÅÎÔÁ. 
%%If for some reason we want a {\tt
%%middlepoint}\index{middlepoint?\texttt{middlepoint}} macro that works
%%for a single path or picture, it would be necessary to do an {\tt
%%if}\index{if?\texttt{if}} test on the argument type. 
åÓÔØ ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ\index{path?\texttt{path}}
$$ {\tt path}\, \descr{ÐÅÒ×ÉÞÎÏÓÔØ}, $$
×ÏÚ×ÒÁÝÁÀÝÉÊ ÌÏÇÉÞÅÓËÉÊ ÒÅÚÕÌØÔÁÔ, ÐÏËÁÚÙ×ÁÀÝÉÊ Ñ×ÌÑÅÔÓÑ ÌÉ ÅÇÏ ÁÒÇÕÍÅÎÔ ÐÕÔÅÍ.
%%This uses the fact
%%there is a unary operator\index{path?\texttt{path}}
%%$$ {\tt path}\, \descr{primary} $$
%%that returns a boolean result indicating whether its argument is a path.
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÐÒÏ×ÅÒËÁ {\tt if} ÉÍÅÅÔ ÂÁÚÏ×ÙÊ 
ÓÉÎÔÁËÓÉÓ\index{else?\texttt{else}}\index{fi?\texttt{fi}}
$$ {\tt if}\, \descr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt:}\, \descr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ}\,
   \hbox{\tt else:}\, \descr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ}\, {\tt fi},
$$
ÇÄÅ \tdescr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ}\index{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ?\tdescr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ}} 
ÍÏÇÕÔ ÂÙÔØ ÞÅÍ-ÕÇÏÄÎÏ, ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÍ 
ÏÔÎÏÓÉÔÅÌØÎÏ {\tt if} É {\tt fi}, ÐÏÌÎÙÊ ÍÁËÒÏÓ {\tt
middlepoint}\index{middlepoint?\texttt{middlepoint}} Ó ÐÒÏ×ÅÒËÏÊ ÔÉÐÁ ÍÏÖÅÔ ×ÙÇÌÑÄÅÔØ 
ÔÁË: 
$$\begin{verbatim}
def middlepoint(expr a) = if path a: (point .5*length a of a)
  else: .5(llcorner a + urcorner a) fi enddef;
\end{verbatim}
$$
%%Since the basic {\tt if} test has the
%%syntax\index{else?\texttt{else}}\index{fi?\texttt{fi}}
%%$$ {\tt if}\, \descr{boolean expression}\hbox{\tt:}\, \descr{balanced tokens}\,
%%   \hbox{\tt else:}\, \descr{balanced tokens}\, {\tt fi}
%%$$
%%where the \tdescr{balanced tokens}\index{balanced
%%tokens?\tdescr{balanced tokens}} can be anything that is balanced with
%%respect to {\tt if} and {\tt fi}, the complete {\tt
%%middlepoint}\index{middlepoint?\texttt{middlepoint}} macro with type test
%%looks like this:
%%$$\begin{verbatim}
%%def middlepoint(expr a) = if path a: (point .5*length a of a)
%%  else: .5(llcorner a + urcorner a) fi enddef;
%%\end{verbatim}
%%$$
ðÏÌÎÙÊ ÓÉÎÔÁËÓÉÓ ÐÒÏ×ÅÒËÉ {\tt if} ÐÏËÁÚÁÎ ÎÁ ÒÉÓ.~\ref{syif}.
%%The complete syntax for {\tt if} tests is shown in Figure~\ref{syif}.
ðÏÚ×ÏÌÑÀÔÓÑ ÍÎÏÇÏËÒÁÔÎÙÅ ÐÒÏ×ÅÒËÉ {\tt if}, ÎÁÐÒÉÍÅÒ, 
$$ \hbox{\tt if $e_1$: \ldots\ else: if $e_2$: \ldots\ else: \ldots\ fi fi},$$ 
ËÏÔÏÒÙÅ ÍÏÖÎÏ ÓÏËÒÁÔÉÔØ ÄÏ\index{elseif?\texttt{elseif}}
$$ \hbox{\tt if $e_1$: \ldots\ elseif $e_2$: \ldots\ else: \ldots\ fi}, $$
ÇÄÅ $e_1$ É $e_2$ ÐÒÅÄÓÔÁ×ÌÑÀÔ ÌÏÇÉÞÅÓËÉÅ ×ÙÒÁÖÅÎÉÑ.
%%It allows multiple {\tt if} tests like
%%$$ \hbox{\tt if $e_1$: \ldots\ else: if $e_2$: \ldots\ else: \ldots\ fi fi} $$
%%to be shortened to\index{elseif?\texttt{elseif}}
%%$$ \hbox{\tt if $e_1$: \ldots\ elseif $e_2$: \ldots\ else: \ldots\ fi} $$
%%where $e_1$ and $e_2$ represent boolean expressions.

ïÂÒÁÔÉÔÅ ×ÎÉÍÁÎÉÅ, ÞÔÏ ÐÒÏ×ÅÒËÉ {\tt if} ÎÅ Ñ×ÌÑÀÔÓÑ ËÏÍÁÎÄÁÍÉ É 
\tdescr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ} 
× ÓÉÎÔÁËÓÉÞÅÓËÉÈ ÐÒÁ×ÉÌÁÈ ÍÏÇÕÔ ÎÅ ÂÙÔØ ÐÏÌÎÙÍÉ ×ÙÒÁÖÅÎÉÑÍÉ ÉÌÉ ËÏÍÁÎÄÁÍÉ.
%%Note that {\tt if} tests are not statements and the \tdescr{balanced
%%tokens} in the syntax rules can be any sequence of balanced tokens even
%%if they do not form a complete expression or statement. 
ðÏÜÔÏÍÕ ÍÏÖÎÏ, ÐÏÖÅÒÔ×Ï×Á× ÎÁÇÌÑÄÎÏÓÔØÀ, ÕÂÒÁÔØ Ä×Á ÚÎÁËÁ × ÏÐÒÅÄÅÌÅÎÉÉ 
{\tt middlepoint}:
$$\begin{verbatim}
def middlepoint(expr a) = if path a: (point .5*length a of
  else: .5(llcorner a + urcorner fi  a) enddef;
\end{verbatim}
$$
%%Thus we could
%%have saved two tokens at the expense of clarity by defining {\tt
%%middlepoint} like this:
%%$$\begin{verbatim}
%%def middlepoint(expr a) = if path a: (point .5*length a of
%%  else: .5(llcorner a + urcorner fi  a) enddef;
%%\end{verbatim}
%%$$

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÐÒÏ×ÅÒËÁ if} \rightarrow if \descr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ} \hbox{\tt :}
        \descr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ} \descr{ÁÌØÔÅÒÎÁÔÉ×Ù} fi$\\
%%$\tt \descr{if test} \rightarrow if \descr{boolean expression} \hbox{\tt :}
%%        \descr{balanced tokens} \descr{alternatives} fi$\\
$\tt \descr{ÁÌØÔÅÒÎÁÔÉ×Ù} \rightarrow \descr{ÐÕÓÔÏ}$\\
%%$\tt \descr{alternatives} \rightarrow \descr{empty}$\\
$\tt \qquad \;|\; else\hbox{\tt :} \descr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ}$\\
%%$\tt \qquad \;|\; else\hbox{\tt :} \descr{balanced tokens}$\\
$\tt \qquad \;|\; elseif \descr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ} \hbox{\tt :}
        \descr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ} \descr{ÁÌØÔÅÒÎÁÔÉ×Ù}$
%%$\tt \qquad \;|\; elseif \descr{boolean expression} \hbox{\tt :}
%%        \descr{balanced tokens} \descr{alternatives}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÐÒÏ×ÅÒËÉ {\tt if}.}
%%\caption{The syntax for {\tt if} tests.}
\label{syif}
\end{figure}

îÁÓÔÏÑÝÅÅ ÎÁÚÎÁÞÅÎÉÅ ÍÁËÒÏÓÏ× É ÐÒÏ×ÅÒÏË {\tt if} × Á×ÔÏÍÁÔÉÚÁÃÉÉ ÒÅÛÅÎÉÑ 
ÐÏ×ÔÏÒÑÀÝÉÈÓÑ ÚÁÄÁÞ, Á ÔÁËÖÅ × ×ÏÚÍÏÖÎÏÓÔÉ ÒÅÛÁÔØ ÐÏÄÚÁÄÁÞÉ ÐÏ-ÏÔÄÅÌØÎÏÓÔÉ.
%%The real purpose of macros and {\tt if} tests is to automate repetitive
%%tasks and allow important subtasks to be solved separately. 
îÁÐÒÉÍÅÒ, ÒÉÓ.~\ref{fig42} ÉÓÐÏÌØÚÕÅÔ ÍÁËÒÏÓÙ \verb|draw_marked|,
\verb|mark_angle| É \verb|mark_rt_angle| ÄÌÑ ÏÔÍÅÔËÉ ÌÉÎÉÊ É ÕÇÌÏ×, 
ÐÏÑ×ÌÑÀÝÉÈÓÑ ÎÁ ÒÉÓÕÎËÅ.
%%For example, Figure~\ref{fig42} uses macros \verb|draw_marked|,
%%\verb|mark_angle|, and \verb|mark_rt_angle| to mark lines and angles
%%that appear in the figure.

\begin{figure}[htp]
$$\begin{verbatim}
beginfig(42);
pair a,b,c,d;
b=(0,0); c=(1.5in,0); a=(0,.6in);
d-c = (a-b) rotated 25;
dotlabel.lft("a",a);
dotlabel.lft("b",b);
dotlabel.bot("c",c);
dotlabel.llft("d",d);
z0=.5[a,d];
z1=.5[b,c];
(z.p-z0) dotprod (d-a) = 0;
(z.p-z1) dotprod (c-b) = 0;
draw a--d;
draw b--c;
draw z0--z.p--z1;
draw_marked(a--b, 1);
draw_marked(c--d, 1);
draw_marked(a--z.p, 2);
draw_marked(d--z.p, 2);
draw_marked(b--z.p, 3);
draw_marked(c--z.p, 3);
mark_angle(z.p, b, a, 1);
mark_angle(z.p, c, d, 1);
mark_angle(z.p, c, b, 2);
mark_angle(c, b, z.p, 2);
mark_rt_angle(z.p, z0, a);
mark_rt_angle(z.p, z1, b);
endfig;
\end{verbatim}
\quad \mathcenter{\includegraphics{manfig-ru-42}}
$$
\caption{ëÏÄ MetaPost É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ÒÉÓÕÎÏË}
%%\caption{MetaPost code and the corresponding figure}
\label{fig42}
\end{figure}

úÁÄÁÞÁ ÍÁËÒÏÓÁ \verb|draw_marked|\index{draw_marked?\texttt{draw\_marked}} 
--- ÎÁÒÉÓÏ×ÁÔØ ÐÕÔØ Ó ÚÁÄÁÎÎÙÍ ÞÉÓÌÏÍ ÐÅÒÅÓÅËÁÀÝÉÈ ÏÔÍÅÔÏË ÐÏÓÅÒÅÄÉÎÅ.
%%The task of the
%%\verb|draw_marked|\index{draw_marked?\texttt{draw\_marked}} macro is to
%%draw a path with a given number of cross marks near its midpoint. 
óÔÏÉÔ ÎÁÞÁÔØ Ó ÐÏÄÚÁÄÁÞÉ ÒÉÓÏ×ÁÎÉÑ ÏÄÎÏÊ ÐÅÒÅÓÅËÁÀÝÅÊ ÐÕÔØ {\tt p} 
ÐÅÒÐÅÎÄÉËÕÌÑÒÎÏ ÏÔÍÅÔËÉ × ÎÅËÏÔÏÒÏÅ ×ÒÅÍÑ {\tt t}.
%%A convenient starting place is the subproblem of drawing a single cross
%%mark perpendicular to a path {\tt p} at some time {\tt t}. 
íÁËÒÏÓ \verb|draw_mark|\index{draw_mark?\texttt{draw\_mark}} ÎÁ 
ÒÉÓ.~\ref{drawmarked} ÒÅÛÁÅÔ ÜÔÕ ÐÏÄÚÁÄÁÞÕ ÎÁÈÏÖÄÅÎÉÅÍ ÓÎÁÞÁÌÁ ×ÅËÔÏÒÁ 
{\tt dm}, ÐÅÒÐÅÎÄÉËÕÌÑÒÎÏÇÏ {\tt p} ×~{\tt t}. 
%%The \verb|draw_mark|\index{draw_mark?\texttt{draw\_mark}} macro in
%%Figure~\ref{drawmarked} does this by first finding a vector {\tt dm}
%%perpendicular to~{\tt p} at~{\tt t}. 
äÌÑ ÕÐÒÏÝÅÎÉÑ ÐÏÚÉÃÉÏÎÉÒÏ×ÁÎÉÑ ÐÅÒÅÓÅËÁÀÝÅÊ ÏÔÍÅÔËÉ ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ 
\verb|draw_marked| ÂÅÒÅÔ ÄÌÉÎÕ ÄÕÇÉ\index{ÄÌÉÎÁ ÄÕÇÉ} {\tt a} 
×ÄÏÌØ {\tt p} É ÏÐÅÒÁÔÏÒÏÍ {\tt
arctime}\index{arctime of?\texttt{arctime of}} ×ÙÞÉÓÌÑÅÔ~{\tt t}
%%To simplify positioning the cross
%%mark, the \verb|draw_marked| macro is defined to take an arc
%%length\index{arc length} {\tt a} along {\tt p} and use the {\tt
%%arctime}\index{arctime} operator to compute~{\tt t}

ó ÒÅÛÅÎÉÅÍ ÐÏÄÚÁÄÁÞÉ ÒÉÓÏ×ÁÎÉÑ ÏÄÎÏÊ ÏÔÍÅÔËÉ, ÍÁËÒÏÓÕ \verb|draw_marked| 
ÏÓÔÁÎÅÔÓÑ ÔÏÌØËÏ ÎÁÒÉÓÏ×ÁÔØ ÐÕÔØ É ×ÙÚ×ÁÔØ \verb|draw_mark| Ó 
ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÊ ÄÌÉÎÏÊ ÄÕÇÉ. 
%%With the subproblem of drawing a single mark out of the way, the
%%\verb|draw_marked| macro only needs to draw the path and call
%%\verb|draw_mark| with the appropriate arc length values. 
íÁËÒÏÓ \verb|draw_marked| ÎÁ ÒÉÓ.~\ref{drawmarked} ÉÓÐÏÌØÚÕÅÔ 
ÁÒÉÆÍÅÔÉÞÅÓËÕÀ ÐÒÏÇÒÅÓÓÉÀ ÉÚ {\tt n} ÚÎÁÞÅÎÉÊ {\tt a}, ÃÅÎÔÒ ËÏÔÏÒÙÈ 
ÐÏÍÅÝÁÅÔÓÑ × {\tt .5*arclength~p}\index{arclength?\texttt{arclength}}.
%%The \verb|draw_marked| macro in Figure~\ref{drawmarked} uses {\tt n}
%%equally-spaced {\tt a} values centered on {\tt
%%.5*arclength~p}\index{arclength?\texttt{arclength}}.

\begin{figure}[htp]
$$\begin{verbatim}
marksize=4pt;

def draw_mark(expr p, a) =
  begingroup
  save t, dm; pair dm;
  t = arctime a of p;
  dm = marksize*unitvector direction t of p
    rotated 90;
  draw (-.5dm.. .5dm) shifted point t of p;
  endgroup
enddef;

def draw_marked(expr p, n) =
  begingroup
  save amid;
  amid = .5*arclength p;
  for i=-(n-1)/2 upto (n-1)/2:
    draw_mark(p, amid+.6marksize*i);
  endfor
  draw p;
  endgroup
enddef;
\end{verbatim}
$$
\caption{íÁËÒÏÓÙ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ ÐÕÔÉ {\tt p} Ó {\tt n} ÐÅÒÅÓÅËÁÀÝÉÍÉ ÏÔÍÅÔËÁÍÉ.}
%%\caption{Macros for drawing a path {\tt p} with {\tt n} cross marks.}
\label{drawmarked}
\end{figure}

éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ \verb|draw_marked| ÒÁÂÏÔÁÅÔ ÄÌÑ ËÒÉ×ÙÈ, ÏÎ ÍÏÖÅÔ ÂÙÔØ 
ÉÓÐÏÌØÚÏ×ÁÎ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ ÄÕÇ, ÇÅÎÅÒÉÒÕÅÍÙÈ ÍÁËÒÏÓÏÍ 
\verb|mark_angle|\index{mark_angle?\texttt{mark\_angle}}.
%%Since \verb|draw_marked| works for curved lines, it can be used to draw
%%the arcs that the
%%\verb|mark_angle|\index{mark_angle?\texttt{mark\_angle}} macro
%%generates. 
ó ÚÁÄÁÎÎÙÍÉ ÔÏÞËÁÍÉ {\tt a}, {\tt b} É {\tt c}, ÏÐÒÅÄÅÌÑÀÝÉÍÉ 
ÎÁÐÒÁ×ÌÅÎÎÙÊ ÐÒÏÔÉ× ÞÁÓÏ×ÏÊ ÓÔÒÅÌËÉ ÕÇÏÌ × {\tt b}, \verb|mark_angle| 
ÄÏÌÖÅÎ ÓÇÅÎÅÒÉÒÏ×ÁÔØ ÍÁÌÅÎØËÕÀ ÄÕÇÕ ÏÔ ÏÔÒÅÚËÁ {\tt ba} ÄÏ 
ÏÔÒÅÚËÁ {\tt bc}. 
%%Given points {\tt a}, {\tt b}, and {\tt c} that define a
%%counter-clockwise angle at {\tt b}, the \verb|mark_angle| needs to
%%generate a small arc from segment {\tt ba} to segment {\tt bc}. 
ïÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ ÎÁ ÒÉÓ.~\ref{markangle} ÄÅÌÁÅÔ ÜÔÏ ÓÏÚÄÁÎÉÅÍ 
ÄÕÇÉ {\tt p} Ó ÅÄÉÎÉÞÎÙÍ ÒÁÄÉÕÓÏÍ É ÚÁÔÅÍ ×ÙÞÉÓÌÅÎÉÅÍ ÍÁÓÛÔÁÂÉÒÕÀÝÅÇÏ 
ÍÎÏÖÉÔÅÌÑ {\tt s}, ËÏÔÏÒÙÊ ÄÅÌÁÅÔ ÅÅ ÄÏÓÔÁÔÏÞÎÏ ÂÏÌØÛÏÊ ÎÁ ×ÉÄ.
%%The
%%macro definition in Figure~\ref{markangle} does this by creating an arc
%%{\tt p} of radius one and then computing a scale factor {\tt s} that
%%makes it big enough to see clearly.

íÁËÒÏÓ \verb|mark_rt_angle|\index{mark_rt_angle?\texttt{mark\_rt\_angle}} 
ÎÁÍÎÏÇÏ ÐÒÏÝÅ.
%%The \verb|mark_rt_angle|\index{mark_rt_angle?\texttt{mark\_rt\_angle}}
%%macro is much simpler. 
ïÎ ÂÅÒÅÔ ÏÂÝÉÊ ÐÒÑÍÏÊ ÕÇÏÌ É ÉÓÐÏÌØÚÕÅÔ ÏÐÅÒÁÔÏÒ {\tt zscaled}\index{zscaled?\texttt{zscaled}} ÄÌÑ ÎÅÏÂÈÏÄÉÍÙÈ ×ÒÁÝÅÎÉÑ É 
ÍÁÓÛÔÁÂÉÒÏ×ÁÎÉÑ.
%%It takes a generic right-angle corner and uses
%%the {\tt zscaled}\index{zscaled?\texttt{zscaled}} operator to rotate it
%%and scale it as necessary.

\begin{figure}[htp]
$$\begin{verbatim}
angle_radius=8pt;

def mark_angle(expr a, b, c, n) =
  begingroup
  save s, p; path p;
  p = unitvector(a-b){(a-b)rotated 90}..unitvector(c-b);
  s = .9marksize/length(point 1 of p - point 0 of p);
  if s<angle_radius: s:=angle_radius; fi
  draw_marked(p scaled s shifted b, n);
  endgroup
enddef;

def mark_rt_angle(expr a, b, c) =
  draw ((1,0)--(1,1)--(0,1))
       zscaled (angle_radius*unitvector(a-b)) shifted b
enddef;
\end{verbatim}
$$
\caption{íÁËÒÏÓÙ ÄÌÑ ÏÔÍÅÔËÉ ÕÇÌÏ×.}
%%\caption{Macros for marking angles.}
\label{markangle}
\end{figure}


\subsection{óÕÆÆÉËÓÎÙÅ É ÔÅËÓÔÏ×ÙÅ ÐÁÒÁÍÅÔÒÙ}
%%\subsection{Suffix and Text Parameters}

ðÁÒÁÍÅÔÒÙ ÍÁËÒÏÓÁ ÎÅ ×ÓÅÇÄÁ ÄÏÌÖÎÙ ÂÙÔØ ×ÙÒÁÖÅÎÉÑÍÉ, ËÁË × ÐÒÅÄÙÄÕÝÉÈ 
ÐÒÉÍÅÒÁÈ.
%%Macro parameters need not always be expressions as in the previous
%%examples. 
úÁÍÅÎÁ ËÌÀÞÅ×ÏÇÏ ÓÌÏ×Á {\tt expr} ÎÁ {\tt
suffix}\index{suffix?\texttt{suffix}} ÉÌÉ {\tt
text}\index{text?\texttt{text}} × ÏÐÒÅÄÅÌÅÎÉÉ ÍÁËÒÏÓÁ ÏÂßÑ×ÌÑÅÔ ÐÁÒÁÍÅÔÒÙ 
ÓÏÏÔ×ÅÔÓÔ×ÅÎÎÏ ÉÍÅÎÁÍÉ ÐÅÒÅÍÅÎÎÙÈ ÉÌÉ ÐÒÏÉÚ×ÏÌØÎÏÊ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØÀ 
ÚÎÁËÏ×.
%%Replacing the keyword {\tt expr} with {\tt
%%suffix}\index{suffix?\texttt{suffix}} or {\tt
%%text}\index{text?\texttt{text}} in a macro definition declares the
%%parameters to be variable names or arbitrary sequences of tokens. 
îÁÐÒÉÍÅÒ, ÅÓÔØ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ Ó ÉÍÅÎÅÍ {\tt
hide}\index{hide?\texttt{hide}} É ÔÅËÓÔÏ×ÙÍ ÐÁÒÁÍÅÔÒÏÍ\index{ÐÁÒÁÍÅÔÒ!text}, 
ÉÎÔÅÒÐÒÅÔÉÒÕÅÍÙÍ ËÁË ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ËÏÍÁÎÄ, 
ÐÒÏÉÚ×ÏÄÑÝÉÊ ÐÕÓÔÏÊ \tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ}. 
%%For example, there is a predefined macro called {\tt
%%hide}\index{hide?\texttt{hide}} that takes a text
%%parameter\index{parameter!text} and interprets it as a sequence of
%%statements while ultimately producing an empty \tdescr{replacement
%%text}. 
äÒÕÇÉÍÉ ÓÌÏ×ÁÍÉ, {\tt hide} ÉÓÐÏÌÎÑÅÔ Ó×ÏÊ ÁÒÇÕÍÅÎÔ, Á ÓÌÅÄÕÀÝÉÊ ÚÎÁË 
ÐÏÓÌÅ ÎÅÇÏ ÂÅÒÅÔÓÑ ÔÁË, ËÁË ÂÕÄÔÏ ÎÉÞÅÇÏ ÎÅ ÐÒÏÉÚÏÛÌÏ.
%%In other words, {\tt hide} executes its argument and then gets
%%the next token as if nothing happened. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, 
$$ \hbox{\tt show hide(numeric a,b; a+b=3; a-b=1) a;} $$
ÐÅÞÁÔÁÅÔ ``\verb|>> 2|.''
%%Thus
%%$$ \hbox{\tt show hide(numeric a,b; a+b=3; a-b=1) a;} $$
%%prints ``\verb|>> 2|.''

åÓÌÉ ÂÙ {\tt hide} ÎÅ ÂÙÌ ÐÒÅÄÏÐÒÅÄÅÌÅÎ, ÔÏ ÅÇÏ ÍÏÖÎÏ ÂÙÌÏ ÏÐÒÅÄÅÌÉÔØ ÐÒÉÍÅÒÎÏ ÔÁË:
%%If the {\tt hide} macro were not predefined, it could be defined like this:
$$\begin{verbatim}
def ignore(expr a) = enddef;
def hide(text t) = ignore(begingroup t; 0 endgroup) enddef;
\end{verbatim}
$$
ëÏÍÁÎÄÙ, ÐÒÅÄÓÔÁ×ÌÅÎÎÙÅ ÐÁÒÁÍÅÔÒÏÍ-ÔÅËÓÔÏÍ {\tt t}, ÂÕÄÕÔ ÓÞÉÔÁÔØÓÑ
ËÁË ÞÁÓÔØ ÇÒÕÐÐÙ, ÆÏÒÍÉÒÕÀÝÅÊ ÁÒÇÕÍÅÎÔ ÄÌÑ {\tt ignore}.
%%The statements represented by the text parameter {\tt t} would be
%%evaluated as part of the group that forms the argument to {\tt ignore}.
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ {\tt ignore} ÉÍÅÅÔ ÐÕÓÔÏÊ \tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ}, ÒÁÓËÒÙÔÉÅ 
{\tt hide} ÎÅ ÐÒÏÉÚ×ÅÄÅÔ ÓÏ×ÅÒÛÅÎÎÏ ÎÉÞÅÇÏ.
%%Since {\tt ignore} has an empty \tdescr{replacement text}, expansion of
%%the {\tt hide} macro ultimately produces nothing.

äÒÕÇÏÊ ÐÒÉÍÅÒ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÏÇÏ ÍÁËÒÏÓÁ Ó ÔÅËÓÔÏ×ÙÍ ÐÁÒÁÍÅÔÒÏÍ --- ÜÔÏ 
{\tt dashpattern}\index{dashpattern?\texttt{dashpattern}}. 
%%Another example of a predefined macro with a text parameter is {\tt
%%dashpattern}\index{dashpattern?\texttt{dashpattern}}. 
ïÐÒÅÄÅÌÅÎÉÅ {\tt dashpattern} ÎÁÞÉÎÁÅÔ 
$$\begin{verbatim}
def dashpattern(text t) =
  begingroup save on, off;
\end{verbatim}
$$
É ÚÁÔÅÍ ÏÎÏ ÏÐÒÅÄÅÌÑÅÔ {\tt on} É {\tt off} ÍÁËÒÏÓÁÍÉ, ÓÏÚÄÁÀÝÉÍÉ 
ÔÒÅÂÕÅÍÕÀ ËÁÒÔÉÎËÕ ÐÒÉ ÐÏÑ×ÌÅÎÉÉ ÔÅËÓÔÏ×ÏÇÏ ÐÁÒÁÍÅÔÒÁ {\tt t} × ÔÅËÓÔÅ ÚÁÍÅÎÙ.
%%The definition of {\tt dashpattern} starts
%%$$\begin{verbatim}
%%def dashpattern(text t) =
%%  begingroup save on, off;
%%\end{verbatim}
%%$$
%%then it defines {\tt on} and {\tt off} to be macros that create the desired
%%picture when the text parameter~{\tt t} appears in the replacement text.

ôÅËÓÔÏ×ÙÅ ÐÁÒÁÍÅÔÒÙ ÏÞÅÎØ ÏÂÝÉÅ, ÎÏ ÉÈ ÏÂÝÎÏÓÔØ ÉÎÏÇÄÁ ÄÏÐÕÓÔÉÍÁ.
%%Text parameters are very general, but their generality sometimes gets in
%%the way. 
åÓÌÉ ÖÅ ×Ù ÈÏÔÉÔÅ × ÔÏÞÎÏÓÔÉ ÐÅÒÅÄÁ×ÁÔØ ÉÍÑ ÐÅÒÅÍÅÎÎÏÊ × ÍÁËÒÏÓ, ÔÏ ÌÕÞÛÅ 
ÏÂßÑ×ÉÔØ ÅÅ ËÁË ÐÁÒÁÍÅÔÒ-ÓÕÆÆÉËÓ\index{ÐÁÒÁÍÅÔÒ!suffix}. 
%%If you just want to pass a variable name to a macro, it is
%%better to declare it as a suffix parameter\index{parameter!suffix}. 
îÁÐÒÉÍÅÒ, \index{incr?\texttt{incr}}
$$ \hbox{\verb|def incr(suffix $) = begingroup $:=$+1; $ endgroup enddef;|} $$
ÏÐÒÅÄÅÌÑÅÔ ÍÁËÒÏÓ, ÞÔÏ ÂÕÄÅÔ ÐÏÌÕÞÁÔØ ÌÀÂÕÀ ÞÉÓÌÏ×ÕÀ ÐÅÒÅÍÅÎÎÕÀ, ÄÏÂÁ×ÌÑÔØ 
ÏÄÉÎ Ë ÎÅÊ É ×ÏÚ×ÒÁÝÁÔØ ÎÏ×ÏÅ ÚÎÁÞÅÎÉÅ. 
%%For example,\index{incr?\texttt{incr}}
%%$$ \hbox{\verb|def incr(suffix $) = begingroup $:=$+1; $ endgroup enddef;|} $$
%%defines a macro that will take any numeric variable, add one to it, and return
%%the new value. 
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÉÍÅÎÁ ÐÅÒÅÍÅÎÎÙÈ ÍÏÇÕÔ ÓÏÓÔÏÑÔØ ÉÚ ÂÏÌÅÅ ÏÄÎÏÇÏ ÚÎÁËÁ,
$$ \hbox{\tt incr(a3b)} $$
×ÐÏÌÎÅ ÄÏÐÕÓÔÉÍÏ, ÅÓÌÉ {\tt a3b} --- ÞÉÓÌÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ.
%%Since variable names can be more than one token long,
%%$$ \hbox{\tt incr(a3b)} $$
%%is perfectly acceptable if {\tt a3b} is a numeric variable. 
ðÁÒÁÍÅÔÒÙ-ÓÕÆÆÉËÓÙ Ñ×ÌÑÀÔÓÑ ÎÅÓËÏÌØËÏ ÂÏÌÅÅ ÏÂÝÉÍÉ, ÞÅÍ ÉÍÅÎÁ ÐÅÒÅÍÅÎÎÙÈ, 
ÐÏÔÏÍÕ ÞÔÏ ÏÐÒÅÄÅÌÅÎÉÑ ÎÁ ÒÉÓ.~\ref{syvar} ÄÏÐÕÓËÁÅÔ 
\tdescr{ÓÕÆÆÉËÓ}\index{ÓÕÆÆÉËÓ?\tdescr{ÓÕÆÆÉËÓ}}, ÎÁÞÉÎÁÀÝÉÊÓÑ 
Ó \tdescr{ÉÎÄÅËÓÁ}\index{ÉÎÄÅËÓ?\tdescr{ÉÎÄÅËÓ}}.
%%Suffix parameters are slightly more general than variable names because the
%%definition in Figure~\ref{syvar} allows a
%%\tdescr{suffix}\index{suffix?\tdescr{suffix}} to start with a
%%\tdescr{subscript}\index{subscript?\tdescr{subscript}}.

òÉÓ.~\ref{fig45} ÐÏËÁÚÙ×ÁÅÔ ËÁË ÐÁÒÁÍÅÔÒÙ suffix É expr ÍÏÇÕÔ ÂÙÔØ 
ÉÓÐÏÌØÚÏ×ÁÎÙ ×ÍÅÓÔÅ.
%%Figure~\ref{fig45} shows how suffix and expr parameters can be used
%%together. 
íÁËÒÏÓ {\tt getmid}\index{getmid?\texttt{getmid}} ÂÅÒÅÔ ÐÅÒÅÍÅÎÎÕÀ-ÐÕÔØ 
É ÓÏÚÄÁÅÔ ÍÁÓÓÉ×Ù ÔÏÞÅË É ÎÁÐÒÁ×ÌÅÎÉÑ, ÞØÉ ÉÍÅÎÁ ÐÏÌÕÞÁÀÔÓÑ 
ÐÒÉÓÏÅÄÉÎÅÎÉÅÍ {\tt mid}, {\tt off} É {\tt dir} Ë ÐÅÒÅÍÅÎÎÏÊ-ÐÕÔÉ.
%%The {\tt getmid}\index{getmid?\texttt{getmid}} macro takes a
%%path variable and creates arrays of points and directions whose names
%%are obtained by appending {\tt mid}, {\tt off}, and {\tt dir} to the
%%path variable. 
íÁËÒÏÓ {\tt joinup}\index{joinup?\texttt{joinup}} ÂÅÒÅÔ 
ÍÁÓÓÉ× ÔÏÞÅË É ÎÁÐÒÁ×ÌÅÎÉÊ É ÓÏÚÄÁÅÔ ÐÕÔØ ÄÌÉÎÙ {\tt
n}, ÐÒÏÈÏÄÑÝÉÊ ÞÅÒÅÚ ËÁÖÄÕÀ {\tt pt[i]} Ó ÎÁÐÒÁ×ÌÅÎÉÅÍ {\tt d[i]} ÉÌÉ
$-\hbox{\tt d[i]}$.
%%The {\tt joinup}\index{joinup?\texttt{joinup}} macro
%%takes arrays of points and directions and creates a path of length {\tt
%%n} that passes through each {\tt pt[i]} with direction {\tt d[i]} or
%%$-\hbox{\tt d[i]}$.

\begin{figure}[htp]
$$\begin{verbatim}
def getmid(suffix p) =
  pair p.mid[], p.off[], p.dir[];
  for i=0 upto 36:
    p.dir[i] = dir(5*i);
    p.mid[i]+p.off[i] = directionpoint p.dir[i] of p;
    p.mid[i]-p.off[i] = directionpoint -p.dir[i] of p;
  endfor
enddef;

def joinup(suffix pt, d)(expr n) =
  begingroup
  save res, g; path res;
  res = pt[0]{d[0]};
  for i=1 upto n:
    g:= if (pt[i]-pt[i-1]) dotprod d[i] <0: - fi 1;
    res := res{g*d[i-1]}...{g*d[i]}pt[i];
  endfor
  res
  endgroup
enddef;

beginfig(45)
path p, q;
p = ((5,2)...(3,4)...(1,3)...(-2,-3)...(0,-5)...(3,-4)
     ...(5,-3)...cycle) scaled .3cm shifted (0,5cm);
getmid(p);
draw p;
draw joinup(p.mid, p.dir, 36)..cycle;
q = joinup(p.off, p.dir, 36);
draw q..(q rotated 180)..cycle;
drawoptions(dashed evenly);
for i=0 upto 3:
  draw p.mid[9i]-p.off[9i]..p.mid[9i]+p.off[9i];
  draw -p.off[9i]..p.off[9i];
endfor
endfig;
\end{verbatim}
\quad \mathcenter{\includegraphics{manfig-ru-45}}
$$
\caption{ëÏÄ MetaPost É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ÒÉÓÕÎÏË}
%%\caption{MetaPost code and the corresponding figure}
\label{fig45}
\end{figure}

îÁÞÉÎÁÀÝÅÅÓÑ Ó 
$$ \hbox{\tt def joinup(suffix pt, d)(expr n) =} $$
ÏÐÒÅÄÅÌÅÎÉÅ ÍÏÖÅÔ ×ÏÓÐÒÉÎÉÍÁÔØÓÑ ÔÁË, ÞÔÏ ×ÙÚÏ× ÍÁËÒÏÓÁ {\tt joinup} ÍÏÖÅÔ 
ÉÍÅÔØ Ä×Á ÎÁÂÏÒÁ ÓËÏÂÏË ËÁË × 
$$ \hbox{\tt joinup(p.mid, p.dir)(36)} $$
×ÍÅÓÔÏ
$$ \hbox{\tt joinup(p.mid, p.dir, 36)} $$
%%A definition that starts
%%$$ \hbox{\tt def joinup(suffix pt, d)(expr n) =} $$
%%might suggest that calls to the {\tt joinup} macro should have two sets of
%%parentheses as in
%%$$ \hbox{\tt joinup(p.mid, p.dir)(36)} $$
%%instead of
%%$$ \hbox{\tt joinup(p.mid, p.dir, 36)} $$
ïÂÅ ÆÏÒÍÙ Ñ×ÌÑÀÔÓÑ ÄÏÐÕÓÔÉÍÙÍÉ.
%%In fact, both forms are acceptable. 
ðÁÒÁÍÅÔÒÙ × ×ÙÚÏ×Å ÍÁËÒÏÓÁ ÍÏÇÕÔ ÒÁÚÄÅÌÑÔØÓÑ ÚÁÐÑÔÙÍÉ ÉÌÉ ÐÁÒÁÍÉ {\tt )(}.
%%Parameters in a macro call can be
%%separated by commas or by {\tt )(} pairs. 
åÓÔØ ÔÏÌØËÏ ÏÄÎÏ ÏÇÒÁÎÉÞÅÎÉÅ --- ÚÁ ÔÅËÓÔÏ×ÙÍ ÐÁÒÁÍÅÔÒÏÍ\index{ÐÁÒÁÍÅÔÒ!text} 
ÄÏÌÖÎÁ ÉÄÔÉ ÐÒÁ×ÁÑ ÓËÏÂËÁ.
%%The only restriction is that
%%a text parameter\index{parameter!text} must be followed by a right
%%parenthesis. 
îÁÐÒÉÍÅÒ, ÍÁËÒÏÓ {\tt foo} Ó ÏÄÎÉÍ ÐÁÒÁÍÅÔÒÏÍ text É ÄÒÕÇÉÍ expr ÍÏÖÅÔ 
ÂÙÔØ ×ÙÚ×ÁÎ 
$$ \hbox{\tt foo(a,b)(c),} $$
× ÜÔÏÍ ÓÌÕÞÁÅ ÔÅËÓÔÏ×ÙÊ ÐÁÒÁÍÅÔÒ --- ÜÔÏ ``{\tt a,b}'', Á ÐÁÒÁÍÅÔÒ-×ÙÒÁÖÅÎÉÅ 
--- {\tt c}, ÎÏ 
$$ \hbox{\tt foo(a,b,c)} $$
ÕÓÔÁÎÁ×ÌÉ×ÁÅÔ ÐÁÒÁÍÅÔÒ-ÔÅËÓÔ × ``{\tt a,b,c}'' É ÏÓÔÁ×ÌÑÅÔ ÉÎÔÅÒÐÒÅÔÁÔÏÒ 
MetaPost ÐÒÏÄÏÌÖÁÔØ ÉÓËÁÔØ ÐÁÒÁÍÅÔÒ-×ÙÒÁÖÅÎÉÅ.
%%For instance, a macro {\tt foo} with one text parameter
%%and one expr parameter can be called
%%$$ \hbox{\tt foo(a,b)(c)} $$
%%in which case the text parameter is ``{\tt a,b}'' and the expr parameter is
%{\tt c}, but
%%$$ \hbox{\tt foo(a,b,c)} $$
%%sets the text parameter to ``{\tt a,b,c}'' and leaves the MetaPost interpreter
%%still looking for the expr parameter.

\subsection{íÁËÒÏÓÙ vardef}
%%\subsection{Vardef Macros}

ïÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ ÍÏÖÅÔ ÎÁÞÉÎÁÔØÓÑ Ó {\tt
vardef}\index{vardef?\texttt{vardef}} ×ÍÅÓÔÏ {\tt def}. 
%%A macro definition can begin with {\tt
%%vardef}\index{vardef?\texttt{vardef}} instead of {\tt def}. 
íÁËÒÏÓ, ÏÐÒÅÄÅÌÅÎÎÙÊ ÔÁËÉÍ ÏÂÒÁÚÏÍ, ÎÁÚÙ×ÁÅÔÓÑ vardef-ÍÁËÒÏÓÏÍ. 
%%Macros defined in this way are called vardef macros. 
ïÎÉ ÏÓÏÂÅÎÎÏ ÈÏÒÏÛÏ ÐÏÄÈÏÄÑÔ Ë ÐÒÉÌÏÖÅÎÉÑÍ, ÇÄÅ ÍÁËÒÏÓÙ ÉÓÐÏÌØÚÕÀÔÓÑ 
ËÁË ÆÕÎËÃÉÉ ÉÌÉ ÐÒÏÃÅÄÕÒÙ.
%%They are particularly
%%well-suited to applications where macros are being used like functions
%%or subroutines. 
çÌÁ×ÎÁÑ ÉÄÅÑ × ÔÏÍ, ÞÔÏ vardef-ÍÁËÒÏÓ ÐÏÄÏÂÅÎ ÐÅÒÅÍÅÎÎÏÊ ÔÉÐÁ ``ÍÁËÒÏÓ''.
%%The main idea is that a vardef macro is like a variable
%%of type ``macro.''

÷ÍÅÓÔÏ {\tt def} \tdescr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} vardef-ÍÁËÒÏÓ ÎÁÞÉÎÁÅÔ 
$$ {\tt vardef}\, \descr{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ}, $$
ÇÄÅ \tdescr{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ}\index{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ?\tdescr{ÏÂÏÂÝÅÎÎÁÑ 
ÐÅÒÅÍÅÎÎÁÑ}} -- ÜÔÏ ÉÍÑ ÐÅÒÅÍÅÎÎÏÊ Ó ÞÉÓÌÏ×ÙÍÉ ÉÎÄÅËÓÁÍÉ, ÚÁÍÅÎÅÎÎÙÍÉ 
ÎÁ ÓÉÍ×ÏÌ ÏÂÏÂÝÅÎÎÏÇÏ ÉÎÄÅËÓÁ\index{ÉÎÄÅËÓ!ÏÂÏÂÝÅÎÎÙÊ} --- {\tt
[]}\index{[]?\texttt{[]}!vardef macro?\texttt{vardef}-ÍÁËÒÏÓ}. 
%%Instead of {\tt def} \tdescr{symbolic token}, a vardef macro begins
%%$$ {\tt vardef}\, \descr{generic variable} $$
%%where a \tdescr{generic variable}\index{generic variable?\tdescr{generic
%%variable}} is a variable name with numeric subscripts replaced by the
%%generic subscript\index{subscript!generic} symbol {\tt
%%[]}\index{[]?\texttt{[]}!vardef macro?\texttt{vardef} macro}. 
äÒÕÇÉÍÉ ÓÌÏ×ÁÍÉ, ÉÍÑ ÐÏÓÌÅ {\tt vardef} ÏÂÑÚÁÎÏ ÉÍÅÔØ × ÔÏÞÎÏÓÔÉ 
ÔÁËÏÊ ÖÅ ÓÉÎÔÁËÓÉÓ ËÁË É ÉÍÑ × ÄÅËÌÁÒÁÃÉÉ ÐÅÒÅÍÅÎÎÏÊ.
%%In other words, the name following {\tt
%%vardef} obeys exactly the same syntax as the name given in a variable
%%declaration. 
ïÎÏ ---  ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÜÔÉËÅÔÏË É ÓÉÍ×ÏÌÏ× ÏÂÏÂÝÅÎÎÏÇÏ ÉÎÄÅËÓÁ, 
ÎÁÞÉÎÁÀÝÁÑÓÑ Ó ÜÔÉËÅÔËÉ, ÇÄÅ ÜÔÉËÅÔËÁ\index{ÜÔÉËÅÔËÉ} --- ÜÔÏ ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË, 
ÎÅ Ñ×ÌÑÀÝÉÊÓÑ ÍÁËÒÏÓÏÍ ÉÌÉ ÐÒÉÍÉÔÉ×ÎÙÍ ÏÐÅÒÁÔÏÒÏÍ, ËÁË ÏÂßÑÓÎÑÌÏÓØ × 
ÒÁÚÄÅÌÅ~\ref{vardecl}.
%%It is a sequence of tags and generic subscript symbols
%%starting with a tag, where a tag\index{tags} is a symbolic token that is
%%not a macro or a primitive operator as explained in
%%Section~\ref{vardecl}.

÷ ÐÒÏÓÔÅÊÛÅÍ ÓÌÕÞÁÅ ÉÍÑ vardef-ÍÁËÒÏÓÁ ÓÏÓÔÏÉÔ ÉÚ ÏÄÎÏÊ ÜÔÉËÅÔËÉ.
%%The simplest case is when the name of a vardef macro consists of a
%%single tag. 
÷ ÔÁËÉÈ ÏÂÓÔÏÑÔÅÌØÓÔ×ÁÈ {\tt def} É {\tt vardef} ÏÂÅÓÐÅÞÉ×ÁÀÔ ÐÏÞÔÉ 
ÏÄÉÎÁËÏ×ÕÀ ÆÕÎËÃÉÏÎÁÌØÎÏÓÔØ.
%%Under such circumstances, {\tt def} and {\tt vardef}
%%provide roughly the same functionality. 
îÁÉÂÏÌÅÅ ÏÞÅ×ÉÄÎÁÑ ÒÁÚÎÉÃÁ × ÔÏÍ, ÞÔÏ {\tt begingroup}\index{begingroup?\texttt{begingroup}} É {\tt
endgroup}\index{endgroup?\texttt{endgroup}} Á×ÔÏÍÁÔÉÞÅÓËÉ ×ÓÔÁ×ÌÑÀÔÓÑ 
ÓÏÏÔ×ÅÔÓÔ×ÅÎÎÏ × ÎÁÞÁÌÏ É ËÏÎÅà \tdescr{ÔÅËÓÔÁ ÚÁÍÅÎÙ} ËÁÖÄÏÇÏ 
vardef-ÍÁËÒÏÓÁ. 
%%The most obvious difference is
%%that {\tt begingroup}\index{begingroup?\texttt{begingroup}} and {\tt
%%endgroup}\index{endgroup?\texttt{endgroup}} are automatically inserted
%%at the beginning and end of the \tdescr{replacement text} of every
%%vardef macro. 
üÔÏ ÄÅÌÁÅÔ \tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ} ÇÒÕÐÐÏÊ É ÐÏÜÔÏÍÕ vardef-ÍÁËÒÏÓ 
×ÅÄÅÔ ÓÅÂÑ ÐÏÄÏÂÎÏ ÐÒÏÃÅÄÕÒÅ ÉÌÉ ÆÕÎËÃÉÉ.
%%This makes the \tdescr{replacement text} a group so that
%%a vardef macro behaves like a subroutine or a function call.

äÒÕÇÏÅ Ó×ÏÊÓÔ×Ï vardef-ÍÁËÒÏÓÏ× ÚÁËÌÀÞÁÅÔÓÑ × ÒÁÚÒÅÛÅÎÉÉ ÉÍÅÎ ÉÚ ÍÎÏÇÉÈ 
ÜÔÉËÅÔÏË É ÉÍÅÎ, ÓÏÄÅÒÖÁÝÉÈ ÏÂÏÂÝÅÎÎÙÅ ÉÎÄÅËÓÙ.
%%Another property of vardef macros is that they allow multi-token macro
%%names and macro names involving generic subscripts. 
ëÏÇÄÁ ÉÍÑ vardef-ÍÁËÒÏÓÁ ÉÍÅÅÔ ÏÂÏÂÝÅÎÎÙÅ ÉÎÄÅËÓÙ, ÔÏ ÞÉÓÌÏ×ÙÅ ÚÎÁÞÅÎÉÑ 
ÄÌÑ ÎÉÈ ÄÏÌÖÎÙ ÂÙÔØ ÚÁÄÁÎÙ ÐÒÉ ×ÙÚÏ×Å ÜÔÏÇÏ ÍÁËÒÏÓÁ.
%%When a vardef macro
%%name has generic subscripts, numeric values have to be given when the
%%macro is called. 
ðÏÓÌÅ ÏÐÒÅÄÅÌÅÎÉÑ ÍÁËÒÏÓÁ 
$$ \hbox{\tt vardef a[]b(expr p) =}\, \descr{ÔÅËÓÔ ÚÁÍÅÎÙ}\,
   \hbox{\tt enddef;}
$$
{\tt a2b((1,2))} É {\tt a3b((1,2)..(3,4))} --- ÜÔÏ ×ÙÚÏ×Ù ÍÁËÒÏÓÁ. 
%%After a macro definition
%%$$ \hbox{\tt vardef a[]b(expr p) =}\, \descr{replacement text}\,
%%   \hbox{\tt enddef;}
%%$$
%%{\tt a2b((1,2))} and {\tt a3b((1,2)..(3,4))} are macro calls. 
îÏ ËÁË ÍÏÖÅÔ \tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ} ÓËÁÚÁÔØ Ï ÒÁÚÎÉÃÅ ÍÅÖÄÕ {\tt a2b}
É {\tt a3b}? 
%%But how
%%can the \tdescr{replacement text} tell the difference between {\tt a2b}
%%and {\tt a3b}? 
ä×Á ÎÅÑ×ÎÙÈ ÐÁÒÁÍÅÔÒÁ-ÓÕÆÆÉËÓÁ\index{ÐÁÒÁÍÅÔÒ!suffix} 
Á×ÔÏÍÁÔÉÞÅÓËÉ ÐÒÅÄÏÓÔÁ×ÌÑÀÔÓÑ ÄÌÑ ÜÔÏÊ ÃÅÌÉ.
%%Two implicit suffix parameters\index{parameter!suffix}
%%are automatically provided for this purpose. 
ëÁÖÄÙÊ vardef-ÍÁËÒÏÓ ÉÍÅÅÔ ÐÁÒÁÍÅÔÒÙ-ÓÕÆÆÉËÓÙ 
\verb|#@|\index{#@?\texttt{\#@}} É
\verb|@|\index{@?\texttt{@}}, ÇÄÅ \verb|@| --- ÜÔÏ ÐÏÓÌÅÄÎÉÊ ÚÎÁË × ÉÍÅÎÉ 
×ÙÚÏ×Á ÍÁËÒÏÓÁ, Á \verb|#@| --- ÜÔÏ ×ÓÅ ÐÒÅÄÛÅÓÔ×ÕÀÝÅÅ ÐÏÓÌÅÄÎÅÍÕ ÚÎÁËÕ.
%%Every vardef macro has
%%suffix parameters \verb|#@|\index{#@?\texttt{\#@}} and
%%\verb|@|\index{@?\texttt{@}}, where \verb|@| is the last token in the
%%name from the macro call and \verb|#@| is everything preceding the last
%%token. 
ðÏÜÔÏÍÕ \verb|#@| ÒÁ×ÎÏ {\tt a2}, ËÏÇÄÁ ÄÁÎÎÏÅ ÉÍÑ --- {\tt a2b}, É 
{\tt a3}, ËÏÇÄÁ ÄÁÎÎÏÅ ÉÍÑ --- {\tt a3b}.
%%Thus \verb|#@| is {\tt a2} when the name is given as {\tt a2b}
%%and {\tt a3} when the name is given as {\tt a3b}.

ðÒÅÄÐÏÌÏÖÉÍ, ÎÁÐÒÉÍÅÒ, ÞÔÏ ÍÁËÒÏÓ {\tt a[]b} ÓÄ×ÉÇÁÅÔ Ó×ÏÊ ÁÒÇÕÍÅÎÔ ÎÁ 
×ÅÌÉÞÉÎÕ, ÚÁ×ÉÓÑÝÕÀ ÏÔ ÉÍÅÎÉ ×ÙÚÏ×Á ÜÔÏÇÏ ÍÁËÒÏÓÁ.
%%Suppose, for example, that the {\tt a[]b} macro is to take its argument
%%and shift it by an amount that depends on the macro name. 
ôÁËÏÊ ÍÁËÒÏÓ ÍÏÖÎÏ ÏÐÒÅÄÅÌÉÔØ ÐÒÉÍÅÒÎÏ ÔÁË:
$$ \hbox{\verb|vardef a[]b(expr p) = p shifted (#@,b) enddef;|} $$
%%The macro could be defined like this:
%%$$ \hbox{\verb|vardef a[]b(expr p) = p shifted (#@,b) enddef;|} $$
ôÏÇÄÁ {\tt a2b((1,2))} ÏÚÎÁÞÁÅÔ {\tt (1,2) shifted (a2,b)}
É {\tt a3b((1,2)..(3,4))} ÏÚÎÁÞÁÅÔ 
$$ \hbox{\tt ((1,2)..(3,4)) shifted (a3,b)}. $$
%%Then {\tt a2b((1,2))} means {\tt (1,2) shifted (a2,b)}
%%and {\tt a3b((1,2)..(3,4))} means
%%$$ \hbox{\tt ((1,2)..(3,4)) shifted (a3,b)}. $$

åÓÌÉ ÍÁËÒÏÓ ÂÙÌ {\tt a.b[]}, ÔÏ \verb|#@| ×ÓÅÇÄÁ ÂÕÄÅÔ {\tt a.b}, 
Á ÐÁÒÁÍÅÔÒ \verb|@| ÂÕÄÅÔ ÄÁ×ÁÔØ ÞÉÓÌÏ×ÏÊ ÉÎÄÅËÓ.
%%If the macro had been {\tt a.b[]}, \verb|#@| would always be {\tt a.b}
%%and the \verb|@| parameter would give the numeric subscript. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, {\tt a@} ÂÕÄÅÔ ÓÓÙÌÁÔØÓÑ ÎÁ ÜÌÅÍÅÎÔ ÍÁÓÓÉ×Á {\tt a[]}.
%%Then {\tt a@} would refer to an element of the array {\tt a[]}. 
úÁÍÅÔØÔÅ, ÞÔÏ \verb|@| --- ÜÔÏ ÐÁÒÁÍÅÔÒ-ÓÕÆÆÉËÓ, Á ÎÅ ÐÁÒÁÍÅÔÒ-×ÙÒÁÖÅÎÉÅ, 
ÐÏÜÔÏÍÕ ×ÙÒÁÖÅÎÉÅ, ÐÏÄÏÂÎÏÅ {\tt @+1}, ÏÛÉÂÏÞÎÏ. 
%%Note that
%%\verb|@| is a suffix parameter, not an expr parameter, so an expression
%%like {\tt @+1} would be illegal. 
åÄÉÎÓÔ×ÅÎÎÙÊ ÓÐÏÓÏ ÐÏÌÕÞÉÔØ ÞÉÓÌÏ×ÙÅ ÚÎÁÞÅÎÉÑ ÉÎÄÅËÓÏ× 
ÐÁÒÁÍÅÔÒÁ-ÓÕÆÆÉËÓÁ\index{ÐÁÒÁÍÅÔÒ!suffix} 
× ÉÚ×ÌÅÞÅÎÉÉ ÉÈ ÉÚ ÓÔÒÏËÉ, ×ÏÚ×ÒÁÝÁÅÍÏÊ ÏÐÅÒÁÔÏÒÏÍ {\tt
str}\index{str?\texttt{str}}\label{Dstr}.
%%The only way to get at the numeric
%%values of subscripts in a suffix parameter\index{parameter!suffix} is by
%%extracting them from the string returned by the {\tt
%%str}\index{str?\texttt{str}}\label{Dstr} operator. 
üÔÏÔ ÏÐÅÒÁÔÏÒ ÐÏ ÓÕÆÆÉËÓÕ ×ÏÚ×ÒÁÝÁÅÔ ÅÇÏ ÓÔÒÏËÏ×ÏÅ ÐÒÅÄÓÔÁ×ÌÅÎÉÅ.
%%This operator takes
%%a suffix and returns a string representation of a suffix. 
ðÏÜÔÏÍÕ {\tt str @} ÂÕÄÅÔ \verb|"3"| ÄÌÑ {\tt a.b3} É \verb|"3.14"| ÄÌÑ {\tt a.b3.14} ÉÌÉ {\tt a.b[3.14]}.
%%Thus {\tt str
%%@} would be \verb|"3"| in {\tt a.b3} and \verb|"3.14"| in {\tt a.b3.14}
%%or {\tt a.b[3.14]}. 
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÓÉÎÔÁËÓÉÓ ÄÌÑ \tdescr{ÓÕÆÆÉËÓÁ}\index{ÓÕÆÆÉËÓ?\tdescr{ÓÕÆÆÉËÓ}} 
ÎÁ ÒÉÓ.~\ref{syvar} ÔÒÅÂÕÅÔ ÚÁËÌÀÞÁÔØ ÏÔÒÉÃÁÔÅÌØÎÙÅ ÉÎÄÅËÓÙ × Ë×ÁÄÒÁÔÎÙÅ 
ÓËÏÂËÉ, {\tt str @} ×ÏÚ×ÒÁÝÁÅÔ {\tt \qq{[-3]}\qq} ÄÌÑ {\tt a.b[-3]}.
%%Since the syntax for a
%%\tdescr{suffix}\index{suffix?\tdescr{suffix}} in Figure~\ref{syvar}
%%requires negative subscripts to be in brackets, {\tt str @} returns {\tt
%%\qq{[-3]}\qq} in {\tt a.b[-3]}.

ïÐÅÒÁÔÏÒ {\tt str}, ËÁË ÐÒÁ×ÉÌÏ, ÉÓÐÏÌØÚÕÅÔÓÑ ÔÏÌØËÏ ÐÒÉ ËÒÁÊÎÅÊ 
ÎÅÏÂÈÏÄÉÍÏÓÔÉ.
%%The {\tt str} operator is generally for emergency use only. 
ìÕÞÛÅ ÉÓÐÏÌØÚÏ×ÁÔØ ÐÁÒÁÍÅÔÒÙ-ÓÕÆÆÉËÓÙ ÔÏÌØËÏ ËÁË ÉÍÅÎÁ ÐÅÒÅÍÅÎÎÙÈ ÉÌÉ 
ÓÕÆÆÉËÓÙ.
%%It is
%%better to use suffix parameters only as variable names or suffixes. 
îÁÉÌÕÞÛÉÊ ÐÒÉÍÅÒ vardef-ÍÁËÒÏÓÁ, ÉÓÐÏÌØÚÕÀÝÅÇÏ ÓÕÆÆÉËÓÙ, --- ÜÔÏ ÍÁËÒÏÓ, 
ÏÐÒÅÄÅÌÑÀÝÉÊ ÓÏÇÌÁÛÅÎÉÅ ÐÏ 
{\tt z}\index{z convention?{\tt z}-ÓÏÇÌÁÛÅÎÉÅ}. 
%%The
%%best example of a vardef macro involving suffixes is the {\tt z} macro
%%that defines the {\tt z} convention\index{z convention?{\tt z}
%%convention}. 
ïÐÒÅÄÅÌÅÎÉÅ ÉÓÐÏÌØÚÕÅÔ ÓÐÅÃÉÁÌØÎÙÊ ÚÎÁË 
\verb|@#|\index{@#?\texttt{@\#}}, ËÏÔÏÒÙÊ ÓÓÙÌÁÅÔÓÑ ÎÁ ÓÕÆÆÉËÓ ÐÏÓÌÅ ÉÍÅÎÉ 
ÍÁËÒÏÓÁ:
$$ \hbox{\verb|vardef z@#=(x@#,y@#) enddef;|} $$
%%The definition involves a special token
%%\verb|@#|\index{@#?\texttt{@\#}} that refers to the suffix following the
%%macro name:
%%$$ \hbox{\verb|vardef z@#=(x@#,y@#) enddef;|} $$
ïÎÏ ÏÚÎÁÞÁÅÔ, ÞÔÏ ÌÀÂÏÅ ÉÍÑ ÐÅÒÅÍÅÎÎÏÊ, ÞÅÊ ÐÅÒ×ÙÊ ÚÎÁË {\tt z}, 
ÜË×É×ÁÌÅÎÔÎÏ ÐÁÒÅ ÐÅÒÅÍÅÎÎÙÈ, ÞØÉ ÉÍÅÎÁ ÐÏÌÕÞÁÀÔÓÑ ÚÁÍÅÎÏÊ {\tt z} ÎÁ 
{\tt x} É~{\tt y}. 
%%This means that any variable name whose first token is {\tt z} is
%%equivalent to a pair of variables whose names are obtained by replacing
%%{\tt z} with {\tt x} and~{\tt y}. 
îÁÐÒÉÍÅÒ, {\tt z.a1} ×ÙÚÙ×ÁÅÔ ÍÁËÒÏÓ {\tt z} Ó ÐÁÒÁÍÅÔÒÏÍ-ÓÕÆÆÉËÓÏÍ 
\verb|@#|, ÕÓÔÁÎÏ×ÌÅÎÎÙÍ × {\tt a1}.
%%For instance, {\tt z.a1} calls the
%%{\tt z} macro with the suffix parameter \verb|@#| set to {\tt a1}.

÷ ÏÂÝÅÍ, 
$$ {\tt vardef}\, \descr{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ} \hbox{\verb|@#|} $$
Ñ×ÌÑÅÔÓÑ ÁÌØÔÅÒÎÁÔÉ×ÏÊ {\tt vardef} \tdescr{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ}, 
ÐÒÉ×ÏÄÑÝÅÊ ÉÎÔÅÒÐÒÅÔÁÔÏÒ MetaPost Ë ×ÙÄÅÌÅÎÉÀ ÓÕÆÆÉËÓÁ, ÓÌÅÄÕÀÝÅÇÏ ÚÁ 
ÉÍÅÎÅÍ, ÚÁÄÁÎÎÙÍ × ×ÙÚÏ×Å ÍÁËÒÏÓÁ, É ÄÅÌÁÀÝÅÊ ÅÇÏ ÄÏÓÔÕÐÎÙÍ ËÁË 
ÐÁÒÁÍÅÔÒ-ÓÕÆÆÉËÓ \verb|@#|. 
%%In general,
%%$$ {\tt vardef}\, \descr{generic variable} \hbox{\verb|@#|} $$
%%is an alternative to {\tt vardef} \tdescr{generic variable} that causes the
%%MetaPost interpreter
%%to look for a suffix following the name given in the macro call and makes this
%%available as the \verb|@#| suffix parameter.

óÕÍÍÉÒÕÅÍ ÏÓÏÂÙÅ Ó×ÏÊÓÔ×Á vardef-ÍÁËÒÏÓÏ×: ÏÎÉ ÄÏÐÕÓËÁÀÔ ËÁË ÛÉÒÏËÉÊ ËÌÁÓÓ 
ÉÍÅÎ ÄÌÑ ÍÁËÒÏÓÏ×, ÔÁË É ÉÍÅÎÁ ÍÁËÒÏÓÏ×, ÚÁ ËÏÔÏÒÙÍÉ ÓÌÅÄÕÅÔ ÓÐÅÃÉÁÌØÎÙÊ 
ÐÁÒÁÍÅÔÒ-ÓÕÆÆÉËÓ.
%%To summarize the special features of vardef macros, they allow a broad
%%class of macro names as well as macro names followed by a special suffix
%%parameter. 
âÏÌÅÅ ÔÏÇÏ, {\tt begingroup} É {\tt endgroup} Á×ÔÏÍÁÔÉÞÅÓËÉ 
ÄÏÂÁ×ÌÑÀÔÓÑ Ë \tdescr{ÔÅËÓÔÕ ÚÁÍÅÎÙ} vardef-ÍÁËÒÏÓÁ. 
%%Furthermore, {\tt begingroup} and {\tt endgroup} are
%%automatically added to the \tdescr{replacement text} of a vardef macro.
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÉÓÐÏÌØÚÏ×ÁÎÉÅ {\tt vardef} ×ÍÅÓÔÏ {\tt def} ÄÌÑ 
ÏÐÒÅÄÅÌÅÎÉÑ ÍÁËÒÏÓÁ {\tt joinup}\index{joinup?\texttt{joinup}} ÎÁ 
ÒÉÓ.~\ref{fig45} ÐÏÚ×ÏÌÉÔ ÉÚÂÅÖÁÔØ ÎÕÖÄÙ Ñ×ÎÏ ×ËÌÀÞÁÔØ {\tt begingroup} 
É {\tt endgroup} × ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ.
%%Thus using {\tt vardef} instead of {\tt def} to define the {\tt
%%joinup}\index{joinup?\texttt{joinup}} macro in Figure~\ref{fig45} would
%%have avoided the need to include {\tt begingroup} and {\tt endgroup}
%%explicitly in the macro definition.

æÁËÔÉÞÅÓËÉ, ÂÏÌØÛÉÎÓÔ×Ï ÏÐÒÅÄÅÌÅÎÉÊ ÍÁËÒÏÓÏ× × ÐÒÅÄÙÄÕÝÉÈ ÐÒÉÍÅÒÁÈ ÍÏÇÕÔ 
ÉÓÐÏÌØÚÏ×ÁÔØ {\tt vardef} ×ÍÅÓÔÏ {\tt def}. 
%%In fact, most of the macro definitions given in previous examples could
%%equally well use {\tt vardef} instead of {\tt def}. 
ïÂÙÞÎÏ ÎÅ ÉÍÅÅÔ ÂÏÌØÛÏÇÏ ÚÎÁÞÅÎÉÑ, ËÏÔÏÒÙÊ ÉÚ ÎÉÈ ÉÓÐÏÌØÚÏ×ÁÔØ, ÎÏ ÅÓÔØ 
ÈÏÒÏÛÅÅ ÏÂÝÅÅ ÐÒÁ×ÉÌÏ: ÉÓÐÏÌØÚÕÊÔÅ {\tt vardef}, ÅÓÌÉ ×Ù ÓÏÂÉÒÁÅÔÅÓØ 
ÉÓÐÏÌØÚÏ×ÁÔØ ÍÁËÒÏÓ ËÁË ÆÕÎËÃÉÀ ÉÌÉ ÐÒÏÃÅÄÕÒÕ.
%%It usually does not
%%matter very much which you use, but a good general rule is to use {\tt
%%vardef} if you intend the macro to be used like a function or a
%%subroutine. 
óÌÅÄÕÀÝÅÅ ÓÒÁ×ÎÅÎÉÅ ÄÏÌÖÎÏ ÐÏÍÏÞØ ÐÒÉ ÒÅÛÅÎÉÉ, ËÏÇÄÁ ÉÓÐÏÌØÚÏ×ÁÔØ 
{\tt vardef}. 
%%The following comparison should help in deciding when to
%%use {\tt vardef}.

\begin{itemize}
\item Vardef-ÍÁËÒÏÓ Á×ÔÏÍÁÔÉÞÅÓËÉ ÏËÒÕÖÅÎ {\tt begingroup} É 
{\tt endgroup}.
%%\item Vardef macros are automatically surrounded by {\tt begingroup}
%%and {\tt endgroup}.
\item éÍÑ vardef-ÍÁËÒÏÓÁ ÍÏÖÅÔ ÂÙÔØ ÂÏÌÅÅ ÏÄÎÏÇÏ ÚÎÁËÁ ÄÌÉÎÏÊ É ÏÎÏ 
ÍÏÖÅÔ ÓÏÄÅÒÖÁÔØ ÉÎÄÅËÓÙ.
%%\item The name of a vardef macro can be more than one token long and it can
%%contain subscripts.
\item Vardef-ÍÁËÒÏÓ ÍÏÖÅÔ ÉÍÅÔØ ÄÏÓÔÕÐ Ë ÓÕÆÆÉËÓÕ, ÓÌÅÄÕÀÝÅÍÕ ÚÁ ÉÍÅÎÅÍ 
ÍÁËÒÏÓÁ ÐÒÉ ÅÇÏ ×ÙÚÏ×Å.
%%\item A vardef macro can have access to the suffix that follows the macro name
%%when the macro is called.
\item ëÏÇÄÁ ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË ÉÓÐÏÌØÚÕÅÔÓÑ × ÉÍÅÎÉ vardef-ÍÁËÒÏÓÁ, ÏÎ 
ÏÓÔÁÅÔÓÑ ÜÔÉËÅÔËÏÊ\index{ÜÔÉËÅÔËÉ} É ÍÏÖÅÔ ÐÏ-ÐÒÅÖÎÅÍÕ ÉÓÐÏÌØÚÏ×ÁÔØÓÑ × ÉÍÅÎÁÈ 
ÄÒÕÇÉÈ ÐÅÒÅÍÅÎÎÙÈ. 
%%\item When a symbolic token is used in the name of a vardef macro it remains
%%a tag\index{tags} and can still be used in other variable names. 
ðÏÜÔÏÍÕ {\tt p5dir} --- ÜÔÏ ÐÒÁ×ÉÌØÎÏÅ ÉÍÑ ÐÅÒÅÍÅÎÎÏÊ, ÎÅÓÍÏÔÒÑ ÎÁ ÔÏ, ÞÔÏ 
{\tt dir} --- ÜÔÏ vardef-ÍÁËÒÏÓ, ÎÏ ÏÂÙÞÎÙÊ ÍÁËÒÏÓ, ÔÁËÏÊ ËÁË {\tt ...}\index{...?\texttt{...}}, ÎÅ ÍÏÖÅÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎ × ÉÍÅÎÉ ÐÅÒÅÍÅÎÎÏÊ. 
%%Thus
%%{\tt p5dir} is a legal variable name even though {\tt dir} is a vardef
%%macro, but an ordinary macro such as {\tt ...}\index{...?\texttt{...}}
%%cannot be used in a variable name. 
üÔÏ Ë ÌÕÞÛÅÍÕ, ÐÏÔÏÍÕ ËÁË {\tt z5...z6} ÅÓÔÅÓÔ×ÅÎÎÏ ÓÞÉÔÁÔØ ×ÙÒÁÖÅÎÉÅÍ-ÐÕÔÅÍ, 
Á ÎÅ ÓÏÓÔÁ×ÎÙÍ ÉÍÅÎÅÍ ÐÅÒÅÍÅÎÎÏÊ.
%%(This is fortunate since {\tt
%%z5...z6} is supposed to be a path expression, not an elaborate variable
%%name).
\end{itemize}

\subsection{ïÐÒÅÄÅÌÅÎÉÅ ÕÎÁÒÎÙÈ É ÂÉÎÁÒÎÙÈ ÍÁËÒÏÓÏ×}
%%\subsection{Defining Unary and Binary Macros}

õÖÅ ÎÅ ÒÁÚ ÕÐÏÍÉÎÁÌÏÓØ, ÞÔÏ ÎÅËÏÔÏÒÙÅ ÏÂÓÕÖÄÁÅÍÙÅ ÄÏ ÓÉÈ ÐÏÒ ÏÐÅÒÁÔÏÒÙ 
É ËÏÍÁÎÄÙ ÎÁ ÓÁÍÏÍ ÄÅÌÅ Ñ×ÌÑÀÔÓÑ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÍÉ ÍÁËÒÏÓÁÍÉ.
%%It has been mentioned several times that some of the operators and
%%commands discussed so far are actually predefined macros. 
üÔÏ ËÁÓÁÅÔÓÑ ÕÎÁÒÎÙÈ ÏÐÅÒÁÔÏÒÏ× {\tt round}\index{round?\texttt{round}} É {\tt
unitvector}\index{unitvector?\texttt{unitvector}}, ËÏÍÁÎÄ 
{\tt fill}\index{fill?\texttt{fill}} É {\tt
draw}\index{draw?\texttt{draw}}, ÂÉÎÁÒÎÙÈ ÏÐÅÒÁÔÏÒÏ× {\tt
dotprod}\index{dotprod?\texttt{dotprod}} É {\tt
intersectionpoint}\index{intersectionpoint?\texttt{intersectionpoint}}.
%%These include
%%unary operators such as {\tt round}\index{round?\texttt{round}} and {\tt
%%unitvector}\index{unitvector?\texttt{unitvector}}, statements such as
%%{\tt fill}\index{fill?\texttt{fill}} and {\tt
%%draw}\index{draw?\texttt{draw}}, and binary operators such as {\tt
%%dotprod}\index{dotprod?\texttt{dotprod}} and {\tt
%%intersectionpoint}\index{intersectionpoint?\texttt{intersectionpoint}}.
çÌÁ×ÎÁÑ ÒÁÚÎÉÃÁ ÍÅÖÄÕ ÜÔÉÍÉ ÍÁËÒÏÓÁÍÉ É ÔÅÍÉ, ÏÐÒÅÄÅÌÅÎÉÑ ËÏÔÏÒÙÈ ÍÙ ÕÖÅ 
ÚÎÁÅÍ, × ÔÏÍ, ËÁË ÏÐÒÅÄÅÌÑÔØ ÓÉÎÔÁËÓÉÓ ÉÈ ÁÒÇÕÍÅÎÔÏ×.
%%The main difference between these macros and the ones we already know
%%how to define is their argument syntax.

íÁËÒÏÓÙ {\tt round} É {\tt unitvector} --- ÜÔÏ ÐÒÉÍÅÒÙ ÔÏÇÏ, ÞÔÏ 
ÎÁ ÒÉÓ.~\ref{syexpr} ÚÏ×ÅÔÓÑ \tdescr{ÕÎÁÒÎÙÍ ÏÐÅÒÁÔÏÒÏÍ}. 
%%The {\tt round} and {\tt unitvector} macros are examples of what
%%Figure~\ref{syexpr} calls \tdescr{unary op}. 
úÁ ÎÉÍÉ ÓÌÅÄÕÅÔ ×ÙÒÁÖÅÎÉÅ-ÐÅÒ×ÉÞÎÏÓÔØ.
%%That is, they are followed by a primary expression. 
äÌÑ ÕËÁÚÁÎÉÑ ÁÒÇÕÍÅÎÔÁ ÍÁËÒÏÓÁ ÔÁËÏÇÏ ÔÉÐÁ ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ ÄÏÌÖÎÏ 
×ÙÇÌÑÄÅÔØ ÐÏÄÏÂÎÏ ÜÔÏÍÕ:
$$ \hbox{\tt vardef round primary u =}\, \descr{ÔÅËÓÔ ÚÁÍÅÎÙ}\,
   \hbox{\tt enddef;}
$$
%%To specify a macro argument of this type, the
%%macro definition should look like this:
%%$$ \hbox{\tt vardef round primary u =}\, \descr{replacement text}\,
%%   \hbox{\tt enddef;}
%%$$
ðÁÒÁÍÅÔÒ {\tt u} --- ÜÔÏ {\tt expr}-ÐÁÒÁÍÅÔÒ\index{ÐÁÒÁÍÅÔÒ!expr} É ÏÎ 
ÍÏÖÅÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎ × ÔÏÞÎÏÓÔÉ ÔÁËÖÅ ËÁË ÐÁÒÁÍÅÔÒ-×ÙÒÁÖÅÎÉÅ, 
ÏÐÒÅÄÅÌÑÅÍÙÊ ÏÂÙÞÎÙÍ ÓÉÎÔÁËÓÉÓÏÍ, 
$$ \hbox{\tt (expr u)} $$
%%The {\tt u} parameter is an expr parameter\index{parameter!expr} and it can be
%%used exactly like the expr parameter defined using the ordinary
%%$$ \hbox{\tt (expr u)} $$
%%syntax.

ëÁË ÐÒÅÄÐÏÌÁÇÁÅÔ ÐÒÉÍÅÒ Ó {\tt round}, ÍÁËÒÏÓ ÍÏÖÅÔ ÏÐÒÅÄÅÌÑÔØÓÑ Ó 
ÐÁÒÁÍÅÔÒÏÍ 
\tdescr{×ÔÏÒÉÞÎÏÓÔØÀ}\index{×ÔÏÒÉÞÎÏÓÔØ?\tdescr{×ÔÏÒÉÞÎÏÓÔØ}},
\tdescr{ÔÒÅÔÉÞÎÏÓÔØÀ}\index{ÔÒÅÔÉÞÎÏÓÔØ?\tdescr{ÔÒÅÔÉÞÎÏÓÔØ}} ÉÌÉ 
\tdescr{×ÙÒÁÖÅÎÉÅÍ}\index{×ÙÒÁÖÅÎÉÅ?\tdescr{×ÙÒÁÖÅÎÉÅ}}.
%%As the {\tt round} example suggests, a macro can be defined to take a
%%\tdescr{secondary}\index{secondary?\tdescr{secondary}},
%%\tdescr{tertiary}\index{tertiary?\tdescr{tertiary}}, or an
%%\tdescr{expression}\index{expression?\tdescr{expression}} parameter.
îÁÐÒÉÍÅÒ, ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÏÅ ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ {\tt fill} ÐÒÉÍÅÒÎÏ ÔÁËÏÅ\index{fill?\texttt{fill}}
$$ \hbox{\tt def fill expr c = addto currentpicture contour c enddef;} $$
%%For example, the predefined definition of the {\tt fill} macro is
%%roughly\index{fill?\texttt{fill}}
%%$$ \hbox{\tt def fill expr c = addto currentpicture contour c enddef;} $$

÷ÏÚÍÏÖÎÏ ÄÁÖÅ ÏÐÒÅÄÅÌÉÔØ ÍÁËÒÏÓ × ÒÏÌÉ \tdescr{of-ÏÐÅÒÁÔÏÒÁ}\index{of operator?\tdescr{of-ÏÐÅÒÁÔÏÒ}} ÉÚ ÒÉÓ.~\ref{syexpr}. 
%%It is even possible to define a macro to play the role of \tdescr{of
%%operator}\index{of operator?\tdescr{of operator}} in
%%Figure~\ref{syexpr}. 
îÁÐÒÉÍÅÒ, ÍÁËÒÏÓ {\tt direction
of}\index{direction of?\texttt{direction of}} ÉÍÅÅÔ ÏÐÒÅÄÅÌÅÎÉÅ ÔÁËÏÊ 
ÆÏÒÍÙ:
$$ \hbox{\tt vardef direction expr t of p =}\, \descr{ÔÅËÓÔ ÚÁÍÅÎÙ}\,
   \hbox{\tt enddef;}
$$
%%For example, the {\tt direction
%%of}\index{direction of?\texttt{direction of}} macro has a definition of
%%this form:
%%$$ \hbox{\tt vardef direction expr t of p =}\, \descr{replacement text}\,
%%   \hbox{\tt enddef;}
%%$$

íÁËÒÏÓÙ ÍÏÖÎÏ ÔÁËÖÅ ÏÐÒÅÄÅÌÑÔØ Ó ÐÏ×ÅÄÅÎÉÅÍ, ÐÏÄÏÂÎÙÍ ÂÉÎÁÒÎÙÍ ÏÐÅÒÁÔÏÒÁÍ.
%%Macros can also be defined to behave like binary operators. 
îÁÐÒÉÍÅÒ, ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ {\tt dotprod} ÉÍÅÅÔ 
ÆÏÒÍÕ\index{dotprod?\texttt{dotprod}}\index{primarydef?\texttt{primarydef}}
$$ \hbox{\tt primarydef w dotprod z =}\,  \descr{ÔÅËÓÔ ÚÁÍÅÎÙ}\,
   \hbox{\tt enddef;}
$$
%%For instance, the
%%definition of the {\tt dotprod} macro has the
%%form\index{dotprod?\texttt{dotprod}}\index{primarydef?\texttt{primarydef}}
%%$$ \hbox{\tt primarydef w dotprod z =}\,  \descr{replacement text}\,
%%   \hbox{\tt enddef;}
%%$$
üÔÁ ÆÏÒÍÁ ÄÅÌÁÅÔ {\tt dotprod} \tdescr{ÐÅÒ×ÉÞÎÙÍ ÂÉÎÁÒÎÙÍ 
ÏÐÅÒÁÔÏÒÏÍ}\index{ÐÅÒ×ÉÞÎÙÊ
binop?\tdescr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}. 
%%This makes {\tt dotprod} a \tdescr{primary binop}\index{primary
%%binop?\tdescr{primary binop}}. 
ðÏÈÏÖÉÍ ÏÂÒÁÚÏÍ {\tt
secondarydef}\index{secondarydef?\texttt{secondarydef}} É {\tt
tertiarydef}\index{tertiarydef?\texttt{tertiarydef}} ××ÏÄÑÔ ÏÐÒÅÄÅÌÅÎÉÑ 
\tdescr{×ÔÏÒÉÞÎÏÇÏ ÂÉÎÁÒÎÏÇÏ ÏÐÅÒÁÔÏÒÁ}\index{×ÔÏÒÉÞÎÙÊ binop?\tdescr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}
É \tdescr{ÔÒÅÔÉÞÎÏÇÏ ÂÉÎÁÒÎÏÇÏ ÏÐÅÒÁÔÏÒÁ}\index{ÔÒÅÔÉÞÎÙÊ binop?\tdescr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}. 
%%Similarly, {\tt
%%secondarydef}\index{secondarydef?\texttt{secondarydef}} and {\tt
%%tertiarydef}\index{tertiarydef?\texttt{tertiarydef}} introduce
%%\tdescr{secondary binop}\index{secondary binop?\tdescr{secondary binop}}
%%and \tdescr{tertiary binop}\index{tertiary binop?\tdescr{tertiary
%%binop}} definitions. 
÷ÓÅ ÏÎÉ ÏÐÒÅÄÅÌÑÀÔ ÏÂÙÞÎÙÅ ÍÁËÒÏÓÙ, Á ÎÅ vardef-ÍÁËÒÏÓÙ, ÎÁÐÒÉÍÅÒ, 
``{\tt primaryvardef}'' ÎÅ ÓÕÝÅÓÔ×ÕÅÔ.
%%These all define ordinary macros, not vardef
%%macros; e.g., there is no ``{\tt primaryvardef}.''

ôÁËÉÍ ÏÂÒÁÚÏÍ, ÏÐÒÅÄÅÌÅÎÉÑ ÍÁËÒÏÓÏ× ÍÏÇÕÔ ××ÏÄÉÔØÓÑ Ó {\tt def}, 
{\tt vardef}, {\tt primarydef}, {\tt secondarydef} ÉÌÉ {\tt tertiarydef}. 
%%Thus macro definitions can be introduced by {\tt def}, {\tt vardef},
%%{\tt primarydef}, {\tt secondarydef}, or {\tt tertiarydef}. 
\tdescr{ôÅËÓÔ ÚÁÍÅÎÙ}\index{ÔÅËÓÔ ÚÁÍÅÎÙ?\tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ}} 
--- ÜÔÏ ÌÀÂÏÊ ÓÐÉÓÏË ÚÎÁËÏ×, ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÊ ÏÔÎÏÓÉÔÅÌØÎÏ ÐÁÒ {\tt
def}-{\tt enddef}, ÇÄÅ ×ÓÅ ÐÑÔØ ÏÐÒÅÄÅÌÑÀÝÉÈ ÍÁËÒÏÓ ÚÎÁËÏ× 
ÒÁÓÓÍÁÔÒÉ×ÁÀÔÓÑ ÐÏÄÏÂÎÙÍÉ {\tt def} × ÓÏÏÔ×ÅÔÓÔ×ÉÉ {\tt def}-{\tt enddef}.
%%A \tdescr{replacement text}\index{replacement text?\tdescr{replacement
%%text}} is any list of tokens that is balanced with respect to {\tt
%%def}-{\tt enddef} pairs where all five macro definition tokens are
%%treated like {\tt def} for the purpose of {\tt def}-{\tt enddef}
%%matching.

÷ÅÓØ ÓÉÎÔÁËÓÉÓ ÄÌÑ ÏÐÒÅÄÅÌÅÎÉÊ ÍÁËÒÏÓÏ× ÐÒÉ×ÏÄÉÔÓÑ ÎÁ ÒÉÓ.~\ref{symacro}.
%%The rest of the syntax for macro definitions is summarized in
%%Figure~\ref{symacro}. 
÷ ÜÔÏÍ ÓÉÎÔÁËÓÉÓÅ ÅÓÔØ ÎÅÓËÏÌØËÏ ÓÀÒÐÒÉÚÏ×.
%%The syntax contains a few surprises. 
ðÁÒÁÍÅÔÒÙ ÍÁËÒÏÓÁ ÍÏÇÕÔ ÉÍÅÔØ \tdescr{ÏÔÄÅÌÅÎÎÕÀ ÞÁÓÔØ} É 
\tdescr{ÎÅÏÔÄÅÌÅÎÎÕÀ ÞÁÓÔØ}.
%%The macro
%%parameters can have a \tdescr{delimited part} and an \tdescr{undelimited
%%part}. 
ïÂÙÞÎÏ ÏÄÎÁ ÉÚ ÎÉÈ \tdescr{ÐÕÓÔÏ}, ÎÏ ×ÏÚÍÏÖÎÏ ÉÍÅÔØ ÏÂÅ ÞÁÓÔÉ ÎÅÐÕÓÔÙÍÉ: 
$$ \hbox{\tt def foo(text a) expr b =}\, \descr{ÔÅËÓÔ ÚÁÍÅÎÙ}\,
   \hbox{\tt enddef;}
$$
%%Normally, one of these is \tdescr{empty}, but it is possible to
%%have both parts nonempty:
%%$$ \hbox{\tt def foo(text a) expr b =}\, \descr{replacement text}\,
%%   \hbox{\tt enddef;}
%%$$
üÔÏ ÏÐÒÅÄÅÌÑÅÔ ÍÁËÒÏÓ {\tt foo} Ó ÔÅËÓÔÏ×ÙÍ ÐÁÒÁÍÅÔÒÏÍ × ÓËÏÂËÁÈ, ÚÁ ËÏÔÏÒÙÍ 
ÉÄÅÔ ×ÙÒÁÖÅÎÉÅ.
%%This defines a macro {\tt foo} to take a text parameter in parentheses followed
%%by an expression.

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ} \rightarrow
        \descr{ÚÁÇÏÌÏ×ÏË ÍÁËÒÏÓÁ} \hbox{\tt =} \descr{ÔÅËÓÔ ÚÁÍÅÎÙ}\, enddef$\\
%%$\tt \descr{macro definition} \rightarrow
%%        \descr{macro heading} \hbox{\tt =} \descr{replacement text}\, enddef$\\
$\tt \descr{ÚÁÇÏÌÏ×ÏË ÍÁËÒÏÓÁ} \rightarrow  def\, \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}
        \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \descr{ÎÅÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}$\\
%%$\tt \descr{macro heading} \rightarrow  def\, \descr{symbolic token}
%%        \descr{delimited part} \descr{undelimited part}$\\
$\tt \qquad \;|\; vardef\, \descr{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ} \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}
        \descr{ÎÅÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}$\\
%%$\tt \qquad \;|\; vardef\, \descr{generic variable} \descr{delimited part}
%%        \descr{undelimited part}$\\
$\tt \qquad \;|\; vardef\, \descr{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ} \hbox{\tt @\#}
        \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \descr{ÎÅÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}$\\
%%$\tt \qquad \;|\; vardef\, \descr{generic variable} \hbox{\tt @\#}
%%        \descr{delimited part} \descr{undelimited part}$\\
$\tt \qquad \;|\; \descr{ÏÐÒÅÄÅÌÅÎÉÅ ÂÉÎÁÒÎÏÓÔÉ} \descr{ÐÁÒÁÍÅÔÒ}
        \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \qquad \;|\; \descr{binary def} \descr{parameter}
%%        \descr{symbolic token} \descr{parameter}$\\
$\tt \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \rightarrow \descr{ÐÕÓÔÏ}$\\
%%$\tt \descr{delimited part} \rightarrow \descr{empty}$\\
$\tt \qquad \;|\; \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}
        \hbox{\tt (}\descr{ÔÉÐ ÐÁÒÁÍÅÔÒÁ} \descr{ÚÎÁËÉ ÐÁÒÁÍÅÔÒÁ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; \descr{delimited part}
%%        \hbox{\tt (}\descr{parameter type} \descr{parameter tokens}\hbox{\tt )}$\\
$\tt \descr{ÔÉÐ ÐÁÒÁÍÅÔÒÁ} \rightarrow expr \;|\; suffix \;|\; text$\\
%%$\tt \descr{parameter type} \rightarrow expr \;|\; suffix \;|\; text$\\
$\tt \descr{ÚÎÁËÉ ÐÁÒÁÍÅÔÒÁ} \rightarrow \descr{ÐÁÒÁÍÅÔÒ} \;|\;
        \descr{ÚÎÁËÉ ÐÁÒÁÍÅÔÒÁ}\hbox{\tt ,} \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \descr{parameter tokens} \rightarrow \descr{parameter} \;|\;
%%        \descr{parameter tokens}\hbox{\tt ,} \descr{parameter}$\\
$\tt \descr{ÐÁÒÁÍÅÔÒ} \rightarrow \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}$\\
%%$\tt \descr{parameter} \rightarrow \descr{symbolic token}$\\
$\tt \descr{ÎÅÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \rightarrow \descr{ÐÕÓÔÏ}$\\
%%$\tt \descr{undelimited part} \rightarrow \descr{empty}$\\
$\tt \qquad \;|\; \descr{ÔÉÐ ÐÁÒÁÍÅÔÒÁ} \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \qquad \;|\; \descr{parameter type} \descr{parameter}$\\
$\tt \qquad \;|\; \descr{ÐÒÉÏÒÉÔÅÔ} \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \qquad \;|\; \descr{precedence level} \descr{parameter}$\\
$\tt \qquad \;|\; expr\, \descr{ÐÁÒÁÍÅÔÒ}\, of\, \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \qquad \;|\; expr\, \descr{parameter}\, of\, \descr{parameter}$\\
$\tt \descr{ÐÒÉÏÒÉÔÅÔ} \rightarrow primary \;|\; secondary \;|\;
        tertiary$\\
%%$\tt \descr{precedence level} \rightarrow primary \;|\; secondary \;|\;
%%        tertiary$\\
$\tt \descr{ÏÐÒÅÄÅÌÅÎÉÅ ÂÉÎÁÒÎÏÓÔÉ} \rightarrow primarydef \;|\; secondarydef \;|\;
        tertiatydef$
%%$\tt \descr{binary def} \rightarrow primarydef \;|\; secondarydef \;|\;
%%        tertiatydef$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÏÐÒÅÄÅÌÅÎÉÊ ÍÁËÒÏÓÏ×}
%%\caption{The syntax for macro definitions}
\label{symacro}
\end{figure}

óÉÎÔÁËÓÉÓ ÔÁËÖÅ ÐÏÚ×ÏÌÑÅÔ \tdescr{ÎÅÏÔÄÅÌÅÎÎÏÊ ÞÁÓÔÉ} ÕËÁÚÙ×ÁÔØ ÔÉÐ 
ÁÒÇÕÍÅÎÔÁ {\tt suffix}\index{suffix?\texttt{suffix}} ÉÌÉ {\tt
text}\index{text?\texttt{text}}. 
%%The syntax also allows the \tdescr{undelimited part} to specify an
%%argument type of {\tt suffix}\index{suffix?\texttt{suffix}} or {\tt
%%text}\index{text?\texttt{text}}. 
ðÒÉÍÅÒ ÍÁËÒÏÓÁ Ó ÎÅÏÔÄÅÌÅÎÎÙÍ ÐÁÒÁÍÅÔÒÏÍ-ÓÕÆÆÉËÓÏÍ\index{ÐÁÒÁÍÅÔÒ!suffix} --- 
ÜÔÏ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ {\tt incr}\index{incr?\texttt{incr}}\label{Dincr}, 
ËÏÔÏÒÙÊ × ÄÅÊÓÔ×ÉÔÅÌØÎÏÓÔÉ ÏÐÒÅÄÅÌÑÅÔÓÑ ÐÒÉÍÅÒÎÏ ÔÁË:
$$ \hbox{\verb|vardef incr suffix $ = $:=$+1; $ enddef;|} $$
%%An example of a macro with an
%%undelimited suffix parameter\index{parameter!suffix} is the predefined
%%macro {\tt incr}\index{incr?\texttt{incr}}\label{Dincr} that is actually
%%defined like this:
%%$$ \hbox{\verb|vardef incr suffix $ = $:=$+1; $ enddef;|} $$
üÔÏ ÄÅÌÁÅÔ {\tt incr} ÆÕÎËÃÉÅÊ, ÞÔÏ ÂÅÒÅÔ ÐÅÒÅÍÅÎÎÕÀ, Õ×ÅÌÉÞÉ×ÁÅÔ ÅÅ É 
×ÏÚ×ÒÁÝÁÅÔ ÎÏ×ÏÅ ÚÎÁÞÅÎÉÅ.
%%This makes {\tt incr} a function that takes a variable, increments it,
%%and returns the new value. 
îÅÏÔÄÅÌÅÎÎÙÅ ÐÁÒÁÍÅÔÒÙ-ÓÕÆÆÉËÓÙ ÍÏÇÕÔ ÂÙÔØ × ÓËÏÂËÁÈ, ÐÏÜÔÏÍÕ É {\tt incr a}, 
É {\tt incr(a)} ÐÒÁ×ÉÌØÎÙ, ÅÓÌÉ {\tt a} --- ÜÔÏ ÞÉÓÌÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ.
%%Undelimited suffix parameters may be
%%parenthesized, so {\tt incr a} and {\tt incr(a)} are both legal if {\tt
%%a} is a numeric variable. 
åÓÔØ ÔÁËÖÅ ÐÏÈÏÖÉÊ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ {\tt
decr}\index{decr?\texttt{decr}}, ×ÙÞÉÔÁÀÝÉÊ~1.
%%There is also a similar predefined macro {\tt
%%decr}\index{decr?\texttt{decr}} that subtracts~1.

îÅÏÔÄÅÌÅÎÎÙÅ ÔÅËÓÔÏ×ÙÅ ÐÁÒÁÍÅÔÒÙ\index{ÐÁÒÁÍÅÔÒ!text} ÒÁÓÐÒÏÓÔÒÁÎÑÀÔÓÑ ÄÏ 
ËÏÎÃÁ ËÏÍÁÎÄÙ.
%%Undelimited text parameters\index{parameter!text} run to the end of a
%%statement. 
âÏÌÅÅ ÔÏÞÎÏ, ÎÅÏÔÄÅÌÅÎÎÙÊ ÔÅËÓÔÏ×ÙÊ ÐÁÒÁÍÅÔÒ --- ÜÔÏ ÓÐÉÓÏË ÚÎÁËÏ×, ÓÌÅÄÕÀÝÉÈ 
ÚÁ ×ÙÚÏ×ÏÍ ÍÁËÒÏÓÁ ÄÏ ÐÅÒ×ÏÇÏ ``{\tt ;}\index{ÔÏÞËÁ Ó ÚÁÐÑÔÏÊ}'' ÉÌÉ ``{\tt
endgroup}\index{endgroup?\texttt{endgroup}}'' ÉÌÉ ``{\tt
end}\index{end?\texttt{end}}'', Ó ÔÅÍ ÕÔÏÞÎÅÎÉÅÍ, ÞÔÏ ÁÒÇÕÍÅÎÔ, ÓÏÄÅÒÖÁÝÉÊ 
``{\tt begingroup}'' ÂÕÄÅÔ ×ÓÅÇÄÁ ×ËÌÀÞÁÔØ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ  ``{\tt endgroup}''.
%%More precisely, an undelimited text parameter is the list of
%%tokens following the macro call up to the first ``{\tt
%%;}\index{semicolon}'' or ``{\tt
%%endgroup}\index{endgroup?\texttt{endgroup}}'' or ``{\tt
%%end}\index{end?\texttt{end}}'' except that an argument containing ``{\tt
%%begingroup}'' will always include the matching ``{\tt endgroup}.'' 
ðÒÉÍÅÒ ÎÅÏÔÄÅÌÅÎÎÏÇÏ ÔÅËÓÔÏ×ÏÇÏ ÐÁÒÁÍÅÔÒÁ --- × ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÏÍ ÍÁËÒÏÓÅ 
{\tt cutdraw}\index{cutdraw?\texttt{cutdraw}}\label{Dctdraw}, ÞØÅ 
ÏÐÒÅÄÅÌÅÎÉÅ ×ÙÇÌÑÄÉÔ ÐÒÉÍÅÒÎÏ ÔÁË\index{linecap?\texttt{linecap}}\index{butt?\texttt{butt}}\index{interim?\texttt{interim}}
$$\begin{verbatim}
def cutdraw text t =
  begingroup interim linecap:=butt; draw t; endgroup enddef;
\end{verbatim}
$$
%%An example of an undelimited text parameter comes from the predefined macro
%%{\tt cutdraw}\index{cutdraw?\texttt{cutdraw}}\label{Dctdraw} whose
%%definition is
%%roughly\index{linecap?\texttt{linecap}}\index{butt?\texttt{butt}}\index{interim?\texttt{interim}}
%%$$\begin{verbatim}
%%def cutdraw text t =
%%  begingroup interim linecap:=butt; draw t; endgroup enddef;
%%\end{verbatim}
%%$$
üÔÏ ÄÅÌÁÅÔ {\tt cutdraw} ÓÉÎÏÎÉÍÏÍ {\tt draw}, ÎÏ Ó ÄÒÕÇÉÍ ÚÎÁÞÅÎÉÅÍ {\tt linecap}. 
%%This makes {\tt cutdraw} synonymous with {\tt draw} except for the {\tt
%%linecap} value. 
üÔÏ ÍÁËÒÏÓ ÐÒÅÄÏÓÔÁ×ÌÑÅÔÓÑ × ÏÓÎÏ×ÎÏÍ ÄÌÑ ÓÏ×ÍÅÓÔÉÍÏÓÔÉ Ó \MF\index{metafont?\MF}.
%%(This macro is provided mainly for compatibility with
%%\MF\index{metafont?\MF}.)

\section{ãÉËÌÙ}
%%\section{Loops}

íÎÏÇÏÞÉÓÌÅÎÎÙÅ ÐÒÉÍÅÒÙ × ÐÒÅÄÙÄÕÝÉÈ ÒÁÚÄÅÌÁÈ ÉÓÐÏÌØÚÏ×ÁÌÉ ÐÒÏÓÔÕÀ ÆÏÒÍÕ ÃÉËÌÁ 
{\tt for}\index{ÃÉËÌÙ}\index{for?\texttt{for}}\index{endfor?\texttt{endfor}},
$$ {\tt for}\, \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}\, \hbox{\tt =}\,
   \descr{×ÙÒÁÖÅÎÉÅ}\, {\tt upto}\, \descr{×ÙÒÁÖÅÎÉÅ}:\
   \descr{ÔÅÌÏ ÃÉËÌÁ}\, {\tt endfor}
$$
%%Numerous examples in previous sections have used simple {\tt for} loops of the
%%form\index{loops}\index{for?\texttt{for}}\index{endfor?\texttt{endfor}}
%%$$ {\tt for}\, \descr{symbolic token}\, \hbox{\tt =}\,
%%   \descr{expression}\, {\tt upto}\, \descr{expression}:\
%%   \descr{loop text}\, {\tt endfor}
%%$$
ëÏÎÓÔÒÕÉÒÏ×ÁÔØ ÃÉËÌ Ó ÕÍÅÎØÛÅÎÉÅÍ ÔÁËÖÅ ÐÒÏÓÔÏ --- ÎÕÖÎÏ ÌÉÛØ ÚÁÍÅÎÉÔØ 
{\tt upto} ÎÁ {\tt
downto}\index{downto?\texttt{downto}}\label{Ddwnto} É ÓÄÅÌÁÔØ ×ÔÏÒÏÅ 
\tdescr{×ÙÒÁÖÅÎÉÅ} ÍÅÎØÛÉÍ ÐÅÒ×ÏÇÏ. 
%%It is equally simple to construct a loop that counts downward: just
%%replace {\tt upto} by {\tt
%%downto}\index{downto?\texttt{downto}}\label{Ddwnto} make the second
%%\tdescr{expression} smaller than the first. 
üÔÏÔ ÒÁÚÄÅÌ ÏÐÉÓÙ×ÁÅÔ ÂÏÌÅÅ ÓÌÏÖÎÙÅ ÓÉÔÕÁÃÉÉ: ÐÒÏÇÒÅÓÓÉÉ; ÃÉËÌÙ, ÇÄÅ ÐÁÒÁÍÅÔÒ 
ÃÉËÌÁ ×ÅÄÅÔ ÓÅÂÑ ËÁË ÓÕÆÆÉËÓ; ÓÐÏÓÏÂÙ ×ÙÈÏÄÁ ÉÚ ÃÉËÌÁ.
%%This section covers more
%%complicated types of progressions, loops where the loop counter behaves
%%like a suffix parameter, and ways of exiting from a loop.

îÁÞÎÅÍ Ó ÐÒÅÄÓÔÁ×ÌÅÎÉÑ ÏÂÝÅÇÏ ÆÁËÔÁ ÔÏÇÏ, ÞÔÏ {\tt
upto}\index{upto?\texttt{upto}} --- ÜÔÏ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ, 
ÒÁ×ÎÙÊ\index{step?\texttt{step}}\index{until?\texttt{until}}
$$ \hbox{\tt step 1 until}, $$
É {\tt downto}\index{downto?\texttt{downto}} --- ÍÁËÒÏÓ, ÒÁ×ÎÙÊ 
{\tt step -1 until}. 
%%The first generalization is suggested by the fact that {\tt
%%upto}\index{upto?\texttt{upto}} is a predefined macro
%%for\index{step?\texttt{step}}\index{until?\texttt{until}}
%%$$ \hbox{\tt step 1 until} $$
%%and {\tt downto}\index{downto?\texttt{downto}} is a macro for {\tt step
%%-1 until}. 
ãÉËÌ, ÎÁÞÉÎÁÀÝÉÊÓÑ Ó 
$$ \hbox{\tt for i=a step b until c}, $$
ÐÅÒÅÂÉÒÁÅÔ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ {\tt i} ÉÚ ÚÎÁÞÅÎÉÊ {\tt a}, ${\tt a}+{\tt b}$, ${\tt
a}+2{\tt b}$, \ldots, ÏÓÔÁÎÁ×ÌÉ×ÁÑÓØ ÄÏ ÔÏÇÏ ËÁË {\tt i} ÐÒÏÊÄÅÔ ÚÁ {\tt c}, 
Ô.~Å. ÃÉËÌ ÐÅÒÅÂÉÒÁÅÔ ÚÎÁÞÅÎÉÑ {\tt i}, ÇÄÅ ${\tt i}\leqslant {\tt c}$ ÐÒÉ ${\tt b}>0$ É
${\tt i}\geqslant {\tt c}$ ÐÒÉ ${\tt b}<0$.
%%A loop begining
%%$$ \hbox{\tt for i=a step b until c} $$
%%scans a sequence of {\tt i} values {\tt a}, ${\tt a}+{\tt b}$, ${\tt
%%a}+2{\tt b}$, \ldots, stopping before {\tt i} passes {\tt c}; i.e., the
%%loop scans {\tt i} values where ${\tt i}\le {\tt c}$ if ${\tt b}>0$ and
%%${\tt i}\ge {\tt c}$ if ${\tt b}<0$.
äÌÑ ${\tt b}=0$ ÃÉËÌ ÎÉËÏÇÄÁ ÎÅ ÚÁËÏÎÞÉÔÓÑ ÄÁÖÅ ÐÒÉ ${\tt a}={\tt c}$.
%%For ${\tt b}=0$ the loop never
%%terminates, even if ${\tt a}={\tt c}$.

ìÕÞÛÅ ×ÓÅÇÏ ÉÓÐÏÌØÚÏ×ÁÔØ ÔÁËÏÊ ÃÉËÌ ÔÏÌØËÏ ÔÏÇÄÁ, ËÏÇÄÁ ÛÁÇ ÃÉËÌÁ --- 
ÜÔÏ ÃÅÌÏÅ\index{ÁÒÉÆÍÅÔÉËÁ} ÉÌÉ ÞÉÓÌÏ, ÐÒÅÄÓÔÁ×ÉÍÏÅ ÔÏÞÎÏ × ×ÉÄÅ ÄÒÏÂÉ, ËÒÁÔÎÏÊ $1\over65536$. 
%%It is best to use this feature only when the step size is an integer or
%%some number that can be represented exactly in fixed point
%%arithmetic\index{arithmetic} as a multiple of $1\over65536$. 
÷ ÐÒÏÔÉ×ÎÏÍ ÓÌÕÞÁÅ ÂÕÄÅÔ ÎÁËÁÐÌÉ×ÁÔØÓÑ ÏÛÉÂËÁ É ÐÁÒÁÍÅÔÒ ÃÉËÌÁ ÍÏÖÅÔ ÎÅ 
ÄÏÓÔÉÞØ ÏÖÉÄÁÅÍÏÇÏ ËÏÎÅÞÎÏÇÏ ÚÎÁÞÅÎÉÑ.
%%Otherwise,
%%error will accumulate and the loop index might not reach the expected
%%termination value. 
îÁÐÒÉÍÅÒ, 
$$ \hbox{\tt for i=0 step .1 until 1: show i; endfor} $$
ÐÏËÁÖÅÔ ÄÅÓÑÔØ ÚÎÁÞÅÎÉÊ {\tt i}, ÐÏÓÌÅÄÎÅÅ ÉÚ ËÏÔÏÒÙÈ ÂÕÄÅÔ 0.90005.
%%For instance,
%%$$ \hbox{\tt for i=0 step .1 until 1: show i; endfor} $$
%%shows ten {\tt i} values the last of which is 0.90005.

óÔÁÎÄÁÒÔÎÙÊ ÓÐÏÓÏ ÉÚÂÅÖÁÔØ ÐÒÏÂÌÅÍÙ, Ó×ÑÚÁÎÎÏÊ Ó ÎÅÃÅÌÙÍ ÒÁÚÍÅÒÏÍ ÛÁÇÁ, 
× ÉÔÅÒÁÃÉÉ ÐÏ ÃÅÌÙÍ ÚÎÁÞÅÎÉÑÍ É ÕÍÎÏÖÅÎÉÀ ÉÈ ÐÒÉ ÉÓÐÏÌØÚÏ×ÁÎÉÉ ÎÁ 
ÍÁÓÛÔÁÂÉÒÕÀÝÉÊ ÍÎÏÖÉÔÅÌØ, ËÁË ÜÔÏ ÂÙÌÏ ÓÄÅÌÁÎÏ ÎÁ ÒÉÓÕÎËÁÈ \ref{fig1} 
É~\ref{fig40}.
%%The standard way of avoid the problems associated with non-integer step
%%sizes is to iterate over integer values and then multiply by a scale
%%factor when using the loop index as was done in Figures \ref{fig1}
%%and~\ref{fig40}.

åÓÔØ ÁÌØÔÅÒÎÁÔÉ×Á --- ÍÏÖÎÏ ÕËÁÚÙ×ÁÔØ ÚÎÁÞÅÎÉÑ ÄÌÑ ÐÅÒÅÂÏÒÁ Ñ×ÎÏ. 
%%Alternatively, the values to iterate over can be given explicitly. 
ìÀÂÁÑ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÉÚ ÎÕÌÑ É ÂÏÌÅÅ ×ÙÒÁÖÅÎÉÊ, ÒÁÚÄÅÌÅÎÎÙÈ ÚÁÐÑÔÙÍÉ, 
ÍÏÖÅÔ ÉÓÐÏÌØÚÏ×ÁÔØÓÑ ÎÁ ÍÅÓÔÅ {\tt a step b upto c}. 
%%Any
%%sequence of zero or more expressions separated by commas can be used in
%%place of {\tt a step b upto c}. 
ðÒÉÞÅÍ, ×ÓÅ ×ÙÒÁÖÅÎÉÑ ÎÅ ÏÂÑÚÁÎÙ ÉÍÅÔØ ÏÄÉÎÁËÏ×ÙÊ ÔÉÐ ÉÌÉ ÉÚ×ÅÓÔÎÙÅ 
ÚÎÁÞÅÎÉÑ. 
%%In fact, the expressions need not all
%%be the same type and they need not have known values. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, 
$$ \hbox{\tt for t=3.14, 2.78, (a,2a), "hello": show t; endfor} $$
ÐÏËÁÖÅÔ ÞÅÔÙÒÅ ÚÎÁÞÅÎÉÑ ÉÚ ÓÐÉÓËÁ.
%%Thus
%%$$ \hbox{\tt for t=3.14, 2.78, (a,2a), "hello": show t; endfor} $$
%%shows the four values listed.

úÁÍÅÔØÔÅ, ÞÔÏ ÔÅÌÏ ÃÉËÌÁ × ÐÒÉÍÅÒÅ ×ÙÛÅ --- ÜÔÏ ËÏÍÁÎÄÁ, ÚÁ ËÏÔÏÒÏÊ ÓÌÅÄÕÅÔ 
ÔÏÞËÁ Ó ÚÁÐÑÔÏÊ.
%%Note that the loop body in the above example is a statement followed by a
%%semicolon. 
äÌÑ ÔÅÌÁ ÃÉËÌÁ ÅÓÔÅÓÔ×ÅÎÎÏ ÓÏÄÅÒÖÁÔØ ÏÄÎÕ ÉÌÉ ÂÏÌÅÅ ËÏÍÁÎÄÕ, ÈÏÔÑ ÜÔÏ É ÎÅ 
ÏÂÑÚÁÔÅÌØÎÏ.
%%It is common for the body of a loop to be one or more statements,
%%but this need not be the case. 
ãÉËÌ ÐÏÄÏÂÅÎ ÏÐÒÅÄÅÌÅÎÉÀ ÍÁËÒÏÓÁ, ÚÁ ËÏÔÏÒÙÍ ÓÌÅÄÕÅÔ ×ÙÚÏ× ÜÔÏÇÏ ÍÁËÒÏÓÁ.
%%A loop is like a macro definition followed by
%%calls to the macro. 
ôÅÌÏ ÃÉËÌÁ ÍÏÖÅÔ ÂÙÔØ ÐÒÁËÔÉÞÅÓËÉ ÌÀÂÏÊ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØÀ ÚÎÁËÏ×, ÉÍÅÀÝÉÈ 
ÓÍÙÓÌ × ÓÏ×ÏËÕÐÎÏÓÔÉ.
%%The loop body can be virtually any sequence of tokens as
%%long as they make sense together. 
ðÏÜÔÏÍÕ (ÎÅÌÅÐÁÑ) ËÏÍÁÎÄÁ 
$$ \hbox{\tt draw for p=(3,1),(6,2),(7,5),(4,6),(1,3): p-{}- endfor cycle;} $$
ÜË×É×ÁÌÅÎÔÁ
$$ \hbox{\tt draw (3,1)-{}-(6,2)-{}-(7,5)-{}-(4,6)-{}-(1,3)-{}-cycle;} $$
%%Thus, the (ridiculous) statement
%%$$ \hbox{\tt draw for p=(3,1),(6,2),(7,5),(4,6),(1,3): p-- endfor cycle;} $$
%%is equivalent to
%%$$ \hbox{\tt draw (3,1)--(6,2)--(7,5)--(4,6)--(1,3)--cycle;} $$
óÍ. ÒÉÓ~\ref{fig17} Ó ÂÏÌÅÅ ÒÅÁÌÉÓÔÉÞÅÓËÉÍ ÐÏÄÈÏÄÑÝÉÍ ÐÒÉÍÅÒÏÍ.
%%(See Figure~\ref{fig17} for a more realistic example of this.)

åÓÌÉ ÃÉËÌ ÐÏÄÏÂÅÎ ÏÐÒÅÄÅÌÅÎÉÀ ÍÁËÒÏÓÁ, ÔÏ ÐÁÒÁÍÅÔÒ ÃÉËÌÁ ÐÏÄÏÂÅÎ 
{\tt expr}-ÐÁÒÁÍÅÔÒÕ\index{ÐÁÒÁÍÅÔÒ!expr}. 
%%If a loop is like a macro definition, the loop index is like an expr
%%parameter\index{parameter!expr}. 
ïÎ ÍÏÖÅÔ ÐÒÅÄÓÔÁ×ÌÑÔØ ÌÀÂÏÅ ÚÎÁÞÅÎÉÅ, ÎÏ ÏÎ ÎÅ Ñ×ÌÑÅÔÓÑ ÐÅÒÅÍÅÎÎÏÊ É 
ÅÇÏ ÎÅÌØÚÑ ÍÅÎÑÔØ ËÏÍÁÎÄÏÊ ÐÒÉÓ×ÁÉ×ÁÎÉÑ\index{ÐÒÉÓ×ÁÉ×ÁÎÉÅ}. 
%%It can represent any value, but it is
%%not a variable and it cannot be changed by an assignment
%%statement\index{assignment}. 
ðÏÓÌÅÄÎÅÅ ÍÏÖÎÏ ÏÔÍÅÎÉÔØ ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ ÃÉËÌÁ {\tt
forsuffixes}\index{forsuffixes?\texttt{forsuffixes}}. 
%%In order to do that, you need a {\tt
%%forsuffixes}\index{forsuffixes?\texttt{forsuffixes}} loop. 
ãÉËÌ {\tt forsuffixes} ×Ï ÍÎÏÇÏÍ ÐÏÈÏÖ ÎÁ ÃÉËÌ {\tt for}, ÎÏ × ÎÅÍ 
ÐÁÒÁÍÅÔÒ ÃÉËÌÁ ×ÅÄÅÔ ÓÅÂÑ ËÁË ÐÁÒÁÍÅÔÒ-ÓÕÆÆÉËÓ\index{ÐÁÒÁÍÅÔÒ!suffix}. 
%%A {\tt
%%forsuffixes} loop is a lot like a {\tt for} loop, except the loop index
%%behaves like a suffix parameter\index{parameter!suffix}. 
éÓÐÏÌØÚÕÅÔÓÑ ÓÉÎÔÁËÓÉÓ 
$$ {\tt forsuffixes}\, \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}\, \hbox{\tt =}\,
   \descr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×}:\ \descr{ÔÅÌÏ ÃÉËÌÁ}\, {\tt endfor},
$$
ÇÄÅ \tdescr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×} --- ÜÔÏ ÒÁÚÄÅÌÅÎÎÙÊ ÚÁÐÑÔÙÍÉ ÓÐÉÓÏË. 
%%The syntax is
%%$$ {\tt forsuffixes}\, \descr{symbolic token}\, \hbox{\tt =}\,
%%   \descr{suffix list}:\ \descr{loop text}\, {\tt endfor}
%%$$
%%where a \tdescr{suffix list} is a comma-separated list of suffixes. 
åÓÌÉ ÎÅËÏÔÏÒÙÅ ÓÕÆÆÉËÓÙ \tdescr{ÐÕÓÔÙ}, ÔÏ \tdescr{ÔÅÌÏ ÃÉËÌÁ} ×ÙÐÏÌÎÑÅÔÓÑ 
Ó ÐÁÒÁÍÅÔÒÏÍ ÃÉËÌÁ, ÕÓÔÁÎÏ×ÌÅÎÎÙÍ × ÐÕÓÔÏÊ ÓÕÆÆÉËÓ.
%%If some of the suffixes are \tdescr{empty}, the \tdescr{loop text} gets
%%executed with the loop index parameter set to the empty suffix.

èÏÒÏÛÉÊ ÐÒÉÍÅÒ ÄÌÑ ÃÉËÌÁ {\tt forsuffixes} --- ÜÔÏ ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ {\tt
dotlabels}\index{dotlabels?\texttt{dotlabels}}\index{str?\texttt{str}}:
$$\begin{verbatim}
vardef dotlabels@#(text t) =
 forsuffixes $=t: dotlabel@#(str$,z$); endfor  enddef;
\end{verbatim}
$$
%%A good example of a {\tt forsuffixes} loop is the definition of the {\tt
%%dotlabels}\index{dotlabels?\texttt{dotlabels}}
%%macro\index{str?\texttt{str}}:
%%$$\begin{verbatim}
%%vardef dotlabels@#(text t) =
%% forsuffixes $=t: dotlabel@#(str$,z$); endfor  enddef;
%%\end{verbatim}
%%$$
ïÎ ÏÂßÑÓÎÑÅÔ, ÐÏÞÅÍÕ ÐÁÒÁÍÅÔÒ {\tt dotlabels} ÄÏÌÖÅÎ ÂÙÔØ ÒÁÚÄÅÌÅÎÎÙÊ ÚÁÐÑÔÙÍÉ 
ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×.
%%This should make it clear why the parameter to {\tt dotlabels} has to be a
%%comma-separated list of suffixes. 
âÏÌØÛÉÎÓÔ×Ï ÍÁËÒÏÓÏ× Ó ÒÁÚÄÅÌÅÎÎÙÍÉ ÚÁÐÑÔÙÍÉ ÓÐÉÓËÁÍÉ ÐÅÒÅÍÅÎÎÏÊ ÄÌÉÎÙ 
ÉÓÐÏÌØÚÕÀÔ ÉÈ × ÃÉËÌÁÈ {\tt for} ÉÌÉ {\tt forsuffixes} ÉÍÅÎÎÏ ÔÁËÉÍ ÏÂÒÁÚÏÍ, 
Ô.~Å. ÄÌÑ ÐÅÒÅÂÏÒÁ ÚÎÁÞÅÎÉÊ.
%%Most macros that accept variable-length
%%comma-separated lists
%%use them in {\tt for} or {\tt forsuffixes} loops in this fashion as values to
%%iterate over.

ëÏÇÄÁ ÎÅÔ ÚÎÁÞÅÎÉÊ ÄÌÑ ÐÅÒÅÂÏÒÁ, ×Ù ÍÏÖÅÔÅ ÉÓÐÏÌØÚÏ×ÁÔØ ÃÉËÌ 
{\tt forever}\index{forever?\texttt{forever}}, 
$$ {\tt forever}\hbox{\tt :}\, \descr{ÔÅÌÏ ÃÉËÌÁ}\, {\tt endfor} $$
%%When there are no values to iterate over, you can use a
%%{\tt forever}\index{forever?\texttt{forever}} loop:
%%$$ {\tt forever}\hbox{\tt :}\, \descr{loop text}\, {\tt endfor} $$
äÌÑ ÚÁ×ÅÒÛÅÎÉÑ ÔÁËÏÇÏ ÃÉËÌÁ, ËÏÇÄÁ ÌÏÇÉÞÅÓËÏÅ ÕÓÌÏ×ÉÅ ÓÔÁÎÅÔ ÉÓÔÉÎÎÙÍ, 
ÉÓÐÏÌØÚÕÊÔÅ ÐÕÎËÔ ×ÙÈÏÄÁ\index{exitif?\texttt{exitif}}:
$$ {\tt exitif}\, \descr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ} \hbox{\tt ;} $$
%%To terminate such a loop when a boolean condition becomes true, use an exit
%%clause\index{exitif?\texttt{exitif}}:
%%$$ {\tt exitif}\, \descr{boolean expression} \hbox{\tt ;} $$
ëÏÇÄÁ ÉÎÔÅÒÐÒÅÔÁÔÏÒ MetaPost ×ÓÔÒÅÞÁÅÔ ÐÕÎËÔ ×ÙÈÏÄÁ, ÏÎ 
×ÙÞÉÓÌÑÅÔ \tdescr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ} É ×ÙÈÏÄÉÔ ÉÚ ÔÅËÕÝÅÇÏ ÃÉËÌÁ, 
ÅÓÌÉ ÏÎÏ ÉÓÔÉÎÎÏ.
%%When the MetaPost interpreter encounters an exit clause, it evaluates
%%the \tdescr{boolean expression} and exits the current loop if the
%%expression is true. 
åÓÌÉ ÂÏÌÅÅ ÕÄÏÂÎÏ ×ÙÊÔÉ ÉÚ ÃÉËÌÁ, ËÏÇÄÁ ×ÙÒÁÖÅÎÉÅ ÓÔÁÎÅÔ ÌÏÖÎÙÍ, 
ÔÏ ÉÓÐÏÌØÚÕÊÔÅ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ {\tt
exitunless}\index{exitunless?\texttt{exitunless}}.
%%If it is more convenient to exit the loop when an
%%expression becomes false, use the predefined macro {\tt
%%exitunless}\index{exitunless?\texttt{exitunless}}.

ðÏÜÔÏÍÕ ×ÁÒÉÁÎÔ MetaPost ÄÌÑ ÃÉËÌÁ {\bf while} --- ÜÔÏ 
$$ \hbox{\tt forever: exitunless}\, \descr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ} \hbox{\tt ;}\,
    \descr{ÔÅÌÏ ÃÉËÌÁ}\, {\tt endfor}
$$
%%Thus MetaPost's version of a {\bf while} loop is
%%$$ \hbox{\tt forever: exitunless}\, \descr{boolean expression} \hbox{\tt ;}\,
%%    \descr{loop text}\, {\tt endfor}
%%$$
ðÕÎËÔ ×ÙÈÏÄÁ ÍÏÖÅÔ ÐÏÍÅÝÁÔØÓÑ ËÁË ÎÅÐÏÓÒÅÄÓÔ×ÅÎÎÏ ÐÅÒÅÄ {\tt endfor}, ÔÁË É 
× ÌÀÂÏÍ ÄÒÕÇÏÍ ÍÅÓÔÅ \tdescr{ÔÅÌÁ ÃÉËÌÁ}. 
%%The exit clause could equally well come just before {\tt endfor} or anywhere
%%in the \tdescr{loop text}. 
ìÀÂÏÊ ÃÉËÌ {\tt for}, {\tt forever} ÉÌÉ {\tt forsuffixes} ÍÏÖÅÔ ÐÒÁËÔÉÞÅÓËÉ 
ÓÏÄÅÒÖÁÔØ ÌÀÂÏÅ ËÏÌÉÞÅÓÔ×Ï ÐÕÎËÔÏ× ×ÙÈÏÄÁ.
%%In fact any {\tt for}, {\tt forever}, or
%%{\tt forsuffixes} loop can contain any number of exit clauses.

ó×ÏÄËÁ ÓÉÎÔÁËÓÉÓÁ ÃÉËÌÁ, ÐÏËÁÚÁÎÎÁÑ ÎÁ ÒÉÓ.~\ref{syloop}, ÎÅ ÕÐÏÍÉÎÁÅÔ 
Ñ×ÎÏ ÐÕÎËÔÙ ×ÙÈÏÄÁ, ÐÏÔÏÍÕ ÞÔÏ \tdescr{ÔÅÌÏ ÃÉËÌÁ} ÍÏÖÅÔ ÂÙÔØ × ÄÅÊÓÔ×ÉÔÅÌØÎÏÓÔÉ 
ÌÀÂÏÊ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØÀ ÚÎÁËÏ×.
%%The summary of loop syntax shown in Figure~\ref{syloop} does not mention
%%exit clauses explicitly because a \tdescr{loop text} can be virtually
%%any sequence of tokens. 
åÄÉÎÓÔ×ÅÎÎÏÅ ÏÇÒÁÎÉÞÅÎÉÅ × ÔÏÍ, ÞÔÏ \tdescr{ÔÅÌÏ ÃÉËÌÁ} ÄÏÌÖÎÏ ÂÙÔØ ÓÂÁÌÁÎÓÉÒÏ×ÁÎÏ 
ÏÔÎÏÓÉÔÅÌØÎÏ {\tt for} É {\tt endfor}. 
%%The only restriction is that a \tdescr{loop
%%text} must be balanced with respect to {\tt for} and {\tt endfor}. 
ëÏÎÅÞÎÏ, × ÜÔÏÍ ÂÁÌÁÎÓÅ {\tt forsuffixes} É {\tt forever} ÒÁÓÓÍÁÔÒÉ×ÁÀÔÓÑ 
ËÁË {\tt for}.
%%Of course this balancing process treats {\tt forsuffixes} and {\tt forever}
%%just like {\tt for}.

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÃÉËÌ} \rightarrow \descr{ÚÁÇÏÌÏ×ÏË ÃÉËÌÁ}\hbox{\tt :}\,
        \descr{ÔÅÌÏ ÃÉËÌÁ} endfor$\\
%%$\tt \descr{loop} \rightarrow \descr{loop header}\hbox{\tt :}\,
%%        \descr{loop text} endfor$\\
$\tt \descr{ÚÁÇÏÌÏ×ÏË ÃÉËÌÁ} \rightarrow for\, \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}\,
        \hbox{\tt =}\, \descr{ÐÒÏÇÒÅÓÓÉÑ}$\\
%%$\tt \descr{loop header} \rightarrow for\, \descr{symbolic token}\,
%%        \hbox{\tt =}\, \descr{progression}$\\
$\tt \qquad \;|\; for\, \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}\, \hbox{\tt =}\,
        \descr{ÓÐÉÓÏË for}$\\
%%$\tt \qquad \;|\; for\, \descr{symbolic token}\, \hbox{\tt =}\,
%%        \descr{for list}$\\
$\tt \qquad \;|\; forsuffixes\, \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}\, \hbox{\tt =}\,
        \descr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×}$\\
%%$\tt \qquad \;|\; forsuffixes\, \descr{symbolic token}\, \hbox{\tt =}\,
%%        \descr{suffix list}$\\
$\tt \qquad \;|\; forever$\\
%%$\tt \qquad \;|\; forever$\\
$\tt \descr{ÐÒÏÇÒÅÓÓÉÑ} \rightarrow \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\, upto\,
        \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{progression} \rightarrow \descr{numeric expression}\, upto\,
%%        \descr{numeric expression}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\, downto\,
        \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; \descr{numeric expression}\, downto\,
%%        \descr{numeric expression}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\, step\,
        \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\, until\, \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} $\\
%%$\tt \qquad \;|\; \descr{numeric expression}\, step\,
%%        \descr{numeric expression}\, until\, \descr{numeric expression} $\\
$\tt \descr{ÓÐÉÓÏË for} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}
        \;|\; \descr{ÓÐÉÓÏË for}\hbox{\tt ,}\, \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{for list} \rightarrow \descr{expression}
%%        \;|\; \descr{for list}\hbox{\tt ,}\, \descr{expression}$\\
$\tt \descr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×} \rightarrow \descr{ÓÕÆÆÉËÓ}
        \;|\; \descr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×}\hbox{\tt ,}\, \descr{ÓÕÆÆÉËÓ}$
%%$\tt \descr{suffix list} \rightarrow \descr{suffix}
%%        \;|\; \descr{suffix list}\hbox{\tt ,}\, \descr{suffix}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÄÌÑ ÃÉËÌÏ×}
%%\caption{The syntax for loops}
\label{syloop}
\end{figure}


\section{éÚÇÏÔÏ×ÌÅÎÉÅ ÒÁÍÏË}
%%\section{Making Boxes}
\label{boxessec}

üÔÏÔ ÒÁÚÄÅÌ ÏÐÉÓÙ×ÁÅÔ ÄÏÐÏÌÎÉÔÅÌØÎÙÅ ÍÁËÒÏÓÙ, ÎÅ ×ËÌÀÞÅÎÎÙÅ × 
Plain MetaPost, ÞÔÏ ÐÒÅÄÏÓÔÁ×ÌÑÀÔ ÕÄÏÂÓÔ×Á ÄÅÌÁÔØ ÔÏ, × ÞÅÍ ÈÏÒÏÛ 
{\it pic} \cite{ke:pic}. 
%%This section describes auxiliary macros not included in Plain MetaPost
%%that make it convenient to do things that {\it pic} is good at
%%\cite{ke:pic}. 
á ÔÏ, ÞÔÏ ÓÌÅÄÕÅÔ ÄÁÌÅÅ --- ÜÔÏ ÏÐÉÓÁÎÉÅ, ËÁË ÉÓÐÏÌØÚÏ×ÁÔØ ÍÁËÒÏÓÙ, 
ÓÏÄÅÒÖÁÝÉÅÓÑ × ÆÁÊÌÅ {\tt boxes.mp}\index{boxes.mp?\texttt{boxes.mp}}.
%%What follows is a description of how to use the macros
%%contained in the file {\tt boxes.mp}\index{boxes.mp?\texttt{boxes.mp}}.
üÔÏÔ ÆÁÊÌ ÒÁÚÍÅÝÁÅÔÓÑ × ÓÐÅÃÉÁÌØÎÏÍ ËÁÔÁÌÏÇÅ ÄÌÑ ÍÁËÒÏÓÏ× MetaPost
É ÏÂÅÓÐÅÞÉ×ÁÀÝÅÇÏ ÐÒÏÇÒÁÍÍÎÏÇÏ ÏÂÅÓÐÅÞÅÎÉÑ\footnote{éÍÑ ÜÔÏÇÏ ËÁÔÁÌÏÇÁ 
ÐÏÄÏÂÎÏ ÞÅÍÕ-ÔÏ ÔÉÐÁ \texttt{/usr/lib/mp/lib}, ÎÏ ÚÁ×ÉÓÉÔ ÏÔ ÓÉÓÔÅÍÙ.} 
É ÄÏÌÖÅÎ ÓÔÁÔØ ÄÏÓÔÕÐÎÙÍ ÞÅÒÅÚ ËÏÍÁÎÄÕ MetaPost {\tt input boxes} 
ÄÏ ÌÀÂÙÈ ÒÉÓÕÎËÏ×, ÉÓÐÏÌØÚÕÀÝÉÈ ÍÁËÒÏÓÙ ÄÌÑ ÓÏÚÄÁÎÉÑ ÒÁÍÏË.
%%This file is included in a special directory reserved for MetaPost
%%macros and support software\footnote{The name of this directory is
%%likely to be something like \texttt{/usr/lib/mp/lib}, but this is system
%%dependent.}  and can be accessed by giving the MetaPost command {\tt
%%input boxes} before any figures that use the box making macros. 
óÉÎÔÁËÓÉÓ ËÏÍÁÎÄÙ {\tt input}\index{input?\texttt{input}} ---
$$ {\tt input}\, \descr{ÉÍÑ ÆÁÊÌÁ}, $$
ÇÄÅ ÏËÏÎÞÁÎÉÅ ``{\tt .mp}'' ÍÏÖÅÔ ÏÐÕÓËÁÔØÓÑ × ÉÍÅÎÉ ÆÁÊÌÁ.
%%The
%%syntax for the {\tt input} command is \index{input?\texttt{input}}
%$$ {\tt input}\, \descr{file name} $$
%%where a final ``{\tt .mp}'' can be omitted from the file name. 
ëÏÍÁÎÄÁ {\tt input} ÓÍÏÔÒÉÔ ÓÎÁÞÁÌÁ × ÔÅËÕÝÅÍ ËÁÔÁÌÏÇÅ, Á ÚÁÔÅÍ × ÓÐÅÃÉÁÌØÎÏÍ 
ËÁÔÁÌÏÇÅ ÄÌÑ ÍÁËÒÏÓÏ×.
%%The {\tt input}
%%command looks first in the current directory and then in the special macro
%%directory. 
ðÏÌØÚÏ×ÁÔÅÌÉ, ÚÁÉÎÔÅÒÅÓÏ×Á×ÛÉÅÓÑ × ÎÁÐÉÓÁÎÉÉ ÍÁËÒÏÓÏ×, ×ÏÚÍÏÖÎÏ ÚÁÈÏÔÑÔ 
ÐÏÓÍÏÔÒÅÔØ ÎÁ ÆÁÊÌ {\tt boxes.mp} × ÜÔÏÍ ËÁÔÁÌÏÇÅ.
%%Users interested in writing macros may want to look at the
%%{\tt boxes.mp} file in this directory.

ó ×ÒÅÍÅÎÉ ÐÏÑ×ÌÅÎÉÑ ÐÁËÅÔÁ \texttt{boxes} × MetaPost-ÓÏÏÂÝÅÓÔ×Å ÂÙÌÉ 
ÒÁÚÒÁÂÏÔÁÎÙ ÎÅÓËÏÌØËÏ ÁÌØÔÅÒÎÁÔÉ×ÎÙÈ ÐÁËÅÔÏ× ÒÁÚÎÙÈ ×ÉÄÏ× ÄÌÑ ÒÉÓÏ×ÁÎÉÑ ÒÁÍÏË.
%%Since the advent of the \texttt{boxes} package several alternative
%%packages for drawing boxes of all kinds have been developed by the
%%MetaPost community. 
îÁÉÂÏÌÅÅ ÉÚ×ÅÓÔÎÙÅ ÉÚ ÎÉÈ --- ÜÔÏ 
%%The most widely known ones are
\texttt{MetaObj}\index{MetaObj?\texttt{MetaObj}},
\texttt{MetaUML}\index{MetaUML?\texttt{MetaUML}},
\texttt{expressg}\index{expressg?\texttt{expressg}} É
%%\texttt{expressg}\index{expressg?\texttt{expressg}}, and
\texttt{blockdraw\_mp}\index{blockdraw\_mp?\texttt{blockdraw\_mp}}. 
åÓÌÉ ×Ù ÓÏÂÉÒÁÅÔÅÓØ ÓÏÚÄÁ×ÁÔØ ÍÎÏÇÏ ÓÔÒÕËÔÕÒÎÙÈ ÒÉÓÕÎËÏ×, ÄÉÁÇÒÁÍÍ É 
Ô.~Ð., ÔÏ ÜÔÉ ÐÁËÅÔÙ ÔÏÖÅ ÍÏÇÕÔ ÓÔÁÔØ ÄÌÑ ×ÁÓ ÉÎÔÅÒÅÓÎÙÍ ÒÅÓÕÒÓÏÍ.
%%If you intend to create lots of structural drawings, flow charts,
%%\emph{etc.}, those packages might be an interesting ressource, too.

\subsection{ðÒÑÍÏÕÇÏÌØÎÙÅ ÒÁÍËÉ}
%%\subsection{Rectangular Boxes}

çÌÁ×ÎÁÑ ÉÄÅÑ ÓÏÚÄÁÀÝÉÈ ÒÁÍËÉ ÍÁËÒÏÓÏ× × ÔÏÍ, ÞÔÏ ÍÏÖÎÏ 
ÓËÁÚÁÔØ\index{boxit?\texttt{boxit}}\label{Dboxit} 
$$ {\tt boxit.} \descr{ÓÕÆÆÉËÓ}
   \hbox{\tt(} \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ} \hbox{\tt),}
$$
ÇÄÅ \tdescr{ÓÕÆÆÉËÓ} ÎÅ ÎÁÞÉÎÁÅÔÓÑ Ó ÉÎÄÅËÓÁ\footnote{îÅËÏÔÏÒÙÅ ÒÁÎÎÉÅ 
×ÅÒÓÉÉ ÄÅÌÁÀÝÉÈ ÒÁÍËÉ ÍÁËÒÏÓÏ× ÎÅ ÐÏÚ×ÏÌÑÌÉ ÎÉËÁËÉÈ ÉÎÄÅËÓÏ× × ÓÕÆÆÉËÓÅ 
{\tt boxit}.}.
%%The main idea of the box-making macros is that one should
%%say\index{boxit?\texttt{boxit}}\label{Dboxit}
%%$$ {\tt boxit.} \descr{suffix}
%%   \hbox{\tt(} \descr{picture expression} \hbox{\tt)}
%%$$
%%where the \tdescr{suffix} does not start with a subscript.\footnote{Some early
%%versions of the box making macros did not allow any subscripts in the
%%{\tt boxit} suffix.}
üÔÁ ËÏÎÓÔÒÕËÃÉÑ ÓÏÚÄÁÅÔ ÐÅÒÅÍÅÎÎÙÅ-ÐÁÒÙ \tdescr{ÓÕÆÆÉËÓ}{\tt.c},
\tdescr{ÓÕÆÆÉËÓ}{\tt.n}, \tdescr{ÓÕÆÆÉËÓ}{\tt.e}, \ldots, ÞÔÏ ÍÏÇÕÔ ÚÁÔÅÍ 
ÉÓÐÏÌØÚÏ×ÁÔØÓÑ ÐÒÉ ÒÁÚÍÅÝÅÎÉÉ ÒÉÓÕÎËÁ ÐÅÒÅÄ ÅÇÏ ÒÉÓÏ×ÁÎÉÅÍ ÏÔÄÅÌØÎÏÊ 
ËÏÍÁÎÄÏÊ\index{drawboxed?\texttt{drawboxed}}\label{Ddrbxed}, ÎÁÐÒÉÍÅÒ, 
$$ \hbox{\tt drawboxed(} \descr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×} \hbox{\tt )} $$
%%This creates pair variables \tdescr{suffix}{\tt.c},
%%\tdescr{suffix}{\tt.n}, \tdescr{suffix}{\tt.e}, \ldots\ that can then be
%%used for positioning the picture before drawing it with a separate command such
%%as\index{drawboxed?\texttt{drawboxed}}\label{Ddrbxed}
%%$$ \hbox{\tt drawboxed(} \descr{suffix list} \hbox{\tt )} $$
áÒÇÕÍÅÎÔ {\tt drawboxed} ÄÏÌÖÅÎ ÂÙÔØ ÒÁÚÄÅÌÅÎÎÙÍ ÚÁÐÑÔÙÍÉ ÓÐÉÓËÏÍ ÉÍÅÎ ÒÁÍÏË,
ÇÄÅ ÉÍÑ ÒÁÍËÉ\index{ÉÍÑ ÒÁÍËÉ} --- ÜÔÏ \tdescr{ÓÕÆÆÉËÓ}, Ó ËÏÔÏÒÙÍ 
×ÙÚÙ×ÁÅÔÓÑ {\tt boxit}.
%%The argument to {\tt drawboxed} should be a comma-separated list of box names,
%%where a box name\index{box name} is a \tdescr{suffix} with which {\tt boxit}
%%has been called.

äÌÑ ËÏÍÁÎÄÙ {\tt boxit.bb(pic)} ÉÍÑ ÒÁÍËÉ --- ÜÔÏ {\tt bb}, Á 
ÓÏÄÅÒÖÉÍÏÅ ÒÁÍËÉ --- ÜÔÏ ÒÉÓÕÎÏË {\tt pic}.
%%For the command {\tt boxit.bb(pic)}, the box name is {\tt bb} and the
%%contents of the box is the picture {\tt pic}. 
÷ ÜÔÏÍ ÓÌÕÞÁÅ, {\tt bb.c} --- ÜÔÏ ÐÏÚÉÃÉÑ ÐÏÍÅÝÅÎÉÑ ÃÅÎÔÒÁ ËÁÒÔÉÎËÉ {\tt pic}, 
Á {\tt bb.sw}, {\tt bb.se}, {\tt bb.ne} É {\tt bb.nw} --- ÜÔÏ ÕÇÌÙ 
ÐÒÑÍÏÕÇÏÌØÎÏÇÏ ÐÕÔÉ, ÞÔÏ ÂÕÄÅÔ ÏËÒÕÖÁÔØ ËÁÒÔÉÎËÕ-ÒÅÚÕÌØÔÁÔ.
%%In this case, {\tt bb.c}
%%the position where the center of picture {\tt pic} is to be placed, and
%%{\tt bb.sw}, {\tt bb.se}, {\tt bb.ne}, and {\tt bb.nw} are the corners
%%of a rectangular path that will surround the resulting picture.
ðÅÒÅÍÅÎÎÙÅ {\tt bb.dx} É {\tt bb.dy} ÄÁÀÔ ÐÒÏÍÅÖÕÔËÉ ÍÅÖÄÕ ÓÄ×ÉÎÕÔÏÊ 
×ÅÒÓÉÅÊ {\tt pic} É ÏËÒÕÖÁÀÝÉÍ ÐÒÑÍÏÕÇÏÌØÎÉËÏÍ, Á {\tt bb.off} --- 
ÜÔÏ ÒÁÓÓÔÏÑÎÉÅ, ÎÁ ËÏÔÏÒÏÅ {\tt pic} ÓÄ×ÉÇÁÅÔÓÑ ÄÌÑ ÄÏÓÔÉÖÅÎÉÑ ×ÓÅÇÏ 
ÜÔÏÇÏ. 
%%Variables {\tt bb.dx} and {\tt bb.dy} give the spacing between the
%%shifted version of {\tt pic} and the surrounding rectangle, and {\tt
%%bb.off} is the amount by which {\tt pic} has to be shifted to achieve
%%all this.

ëÏÇÄÁ ÍÁËÒÏÓ {\tt boxit} ×ÙÚÙ×ÁÅÔÓÑ Ó ÉÍÅÎÅÍ ÒÁÍËÉ~$b$, ÔÏ ÜÔÏ ÄÁÅÔ 
ÌÉÎÅÊÎÙÅ ÕÒÁ×ÎÅÎÉÑ, ÞÔÏ ÚÁÓÔÁ×ÌÑÀÔ $b${\tt.sw}, $b${\tt.se}, $b${\tt.ne} 
É  $b${\tt.nw} ÂÙÔØ ÕÇÌÁÍÉ ÐÒÑÍÏÕÇÏÌØÎÉËÁ ×ÄÏÌØ ÏÓÅÊ $x$ É $y$,
ÓÏÄÅÒÖÁÝÉÍ ×ÎÕÔÒÉ ËÁÒÔÉÎËÕ, ÐÏËÁÚÁÎÎÕÀ ÓÅÒÙÍ ÐÒÑÍÏÕÇÏÌØÎÉËÏÍ ÎÁ 
ÒÉÓ.~\ref{fig48}. 
%%When the {\tt boxit} macro is called with box name~$b$, it gives linear
%%equations that force $b${\tt.sw}, $b${\tt.se}, $b${\tt.ne}, and
%%$b${\tt.nw} to be the corners of a rectangle aligned on the $x$ and $y$
%%axes with the box contents centered inside as indicated by the gray
%%rectangle in Figure~\ref{fig48}. 
úÎÁÞÅÎÉÑ $b${\tt.dx}, $b${\tt.dy} É $b${\tt.c} ÏÓÔÁÀÔÓÑ ÎÅÕËÁÚÁÎÎÙÍÉ, ÔÁË ÞÔÏ 
ÐÏÌØÚÏ×ÁÔÅÌØ ÍÏÖÅÔ ÚÁÄÁÔØ ÕÒÁ×ÎÅÎÉÑ ÄÌÑ ÒÁÚÍÅÝÅÎÉÑ ÒÁÍÏË.
%%The values of $b${\tt.dx},
%%$b${\tt.dy}, and $b${\tt.c} are left unspecified so that the user can
%%give equations for positioning the boxes. 
åÓÌÉ ÔÁËÉÅ ÕÒÁ×ÎÅÎÉÑ ÎÅ ÚÁÄÁÀÔÓÑ, ÔÏ ÍÁËÒÏÓÙ ÔÉÐÁ {\tt drawboxed} ÍÏÇÕÔ 
ÜÔÏ ÏÂÎÁÒÕÖÉ×ÁÔØ É ÚÁÄÁ×ÁÔØ ÓÔÁÎÄÁÒÔÎÙÅ ÚÎÁÞÅÎÉÑ.
%%If no such equations are
%%given, macros such as {\tt drawboxed} can detect this and give default
%%values. 
óÔÁÎÄÁÒÔÎÙÅ ÚÎÁÞÅÎÉÑ ÄÌÑ ÐÅÒÅÍÅÎÎÙÈ {\tt dx} É {\tt dy} ÕÐÒÁ×ÌÑÀÔÓÑ 
×ÎÕÔÒÅÎÎÉÍÉ ÐÅÒÅÍÅÎÎÙÍÉ\index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} {\tt
defaultdx}\index{defaultdx?\texttt{defaultdx}}\label{Ddefaultdx} É 
{\tt defaultdy}\index{defaultdy?\texttt{defaultdy}}\label{Ddefaultdy}.
%%The default values for {\tt dx} and {\tt dy} variables are
%%controlled by the internal variables\index{internal
%%variables}\index{variables!internal} {\tt
%%defaultdx}\index{defaultdx?\texttt{defaultdx}}\label{Ddefaultdx} and
%%{\tt defaultdy}\index{defaultdy?\texttt{defaultdy}}\label{Ddefaultdy}.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-48} $$
\caption[ëÁË {\tt boxit}-ÒÉÓÕÎÏË ÓÏÏÔÎÏÓÉÔÓÑ Ó ÁÓÓÏÃÉÉÒÏ×ÁÎÎÙÍ ÐÅÒÅÍÅÎÎÙÍÉ]
        {ïÔÎÏÛÅÎÉÑ ÍÅÖÄÕ ÒÉÓÕÎËÏÍ, ÚÁÄÁÎÎÙÍ ÄÌÑ {\tt boxit}, É 
        Ó×ÑÚÁÎÎÙÍÉ Ó ÜÔÉÍ ÐÅÒÅÍÅÎÎÙÍÉ.  òÉÓÕÎÏË ÉÚÏÂÒÁÖÅÎ ÓÅÒÙÍ ÐÒÑÍÏÕÇÏÌØÎÉËÏÍ.}
%%\caption[How a {\tt boxit} picture relates to the associated variables]
%%        {The relationship between the picture given to {\tt boxit} and the
%%        associated variables.  The picture is indicated by a gray rectangle.}
\label{fig48}
\end{figure}

åÓÌÉ $b$ ÐÒÅÄÓÔÁ×ÌÑÅÔ ÉÍÑ ÒÁÍËÉ, ÔÏ {\tt drawboxed($b$)} ÒÉÓÕÅÔ 
ÐÒÑÍÏÕÇÏÌØÎÕÀ ÇÒÁÎÉÃÕ ÓÏÄÅÒÖÉÍÏÇÏ~$b$, Á ÚÁÔÅÍ É ÓÁÍÏ ÓÏÄÅÒÖÉÍÏÅ.
%%If $b$ represents a box name, {\tt drawboxed($b$)} draws the rectangular
%%boundary of box~$b$ and then the contents of the box. 
üÔÏÔ ÏÈ×ÁÔÙ×ÁÀÝÉÊ ÐÒÑÍÏÕÇÏÌØÎÉË ÍÏÖÅÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎ ÏÔÄÅÌØÎÏ ËÁË 
{\tt bpath~$b$} ÉÌÉ, × ÏÂÝÅÍ ÓÌÕÞÁÅ,\index{bpath?\texttt{bpath}}\label{Dbpath}
$$ {\tt bpath}\, \descr{ÉÍÑ ÒÁÍËÉ} $$
%%This bounding
%%rectangle can be accessed separately as {\tt bpath~$b$}, or in
%%general\index{bpath?\texttt{bpath}}\label{Dbpath}
%%$$ {\tt bpath}\, \descr{box name} $$
üÔÏ ÐÏÌÅÚÎÏ × ËÏÍÂÉÎÁÃÉÉ Ó ÏÐÅÒÁÔÏÒÁÍÉ ÔÉÐÁ {\tt 
cutbefore}\index{cutbefore?\texttt{cutbefore}} É {\tt 
cutafter}\index{cutafter?\texttt{cutafter}} ÄÌÑ ËÏÎÔÒÏÌÑ 
ÚÁ ÐÕÔÑÍÉ, ×ÈÏÄÑÝÉÍÉ × ÒÁÍËÕ.
%%It is useful in combination with operators like
%%{\tt cutbefore}\index{cutbefore?\texttt{cutbefore}} and {\tt %%cutafter}\index{cutafter?\texttt{cutafter}}
%%in order to control paths that enter the box.
îÁÐÒÉÍÅÒ, ÅÓÌÉ $a$ É $b$ --- ÜÔÏ ÉÍÅÎÁ ÒÁÍÏË É $p$ --- ÜÔÏ ÐÕÔØ ÉÚ $a${\tt.c}
× $b${\tt.c},\index{drawarrow?\texttt{drawarrow}} ÔÏ 
$$ \hbox{\tt drawarrow $p$ cutbefore bpath $a$ cutafter bpath $b$} $$
ÒÉÓÕÅÔ ÓÔÒÅÌËÕ ÏÔ ËÒÁÑ ÒÁÍËÉ $a$ ÄÏ ËÒÁÑ ÒÁÍËÉ $b$.
%%For example, if $a$ and $b$ are box names and $p$ is a path from $a${\tt.c}
%%to $b${\tt.c},\index{drawarrow?\texttt{drawarrow}}
%%$$ \hbox{\tt drawarrow $p$ cutbefore bpath $a$ cutafter bpath $b$} $$
%%draws an arrow from the edge of box $a$ to the edge of box $b$.

òÉÓ.~\ref{fig49} ÐÏËÁÚÙ×ÁÅÔ ÐÒÁËÔÉÞÅÓËÉÊ ÐÒÉÍÅÒ ×ËÌÀÞÅÎÉÑ ÎÅÓËÏÌØËÉÈ 
ÓÔÒÅÌÏË, ÎÁÒÉÓÏ×ÁÎÎÙÈ Ó {\tt cutafter bpath} \tdescr{ÉÍÑ ÒÁÍËÉ}. 
%%Figure~\ref{fig49} shows a practical example including some arrows drawn
%%with {\tt cutafter bpath} \tdescr{box name}. 
ðÏÕÞÉÔÅÌØÎÏ ÓÒÁ×ÎÉÔØ ÒÉÓ.~\ref{fig49} Ó ÐÏÈÏÖÅÊ ËÁÒÔÉÎËÏÊ × ÒÕËÏ×ÏÄÓÔ×Å ÐÏ 
{\it pic} \cite{ke:pic}. 
%%It is instructive to
%%compare Figure~\ref{fig49} to the similar figure in the pic manual
%%\cite{ke:pic}. 
òÉÓÕÎÏË ÉÓÐÏÌØÚÕÅÔ ÍÁËÒÏÓ\index{boxjoin?\texttt{boxjoin}}\label{Dbxjoin}
$$ \hbox{\tt boxjoin(} \descr{ÔÅËÓÔ ÕÒÁ×ÎÅÎÉÊ} \hbox{\tt )} $$ 
ÄÌÑ ÕÐÒÁ×ÌÅÎÉÑ ÏÔÎÏÛÅÎÉÑÍÉ ÍÅÖÄÕ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÙÍÉ ÒÁÍËÁÍÉ.
%%The figure uses a
%%macro\index{boxjoin?\texttt{boxjoin}}\label{Dbxjoin}
%%$$ \hbox{\tt boxjoin(} \descr{equation text} \hbox{\tt )} $$
%%to control the relationship between consecutive boxes. 
÷ \tdescr{ÔÅËÓÔÅ ÕÒÁ×ÎÅÎÉÊ} {\tt a} É {\tt b} ÐÒÅÄÓÔÁ×ÌÑÀÔ ÉÍÅÎÁ ÒÁÍÏË, 
ÚÁÄÁÎÎÙÅ × ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÙÈ ×ÙÚÏ×ÁÈ {\tt boxit}, Á \tdescr{ÔÅËÓÔ ÕÒÁ×ÎÅÎÉÊ} 
ÄÁÅÔ ÕÒÁ×ÎÅÎÉÑ ÄÌÑ ËÏÎÔÒÏÌÑ ÚÁ ÏÔÎÏÓÉÔÅÌØÎÙÍÉ ÒÁÚÍÅÒÁÍÉ É ÐÏÚÉÃÉÑÍÉ ÒÁÍÏË.
%%Within the
%%\tdescr{equation text}, {\tt a} and {\tt b} represent the box names given in
%%consecutive calls to {\tt boxit} and the \tdescr{equation text} gives equations
%%to control the relative sizes and positions of the boxes.

\begin{figure}[htp]
$$\hbox{$\begin{verbatim}
input boxes
beginfig(49);
boxjoin(a.se=b.sw; a.ne=b.nw);
boxit.a(btex\strut$\cdots$ etex);    boxit.ni(btex\strut$n_i$ etex);
boxit.di(btex\strut$d_i$ etex);      boxit.ni1(btex\strut$n_{i+1}$ etex);
boxit.di1(btex\strut$d_{i+1}$ etex); boxit.aa(btex\strut$\cdots$ etex);
boxit.nk(btex\strut$n_k$ etex);      boxit.dk(btex\strut$d_k$ etex);
drawboxed(di,a,ni,ni1,di1,aa,nk,dk); label.lft("ndtable:", a.w);
interim defaultdy:=7bp;
boxjoin(a.sw=b.nw; a.se=b.ne);
boxit.ba(); boxit.bb(); boxit.bc();
boxit.bd(btex $\vdots$ etex); boxit.be(); boxit.bf();
bd.dx=8bp; ba.ne=a.sw-(15bp,10bp);
drawboxed(ba,bb,bc,bd,be,bf); label.lft("hashtab:",ba.w);
vardef ndblock suffix $ =
  boxjoin(a.sw=b.nw; a.se=b.ne);
  forsuffixes $$=$1,$2,$3: boxit$$(); ($$dx,$$dy)=(5.5bp,4bp);
  endfor; enddef;
ndblock nda;  ndblock ndb;  ndblock ndc;
nda1.c-bb.c = ndb1.c-nda3.c = (whatever,0);
xpart ndb3.se = xpart ndc1.ne = xpart di.c;
ndc1.c - be.c = (whatever,0);
drawboxed(nda1,nda2,nda3, ndb1,ndb2,ndb3, ndc1,ndc2,ndc3);
drawarrow bb.c -- nda1.w;
drawarrow be.c -- ndc1.w;
drawarrow nda3.c -- ndb1.w;
drawarrow nda1.c{right}..{curl0}ni.c cutafter bpath ni;
drawarrow nda2.c{right}..{curl0}di.c cutafter bpath di;
drawarrow ndc1.c{right}..{curl0}ni1.c cutafter bpath ni1;
drawarrow ndc2.c{right}..{curl0}di1.c cutafter bpath di1;
drawarrow ndb1.c{right}..nk.c cutafter bpath nk;
drawarrow ndb2.c{right}..dk.c cutafter bpath dk;
x.ptr=xpart aa.c;   y.ptr=ypart ndc1.ne;
drawarrow subpath (0,.7) of (z.ptr..{left}ndc3.c) dashed evenly;
label.rt(btex \strut ndblock etex, z.ptr); endfig;
\end{verbatim}
$}
\atop \vcenter{\vskip8pt\hbox{\includegraphics{manfig-ru-49}}}
$$
\caption{ëÏÄ MetaPost É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ÒÉÓÕÎÏË}
%%\caption{MetaPost code and the corresponding figure}
\label{fig49}
\end{figure}

îÁÐÒÉÍÅÒ, ×ÔÏÒÁÑ ÓÔÒÏËÁ ××ÏÄÁ ÄÌÑ ÐÒÉ×ÅÄÅÎÎÏÇÏ ÒÉÓÕÎËÁ ÓÏÄÅÒÖÉÔ 
$$ \hbox{\tt boxjoin(a.se=b.sw; a.ne=b.nw)} $$
%%For example, the second line of input for the above figure contains
%%$$ \hbox{\tt boxjoin(a.se=b.sw; a.ne=b.nw)} $$
üÔÏ ÒÁÚÍÅÝÁÅÔ ÒÁÍËÉ ÇÏÒÉÚÏÎÔÁÌØÎÏ × ÒÑÄ, ÂÌÁÇÏÄÁÒÑ ÚÁÄÁÎÉÀ ÄÏÐÏÌÎÉÔÅÌØÎÙÈ 
ÕÒÁ×ÎÅÎÉÊ, ×ÙÚÙ×ÁÅÍÙÈ ×ÓÑËÉÊ ÒÁÚ, ËÏÇÄÁ ÎÅËÏÔÏÒÁÑ ÒÁÍËÁ {\tt b} ÓÌÅÄÕÅÔ ÚÁ 
ÎÅËÏÔÏÒÏÊ ÒÁÍËÏÊ {\tt a}.
%%This causes boxes to line up horizontally by giving additional equations that
%%are invoked each time some box {\tt a} is followed by some other box~{\tt b}.
%%These equations are first invoked on the next line when box~{\tt a} is followed
%%by box~{\tt ni}. 
üÔÉÍ ÄÏÓÔÉÇÁÅÔÓÑ
$$ \hbox{\tt a.se=ni.sw; a.ne=ni.nw} $$
%%This yields
%%$$ \hbox{\tt a.se=ni.sw; a.ne=ni.nw} $$
óÌÅÄÕÀÝÁÑ ÐÁÒÁ ÒÁÍÏË --- ÜÔÏ ~{\tt ni} É~{\tt di}.
%%The next pair of boxes is box~{\tt ni} and box~{\tt di}. 
îÁ ÜÔÏÔ ÒÁÚ ÎÅÑ×ÎÏ ÇÅÎÅÒÉÒÕÅÍÙÅ ÕÒÁ×ÎÅÎÉÑ --- 
$$ \hbox{\tt ni.se=di.sw; ni.ne=di.nw} $$
%%This time the implicitly generated equations are
%%$$ \hbox{\tt ni.se=di.sw; ni.ne=di.nw} $$
üÔÏÔ ÐÒÏÃÅÓÓ ÐÒÏÄÏÌÖÁÅÔÓÑ ÄÏ ÔÅÈ ÐÏÒ, ÐÏËÁ ÎÏ×ÙÊ {\tt
boxjoin}\index{boxjoin?\texttt{boxjoin}} ÎÅ ÂÕÄÅÔ ÚÁÄÁÎ.
%%This process continues until a new {\tt
%%boxjoin}\index{boxjoin?\texttt{boxjoin}} is given. 
÷ ÎÁÛÅÍ ÓÌÕÞÁÅ ÎÏ×ÏÊ ÄÅËÌÁÒÁÃÉÅÊ ÂÕÄÅÔ 
$$ \hbox{\tt boxjoin(a.sw=b.nw; a.se=b.ne)} $$
--- ÏÎÁ ÓÏÅÄÉÎÑÅÔ ÒÁÍËÉ ÄÒÕÇ ÐÏÄ ÄÒÕÇÏÍ.
%%In this case the new declaration is
%%$$ \hbox{\tt boxjoin(a.sw=b.nw; a.se=b.ne)} $$
%%which causes boxes to be stacked below each other.

ðÏÓÌÅ ×ÙÚÏ×Á {\tt boxit} ÄÌÑ ÐÅÒ×ÙÈ ×ÏÓØÍÉ ÒÁÍÏË ÏÔ {\tt a} ÄÏ {\tt
dk}, ×ÙÓÏÔÙ ÒÁÍÏË ÐÒÉÎÕÖÄÁÀÔÓÑ Ë ×ÚÁÉÍÎÏÍÕ ÓÏÏÔ×ÅÔÓÔ×ÉÀ, ÎÏ ÛÉÒÏÔÙ 
ÏÓÔÁÀÔÓÑ ÎÅÉÚ×ÅÓÔÎÙÍÉ.
%%After calling {\tt boxit} for the first eight boxes {\tt a} through {\tt
%%dk}, the box heights are constrained to match but the widths are still
%%unknown. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÍÁËÒÏÓ {\tt drawboxed}\index{drawboxed?\texttt{drawboxed}} 
ÎÕÖÄÁÅÔÓÑ × ÐÒÉÓ×ÁÉ×ÁÎÉÉ ÔÉÐÏ×ÙÈ ÚÎÁÞÅÎÉÊ ÐÅÒÅÍÅÎÎÙÍ \tdescr{ÉÍÑ ÒÁÍËÉ}{\tt.dx}
É \tdescr{ÉÍÑ ÒÁÍËÉ}{\tt.dy}. 
%%Thus the {\tt drawboxed}\index{drawboxed?\texttt{drawboxed}}
%%macro needs to assign default values to the \tdescr{box name}{\tt.dx}
%%and \tdescr{box name}{\tt.dy} variables. 
ðÅÒ×ÙÍ ÄÅÌÏÍ {\tt di.dx} É {\tt di.dy} ÐÏÌÕÞÁÀÔ ÚÎÁÞÅÎÉÑ ÐÏ-ÕÍÏÌÞÁÎÉÀ, ÔÁË 
ÞÔÏ ×ÓÅ ÒÁÍËÉ ÐÒÉÎÕÖÄÁÀÔÓÑ ÂÙÔØ ÄÏÓÔÁÔÏÞÎÏ ÂÏÌØÛÉÍÉ ÄÌÑ ×ÍÅÝÅÎÉÑ 
ÓÏÄÅÒÖÉÍÏÇÏ~{\tt di}.
%%First, {\tt di.dx} and {\tt
%%di.dy} get default values so that all the boxes are forced to be large
%%enough to contain the contents of box~{\tt di}.

íÁËÒÏÓ, ËÏÔÏÒÙÊ × ÄÅÊÓÔ×ÉÔÅÌØÎÏÓÔÉ ÐÒÉÓ×ÁÉ×ÁÅÔ ÔÉÐÏ×ÙÅ ÚÎÁÞÅÎÉÑ 
ÐÅÒÅÍÅÎÎÙÍ {\tt dx} É {\tt dy}, ÚÏ×ÅÔÓÑ {\tt
fixsize}\index{fixsize?\texttt{fixsize}}\label{Dfixsiz}. 
%%The macro that actually assigns default values to {\tt dx} and {\tt dy}
%%variables is called {\tt
%%fixsize}\index{fixsize?\texttt{fixsize}}\label{Dfixsiz}. 
ïÎ ÂÅÒÅÔ ÓÐÉÓÏË ÉÍÅÎ ÒÁÍÏË É ÒÁÓÓÍÁÔÒÉ×ÁÅÔ ÉÈ ÐÏ-ÏÄÎÏÍÕ ÚÁ ÒÁÚ, 
ÇÁÒÁÎÔÉÒÕÑ, ÞÔÏ ËÁÖÄÁÑ ÒÁÍËÁ ÂÕÄÅÔ ÉÍÅÔØ ÚÁÄÁÎÎÙÅ ÒÁÚÍÅÒ É ÆÏÒÍÕ.
%%It takes a
%%list of box names and considers them one at a time, making sure that
%%each box has a fixed size and shape. 
úÁÔÅÍ ÍÁËÒÏÓ Ó ÉÍÅÎÅÍ {\tt
fixpos}\index{fixpos?\texttt{fixpos}}\label{Dfixpos} ÂÅÒÅÔ ÜÔÏÔ ÖÅ 
ÓÁÍÙÊ ÓÐÉÓÏË ÉÍÅÎ ÒÁÍÏË É ÐÒÉÓ×ÁÉ×ÁÅÔ ÔÉÐÏ×ÙÅ ÚÎÁÞÅÎÉÑ ÐÅÒÅÍÅÎÎÙÍ \tdescr{ÉÍÑ 
ÒÁÍËÉ}{\tt.off}, ËÁË ÎÅÏÂÈÏÄÉÍÏ ÄÌÑ ÆÉËÓÁÃÉÉ ÐÏÚÉÃÉÉ ËÁÖÄÏÊ ÒÁÍËÉ. 
%%A macro called {\tt
%%fixpos}\index{fixpos?\texttt{fixpos}}\label{Dfixpos} then takes this
%%same list of box names and assigns default values to the \tdescr{box
%%name}{\tt.off} variables as needed to fix the position of each box. 
éÓÐÏÌØÚÏ×ÁÎÉÅ {\tt fixsize} ÄÌÑ ÆÉËÓÁÃÉÉ ÒÁÚÍÅÒÏ× ËÁÖÄÏÊ ÒÁÍËÉ ÄÏ 
ÐÒÉÓ×ÁÉ×ÁÎÉÑ ÐÏÚÉÃÉÉ ÌÀÂÏÊ ÉÚ ÎÉÈ ÍÏÖÅÔ ÏÂÙÞÎÏ ÓÏËÒÁÔÉÔØ ÞÉÓÌÏ 
ÔÒÅÂÕÅÍÙÈ ÐÏÚÉÃÉÊ ÐÏ-ÕÍÏÌÞÁÎÉÀ ÄÏ ÏÄÎÏÊ.
%%By using {\tt fixsize} to fix the dimensions of each box before assigning
%%default positions to any of them, the number of needing default
%%positions can usually be cut to at most one.

éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÏÈ×ÁÔÙ×ÁÀÝÉÊ ÐÕÔØ ÄÌÑ ÒÁÍËÉ ÎÅ ÍÏÖÅÔ ÂÙÔØ ×ÙÞÉÓÌÅÎ 
ÄÏ ÔÅÈ ÐÏÒ, ÐÏËÁ ÒÁÚÍÅÒ, ÆÏÒÍÁ É ÐÏÚÉÃÉÑ ÒÁÍËÉ ÎÅÏÐÒÅÄÅÌÅÎÙ, ÍÁËÒÏÓ 
{\tt bpath}\index{bpath?\texttt{bpath}} ÐÒÉÍÅÎÑÅÔ {\tt fixsize} É {\tt
fixpos} Ë Ó×ÏÉÍ ÁÒÇÕÍÅÎÔÁÍ. 
%%Since the bounding path for a box cannot be computed until the size,
%%shape, and position of the box is determined, the {\tt
%%bpath}\index{bpath?\texttt{bpath}} macro applies {\tt fixsize} and {\tt
%%fixpos} to its argument. 
äÒÕÇÉÅ ÍÁËÒÏÓÙ, ÞÔÏ ÄÅÌÁÀÔ ÔÁËÖÅ, ×ËÌÀÞÁÀÔ\index{pic?\texttt{pic}}\label{Dpic}
$$ {\tt pic}\, \descr{ÉÍÑ ÒÁÍËÉ}, $$
ÇÄÅ \tdescr{ÉÍÑ ÒÁÍËÉ} --- ÜÔÏ ÓÕÆÆÉËÓ, ×ÏÚÍÏÖÎÏ, × ÓËÏÂËÁÈ.
%%Other macros that do this
%%include\index{pic?\texttt{pic}}\label{Dpic}
%%$$ {\tt pic}\, \descr{box name} $$
%%where the \tdescr{box name} is a suffix, possibly in parentheses. 
ïÎ ×ÏÚ×ÒÁÝÁÅÔ ÓÏÄÅÒÖÁÎÉÅ ÉÍÅÎÏ×ÁÎÎÏÊ ÒÁÍËÉ ËÁË ËÁÒÔÉÎËÉ, ÐÏÚÉÃÉÏÎÉÒÏ×ÁÎÎÏÊ 
ÔÁË, ÞÔÏ 
$$ {\tt draw\ pic} \descr{ÉÍÑ ÒÁÍËÉ} $$
ÉÚÏÂÒÁÖÁÅÔ ÓÏÄÅÒÖÉÍÏÅ ÒÁÍËÉ ÂÅÚ ÏÈ×ÁÔÙ×ÁÀÝÅÇÏ ÐÒÑÍÏÕÇÏÌØÎÉËÁ.
%%This returns
%%the contents of the named box as a picture positioned so that
%%$$ {\tt draw\ pic} \descr{box name} $$
%%draws the box contents without the bounding rectangle. 
üÔÁ ÏÐÅÒÁÃÉÑ ÍÏÖÅÔ ÔÁËÖÅ ÂÙÔØ ÕÓÏ×ÅÒÛÅÎÓÔ×Ï×ÁÎÁ ÍÁËÒÏÓÏÍ {\tt
drawunboxed}\index{drawunboxed?\texttt{drawunboxed}}\label{Ddrunbx}, 
ÂÅÒÕÝÉÍ ÒÁÚÄÅÌÅÎÎÙÊ ÚÁÐÑÔÙÍÉ ÓÐÉÓÏË ÉÍÅÎ ÒÁÍÏË.
%%This operation can also be accomplished by the {\tt
%%drawunboxed}\index{drawunboxed?\texttt{drawunboxed}}\label{Ddrunbx}
%%macro that takes a comma-separated list of box names. 
åÓÔØ ÅÝÅ ÍÁËÒÏÓ {\tt drawboxes}\index{drawboxes?\texttt{drawboxes}}\label{Ddrbxes}, 
ÒÉÓÕÀÝÉÊ ÔÏÌØËÏ ÏÈ×ÁÔÙ×ÁÀÝÉÅ ÐÒÑÍÏÕÇÏÌØÎÉËÉ.
%%There is also a
%%{\tt drawboxes}\index{drawboxes?\texttt{drawboxes}}\label{Ddrbxes} macro
%%that draws just the bounding rectangles.

äÒÕÇÏÊ ÓÐÏÓÏ ÎÁÒÉÓÏ×ÁÔØ ÐÕÓÔÙÅ ÐÒÑÍÏÕÇÏÌØÎÉËÉ --- ÜÔÏ ÐÒÏÓÔÏ\label{Deboxit} 
$$ {\tt boxit} \descr{ÉÍÑ ÒÁÍËÉ} \hbox{\tt ()} $$
ÂÅÚ ÒÉÓÕÎËÁ-ÁÒÇÕÍÅÎÔÁ, ËÁË ÜÔÏ ÄÅÌÁÌÏÓØ ÎÅÓËÏÌØËÏ ÒÁÚ ÎÁ ÒÉÓ.~\ref{fig49}.
%%Another way to draw empty rectangles is by just saying\label{Deboxit}
%%$$ {\tt boxit} \descr{box name} \hbox{\tt ()} $$
%%with no picture argument as is done several times in Figure~\ref{fig49}.
üÔÏ ÐÏÈÏÖÅ ÎÁ ×ÙÚÏ× {\tt boxit} Ó ÐÕÓÔÙÍ ÁÒÇÕÍÅÎÔÏÍ.
%%This is like calling {\tt boxit} with an empty picture.
ëÒÏÍÅ ÔÏÇÏ, ÁÒÇÕÍÅÎÔ ÍÏÖÅÔ ÂÙÔØ ÓÔÒÏËÏ×ÙÍ\label{Dsboxit} ×ÙÒÁÖÅÎÉÅÍ 
×ÍÅÓÔÏ ×ÙÒÁÖÅÎÉÑ-ÒÉÓÕÎËÁ É × ÜÔÏÍ ÓÌÕÞÁÅ ÓÔÒÏËÁ ÉÚÏÂÒÁÖÁÅÔÓÑ 
ÛÒÉÆÔÏÍ ÐÏ-ÕÍÏÌÞÁÎÉÀ.
%%Alternatively the argument can be a string\label{Dsboxit} expression
%%instead of a picture
%%expression in which case the string is typeset in the default font.

\subsection{ëÒÕÇÌÙÅ É Ï×ÁÌØÎÙÅ ÒÁÍËÉ}
%%\subsection{Circular and Oval Boxes}

ëÒÕÇÏ×ÙÅ É Ï×ÁÌØÎÙÅ ÒÁÍËÉ ×Ï ÍÎÏÇÏÍ ÐÏÈÏÖÉ ÎÁ ÐÒÑÍÏÕÇÏÌØÎÙÅ, ÏÔÌÉÞÁÑÓØ 
ÔÏÌØËÏ ÆÏÒÍÏÊ ÏÈ×ÁÔÙ×ÁÀÝÅÇÏ ÐÕÔÉ.
%%Circular and oval boxes are a lot like rectangular boxes except for the shape
%%of the bounding path. 
ôÁËÉÅ ÒÁÍËÉ ÕÓÔÁÎÁ×ÌÉ×ÁÀÔÓÑ ÍÁËÒÏÓÏÍ 
{\tt circleit}\index{circleit?\texttt{circleit}}\label{Dcircit}:
$$ {\tt circleit} \descr{ÉÍÑ ÒÁÍËÉ}
   \hbox{\tt(} \descr{ÓÏÄÅÒÖÁÎÉÅ ÒÁÍËÉ} \hbox{\tt)},
$$
ÇÄÅ \tdescr{ÉÍÑ ÒÁÍËÉ} --- ÜÔÏ ÓÕÆÆÉËÓ, Á \tdescr{ÓÏÄÅÒÖÁÎÉÅ ÒÁÍËÉ} --- ÜÔÏ ÌÉÂÏ 
×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ, ÌÉÂÏ ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ, ÌÉÂÏ \tdescr{ÐÕÓÔÏ}.
%%Such boxes are set up by the
%%{\tt circleit}\index{circleit?\texttt{circleit}}\label{Dcircit} macro:
%%$$ {\tt circleit} \descr{box name}
%%   \hbox{\tt(} \descr{box contents} \hbox{\tt)}
%%$$
%%where \tdescr{box name} is a suffix and \tdescr{box contents} is either a
%%picture expression, a string expression, or \tdescr{empty}.

íÁËÒÏÓ {\tt circleit} ÏÐÒÅÄÅÌÑÅÔ ÐÅÒÅÍÅÎÎÙÅ-ÐÁÒÙ ÔÁËÖÅ, ËÁË {\tt boxit}, ÎÏ ÂÅÚ 
ÕÇÌÏ×ÙÈ ÔÏÞÅË \tdescr{ÉÍÑ ÒÁÍËÉ}{\tt.ne}, \tdescr{ÉÍÑ ÒÁÍËÉ}{\tt.sw} É Ô.~Ä. 
%%The {\tt circleit} macro defines pair variables just as {\tt boxit} does, except
%%that there are no corner points \tdescr{box name}{\tt.ne},
%%\tdescr{box name}{\tt.sw}, etc. 
÷ÙÚÏ× 
$$ \hbox{\tt circleit.a(}\ldots \hbox{\tt )} $$
ÚÁÄÁÅÔ ÏÔÎÏÛÅÎÉÑ ÍÅÖÄÕ ÔÏÞËÁÍÉ {\tt a.c}, {\tt a.s}, {\tt a.e}, {\tt
a.n}, {\tt a.w} É ÒÁÓÓÔÏÑÎÉÑ {\tt a.dx} É {\tt a.dy}. 
%%A call to
%%$$ \hbox{\tt circleit.a(}\ldots \hbox{\tt )} $$
%%gives relationships among points {\tt a.c}, {\tt a.s}, {\tt a.e}, {\tt
%%a.n}, {\tt a.w} and distances {\tt a.dx} and {\tt a.dy}. 
÷ÍÅÓÔÅ Ó {\tt a.c} É {\tt a.off} ÜÔÉ ÐÅÒÅÍÅÎÎÙÅ ÏÐÒÅÄÅÌÑÀÔ, ËÁË ËÁÒÔÉÎËÁ 
ÃÅÎÔÒÉÒÕÅÔÓÑ × Ï×ÁÌÅ, ÞÔÏ ÍÏÖÎÏ Õ×ÉÄÅÔØ ÎÁ ÒÉÓ.~\ref{fig50}.
%%Together with
%%{\tt a.c} and {\tt a.off}, these variables describe how the picture is
%%centered in an oval as can be seen from the Figure~\ref{fig50}.

\begin{figure}[htp]
$$ \includegraphics{manfig-ru-50} $$
\caption[ëÁË {\tt circleit}-ÒÉÓÕÎÏË ÓÏÏÔÎÏÓÉÔÓÑ Ó ÁÓÓÏÃÉÉÒÏ×ÁÎÎÙÍÉ ÐÅÒÅÍÅÎÎÙÍÉ]
        {ïÔÎÏÛÅÎÉÑ ÍÅÖÄÕ ÚÁÄÁÎÎÙÍ {\tt circleit} ÒÉÓÕÎËÏÍ É Ó×ÑÚÁÎÎÙÍÉ
        Ó ÜÔÉÍ ÐÅÒÅÍÅÎÎÙÍÉ.  òÉÓÕÎÏË ÉÚÏÂÒÁÖÅÎ ÓÅÒÙÍ ÐÒÑÍÏÕÇÏÌØÎÉËÏÍ.}
%%\caption[How a {\tt circleit} picture relates to the associated variables]
%%        {The relationship between the picture given to {\tt circleit} and the
%%        associated variables.  The picture is indicated by a gray rectangle.}
\label{fig50}
\end{figure}

íÁËÒÏÓÙ {\tt drawboxed}\index{drawboxed?\texttt{drawboxed}}, {\tt
drawunboxed}\index{drawunboxed?\texttt{drawunboxed}}, {\tt
drawboxes}\index{drawboxes?\texttt{drawboxes}}, {\tt
pic}\index{pic?\texttt{pic}} É {\tt
bpath}\index{bpath?\texttt{bpath}} ÒÁÂÏÔÁÀÔ ÄÌÑ ÒÁÍÏË {\tt circleit} 
ÔÁËÖÅ ËÁË É ÄÌÑ ÒÁÍÏË {\tt boxit}. 
%%The {\tt drawboxed}\index{drawboxed?\texttt{drawboxed}}, {\tt
%%drawunboxed}\index{drawunboxed?\texttt{drawunboxed}}, {\tt
%%drawboxes}\index{drawboxes?\texttt{drawboxes}}, {\tt
%%pic}\index{pic?\texttt{pic}}, and {\tt
%%bpath}\index{bpath?\texttt{bpath}} macros work for {\tt circleit} boxes
%%just as they do for {\tt boxit} boxes. 

ôÉÐÏ×ÏÊ ÏÈ×ÁÔÙ×ÁÀÝÉÊ ÐÕÔØ ÄÌÑ ÒÁÍËÉ {\tt circleit} ÄÏÓÔÁÔÏÞÎÏ ×ÅÌÉË ÄÌÑ 
ÏËÒÕÖÅÎÉÑ ÓÏÄÅÒÖÉÍÏÇÏ ÒÁÍËÉ Ó ÍÁÌÅÎØËÉÍÉ ÐÒÅÄÏÈÒÁÎÑÀÝÉÍÉ ÏÔÓÔÕÐÁÍÉ, 
ÕÐÒÁ×ÌÑÅÍÙÍÉ ×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ\index{×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} 
{\tt circmargin}\label{Dcmargin}. 
%%By default, the boundary path
%%for a {\tt circleit} box is a circle large enough to surround the box
%%contents with a small safety margin controlled by the internal
%%variable\index{internal variables}\index{variables!internal} {\tt
%%circmargin}\label{Dcmargin}. 
òÉÓ.~\ref{fig51} ÐÒÅÄÏÓÔÁ×ÌÑÅÔ ÂÁÚÏ×ÙÊ ÐÒÉÍÅÒ ÉÓÐÏÌØÚÏ×ÁÎÉÑ 
{\tt bpath} Ó ÒÁÍËÁÍÉ {\tt circleit}.
%%Figure~\ref{fig51} gives a basic example
%%of the use of {\tt bpath} with {\tt circleit} boxes.

\begin{figure}[htbp]
$$\begin{verbatim}
vardef drawshadowed(text t) =
  fixsize(t);
  forsuffixes s=t:
    fill bpath.s shifted (1pt,-1pt);
    unfill bpath.s;
    drawboxed(s);
  endfor
enddef;

beginfig(51)
circleit.a(btex Box 1 etex);
circleit.b(btex Box 2 etex);
b.n = a.s - (0,20pt);
drawshadowed(a,b);
drawarrow a.s -- b.n;
endfig;
\end{verbatim}
\qquad \mathcenter{\includegraphics{manfig-ru-51}} $$
\caption[ëÏÄ MetaPost É ÒÉÓÕÎÏË-ÒÅÚÕÌØÔÁÔ.]  {ëÏÄ MetaPost É 
        ÒÉÓÕÎÏË-ÒÅÚÕÌØÔÁÔ.  úÁÍÅÔØÔÅ, ÞÔÏ ÍÁËÒÏÓ {\tt drawshadowed}, 
        ÉÓÐÏÌØÚÕÅÍÙÊ ÚÄÅÓØ, ÎÅ ×ÈÏÄÉÔ × ÍÁËÒÏÐÁËÅÔ {\tt boxes.mp}.}
%%\caption[MetaPost code and the resulting figure.]  {MetaPost code and
%%        the resulting figure.  Note that the {\tt drawshadowed} macro
%%        used here is not part of the {\tt boxes.mp} macro package.}
\label{fig51}
\index{drawshadowed?\texttt{drawshadowed}}
\end{figure}

ðÏÌÎÙÊ ÐÒÉÍÅÒ ÒÁÍÏË {\tt circleit} ÐÒÉ×ÏÄÉÔÓÑ ÎÁ ÒÉÓ.~\ref{fig52}.
%%A full example of {\tt circleit} boxes appears in Figure~\ref{fig52}.
ðÕÔÉ Ï×ÁÌØÎÏÊ ÇÒÁÎÉÃÙ ×ÏËÒÕÇ ``Start'' É ``Stop'' ÓÏÏÔ×ÅÔÓÔ×ÕÀÔ ÕÒÁ×ÎÅÎÉÑÍ 
$$ \hbox{\tt aa.dx=aa.dy;} \quad \hbox{\rm É}\quad \hbox{\tt ee.dx=ee.dy} $$
ÐÏÓÌÅ 
$$ \hbox{\verb|circleit.ee(btex\strut Stop etex)|}
    \quad\hbox{\rm É}\quad
   \hbox{\verb|circleit.ee(btex\strut Stop etex)|}.
$$
%%The oval boundary paths around ``Start'' and ``Stop'' are due to the equations
%%$$ \hbox{\tt aa.dx=aa.dy;} \quad {\rm and}\quad \hbox{\tt ee.dx=ee.dy} $$
%%after
%%$$ \hbox{\verb|circleit.ee(btex\strut Stop etex)|}
%%    \quad{\rm and}\quad
%%   \hbox{\verb|circleit.ee(btex\strut Stop etex)|}.
%%$$
ïÂÝÅÅ ÐÒÁ×ÉÌÏ × ÔÏÍ, ÞÔÏ {\tt bpath.}$c$ ×ÙÈÏÄÉÔ ËÒÕÇÌÙÍ, ÅÓÌÉ ×ÓÅ 
$c${\tt.dx}, $c${\tt.dy} É $c\hbox{\tt.dx}-c\hbox{\tt.dy}$ ÎÅÉÚ×ÅÓÔÎÙ. 
%%The general rule is that {\tt bpath.}$c$ comes out circular if
%%$c${\tt.dx}, $c${\tt.dy}, and $c\hbox{\tt.dx}-c\hbox{\tt.dy}$ are all
%%unknown. 
éÎÁÞÅ ÍÁËÒÏÓÙ ×ÙÂÉÒÁÀÔ ÄÏÓÔÁÔÏÞÎÏ ÂÏÌØÛÏÊ Ï×ÁÌ ÄÌÑ ×ÍÅÝÅÎÉÑ ÄÁÎÎÏÊ 
ËÁÒÔÉÎËÉ Ó ÐÒÅÄÏÈÒÁÎÑÀÝÉÍÉ ÏÔÓÔÕÐÁÍÉ {\tt
circmargin}\index{circmargin?\texttt{circmargin}}.
%%Otherwise, the macros select an oval big enough to contain the
%%given picture with the safety margin {\tt
%%circmargin}\index{circmargin?\texttt{circmargin}}.


\begin{figure}[htp]
$$\hbox{$\begin{verbatim}
vardef cuta(suffix a,b) expr p =
  drawarrow p cutbefore bpath.a cutafter bpath.b;
  point .5*length p of p
enddef;

vardef self@# expr p =
  cuta(@#,@#) @#.c{curl0}..@#.c+p..{curl0}@#.c  enddef;

beginfig(52);
verbatimtex \def\stk#1#2{$\displaystyle{\matrix{#1\cr#2\cr}}$} etex
circleit.aa(btex\strut Start etex); aa.dx=aa.dy;
circleit.bb(btex \stk B{(a|b)^*a} etex);
circleit.cc(btex \stk C{b^*} etex);
circleit.dd(btex \stk D{(a|b)^*ab} etex);
circleit.ee(btex\strut Stop etex); ee.dx=ee.dy;
numeric hsep;
bb.c-aa.c = dd.c-bb.c = ee.c-dd.c = (hsep,0);
cc.c-bb.c = (0,.8hsep);
xpart(ee.e - aa.w) = 3.8in;
drawboxed(aa,bb,cc,dd,ee);
label.ulft(btex$b$etex, cuta(aa,cc) aa.c{dir50}..cc.c);
label.top(btex$b$etex, self.cc(0,30pt));
label.rt(btex$a$etex, cuta(cc,bb) cc.c..bb.c);
label.top(btex$a$etex, cuta(aa,bb) aa.c..bb.c);
label.llft(btex$a$etex, self.bb(-20pt,-35pt));
label.top(btex$b$etex, cuta(bb,dd) bb.c..dd.c);
label.top(btex$b$etex, cuta(dd,ee) dd.c..ee.c);
label.lrt(btex$a$etex, cuta(dd,bb) dd.c..{dir140}bb.c);
label.bot(btex$a$etex, cuta(ee,bb) ee.c..tension1.3 ..{dir115}bb.c);
label.urt(btex$b$etex, cuta(ee,cc) ee.c{(cc.c-ee.c)rotated-15}..cc.c);
endfig;
\end{verbatim}
$}
\atop \vcenter{\vskip8pt\hbox{\includegraphics{manfig-ru-52}}}
$$
\caption{ëÏÄ MetaPost É ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ ÒÉÓÕÎÏË}
%%\caption{MetaPost code and the corresponding figure}
\label{fig52}
\end{figure}


\section{æÁÊÌÏ×ÙÅ ÞÔÅÎÉÅ É ÚÁÐÉÓØ}
%%\section{Reading and Writing Files}

äÏÓÔÕÐ Ë ÆÁÊÌÁÍ --- ÜÔÏ ÏÄÎÏ ÉÚ ÎÏ×ÙÈ Ó×ÏÊÓÔ×, ××ÅÄÅÎÎÏÅ × ×ÅÒÓÉÀ~0.60 
ÑÚÙËÁ MetaPost. 
%%File access was one of the new language features introduced in version~0.60
%%of the MetaPost language. 
îÏ×ÙÊ ÏÐÅÒÁÔÏÒ 
$$ {\tt readfrom}\ \descr{ÉÍÑ ÆÁÊÌÁ} $$\index{readfrom?\texttt{readfrom}}\label{Dreadfrom}%
×ÏÚ×ÒÁÝÁÅÔ ÏÞÅÒÅÄÎÕÀ ÓÔÒÏËÕ ÉÚ ÉÍÅÎÏ×ÁÎÎÏÇÏ ×ÈÏÄÎÏÇÏ ÆÁÊÌÁ\index{ÆÁÊÌÙ!ÞÔÅÎÉÅ}. 
%%A new operator
%%$$ {\tt readfrom}\ \descr{file name} $$\index{readfrom?\texttt{readfrom}}\label{Dreadfrom}%
%%returns a string giving the next line of input from the named
%%file\index{files!reading}. 
\tdescr{éÍÑ ÆÁÊÌÁ} ÍÏÖÅÔ ÂÙÔØ ÌÀÂÙÍ ÐÅÒ×ÉÞÎÙÍ ×ÙÒÁÖÅÎÉÅÍ ÔÉÐÁ ÓÔÒÏËÁ. 
%%The \tdescr{file name} can be any primary expression of type string. 
åÓÌÉ ÆÁÊÌ ÚÁËÏÎÞÉÌÓÑ ÉÌÉ ÎÅ ÍÏÖÅÔ ÞÉÔÁÔØÓÑ, ÔÏ ÒÅÚÕÌØÔÁÔ ÞÔÅÎÉÑ --- ÜÔÏ ÓÔÒÏËÁ 
ÉÚ ÏÄÎÏÇÏ ÎÕÌÅ×ÏÇÏ ÓÉÍ×ÏÌÁ.
%%If the file has ended or cannot be read, the
%%result is a string consisting of a single null character. 
íÁËÒÏÐÁËÅÔ {\tt plain} ××ÏÄÉÔ ÉÍÑ {\tt EOF}\index{EOF?\texttt{EOF}}\label{Deof} 
ÄÌÑ ÔÁËÏÊ ÓÔÒÏËÉ. 
%%The preloaded {\tt plain} macro package introduces the name
%%{\tt EOF}\index{EOF?\texttt{EOF}}\label{Deof} for this string. 
ðÏÓÌÅ ×ÏÚ×ÒÁÝÅÎÉÑ {\tt EOF} ÏÔ {\tt readfrom}, ÓÌÅÄÕÀÝÉÅ ÞÔÅÎÉÑ ÜÔÏÇÏ ÖÅ 
ÆÁÊÌÁ ÐÒÉ×ÅÄÕÔ Ë ÅÇÏ ÐÏ×ÔÏÒÎÏÍÕ ÞÔÅÎÉÀ ÓÎÁÞÁÌÁ.
%%After
%%{\tt readfrom} has returned {\tt EOF}, additional reads from the same file
%%cause the file to be reread from the start.

÷ÓÅ ÆÁÊÌÙ, ÏÔËÒÙÔÙÅ \ttt{readfrom}, ÞÔÏ ÅÝÅ ÎÅ ÓÞÉÔÁÎÙ ÐÏÌÎÏÓÔØÀ, 
ÚÁËÒÙ×ÁÀÔÓÑ\index{ÆÁÊÌÙ!ÚÁËÒÙÔÉÅ} Á×ÔÏÍÁÔÉÞÅÓËÉ, ËÏÇÄÁ ÐÒÏÇÒÁÍÍÁ ÚÁËÁÎÞÉ×ÁÅÔ 
×ÙÐÏÌÎÅÎÉÅ, ÈÏÔÑ ÓÕÝÅÓÔ×ÕÅÔ ËÏÍÁÎÄÁ 
$${\tt closefrom}\ \descr{ÉÍÑ ÆÁÊÌÁ}$$%
\index{closefrom?\texttt{closefrom}}\label{Dclosefrom}%
ÄÌÑ Ñ×ÎÏÇÏ ÚÁËÒÙÔÉÑ ÆÁÊÌÏ×, ÏÔËÒÙÔÙÈ {\tt readfrom}.
%%All files opened by \ttt{readfrom} that have not completely been read
%%yet are closed\index{files!closing} automatically when the program
%%terminates, but there exists a command
%%$${\tt closefrom}\ \descr{file name}$$%
%%\index{closefrom?\texttt{closefrom}}\label{Dclosefrom}%
%%to close files opened by {\tt readfrom} explicitly. 
òÁÚÕÍÎÏ Ñ×ÎÏ ÚÁËÒÙ×ÁÔØ ÆÁÊÌÙ, ËÏÔÏÒÙÅ ÎÅ ÎÕÖÎÏ ÓÞÉÔÙ×ÁÔØ ÐÏÌÎÏÓÔØÀ, Ô.~Å. ÄÏ 
ÐÏÌÕÞÅÎÉÑ {\tt EOF}, ÐÏÔÏÍÕ ÞÔÏ × ÐÒÏÔÉ×ÎÏÍ ÓÌÕÞÁÅ ÔÁËÉÅ ÆÁÊÌÙ ÐÒÏÄÏÌÖÁÔ 
ÉÓÐÏÌØÚÏ×ÁÔØ ×ÎÕÔÒÅÎÎÉÅ ÒÅÓÕÒÓÙ É ×ÏÚÍÏÖÎÏ ÏÂÕÓÌÏ×ÑÔ ÏÛÉÂËÕ 
\ttt{capacity exceeded!}\footnote{ÅÍËÏÓÔØ ÐÒÅ×ÙÛÅÎÁ!}
%%It is wise to
%%manually close files you do not need to read completely (i.e. until {\tt
%% EOF} is returned) because otherwise such files will continue to use
%%internal resources and perhaps cause a \ttt{capacity exceeded!} error.

ðÒÏÔÉ×ÏÐÏÌÏÖÎÏÓÔØÀ {\tt readfrom} Ñ×ÌÑÅÔÓÑ ËÏÍÁÎÄÁ 
$$ {\tt write}\ \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\ {\tt to}\ \descr{ÉÍÑ ÆÁÊÌÁ} $$%
\index{write to?\texttt{write to}}\label{Dwrite}%
%%The opposite of {\tt readfrom} is the command
%%$$ {\tt write}\ \descr{string expression}\ {\tt to}\ \descr{file name} $$%
%%\index{write to?\texttt{write to}}\label{Dwrite}%
ïÎÁ ÐÉÛÅÔ\index{ÆÁÊÌÙ!ÚÁÐÉÓØ} ÓÔÒÏËÕ ÔÅËÓÔÁ × ÕËÁÚÁÎÎÙÊ ÆÁÊÌ ×Ù×ÏÄÁ, 
ÏÔËÒÙ×ÁÑ ÓÎÁÞÁÌÁ ÆÁÊÌ, ÅÓÌÉ ÜÔÏ ÎÕÖÎÏ.
%%This writes\index{files!writing} a line of text to the specified output file,
%%opening the file first if necessary. 
÷ÓÅ ÔÁËÉÅ ÆÁÊÌÙ ÚÁËÒÙ×ÁÀÔÓÑ\index{ÆÁÊÌÙ!ÚÁËÒÙÔÉÅ} Á×ÔÏÍÁÔÉÞÅÓËÉ, ËÏÇÄÁ ÐÒÏÇÒÁÍÍÁ 
ÚÁ×ÅÒÛÁÅÔÓÑ.
%%All such files are
%%closed\index{files!closing} automatically when the program terminates. 
ïÎÉ ÍÏÇÕÔ ÂÙÔØ ÔÁËÖÅ ÚÁËÒÙÔÙ Ñ×ÎÏ ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ {\tt EOF}\index{EOF?\texttt{EOF}}
ËÁË \tdescr{ÓÔÒÏËÏ×ÏÇÏ ×ÙÒÁÖÅÎÉÑ}. 
%%They
%%can also be closed explicitly by using {\tt EOF}\index{EOF?\texttt{EOF}}
%%as the \tdescr{string expression}. 
åÄÉÎÓÔ×ÅÎÎÙÊ ÓÐÏÓÏ ÕÚÎÁÔØ ÂÙÌÁ ÌÉ ËÏÍÁÎÄÁ {\tt write} ÕÓÐÅÛÎÏÊ × ÚÁËÒÙÔÉÉ 
ÆÁÊÌÁ É ÉÓÐÏÌØÚÏ×ÁÎÉÉ {\tt readfrom} ÄÌÑ ÅÇÏ ÐÒÏÓÍÏÔÒÁ.
%%The only way to tell if a {\tt write}
%%command has succeeded is to close the file and use {\tt readfrom} to look
%%at it.

\section{ðÏÌÅÚÎÙÅ ÓÒÅÄÓÔ×Á}
%%\section{Utility Routines}

\index{ÐÏÌÅÚÎÙÅ ÓÒÅÄÓÔ×Á}
%%\index{utility routines}
\index{mplib?\texttt{mplib}}
\index{metapost/base?\texttt{metapost/base}}

üÔÏÔ ÒÁÚÄÅÌ ÏÐÉÓÙ×ÁÅÔ ÎÅËÏÔÏÒÙÅ ÐÏÌÅÚÎÙÅ ÓÒÅÄÓÔ×Á, ×ËÌÀÞÅÎÎÙÅ × ËÁÔÁÌÏÇ 
\texttt{mplib} ÉÅÒÁÒÈÉÉ ÒÁÚÒÁÂÏÔËÉ ÉÓÈÏÄÎÉËÏ×.
%%This section describes some of the utility routines included in the
%%\texttt{mplib} directory of the development source hierarchy. 
âÕÄÕÝÉÅ ×ÅÒÓÉÉ ÜÔÏÊ ÄÏËÕÍÅÎÔÁÃÉÉ ÄÏÌÖÎÙ ÓÏÄÅÒÖÁÔØ ÂÏÌØÛÅ ÉÎÆÏÒÍÁÃÉÉ, ÐÏËÁ ÖÅ, 
ÐÏÖÁÌÕÊÓÔÁ, ÞÉÔÁÊÔÅ ÆÁÊÌÙ ÉÓÈÏÄÎÉËÏ× --- ÂÏÌØÛÉÎÓÔ×Ï ÉÚ ÎÉÈ ÉÍÅÀÔ 
ÏÂßÑÓÎÉÔÅÌØÎÙÅ ËÏÍÍÅÎÔÁÒÉÉ × ÎÁÞÁÌÅ.
%%Future
%%versions of this documentation may include more; meanwhile, please read
%%the source files, most have explanatory comments at the top. 
éÓÈÏÄÎÉËÉ ÔÁËÖÅ ×ËÌÀÞÁÀÔ × ÄÉÓÔÒÉÂÕÔÉ×Ù ËÁË MetaPost, ÔÁË É × Â\'ÏÌØÛÉÅ \TeX, ËÁË 
ÐÒÁ×ÉÌÏ, × ËÁÔÁÌÏÇ \texttt{texmf/metapost/base}.
%%They are
%%also included in the MetaPost and larger \TeX\ distributions, typically
%%in a \texttt{texmf/metapost/base} directory.


\subsection{\texttt{TEX.mp}}

\label{dTEX}
\index{TEX.mp?\texttt{TEX.mp}}
\index{ÍÅÔËÉ Ó ÐÅÒÅÍÅÎÎÙÍ ÔÅËÓÔÏÍ}
%%\index{labels, with variable text}
\index{ÓÔÒÏËÏ×ÙÅ ×ÙÒÁÖÅÎÉÑ, ËÁË ÍÅÔËÉ}
%%\index{string expressions, as labels}

\texttt{TEX.mp} ÐÒÅÄÏÓÔÁ×ÌÑÅÔ ÓÐÏÓÏ ÐÅÞÁÔÁÔØ ÔÅËÓÔ ÓÔÒÏËÏ×ÙÈ ×ÙÒÁÖÅÎÉÊ 
MetaPost.
%%\texttt{TEX.mp} provides a way to typeset the text of a MetaPost string
%%expression. 
ðÒÅÄÐÏÌÏÖÉÍ, ÎÁÐÒÉÍÅÒ, ÞÔÏ ×ÁÍ ÎÕÖÎÙ ÍÅÔËÉ × ÆÏÒÍÅ  $n_0$,
$n_1$, \ldots, $n_{10}$ ÐÏ ÏÓÉ $x$. 
%%Suppose, for example, you need labels of the form $n_0$,
%%$n_1$, \ldots, $n_{10}$ across the $x$ axis. 
÷Ù ÍÏÖÅÔÅ ÓÄÅÌÁÔØ ÉÈ Ó (ÏÔÎÏÓÉÔÅÌØÎÙÍ) ÕÄÏÂÓÔ×ÏÍ Ó \texttt{TEX.mp}:
%%You can do this (relatively) conveniently with \texttt{TEX.mp}, as follows:
$$\begin{verbatim}
input TEX;
beginfig(100)
  last := 10;
  for i := 0 upto last:
   label(TEX("$n_{" & decimal(i) & "}$"), (5mm*i,0));
  endfor
  ...
endfig;
\end{verbatim}
$$
÷ ÏÔÌÉÞÉÉ ÏÔ ÜÔÏÇÏ, ÂÁÚÏ×ÁÑ ËÏÍÁÎÄÁ \texttt{btex} (ÓÍ. ÓÔÒ.\ \pageref{Dbtex}) 
ÐÅÞÁÔÁÅÔ ÔÅËÓÔ ÂÕË×ÁÌØÎÏ.
%%In contrast, the basic \texttt{btex} command (see p.\ \pageref{Dbtex})
%%typesets verbatim text. 
ðÏÌÕÞÁÅÔÓÑ, ÞÔÏ \texttt{btex~s~etex} ÐÅÞÁÔÁÅÔ ÌÉÔÅÒÁÌØÎÙÊ ÓÉÍ×ÏÌ `s', Á 
\texttt{TEX(s)} ÐÅÞÁÔÁÅÔ ÚÎÁÞÅÎÉÅ ÔÅËÓÔÏ×ÏÊ ÐÅÒÅÍÅÎÎÏÊ MetaPost~$s$.
%%That is, \texttt{btex~s~etex} typesets the
%%literal character `s'; \texttt{TEX(s)} typesets the value of the
%%MetaPost text variable~$s$.

\index{LaTeX?\LaTeX!ÎÁÂÏÒ ÍÅÔÏË Ó} ÷ ×ÅÒÓÉÀ 0.9
\texttt{TEX.mp} ÄÏÂÁ×ÌÅÎÙ Ä×Á ÄÏÐÏÌÎÉÔÅÌØÎÙÈ ÓÒÅÄÓÔ×Á, ÐÏÚ×ÏÌÑÀÝÉÅ 
ÉÓÐÏÌØÚÏ×ÁÔØ \LaTeX\ ÄÌÑ ÐÅÞÁÔÉ ÍÅÔÏË: \texttt{TEXPRE} É \texttt{TEXPOST}. 
%%\index{LaTeX?\LaTeX!typesetting labels with} In version 0.9,
%%\texttt{TEX.mp} acquired two additional routines to facilitate using
%%\LaTeX\ to typeset labels: \texttt{TEXPRE} and \texttt{TEXPOST}. 
éÈ ÚÎÁÞÅÎÉÑ ÚÁÐÏÍÉÎÁÀÔÓÑ É ×ËÌÀÞÁÀÔÓÑ ÓÏÏÔ×ÅÔÓÔ×ÅÎÎÏ ÐÅÒÅÄ É ÐÏÓÌÅ 
ËÁÖÄÏÇÏ ×ÙÚÏ×Á \texttt{TEX}. 
%%Their
%%values are remembered, and included before and after (respectively) each
%%call to \texttt{TEX}. 
âÅÚ ÎÉÈ ËÁÖÄÙÊ ×ÙÚÏ× \texttt{TEX} ÐÅÞÁÔÁÅÔ ÓÏ×ÅÒÛÅÎÎÏ ÎÅÚÁ×ÉÓÉÍÏ.
%%Otherwise, each \texttt{TEX} call is effectively
%%typeset independently. 
÷ÙÚÏ×Ù \texttt{TEX} ÔÁËÖÅ ÎÅ ×ÚÁÉÍÏÄÅÊÓÔ×ÕÀÔ Ó ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ 
{\tt verbatimtex}\index{verbatimtex?\texttt{verbatimtex}} (ÓÔÒ.\ \pageref{Dverbatimtex}).
%%\texttt{TEX} calls also do not interfere with
%%uses of {\tt verbatimtex}\index{verbatimtex?\texttt{verbatimtex}} (p.\ \pageref{Dverbatimtex}).

÷ÏÔ ÔÏÔ ÖÅ ÓÁÍÙÊ ÐÒÉÍÅÒ, ÞÔÏ É ×ÙÛÅ, ÎÏ Ó ÉÓÐÏÌØÚÏ×ÁÎÉÅÍ ËÏÍÁÎÄ 
\LaTeX\ \verb|\(| É \verb|\)|:
%%Here's the same example as above, using the \LaTeX\ commands \verb|\(|
%%and \verb|\)|:

$$\begin{verbatim}
input TEX;
TEXPRE("%&latex" & char(10) & "\documentclass{article}\begin{document}");
TEXPOST("\end{document}");
beginfig(100)
  last := 10;
  for i := 0 upto last:
   label(TEX("\( n_{" & decimal(i) & "} \)"), (5mm*i,0));
  endfor
  ...
endfig;
\end{verbatim}
$$
ïÂßÑÓÎÅÎÉÑ:
%%Explanation: 
\begin{itemize}

\item 
\texttt{\%\&latex} ÐÒÉ×ÏÄÉÔ Ë ×ÙÚÏ×Õ \LaTeX\ ×ÍÅÓÔÏ \TeX\ (ÓÍ. ÔÁËÖÅ ÎÉÖÅ). 
%%The \texttt{\%\&latex} causes \LaTeX\ to be invoked instead of \TeX.
%%(See below, also.) 
ïÓÎÏ×ÁÎÎÙÅ ÎÁ Web2C É MiKTeX ÄÉÓÔÒÉÂÕÔÉ×Ù \TeX, ËÁË ÍÉÎÉÍÕÍ, 
ÐÏÎÉÍÁÀÔ \texttt{\%\&} ÓÐÅÃÉÆÉËÁÃÉÀ; ÓÍ., ÎÁÐÒÉÍÅÒ, ÄÏËÕÍÅÎÔÁÃÉÀ Web2C
ÄÌÑ ÄÅÔÁÌÅÊ, \url{http://tug.org/web2c}. 
%%Web2C- and MiKTeX-based \TeX\ implementations, at
%%least, understand this \texttt{\%\&} specification; see, e.g., the Web2C
%%documentation for details, \url{http://tug.org/web2c}. 
(éÎÆÏÒÍÁÃÉÑ Ï ÔÏÍ, ËÁË ÄÅÌÁÔØ ÜÔÏ ÖÅ × ÄÒÕÇÉÈ ÓÉÓÔÅÍÁÈ ÂÕÄÅÔ ×ÅÓØÍÁ ÐÒÉ×ÅÔÓÔ×Ï×ÁÔØÓÑ.)
%%(Information on
%%how to do the same with other systems would be most welcome.)

\item
\texttt{char(10)} ÐÏÍÅÝÁÅÔ ÍÁÒËÅÒ ÎÏ×ÏÊ ÓÔÒÏËÉ (ÄÅÓÑÔÉÞÎÙÊ ËÏÄ ÓÉÍ×ÏÌÁ ASCII --- 10)
× ×Ù×ÏÄ.
%%The \texttt{char(10)} puts a newline (ASCII character code 10, decimal)
%%in the output.

\item
\verb|\documentclass...| --- ÏÂÙÞÎÙÊ ÓÐÏÓÏÂ ÎÁÞÁÔØ ÄÏËÕÍÅÎÔ \LaTeX.
%%The \verb|\documentclass...| is the usual way to start a \LaTeX\
%%document.

\item
éÚ-ÚÁ ÐÏ×ÅÄÅÎÉÑ \texttt{mpto} \verb|TEXPOST("\end{document}")| ÎÅ Ñ×ÌÑÅÔÓÑ 
ÓÔÒÏÇÏ ÎÅÏÂÈÏÄÉÍÙÍ, ÎÏ ÎÁÄÅÖÎÅÅ ÅÇÏ ×ËÌÀÞÁÔØ.
%%The \verb|TEXPOST("\end{document}")| is not strictly necessary, due to
%%the behavior of \texttt{mpto}, but it is safer to include it.

\end{itemize}

ë ÓÏÖÁÌÅÎÉÀ, ÉÎÓÔÒÕËÃÉÉ \TeX\ \verb|\special| ÉÓÞÅÚÁÀÔ × ÜÔÏÍ ÐÒÏÃÅÓÓÅ.
%%Unfortunately, \TeX\ \verb|\special| instructions vanish in this
%%process. 
ðÏÜÔÏÍÕ ÎÅÌØÚÑ ÉÓÐÏÌØÚÏ×ÁÔØ ÐÁËÅÔÙ, ÐÏÄÏÂÎÙÅ \texttt{xcolor}
É \texttt{hyperref}. 
%%So it is not possible to use packages such as \texttt{xcolor}
%%and \texttt{hyperref}.

÷ ÓÌÕÞÁÅ, ÅÓÌÉ ×Ù ÌÀÂÏÐÙÔÎÙ, ÔÏ ÓÒÅÄÓÔ×Á \texttt{TEX.mp} ÒÅÁÌÉÚÕÀÔÓÑ ÏÞÅÎØ ÐÒÏÓÔÏ: 
ÏÎÉ ÐÉÛÕÔ ËÏÍÁÎÄÙ \texttt{btex} ×Ï ×ÒÅÍÅÎÎÙÊ ÆÁÊÌ É ÚÁÔÅÍ ÉÓÐÏÌØÚÕÀÔ 
\texttt{scantokens} (ÓÔÒ.\ \pageref{Dscantokens}) ÄÌÑ ÅÇÏ ÏÂÒÁÂÏÔËÉ. 
%%In case you're curious, these routines are implemented very simply: they
%%write \texttt{btex} commands to a temporary file and then use
%%\texttt{scantokens} (p.\ \pageref{Dscantokens}) to process it. 
íÅÈÁÎÉÚÍ \texttt{makempx} (ÓÔÒ.\ \pageref{Dmakempx}) ×ÙÐÏÌÎÑÅÔ ×ÓÀ ÒÁÂÏÔÕ 
ÐÏ ÉÓÐÏÌØÚÏ×ÁÎÉÀ \TeX.
%%The
%%\texttt{makempx} mechanism (p.\ \pageref{Dmakempx}) does all the work of
%%running \TeX.

íÁÇÉÞÅÓËÉÅ \verb|%&| × ÐÅÒ×ÏÊ ÓÔÒÏËÅ --- ÜÔÏ ÎÅ ÅÄÉÎÓÔ×ÅÎÎÙÊ ÐÕÔØ ÕËÁÚÁÔØ 
ÎÁ ×ÙÚÏ× ÐÒÏÇÒÁÍÍÙ, ÏÔÌÉÞÎÏÊ ÏÔ (plain) \TeX. 
%%The \verb|%&| magic on the first line is not the only way to specify
%%invoking a different program than (plain) \TeX. 
úÄÅÓØ ÐÒÏÑ×ÌÑÅÔÓÑ ÐÒÅÉÍÕÝÅÓÔ×Ï ÍÁËÓÉÍÕÍÁ ÇÉÂËÏÓÔÉ: ÒÁÚÎÙÅ ËÏÎÓÔÒÕËÃÉÉ \texttt{TEX} 
ÍÏÇÕÔ ÉÓÐÏÌØÚÏ×ÁÔØ ÒÁÚÎÙÅ ÐÒÏÃÅÓÓÏÒÙ \TeX.
%%It has the advantage of
%%maximum flexibility: different \texttt{TEX} constructs can use different
%%\TeX\ processors. 
÷ÏÚÍÏÖÎÙ ÎÅ ÍÅÎÅÅ Ä×ÕÈ ÄÒÕÇÉÈ ÓÐÏÓÏÂÏ×:
%%But at least two other methods are possible:

\begin{itemize}
\item õÓÔÁÎÏ×ËÁ ÐÅÒÅÍÅÎÎÙÊ ÓÒÅÄÙ \texttt{TEX} × \texttt{latex} ÉÌÉ 
× ËÁËÏÊ-ÕÇÏÄÎÏ ÐÒÏÃÅÓÓÏÒ, ÖÅÌÁÅÍÙÊ ÄÌÑ ×ÙÚÏ×Á.
%%Set the environment variable \texttt{TEX} to \texttt{latex}---or
%%whatever processor you want to invoke. 
(äÌÑ ÒÁÂÏÔÙ Ó ÆÒÁÇÍÅÎÔÁÍÉ \ConTeXt\ ÎÕÖÎÏ ×ÙÚÙ×ÁÔØ \ttt{texexec}.) 
%%(To handle \ConTeXt\ fragments,
%%\ttt{texexec} could be used.) 
üÔÏÔ ÓÐÏÓÏÂ ÕÄÏÂÅÎ, ËÏÇÄÁ ÐÉÛÅÔÓÑ ÓÃÅÎÁÒÉÊ ÉÌÉ ÉÄÅÔ ÒÁÂÏÔÁ ÎÁÄ ÐÒÏÅËÔÏÍ, 
×ÓÅÇÄÁ ÔÒÅÂÕÀÝÉÍ \texttt{latex}. 
%%This might be convenient when writing a
%%script, or working on a project that always requires \texttt{latex}.

\item ÷ÙÚÏ× MetaPost Ó ÏÐÃÉÅÊ ËÏÍÁÎÄÎÏÊ ÓÔÒÏËÉ \ttt{-tex=latex} (ÉÌÉ ÄÒÕÇÉÍ 
ÐÒÏÃÅÓÓÏÒÏÍ, ËÏÎÅÞÎÏ). 
%%Invoke MetaPost with the command-line option \ttt{-tex=latex} (or
%%whatever processor, of course). 
üÔÏ ÍÏÖÅÔ ÂÙÔØ ÐÏÌÅÚÎÏ × Makefile ÉÌÉ ÐÒÉ ÅÄÉÎÓÔ×ÅÎÎÏÍ ÉÓÐÏÌÎÅÎÉÉ.
%%This might be useful from a Makefile,
%%or just a one-off run.
\end{itemize}

\subsection{\texttt{mproof.tex}}

\index{mproof.tex?\texttt{mproof.tex}}

\texttt{mproof.tex} --- ÜÔÏ ÓÒÅÄÓÔ×Ï (plain) \TeX, Á ÎÅ MetaPost. 
%%\texttt{mproof.tex} is a (plain) \TeX\ routine, not MetaPost at all. 
ïÎÏ ÐÅÞÁÔÁÅÔ ÇÒÁÎËÉ ×Ù×ÏÄÁ MetaPost.
%%It writes a proof sheet for MetaPost output. 
÷ÙÚÙ×ÁÊÔÅ ÅÇÏ ÐÒÉÍÅÒÎÏ ÔÁË:
%%Call it like this:
$$\hbox{\tt tex mproof {\sl ÉÍÑ-×ÙÈÏÄÎÏÇÏ-ÆÁÊÌÁ-MetaPost}}$$
%%$$\hbox{\tt tex mproof {\sl MetaPost-output-filename}}$$
úÁÔÅÍ ÒÁÂÏÔÁÊÔÅ Ó ÒÅÚÕÌØÔÉÒÕÀÝÉÍ ÆÁÊÌÏÍ \texttt{dvi} ÏÂÙÞÎÙÍ ÏÂÒÁÚÏÍ.
%%Then process the resulting \texttt{dvi} file as usual.

\section{ïÔÌÁÄËÁ}
%%\section{Debugging}

MetaPost ÕÎÁÓÌÅÄÏ×ÁÌ ÍÎÏÇÉÅ ×ÏÚÍÏÖÎÏÓÔÉ \MF\index{metafont?\MF} ÄÌÑ 
ÉÎÔÅÒÁËÔÉ×ÎÏÊ ÏÔÌÁÄËÉ, ÚÎÁÞÉÔÅÌØÎÁÑ ÞÁÓÔØ ËÏÔÏÒÙÈ ÍÏÖÅÔ ÌÉÛØ ×ËÒÁÔÃÅ ÂÙÔØ ÕÐÏÍÑÎÕÔÁ 
ÚÄÅÓØ. 
%%MetaPost inherits from \MF\index{metafont?\MF} numerous facilities for
%%interactive debugging, most of which can only be mentioned briefly here.
âÏÌØÛÅ ÉÎÆÏÒÍÁÃÉÉ ÐÏ ÓÏÏÂÝÅÎÉÑÍ Ï ÏÛÉÂËÁÈ, ÏÔÌÁÄËÅ, ÇÅÎÅÒÁÃÉÉ 
ÔÒÁÓÓÉÒÕÀÝÅÊ ÉÎÆÏÒÍÁÃÉÉ ÍÏÖÎÏ ÎÁÊÔÉ × {\sl The\ \MF book} \cite{kn:c}.
%%Further information on error messages, debugging, and generating tracing
%%information can be found in {\sl The\ \MF book} \cite{kn:c}.

ðÒÅÄÐÏÌÏÖÉÍ, ÞÔÏ ×ÁÛ ×ÈÏÄÎÏÊ ÆÁÊÌ ÓÏÄÅÒÖÉÔ × ÓÔÒÏËÅ 17 
$$ \hbox{\tt draw z1-{}-z2;} $$
ÂÅÚ ÐÒÅÄ×ÁÒÉÔÅÌØÎÏÇÏ ÏÐÒÅÄÅÌÅÎÉÑ ÚÎÁÞÅÎÉÊ {\tt z1} É {\tt z2}.
%%Suppose your input file says
%%$$ \hbox{\tt draw z1--z2;} $$
%%on line 17 without first giving known values to {\tt z1} and {\tt z2}.
òÉÓ.~\ref{errmsg} ÐÏËÁÚÙ×ÁÅÔ ÔÏ, ÞÔÏ ÉÎÔÅÒÐÒÅÔÁÔÏÒ MetaPost ÐÅÞÁÔÁÅÔ ÎÁ 
×ÁÛÅÍ ÔÅÒÍÉÎÁÌÅ, ËÏÇÄÁ ÎÁÈÏÄÉÔ ÏÛÉÂËÕ. 
%%Figure~\ref{errmsg} shows what the MetaPost interpreter prints on your
%%terminal when it finds the error. 
óÏÂÓÔ×ÅÎÎÏ ÓÏÏÂÝÅÎÉÅ Ï ÏÛÉÂËÅ --- ÜÔÏ ÓÔÒÏËÁ, ÎÁÞÉÎÁÀÝÁÑÓÑ Ó ``{\tt !}'', 
ÓÌÅÄÕÀÝÉÅ ÛÅÓÔØ ÓÔÒÏË ÄÁÀÔ ËÏÎÔÅËÓÔ, ÔÏÞÎÏ ÐÏËÁÚÙ×ÁÀÝÉÊ, ÞÔÏ ÞÉÔÁÌÏÓØ Ó ××ÏÄÁ, 
ËÏÇÄÁ ÂÙÌÁ ÏÂÎÁÒÕÖÅÎÁ ÏÛÉÂËÁ, Á ``{\tt ?}'' ÎÁ ÐÏÓÌÅÄÎÅÊ ÓÔÒÏËÅ --- ÜÔÏ 
ÐÒÉÇÌÁÛÅÎÉÅ ÄÌÑ ×ÁÛÅÇÏ ÏÔ×ÅÔÁ. 
%%The actual error message is the line
%%beginning with ``{\tt !}''; the next six lines give the context that
%%shows exactly what input was being read when the error was found; and
%%the ``{\tt ?}'' on last line is a prompt for your response. 
éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÓÏÏÂÝÅÎÉÅ Ï ÏÛÉÂËÅ ÇÏ×ÏÒÉÔ Ï ÎÅÏÐÒÅÄÅÌÅÎÎÏÊ ËÏÏÒÄÉÎÁÔÅ $x$, 
ÜÔÏ ÚÎÁÞÅÎÉÅ ÐÅÞÁÔÁÅÔÓÑ × ÐÅÒ×ÏÊ ÓÔÒÏËÅ ÐÏÓÌÅ `{\tt >{}>}''. 
%%Since the
%%error message talks about an undefined $x$~coordinate, this value is
%%printed on the first line after the ``{\tt >>}''. 
÷ ÜÔÏÍ ÓÌÕÞÁÅ ËÏÏÒÄÉÎÁÔÁ $x$ ÐÁÒÙ {\tt z1} --- ÜÔÏ ÎÅÉÚ×ÅÓÔÎÁÑ 
ÐÅÒÅÍÅÎÎÁÑ {\tt x1}, ÐÏÜÔÏÍÕ ÉÎÔÅÒÐÒÅÔÁÔÏÒ ÐÅÞÁÔÁÅÔ ÉÍÑ ÐÅÒÅÍÅÎÎÏÊ 
{\tt x1} ÔÏÞÎÏ ÔÁËÖÅ, ËÁË ÅÓÌÉ ÂÙ × ÜÔÏÍ ÍÅÓÔÅ ÂÙÌÏ 
ÓËÁÚÁÎÏ\index{show?\texttt{show}} ``{\tt show x1}''.
%%In this case the
%%$x$~coordinate of {\tt z1} is just the unknown variable {\tt x1}, so the
%%interpreter prints the variable name {\tt x1} just as it would if it
%%were told to\index{show?\texttt{show}} ``{\tt show x1}'' at this point.

\begin{figure}[htp]
$$\begin{verbatim}
>> x1
! Undefined x coordinate has been replaced by 0.
<to be read again> 
                   {
--->{
     curl1}..{curl1}
l.17 draw z1--
             z2;
?
\end{verbatim}
$$
\caption{ðÒÉÍÅÒ ÓÏÏÂÝÅÎÉÑ ÏÂ ÏÛÉÂËÅ.}
%%\caption{An example of an error message.}
\label{errmsg}
\end{figure}

ìÉÓÔÉÎÇ ËÏÎÔÅËÓÔÁ ÍÏÖÅÔ ÐÏËÁÚÁÔØÓÑ ÓÌÅÇËÁ ÐÕÔÁÎÙÍ × ÐÅÒ×ÙÊ ÒÁÚ, ÎÏ ÏÎ 
ÐÏ-ÐÒÏÓÔÕ ×ÙÄÁÅÔ ÎÅÓËÏÌØËÏ ÓÔÒÏË ÔÅËÓÔÁ, ÐÏËÁÚÙ×ÁÑ, ËÁË ÍÎÏÇÏ ÉÚ 
ËÁÖÄÏÊ ÓÔÒÏËÉ ÂÙÌÏ ÕÖÅ ÓÞÉÔÁÎÏ.
%%The context listing may seem a little confusing at first, but it really just
%%gives a few lines of text showing how much of each line has been read so far.
ëÁÖÄÁÑ ÓÔÒÏËÁ ××ÏÄÁ ÐÅÞÁÔÁÅÔÓÑ × Ä×Å ÓÔÒÏËÉ, ÐÏÄÏÂÎÙÅ ÓÌÅÄÕÀÝÉÍ:
%%Each line of input is printed on two lines like this:
\begin{eqnarray*}
 \descr{ÄÅÓËÒÉÐÔÏÒ}\ \hbox{õÖÅ ÓÞÉÔÁÎÎÙÊ ÔÅËÓÔ} \\
        && \hbox{ôÅËÓÔ ÄÌÑ ÓÞÉÔÙ×ÁÎÉÑ}
%%\descr{descriptor}\ \hbox{Text read so far} \\
%%        && \hbox{Text yet to be read}
\end{eqnarray*}
\tdescr{äÅÓËÒÉÐÔÏÒ} ÉÄÅÎÔÉÆÉÃÉÒÕÅÔ ÉÓÈÏÄÎÉË.
%%The \tdescr{descriptor} identifies the input source. 
üÔÏ ÌÉÂÏ ÎÏÍÅÒ ÓÔÒÏËÉ ÔÉÐÁ ``{\tt l.17}'' ÄÌÑ ÓÔÒÏËÉ 17 ÔÅËÕÝÅÇÏ ÆÁÊÌÁ, ÌÉÂÏ 
ÉÍÑ ÍÁËÒÏÓÁ ÐÅÒÅÄ ``{\tt ->}'', ÌÉÂÏ ÏÂßÑÓÎÑÀÝÁÑ ÆÒÁÚÁ × ÕÇÌÏ×ÙÈ ÓËÏÂËÁÈ.
%%It is either a
%%line number like ``{\tt l.17}'' for line 17 of the current file; or it
%%can be a macro name followed by ``{\tt ->}''; or it is a descriptive
%%phrase in angle brackets. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÚÎÁÞÅÎÉÅ ÌÉÓÔÉÎÇÁ ËÏÎÔÅËÓÔÁ ÎÁ ÒÉÓ.~\ref{errmsg}: ÉÎÔÅÒÐÒÅÔÁÔÏÒ 
ÔÏÌØËÏ ÞÔÏ ÓÞÉÔÁÌ ÓÔÒÏËÕ 17 ×ÈÏÄÎÏÇÏ ÆÁÊÌÁ ÄÏ ``{\tt -{}-}'', ÒÁÓËÒÙÔÉÅ ÍÁËÒÏÓÁ 
{\tt -{}-} ËÁË ÒÁÚ ÎÁÞÁÌÏÓØ É ÎÁÞÁÌØÎÙÊ ``\verb|{|'' ×ÏÚ×ÒÁÝÅÎ ÎÁÚÁÄ, ÐÏÚ×ÏÌÑÑ 
××ÏÄ ÐÏÌØÚÏ×ÁÔÅÌÑ ÄÏ ÒÁÚÂÏÒÁ ÜÔÏÇÏ ÚÎÁËÁ.
%%Thus, the meaning of the context listing in
%%Figure~\ref{errmsg} is that the interpreter has just read line 17 of the
%%input file up to ``{\tt --},'' the expansion of the {\tt --} macro has
%%just started, and the initial ``\verb|{|'' has been reinserted to allow
%%for user input before scanning this token.

óÒÅÄÉ ×ÏÚÍÏÖÎÙÈ ÏÔ×ÅÔÏ× ÎÁ ÐÒÉÇÌÁÛÅÎÉÅ {\tt ?} ÅÓÔØ ÔÁËÉÅ:
%%Among the possible responses to a {\tt ?} prompt are the following:
\begin{description}
\item[x] ÐÒÅËÒÁÝÁÅÔ ÉÓÐÏÌÎÅÎÉÅ --- ×Ù ÍÏÖÅÔÅ ÉÓÐÒÁ×ÉÔØ ×ÁÛ ×ÈÏÄÎÏÊ ÆÁÊÌ É ÐÅÒÅÚÁÐÕÓÔÉÔØ MetaPost.
%%\item[x] terminates the run so that you can fix your input file and start over.
\item[h] ÐÅÞÁÔÁÅÔ ÐÏÄÓËÁÚËÕ, ÚÁ ËÏÔÏÒÏÊ ÉÄÅÔ ÄÒÕÇÏÅ {\tt ?}-ÐÒÉÇÌÁÛÅÎÉÅ.
%%\item[h] prints a help message followed by another {\tt ?} prompt.
\item[\tdescr{return}] ÐÒÉ×ÏÄÉÔ ÉÎÔÅÒÐÒÅÔÁÔÏÒ Ë ÐÒÏÄÏÌÖÅÎÉÀ ÒÁÂÏÔÙ ÔÁË ÈÏÒÏÛÏ, ËÁË 
ÏÎ ÓÍÏÖÅÔ.
%%\item[\tdescr{return}] causes the interpreter to proceed as best it can.
\item[?] ÐÅÞÁÔÁÅÔ ÓÐÉÓÏË ×ÏÚÍÏÖÎÙÈ ÏÐÃÉÊ, ÚÁ ËÏÔÏÒÙÍÉ ÓÌÅÄÕÅÔ {\tt ?}-ÐÒÉÇÌÁÛÅÎÉÅ.
%%\item[?] prints a listing of the options available, followed by another
%%        {\tt ?} prompt.
\end{description}

óÏÏÂÝÅÎÉÑ Ï ÏÛÉÂËÁÈ É ÏÔ×ÅÔÙ ÎÁ ËÏÍÁÎÄÙ {\tt show} ÔÁËÖÅ ÐÅÞÁÔÁÀÔÓÑ É × 
ÆÁÊÌ-ÄÕÂÌÉËÁÔ\index{ÆÁÊÌÙ!ÄÕÂÌÉËÁÔ}, ÞØÅ ÉÍÑ ÐÏÌÕÞÁÅÔÓÑ ÉÚ ÉÍÅÎÉ 
ÇÌÁ×ÎÏÇÏ ×ÈÏÄÎÏÇÏ ÆÁÊÌÁ ÉÚÍÅÎÅÎÉÅÍ ``{\tt .mp}'' ÎÁ ``{\tt .log}''. 
%%Error messages and responses to {\tt show} commands are also written
%%into the transcript\index{files!transcript} file whose name is obtained
%%from the name of the main input file by changing ``{\tt .mp}'' to ``{\tt
%%.log}''. 
ëÏÇÄÁ ×ÎÕÔÒÅÎÎÑÑ ÐÅÒÅÍÅÎÎÁÑ\index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} {\tt
tracingonline}\index{tracingonline?\texttt{tracingonline}} ÉÍÅÅÔ ÉÓÈÏÄÎÏÅ 
ÚÎÁÞÅÎÉÅ ÎÏÌØ, ÔÏ ÎÅËÏÔÏÒÙÅ ËÏÍÁÎÄÙ  {\tt show} ÐÅÞÁÔÁÀÔ Ó×ÏÉ ÒÅÚÕÌØÔÁÔÙ ×Ï 
×ÓÅÈ ÄÅÔÁÌÑÈ ÔÏÌØËÏ × ÆÁÊÌ-ÄÕÂÌÉËÁÔ.
%%When the internal variable\index{internal
%%variables}\index{variables!internal} {\tt
%%tracingonline}\index{tracingonline?\texttt{tracingonline}} is at its
%%default value of zero, some {\tt show} commands print their results in
%%full detail only in the transcript file.

ôÏÌØËÏ ÏÄÉÎ ÔÉÐ ËÏÍÁÎÄÙ {\tt show}\index{show?\texttt{show}} ÏÂÓÕÖÄÁÌÓÑ ÄÏ 
ÓÉÈ ÐÏÒ: {\tt show} Ó ÒÁÚÄÅÌÅÎÎÙÍ ÚÁÐÑÔÙÍÉ ÓÐÉÓËÏÍ ×ÙÒÁÖÅÎÉÊ ÐÅÞÁÔÁÅÔ 
ÓÉÍ×ÏÌØÎÏÅ ÐÒÅÄÓÔÁ×ÌÅÎÉÅ ÜÔÉÈ ×ÙÒÁÖÅÎÉÊ.
%%Only one type of {\tt show}\index{show?\texttt{show}} command has been
%%discussed so far: {\tt show} followed by a comma-separated list of
%%expressions prints symbolic representations of the expressions.

ëÏÍÁÎÄÁ {\tt showtoken}\index{showtoken?\texttt{showtoken}}\label{Dshtok}
ÍÏÖÅÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎÁ ÄÌÑ ÐÏËÁÚÁ ÐÁÒÁÍÅÔÒÏ× É ÔÅËÓÔÁ ÚÁÍÅÎÙ ÍÁËÒÏÓÁ.
%%The {\tt showtoken}\index{showtoken?\texttt{showtoken}}\label{Dshtok}
%%command can be used to show the
%%parameters and replacement text of a macro. 
ïÎÁ ÂÅÒÅÔ ÒÁÚÄÅÌÅÎÎÙÊ ÚÁÐÑÔÙÍÉ ÓÐÉÓÏË ÚÎÁËÏ× É ÉÄÅÎÔÉÆÉÃÉÒÕÅÔ ËÁÖÄÙÊ ÉÚ ÎÉÈ.
%%It takes a comma-separated list of tokens and identifies each one. 
åÓÌÉ ÚÎÁË --- ÜÔÏ ÐÒÉÍÉÔÉ×, ÎÁÐÒÉÍÅÒ, 
``\verb|showtoken +|'', ÔÏ ÏÎ ÐÏ-ÐÒÏÓÔÕ ÉÄÅÎÔÉÆÉÃÉÒÕÅÔÓÑ ÓÏÂÏÊ:
$$ \hbox{\verb|> +=+|} $$
%%If the token is a primitive as in
%%``\verb|showtoken +|'' it is just identified as being itself:
%%$$ \hbox{\verb|> +=+|} $$
ðÒÉÍÅÎÅÎÉÅ {\tt showtoken} Ë ÐÅÒÅÍÅÎÎÏÊ ÉÌÉ {\tt vardef}-ÍÁËÒÏÓÕ ÐÒÉ×ÅÄÅÔ Ë 
$$ \hbox{\tt > } \descr{ÚÎÁË}\hbox{\tt =variable} $$
%%Applying {\tt showtoken} to a variable or a {\tt vardef} macro yields
%%$$ \hbox{\tt > } \descr{token}\hbox{\tt =variable} $$

äÌÑ ÐÏÌÕÞÅÎÉÑ ÄÏÐÏÌÎÉÔÅÌØÎÏÊ ÉÎÆÏÒÍÁÃÉÉ Ï ÐÅÒÅÍÅÎÎÏÊ ÉÓÐÏÌØÚÕÊÔÅ 
{\tt showvariable}\index{showvariable?\texttt{showvariable}}\label{Dshvar}
×ÍÅÓÔÏ {\tt showtoken}. 
%%To get more information about a variable, use
%%{\tt showvariable}\index{showvariable?\texttt{showvariable}}\label{Dshvar}
%%instead of {\tt showtoken}. 
áÒÇÕÍÅÎÔ Ë {\tt showvariable} --- ÜÔÏ ÒÁÚÄÅÌÅÎÎÙÊ ÚÁÐÑÔÙÍÉ ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ 
ÚÎÁËÏ×, Á ÅÅ ÒÅÚÕÌØÔÁÔ --- ÜÔÏ ÏÐÉÓÁÎÉÅ ×ÓÅÈ ÐÅÒÅÍÅÎÎÙÈ, ÞØÉ ÉÍÅÎÁ ÎÁÞÉÎÁÀÔÓÑ Ó 
ÏÄÎÏÇÏ ÉÚ ÚÎÁËÏ× ÉÚ ÓÐÉÓËÁ.
%%The
%%argument to {\tt showvariable} is a comma-separated list of symbolic tokens
%%and the result is a description of all the variables whose names begin with
%%one of the listed tokens. 
üÔÏ ÒÁÂÏÔÁÅÔ ÄÁÖÅ ÄÌÑ vardef-ÍÁËÒÏÓÏ×.
%%This even works for {\tt vardef} macros. 
îÁÐÒÉÍÅÒ, {\tt showvariable z} ÐÅÞÁÔÁÅÔ
$$ \hbox{\verb|z@#=macro:->begingroup(x(SUFFIX2),y(SUFFIX2))endgroup|} $$
%%For example, {\tt showvariable z} yields
%%$$ \hbox{\verb|z@#=macro:->begingroup(x(SUFFIX2),y(SUFFIX2))endgroup|} $$

åÓÔØ ÅÝÅ ËÏÍÁÎÄÁ {\tt
showdependencies}\index{showdependencies?\texttt{showdependencies}}\label{Dshdep},
ÎÅ ÉÍÅÀÝÁÑ ÁÒÇÕÍÅÎÔÏ× É ÐÅÞÁÔÁÀÝÁÑ ÓÐÉÓÏË ×ÓÅÈ {\em ÚÁ×ÉÓÉÍÙÈ} ÐÅÒÅÍÅÎÎÙÈ É ÔÏ, ËÁË 
ÌÉÎÅÊÎÙÅ ÕÒÁ×ÎÅÎÉÑ ÚÁÄÁÎÎÙÅ ÒÁÎÅÅ ÄÅÌÁÀÔ ÉÈ ÚÁ×ÉÓÉÍÙÍÉ Ó ÄÒÕÇÉÍÉ ÐÅÒÅÍÅÎÎÙÍÉ.
%%There is also a {\tt
%%showdependencies}\index{showdependencies?\texttt{showdependencies}}\label{Dshdep}
%%command that takes no arguments and prints a list of all {\em dependent}
%%variables and how the linear equations given so far make them depend on
%%other variables. 
ôÁËÉÍ ÏÂÒÁÚÏÍ, ÐÏÓÌÅ 
$$ \hbox{\tt z2-z1=(5,10); z1+z2=(a,b);} $$
{\tt showdependencies} ÎÁÐÅÞÁÔÁÅÔ ÔÏ, ÞÔÏ ÐÏËÁÚÁÎÏ ÎÁ ÒÉÓ.~\ref{shdep}.
%%Thus after
%%$$ \hbox{\tt z2-z1=(5,10); z1+z2=(a,b);} $$
%%{\tt showdependencies} prints what is shown in Figure~\ref{shdep}. 
üÔÏ ÍÏÖÅÔ ÂÙÔØ ÐÏÌÅÚÎÙÍ ÐÒÉ ÏÔ×ÅÔÅ ÎÁ ×ÏÐÒÏÓ ÔÉÐÁ ``þÔÏ ÚÎÁÞÉÔ, ÞÔÏ 
`{\tt !\ Undefined x coordinate}?'\footnote{ëÏÏÒÄÉÎÁÔÁ x --- 
ÎÅÏÐÒÅÄÅÌÅÎÁ} --- Ñ ÄÕÍÁÀ, ÞÔÏ ÐÒÉ×ÅÄÅÎÎÙÅ ÒÁÎÅÅ ÕÒÁ×ÎÅÎÉÑ ÏÐÒÅÄÅÌÑÀÔ 
{\tt x1}.'' 
%%This could
%%be useful in answering a question like ``What does it mean
%%`{\tt !\ Undefined x coordinate}?'
%%I thought the equations given so far would determine {\tt x1}.''

\begin{figure}[htp]
$$\begin{verbatim}
x2=0.5a+2.5
y2=0.5b+5
x1=0.5a-2.5
y1=0.5b-5
\end{verbatim}
$$
\caption{òÅÚÕÌØÔÁÔ {\tt z2-z1=(5,10); z1+z2=(a,b); showdependencies;}}
%%\caption{The result of {\tt z2-z1=(5,10); z1+z2=(a,b); showdependencies;}}
\label{shdep}
\end{figure}

åÓÌÉ ×ÓÅ ÜÔÏ ÎÅ ÐÒÉ×ÏÄÉÔ Ë ÕÓÐÅÈÕ, ÔÏ ÅÓÔØ ÅÝÅ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÊ ÍÁËÒÏÓ 
{\tt tracingall}\index{tracingall?\texttt{tracingall}}\label{Dtall}, 
ÐÒÉ×ÏÄÑÝÉÊ ÉÎÔÅÒÐÒÅÔÁÔÏÒ Ë ÐÅÞÁÔÉ ÄÅÔÁÌØÎÏÇÏ ÏÔÞÅÔÁ ÏÂÏ ×ÓÅÍ, ÞÔÏ ÏÎ 
ÄÅÌÁÅÔ.
%%When all else fails, the predefined macro {\tt
%%tracingall}\index{tracingall?\texttt{tracingall}}\label{Dtall} causes
%%the interpreter to print a detailed listing of everything it is doing.
÷ÓÌÅÄÓÔ×ÉÅ ÔÏÇÏ, ÞÔÏ ÔÒÁÓÓÉÒÕÀÝÁÑ ÉÎÆÏÒÍÁÃÉÑ ÞÁÓÔÏ ÉÍÅÅÔ ×ÅÓØÍÁ ÂÏÌØÛÏÊ 
ÒÁÚÍÅÒ, ×ÏÚÍÏÖÎÏ ÂÕÄÅÔ ÌÕÞÛÅ ÉÓÐÏÌØÚÏ×ÁÔØ ÍÁËÒÏÓ {\tt 
loggingall}\index{loggingall?\texttt{loggingall}}\label{Dlogall}, 
ÐÒÏÉÚ×ÏÄÑÝÉÊ ÔÕ ÖÅ ÓÁÍÕÀ ÉÎÆÏÒÍÁÃÉÀ, ÎÏ ÔÏÌØËÏ ÄÌÑ ÚÁÐÉÓÉ × 
ÆÁÊÌ-ÄÕÂÌÉËÁÔ\index{ÆÁÊÌÙ!ÄÕÂÌÉËÁÔ}.
%%Since the tracing information is often quite voluminous, it may be
%%better to use the {\tt
%%loggingall}\index{loggingall?\texttt{loggingall}}\label{Dlogall} macro
%%that produces the same information but only writes it in the
%%transcript\index{files!transcript} file. 
åÓÔØ ÅÝÅ ÍÁËÒÏÓ {\tt
tracingnone}\index{tracingnone?\texttt{tracingnone}}\label{Dtnone}, 
ÏÔËÌÀÞÁÀÝÉÊ ×ÓÅ ÒÁÓÐÅÞÁÔËÉ ÐÏ ÔÒÁÓÓÉÒÏ×ËÅ.
%%There is also a {\tt
%%tracingnone}\index{tracingnone?\texttt{tracingnone}}\label{Dtnone} macro
%%that turns off all the tracing output.

÷Ù×ÏÄ ÔÒÁÓÓÉÒÏ×ËÉ ËÏÎÔÒÏÌÉÒÕÅÔÓÑ ÍÎÏÖÅÓÔ×ÏÍ ×ÎÕÔÒÅÎÎÉÈ 
ÐÅÒÅÍÅÎÎÙÈ\index{×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ}, 
ÐÒÉ×ÏÄÉÍÙÈ ÄÁÌÅÅ.
%%Tracing output is controlled by the set of internal
%%variables\index{internal variables}\index{variables!internal} summarized
%%below. 
ëÏÇÄÁ ÌÀÂÏÊ ÉÚ ÜÔÉÈ ÐÅÒÅÍÅÎÎÙÈ ÚÁÄÁÀÔ ÐÏÌÏÖÉÔÅÌØÎÏÅ ÚÎÁÞÅÎÉÅ, ÔÏ ÜÔÉÍ 
ÕÓÔÁÎÁ×ÌÉ×ÁÅÔÓÑ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÁÑ ÆÏÒÍÁ ÔÒÁÓÓÉÒÏ×ËÉ. 
%%When any one of these variables is given a positive value, the
%%corresponding form of tracing is turned on. 
úÄÅÓØ ÐÒÉ×ÅÄÅÎÏ ÍÎÏÖÅÓÔ×Ï ÐÅÒÅÍÅÎÎÙÈ ÔÒÁÓÓÉÒÏ×ËÉ É ÔÏ, ÞÔÏ ÓÌÕÞÁÅÔÓÑ, ËÏÇÄÁ 
ËÁÖÄÁÑ ÉÚ ÎÉÈ ÓÔÁÎÏ×ÉÔÓÑ ÐÏÌÏÖÉÔÅÌØÎÏÊ.
%%Here is the set of tracing
%%variables and what happens when each of them is positive:
\begin{description}
\item[{\tt tracingcapsules}]\index{tracingcapsules?\texttt{tracingcapsules}}\label{Dtcapsules}%
ÐÏËÁÚÙ×ÁÅÔ ÚÎÁÞÅÎÉÑ ×ÒÅÍÅÎÎÙÈ ËÏÌÉÞÅÓÔ× (ËÁÐÓÕÌ), ËÏÇÄÁ ÏÎÉ ÓÔÁÎÏ×ÑÔÓÑ ÉÚ×ÅÓÔÎÙÍÉ.
%%\item[{\tt tracingcapsules}]\index{tracingcapsules?\texttt{tracingcapsules}}\label{Dtcapsules}%
%%shows the values of temporary quantities (capsules) when they become known.
%
\item[{\tt tracingchoices}]\index{tracingchoices?\texttt{tracingchoices}}\label{Dtchoices}%
ÐÏËÁÚÙ×ÁÅÔ ËÏÎÔÒÏÌØÎÙÅ ÔÏÞËÉ âÅÚØÅ\index{ÕÐÒÁ×ÌÑÀÝÉÅ ÔÏÞËÉ} ÎÁ ËÁÖÄÏÍ ÐÕÔÉ, ÇÄÅ ÏÎÉ 
×ÙÂÉÒÁÀÔÓÑ.  %
%%\item[{\tt tracingchoices}]\index{tracingchoices?\texttt{tracingchoices}}\label{Dtchoices}%
%%shows the B\'ezier control\index{control points} points of each new path
%%when they are chosen.  %
\item[{\tt tracingcommands}]\index{tracingcommands?\texttt{tracingcommands}}\label{Dtcommands}%
ÐÏËÁÚÙ×ÁÅÔ ËÏÍÁÎÄÙ ÐÅÒÅÄ ÉÈ ×ÙÐÏÌÎÅÎÉÅÍ.  õÓÔÁÎÏ×ËÁ × ${}>1$ ÔÁËÖÅ ÐÏËÁÖÅÔ ÐÒÏ×ÅÒËÉ 
{\tt if}\index{if?\texttt{if}} É ÃÉËÌÙ ÄÏ ÉÈ ÒÁÓËÒÙÔÉÑ;
ÕÓÔÁÎÏ×ËÁ × ${}>2$ ÐÏËÁÖÅÔ ÁÌÇÅÂÒÁÉÞÅÓËÉÅ ÏÐÅÒÁÃÉÉ ÄÏ ÉÈ ×ÙÐÏÌÎÅÎÉÑ.
%%\item[{\tt tracingcommands}]\index{tracingcommands?\texttt{tracingcommands}}\label{Dtcommands}%
%%shows the commands before they are performed.  A setting ${}>1$ also shows
%%{\tt if}\index{if?\texttt{if}} tests and loops before they are expanded;
%%a setting ${}>2$ shows algebraic operations before they are performed.
%
\item[{\tt tracingequations}]\index{tracingequations?\texttt{tracingequations}}\label{Dtequations}%
ÐÏËÁÚÙ×ÁÅÔ ËÁÖÄÕÀ ÐÅÒÅÍÅÎÎÕÀ, ËÏÇÄÁ ÏÎÁ ÓÔÁÎÏ×ÉÔÓÑ ÉÚ×ÅÓÔÎÏÊ.
%%\item[{\tt %%tracingequations}]\index{tracingequations?\texttt{tracingequations}}\label{Dtequations}%
%%shows each variable when it becomes known.
%
\item[{\tt tracinglostchars}]\index{tracinglostchars?\texttt{tracinglostchars}}\label{Dtlostchars}%
ÐÒÅÄÕÐÒÅÖÄÁÅÔ Ï ÓÉÍ×ÏÌÁÈ, ÏÔÓÕÔÓÔ×ÕÀÝÉÈ × ËÁÒÔÉÎËÅ, ÉÚ-ÚÁ ÉÈ ÏÔÓÕÔÓÔ×ÉÑ × ÛÒÉÆÔÅ, ÉÓÐÏÌØÚÕÅÍÏÍ 
ÄÌÑ ÐÅÞÁÔÉ ÍÅÔÏË.
%%\item[{\tt tracinglostchars}]\index{tracinglostchars?\texttt{tracinglostchars}}\label{Dtlostchars}%
%%warns about characters omitted from a picture because they are not in the font
%%being used to typeset labels.
%
\item[{\tt tracingmacros}]\index{tracingmacros?\texttt{tracingmacros}}\label{Dtmacros}%
ÐÅÞÁÔÁÅÔ ÍÁËÒÏÓÙ ÄÏ ÉÈ ÒÁÓËÒÙÔÉÑ.
%%\item[{\tt tracingmacros}]\index{tracingmacros?\texttt{tracingmacros}}\label{Dtmacros}%
%%shows macros before they are expanded.
%
\item[{\tt tracingoutput}]\index{tracingoutput?\texttt{tracingoutput}}\label{Dtoutput}%
ÐÅÞÁÔÁÅÔ ËÁÒÔÉÎËÉ ÐÒÉ ÉÈ ÏÔÐÒÁ×ËÅ × PostScript-ÆÁÊÌÙ.
%%\item[{\tt tracingoutput}]\index{tracingoutput?\texttt{tracingoutput}}\label{Dtoutput}%
%%shows pictures as they are being shipped out as PostScript files.
%
\item[{\tt tracingrestores}]\index{tracingrestores?\texttt{tracingrestores}}\label{Dtrestores}%
ÐÏËÁÚÙ×ÁÅÔ ÓÉÍ×ÏÌÙ É ×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ ÐÒÉ ÉÈ ×ÏÓÓÔÁÎÏ×ÌÅÎÉÉ × ËÏÎÃÅ ÇÒÕÐÐÙ. 
%%\item[{\tt tracingrestores}]\index{tracingrestores?\texttt{tracingrestores}}\label{Dtrestores}%
%%shows symbols and internal variables as they are being restored at the end
%%of a group.
%
\item[{\tt tracingspecs}]\index{tracingspecs?\texttt{tracingspecs}}\label{Dtspecs}%
ÐÏËÁÚÙ×ÁÅÔ ×ÙÄÅÌÅÎÉÑ, ÇÅÎÅÒÉÒÕÅÍÙÅ ÐÒÉ ÒÉÓÏ×ÁÎÉÉ ÍÎÏÇÏÕÇÏÌØÎÙÍ ÐÅÒÏÍ\index{ÐÅÒØÑ!ÍÎÏÇÏÕÇÏÌØÎÙÅ}.
%%\item[{\tt tracingspecs}]\index{tracingspecs?\texttt{tracingspecs}}\label{Dtspecs}%
%%shows the outlines generated when drawing with a
%%polygonal pen\index{pens!polygonal}.
%
\item[{\tt tracingstats}]\index{tracingstats?\texttt{tracingstats}}\label{Dtstats}
× ËÏÎÃÅ ÒÁÂÏÔÙ ÐÅÞÁÔÁÅÔ × ÆÁÊÌ-ÄÕÂÌÉËÁÔ Ï ÔÏÍ, ËÁË ÍÎÏÇÏ ÏÇÒÁÎÉÞÅÎÎÙÈ ÒÅÓÕÒÓÏ× 
ÉÎÔÅÒÐÒÅÔÁÔÏÒÁ MetaPost ÂÙÌÏ ÉÓÐÏÌØÚÏ×ÁÎÏ.
%%\item[{\tt tracingstats}]\index{tracingstats?\texttt{tracingstats}}\label{Dtstats}
%%shows in the transcript file at the end of the job how many of the
%%MetaPost interpreter's limited resources were used.
\end{description}

\section*{ðÒÉÚÎÁÔÅÌØÎÏÓÔØ}
%%\section*{Acknowledgement}

ñ ÒÁÄ ÐÏÂÌÁÇÏÄÁÒÉÔØ äÏÎÁÌØÄÁ ëÎÕÔÁ ÚÁ ×ÏÚÍÏÖÎÏÓÔØ ÐÒÏÄÅÌÁÔØ ÜÔÕ ÒÁÂÏÔÕ --- 
ÚÁ ÒÁÚ×ÉÔÉÅ \MF\ É ÐÏÍÅÝÅÎÉÑ ÅÇÏ × ÏÔËÒÙÔÙÊ ÄÏÓÔÕÐ. 
%%I would like to thank Don Knuth for making this work possible by
%%developing \MF\ and placing it in the public domain. 
ñ ÔÁËÖÅ × ÄÏÌÇÕ ÐÅÒÅÄ ÎÉÍ ÚÁ ÐÏÌÅÚÎÙÅ ÐÒÅÄÌÏÖÅÎÉÑ, ÏÓÏÂÅÎÎÏ × 
Ó×ÑÚÉ Ó ÏÂÒÁÂÏÔËÏÊ ×ËÌÀÞÁÅÍÏÇÏ ÍÁÔÅÒÉÁÌÁ \TeX.
%%I am also indebted
%%to him for helpful suggestions, particularly with regard to the
%%treatment of included \TeX\ material.


\appendix
\section{óÐÒÁ×ÏÞÎÏÅ ÒÕËÏ×ÏÄÓÔ×Ï}
%%\section{Reference Manual}

\let\svtopfrac=\topfraction     % prepare to restore values at end of this appendix
\let\svtxtfrac=\textfraction    % grouping would fail because \setcounter is global
\newcounter{svtopnum}
\newcounter{svtotnum}
\setcounter{svtopnum}{\value{topnumber}}
\setcounter{svtotnum}{\value{totalnumber}}

\renewcommand\topfraction{1.0}  % set values to allow *lots* of figures and tables
\renewcommand\textfraction{0.0}
\setcounter{topnumber}{10}
\setcounter{totalnumber}{10}

ôÁÂÌÉÃÙ \ref{ivartab}--\ref{pseudotab} ÓÕÍÍÉÒÕÀÔ ×ÓÔÒÏÅÎÎÙÅ ×ÏÚÍÏÖÎÏÓÔÉ 
Plain MetaPost É ×ÏÚÍÏÖÎÏÓÔÉ, ÏÐÒÅÄÅÌÅÎÎÙÅ × ÆÁÊÌÅ Ó ÍÁËÒÏÓÁÍÉ {\tt
boxes.mp}\index{boxes.mp?\texttt{boxes.mp}}.
%%Tables \ref{ivartab}--\ref{pseudotab} summarize the built-in features of
%%Plain MetaPost and the features defined in the {\tt
%%boxes.mp}\index{boxes.mp?\texttt{boxes.mp}} macro file. 
ëÁË ÏÂßÑÓÎÑÌÏÓØ × ÒÁÚÄÅÌÅ ~\ref{boxessec}, ÆÁÊÌ Ó ÍÁËÒÏÓÁÍÉ {\tt boxes.mp} 
ÎÅ ×ËÌÀÞÁÅÔÓÑ Á×ÔÏÍÁÔÉÞÅÓËÉ É ÍÁËÒÏÓÙ ÉÚ ÎÅÇÏ ÎÅÄÏÓÔÕÐÎÙ ÄÏ ÔÅÈ ÐÏÒ, ÐÏËÁ 
×Ù ÎÅ ÚÁÐÒÏÓÉÔÅ ÉÈ ËÏÍÁÎÄÏÊ\index{input?\texttt{input}}
$$ \hbox{\tt input boxes} $$
%%As explained in
%%Section~\ref{boxessec}, the {\tt boxes.mp} macro file is not
%%automatically preloaded and the macros defined there are not accessible
%%until you ask for them via the command\index{input?\texttt{input}}
%%$$ \hbox{\tt input boxes} $$

÷ÏÚÍÏÖÎÏÓÔÉ, ÚÁ×ÉÓÑÝÉÅ ÏÔ {\tt boxes.mp} ÏÔÍÅÞÅÎÙ ÓÉÍ×ÏÌÁÍÉ \bx.
%%Features that depend on {\tt boxes.mp} are marked by \bx\ symbols.
÷ÏÚÍÏÖÎÏÓÔÉ ÉÚ ÍÁËÒÏÐÁËÅÔÁ Plain\index{ÍÁËÒÏÓÙ Plain} ÏÔÍÅÞÅÎÙ ÓÉÍ×ÏÌÁÍÉ 
\pl, Á ÐÒÉÍÉÔÉ×Ù MetaPost ÐÒÉ×ÏÄÑÔÓÑ ÂÅÚ \bx\ ÉÌÉ \pl.
%%Features from the Plain\index{Plain macros} macro package are marked by
%%\pl\ symbols, and MetaPost primitives are not marked by \bx\ or \pl.
òÁÚÎÉÃÁ ÍÅÖÄÕ ÐÒÉÍÉÔÉ×ÁÍÉ É ÍÁËÒÏÓÁÍÉ ÉÚ plain ÍÏÖÅÔ ÉÇÎÏÒÉÒÏ×ÁÔØÓÑ 
ÓÌÕÞÁÊÎÙÍ ÐÏÌØÚÏ×ÁÔÅÌÅÍ, ÎÏ ×ÁÖÎÏ ÐÏÍÎÉÔØ, ÞÔÏ ×ÏÚÍÏÖÎÏÓÔÉ Ó ÍÅÔËÏÊ \bx\ 
ÍÏÇÕÔ ÂÙÔØ ÉÓÐÏÌØÚÏ×ÁÎÙ ÔÏÌØËÏ ÐÏÓÌÅ ÞÔÅÎÉÑ ÆÁÊÌÁ {\tt 
boxes.mp}\index{boxes.mp?\texttt{boxes.mp}} Ó ÍÁËÒÏÓÁÍÉ.
%%The distinction between primitives and plain macros can be ignored by
%%the casual user, but it is important to remember that features marked by
%%a \bx\ can only be used after reading in the {\tt
%%boxes.mp}\index{boxes.mp?\texttt{boxes.mp}} macro file.

ôÁÂÌÉÃÙ × ÜÔÏÍ ÐÒÉÌÏÖÅÎÉÉ ÐÒÉ×ÏÄÑÔ ÉÍÑ ËÁÖÄÏÊ ×ÏÚÍÏÖÎÏÓÔÉ, ÎÏÍÅÒ ÓÔÒÁÎÉÃÙ, 
ÇÄÅ ÏÎÁ ÏÂßÑÓÎÑÅÔÓÑ, É ËÒÁÔËÏÅ ÏÐÉÓÁÎÉÅ.
%%The tables in this appendix give the name of each feature, the page
%%number where it is explained, and a short description. 
îÅÂÏÌØÛÏÅ ÞÉÓÌÏ Ó×ÏÊÓÔ× ÎÉÇÄÅ ÎÅ ÏÂßÑÓÎÑÌÏÓØ É ÏÎÉ ÎÅ ÉÍÅÀÔ ÎÏÍÅÒÏ× ÓÔÒÁÎÉÃ.
%%A few features
%%are not explained elsewhere and have no page number listed. 
üÔÉ ×ÏÚÍÏÖÎÏÓÔÉ ÓÕÝÅÓÔ×ÕÀÔ, × ÏÓÎÏ×ÎÏÍ, ÄÌÑ ÓÏ×ÍÅÓÔÉÍÏÓÔÉ Ó 
\MF\index{metafont?\MF} É ÐÒÅÄÐÏÌÁÇÁÀÔÓÑ ÓÁÍÏÏÂßÑÓÎÑÀÝÉÍÉ.
%%These
%%features exist primarily for compatibility with \MF\index{metafont?\MF}
%%and are intended to be self-explanatory. 
îÅËÏÔÏÒÙÅ ÏÐÒÅÄÅÌÅÎÎÙÅ ×ÏÚÍÏÖÎÏÓÔÉ \MF\ ÐÏÌÎÏÓÔØÀ ÏÔÓÕÔÓÔ×ÕÀÔ ÉÚ-ÚÁ 
ÏÇÒÁÎÉÞÅÎÎÏÇÏ ÉÎÔÅÒÅÓÁ Ë ÎÉÍ ÐÏÌØÚÏ×ÁÔÅÌÅÊ MetaPost É/ÉÌÉ ÉÚ-ÚÁ ÔÒÅÂÕÅÍÙÈ 
ÄÌÉÎÎÙÈ ÏÂßÑÓÎÅÎÉÊ.
%%Certain other features from
%%\MF\ are omitted entirely because they are of limited interest to the
%%MetaPost users and/or would require long explanations. 
÷ÓÅ ÏÎÉ ÄÏËÕÍÅÎÔÉÒÏ×ÁÎÙ × {\sl The \MF book} \cite{kn:c} ËÁË ÏÂßÑÓÎÅÎÏ × 
ÐÒÉÌÏÖÅÎÉÉ~\ref{MPvsMF}.
%%All of these are
%%documented in {\sl The \MF book} \cite{kn:c} as explained in
%%Appendix~\ref{MPvsMF}.

ôÁÂÌÉÃÁ~\ref{ivartab} ÐÅÒÅÞÉÓÌÑÅÔ ×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ Ó ÞÉÓÌÏ×ÙÍÉ ÚÎÁÞÅÎÉÑÍÉ.
%%Table~\ref{ivartab} lists internal variables that take on numeric values.
ôÁÂÌÉÃÁ~\ref{pvartab} ÐÅÒÅÞÉÓÌÑÅÔ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÅ ÐÅÒÅÍÅÎÎÙÅ ÄÒÕÇÉÈ ÔÉÐÏ×.
%%Table~\ref{pvartab} lists predefined variables of other types.
ôÁÂÌÉÃÁ~\ref{consttab} ÐÅÒÅÞÉÓÌÑÅÔ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÅ ËÏÎÓÔÁÎÔÙ.
%%Table~\ref{consttab} lists predefined constants. 
îÅËÏÔÏÒÙÅ ÉÚ ÎÉÈ ÒÅÁÌÉÚÏ×ÁÎÙ ËÁË ÐÅÒÅÍÅÎÎÙÅ, ÞØÉ ÚÎÁÞÅÎÉÑ ÐÒÅÄÐÏÌÁÇÁÅÔÓÑ ÎÅ 
ÍÅÎÑÔØ.
%%Some of these are implemented
%%as variables whose values are intended to be left unchanged.

ôÁÂÌÉÃÁ~\ref{optab} ÐÒÉ×ÏÄÉÔ ÏÐÅÒÁÔÏÒÙ MetaPost É ÐÅÒÅÞÉÓÌÑÅÔ 
×ÏÚÍÏÖÎÙÅ ÔÉÐÙ ÄÌÑ ÁÒÇÕÍÅÎÔÏ× É ÒÅÚÕÌØÔÁÔÁ ËÁÖÄÏÇÏ ÉÚ ÎÉÈ.
%%Table~\ref{optab} summarizes MetaPost operators and lists
%%the possible argument and result types for each one. 
ðÕÎËÔ ``--'' ÄÌÑ ÌÅ×ÏÇÏ ÁÒÇÕÍÅÎÔÁ ÚÁÄÁÅÔ ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ, Á ``--'' ÄÌÑ 
ÏÂÏÉÈ ÚÁÄÁÅÔ ÏÐÅÒÁÔÏÒ ÂÅÚ ÁÒÇÕÍÅÎÔÏ×.
%%A ``--'' entry for
%%the left argument indicates a unary operator; ``--'' entries for both
%%arguments indicate a nullary operator. 
ïÐÅÒÁÔÏÒÙ Ó ÐÁÒÁÍÅÔÒÁÍÉ-ÓÕÆÆÉËÓÁÍÉ ÎÅ ÐÒÉ×ÏÄÑÔÓÑ × ÜÔÏÊ ÔÁÂÌÉÃÅ, ÐÏÔÏÍÕ ÞÔÏ ÏÎÉ 
ÏÂÒÁÂÁÔÙ×ÁÀÔÓÑ ËÁË ``ÐÏÈÏÖÉÅ ÎÁ ÆÕÎËÃÉÉ ÍÁËÒÏÓÙ''.
%%Operators that take suffix
%%parameters are not listed in this table because they are treated as
%%``function-like macros''.

ä×Å ÐÏÓÌÅÄÎÉÅ ÔÁÂÌÉÃÙ --- ÜÔÏ ÔÁÂÌÉÃÁ~\ref{cmdtab} ÄÌÑ ËÏÍÁÎÄ É 
ÔÁÂÌÉÃÁ~\ref{pseudotab} ÄÌÑ ÍÁËÒÏÓÏ×, ×ÅÄÕÝÉÈ ÓÅÂÑ ËÁË ÆÕÎËÃÉÉ ÉÌÉ 
ÐÒÏÃÅÄÕÒÙ.
%%The last two tables are Table~\ref{cmdtab} for commands and
%%Table~\ref{pseudotab} macros that behave like functions or procedures.
ôÁËÉÅ ÍÁËÒÏÓÙ ÂÅÒÕÔ ÓÐÉÓËÉ ÁÒÇÕÍÅÎÔÏ× × ÓËÏÂËÁÈ É/ÉÌÉ ÐÁÒÁÍÅÔÒÙ-ÓÕÆÆÉËÓÙ É 
×ÏÚ×ÒÁÝÁÀÔ ÌÉÂÏ ÚÎÁÞÅÎÉÅ ÐÒÉ×ÅÄÅÎÎÏÇÏ × ÔÁÂÌÉÃÅ ÔÉÐÁ, ÌÉÂÏ ÎÉÞÅÇÏ.
%%Such macros take parenthesized argument lists and/or suffix parameters,
%%returning either a value whose type is listed in the table, or nothing.
ðÏÓÌÅÄÎÉÊ ÓÌÕÞÁÊ ÄÌÑ ÍÁËÒÏÓÏ×, ×ÅÄÕÝÉÈ ÓÅÂÑ ËÁË ÐÒÏÃÅÄÕÒÙ.  
%%The latter case is for macros that behave like procedures. 
éÈ ×ÏÚ×ÒÁÝÁÅÍÙÅ ÚÎÁÞÅÎÉÑ ÐÒÉ×ÏÄÉÔÓÑ ËÁË ``--''.
%%Their return values are listed as ``--''.

ëÁÒÔÉÎËÉ × ÜÔÏÍ ÐÒÉÌÏÖÅÎÉÉ ÐÒÅÄÓÔÁ×ÌÑÀÔ ÓÉÎÔÁËÓÉÓ ÑÚÙËÁ MetaPost, ÎÁÞÉÎÁÑ 
Ó ×ÙÒÁÖÅÎÉÊ ÎÁ ÒÉÓÕÎËÁÈ \ref{syexpr1}--\ref{sypseudo}.
%%The figures in this appendix present the syntax of the MetaPost language
%%starting with expressions in Figures \ref{syexpr1}--\ref{sypseudo}.
èÏÔÑ ÐÒÁ×ÉÌÁ ÉÎÏÇÄÁ ÕËÁÚÙ×ÁÀÔ ÔÉÐÙ ÄÌÑ ×ÙÒÁÖÅÎÉÊ, ÐÅÒ×ÉÞÎÏÓÔÅÊ, ×ÔÏÒÉÞÎÏÓÔÅÊ É 
ÔÒÅÔÉÞÎÏÓÔÅÊ, ÎÏ ÏÔÄÅÌØÎÙÊ ÓÉÎÔÁËÓÉÓ ÄÌÑ \tdescr{ÞÉÓÌÏ×ÏÇÏ ×ÙÒÁÖÅÎÉÑ}, 
\tdescr{×ÙÒÁÖÅÎÉÑ-ÐÁÒÙ} É Ô.~Ð. ÎÅ ÐÒÉ×ÏÄÉÔÓÑ. 
%%Although the productions sometimes specify types for expressions, primaries,
%%secondaries, and tertiaries, no attempt is made to give separate syntaxes
%%for \tdescr{numeric expression}, \tdescr{pair expression}, etc.
ó×ÏÅÊ ÐÒÏÓÔÏÔÅ ÐÒÁ×ÉÌÁ ÎÁ ÒÉÓ.~\ref{sytypexpr} ÏÂÑÚÁÎÙ ÜÔÉÍ ÏÔÓÕÔÓÔ×ÉÅÍ 
ÉÎÆÏÒÍÁÃÉÉ Ï ÔÉÐÁÈ. 
%%The simplicity of the productions in Figure~\ref{sytypexpr} is due to this
%%lack of type information. 
éÎÆÏÒÍÁÃÉÑ Ï ÔÉÐÁÈ ÍÏÖÅÔ ÂÙÔØ ÎÁÊÄÅÎÁ × ÔÁÂÌÉÃÁÈ \ref{ivartab}--\ref{pseudotab}.
%%Type information can be found in Tables \ref{ivartab}--\ref{pseudotab}.

òÉÓÕÎËÉ \ref{syprog} É \ref{sycmds} ÓÏÄÅÒÖÁÔ ÓÉÎÔÁËÓÉÓ ÐÒÏÇÒÁÍÍ MetaPost, 
×ËÌÀÞÁÑ ËÏÍÁÎÄÙ É ÉÈ ÏÂÏÂÝÅÎÉÑ.
%%Figures \ref{syprog} and \ref{sycmds} give the syntax for MetaPost programs,
%%including statements and commands. 
ïÎÉ ÎÅ ÕÐÏÍÉÎÁÀÔ ÃÉËÌÏ×\index{ÃÉËÌÙ} É ÐÒÏ×ÅÒÏË {\tt if}\index{if?\texttt{if}}, 
ÐÏÔÏÍÕ ÞÔÏ ÜÔÉ ËÏÎÓÔÒÕËÃÉÉ ÎÅ ×ÅÄÕÔ ÓÅÂÑ ËÁË ËÏÍÁÎÄÙ. 
%%They do not mention loops\index{loops}
%%and {\tt if}\index{if?\texttt{if}}
%%tests because these constructions do not behave like statements. 
óÉÎÔÁËÓÉÓ ÎÁ ÒÉÓÕÎËÁÈ \ref{syexpr1}--\ref{sycondloop} ÐÒÉÍÅÎÉÍ Ë ÒÅÚÕÌØÔÁÔÁÍ 
ÒÁÓËÒÙÔÉÑ ×ÓÅÈ ÕÓÌÏ×ÎÙÈ ËÏÎÓÔÒÕËÃÉÊ É ÃÉËÌÏ×. 
%%The syntax
%%given in Figures \ref{syexpr1}--\ref{sycondloop} applies to the result of
%%expanding all conditionals and loops. 
õÓÌÏ×ÎÙÅ ËÏÎÓÔÒÕËÃÉÉ É ÃÉËÌÙ ÉÍÅÀÔ ÓÉÎÔÁËÓÉÓ, ÎÏ ÏÎÉ ÒÁÂÏÔÁÀÔ ÐÒÁËÔÉÞÅÓËÉ 
Ó ÐÒÏÉÚ×ÏÌØÎÙÍÉ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔÑÍÉ ÚÎÁËÏ×. 
%%Conditionals and loops do have a
%%syntax, but they deal with almost arbitrary sequences of tokens.
òÉÓ.~\ref{sycondloop} ÏÐÒÅÄÅÌÑÅÔ ÕÓÌÏ×ÎÙÅ ËÏÎÓÔÒÕËÃÉÉ ÞÅÒÅÚ 
\tdescr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ}, Á ÃÉËÌÙ ÞÅÒÅÚ \tdescr{ÔÅÌÏ ÃÉËÌÁ}, ÇÄÅ 
\tdescr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ} --- ÜÔÏ ÌÀÂÁÑ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÚÎÁËÏ×, 
ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÁÑ ÏÔÎÏÓÉÔÅÌØÎÏ {\tt if} É {\tt fi}, Á \tdescr{ÔÅÌÏ ÃÉËÌÁ} --- 
ÜÔÏ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ÚÎÁËÏ×, ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÁÑ ÏÔÎÏÓÉÔÅÌØÎÏ {\tt for}, 
{\tt forsuffixes}, {\tt forever} É {\tt endfor}.
%%Figure~\ref{sycondloop} specifies conditionals in terms of
%%\tdescr{balanced tokens} and loops in terms of \tdescr{loop text}, where
%%\tdescr{balanced tokens} is any sequence of tokens balanced with respect
%%to {\tt if} and {\tt fi}, and \tdescr{loop text} is a sequence of tokens
%%balanced with respect to {\tt for}, {\tt forsuffixes}, {\tt forever},
%%and {\tt endfor}.

\begin{table}[htp]
\caption{÷ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ Ó ÞÉÓÌÏ×ÙÍÉ ÚÎÁÞÅÎÉÑÍÉ}
%%\caption{Internal variables with numeric values}
$$\begin{tabular}{|l|r|l|}
\hline
\multicolumn1{|c}{éÍÑ}&  \multicolumn1{|c}{óÔÒ.}&  \multicolumn1{|c|}{ïÐÉÓÁÎÉÅ}\\
%%\multicolumn1{|c}{Name}&  \multicolumn1{|c}{Page}&  \multicolumn1{|c|}{Explanation}\\
\hline
\hline
\pl\tt  ahangle&        \pageref{Dahangle}&
        ÕÇÏÌ ÄÌÑ ÎÁËÏÎÅÞÎÉËÁ ÓÔÒÅÌËÉ × ÇÒÁÄÕÓÁÈ (ÓÔÁÎÄÁÒÔÎÏ 45)\\\hline
%%       angle for arrowheads in degrees (default: 45)\\\hline
\pl\tt  ahlength&       \pageref{Dahlength}&
        ÒÁÚÍÅÒ ÎÁËÏÎÅÞÎÉËÁ ÓÔÒÅÌËÉ (ÓÔÄ. 4{\tt bp})\\\hline
%%        size of arrowheads (default: 4{\tt bp})\\\hline
\pl\tt  bboxmargin&     \pageref{Dbbmargin}&
        ÏÓÏÂÙÊ ÐÒÏÍÅÖÕÔÏË, ÄÏÐÕÓËÁÅÍÙÊ {\tt bbox} (ÓÔÄ. 2{\tt bp})\\\hline
%%        extra space allowed by {\tt bbox} (default 2{\tt bp})\\\hline
\tt     charcode&       \pageref{Dcharcode}&
        ÎÏÍÅÒ ÔÅËÕÝÅÊ ËÁÒÔÉÎËÉ\\\hline
%%        the number of the current figure\\\hline
\bx\tt  circmargin&     \pageref{Dcmargin}&
        ÐÕÓÔÏÔÁ ×ÏËÒÕÇ ÓÏÄÅÒÖÉÍÏÇÏ ËÒÕÇÏ×ÏÊ ÉÌÉ Ï×ÁÌØÎÏÊ ÒÁÍËÉ\\\hline
%%        clearance around contents of a circular or oval box\\\hline
\tt     day&    --&
        ÔÅËÕÝÉÊ ÄÅÎØ ÍÅÓÑÃÁ\\\hline
%%        the current day of the month\\\hline
\tt     defaultcolormodel&    --&
        ÎÁÞÁÌØÎÁÑ Ã×ÅÔÏ×ÁÑ ÍÏÄÅÌØ  (ÓÔÄ. 5, rgb)\\\hline
%%        the initial color model  (default: 5, rgb)\\\hline
\bx\tt  defaultdx&      \pageref{Ddefaultdx}&
        ÏÂÙÞÎÙÊ ÇÏÒÉÚ. ÏÔÓÔÕÐ ×ÏËÒÕÇ ÓÏÄÅÒÖÉÍÏÇÏ ÒÁÍËÉ (ÓÔÄ. 3{\tt bp})\\\hline
%%        usual horizontal space around box contents (default 3{\tt bp})\\\hline
\bx\tt  defaultdy&      \pageref{Ddefaultdy}&
        ÏÂÙÞÎÙÊ ×ÅÒÔ. ÏÔÓÔÕÐ ×ÏËÒÕÇ ÓÏÄÅÒÖÉÍÏÇÏ ÒÁÍËÉ (ÓÔÄ. 3{\tt bp})\\\hline
%%        usual vertical space around box contents (default 3{\tt bp})\\\hline
\pl\tt  defaultpen&     \pageref{Ddefaultpen}&
        ÞÉÓÌÏ, ÉÓÐÏÌØÚÕÅÍÏÅ {\tt pickup} ÄÌÑ ×ÙÂÏÒÁ ÓÔÄ. ÐÅÒÁ\\\hline
%%        numeric index used by {\tt pickup} to select default pen\\\hline
\pl\tt  defaultscale&   \pageref{Ddfscale}&
        ÍÁÓÛÔÁÂÉÒÕÀÝÉÊ ÍÎÏÖÉÔÅÌØ ÛÒÉÆÔÁ ÄÌÑ ÓÔÒÏË-ÍÅÔÏË (ÓÔÄ. 1)\\\hline
%%        font scale factor for label strings (default 1)\\\hline
\pl\tt  labeloffset&    \pageref{Dlaboff}&
        ÒÁÓÓÔÏÑÎÉÅ ÏÔÓÔÕÐÁ ÄÌÑ ÍÅÔÏË (ÓÔÄ. 3{\tt bp})\\\hline
%%        offset distance for labels (default 3{\tt bp})\\\hline
\tt     linecap&        \pageref{Dlinecap}&
        0 ÄÌÑ butt, 1 ÄÌÑ round, 2 ÄÌÑ square\\\hline
%%        0 for butt, 1 for round, 2 for square\\\hline
\tt     linejoin&       \pageref{Dlinejoin}&
        0 ÄÌÑ mitered, 1 ÄÌÑ round, 2 ÄÌÑ beveled\\\hline
%%        0 for mitered, 1 for round, 2 for beveled\\\hline
\tt     miterlimit&     \pageref{Dmiterlim}&
        ËÏÎÔÒÏÌÉÒÕÅÔ ÄÌÉÎÕ ÏÓÔÒÉÑ ËÁË × PostScript\\\hline
%%        controls miter length as in PostScript\\\hline
\tt     month&  --&
        ÔÅËÕÝÉÊ ÍÅÓÑà (ÎÁÐÒÉÍÅÒ, 3 $\equiv$ íÁÒÔ)\\\hline
%%        the current month (e.g, 3 $\equiv$ March)\\\hline
\tt     mpprocset&  --&
        \vtop{\hbox{ÕÓÔÁÎÏ×ÉÔÅ ×~1, ÅÓÌÉ ÈÏÔÉÔÅ ×ËÌÀÞÉÔØ ÓÌÏ×ÁÒØ 
ÓÏËÒÁÝÅÎÉÊ}\hbox{PostScript × ×Ù×ÏÄ}}\\\hline
%%        \vtop{\hbox{set this to~1 if you want to include a PostScript
%%dictionary}\hbox{of      abbreviations in the output}}\\\hline
\tt     pausing&        --&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÓÔÒÏËÉ ÎÁ ÔÅÒÍÉÎÁÌÅ ÄÏ ÉÈ ÞÔÅÎÉÑ\\\hline
%%        ${}>0$ to display lines on the terminal before they are read\\\hline
\tt     prologues&      \pageref{Dprologues}&
        ${}>0$ --- ×Ù×ÏÄÉÔØ PostScript Ó ×ÓÔÒÏÅÎÎÙÍÉ ÛÒÉÆÔÁÍÉ\\\hline
%%        ${}>0$ to output conforming PostScript using built-in fonts\\\hline
\tt     restoreclipcolor&    --&
        ×ÏÓÓÔÁÎÏ×ÌÅÎÉÅ ÓÏÓÔÏÑÎÉÑ ÇÒÁÆÉËÉ ÐÏÓÌÅ ×ÙÒÅÚËÉ (ÓÔÄ. 1)\\\hline
%%        restore the graphics state after clip operations (default: 1)\\\hline
\tt     showstopping&   --&
        ${}>0$ --- ÏÓÔÁÎÁ×ÌÉ×ÁÔØ ÐÏÓÌÅ ËÁÖÄÏÊ ËÏÍÁÎÄÙ {\tt show}\\\hline
%%        ${}>0$ to stop after each {\tt show} command\\\hline
\tt     time&   --&
        ÞÉÓÌÏ ÍÉÎÕÔ ÐÏÓÌÅ ÐÏÌÕÎÏÞÉ × ÎÁÞÁÌÅ ÜÔÏÊ ÒÁÂÏÔÙ\\\hline
%%        the number of minutes past midnight when this job started\\\hline
\tt     tracingcapsules&        \pageref{Dtcapsules}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ É ËÁÐÓÕÌÙ\\\hline
%%        ${}>0$ to show capsules too\\\hline
\tt     tracingchoices& \pageref{Dtchoices}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ËÏÎÔÒÏÌØÎÙÅ ÔÏÞËÉ ÄÌÑ ÐÕÔÅÊ\\\hline
%%        ${}>0$ to show the control points chosen for paths\\\hline
\tt     tracingcommands&        \pageref{Dtcommands}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ËÏÍÁÎÄÙ ÐÒÉ ÉÈ ×ÙÐÏÌÎÅÎÉÉ\\\hline
%%        ${}>0$ to show commands and operations as they are performed\\\hline
\tt     tracingequations&       \pageref{Dtequations}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ËÁÖÄÕÀ ÓÔÁ×ÛÕÀ ÉÚ×ÅÓÔÎÏÊ ÐÅÒÅÍÅÎÎÕÀ\\\hline
%%        ${}>0$ to show each variable when it becomes known\\\hline
\tt     tracinglostchars&       \pageref{Dtlostchars}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÓÉÍ×ÏÌÙ ÎÅ ÉÚ {\tt infont}\\\hline
%%        ${}>0$ to show characters that aren't {\tt infont}\\\hline
\tt     tracingmacros&  \pageref{Dtmacros}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÍÁËÒÏÓÙ ÄÏ ÉÈ ÒÁÓËÒÙÔÉÑ\\\hline
%%        ${}>0$ to show macros before they are expanded\\\hline
\tt     tracingonline&  \pageref{Dtonline}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÄÌÉÎÎÙÅ ÄÉÁÇÎÏÓÔÉËÉ ÎÁ ÔÅÒÍÉÎÁÌÅ\\\hline
%%        ${}>0$ to show long diagnostics on the terminal\\\hline
\tt     tracingoutput&  \pageref{Dtoutput}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÃÉÆÒÏ×ÙÅ ËÒÁÑ ÐÒÉ ×Ù×ÏÄÅ\\\hline
%%        ${}>0$ to show digitized edges as they are output\\\hline
\tt     tracingrestores&        \pageref{Dtrestores}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÐÅÒÅÍÅÎÎÙÅ ÐÒÉ ÉÈ ×ÏÓÓÔÁÎÏ×ÌÅÎÉÉ\\\hline
%%        ${}>0$ to show when a variable or internal is restored\\\hline
\tt     tracingspecs&   \pageref{Dtspecs}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÄÅÌÅÎÉÑ ÐÕÔÉ (ÉÓÐ-ÓÑ ÍÎÏÇÏÕÇÏÌØÎÏÅ ÐÅÒÏ)\\\hline
%%        ${}>0$ to show path subdivision when using a polygonal a pen\\\hline
\tt     tracingstats&   \pageref{Dtstats}&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÉÓÐÏÌØÚÏ×ÁÎÉÅ ÐÁÍÑÔÉ × ËÏÎÃÅ ÒÁÂÏÔÙ\\\hline
%%        ${}>0$ to show memory usage at end of job\\\hline
\tt     tracingtitles&  --&
        ${}>0$ --- ÐÏËÁÚÙ×ÁÔØ ÚÁÇÏÌÏ×ËÉ ÐÒÉ ÉÈ ÐÏÑ×ÌÅÎÉÉ\\\hline
%%        ${}>0$ to show titles online when they appear\\\hline
\tt     troffmode&    \pageref{Dtroffmode}&
        ÂÕÄÅÔ~1, ÅÓÌÉ ÅÓÔØ ÏÐÃÉÑ {\tt -troff} ÉÌÉ {\tt -T}\\\hline
%%        set to~1 if a {\tt -troff} or {\tt -T} option was given\\\hline
\tt     truecorners&    \pageref{Dtruecorn}&
        ${}>0$ --- ÄÅÌÁÔØ {\tt llcorner} É Ô.~Ä., ÉÇÎÏÒÉÒÏ×ÁÔØ {\tt setbounds}\\\hline
%%        ${}>0$ to make {\tt llcorner} etc. ignore {\tt setbounds}\\\hline
\tt     warningcheck&   \pageref{Dwarncheck}&
        ÓÏÏÂÝÅÎÉÅ ÏÂ ÏÛÉÂËÅ ÐÒÉ ÂÏÌØÛÏÍ ÚÎÁÞÅÎÉÉ ÐÅÒÅÍÅÎÎÏÊ\\\hline
%%        controls error message when variable value is large\\\hline
\tt     year&   --&
        ÔÅËÕÝÉÊ ÇÏÄ (ÎÁÐÒÉÍÅÒ, 1992)\\\hline
%%        the current year (e.g., 1992)\\\hline
\end{tabular}
$$
\label{ivartab}%
\index{day?\texttt{day}}\index{month?\texttt{month}}\index{pausing?\texttt{pausing}}\index{showstopping?\texttt{showstopping}}%
\index{time?\texttt{time}}\index{tracingtitles?\texttt{tracingtitles}}\index{year?\texttt{year}}
\end{table}


\begin{table}[htp]
\caption{äÒÕÇÉÅ ÐÒÅÄÏÐÒÅÄÅÌÅÎÎÙÅ ÐÅÒÅÍÅÎÎÙÅ}
%%\caption{Other Predefined Variables}
$$\begin{tabular}{|l|l|r|l|}
\hline
\multicolumn1{|c}{éÍÑ}&  \multicolumn1{|c}{ôÉÐ}&  \multicolumn1{|c}{óÔÒ.}&
        \multicolumn1{|c|}{ïÂßÑÓÎÅÎÉÅ}\\
%%\multicolumn1{|c}{Name}&  \multicolumn1{|c}{Type}&  \multicolumn1{|c}{Page}&
%%        \multicolumn1{|c|}{Explanation}\\
\hline
\hline
\pl\tt  background&     color&  \pageref{Dbground}&
        ã×ÅÔ ÄÌÑ {\tt unfill} É {\tt undraw} (ÏÂÙÞÎÏ ÂÅÌÙÊ)\\\hline
%%        Color for {\tt unfill} and {\tt undraw} (usually white)\\\hline
\pl\tt  currentpen&     pen&    \pageref{Dcurpen}&
        ôÅËÕÝÅÅ ÐÅÒÏ (ÄÌÑ ËÏÍÁÎÄÙ {\tt draw})\\\hline
%%        Last pen picked up (for use by the {\tt draw} command)\\\hline
\pl\tt  currentpicture& picture&        \pageref{Dcurpic}&
        òÅÚÕÌØÔÁÔ ËÏÍÁÎÄ {\tt draw} É {\tt fill}\\\hline
%%        Accumulate results of {\tt draw} and {\tt fill} commands\\\hline
\pl\tt  cuttings&       path&   \pageref{Dcuttings}&
        ðÏÄÐÕÔØ, ÏÔÒÅÚÁÎÎÙÊ ÐÏÓÌÅÄÎÅÊ {\tt cutbefore} ÉÌÉ {\tt cutafter}\\\hline
%%        subpath cut off by last {\tt cutbefore} or {\tt cutafter}\\\hline
\pl\tt  defaultfont&    string& \pageref{Ddffont}&
        ûÒÉÆÔ ÄÌÑ ËÏÍÁÎÄ ÐÅÞÁÔÉ ÓÔÒÏË\\\hline
%%        Font used by label commands for typesetting strings\\\hline
\pl\tt  extra\_beginfig&        string& \pageref{Dxbfig}&
        äÏÐÏÌÎÉÔÅÌØÎÙÅ ËÏÍÁÎÄÙ ÄÌÑ {\tt beginfig}\\\hline
%%        Commands for {\tt beginfig} to scan\\\hline
\pl\tt  extra\_endfig&  string& \pageref{Dxefig}&
        äÏÐÏÌÎÉÔÅÌØÎÙÅ ËÏÍÁÎÄÙ ÄÌÑ {\tt endfig}\\\hline
%%        Commands for {\tt endfig} to scan\\\hline
\end{tabular}
$$
\label{pvartab}
\end{table}


\begin{table}[htp]
\caption{ðÒÅÄÏÐÒÅÄÅÌÅÎÎÙÅ ËÏÎÓÔÁÎÔÙ}
%%\caption{Predefined Constants}
$$\begin{tabular}{|l|l|r|l|}
\hline
\multicolumn1{|c}{éÍÑ}&  \multicolumn1{|c}{ôÉÐ}&  \multicolumn1{|c}{óÔÒ.}&
        \multicolumn1{|c|}{ïÂßÑÓÎÅÎÉÅ}\\
%%\multicolumn1{|c}{Name}&  \multicolumn1{|c}{Type}&  \multicolumn1{|c}{Page}&
%%        \multicolumn1{|c|}{Explanation}\\
\hline
\hline
\pl\tt  beveled&        numeric&        \pageref{Dbvled}&
        úÎÁÞÅÎÉÅ {\tt linejoin} ÄÌÑ ÓÒÅÚÁÎÎÙÈ ÓÏÅÄÉÎÅÎÉÊ [2]\\\hline
%%\pl\tt  beveled&        numeric&        \pageref{Dbvled}&
%%        {\tt linejoin} value for beveled joins [2]\\\hline
\pl\tt  black&  color&  \pageref{Dblack}&
        üË×É×ÁÌÅÎÔÎÏ {\tt (0,0,0)}\\\hline
%%\pl\tt  black&  color&  \pageref{Dblack}&
%%        Equivalent to {\tt (0,0,0)}\\\hline
\pl\tt  blue&   color&  \pageref{Dblue}&
        üË×É×ÁÌÅÎÔÎÏ {\tt (0,0,1)}\\\hline
%%\pl\tt  blue&   color&  \pageref{Dblue}&
%%        Equivalent to {\tt (0,0,1)}\\\hline
\pl\tt  bp&     numeric&        \pageref{Dbp}&
        ïÄÉÎ ÐÕÎËÔ PostScript × {\tt bp}-ÅÄÉÎÉÃÁÈ [1]\\\hline
%%\pl\tt  bp&     numeric&        \pageref{Dbp}&
%%        One PostScript point in {\tt bp} units [1]\\\hline
\pl\tt  butt&   numeric&        \pageref{Dbutt}&
        úÎÁÞÅÎÉÅ {\tt linecap} ÄÌÑ butt-ËÏÎÃÁ [0]\\\hline
%%\pl\tt  butt&   numeric&        \pageref{Dbutt}&
%%        {\tt linecap} value for butt end caps [0]\\\hline
\pl\tt  cc&     numeric&        --&
        ïÄÎÁ ÅÄÉÎÉÃÁ ÃÉÃÅÒÏ × {\tt bp}-ÅÄÉÎÉÃÁÈ [12.79213]\\\hline
%%\pl\tt  cc&     numeric&        --&
%%        One cicero in {\tt bp} units [12.79213]\\\hline
\pl\tt  cm&     numeric&        \pageref{Dcm}&
        ïÄÉÎ ÓÁÎÔÉÍÅÔÒ × {\tt bp}-ÅÄÉÎÉÃÁÈ [28.34645]\\\hline
%%\pl\tt  cm&     numeric&        \pageref{Dcm}&
%%        One centimeter in {\tt bp} units [28.34645]\\\hline
\pl\tt  dd&     numeric&        --&
        ïÄÉÎ ÄÉÄÏÔ × {\tt bp}-ÅÄÉÎÉÃÁÈ [1.06601]\\\hline
%%\pl\tt  dd&     numeric&        --&
%%        One didot point in {\tt bp} units [1.06601]\\\hline
\pl\tt  ditto&  string& --&
        óÔÒÏËÁ {\tt \qq} ÄÌÉÎÙ 1\\\hline
%%\pl\tt  ditto&  string& --&
%%        The {\tt \qq} character as a string of length 1\\\hline
\pl\tt  down&   pair&   \pageref{Ddown}&
        ÷ÅËÔÏÒ ×ÎÉÚ $(0,-1)$\\\hline
%%\pl\tt  down&   pair&   \pageref{Ddown}&
%%        Downward direction vector $(0,-1)$\\\hline
\pl\tt  epsilon&        numeric&        --&
        îÁÉÍÅÎØÛÅÅ ÐÏÌÏÖÉÔÅÌØÎÏÅ ÞÉÓÌÏ MetaPost [$1\over65536$]\\\hline
%%\pl\tt  epsilon&        numeric&        --&
%%        Smallest positive MetaPost number [$1\over65536$]\\\hline
\pl\tt  evenly& picture&        \pageref{Devenly}&
        ïÂÒÁÚÅà ÐÕÎËÔÉÒÁ ÉÚ ÔÉÒÅ É ÒÁ×ÎÙÈ ÐÒÏÍÅÖÕÔËÏ×\\\hline
%%\pl\tt  evenly& picture&        \pageref{Devenly}&
%%        Dash pattern for equal length dashes\\\hline
\pl\tt  EOF& string&        \pageref{Deof}&
        ïÄÉÎÏÞÎÙÊ ÎÕÌÅ×ÏÊ ÓÉÍ×ÏÌ\\\hline
%%\pl\tt  EOF& string&        \pageref{Deof}&
%%        Single null character\\\hline
\tt     false&  boolean&        \pageref{Dfalse}&
        ìÏÇÉÞÅÓËÏÅ ÚÎÁÞÅÎÉÅ {\it false\/}\\\hline
%%\tt     false&  boolean&        \pageref{Dfalse}&
%%        The boolean value {\it false\/}\\\hline
\pl\tt  fullcircle&     path&   \pageref{Dfcirc}&
        ïËÒÕÖÎÏÓÔØ ÄÉÁÍÅÔÒÁ 1 Ó ÃÅÎÔÒÏÍ × $(0,0)$\\\hline
%%\pl\tt  fullcircle&     path&   \pageref{Dfcirc}&
%%        Circle of diameter 1 centered on $(0,0)$\\\hline
\pl\tt  green&  color&  \pageref{Dgreen}&
        üË×É×ÁÌÅÎÔÎÏ {\tt (0,1,0)}\\\hline
%%\pl\tt  green&  color&  \pageref{Dgreen}&
%%        Equivalent to {\tt (0,1,0)}\\\hline
\pl\tt  halfcircle&     path&   \pageref{Dhcirc}&
        ÷ÅÒÈÎÑÑ ÐÏÌÕÏËÒÕÖÎÏÓÔØ ÄÉÁÍÅÔÒÁ 1\\\hline
%%\pl\tt  halfcircle&     path&   \pageref{Dhcirc}&
%%        Upper half of a circle of diameter 1\\\hline
\pl\tt  identity&       transform&      \pageref{Dident}&
        ôÏÖÄÅÓÔ×ÅÎÎÁÑ ÔÒÁÎÓÆÏÒÍÁÃÉÑ\\\hline
%%\pl\tt  identity&       transform&      \pageref{Dident}&
%%        Identity transformation\\\hline
\pl\tt  in&     numeric&        \pageref{Din}&
        ïÄÉÎ ÄÀÊÍ × {\tt bp}-ÅÄÉÎÉÃÁÈ [72]\\\hline
%%\pl\tt  in&     numeric&        \pageref{Din}&
%%        One inch in {\tt bp} units [72]\\\hline
\pl\tt  infinity&       numeric&        \pageref{Dinf}&
        îÁÉÂÏÌØÛÅÅ ÐÏÌÏÖÉÔÅÌØÎÏÅ ÚÎÁÞÅÎÉÅ [4095.99998]\\\hline
%%\pl\tt  infinity&       numeric&        \pageref{Dinf}&
%%        Large positive value [4095.99998]\\\hline
\pl\tt  left&   pair&   \pageref{Dleft}&
        îÁÐÒÁ×ÌÅÎÉÅ ×ÌÅ×Ï $(-1,0)$\\\hline
%%\pl\tt  left&   pair&   \pageref{Dleft}&
%%        Leftward direction $(-1,0)$\\\hline
\pl\tt  mitered&        numeric&        \pageref{Dmitred}&
        úÎÁÞÅÎÉÅ {\tt linejoin} ÄÌÑ ``ÏÓÔÒÙÈ'' ÓÏÅÄÉÎÅÎÉÊ [0]\\\hline
%%\pl\tt  mitered&        numeric&        \pageref{Dmitred}&
%%        {\tt linejoin} value for mitered joins [0]\\\hline
\pl\tt  mm&     numeric&        \pageref{Dmm}&
        ïÄÉÎ ÍÉÌÌÉÍÅÔÒ × {\tt bp}-ÅÄÉÎÉÃÁÈ [2.83464]\\\hline
%%\pl\tt  mm&     numeric&        \pageref{Dmm}&
%%        One millimeter in {\tt bp} units [2.83464]\\\hline
\tt     mpversion&  string&   \pageref{Dmpversion}&
        îÏÍÅÒ ×ÅÒÓÉÉ MetaPost\\\hline
%%\tt     mpversion&  string&   \pageref{Dmpversion}&
%%        MetaPost version number\\\hline
\tt     nullpen&    pen&        \pageref{Dnlpen}&
        ðÕÓÔÏÅ ÐÅÒÏ\\\hline
%%\tt     nullpen&    pen&        \pageref{Dnlpen}&
%%        Empty pen\\\hline
\tt     nullpicture&    picture&        \pageref{Dnlpic}&
        ðÕÓÔÁÑ ËÁÒÔÉÎËÁ\\\hline
%%\tt     nullpicture&    picture&        \pageref{Dnlpic}&
%%        Empty picture\\\hline
\pl\tt  origin& pair&   --&
        ðÁÒÁ $(0,0)$\\\hline
%%\pl\tt  origin& pair&   --&
%%        The pair $(0,0)$\\\hline
\pl\tt  pc&     numeric&        --&
        ïÄÎÁ ÐÉËÁ × {\tt bp}-ÅÄÉÎÉÃÁÈ [11.95517]\\\hline
%%\pl\tt  pc&     numeric&        --&
%%        One pica in {\tt bp} units [11.95517]\\\hline
\tt     pencircle&      pen&    \pageref{Dpncirc}&
        ëÒÕÇÏ×ÏÅ ÐÅÒÏ ÄÉÁÍÅÔÒÁ 1\\\hline
%%\tt     pencircle&      pen&    \pageref{Dpncirc}&
%%        Circular pen of diameter 1\\\hline
\pl\tt  pensquare&      pen&    \pageref{Dpnsqr}&
        ë×ÁÄÒÁÔÎÏÅ ÐÅÒÏ ×ÙÓÏÔÙ É ÛÉÒÉÎÙ 1\\\hline
%%\pl\tt  pensquare&      pen&    \pageref{Dpnsqr}&
%%        square pen of height 1 and width 1\\\hline
\pl\tt  pt&     numeric&        \pageref{Dpt}&
        ïÄÉÎ ÐÒÉÎÔÅÒÎÙÊ ÐÕÎËÔ × {\tt bp}-ÅÄÉÎÉÃÁÈ [0.99626]\\\hline
%%\pl\tt  pt&     numeric&        \pageref{Dpt}&
%%        One printer's point in {\tt bp} units [0.99626]\\\hline
\pl\tt  quartercircle&  path&   --&
        ðÅÒ×ÙÊ Ë×ÁÄÒÁÎÔ ÏËÒÕÖÎÏÓÔÉ ÄÉÁÍÅÔÒÁ 1\\\hline
%%\pl\tt  quartercircle&  path&   --&
%%        First quadrant of a circle of diameter 1\\\hline
\pl\tt  red&    color&  \pageref{Dred}&
        üË×É×ÁÌÅÎÔÎÏ {\tt (1,0,0)}\\\hline
%%\pl\tt  red&    color&  \pageref{Dred}&
%%        Equivalent to {\tt (1,0,0)}\\\hline
\pl\tt  right&  pair&   \pageref{Dright}&
        îÁÐÒÁ×ÌÅÎÉÅ ×ÐÒÁ×Ï $(1,0)$\\\hline
%%\pl\tt  right&  pair&   \pageref{Dright}&
%%        Rightward direction $(1,0)$\\\hline
\pl\tt  rounded&        numeric&        \pageref{Drnded}&
        úÎÁÞÅÎÉÅ ÄÌÑ {\tt linecap} É {\tt linejoin} ÄÌÑ ËÒÕÇÌÙÈ\\
\tt     &       &       &
        ÓÏÅÄÉÎÅÎÉÊ É ËÏÎÃÏ× [1]\\\hline
%%\pl\tt  rounded&        numeric&        \pageref{Drnded}&
%%        {\tt linecap} and {\tt linejoin} value for round joins\\
%%\tt     &       &       &
%%        and end caps [1]\\\hline
\pl\tt  squared&        numeric&        \pageref{Dsqred}&
        úÎÁÞÅÎÉÅ {\tt linecap} ÄÌÑ Ë×ÁÄÒÁÔÎÙÈ ËÏÎÃÏ× [2]\\\hline
%%\pl\tt  squared&        numeric&        \pageref{Dsqred}&
%%        {\tt linecap} value for square end caps [2]\\\hline
\tt     true&   boolean&        \pageref{Dtrue}&
        ìÏÇÉÞÅÓËÁÑ ×ÅÌÉÞÉÎÁ {\tt true}\\\hline
%%\tt     true&   boolean&        \pageref{Dtrue}&
%%        The boolean value {\tt true}\\\hline
\pl\tt  unitsquare&     path&   --&
        ðÕÔØ {\tt (0,0)-{}-(1,0)-{}-(1,1)-{}-(0,1)-{}-cycle}\\\hline
%%\pl\tt  unitsquare&     path&   --&
%%        The path {\tt (0,0)--(1,0)--(1,1)--(0,1)--cycle}\\\hline
\pl\tt  up&     pair&   \pageref{Dup}&
        îÁÐÒÁ×ÌÅÎÉÅ ××ÅÒÈ $(0,1)$\\\hline
%%\pl\tt  up&     pair&   \pageref{Dup}&
%%        Upward direction $(0,1)$\\\hline
\pl\tt  white&  color&  \pageref{Dwhite}&
        üË×É×ÁÌÅÎÔÎÏ {\tt (1,1,1)}\\\hline
%%\pl\tt  white&  color&  \pageref{Dwhite}&
%%        Equivalent to {\tt (1,1,1)}\\\hline
\pl\tt  withdots&       picture&        \pageref{Dwdots}&
        ïÂÒÁÚÅà ÐÕÎËÔÉÒÁ ÉÚ ÔÏÞÅË\\\hline
%%\pl\tt  withdots&       picture&        \pageref{Dwdots}&
%%        Dash pattern that produces dotted lines\\\hline
\end{tabular}
$$
\label{consttab}%
\index{cc?\texttt{cc}}\index{dd?\texttt{dd}}\index{ditto?\texttt{ditto}}\index{epsilon?\texttt{epsilon}}%
\index{origin?\texttt{origin}}\index{pc?\texttt{pc}}\index{quartercircle?\texttt{quartercircle}}%
\index{unitsquare?\texttt{unitsquare}}
\end{table}


\clearpage
\LTXtable{\textwidth}{mpman-optab-ru}

\begin{table}[htp]
\caption{ëÏÍÁÎÄÙ}
%%\caption{Commands}
$$\begin{tabular}{|l|r|l|}
\hline
\multicolumn1{|c}{éÍÑ}&  \multicolumn1{|c}{óÔÒ.}&  \multicolumn1{|c|}{ïÂßÑÓÎÅÎÉÅ}\\
%%\multicolumn1{|c}{Name}&  \multicolumn1{|c}{Page}&  \multicolumn1{|c|}{Explanation}\\
\hline
\hline
\tt \verb|addto|&       \pageref{sydraw}&
        îÉÚËÏÕÒÏ×ÎÅ×ÁÑ ËÏÍÁÎÄÁ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ É ÚÁÐÏÌÎÅÎÉÑ\\\hline
%%        Low-level command for drawing and filling\\\hline
\tt \verb|clip|&        \pageref{Dclip}&
        ðÒÉÍÅÎÑÅÔ ÐÕÔØ ×ÙÒÅÚËÉ Ë ËÁÒÔÉÎËÅ\\\hline
%%	  Applies a clipping path to a picture\\\hline
\tt \verb|closefrom|&  \pageref{Dclosefrom}&
        úÁËÒÙ×ÁÅÔ ÆÁÊÌ, ÏÔËÒÙÔÙÊ {\tt readfrom}\\\hline
%%        Close a file opened by {\tt readfrom}\\\hline
\pl\tt \verb|cutdraw|&  \pageref{Dctdraw}&
        òÉÓÏ×ÁÔØ Ó butt-ËÏÎÃÏÍ\\\hline
%%        Draw with butt end caps\\\hline
\tt \verb|dashed|&     \pageref{Ddashed}&
	ðÒÉÍÅÎÑÔØ ÏÂÒÁÚÅà ÐÕÎËÔÉÒÁ × ËÏÍÁÎÄÅ ÒÉÓÏ×ÁÎÉÑ\\\hline
%%        Apply dash pattern to drawing command\\\hline
\pl\tt \verb|draw|&     \pageref{curves}&
        òÉÓÏ×ÁÔØ ÌÉÎÉÀ ÉÌÉ ËÁÒÔÉÎËÕ\\\hline
%%        Draw a line or a picture\\\hline
\pl\tt \verb|drawarrow|&        \pageref{Ddrwarr}&
        òÉÓÏ×ÁÔØ ÌÉÎÉÀ ÓÏ ÓÔÒÅÌËÏÊ ÎÁ ËÏÎÃÅ\\\hline
%%	  Draw a line with an arrowhead at the end\\\hline
\pl\tt \verb|drawdblarrow|&     \pageref{Ddrwdar}&
        òÉÓÏ×ÁÔØ ÌÉÎÉÀ ÓÏ ÓÔÒÅÌËÁÍÉ × ÏÂÏÉÈ ËÏÎÃÁÈ\\\hline
%%        Draw a line with arrowheads at both ends\\\hline
\tt \verb|filenametemplate|&     \pageref{Dfilenametemplate}&
        õÓÔÁÎÏ×ÉÔØ ÛÁÂÌÏÎ ÉÍÅÎÉ ×ÙÈÏÄÎÏÇÏ ÆÁÊÌÁ\\\hline
%%        Set output file name pattern\\\hline
\pl\tt \verb|fill|&     \pageref{Dfill}&
        úÁÐÏÌÎÉÔØ ÃÉËÌÉÞÅÓËÉÊ ÐÕÔØ\\\hline
%%        Fill inside a cyclic path\\\hline
\pl\tt \verb|filldraw|& \pageref{Dfildrw}&
        òÉÓÏ×ÁÔØ ÃÉËÌÉÞÅÓËÉÊ ÐÕÔØ É ÚÁÐÏÌÎÉÔØ ÅÇÏ ×ÎÕÔÒÉ\\\hline
%%        Draw a cyclic path and fill inside it\\\hline
\tt \verb|interim|&     \pageref{Dinterm}&
        óÄÅÌÁÔØ ÌÏËÁÌØÎÏÅ ÉÚÍÅÎÅÎÉÅ ×ÎÕÔÒÅÎÎÅÊ ÐÅÒÅÍÅÎÎÏÊ\\\hline
%%        Make a local change to an internal variable\\\hline
\tt \verb|let|& --&
        îÁÚÎÁÞÉÔØ ÓÉÍ×ÏÌÉÞÅÓËÏÍÕ ÚÎÁËÕ ÚÎÁÞÅÎÉÅ ÄÒÕÇÏÇÏ ÚÎÁËÁ\\\hline
%%        Assign one symbolic token the meaning of another\\\hline
\pl\tt \verb|loggingall|&       \pageref{Dlogall}&
        ÷ËÌÀÞÉÔØ ÔÒÁÓÓÉÒÏ×ËÕ (ÔÏÌØËÏ ÄÌÑ ÆÁÊÌÁ-ÖÕÒÎÁÌÁ)\\\hline
%%        Turn on all tracing (log file only)\\\hline
\tt \verb|newinternal|& \pageref{Dnewint}&
        ïÂßÑ×ÉÔØ ÎÏ×ÙÅ ×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ\\\hline
%%        Declare new internal variables\\\hline
\pl\tt \verb|pickup|&   \pageref{Dpickup}&
        õËÁÚÁÔØ ÎÏ×ÏÅ ÐÅÒÏ ÄÌÑ ÒÉÓÏ×ÁÎÉÑ ÌÉÎÉÉ\\\hline
%%        Specify new pen for line drawing\\\hline
\tt \verb|save|&        \pageref{Dsave}&
        äÅÌÁÅÔ ÐÅÒÅÍÅÎÎÙÅ ÌÏËÁÌØÎÙÍÉ\\\hline
%%        Make variables local\\\hline
\tt \verb|setbounds|&   \pageref{Dsetbnd}&
        õÓÔÁÎÁ×ÌÉ×ÁÅÔ ÏÈ×ÁÔÙ×ÁÀÝÕÀ ÒÁÍËÕ ÄÌÑ ËÁÒÔÉÎËÉ\\\hline
%%        Make a picture lie about its bounding box\\\hline
\tt \verb|shipout|&     \pageref{Dship}&
        îÉÚËÏÕÒÏ×ÎÅ×ÁÑ ËÏÍÁÎÄÁ ÐÅÞÁÔÉ ÒÉÓÕÎËÁ\\\hline
%%        Low-level command to output a figure\\\hline
\tt \verb|show|&        \pageref{Dshow}&
        ðÅÞÁÔØ ×ÙÒÁÖÅÎÉÊ × ÓÉÍ×ÏÌÉÞÅÓËÏÊ ÆÏÒÍÅ\\\hline
%%        print out expressions symbolically\\\hline
\tt \verb|showdependencies|&    \pageref{Dshdep}&
        ðÅÞÁÔØ ×ÓÅÈ ÎÅÒÅÛÅÎÎÙÈ ÕÒÁ×ÎÅÎÉÊ\\\hline
%%        print out all unsolved equations\\\hline
\tt \verb|showtoken|&   \pageref{Dshtok}&
        ðÅÞÁÔØ ÉÎÆÏÒÍÁÃÉÉ ÐÏ ÚÎÁËÕ\\\hline
%%        print an explanation of what a token is\\\hline
\tt \verb|showvariable|&        \pageref{Dshvar}&
        ðÅÞÁÔØ ÐÅÒÅÍÅÎÎÙÈ × ÓÉÍ×ÏÌØÎÏÊ ÆÏÒÍÅ\\\hline
%%        print variables symbolically\\\hline
\tt \verb|special|&     \pageref{Dspecl}&
        ðÅÞÁÔØ ÓÔÒÏËÉ ÐÒÑÍÏ × PostScript-ÆÁÊÌ ×Ù×ÏÄÁ\\\hline
%%        print a string directly in the PostScript output file\\\hline
\pl\tt \verb|tracingall|&       \pageref{Dtall}&
        ÷ËÌÀÞÉÔØ ÔÒÁÓÓÉÒÏ×ËÕ\\\hline
%%        Turn on all tracing\\\hline
\pl\tt \verb|tracingnone|&      \pageref{Dtnone}&
        ïÔËÌÀÞÉÔØ ÔÒÁÓÓÉÒÏ×ËÕ\\\hline
%%        Turn off all tracing\\\hline
\pl\tt \verb|undraw|&   \pageref{Dundraw}&
        óÔÅÒÅÔØ ÌÉÎÉÀ ÉÌÉ ÒÉÓÕÎÏË\\\hline
%%        Erase a line or a picture\\\hline
\pl\tt \verb|unfill|&   \pageref{Dunfill}&
        óÔÅÒÅÔØ ×ÎÕÔÒÉ ÚÁÍËÎÕÔÏÇÏ ÐÕÔÉ\\\hline
%%        Erase inside a cyclic path\\\hline
\pl\tt \verb|unfilldraw|&       \pageref{Dunfdrw}&
        óÔÅÒÅÔØ ÃÉËÌÉÞÅÓËÉÊ ÐÕÔØ É ×ÓÅ ×ÎÕÔÒÉ ÎÅÇÏ\\\hline
%%        Erase a cyclic path and its inside\\\hline
\tt \verb|withcmykcolor|&    \pageref{Dwithcmykcolor}&
	éÓÐÏÌØÚÕÊ CMYK-Ã×ÅÔ × ËÏÍÁÎÄÅ ÒÉÓÏ×ÁÎÉÑ\\\hline
%         Apply CMYK color to drawing command\\\hline
 \tt \verb|withcolor|&        \pageref{Dwithcolor}&
	éÓÐÏÌØÚÕÊ ÏÂÙÞÎÙÊ Ã×ÅÔ × ËÏÍÁÎÄÅ ÒÉÓÏ×ÁÎÉÑ\\\hline
%         Apply generic color specification to drawing command\\\hline
 \tt \verb|withgreyscale|&    \pageref{Dwithgreyscale}&
	éÓÐÏÌØÚÕÊ ÏÔÔÅÎÏË ÓÅÒÏÇÏ × ËÏÍÁÎÄÅ ÒÉÓÏ×ÁÎÉÑ\\\hline
%         Apply greyscale color to drawing command\\\hline
 \tt \verb|withoutcolor|&     \pageref{Dwithoutcolor}&
	îÅ ÉÓÐÏÌØÚÕÊ ÓÐÅÃÉÆÉËÁÃÉÉ Ã×ÅÔÁ × ËÏÍÁÎÄÅ ÒÉÓÏ×ÁÎÉÑ\\\hline
%         Don't apply any color specification to drawing command\\\hline
 \tt \verb|withpen|&          \pageref{sec.pens}&
	éÓÐÏÌØÚÕÊ ÐÅÒÏ × ËÏÍÁÎÄÅ ÒÉÓÏ×ÁÎÉÑ\\\hline
%         Apply pen to drawing operation\\\hline
 \tt \verb|withpostscript|&   \pageref{Dwithpost}&
	ëÏÎÅà ËÏÄÁ PostScript\\\hline
%         End raw PostScript code\\\hline
 \tt \verb|withprescript|&    \pageref{Dwithpre}&
	îÁÞÁÌÏ ËÏÄÁ PostScript\\\hline
%         Begin raw PostScript code\\\hline
 \tt \verb|withrgbcolor|&     \pageref{Dwithrgbcolor}&
	éÓÐÏÌØÚÕÊ RGB-Ã×ÅÔ × ËÏÍÁÎÄÅ ÒÉÓÏ×ÁÎÉÑ\\\hline
%         Apply RGB color to drawing command\\\hline
\tt \verb|write to|&         \pageref{Dwrite}&
        ðÉÓÁÔØ ÓÔÒÏËÕ × ÆÁÊÌ\\\hline
%%        Write string to file\\\hline
\end{tabular}
$$
\index{let?\texttt{let}}%
\label{cmdtab}
\end{table}


\begin{table}[htp]
\caption{íÁËÒÏÓÙ, ÐÏÈÏÖÉÅ ÎÁ ÆÕÎËÃÉÉ}
%%\caption{Function-Like Macros}
$$\begin{tabular}{|l|l|l|r|p{5.7cm}|}
%%$$\begin{tabular}{|l|l|l|r|l|}
\hline
\multicolumn1{|c}{éÍÑ}&  \multicolumn1{|c}{áÒÇÕÍÅÎÔÙ}&
        \multicolumn1{|c}{òÅÚÕ-Ô}&  \multicolumn1{|c}{ó.}&
        \multicolumn1{|c|}{ïÂßÑÓÎÅÎÉÅ}\\
%%\multicolumn1{|c}{Name}&  \multicolumn1{|c}{Arguments}&
%%        \multicolumn1{|c}{Result}&  \multicolumn1{|c}{Page}&
%%        \multicolumn1{|c|}{Explanation}\\
\hline
\hline
\bx\tt \verb|boxit|&    \small ÓÕÆÆÉËÓ, ËÁÒÔÉÎËÁ&        --&     \pageref{Dboxit}&
%%\bx\tt \verb|boxit|&    suffix, picture&        --&     \pageref{Dboxit}&
        \small úÁÄÁÅÔ ÒÁÍËÕ, ÓÏÄÅÒÖÁÝÕÀ ËÁÒÔÉÎËÕ\\\hline
%%        Define a box containing the picture\\\hline
\bx\tt \verb|boxit|&    \small ÓÕÆÆÉËÓ, ÓÔÒÏËÁ& --&     \pageref{Dsboxit}&
%%\bx\tt \verb|boxit|&    suffix, string& --&     \pageref{Dsboxit}&
        \small ïÐÒÅÄÅÌÑÅÔ ÒÁÍËÕ, ÓÏÄÅÒÖÁÝÕÀ ÔÅËÓÔ\\\hline
%%        Define a box containing text\\\hline
\bx\tt \verb|boxit|&    \small ÓÕÆÆÉËÓ, \tdescr{ÐÕÓÔÏ}& --&     \pageref{Deboxit}&
%%\bx\tt \verb|boxit|&    suffix, \tdescr{empty}& --&     \pageref{Deboxit}&
        \small ïÐÒÅÄÅÌÑÅÔ ÐÕÓÔÕÀ ÒÁÍËÕ\\\hline
%%        Define an empty box\\\hline
\bx\tt \verb|boxjoin|&  \small ÕÒÁ×ÎÅÎÉÑ&      --&     \pageref{Dbxjoin}&
%%\bx\tt \verb|boxjoin|&  equations&      --&     \pageref{Dbxjoin}&
        \small úÁÄÁÅÔ ÕÒÁ×ÎÅÎÉÑ ÄÌÑ ÓÏÅÄÉÎÑÅÍÙÈ ÒÁÍÏË\\\hline
%%        Give equations for connecting boxes\\\hline
\bx\tt \verb|bpath|&    \small ÓÕÆÆÉËÓ& path&   \pageref{Dbpath}&
%%\bx\tt \verb|bpath|&    suffix& path&   \pageref{Dbpath}&
        \small ïÈ×ÁÔÙ×ÁÀÝÉÊ ËÒÕÇ ÉÌÉ ÐÒÑÍÏÕÇÏÌØÎÉË\\\hline
%%        A box's bounding circle or rectangle\\\hline
\pl\tt \verb|buildcycle|&       \small ÓÐÉÓÏË ÐÕÔÅÊ&  path&   \pageref{buildcy}&
%%\pl\tt \verb|buildcycle|&       list of paths&  path&   \pageref{buildcy}&
        \small óÔÒÏÉÔØ ÚÁÍËÎÕÔÙÊ ÐÕÔØ\\\hline
%%        Build a cyclic path\\\hline
\bx\tt \verb|circleit|& \small ÓÕÆÆÉËÓ, ËÁÒÔÉÎËÁ&        --&     \pageref{Dcircit}&
%%\bx\tt \verb|circleit|& suffix, picture&        --&     \pageref{Dcircit}&
        \small ðÏÍÅÓÔÉÔØ ËÁÒÔÉÎËÕ × ËÒÕÇÏ×ÕÀ ÒÁÍËÕ\\\hline
%%        Put picture in a circular box\\\hline
\bx\tt \verb|circleit|& \small ÓÕÆÆÉËÓ, ËÁÒÔÉÎËÁ&        --&     \pageref{Dcircit}&
%%\bx\tt \verb|circleit|& suffix, picture& 
        \small ðÏÍÅÓÔÉÔØ ÓÔÒÏËÕ × ËÒÕÇÏ×ÕÀ ÒÁÍËÕ\\\hline
%%        Put a string in a circular box\\\hline
\bx\tt \verb|circleit|& \small ÓÕÆÆÉËÓ, \tdescr{ÐÕÓÔÏ}& --&     \pageref{Dcircit}&
%%\bx\tt \verb|circleit|& suffix, \tdescr{empty}& --&     \pageref{Dcircit}&
        \small ïÐÒÅÄÅÌÉÔØ ÐÕÓÔÕÀ ËÒÕÇÏ×ÕÀ ÒÁÍËÕ\\\hline
%%        Define an empty circular box\\\hline
\pl\tt \verb|dashpattern|&      \small ÒÁÓÓÔÏÑÎÉÑ ×ËÌ./×ÙËÌ.&       picture&        \pageref{Ddshpat}&
%%\pl\tt \verb|dashpattern|&      on/off distances&       picture&        \pageref{Ddshpat}&
        \small óÏÚÄÁÔØ ÏÂÒÁÚÅÃ ÐÕÎËÔÉÒÎÙÈ ÌÉÎÉÊ\\\hline
%%        Create a pattern for dashed lines\\\hline
\pl\tt \verb|decr|&     \small ÞÉÓÌÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ&       numeric&        \pageref{Dincr}&
%%\pl\tt \verb|decr|&     numeric variable&       numeric&        \pageref{Dincr}&
        \small õÍÅÎØÛÉÔØ É ×ÏÚ×ÒÁÔÉÔØ ÎÏ×ÏÅ ÚÎÁÞÅÎÉÅ\\\hline
%%        Decrement and return new value\\\hline
\pl\tt \verb|dotlabel|& \small ÓÕÆÆÉËÓ, ËÁÒÔÉÎËÁ, ÐÁÒÁ&  --&     \pageref{Ddotlab}&
%%\pl\tt \verb|dotlabel|& suffix, picture, pair&  --&     \pageref{Ddotlab}&
        \small îÁÒÉÓÏ×ÁÔØ ÔÏÞËÕ É ÒÑÄÏÍ ËÁÒÔÉÎËÕ\\\hline
%%        Mark point and draw picture nearby\\\hline
\pl\tt \verb|dotlabel|& \small ÓÕÆÆÉËÓ, ÓÔÒÏËÁ, ÐÁÒÁ&   --&     \pageref{Ddotlab}&
%%\pl\tt \verb|dotlabel|& suffix, string, pair&   --&     \pageref{Ddotlab}&
        \small ïÔÍÅÔÉÔØ ÔÏÞËÕ É ÐÏÍÅÓÔÉÔØ ÒÑÄÏÍ ÔÅËÓÔ\\\hline
%%        Mark point and place text nearby\\\hline
\pl\tt \verb|dotlabels|&        \small ÓÕÆÆÉËÓ, ÎÏÍÅÒÁ ÔÏÞÅË&  --&     \pageref{Ddotlbs}&
%%\pl\tt \verb|dotlabels|&        suffix, point numbers&  --&     \pageref{Ddotlbs}&
        \small ïÔÍÅÔÉÔØ ÔÏÞËÉ {\tt z} ÉÈ ÎÏÍÅÒÁÍÉ\\\hline
%%        Mark {\tt z} points with their numbers\\\hline
\bx\tt \verb|drawboxed|&        \small ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×&       --&     \pageref{Ddrbxed}&
%%\bx\tt \verb|drawboxed|&        list of suffixes&       --&     \pageref{Ddrbxed}&
        \small îÁÒÉÓÏ×ÁÔØ ÉÍÅÎÏ×ÁÎÎÙÅ ÒÁÍËÉ É ÉÈ ÓÏÄÅÒÖÉÍÏÅ\\\hline
%%        Draw the named boxes and their\\
%%&       &       &       &
%%        contents\\\hline
\bx\tt \verb|drawboxes|&        \small ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×&       --&     \pageref{Ddrbxes}&
%%\bx\tt \verb|drawboxes|&        list of suffixes&       --&     \pageref{Ddrbxes}&
        \small îÁÒÉÓÏ×ÁÔØ ÉÍÅÎÏ×ÁÎÎÙÅ ÒÁÍËÉ\\\hline
%%        Draw the named boxes\\\hline
\pl\tt \verb|drawdot|&          \small ÐÁÒÁ&       --&     \pageref{Ddrawdot}&
%%\pl\tt \verb|drawdot|&          pair&       --&     \pageref{Ddrawdot}&
        \small ðÏÓÔÁ×ÉÔØ ÔÏÞËÕ × ÄÁÎÎÏÍ ÍÅÓÔÅ\\\hline
%%        Draw a dot at the given point\\\hline
\pl\tt \verb|drawoptions|&      \small ÏÐÃÉÉ ÒÉÓÏ×ÁÎÉÑ&        --&     \pageref{Ddropts}&
%%\pl\tt \verb|drawoptions|&      drawing options&        --&     \pageref{Ddropts}&
        \small õÓÔÁÎÏ×ÉÔØ ÏÐÃÉÉ ÄÌÑ ËÏÍÁÎÄ ÒÉÓÏ×ÁÎÉÑ\\\hline
%%        Set options for drawing commands\\\hline
\bx\tt \verb|drawunboxed|&      \small ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×&       --&     \pageref{Ddrunbx}&
%%\bx\tt \verb|drawunboxed|&      list of suffixes&       --&     \pageref{Ddrunbx}&
        \small òÉÓÏ×ÁÔØ ÓÏÄÅÒÖÉÍÏÅ ÉÍÅÎÏ×ÁÎÎÙÈ ÒÁÍÏË\\\hline
%%        Draw contents of named boxes\\\hline
\bx\tt \verb|fixpos|&   \small ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×&       --&     \pageref{Dfixpos}&
%%\bx\tt \verb|fixpos|&   list of suffixes&       --&     \pageref{Dfixpos}&
        \small îÁÊÔÉ ÒÁÚÍÅÒ É ÐÏÚÉÃÉÀ ÉÍÅÎÏ×ÁÎÎÙÈ ÒÁÍÏË\\\hline
%%        Solve for the size and position of the\\
%%&       &       &       &
%%        named boxes\\\hline
\bx\tt \verb|fixsize|&  \small ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×&       --&     \pageref{Dfixsiz}&
%%\bx\tt \verb|fixsize|&  list of suffixes&       --&     \pageref{Dfixsiz}&
        \small îÁÊÔÉ ÒÁÚÍÅÒ ÉÍÅÎÏ×ÁÎÎÙÈ ÒÁÍÏË\\\hline
%%        Solve for size of named boxes\\\hline
\pl\tt \verb|image|&              \small ÓÔÒÏËÁ&       picture&      \pageref{Dimage}&
%%\pl\tt \verb|image|&              string&       picture&      \pageref{Dimage}&
        \small ÷ÏÚ×ÒÁÝÁÅÔ ÒÉÓÕÎÏË ÉÚ ÔÅËÓÔÁ\\\hline
%%        Return picture from text\\\hline
\pl\tt \verb|incr|&     \small ÞÉÓÌÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ&       numeric&       \pageref{Dincr}&
%%\pl\tt \verb|incr|&     numeric variable&       numeric&       \pageref{Dincr}&
        \small õ×ÅÌÉÞÉÔØ É ×ÏÚ×ÒÁÔÉÔØ ÎÏ×ÏÅ ÚÎÁÞÅÎÉÅ\\\hline
%%        Increment and return new value\\\hline
\pl\tt \verb|label|&    \small ÓÕÆÆÉËÓ, ËÁÒÔÉÎËÁ, ÐÁÒÁ&  --&     \pageref{Dlabel}&
%%\pl\tt \verb|label|&    suffix, picture, pair&  --&     \pageref{Dlabel}&
        \small éÚÏÂÒÁÚÉÔØ ÒÉÓ. ×ÏÚÌÅ ÚÁÄÁÎÎÏÊ ÔÏÞËÉ\\\hline
%%        Draw picture near given point\\\hline
\pl\tt \verb|label|&    \small ÓÕÆÆÉËÓ, ÓÔÒÏËÁ, ÐÁÒÁ&   --&     \pageref{Dlabel}&
%%\pl\tt \verb|label|&    suffix, string, pair&   --&     \pageref{Dlabel}&
        \small ðÏÍÅÓÔÉÔØ ÔÅËÓÔ ×ÏÚÌÅ ÚÁÄÁÎÎÏÊ ÔÏÞËÉ\\\hline
%%        Place text near given point\\\hline
\pl\tt \verb|labels|&   \small ÓÕÆÆÉËÓ, ÎÏÍÅÒÁ ÔÏÞÅË&  --&     \pageref{Dlabels}&
%%\pl\tt \verb|labels|&   suffix, point numbers&  --&     \pageref{Dlabels}&
        \small îÁÒÉÓÏ×ÁÔØ ÞÉÓÌÁ ÐÁÒ {\tt z}, ÂÅÚ ÔÏÞÅË\\\hline
%%        Draw {\tt z} point numbers; no dots\\\hline
\pl\tt \verb|max|&      \small ÓÐÉÓÏË ÞÉÓÅÌ&       numeric&        --&
%%\pl\tt \verb|max|&      list of numerics&       numeric&        --&
        \small îÁÊÔÉ ÍÁËÓÉÍÕÍ\\\hline
%%        Find the maximum\\\hline
\pl\tt \verb|max|&      \small ÓÐÉÓÏË ÓÔÒÏË&        string& --&
%%\pl\tt \verb|max|&      list of strings&        string& --&
        \small îÁÊÔÉ ÓÌÏ×ÁÒÎÏ ÐÏÓÌÅÄÎÀÀ ÓÔÒÏËÕ\\\hline
%%        Find the lexicographically last string\\\hline
\pl\tt \verb|min|&      \small ÓÐÉÓÏË ÞÉÓÅÌ&       numeric&        --&
%%\pl\tt \verb|min|&      list of numerics&       numeric&        --&
        \small îÁÊÔÉ ÍÉÎÉÍÕÍ\\\hline
%%        Find the minimum\\\hline
\pl\tt \verb|min|&      \small ÓÐÉÓÏË ÓÔÒÏË&        string& --&
%%\pl\tt \verb|min|&      list of strings&        string& --&
        \small îÁÊÔÉ ÓÌÏ×ÁÒÎÏ ÐÅÒ×ÕÀ ÓÔÒÏËÕ\\\hline
%%        Find the lexicographically first string\\\hline
\bx\tt \verb|pic|&      \small ÓÕÆÆÉËÓ& picture&        \pageref{Dpic}&
%%\bx\tt \verb|pic|&      suffix& picture&        \pageref{Dpic}&
        \small óÏÄÅÒÖÉÍÏÅ ÒÁÍËÉ, ÓÄ×ÉÎÕÔÏÅ × ÐÏÚÉÃÉÀ\\\hline
%%        Box contents shifted into position\\\hline
\pl\tt \verb|thelabel|& \small ÓÕÆÆÉËÓ, ËÁÒÔÉÎËÁ, ÐÁÒÁ&  picture&        \pageref{Dthelab}&
%%\pl\tt \verb|thelabel|& suffix, picture, pair&  picture&        \pageref{Dthelab}&
        \small ëÁÒÔÉÎËÁ, \small ÓÄ×ÉÎÕÔÁÑ ËÁË ÄÌÑ ÍÅÔËÉ ÔÏÞËÉ\\\hline
%%        Picture shifted as if to label a point\\\hline
\pl\tt \verb|thelabel|& \small ÓÕÆÆÉËÓ, ÓÔÒÏËÁ, ÐÁÒÁ&   picture&        \pageref{Dthelab}&
%%\pl\tt \verb|thelabel|& suffix, string, pair&   picture&        \pageref{Dthelab}&
        \small ôÅËÓÔ, ÒÁÚÍÅÝÅÎÎÙÊ ËÁË ÄÌÑ ÍÅÔËÉ ÔÏÞËÉ\\\hline
%%        text positioned as if to label a point\\\hline
\pl\tt \verb|z|&        \small ÓÕÆÆÉËÓ& pair&   \pageref{Dzconv}&
%%\pl\tt \verb|z|&        suffix& pair&   \pageref{Dzconv}&
        \small ðÁÒÁ ${\tt x}\descr{ÓÕÆÆÉËÓ},{\tt y}\descr{ÓÕÆÆÉËÓ})$\\\hline
%%        The pair ${\tt x}\descr{suffix},{\tt y}\descr{suffix})$\\\hline
\end{tabular}
$$
\index{min?\texttt{min}}\index{max?\texttt{max}}%
\label{pseudotab}
\end{table}

\clearpage

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÁÔÏÍ} \rightarrow \descr{ÐÅÒÅÍÅÎÎÁÑ} \;|\; \descr{ÁÒÇÕÍÅÎÔ}$\\
%%$\tt \descr{atom} \rightarrow \descr{variable} \;|\; \descr{argument}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ ÉÌÉ ÄÒÏÂØ}$\\
%%$\tt \qquad \;|\; \descr{number or fraction}$\\
$\tt \qquad \;|\; \descr{×ÎÕÔÒÅÎÎÑÑ ÐÅÒÅÍÅÎÎÁÑ}$\\
%%$\tt \qquad \;|\; \descr{internal variable}$\\
$\tt \qquad \;|\; \hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; \hbox{\tt (}\descr{expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; begingroup \descr{ÓÐÉÓÏË ËÏÍÁÎÄ} \descr{×ÙÒÁÖÅÎÉÅ} endgroup$\\
%%$\tt \qquad \;|\; begingroup \descr{statement list} \descr{expression} endgroup$\\
$\tt \qquad \;|\; \descr{ÏÐÅÒÁÔÏÒ 0-ÕÒÏ×ÎÑ}$\\
%%$\tt \qquad \;|\; \descr{nullary op}$\\
$\tt \qquad \;|\; btex \descr{ËÏÍÁÎÄÙ ÐÅÞÁÔÉ} etex$\\
%%$\tt \qquad \;|\; btex \descr{typesetting commands} etex$\\
$\tt \qquad \;|\; \descr{ÐÓÅ×ÄÏÆÕÎËÃÉÑ}$\\
%%$\tt \qquad \;|\; \descr{pseudo function}$\\
$\tt \descr{ÐÅÒ×ÉÞÎÏÓÔØ} \rightarrow \descr{ÁÔÏÍ}$\\
%%$\tt \descr{primary} \rightarrow \descr{atom}$\\
$\tt \qquad \;|\; \hbox{\tt (}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,} \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; \hbox{\tt (}\descr{numeric expression}\hbox{\tt ,} \descr{numeric expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; \hbox{\tt (}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,} \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,} \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; \hbox{\tt (}\descr{numeric expression}\hbox{\tt ,} \descr{numeric expression}\hbox{\tt ,} \descr{numeric expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; \descr{of-ÏÐÅÒÁÔÏÒ} \descr{×ÙÒÁÖÅÎÉÅ} of \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{of operator} \descr{expression} of \descr{primary}$\\
$\tt \qquad \;|\; \descr{ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{unary op} \descr{primary}$\\
$\tt \qquad \;|\; str \descr{ÓÕÆÆÉËÓ}$\\
%%$\tt \qquad \;|\; str \descr{suffix}$\\
$\tt \qquad \;|\; z \descr{ÓÕÆÆÉËÓ}$\\
%%$\tt \qquad \;|\; z \descr{suffix}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ}\hbox{\tt [}\descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,}\descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt ]}$\\
%%$\tt \qquad \;|\; \descr{numeric atom}\hbox{\tt [}\descr{expression}\hbox{\tt ,}\descr{expression}\hbox{\tt ]}$\\
$\tt \qquad \;|\; \descr{ÏÐÅÒÁÃÉÑ ÓËÁÌÑÒÎÏÇÏ ÕÍÎÏÖÅÎÉÑ} \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{scalar multiplication op} \descr{primary}$\\
$\tt \descr{×ÔÏÒÉÞÎÏÓÔØ} \rightarrow \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \descr{secondary} \rightarrow \descr{primary}$\\
$\tt \qquad \;|\; \descr{×ÔÏÒÉÞÎÏÓÔØ} \descr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{secondary} \descr{primary binop} \descr{primary}$\\
$\tt \qquad \;|\; \descr{×ÔÏÒÉÞÎÏÓÔØ} \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ}$\\
%%$\tt \qquad \;|\; \descr{secondary} \descr{transformer}$\\
$\tt \descr{ÔÒÅÔÉÞÎÏÓÔØ} \rightarrow \descr{×ÔÏÒÉÞÎÏÓÔØ}$\\
%%$\tt \descr{tertiary} \rightarrow \descr{secondary}$\\
$\tt \qquad \;|\; \descr{ÔÒÅÔÉÞÎÏÓÔØ} \descr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \descr{×ÔÏÒÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{tertiary} \descr{secondary binop} \descr{secondary}$\\
$\tt \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ} \rightarrow \descr{ÔÒÅÔÉÞÎÏÓÔØ}$\\
%%$\tt \descr{subexpression} \rightarrow \descr{tertiary}$\\
$\tt \qquad \;|\; \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÓÏÅÄÉÎÅÎÉÅ ÐÕÔÅÊ} \descr{ÕÚÅÌ ÐÕÔÉ}$\\
%%$\tt \qquad \;|\; \descr{path expression} \descr{path join} \descr{path knot}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ} \rightarrow \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{expression} \rightarrow \descr{subexpression}$\\
$\tt \qquad \;|\; \descr{×ÙÒÁÖÅÎÉÅ} \descr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \descr{ÔÒÅÔÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{expression} \descr{tertiary binop} \descr{tertiary}$\\
$\tt \qquad \;|\; \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ ÐÕÔÉ} \descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ}$\\
%%$\tt \qquad \;|\; \descr{path subexpression} \descr{direction specifier}$\\
$\tt \qquad \;|\; \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ ÐÕÔÉ} \descr{ÓÏÅÄÉÎÅÎÉÅ ÐÕÔÅÊ} cycle$\\
%%$\tt \qquad \;|\; \descr{path subexpression} \descr{path join} cycle$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ÕÚÅÌ ÐÕÔÉ} \rightarrow \descr{ÔÒÅÔÉÞÎÏÓÔØ}$\\
%%$\tt \descr{path knot} \rightarrow \descr{tertiary}$\\
$\tt \descr{ÓÏÅÄÉÎÅÎÉÅ ÐÕÔÅÊ} \rightarrow -{}-$\\
%%$\tt \descr{path join} \rightarrow --$\\
$\tt \qquad \;|\; \descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ} \descr{ÂÁÚÏ×ÏÅ ÓÏÅÄÉÎÅÎÉÅ ÐÕÔÅÊ} \descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ}$\\
%%$\tt \qquad \;|\; \descr{direction specifier} \descr{basic path join} \descr{direction specifier}$\\
$\tt \descr{ÕËÁÚÁÔÅÌØ ÎÁÐÒÁ×ÌÅÎÉÑ} \rightarrow \descr{ÐÕÓÔÏ}$\\
%%$\tt \descr{direction specifier} \rightarrow \descr{empty}$\\
$\tt \qquad \;|\; \{{curl \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\}}$\\
%%$\tt \qquad \;|\; \char`\{curl \descr{numeric expression}\char`\}$\\
$\tt \qquad \;|\; \{{\descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\}}$\\
%%$\tt \qquad \;|\; \char`\{\descr{pair expression}\char`\}$\\
$\tt \qquad \;|\; \{{\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\}}$\\
%%$\tt \qquad \;|\; \char`\{\descr{numeric expression}\hbox{\tt ,}\descr{numeric expression}\char`\}$\\
$\tt \descr{ÂÁÚÏ×ÏÅ ÓÏÅÄÉÎÅÎÉÅ ÐÕÔÅÊ} \rightarrow \hbox{\tt ..} \;|\; \hbox{\tt ...} \;|\; \hbox{\tt ..}\descr{ÎÁÐÒÑÖÅÎÉÅ}\hbox{\tt ..} \;|\; \hbox{\tt ..}\descr{ÕÐÒÁ×ÌÅÎÉÅ}\hbox{\tt ..}$\\
%%$\tt \descr{basic path join} \rightarrow \hbox{\tt ..} \;|\; \hbox{\tt ...} \;|\; \hbox{\tt ..}\descr{tension}\hbox{\tt ..} \;|\; \hbox{\tt ..}\descr{controls}\hbox{\tt ..}$\\
$\tt \descr{ÎÁÐÒÑÖÅÎÉÅ} \rightarrow tension \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \descr{tension} \rightarrow tension \descr{numeric primary}$\\
$\tt \qquad \;|\; tension \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ} and \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; tension \descr{numeric primary} and \descr{numeric primary}$\\
$\tt \descr{ÕÐÒÁ×ÌÅÎÉÅ} \rightarrow controls \descr{ÐÅÒ×ÉÞÎÏÓÔØ-ÐÁÒÁ}$\\
%%$\tt \descr{controls} \rightarrow controls \descr{pair primary}$\\
$\tt \qquad \;|\; controls \descr{ÐÅÒ×ÉÞÎÏÓÔØ-ÐÁÒÁ} and \descr{ÐÅÒ×ÉÞÎÏÓÔØ-ÐÁÒÁ}$\\
%%$\tt \qquad \;|\; controls \descr{pair primary} and \descr{pair primary}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ÁÒÇÕÍÅÎÔ} \rightarrow \descr{ÓÉÍ×ÏÌÉÞÅÓËÉ ÚÎÁË}$\\
%%$\tt \descr{argument} \rightarrow \descr{symbolic token}$\\
$\tt \descr{ÞÉÓÌÏ ÉÌÉ ÄÒÏÂØ} \rightarrow \descr{ÞÉÓÌÏ}\hbox{\tt /}\descr{ÞÉÓÌÏ}$\\
%%$\tt \descr{number or fraction} \rightarrow \descr{number}\hbox{\tt /}\descr{number}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ, ÚÁ ËÏÔÏÒÙÍ ÎÅÔ `\hbox{\tt /}\tdescr{ÞÉÓÌÏ}'}$\\
%%$\tt \qquad \;|\; \descr{number not followed by `\hbox{\tt /}\tdescr{number}'}$\\
$\tt \descr{ÏÐÅÒÁÃÉÑ ÓËÁÌÑÒÎÏÇÏ ÕÍÎÏÖÅÎÉÑ} \rightarrow + \;|\; -$\\
%%$\tt \descr{scalar multiplication op} \rightarrow + \;|\; -$\\
$\tt \qquad \;|\; \descr{`\tdescr{ÞÉÓÌÏ ÉÌÉ ÄÒÏÂØ}', ÚÁ ËÏÔÏÒÙÍ ÎÅÔ `\tdescr{ÏÐÅÒÁÃÉÉ ÓÌÏÖÅÎÉÑ}\tdescr{ÞÉÓÌÏ}'}$
%%$\tt \qquad \;|\; \descr{`\tdescr{number or fraction}' not followed by `\tdescr{add op}\tdescr{number}'}$
\end{ctabbing}
\caption{þÁÓÔØ 1 ÓÉÎÔÁËÓÉÓÁ ×ÙÒÁÖÅÎÉÊ}
%%\caption{Part 1 of the syntax for expressions}
\index{×ÙÒÁÖÅÎÉÅ?\tdescr{×ÙÒÁÖÅÎÉÅ}}\index{ÏÐÅÒÁÔÏÒ 0?\tdescr{ÏÐÅÒÁÔÏÒ 0-ÕÒÏ×ÎÑ}}\index{of operator?\tdescr{of-ÏÐÅÒÁÔÏÒ}}%
\index{ÕÚÅÌ ÐÕÔÉ?\tdescr{ÕÚÅÌ ÐÕÔÉ}}\index{ÐÅÒ×ÉÞÎÏÓÔØ?\tdescr{ÐÅÒ×ÉÞÎÏÓÔØ}}\index{ÐÅÒ×ÉÞÎÙÊ binop?\tdescr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}%
\index{×ÔÏÒÉÞÎÏÓÔØ?\tdescr{×ÔÏÒÉÞÎÏÓÔØ}}\index{×ÔÏÒÉÞÎÙÊ binop?\tdescr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}\index{ÓÕÆÆÉËÓ?\tdescr{ÓÕÆÆÉËÓ}}%
\index{ÔÒÅÔÉÞÎÏÓÔØ?\tdescr{ÔÒÅÔÉÞÎÏÓÔØ}}\index{ÔÒÅÔÉÞÎÙÊ binop?\tdescr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}\index{ÕÎÁÒÎÙÊ op?\tdescr{ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}%
%%\index{expression?\tdescr{expression}}\index{nullary op?\tdescr{nullary op}}\index{of operator?\tdescr{of operator}}%
%%\index{path knot?\tdescr{path knot}}\index{primary?\tdescr{primary}}\index{primary binop?\tdescr{primary binop}}%
%%\index{secondary?\tdescr{secondary}}\index{secondary binop?\tdescr{secondary binop}}\index{suffix?\tdescr{suffix}}%
%%\index{tertiary?\tdescr{tertiary}}\index{tertiary binop?\tdescr{tertiary binop}}\index{unary op?\tdescr{unary op}}%
\label{syexpr1}
\end{figure}

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ} \rightarrow rotated \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \descr{transformer} \rightarrow rotated \descr{numeric primary}$\\
$\tt \qquad \;|\; scaled \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; scaled \descr{numeric primary}$\\
$\tt \qquad \;|\; shifted \descr{ÐÅÒ×ÉÞÎÏÓÔØ-ÐÁÒÁ}$\\
%%$\tt \qquad \;|\; shifted \descr{pair primary}$\\
$\tt \qquad \;|\; slanted \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; slanted \descr{numeric primary}$\\
$\tt \qquad \;|\; transformed \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ-ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; transformed \descr{transform primary}$\\
$\tt \qquad \;|\; xscaled \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; xscaled \descr{numeric primary}$\\
$\tt \qquad \;|\; yscaled \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \qquad \;|\; yscaled \descr{numeric primary}$\\
$\tt \qquad \;|\; zscaled \descr{ÐÅÒ×ÉÞÎÏÓÔØ-ÐÁÒÁ}$\\
%%$\tt \qquad \;|\; zscaled \descr{pair primary}$\\
$\tt \qquad \;|\; reflectedabout\hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; reflectedabout\hbox{\tt (}\descr{pair expression}\hbox{\tt ,} \descr{pair expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; rotatedaround\hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; rotatedaround\hbox{\tt (}\descr{pair expression}\hbox{\tt ,} \descr{numeric expression}\hbox{\tt )}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ÏÐÅÒÁÔÏÒ 0-ÕÒÏ×ÎÑ} \rightarrow false \;|\; normaldeviate \;|\; nullpen \;|\; nullpicture \;|\; pencircle$\\
%%$\tt \descr{nullary op} \rightarrow false \;|\; normaldeviate \;|\; nullpen \;|\; nullpicture \;|\; pencircle$\\
$\tt \qquad \;|\; true \;|\; whatever$\\
$\tt \descr{ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \rightarrow \descr{ÔÉÐ}$\\
%%$\tt \descr{unary op} \rightarrow \descr{type}$\\
$\tt \qquad \;|\; abs \;|\; angle \;|\; arclength \;|\; ASCII \;|\; bbox \;|\; blackpart \;|\; bluepart \;|\; bot \;|\; bounded$\\
$\tt \qquad \;|\; ceiling \;|\; center \;|\; char \;|\; clipped \;|\; colormodel \;|\; cosd \;|\; cyanpart  \;|\; cycle$\\
$\tt \qquad \;|\; dashpart \;|\; decimal \;|\; dir \;|\; floor \;|\; filled \;|\; fontpart \;|\; fontsize$\\
$\tt \qquad \;|\; greenpart \;|\; greypart \;|\; hex \;|\; inverse \;|\; known \;|\; length \;|\; lft \;|\; llcorner$\\
$\tt \qquad \;|\; lrcorner\;|\; magentapart \;|\; makepath \;|\; makepen \;|\; mexp \;|\; mlog \;|\; not \;|\; oct \;|\; odd$\\
$\tt \qquad \;|\; pathpart \;|\; penpart \;|\; readfrom \;|\; redpart \;|\; reverse \;|\; round \;|\; rt \;|\; sind \;|\; sqrt$\\
$\tt \qquad  \;|\; stroked \;|\; textpart \;|\; textual \;|\; top \;|\; ulcorner$\\
$\tt \qquad \;|\; uniformdeviate \;|\; unitvector \;|\; unknown \;|\; urcorner \;|\; xpart \;|\; xxpart$\\
$\tt \qquad \;|\; xypart \;|\; yellowpart \;|\; ypart \;|\; yxpart \;|\; yypart$\\
$\tt \descr{ÔÉÐ} \rightarrow boolean \;|\; cmykcolor \;|\; color \;|\; numeric \;|\; pair$\\
%%$\tt \descr{type} \rightarrow boolean \;|\; cmykcolor \;|\; color \;|\; numeric \;|\; pair$\\
$\tt \qquad \;|\; path \;|\; pen \;|\; picture \;|\; rgbcolor \;|\; string \;|\; transform$\\
$\tt \descr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \rightarrow \hbox{\tt *} \;|\; \hbox{\tt /} \;|\; \hbox{\tt **} \;|\; and$\\
%%$\tt \descr{primary binop} \rightarrow \hbox{\tt *} \;|\; \hbox{\tt /} \;|\; \hbox{\tt **} \;|\; and$\\
$\tt \qquad \;|\; dotprod \;|\; div \;|\; infont \;|\; mod$\\
$\tt \descr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \rightarrow + \;|\; - \;|\; ++ \;|\; +-+ \;|\; or$\\
%%$\tt \descr{secondary binop} \rightarrow + \;|\; - \;|\; ++ \;|\; +-+ \;|\; or$\\
$\tt \qquad \;|\; intersectionpoint \;|\; intersectiontimes$\\
$\tt \descr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ} \rightarrow \hbox{\tt \&} \;|\; \hbox{\verb|<|} \;|\; \hbox{\verb|<=|} \;|\; \hbox{\verb|<>|} \;|\; \hbox{\tt =} \;|\; \hbox{\verb|>|} \;|\; \hbox{\verb|>=|}$\\
%%$\tt \descr{tertiary binop} \rightarrow \hbox{\tt \&} \;|\; \hbox{\verb|<|} \;|\; \hbox{\verb|<=|} \;|\; \hbox{\verb|<>|} \;|\; \hbox{\tt =} \;|\; \hbox{\verb|>|} \;|\; \hbox{\verb|>=|}$\\
$\tt \qquad \;|\; cutafter \;|\; cutbefore$\\
$\tt \descr{of-ÏÐÅÒÁÔÏÒ} \rightarrow arctime \;|\; direction \;|\; directiontime \;|\; directionpoint$\\
%%$\tt \descr{of operator} \rightarrow arctime \;|\; direction \;|\; directiontime \;|\; directionpoint$\\
$\tt \qquad \;|\; penoffset \;|\; point \;|\; postcontrol \;|\; precontrol \;|\; subpath$\\
$\tt \qquad \;|\; substring$\\
$\tt $\\
$\tt \descr{ÐÅÒÅÍÅÎÎÁÑ} \rightarrow \descr{ÜÔÉËÅÔËÁ}\descr{ÓÕÆÆÉËÓ}$\\
%%$\tt \descr{variable} \rightarrow \descr{tag}\descr{suffix}$\\
$\tt \descr{ÓÕÆÆÉËÓ} \rightarrow \descr{ÐÕÓÔÏ} \;|\; \descr{ÓÕÆÆÉËÓ}\descr{ÉÎÄÅËÓ} \;|\; \descr{ÓÕÆÆÉËÓ}\descr{ÜÔÉËÅÔËÁ}$\\
%%$\tt \descr{suffix} \rightarrow \descr{empty} \;|\; \descr{suffix}\descr{subscript} \;|\; \descr{suffix}\descr{tag}$\\
$\tt \qquad \;|\; \descr{ÐÁÒÁÍÅÔÒ-ÓÕÆÆÉËÓ}$\\
%%$\tt \qquad \;|\; \descr{suffix parameter}$\\
$\tt \descr{ÉÎÄÅËÓ} \rightarrow \descr{ÞÉÓÌÏ} \;|\; \hbox{\tt [}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ]}$\\
%%$\tt \descr{subscript} \rightarrow \descr{number} \;|\; \hbox{\tt [}\descr{numeric expression}\hbox{\tt ]}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{×ÎÕÔÒÅÎÎÑÑ ÐÅÒÅÍÅÎÎÁÑ} \rightarrow ahangle \;|\; ahlength \;|\; bboxmargin$\\
%%$\tt \descr{internal variable} \rightarrow ahangle \;|\; ahlength \;|\; bboxmargin$\\
$\tt \qquad \;|\; charcode \;|\; day \;|\; defaultcolormodel \;|\; defaultpen \;|\; defaultscale$\\
$\tt \qquad \;|\; labeloffset \;|\; linecap \;|\; linejoin \;|\; miterlimit \;|\; month$\\
$\tt \qquad \;|\; pausing \;|\; prologues \;|\; showstopping \;|\; time \;|\; tracingoutput$\\
$\tt \qquad \;|\; tracingcapsules \;|\; tracingchoices \;|\; tracingcommands$\\
$\tt \qquad \;|\; tracingequations \;|\; tracinglostchars \;|\; tracingmacros$\\
$\tt \qquad \;|\; tracingonline \;|\; tracingrestores \;|\; tracingspecs$\\
$\tt \qquad \;|\; tracingstats \;|\; tracingtitles \;|\; truecorners$\\
$\tt \qquad \;|\; warningcheck \;|\; year$\\
$\tt \qquad \;|\; \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË, ÏÐÒÅÄÅÌÅÎÎÙÊ {\tt newinternal}}$
%%$\tt \qquad \;|\; \descr{symbolic token defined by {\tt newinternal}}$
\end{ctabbing}
\caption{þÁÓÔØ 2 ÓÉÎÔÁËÓÉÓÁ ×ÙÒÁÖÅÎÉÊ}
%%\caption{Part 2 of the syntax for expressions}
\index{ÏÐÅÒÁÔÏÒ 0?\tdescr{ÏÐÅÒÁÔÏÒ 0-ÕÒÏ×ÎÑ}}\index{of operator?\tdescr{of-ÏÐÅÒÁÔÏÒ}}\index{ÐÅÒ×ÉÞÎÙÊ binop?\tdescr{ÐÅÒ×ÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}%
\index{×ÔÏÒÉÞÎÙÊ binop?\tdescr{×ÔÏÒÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}\index{ÉÎÄÅËÓ?\tdescr{ÉÎÄÅËÓ}}\index{ÓÕÆÆÉËÓ?\tdescr{ÓÕÆÆÉËÓ}}%
\index{ÔÒÅÔÉÞÎÙÊ binop?\tdescr{ÔÒÅÔÉÞÎÙÊ ÂÉÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}\index{ÕÎÁÒÎÙÊ op?\tdescr{ÕÎÁÒÎÙÊ ÏÐÅÒÁÔÏÒ}}%
%%\index{nullary op?\tdescr{nullary op}}\index{of operator?\tdescr{of operator}}\index{primary binop?\tdescr{primary binop}}%
%%\index{secondary binop?\tdescr{secondary binop}}\index{subscript?\tdescr{subscript}}\index{suffix?\tdescr{suffix}}%
%%\index{tertiary binop?\tdescr{tertiary binop}}\index{unary op?\tdescr{unary op}}%
\label{syexpr2}
\end{figure}

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÐÓÅ×ÄÏÆÕÎËÃÉÑ} \rightarrow min\hbox{\tt (}\descr{ÓÐÉÓÏË ×ÙÒÁÖÅÎÉÊ}\hbox{\tt )}$\\
%%$\tt \descr{pseudo function} \rightarrow min\hbox{\tt (}\descr{expression list}\hbox{\tt )}$\\
$\tt \qquad \;|\; max\hbox{\tt (}\descr{ÓÐÉÓÏË ×ÙÒÁÖÅÎÉÊ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; max\hbox{\tt (}\descr{expression list}\hbox{\tt )}$\\
$\tt \qquad \;|\; incr\hbox{\tt (}\descr{ÞÉÓÌÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; incr\hbox{\tt (}\descr{numeric variable}\hbox{\tt )}$\\
$\tt \qquad \;|\; decr\hbox{\tt (}\descr{ÞÉÓÌÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; decr\hbox{\tt (}\descr{numeric variable}\hbox{\tt )}$\\
$\tt \qquad \;|\; dashpattern\hbox{\tt (}\descr{ÓÐÉÓÏË on\hbox{\tt /}off}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; dashpattern\hbox{\tt (}\descr{on\hbox{\tt /}off list}\hbox{\tt )}$\\
$\tt \qquad \;|\; interpath\hbox{\tt (}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; interpath\hbox{\tt (}\descr{numeric expression}\hbox{\tt ,} \descr{path expression}\hbox{\tt ,} \descr{path expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; buildcycle\hbox{\tt (}\descr{ÓÐÉÓÏË ×ÙÒÁÖÅÎÉÊ-ÐÕÔÅÊ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; buildcycle\hbox{\tt (}\descr{path expression list}\hbox{\tt )}$\\
$\tt \qquad \;|\; thelabel\descr{ÓÕÆÆÉËÓ ÍÅÔËÉ}\hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; thelabel\descr{label suffix}\hbox{\tt (}\descr{expression}\hbox{\tt ,} \descr{pair expression}\hbox{\tt )}$\\
$\tt \descr{ÓÐÉÓÏË ×ÙÒÁÖÅÎÉÊ-ÐÕÔÅÊ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}$\\
%%$\tt \descr{path expression list} \rightarrow \descr{path expression}$\\
$\tt \qquad \;|\; \descr{ÓÐÉÓÏË ×ÙÒÁÖÅÎÉÊ-ÐÕÔÅÊ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}$\\
%%$\tt \qquad \;|\; \descr{path expression list}\hbox{\tt ,} \descr{path expression}$\\
$\tt \descr{ÓÐÉÓÏË on\hbox{\tt /}off} \rightarrow \descr{ÓÐÉÓÏË on\hbox{\tt /}off}\descr{ÐÕÎËÔ on\hbox{\tt /}off} \;|\; \descr{ÐÕÎËÔ on\hbox{\tt /}off}$\\
%%$\tt \descr{on\hbox{\tt /}off list} \rightarrow \descr{on\hbox{\tt /}off list}\descr{on\hbox{\tt /}off clause} \;|\; \descr{on\hbox{\tt /}off clause}$\\
$\tt \descr{ÐÕÎËÔ on\hbox{\tt /}off} \rightarrow on \descr{ÞÉÓÌÏ×ÁÑ ÔÒÅÔÉÞÎÏÓÔØ} \;|\; off \descr{ÞÉÓÌÏ×ÁÑ ÔÒÅÔÉÞÎÏÓÔØ}$
%%$\tt \descr{on\hbox{\tt /}off clause} \rightarrow on \descr{numeric tertiary} \;|\; off \descr{numeric tertiary}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÍÁËÒÏÓÏ×, ÐÏÈÏÖÉÈ ÎÁ ÆÕÎËÃÉÉ}
%%\caption{The syntax for function-like macros}
\index{label suffix?\tdescr{ÓÕÆÆÉËÓ ÍÅÔËÉ}}%
%%\index{label suffix?\tdescr{label suffix}}%
\label{sypseudo}
\end{figure}

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{boolean expression} \rightarrow \descr{expression}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ-cmyk-Ã×ÅÔ } \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{cmykcolor expression} \rightarrow \descr{expression}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ-Ã×ÅÔ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{color expression} \rightarrow \descr{expression}$\\
$\tt \descr{ÞÉÓÌÏ×ÏÊ ÁÔÏÍ} \rightarrow \descr{ÁÔÏÍ}$\\
%%$\tt \descr{numeric atom} \rightarrow \descr{atom}$\\
$\tt \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{numeric expression} \rightarrow \descr{expression}$\\
$\tt \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒ×ÉÞÎÏÓÔØ} \rightarrow \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \descr{numeric primary} \rightarrow \descr{primary}$\\
$\tt \descr{ÞÉÓÌÏ×ÁÑ ÔÒÅÔÉÞÎÏÓÔØ} \rightarrow \descr{ÔÒÅÔÉÞÎÏÓÔØ}$\\
%%$\tt \descr{numeric tertiary} \rightarrow \descr{tertiary}$\\
$\tt \descr{ÞÉÓÌÏ×ÁÑ ÐÅÒÅÍÅÎÎÁÑ} \rightarrow \descr{ÐÅÒÅÍÅÎÎÁÑ} \;|\; \descr{×ÎÕÔÒÅÎÎÑÑ ÐÅÒÅÍÅÎÎÁÑ}$\\
%%$\tt \descr{numeric variable} \rightarrow \descr{variable} \;|\; \descr{internal variable}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{pair expression} \rightarrow \descr{expression}$\\
$\tt \descr{ÐÁÒÁ-ÐÅÒ×ÉÞÎÏÓÔØ} \rightarrow \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$\\
%%$\tt \descr{pair primary} \rightarrow \descr{primary}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{path expression} \rightarrow \descr{expression}$\\
$\tt \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \rightarrow \descr{ÐÏÄ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{path subexpression} \rightarrow \descr{subexpression}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{pen expression} \rightarrow \descr{expression}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{picture expression} \rightarrow \descr{expression}$\\
$\tt \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ} \rightarrow \descr{ÐÅÒÅÍÅÎÎÁÑ}$\\
%%$\tt \descr{picture variable} \rightarrow \descr{variable}$\\
$\tt \descr{×ÙÒÁÖÅÎÉÅ-rgb-Ã×ÅÔ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{rgbcolor expression} \rightarrow \descr{expression}$\\
$\tt \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{string expression} \rightarrow \descr{expression}$\\
$\tt \descr{ÐÁÒÁÍÅÔÒ-ÓÕÆÆÉËÓ} \rightarrow \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \descr{suffix parameter} \rightarrow \descr{parameter}$\\
$\tt \descr{ÔÒÁÎÓÆÏÒÍÁÃÉÑ-ÐÅÒ×ÉÞÎÏÓÔØ} \rightarrow \descr{ÐÅÒ×ÉÞÎÏÓÔØ}$
%%$\tt \descr{transform primary} \rightarrow \descr{primary}$
\end{ctabbing}
\caption{òÁÚÌÉÞÎÙÅ ÐÒÁ×ÉÌÁ, ÎÕÖÎÙÅ ÄÌÑ ÚÁ×ÅÒÛÅÎÉÑ îæâî}
%%\caption{Miscellaneous productions needed to complete the BNF}
\label{sytypexpr}
\end{figure}

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÐÒÏÇÒÁÍÍÁ} \rightarrow \descr{ÓÐÉÓÏË ÍÅÔÁËÏÍÁÎÄ} end$\\
%%$\tt \descr{program} \rightarrow \descr{statement list} end$\\
$\tt \descr{ÓÐÉÓÏË ÍÅÔÁËÏÍÁÎÄ} \rightarrow \descr{ÐÕÓÔÏ} \;|\; \descr{ÓÐÉÓÏË ÍÅÔÁËÏÍÁÎÄ} \hbox{\tt ;} \descr{ÍÅÔÁËÏÍÁÎÄÁ}$\\
%%$\tt \descr{statement list} \rightarrow \descr{empty} \;|\; \descr{statement list} \hbox{\tt ;} \descr{statement}$\\
$\tt \descr{ÍÅÔÁËÏÍÁÎÄÁ} \rightarrow \descr{ÐÕÓÔÏ}$\\
%%$\tt \descr{statement} \rightarrow \descr{empty}$\\
$\tt \qquad \;|\; \descr{ÕÒÁ×ÎÅÎÉÅ} \;|\; \descr{ÐÒÉÓ×ÁÉ×ÁÎÉÅ}$\\
%%$\tt \qquad \;|\; \descr{equation} \;|\; \descr{assignment}$\\
$\tt \qquad \;|\; \descr{ÄÅËÌÁÒÁÃÉÑ} \;|\; \descr{ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ}$\\
%%$\tt \qquad \;|\; \descr{declaration} \;|\; \descr{macro definition}$\\
$\tt \qquad \;|\; \descr{ÂÌÏË} \;|\; \descr{ÐÓÅ×ÄÏÐÒÏÃÅÄÕÒÁ}$\\
%%$\tt \qquad \;|\; \descr{compound} \;|\; \descr{pseudo procedure}$\\
$\tt \qquad \;|\; \descr{ËÏÍÁÎÄÁ}$\\
%%$\tt \qquad \;|\; \descr{command}$\\
$\tt \descr{ÂÌÏË} \rightarrow begingroup \descr{ÓÐÉÓÏË ÍÅÔÁËÏÍÁÎÄ} endgroup$\\
%%$\tt \descr{compound} \rightarrow begingroup \descr{statement list} endgroup$\\
$\tt \qquad \;|\; beginfig\hbox{\tt (}\descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}\hbox{\tt );} \descr{ÓÐÉÓÏË ÍÅÔÁËÏÍÁÎÄ}\hbox{\tt ;} endfig$\\
%%$\tt \qquad \;|\; beginfig\hbox{\tt (}\descr{numeric expression}\hbox{\tt );} \descr{statement list}\hbox{\tt ;} endfig$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ÕÒÁ×ÎÅÎÉÅ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ} \hbox{\tt =} \descr{ÐÒÁ×ÁÑ ÞÁÓÔØ}$\\
%%$\tt \descr{equation} \rightarrow \descr{expression} \hbox{\tt =} \descr{right-hand side}$\\
$\tt \descr{ÐÒÉÓ×ÁÉ×ÁÎÉÅ} \rightarrow \descr{ÐÅÒÅÍÅÎÎÁÑ} \hbox{\tt :=} \descr{ÐÒÁ×ÁÑ ÞÁÓÔØ}$\\
%%$\tt \descr{assignment} \rightarrow \descr{variable} \hbox{\tt :=} \descr{right-hand side}$\\
$\tt \qquad \;|\; \descr{×ÎÕÔÒÅÎÎÑÑ ÐÅÒÅÍÅÎÎÁÑ} \hbox{\tt :=} \descr{ÐÒÁ×ÁÑ ÞÁÓÔØ}$\\
%%$\tt \qquad \;|\; \descr{internal variable} \hbox{\tt :=} \descr{right-hand side}$\\
$\tt \descr{ÐÒÁ×ÁÑ ÞÁÓÔØ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ} \;|\; \descr{ÕÒÁ×ÎÅÎÉÅ} \;|\; \descr{ÐÒÉÓ×ÁÉ×ÁÎÉÅ}$\\
%%$\tt \descr{right-hand side} \rightarrow \descr{expression} \;|\; \descr{equation} \;|\; \descr{assignment}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ÄÅËÌÁÒÁÃÉÑ} \rightarrow \descr{ÔÉÐ} \descr{ÓÐÉÓÏË ÄÅËÌÁÒÁÃÉÉ}$\\
%%$\tt \descr{declaration} \rightarrow \descr{type} \descr{declaration list}$\\
$\tt \descr{ÓÐÉÓÏË ÄÅËÌÁÒÁÃÉÉ} \rightarrow \descr{ÏÂÏÂÝÅÎÉÅ ÐÅÒÅÍÅÎÎÏÊ}$\\
%%$\tt \descr{declaration list} \rightarrow \descr{generic variable}$\\
$\tt \qquad \;|\; \descr{ÓÐÉÓÏË ÄÅËÌÁÒÁÃÉÉ}\hbox{\tt ,} \descr{ÏÂÏÂÝÅÎÉÅ ÐÅÒÅÍÅÎÎÏÊ}$\\
%%$\tt \qquad \;|\; \descr{declaration list}\hbox{\tt ,} \descr{generic variable}$\\
$\tt \descr{ÏÂÏÂÝÅÎÉÅ ÐÅÒÅÍÅÎÎÏÊ} \rightarrow \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \descr{ÏÂÏÂÝÅÎÉÅ ÓÕÆÆÉËÓÁ}$\\
%%$\tt \descr{generic variable} \rightarrow \descr{symbolic token} \descr{generic suffix}$\\
$\tt \descr{ÏÂÏÂÝÅÎÉÅ ÓÕÆÆÉËÓÁ} \rightarrow \descr{ÐÕÓÔÏ} \;|\; \descr{ÏÂÏÂÝÅÎÉÅ ÓÕÆÆÉËÓÁ} \descr{ÜÔÉËÅÔËÁ}$\\
%%$\tt \descr{generic suffix} \rightarrow \descr{empty} \;|\; \descr{generic suffix} \descr{tag}$\\
$\tt \qquad \;|\; \descr{ÏÂÏÂÝÅÎÉÅ ÓÕÆÆÉËÓÁ} \hbox{\tt []}$\\
%%$\tt \qquad \;|\; \descr{generic suffix} \hbox{\tt []}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ÏÐÒÅÄÅÌÅÎÉÅ ÍÁËÒÏÓÁ} \rightarrow \descr{ÚÁÇÏÌÏ×ÏË ÍÁËÒÏÓÁ} \hbox{\tt =} \descr{ÔÅËÓÔ ÚÁÍÅÎÙ} enddef$\\
%%$\tt \descr{macro definition} \rightarrow \descr{macro heading} \hbox{\tt =} \descr{replacement text} enddef$\\
$\tt \descr{ÚÁÇÏÌÏ×ÏË ÍÁËÒÏÓÁ} \rightarrow def \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \descr{ÎÅÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}$\\
%%$\tt \descr{macro heading} \rightarrow def \descr{symbolic token} \descr{delimited part} \descr{undelimited part}$\\
$\tt \qquad \;|\; vardef \descr{ÏÂÏÂÝÅÎÉÅ ÐÅÒÅÍÅÎÎÏÊ} \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \descr{ÎÅÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}$\\
%%$\tt \qquad \;|\; vardef \descr{generic variable} \descr{delimited part} \descr{undelimited part}$\\
$\tt \qquad \;|\; vardef \descr{ÏÂÏÂÝÅÎÉÅ ÐÅÒÅÍÅÎÎÏÊ} \hbox{\verb|@#|} \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \descr{ÎÅÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}$\\
%%$\tt \qquad \;|\; vardef \descr{generic variable} \hbox{\verb|@#|} \descr{delimited part} \descr{undelimited part}$\\
$\tt \qquad \;|\; \descr{ÏÐÒÅÄÅÌÅÎÉÅ ÂÉÎÁÒÎÏÓÔÉ} \descr{ÐÁÒÁÍÅÔÒ} \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \qquad \;|\; \descr{binary def} \descr{parameter} \descr{symbolic token} \descr{parameter}$\\
$\tt \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \rightarrow \descr{ÐÕÓÔÏ}$\\
%%$\tt \descr{delimited part} \rightarrow \descr{empty}$\\
$\tt \qquad \;|\; \descr{ÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ}\hbox{\tt (}\descr{ÔÉÐ ÐÁÒÁÍÅÔÒÁ} \descr{ÐÁÒÁÍÅÔÒÙ-ÚÎÁËÉ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; \descr{delimited part}\hbox{\tt (}\descr{parameter type} \descr{parameter tokens}\hbox{\tt )}$\\
$\tt \descr{ÔÉÐ ÐÁÒÁÍÅÔÒÁ} \rightarrow expr \;|\; suffix \;|\; text$\\
%%$\tt \descr{parameter type} \rightarrow expr \;|\; suffix \;|\; text$\\
$\tt \descr{ÐÁÒÁÍÅÔÒÙ-ÚÎÁËÉ} \rightarrow \descr{ÐÁÒÁÍÅÔÒ} \;|\; \descr{ÐÁÒÁÍÅÔÒÙ-ÚÎÁËÉ}\hbox{\tt ,} \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \descr{parameter tokens} \rightarrow \descr{parameter} \;|\; \descr{parameter tokens}\hbox{\tt ,} \descr{parameter}$\\
$\tt \descr{ÐÁÒÁÍÅÔÒ} \rightarrow \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}$\\
%%$\tt \descr{parameter} \rightarrow \descr{symbolic token}$\\
$\tt \descr{ÎÅÏÔÄÅÌÅÎÎÁÑ ÞÁÓÔØ} \rightarrow \descr{ÐÕÓÔÏ}$\\
%%$\tt \descr{undelimited part} \rightarrow \descr{empty}$\\
$\tt \qquad \;|\; \descr{ÔÉÐ ÐÁÒÁÍÅÔÒÁ} \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \qquad \;|\; \descr{parameter type} \descr{parameter}$\\
$\tt \qquad \;|\; \descr{ÕÒÏ×ÅÎØ ÐÒÉÏÒÉÔÅÔÁ} \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \qquad \;|\; \descr{precedence level} \descr{parameter}$\\
$\tt \qquad \;|\; expr \descr{ÐÁÒÁÍÅÔÒ} of \descr{ÐÁÒÁÍÅÔÒ}$\\
%%$\tt \qquad \;|\; expr \descr{parameter} of \descr{parameter}$\\
$\tt \descr{ÕÒÏ×ÅÎØ ÐÒÉÏÒÉÔÅÔÁ} \rightarrow primary \;|\; secondary \;|\; tertiary$\\
%%$\tt \descr{precedence level} \rightarrow primary \;|\; secondary \;|\; tertiary$\\
$\tt \descr{ÏÐÒÅÄÅÌÅÎÉÅ ÂÉÎÁÒÎÏÓÔÉ} \rightarrow primarydef \;|\; secondarydef \;|\; tertiarydef$\\
%%$\tt \descr{binary def} \rightarrow primarydef \;|\; secondarydef \;|\; tertiarydef$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ÐÓÅ×ÄÏÐÒÏÃÅÄÕÒÁ} \rightarrow drawoptions\hbox{\tt (}\descr{ÓÐÉÓÏË ÏÐÃÉÊ}\hbox{\tt )}$\\
%%$\tt \descr{pseudo procedure} \rightarrow drawoptions\hbox{\tt (}\descr{option list}\hbox{\tt )}$\\
$\tt \qquad \;|\; label\descr{ÓÕÆÆÉËÓ ÍÅÔËÉ}\hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; label\descr{label suffix}\hbox{\tt (}\descr{expression}\hbox{\tt ,} \descr{pair expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; dotlabel\descr{ÓÕÆÆÉËÓ ÍÅÔËÉ}\hbox{\tt (}\descr{×ÙÒÁÖÅÎÉÅ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ-ÐÁÒÁ}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; dotlabel\descr{label suffix}\hbox{\tt (}\descr{expression}\hbox{\tt ,} \descr{pair expression}\hbox{\tt )}$\\
$\tt \qquad \;|\; labels\descr{ÓÕÆÆÉËÓ ÍÅÔËÉ}\hbox{\tt (}\descr{ÓÐÉÓÏË ÎÏÍÅÒÏ× ÔÏÞÅË}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; labels\descr{label suffix}\hbox{\tt (}\descr{point number list}\hbox{\tt )}$\\
$\tt \qquad \;|\; dotlabels\descr{ÓÕÆÆÉËÓ ÍÅÔËÉ}\hbox{\tt (}\descr{ÓÐÉÓÏË ÎÏÍÅÒÏ× ÔÏÞÅË}\hbox{\tt )}$\\
%%$\tt \qquad \;|\; dotlabels\descr{label suffix}\hbox{\tt (}\descr{point number list}\hbox{\tt )}$\\
$\tt \descr{ÓÐÉÓÏË ÎÏÍÅÒÏ× ÔÏÞÅË} \rightarrow \descr{ÓÕÆÆÉËÓ} \;|\; \descr{ÓÐÉÓÏË ÎÏÍÅÒÏ× ÔÏÞÅË}\hbox{\tt ,} \descr{ÓÕÆÆÉËÓ}$\\
%%$\tt \descr{point number list} \rightarrow \descr{suffix} \;|\; \descr{point number list}\hbox{\tt ,} \descr{suffix}$\\
$\tt \descr{ÓÕÆÆÉËÓ ÍÅÔËÉ} \rightarrow \descr{ÐÕÓÔÏ} \;|\; lft \;|\; rt \;|\; top \;|\; bot \;|\; ulft \;|\; urt \;|\; llft \;|\; lrt$
%%$\tt \descr{label suffix} \rightarrow \descr{empty} \;|\; lft \;|\; rt \;|\; top \;|\; bot \;|\; ulft \;|\; urt \;|\; llft \;|\; lrt$
\end{ctabbing}
\caption{ðÏÌÎÙÊ ÓÉÎÔÁËÓÉÓ ÐÒÏÇÒÁÍÍ MetaPost}
%%\caption{Overall syntax for MetaPost programs}
\index{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ?\tdescr{ÏÂÏÂÝÅÎÎÁÑ ÐÅÒÅÍÅÎÎÁÑ}}\index{label suffix?\tdescr{ÓÕÆÆÉËÓ ÍÅÔËÉ}}\index{ÔÅËÓÔ ÚÁÍÅÎÙ?\tdescr{ÔÅËÓÔ ÚÁÍÅÎÙ}}%
%%\index{suffix?\tdescr{ÓÕÆÆÉËÓ}}%
%%\index{generic variable?\tdescr{generic variable}}\index{label suffix?\tdescr{label suffix}}\index{replacement text?\tdescr{replacement text}}%
%%\index{suffix?\tdescr{suffix}}%
\label{syprog}
\end{figure}

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ËÏÍÁÎÄÁ} \rightarrow clip \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ} to \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}$\\
%%$\tt \descr{command} \rightarrow clip \descr{picture variable} to \descr{path expression}$\\
$\tt \qquad \;|\; interim \descr{×ÎÕÔÒÅÎÎÑÑ ÐÅÒÅÍÅÎÎÁÑ} \hbox{\tt :=} \descr{ÐÒÁ×ÁÑ ÞÁÓÔØ}$\\
%%$\tt \qquad \;|\; interim \descr{internal variable} \hbox{\tt :=} \descr{right-hand side}$\\
$\tt \qquad \;|\; let \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \hbox{\tt =} \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}$\\
%%$\tt \qquad \;|\; let \descr{symbolic token} \hbox{\tt =} \descr{symbolic token}$\\
$\tt \qquad \;|\; newinternal \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×}$\\
%%$\tt \qquad \;|\; newinternal \descr{symbolic token list}$\\
$\tt \qquad \;|\; pickup \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; pickup \descr{expression}$\\
$\tt \qquad \;|\; randomseed \hbox{\tt :=} \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; randomseed \hbox{\tt :=} \descr{numeric expression}$\\
$\tt \qquad \;|\; save \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×}$\\
%%$\tt \qquad \;|\; save \descr{symbolic token list}$\\
$\tt \qquad \;|\; setbounds \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ} to \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ}$\\
%%$\tt \qquad \;|\; setbounds \descr{picture variable} to \descr{path expression}$\\
$\tt \qquad \;|\; shipout \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ}$\\
%%$\tt \qquad \;|\; shipout \descr{picture expression}$\\
$\tt \qquad \;|\; special \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; special \descr{string expression}$\\
$\tt \qquad \;|\; write \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} to \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; write \descr{string expression} to \descr{string expression}$\\
$\tt \qquad \;|\; \descr{ËÏÍÁÎÄÁ addto}$\\
%%$\tt \qquad \;|\; \descr{addto command}$\\
$\tt \qquad \;|\; \descr{ËÏÍÁÎÄÁ ÒÉÓÏ×ÁÎÉÑ}$\\
%%$\tt \qquad \;|\; \descr{drawing command}$\\
$\tt \qquad \;|\; \descr{ËÏÍÁÎÄÁ ÍÅÔÒÉËÉ ÛÒÉÆÔÁ}$\\
%%$\tt \qquad \;|\; \descr{font metric command}$\\
$\tt \qquad \;|\; \descr{ËÏÍÁÎÄÁ-ÓÏÏÂÝÅÎÉÅ}$\\
%%$\tt \qquad \;|\; \descr{message command}$\\
$\tt \qquad \;|\; \descr{ËÏÍÁÎÄÁ show}$\\
%%$\tt \qquad \;|\; \descr{show command}$\\
$\tt \qquad \;|\; \descr{ËÏÍÁÎÄÁ ÔÒÁÓÓÉÒÏ×ËÉ}$\\
%%$\tt \qquad \;|\; \descr{tracing command}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ËÏÍÁÎÄÁ show} \rightarrow show \descr{ÓÐÉÓÏË ×ÙÒÁÖÅÎÉÊ}$\\
%%$\tt \descr{show command} \rightarrow show \descr{expression list}$\\
$\tt \qquad \;|\; showvariable \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×}$\\
%%$\tt \qquad \;|\; showvariable \descr{symbolic token list}$\\
$\tt \qquad \;|\; showtoken \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×}$\\
%%$\tt \qquad \;|\; showtoken \descr{symbolic token list}$\\
$\tt \qquad \;|\; showdependencies$\\
%%$\tt \qquad \;|\; showdependencies$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×} \rightarrow \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}$\\
%%$\tt \descr{symbolic token list} \rightarrow \descr{symbolic token}$\\
$\tt \qquad \;|\; \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË}\hbox{\tt ,} \descr{ÓÐÉÓÏË ÓÉÍ×ÏÌÉÞÅÓËÉÈ ÚÎÁËÏ×}$\\
%%$\tt \qquad \;|\; \descr{symbolic token}\hbox{\tt ,} \descr{symbolic token list}$\\
$\tt \descr{ÓÐÉÓÏË ×ÙÒÁÖÅÎÉÊ} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ} \;|\; \descr{ÓÐÉÓÏË ×ÙÒÁÖÅÎÉÊ}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{expression list} \rightarrow \descr{expression} \;|\; \descr{expression list}\hbox{\tt ,} \descr{expression}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ËÏÍÁÎÄÁ addto} \rightarrow$\\
%%$\tt \descr{addto command} \rightarrow$\\
$\tt \qquad addto \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ} also \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \qquad addto \descr{picture variable} also \descr{picture expression} \descr{option list}$\\
$\tt \qquad \;|\; addto \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ} contour \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \qquad \;|\; addto \descr{picture variable} contour \descr{path expression} \descr{option list}$\\
$\tt \qquad \;|\; addto \descr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ} doublepath \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \qquad \;|\; addto \descr{picture variable} doublepath \descr{path expression} \descr{option list}$\\
$\tt \descr{ÓÐÉÓÏË ÏÐÃÉÊ} \rightarrow \descr{ÐÕÓÔÏ} \;|\; \descr{ÏÐÃÉÑ ÒÉÓÏ×ÁÎÉÑ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \descr{option list} \rightarrow \descr{empty} \;|\; \descr{drawing option} \descr{option list}$\\
$\tt \descr{ÏÐÃÉÑ ÒÉÓÏ×ÁÎÉÑ} \rightarrow withcolor \descr{×ÙÒÁÖÅÎÉÅ-Ã×ÅÔ}$\\
%%$\tt \descr{drawing option} \rightarrow withcolor \descr{color expression}$\\
$\tt \qquad \;|\; withrgbcolor \descr{×ÙÒÁÖÅÎÉÅ-rgb-Ã×ÅÔ} \;|\; withcmykcolor \descr{×ÙÒÁÖÅÎÉÅ-cmyk-Ã×ÅÔ}$\\
%%$\tt \qquad \;|\; withrgbcolor \descr{rgbcolor expression} \;|\; withcmykcolor \descr{cmykcolor expression}$\\
$\tt \qquad \;|\; withgreyscale \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} \;|\; withoutcolor$\\
%%$\tt \qquad \;|\; withgreyscale \descr{numeric expression} \;|\; withoutcolor$\\
$\tt \qquad \;|\; withprescript \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} \;|\; withpostscript \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; withprescript \descr{string expression} \;|\; withpostscript \descr{string expression}$\\
$\tt \qquad \;|\; withpen \descr{×ÙÒÁÖÅÎÉÅ-ÐÅÒÏ} \;|\; dashed \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ}$\\
%%$\tt \qquad \;|\; withpen \descr{pen expression} \;|\; dashed \descr{picture expression}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ËÏÍÁÎÄÁ ÒÉÓÏ×ÁÎÉÑ} \rightarrow draw \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \descr{drawing command} \rightarrow draw \descr{picture expression} \descr{option list}$\\
$\tt \qquad \;|\; \descr{ÔÉÐ ÚÁÐÏÌÎÅÎÉÑ} \descr{×ÙÒÁÖÅÎÉÅ-ÐÕÔØ} \descr{ÓÐÉÓÏË ÏÐÃÉÊ}$\\
%%$\tt \qquad \;|\; \descr{fill type} \descr{path expression} \descr{option list}$\\
$\tt \descr{ÔÉÐ ÚÁÐÏÌÎÅÎÉÑ} \rightarrow fill \;|\; draw \;|\; filldraw \;|\; unfill \;|\; undraw \;|\; unfilldraw$\\
%%$\tt \descr{fill type} \rightarrow fill \;|\; draw \;|\; filldraw \;|\; unfill \;|\; undraw \;|\; unfilldraw$\\
$\tt \qquad \;|\; drawarrow \;|\; drawdblarrow \;|\; cutdraw$\\
%%$\tt \qquad \;|\; drawarrow \;|\; drawdblarrow \;|\; cutdraw$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ËÏÍÁÎÄÁ-ÓÏÏÂÝÅÎÉÅ} \rightarrow errhelp \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{message command} \rightarrow errhelp \descr{string expression}$\\
$\tt \qquad \;|\; errmessage \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; errmessage \descr{string expression}$\\
$\tt \qquad \;|\; filenametemplate \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; filenametemplate \descr{string expression}$\\
$\tt \qquad \;|\; message \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; message \descr{string expression}$\\
$\tt $\\
%%$\tt $\\
$\tt \descr{ËÏÍÁÎÄÁ ÔÒÁÓÓÉÒÏ×ËÉ} \rightarrow tracingall \;|\; loggingall \;|\; tracingnone$
%%$\tt \descr{tracing command} \rightarrow tracingall \;|\; loggingall \;|\; tracingnone$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ËÏÍÁÎÄ}
%%\caption{The syntax for commands}
\index{ÓÐÉÓÏË ÏÐÃÉÊ?\tdescr{ÓÐÉÓÏË ÏÐÃÉÊ}}\index{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ?\tdescr{ÐÅÒÅÍÅÎÎÁÑ-ËÁÒÔÉÎËÁ}}%
%%\index{option list?\tdescr{option list}}\index{picture variable?\tdescr{picture variable}}%
\label{sycmds}

% is this really true?  in practice, in real implementations?
%\bigskip
%By the way, the default for \ttindex{randomseed} is, in effect,
%$\textsl{day} + \textsl{time}*\epsilon$.  Unfortunately, \textsl{time}
%is in minutes.
\end{figure}

\begin{figure}[htp]
\begin{ctabbing}
$\tt \descr{ÐÒÏ×ÅÒËÁ if} \rightarrow if \descr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ} \hbox{\tt :} \descr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ} \descr{ÁÌØÔÅÒÎÁÔÉ×Ù} fi$\\
%%$\tt \descr{if test} \rightarrow if \descr{boolean expression} \hbox{\tt :} \descr{balanced tokens} \descr{alternatives} fi$\\
$\tt \descr{ÁÌØÔÅÒÎÁÔÉ×Ù} \rightarrow \descr{ÐÕÓÔÏ}$\\
%%$\tt \descr{alternatives} \rightarrow \descr{empty}$\\
$\tt \qquad \;|\; else\hbox{\tt :} \descr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ}$\\
%%$\tt \qquad \;|\; else\hbox{\tt :} \descr{balanced tokens}$\\
$\tt \qquad \;|\; elseif \descr{ÌÏÇÉÞÅÓËÏÅ ×ÙÒÁÖÅÎÉÅ} \hbox{\tt :} \descr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ} \descr{ÁÌØÔÅÒÎÁÔÉ×Ù}$\\
%%$\tt \qquad \;|\; elseif \descr{boolean expression} \hbox{\tt :} \descr{balanced tokens} \descr{alternatives}$\\
$\tt $\\
$\tt \descr{ÃÉËÌ} \rightarrow \descr{ÚÁÇÏÌÏ×ÏË ÃÉËÌÁ}\hbox{\tt :} \descr{ÔÅÌÏ ÃÉËÌÁ} endfor$\\
%%$\tt \descr{loop} \rightarrow \descr{loop header}\hbox{\tt :} \descr{loop text} endfor$\\
$\tt \descr{ÚÁÇÏÌÏ×ÏË ÃÉËÌÁ} \rightarrow for \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \hbox{\tt =} \descr{ÐÒÏÇÒÅÓÓÉÑ}$\\
%%$\tt \descr{loop header} \rightarrow for \descr{symbolic token} \hbox{\tt =} \descr{progression}$\\
$\tt \qquad \;|\; for \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \hbox{\tt =} \descr{ÓÐÉÓÏË for}$\\
%%$\tt \qquad \;|\; for \descr{symbolic token} \hbox{\tt =} \descr{for list}$\\
$\tt \qquad \;|\; for \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \hbox{\tt within} \descr{×ÙÒÁÖÅÎÉÅ-ËÁÒÔÉÎËÁ}$\\
%%$\tt \qquad \;|\; for \descr{symbolic token} \hbox{\tt within} \descr{picture expression}$\\
$\tt \qquad \;|\; forsuffixes \descr{ÓÉÍ×ÏÌÉÞÅÓËÉÊ ÚÎÁË} \hbox{\tt =} \descr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×}$\\
%%$\tt \qquad \;|\; forsuffixes \descr{symbolic token} \hbox{\tt =} \descr{suffix list}$\\
$\tt \qquad \;|\; forever$\\
%%$\tt \qquad \;|\; forever$\\
$\tt \descr{ÐÒÏÇÒÅÓÓÉÑ} \rightarrow \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} upto \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{progression} \rightarrow \descr{numeric expression} upto \descr{numeric expression}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} downto \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \qquad \;|\; \descr{numeric expression} downto \descr{numeric expression}$\\
$\tt \qquad \;|\; \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} step \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} until \descr{ÞÉÓÌÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} $\\
%%$\tt \qquad \;|\; \descr{numeric expression} step \descr{numeric expression} until \descr{numeric expression} $\\
$\tt \descr{ÓÐÉÓÏË for} \rightarrow \descr{×ÙÒÁÖÅÎÉÅ} \;|\; \descr{ÓÐÉÓÏË for}\hbox{\tt ,} \descr{×ÙÒÁÖÅÎÉÅ}$\\
%%$\tt \descr{for list} \rightarrow \descr{expression} \;|\; \descr{for list}\hbox{\tt ,} \descr{expression}$\\
$\tt \descr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×} \rightarrow \descr{ÓÕÆÆÉËÓ} \;|\; \descr{ÓÐÉÓÏË ÓÕÆÆÉËÓÏ×}\hbox{\tt ,} \descr{ÓÕÆÆÉËÓ}$
%%$\tt \descr{suffix list} \rightarrow \descr{suffix} \;|\; \descr{suffix list}\hbox{\tt ,} \descr{suffix}$
\end{ctabbing}
\caption{óÉÎÔÁËÓÉÓ ÄÌÑ ÕÓÌÏ×ÉÊ É ÃÉËÌÏ×}
%%\caption{The syntax for conditionals and loops}
\index{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ?\tdescr{ÓÂÁÌÁÎÓÉÒÏ×ÁÎÎÙÅ ÚÎÁËÉ}}\index{ÓÕÆÆÉËÓ?\tdescr{ÓÕÆÆÉËÓ}}%
%%\index{balanced tokens?\tdescr{balanced tokens}}\index{suffix?\tdescr{suffix}}%
\label{sycondloop}
\end{figure}

\clearpage

\let\topfraction=\svtopfrac     % restore values from the start of this appendix
\let\textfraction=\svtxtfrac
\setcounter{topnumber}{\value{svtopnum}}
\setcounter{totalnumber}{\value{svtotnum}}

\section{MetaPost É \MF}
%%\section{MetaPost Versus \MF}
\label{MPvsMF}

éÚ-ÚÁ ÔÏÇÏ, ÞÔÏ ÑÚÙËÉ \MF\index{metafont?\MF} É MetaPost ÉÍÅÀÔ ÔÁË ÍÎÏÇÏ 
ÏÂÝÅÇÏ, ÐÏÌØÚÏ×ÁÔÅÌÉ-ÜËÓÐÅÒÔÙ \MF\ ×ÏÚÍÏÖÎÏ ÚÁÈÏÔÑÔ ÐÒÏÐÕÓÔÉÔØ ÂÏÌØÛÕÀ 
ÞÁÓÔØ ÏÂßÑÓÎÅÎÉÊ ÉÚ ÜÔÏÇÏ ÄÏËÕÍÅÎÔÁ É ÓËÏÎÃÅÎÔÒÉÒÏ×ÁÔØÓÑ ÎÁ ÕÎÉËÁÌØÎÙÈ 
ËÏÎÃÅÐÃÉÑÈ MetaPost.
%%Since the \MF\index{metafont?\MF} and MetaPost languages have so much in
%%common, expert users of \MF\ will want to skip most of the explanations
%%in this document and concentrate on concepts that are unique to
%%MetaPost. 
óÒÁ×ÎÅÎÉÑ × ÜÔÏÍ ÐÒÉÌÏÖÅÎÉÅ ÐÒÉ×ÏÄÑÔÓÑ ÄÌÑ ÐÏÍÏÝÉ ÜËÓÐÅÒÔÁÍ, ÈÏÒÏÛÏ 
ÚÎÁËÏÍÙÍ Ó {\sl The\ \MF book}, Á ÔÁËÖÅ ÄÒÕÇÉÍ ÐÏÌØÚÏ×ÁÔÅÌÑÍ, ÞÔÏ 
ÈÏÔÑÔ ÐÏÌÕÞÉÔØ ÐÏÌØÚÕ ÉÚ ÂÏÌÅÅ ÄÅÔÁÌØÎÙÈ ÏÂßÑÓÎÅÎÉÊ ÒÁÂÏÔÙ ëÎÕÔÁ \cite{kn:c}.
%%The comparisons in this appendix are intended to help experts
%%that are familiar with {\sl The\ \MF book} as well as other users that
%%want to benefit from Knuth's more detailed explanations \cite{kn:c}.

÷ÓÌÅÄÓÔ×ÉÅ ÔÏÇÏ, ÞÔÏ \MF\ ÐÒÅÄÎÁÚÎÁÞÅÎ ÄÌÑ ÉÚÇÏÔÏ×ÌÅÎÉÑ ÛÒÉÆÔÏ× \TeX, 
ÏÎ ÉÍÅÅÔ ÒÑÄ ÐÒÉÍÉÔÉ×Ï× ÄÌÑ ÇÅÎÅÒÁÃÉÉ 
{\tt tfm}\index{tfm file?{\tt tfm}-ÆÁÊÌ}\index{ÆÁÊÌÙ!tfm?{\tt tfm}}-ÆÁÊÌÏ×, 
ÎÕÖÎÙÈ \TeX\ ÄÌÑ ÉÚÍÅÒÅÎÉÑ 
ÓÉÍ×ÏÌÏ×, ÉÎÆÏÒÍÁÃÉÉ Ï ÏÔÓÔÕÐÁÈ, ÌÉÇÁÔÕÒÁÈ\index{ÌÉÇÁÔÕÒÙ} É 
ËÅÒÎÉÎÇÅ\index{ËÅÒÎÉÎÇ}. 
%%Since \MF\ is intended for making \TeX\ fonts, it has a number of
%%primitives for generating the {\tt tfm}\index{tfm file?{\tt tfm}
%%file}\index{files!tfm?{\tt tfm}} files that \TeX\ needs for character
%%dimensions, spacing information, ligatures\index{ligatures} and
%%kerning\index{kerning}. 
MetaPost ÍÏÖÅÔ ÔÁËÖÅ ÉÓÐÏÌØÚÏ×ÁÔØÓÑ ÄÌÑ ÇÅÎÅÒÁÃÉÉ ÛÒÉÆÔÏ× É ÏÎ 
ÔÁËÖÅ ÉÍÅÅÔ ÐÒÉÍÉÔÉ×Ù \MF\ ÄÌÑ ÓÏÚÄÁÎÉÑ {\tt tfm}-ÆÁÊÌÏ×. 
%%MetaPost can also be used for generating fonts,
%%and it also has \MF's primitives for making {\tt tfm} files. 
ïÎÉ ÐÅÒÅÞÉÓÌÑÀÔÓÑ × ÔÁÂÌÉÃÅ~\ref{tfmprim}. 
%%These are listed in Table~\ref{tfmprim}. 
éÈ ÏÂßÑÓÎÅÎÉÑ ÍÏÇÕÔ ÂÙÔØ ÎÁÊÄÅÎÙ × ÄÏËÕÍÅÎÔÁÃÉÉ \MF\ \cite{kn:c,kn:mf3}.
%%Explanations can be found in the \MF\
%%documentation \cite{kn:c,kn:mf3}.

\begin{table}[htp]
$$\begin{tabular}{|l|l|}  \hline
ËÏÍÁÎÄÙ&                {\tt charlist}, {\tt extensible},
%%commands&               {\tt charlist}, {\tt extensible},
                        {\tt fontdimen}, {\tt headerbyte}               \\
        &               {\tt kern}, {\tt ligtable}                      \\ \hline
ÏÐÅÒÁÔÏÒÙ ÌÉÇÁÔÕÒÎÙÈ&     \verb!::!, \verb!=:!, \verb!=:|!, \verb!=:|>!,
%%ligtable operators&     \verb!::!, \verb!=:!, \verb!=:|!, \verb!=:|>!,
                        \verb!|=:!, \verb!|=:>!,                        \\
ÔÁÂÌÉÃ&               \verb!|=:|!, \verb!|=:|>!, \verb!|=:|>>!,
%%        &               \verb!|=:|!, \verb!|=:|>!, \verb!|=:|>>!,
                        \verb!||:!                                      \\ \hline
×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ\index{×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ}&
%%internal variables\index{internal variables}\index{variables!internal}&
                        {\tt boundarychar}, {\tt chardp},
                        {\tt charext}, {\tt charht},                    \\
        &               {\tt charic}, {\tt charwd},
                        {\tt designsize}, {\tt fontmaking}              \\ \hline
ÄÒÕÇÉÅ ÏÐÅÒÁÔÏÒÙ&       {\tt charexists}                                \\ \hline
%%other operators&        {\tt charexists}                                \\ \hline
\end{tabular}
$$
\caption{ðÒÉÍÉÔÉ×Ù MetaPost ÄÌÑ ÓÏÚÄÁÎÉÑ {\tt tfm}-ÆÁÊÌÏ×.}
%%\caption{MetaPost primitives for making {\tt tfm} files.}
\label{tfmprim}
\end{table}

äÁÖÅ ÈÏÔÑ  MetaPost ÉÍÅÅÔ ÐÒÉÍÉÔÉ×Ù ÄÌÑ ÇÅÎÅÒÁÃÉÉ ÛÒÉÆÔÏ×, ÍÎÏÇÉÅ 
ÔÁËÉÅ ÐÒÉÍÉÔÉ×Ù É ×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ, ËÏÔÏÒÙÅ ×ÈÏÄÑÔ × Plain
\MF\index{metafont?\MF}, ÎÅ ÏÐÒÅÄÅÌÅÎÙ × Plain MetaPost\index{ÍÁËÒÏÓÙ Plain}. 
%%Even though MetaPost has the primitives for generating fonts, many of
%%the font-making primitives and internal variables that are part of Plain
%%\MF\index{metafont?\MF} are not defined in Plain MetaPost\index{Plain
%%macros}. 
÷ÍÅÓÔÏ ÜÔÏÇÏ ÉÍÅÅÔÓÑ ÏÔÄÅÌØÎÙÊ ÍÁËÒÏÐÁËÅÔ {\tt
mfplain}\index{mfplain?\texttt{mfplain}}, ÏÐÒÅÄÅÌÑÀÝÉÊ ÍÁËÒÏÓÙ, 
ÔÒÅÂÕÅÍÙÅ ÄÌÑ ×ÏÚÍÏÖÎÏÓÔÉ ÏÂÒÁÂÏÔÁÔØ ÞÅÒÅÚ MetaPost ÛÒÉÆÔÙ Computer Modern 
ëÎÕÔÁ, --- ÏÎÉ ÐÏËÁÚÁÎÙ × ÔÁÂÌÉÃÅ~\ref{mfponly} \cite{kn:e}. 
%%Instead, there is a separate macro package called {\tt
%%mfplain}\index{mfplain?\texttt{mfplain}} that defines the macros
%%required to allow MetaPost to process Knuth's Computer Modern fonts as
%%shown in Table~\ref{mfponly} \cite{kn:e}. 
äÌÑ ÚÁÇÒÕÚËÉ ÜÔÉÈ ÍÁËÒÏÓÏ× ÐÏÓÔÁ×ØÔÅ ``\verb|&mfplain|'' ÐÅÒÅÄ ÉÍÅÎÅÍ 
×ÈÏÄÎÏÇÏ ÆÁÊÌÁ. 
%%To load these macros, put
%%``\verb|&mfplain|'' before the name of the input file. 
üÔÏ ÍÏÖÅÔ ÂÙÔØ ÓÄÅÌÁÎÏ ÐÏ ÐÒÉÇÌÁÛÅÎÉÀ {\tt **} ÐÏÓÌÅ ×ÙÚÏ×Á ÉÎÔÅÒÐÒÅÔÁÔÏÒÁ 
MetaPost ÂÅÚ ÁÒÇÕÍÅÎÔÏ× ÉÌÉ × ËÏÍÁÎÄÎÏÊ ÓÔÒÏËÅ, 
ÎÁÐÒÉÍÅÒ\footnote{óÉÎÔÁËÓÉÓ ËÏÍÁÎÄÎÏÊ ÓÔÒÏËÉ ÚÁ×ÉÓÉÔ ÏÔ ÓÉÓÔÅÍÙ.  ëÁ×ÙÞËÉ ÎÕÖÎÙ
× ÂÏÌØÛÉÎÓÔ×Å ÓÉÓÔÅÍ Unix ÄÌÑ ÚÁÝÉÔÙ ÓÐÅÃÉÁÌØÎÙÈ ÓÉÍ×ÏÌÏ×, ÐÏÄÏÂÎÙÈ {\tt\&}.}, 
%%This can be done
%%at the {\tt **} prompt after invoking the MetaPost interpreter with no
%%arguments, or on a command line that looks something like
%%this:\footnote{Command line syntax is system dependent.  Quotes are
%%needed on most Unix systems to protect special characters like
%%{\tt\&}.}
$$ \hbox{\verb|mpost '&mfplain' cmr10|} $$
%%$$ \hbox{\verb|mpost '&mfplain' cmr10|} $$
ëÏÍÁÎÄÏÊ, ÁÎÁÌÏÇÉÞÎÏÊ \MF-ËÏÍÁÎÄÅ
%%The analog of a \MF\ command line like
$$ \hbox{\verb|mf '\mode=lowres; mag=1.2; input cmr10'|,} $$
%%$$ \hbox{\verb|mf '\mode=lowres; mag=1.2; input cmr10'|} $$
ÂÕÄÅÔ
%%is
$$ \hbox{\verb|mpost '&mfplain \mode=lowres; mag=1.2; input cmr10'|} $$
%%$$ \hbox{\verb|mpost '&mfplain \mode=lowres; mag=1.2; input cmr10'|} $$
òÅÚÕÌØÔÁÔ --- ÜÔÏ ÍÎÏÖÅÓÔ×Ï ÆÁÊÌÏ× PostScript\index{PostScript}, ÐÏ ÏÄÎÏÍÕ 
ÎÁ ËÁÖÄÙÊ ÓÉÍ×ÏÌ ÛÒÉÆÔÁ.
%%The result is a set of PostScript\index{PostScript} files, one for each
%%character in the font. 
ðÏÔÒÅÂÕÅÔÓÑ ÎÅËÏÔÏÒÏÅ ÒÅÄÁËÔÉÒÏ×ÁÎÉÅ ÄÌÑ ÉÈ ÓÏÅÄÉÎÅÎÉÑ × ÚÁÇÒÕÖÁÅÍÙÊ PostScript 
Type 3 ÛÒÉÆÔ~\cite{ad:red2}..
%%Some editing would be required in order to
%%merge them into a downloadable Type~3 PostScript font~\cite{ad:red2}.

\begin{table}[htp]
$$
\renewcommand{\FancyVerbFormatLine}[1]{\hbox{#1}\strut}
\begin{tabular}{|l|} \hline
\multicolumn 1{|c|}
{ïÐÒÅÄÅÌÅÎÙ × ÐÁËÅÔÅ {\tt mfplain}}          \\ \hline
%%{Defined in the {\tt mfplain} package}          \\ \hline
\begin{verbatim}
beginchar                              font_identifier
blacker                                font_normal_shrink
capsule_def                            font_normal_space
change_width                           font_normal_stretch
define_blacker_pixels                  font_quad
define_corrected_pixels                font_size
define_good_x_pixels                   font_slant
define_good_y_pixels                   font_x_height
define_horizontal_corrected_pixels     italcorr
define_pixels                          labelfont
define_whole_blacker_pixels            makebox
define_whole_pixels                    makegrid
define_whole_vertical_blacker_pixels   maketicks
define_whole_vertical_pixels           mode_def
endchar                                mode_setup
extra_beginchar                        o_correction
extra_endchar                          proofrule
extra_setup                            proofrulethickness
font_coding_scheme                     rulepen
font_extra_space                       smode
\end{verbatim}
                                               \\ \hline
\multicolumn 1{|c|}
{ïÐÒÅÄÅÌÅÎÙ ËÁË ÐÕÓÔÙÅ ÏÐÅÒÁÃÉÉ × ÐÁËÅÔÅ {\tt mfplain}}\\ \hline
%%{Defined as no-ops in the {\tt mfplain} package}\\ \hline
\begin{verbatim}
cullit                                 proofoffset
currenttransform                       screenchars
gfcorners                              screenrule
grayfont                               screenstrokes
hround                                 showit
imagerules                             slantfont
lowres_fix                             titlefont
nodisplays                             unitpixel
notransforms                           vround
openit
\end{verbatim}
                                       \\ \hline
\end{tabular}
\renewcommand{\FancyVerbFormatLine}[1]{#1}
$$
\caption{íÁËÒÏÓÙ É ×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ, ÏÐÒÅÄÅÌÅÎÎÙÅ ÔÏÌØËÏ × ÐÁËÅÔÅ {\tt mfplain}.}
%%\caption{Macros and internal variables defined only in the {\tt mfplain}
%%package.}
\label{mfponly}
\end{table}

äÒÕÇÉÍ ÏÇÒÁÎÉÞÅÎÉÅÍ ÐÁËÅÔÁ {\tt mfplain} Ñ×ÌÑÅÔÓÑ ÔÏ, ÞÔÏ ÏÐÒÅÄÅÌÅÎÎÙÅ 
ÐÅÒÅÍÅÎÎÙÅ ÉÚ Plain \MF\index{metafont?\MF} ÎÅ ÍÏÇÕÔ ÐÏÌÕÞÉÔØ ÒÁÚÕÍÎÙÈ 
ÏÐÒÅÄÅÌÅÎÉÊ × MetaPost. 
%%Another limitation of the {\tt mfplain} package is that certain internal
%%variables from Plain \MF\index{metafont?\MF} cannot be given reasonable
%%MetaPost definitions. 
óÒÅÄÉ ÎÉÈ {\tt displaying}, {\tt
currentwindow}, \verb|screen_rows| É \verb|screen_cols|, ËÏÔÏÒÙÅ ÚÁ×ÉÓÑÔ 
ÏÔ ÓÐÏÓÏÂÎÏÓÔÉ \MF\ ÉÚÏÂÒÁÖÁÔØ ÒÉÓÕÎËÉ ÎÁ ÜËÒÁÎÅ ËÏÍÐØÀÔÅÒÁ. 
%%These include {\tt displaying}, {\tt
%%currentwindow}, \verb|screen_rows|, and \verb|screen_cols| which depend
%%on \MF's ability to display images on the computer screen. 
ëÒÏÍÅ ÔÏÇÏ, \verb|pixels_per_inch| Ñ×ÌÑÅÔÓÑ ÎÅÕÍÅÓÔÎÙÍ ÉÚ-ÚÁ ÔÏÇÏ, ÞÔÏ MetaPost 
ÉÓÐÏÌØÚÕÅÔ ÆÉËÓÉÒÏ×ÁÎÎÙÅ ÅÄÉÎÉÃÙ ÐÕÎËÔÏ× PostScript\index{PostScript!ÐÕÎËÔ}\index{ÐÕÎËÔ!PostScript}.
%%In addition,
%%\verb|pixels_per_inch| is irrelevant since MetaPost uses fixed units of
%%PostScript\index{PostScript!point}\index{point!PostScript} points.

ïÓÎÏ×ÁÎÉÑ ÔÏÇÏ, ÞÔÏ ÎÅËÏÔÏÒÙÅ ÍÁËÒÏÓÙ É ×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ\index{×ÎÕÔÒÅÎÎÉÅ 
ÐÅÒÅÍÅÎÎÙÅ}\index{ÐÅÒÅÍÅÎÎÙÅ!×ÎÕÔÒÅÎÎÉÅ} ÎÉÞÅÇÏ ÎÅ ÚÎÁÞÁÔ × MetaPost × ÔÏÍ, 
ÞÔÏ ÐÒÉÍÉÔÉ×ÎÙÅ ËÏÍÁÎÄÙ \MF\ {\tt cull}, {\tt display}, {\tt
openwindow}, {\tt numspecial} É {\tt totalweight} ÎÅ ÒÅÁÌÉÚÏ×ÁÎÙ × 
MetaPost. 
%%The reason why some macros and internal variables\index{internal
%%variables}\index{variables!internal} are not meaningful in MetaPost is
%%that \MF\ primitive commands {\tt cull}, {\tt display}, {\tt
%%openwindow}, {\tt numspecial} and {\tt totalweight} are not implemented
%%in MetaPost. 
ôÁËÖÅ ÎÅ ÒÅÁÌÉÚÏ×ÁÎÙ ÒÑÄ ×ÎÕÔÒÅÎÎÉÈ ÐÅÒÅÍÅÎÎÙÈ É 
\tdescr{ÏÐÃÉÑ ÒÉÓÏ×ÁÎÉÑ} {\tt withweight}. 
%%Also not implemented are a number of internal variables as
%%well as the \tdescr{drawing option} {\tt withweight}. 
äÁÌÅÅ ÓÌÅÄÕÅÔ ÐÏÌÎÙÊ ÓÐÉÓÏË ×ÎÕÔÒÅÎÎÉÈ ÐÅÒÅÍÅÎÎÙÈ, ÞØÉ ÐÒÉÍÉÔÉ×ÎÙÅ 
\MF-ÚÎÁÞÅÎÉÑ ÎÅ ÉÍÅÀÔ ÓÍÙÓÌÁ × MetaPost:
%%Here is a
%%complete listing of the internal variables whose primitive meanings in
%%\MF\ do not make sense in MetaPost:
$$\begin{verbatim}
autorounding fillin       proofing     tracingpens   xoffset
chardx       granularity  smoothing    turningcheck  yoffset
chardy       hppp         tracingedges vppp
\end{verbatim}
$$

åÓÔØ ÅÝÅ ÐÒÉÍÉÔÉ× \MF, ÉÍÅÀÝÉÊ ÎÅÓËÏÌØËÏ ÉÎÏÅ ÚÎÁÞÅÎÉÅ × MetaPost. 
%%There is also one \MF\ primitive that has a slightly different meaning in
%%MetaPost. 
ïÂÁ ÑÚÙËÁ ÄÏÐÕÓËÁÀÔ ËÏÍÁÎÄÕ × ÆÏÒÍÅ\index{special?\texttt{special}}\label{Dspecl}
$$ {\tt special}\, \descr{ÓÔÒÏËÏ×ÏÅ ×ÙÒÁÖÅÎÉÅ} \hbox{\tt; }, $$
ÎÏ \MF\ ËÏÐÉÒÕÅÔ ÓÔÒÏËÕ × Ó×ÏÊ ×ÙÈÏÄÎÏÊ ÆÁÊÌ ``ÏÂÏÂÝÅÎÎÏÇÏ ÛÒÉÆÔÁ'', ÔÏÇÄÁ ËÁË 
MetaPost ÉÎÔÅÒÐÒÅÔÉÒÕÅÔ ÓÔÒÏËÕ ËÁË ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÓÔØ ËÏÍÁÎÄ PostScript\index{PostScript}, 
ËÏÔÏÒÙÅ ÐÏÍÅÝÁÀÔÓÑ × ÎÁÞÁÌÏ ÓÌÅÄÕÀÝÅÇÏ ×ÙÈÏÄÎÏÇÏ ÆÁÊÌÁ
%%Both languages allow statements of the
%%form\index{special?\texttt{special}}\label{Dspecl}
%%$$ {\tt special}\, \descr{string expression} \hbox{\tt;} $$
%%but \MF\ copies the string into its ``generic font'' output file, while
%%MetaPost interprets the string as a sequence of PostScript\index{PostScript}
%%commands that are to be placed at the beginning of the next output file.

÷ ÜÔÏÍ ÒÁÓÓÍÏÔÒÅÎÉÉ ÓÔÏÉÔ ÚÁÍÅÔÉÔØ, ÞÔÏ ÌÉÎÅÊËÉ × ÍÁÔÅÒÉÁÌÅ \TeX, 
×ËÌÀÞÁÅÍÏÍ ÞÅÒÅÚ {\tt btex..etex}, × MetaPost ÏËÒÕÇÌÑÀÔÓÑ ÄÏ ÐÒÁ×ÉÌØÎÏÇÏ 
ÞÉÓÌÁ ÐÉËÓÅÌÏ×, ÓÏÇÌÁÓÎÏ ÐÒÁ×ÉÌÁÍ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÑ 
PostScript\index{PostScript!ÐÒÁ×ÉÌÁ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÑ}~\cite{ad:red2}. 
%%In this regard, it is worth mentioning that rules in \TeX\ material
%%included via {\tt btex..etex} in MetaPost are rounded to the correct
%%number of pixels according to PostScript\index{PostScript!conversion rules}
%%conversion rules~\cite{ad:red2}. 
÷ \MF ÌÉÎÅÊËÉ ÎÁÐÒÑÍÕÀ ÎÅ ÇÅÎÅÒÉÒÕÀÔÓÑ, Á ÐÒÏÓÔÏ ×ËÌÀÞÁÀÔÓÑ × 
special-ËÏÍÁÎÄÙ É ÉÎÔÅÒÐÒÅÔÉÒÕÀÔÓÑ ÐÏÚÖÅ ÄÒÕÇÉÍÉ ÐÒÏÇÒÁÍÍÁÍÉ, ÔÁËÉÍÉ 
ËÁË {\tt gftodvi}\index{gftodvi?\ttt{gftodvi}}, ÐÏÜÔÏÍÕ ÚÄÅÓØ ÎÅÔ 
ÎÉËÁËÉÈ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÊ.
%%In \MF, rules are not generated
%%directly, but simply included in specials and interpreted later by
%%other programs, such as {\tt gftodvi}\index{gftodvi?\ttt{gftodvi}},
%%so there is no special conversion.

÷ÓÅ ÄÒÕÇÉÅ ÒÁÚÌÉÞÉÑ ÍÅÖÄÕ \MF\ É MetaPost --- ÜÔÏ ×ÏÚÍÏÖÎÏÓÔÉ, ËÏÔÏÒÙÅ 
ÍÏÖÎÏ ÎÁÊÔÉ ÔÏÌØËÏ × MetaPost. 
%%All the other differences between \MF\ and MetaPost are features found
%%only in MetaPost. 
ïÎÉ ÐÅÒÅÞÉÓÌÅÎÙ × ÔÁÂÌÉÃÅ~\ref{mponly}. 
%%These are listed in Table~\ref{mponly}. 
åÄÉÎÓÔ×ÅÎÎÙÍÉ ËÏÍÁÎÄÁÍÉ, ËÏÔÏÒÙÅ ÎÅ ÏÂÓÕÖÄÁÌÉÓØ × ÐÒÅÄÙÄÕÝÉÈ ÒÁÚÄÅÌÁÈ É ËÏÔÏÒÙÅ 
ÅÓÔØ × ÜÔÏÊ ÔÁÂÌÉÃÅ, Ñ×ÌÑÀÔÓÑ 
\verb|extra_beginfig|\index{extra_beginfig?\texttt{extra\_beginfig}}\label{Dxbfig},
\verb|extra_endfig|\index{extra_endfig?\texttt{extra\_endfig}}\label{Dxefig}
É {\tt mpxbreak}. 
%%The only
%%commands listed in this table that the preceding sections do not discuss
%%are
%%\verb|extra_beginfig|\index{extra_beginfig?\texttt{extra\_beginfig}}\label{Dxbfig},
%%\verb|extra_endfig|\index{extra_endfig?\texttt{extra\_endfig}}\label{Dxefig},
%%and {\tt mpxbreak}. 
ðÅÒ×ÙÅ Ä×Å --- ÜÔÏ ÓÔÒÏËÉ, ÓÏÄÅÒÖÁÝÉÅ ÄÏÐÏÌÎÉÔÅÌØÎÙÅ ËÏÍÁÎÄÙ ÄÌÑ ÏÂÒÁÂÏÔËÉ × 
ÓÏÏÔ×ÅÔÓÔ×ÅÎÎÏ {\tt
beginfig}\index{beginfig?\texttt{beginfig}} É {\tt
endfig}\index{endfig?\texttt{endfig}}, --- ÏÎÉ ÐÏÄÏÂÎÙ \verb|extra_beginchar| É 
\verb|extra_endchar|, ÏÂÒÁÂÁÔÙ×ÁÅÍÙÍ × {\tt beginchar} É {\tt endchar}.
%%The first two are strings that contain extra
%%commands to be processed by {\tt
%%beginfig}\index{beginfig?\texttt{beginfig}} and {\tt
%%endfig}\index{endfig?\texttt{endfig}} just as \verb|extra_beginchar| and
%%\verb|extra_endchar| are processed by {\tt beginchar} and {\tt endchar}.
æÁÊÌ {\tt boxes.mp}\index{boxes.mp?\texttt{boxes.mp}} ÉÓÐÏÌØÚÕÅÔ ÜÔÉ 
×ÏÚÍÏÖÎÏÓÔÉ.
%%(The file {\tt boxes.mp}\index{boxes.mp?\texttt{boxes.mp}} uses these
%%features).

äÒÕÇÏÊ ÎÏ×ÏÊ ×ÏÚÍÏÖÎÏÓÔØÀ, ÐÒÉ×ÅÄÅÎÎÏÊ × ÔÁÂÌÉÃÅ~\ref{mponly}, Ñ×ÌÑÅÔÓÑ 
{\tt mpxbreak}\index{mpxbreak?\texttt{mpxbreak}}. 
%%The other new feature listed in Table~\ref{mponly} not listed in the
%%index is {\tt mpxbreak}\index{mpxbreak?\texttt{mpxbreak}}. 
ïÎÁ ÉÓÐÏÌØÚÕÅÔÓÑ ÄÌÑ ÒÁÚÄÅÌÅÎÉÑ ÂÌÏËÏ× ÔÒÁÎÓÌÉÒÏ×ÁÎÎÙÈ ËÏÍÁÎÄ 
\TeX\index{TeX?\TeX} ÉÌÉ troff\index{troff} × 
{\tt mpx}\index{ÆÁÊÌÙ!mpx?{\tt mpx}}-ÆÁÊÌÁÈ.
%%This is used
%%to separate blocks of translated \TeX\index{TeX?\TeX} or
%%troff\index{troff} commands in {\tt mpx}\index{files!mpx?{\tt mpx}}
%%files. 
ïÎÁ ÎÅ ÄÏÌÖÎÁ ÚÁÔÒÁÇÉ×ÁÔØ ÐÏÌØÚÏ×ÁÔÅÌÅÊ, Ô.Ë. {\tt mpx}-ÆÁÊÌÙ 
ÇÅÎÅÒÉÒÕÀÔÓÑ Á×ÔÏÍÁÔÉÞÅÓËÉ.
%%It should be of no concern to users since {\tt mpx} files are
%%generated automatically.

\begin{table}
\centering
\begin{tabular}{|c|}\hline
ðÒÉÍÉÔÉ×Ù MetaPost, ÏÔÓÕÔÓÔ×ÕÀÝÉÅ × \MF\\\hline
%%MetaPost primitives not found in \MF\\\hline
\begin{minipage}[b]{.75\linewidth}\ttfamily
\begin{multicols}{3}
blackpart\\
bluepart\\
bounded\\
btex\\
clip\\
clipped\\
closefrom\\
cmykcolor\\
color\\
colormodel\\
cyanpart\\
dashed\\
dashpart\\
defaultcolormodel\\
etex\\
filenametemplate\\
filled\\
fontmapfile\\
fontmapline\\
fontpart\\
fontsize\\
for within\\
greenpart\\
greypart\\
infont\\
linecap\\
linejoin\\
llcorner\\
lrcorner\\
magentapart\\
miterlimit\\
mpprocset\\
mpxbreak\\
pathpart\\
penpart\\
prologues\\
readfrom\\
redpart\\
restoreclipcolor\\
rgbcolor\\
setbounds\\
stroked\\
textpart\\
textual\\
tracinglostchars\\
troffmode\\
truecorners\\
ulcorner\\
urcorner\\
verbatimtex\\
withcmykcolor\\
withcolor\\
withgreyscale\\
withoutcolor\\
withpostscript\\
withprescript\\
withrgbcolor\\
write to\\
yellowpart
\end{multicols}
\end{minipage}\\\hline

ðÅÒÅÍÅÎÎÙÅ É ÍÁËÒÏÓÙ, ÏÐÒÅÄÅÌÅÎÎÙÅ ÔÏÌØËÏ × Plain MetaPost\\\hline
%%Variables and Macros defined only in Plain MetaPost\\\hline
\begin{minipage}[b]{.75\linewidth}\ttfamily
\begin{multicols}{3}
ahangle\\
ahlength\\
background\\
bbox\\
bboxmargin\\
beginfig\\
beveled\\
black\\
blue\\
buildcycle\\
butt\\
center\\
cutafter\\
cutbefore\\
cuttings\\
dashpattern\\
defaultfont\\
defaultpen\\
defaultscale\\
dotlabel\\
dotlabels\\
drawarrow\\
drawdblarrow\\
drawoptions\\
endfig\\
EOF\\
evenly\\
extra\_beginfig\\
extra\_endfig\\
green\\
image\\
label\\
labeloffset\\
mitered\\
red\\
rounded\\
squared\\
thelabel\\
white
\end{multicols}
\end{minipage}\\\hline
\end{tabular}
\caption{íÁËÒÏÓÙ É ×ÎÕÔÒÅÎÎÉÅ ÐÅÒÅÍÅÎÎÙÅ, ÏÐÒÅÄÅÌÅÎÎÙÅ ÔÏÌØËÏ × MetaPost, --- ÉÈ ÎÅÔ × \MF.}
%%\caption{Macros and internal variables defined in MetaPost but not \MF.}
\label{mponly}
\end{table}


\bibliographystyle{plain}
\bibliography{mpman-ru}


\printindex


\end{document}

% Copyright 1990 - 1995 by AT&T Bell Laboratories.
% Updated 2006 by Taco Hoekwater, Karl Berry, and others.

% Permission to use, copy, modify, and distribute this software
% and its documentation for any purpose and without fee is hereby
% granted, provided that the above copyright notice appear in all
% copies and that both that the copyright notice and this
% permission notice and warranty disclaimer appear in supporting
% documentation, and that the names of AT&T Bell Laboratories or
% any of its entities not be used in advertising or publicity
% pertaining to distribution of the software without specific,
% written prior permission.

% AT&T disclaims all warranties with regard to this software,
% including all implied warranties of merchantability and fitness.
% In no event shall AT&T be liable for any special, indirect or
% consequential damages or any damages whatsoever resulting from
% loss of use, data or profits, whether in an action of contract,
% negligence or other tortious action, arising out of or in
% connection with the use or performance of this software.

% In addition, John Hobby, the original author of MetaPost and this
% manual, makes the following requests:
% - I request that it remain clear that I am the author of
%   "A User's Manual for MetaPost" and "Drawing Graphs with MetaPost".
% - I request to be consulted before significant changes are made.