new latex package xpicture (2jan13)

git-svn-id: svn://tug.org/texlive/trunk@28704 c570f23f-e606-0410-a88d-b1316a301751

8 files changed, 6794 insertions, 1 deletions

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+
+   The xpicture package, version 1.2a
+   (Several extensions of the "picture" standard environment,
+    including graphs of functions and parametric curves)
+   Robert Fuster, 2012/12/17
+
+
+1. Licence
+----------
+This material is subject to the LaTeX Project Public License. 
+
+See http://www.ctan.org/tex-archive/help/Catalogue/licenses.lppl.html 
+for the details of that license.
+
+
+2. About this package
+---------------------
+
+The xpicture package introduces several new graphical instructions, 
+and some enriched versions of standard instructions used inside the picture 
+environment that, among other utilities, will provide the possibility of 
+using different reference systems and a fine control the precise position 
+where the objects are placed in your drawing.
+
+But the most interesting feature of this package is the ability to draw high
+quality curves such that conic sections, graphs of elementary functions and 
+parametric curves, from LaTeX and using the typical LaTeX syntax.
+
+The new instructions defined by this package can be classified as follows:
+
+       -- Reference systems and coordinates:
+
+             - Declaration and use of different reference systems, 
+               with Cartesian or polar coordinates.
+             - Instructions to show Cartesian or polar reference systems.
+
+       -- An alternative to the picture environment, compatible with 
+          the new reference systems.
+  
+       -- Alternative instructions or extensions of the standard picture
+          commands and those defined by the packages pict2e and curve2e:
+
+             - Enriched versions of marks \put and \multiput, providing an
+               adequate control of the precise position in which objects 
+               are composed.
+             - Instructions for drawing straight segments, vectors
+               (in any direction and using any reference system), polygonal 
+               lines, and regular and arbitrary polygons.
+
+       -- Regular curves:
+
+             - Instructions for drawing conic sections (circles, ellipses, 
+               hyperbolas and parabolas) and arcs of these curves.
+             - Instructions to graph functions and parametrically defined 
+               curves.
+
+
+This package requires the "calculator" and "calculus" packages. You can
+download these packages from CTAN:
+
+        /macros/latex/contrib/calculator
+
+Packages "pict2e", "curve2e" and "xcolor" are also needed. These packages are 
+included in major TeX distributions.
+
+
+3. Installation and documentation
+---------------------------------
+
+After uncompressing "xpicture.zip" you will have the following files:
+
+   -- "README". This file.
+   -- "xpicture.dtx". The source file.
+   -- "xpicture-doc.pdf". The compiled "xpicture" user manual.
+   -- "xpicture-doc.tex". The user manual source file.
+   -- "xpicture.tds.zip". Ready to use tds-structures zip file.
+
+Then, you can install the package in two ways: 
+
+   a) Unpacking the zip file xpicture.tds.zip into your local texmf tree 
+      and updating the file database, or
+
+   b) By compiling the source file "xpicture.dtx" in the following sequence 
+
+         >> pdflatex xpicture.dtx
+         >> pdflatex xpicture.dtx
+         >> makeindex -s gind.ist -o xpicture.ind xpicture.idx
+         >> pdflatex xpicture.dtx 
+
+      Then, several files will be generated:
+
+         "xpicture.sty" (the package). 
+          Move this file where LaTeX search for (typically, in a local
+          texmf tree, at tex/latex/xpicture/) and refresh the file database.
+   
+         "xpicture.pdf" (documented source and reference manual).
+
+         "xpicture.cfgxmpl" (costumizable local configuration file).
+
+      Recall that the user manual is not "xpicture.pdf", but 
+      "xpicture-doc.pdf". If you re-compile this file,
+       many small files, named "xpictureNN.tex" are generated.
+      These files contain the source code of all examples included 
+      in the manual.
+      You can store or discard this files.
+
+Please, visit the "xpicture" homepage at
+
+        http://www.upv.es/~rfuster/xpicture
+
+---------------------------------------------------
+Robert Fuster
+rfuster@mat.upv.es
+
+Universitat Polit\`ecnica de Val\`encia, 2012/12/17
+---------------------------------------------------
+
diff --git a/Master/texmf-dist/doc/latex/xpicture/xpicture-doc.pdf b/Master/texmf-dist/doc/latex/xpicture/xpicture-doc.pdf
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diff --git a/Master/texmf-dist/doc/latex/xpicture/xpicture-doc.tex b/Master/texmf-dist/doc/latex/xpicture/xpicture-doc.tex
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+\documentclass{article}
+
+\usepackage[a4paper,margin=2cm]{geometry}
+\usepackage[T1]{fontenc}
+
+\usepackage{xpicture}
+
+\usepackage{ifthen}
+\usepackage{array}
+\usepackage{fancyvrb}
+\usepackage[colorlinks]{hyperref}
+
+\usepackage{amsmath}
+\usepackage{paralist}
+\usepackage{graphicx}
+\usepackage{makeidx}
+\makeindex
+\renewcommand{\today}{2012/12/17}
+
+\newcommand{\TIT}{\textit}
+\newcommand{\TTT}{\texttt}
+\newcommand{\TTTit}[1]{\TTT{\TIT{#1}}}
+\newcommand{\cs}[1]{\mbox{\textnormal{\TTT{\textbackslash #1}}}}
+\newcommand{\environ}[1]{\textnormal{\TTT{#1}}}
+\newcommand{\package}[1]{\textnormal{\TTT{#1}}}
+\newcommand{\ttindex}[1]{\index{#1@\texttt{#1}}}
+\newcommand{\ttslashindex}[1]{\index{#1@\texttt{\textbackslash #1}}}
+\newcommand{\csdef}[1]{\cs{#1}\ttslashindex{#1}}
+\newcommand{\packagedef}[1]{%
+   \package{#1}\index{#1@\texttt{#1} (package)}}
+\newcommand{\environdef}[1]{%
+   \package{#1}\index{#1@\texttt{#1} (environment)}}
+\newcommand{\optiondef}[1]{%
+   \textnormal{\TTT{#1}}\index{#1@\texttt{#1} (package option)}}
+\newcounter{exem}\stepcounter{exem}
+\newenvironment{exemple}{%
+   \VerbatimEnvironment\begin{VerbatimOut}{./xpicture\theexem.tex}}{%
+   \end{VerbatimOut}
+   \par\medskip\noindent
+   \marginpar{\fbox{Ex. \theexem}}\begin{minipage}{\linewidth}
+      \begin{minipage}{0.45\linewidth}
+         \setlength{\parindent}{2ex}
+         \catcode`\%=14
+         \input{./xpicture\theexem}
+      \end{minipage}\hfill
+      \begin{minipage}{0.45\linewidth}
+         \small
+         \VerbatimInput{./xpicture\theexem.tex}
+      \end{minipage}
+   \end{minipage}
+   \stepcounter{exem}\par\bigskip\noindent}
+\newenvironment{Exemple}{%
+   \VerbatimEnvironment\begin{VerbatimOut}{./xpicture\theexem.tex}}{%
+   \end{VerbatimOut}
+   \par\noindent
+   \marginpar{\fbox{Ex. \theexem}}\fbox{\begin{minipage}{\linewidth}
+      \begin{minipage}{\linewidth}
+         \setlength{\parindent}{2ex}
+         \bigskip\par
+         \catcode`\%=14
+         \input{./xpicture\theexem}
+      \end{minipage}\medskip\par
+      \hspace*{0.125\linewidth}\rule{0.75\linewidth}{0.4pt}\par\medskip
+      \small
+      \VerbatimInput{./xpicture\theexem.tex}
+   \end{minipage}}\stepcounter{exem}\par\bigskip\noindent}
+
+\begin{document}
+\begin{titlepage}
+   \centering
+   \bfseries\Large Robert Fuster
+
+   \rule{\textwidth}{1pt}
+
+   The \textsf{xpicture} package 
+
+   (\Verb+http://www.upv.es/~rfuster/xpicture+)
+
+   Several extensions of the \textsf{picture} standard environment
+
+   User Manual
+   \vspace{\stretch{1}}
+   \begin{Exemple}
+      \setlength{\unitlength}{1cm}
+      \footnotesize
+      \DIVIDE{1}{12}{\invXII}
+      \MULTIPLY{12}{\numberTWOPI}{\phione}
+      \MULTIPLY{12}{64}{\divisions}
+
+      \COMPOSITIONfunction{\EXPfunction}{\COSfunction}{\Afunction}
+      \SCALEVARIABLEfunction{4}{\COSfunction}{\Bfunction}
+      \SCALEVARIABLEfunction{\invXII}{\SINfunction}{\cfunction}
+      \POWERfunction{\cfunction}{5}{\Cfunction}
+      \LINEARCOMBINATIONfunction{1}{\Afunction}{-2}{\Bfunction}{\ABfunction}
+      \SUMfunction{\ABfunction}{\Cfunction}{\ABCfunction}
+      \PRODUCTfunction{\SINfunction}{\ABCfunction}{\Xfunction}
+         % x=(sin t)(exp(cos t)-2 cos 4t + (sin(t/12))^5)
+      \PRODUCTfunction{\COSfunction}{\ABCfunction}{\Yfunction}
+         % y=(cos t)(exp(cos t)-2 cos 4t + (sin(t/12))^5)
+      \PARAMETRICfunction{\Xfunction}{\Yfunction}{\butterfly}
+      \centering
+      \begin{Picture}(-4,-3)(4,4)
+         \PlotParametricFunction[\divisions]\butterfly{0}{\phione}
+      \end{Picture}
+      \begin{gather*}
+         x=\sin t\left(\mathrm e^{\cos t}-2\cos 4t 
+                      +\sin^5\left(\frac t{12}\right)\right) \\
+         y=\cos t\left(\mathrm e^{\cos t}-2\cos 4t 
+                      +\sin^5\left(\frac t{12}\right)\right)
+     \end{gather*}
+   \end{Exemple}
+    \footnotesize\today
+\end{titlepage}
+\stepcounter{page}
+
+\tableofcontents
+\newpage
+
+   The \package{xpicture} package extends the 
+   \environ{picture} standard environment
+   and packages \package{pict2e} and \package{curve2e}, 
+   adding the ability to work with arbitrary 
+   reference systems and with Cartesian or polar coordinates. 
+   In addition to other utilities,
+   the greater interest of \package{xpicture} 
+   lies in its capacity to draw function graphs,
+   conic sections and arcs, and parametrically defined curves.
+    
+   This is the user manual of \package{xpicture}.
+   Technical documentation and reference manual are contained 
+   in file \texttt{xpicture.pdf}, distributed together with the package.
+
+\section{Introduction. New graphical instructions}
+The \package{xpicture} package introduces several new graphical 
+instructions, and some enriched versions of standard
+instructions used inside the \environ{picture} environment.
+All these new instructions can be classified as follows:
+\begin{itemize}
+ \item Reference systems and coordinates:
+\begin{itemize}
+\item Declaration and use of different reference systems,
+with Cartesian or polar coordinates.
+\item Instructions to show Cartesian or polar reference systems.
+\end{itemize}
+ \item  An alternative to the \environ{picture} environment,
+compatible with the new reference systems.
+ \item Alternative instructions or extensions of the standard
+ \environ{picture} commands and those defined by the packages
+ \packagedef{pict2e} and \packagedef{curve2e}:
+\begin{itemize}
+ \item Enriched versions of marks \cs{put} and \cs{multiput},
+ providing an adequate control of the precise position 
+in which objects are composed
+(this functionality is especially useful in the composition
+of not strictly graphical objects, such as formulas or labels).
+\item Instructions for drawing straight segments, vectors
+(in any direction and using any reference system), polygonal lines,
+and regular and arbitrary polygons.
+\end{itemize}
+\item Regular curves:
+\begin{itemize}
+\item Instructions for drawing conic sections (circles, ellipses,
+hyperbolas and parabolas) and arcs of these curves.
+\item Instructions to graph functions and parametrically defined curves
+(this is the most interesting feature of this package).
+\end{itemize}
+\end{itemize}
+
+The only requeriments for \package{xpicture} are packages 
+\packagedef{calculator}, \packagedef{calculus}, 
+\packagedef{curve2e} and \packagedef{xcolor}.
+Therefore, it works with any \TeX{}
+extension compatible with these packages. You can compile a document 
+including \package{xpicture} pictures directly with 
+\TTT{pdflatex},\ttindex{pdflatex}
+\TTT{lualatex},\ttindex{lualatex} 
+\TTT{xelatex}\ttindex{xelatex} 
+or indirectly, via \TTT{latex/dvips}\ttindex{latex},\ttindex{dvips}
+ \TTT{latex/dvips/dvipdfm},\ttindex{dvipdfm} \ldots
+Pure \TTT{dvi} files are not supported, but some \TTT{dvi} previewers
+may show partially \package{xpicture} draws included in \TTT{dvi} files. 
+
+\section{A preliminary observation.
+         Compatibility with text composition in color}
+The \package{xpicture} package automatically loads the
+\packagedef{xcolor} package.
+So, we can compose our
+pictures (and the whole document) in various colors. However,
+when used in the body of the \textsf{picture} environment,
+marks \cs{color} and \cs{colortext}
+often introduce spurious spaces.
+For this reason, the \package{xpicture} package introduces the new command
+\csdef{pictcolor}.
+\begin{Verbatim}[commandchars=\|\[\]]
+\pictcolor{|TIT[color]}
+\end{Verbatim}
+This mark behaves like the \cs{color} command, but does not produces these
+inappropriate spaces.
+To change colors inside a picture, instead of \cs{color} or \cs{colortext},
+use always the \cs{pictcolor} declaration.
+
+\section{Coordinate systems and the \environ{Picture} environment}
+\subsection{Coordinates}
+The standard \environ{picture} environment establishes
+a rectangular coordinate system, so that all
+graphic objects are placed in the picture using the canonical
+coordinates of the plane. From now on, we will call
+this reference system \emph{the standard reference system}.
+Loading the \package{xpicture} package, we can use any other affine
+reference system and combine it with the use of polar coordinates.
+
+\subsubsection{Reference systems}
+The \package{xpicture} package allows us to use other reference systems.
+For the purpose we are interested, a reference system consists
+of an origin of coordinates and a pair of linearly independent vectors.
+Typing\ttslashindex{referencesystem}
+\begin{Verbatim}[commandchars=\|\[\]]
+\referencesystem(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])(|TIT[x2],|TIT[y2])
+\end{Verbatim}
+we declare the new reference system  with origin at point
+$(\TTT{\TIT{x0}},\TTT{\TIT{y0})} $ and coordinate vectors
+$(\TTT{\TIT{x1}},\TTT{\TIT{y1}})$ and
+$(\TTT{\TIT{x2}},\TTT{\TIT{y2}})$.
+If the coordinates of the point $P$ with respect to this reference system
+are $(\bar{\TTT{\TIT{x}}},\bar{\TTT{\TIT{y}}})$, then the
+coordinates of $ P $ with respect to the standard system,
+$(\TTT{\TIT{x}},\TTT{\TIT{y}})$, are calculated with the formula
+\newenvironment{qmatrix}{\left[\begin{matrix}}{\end{matrix}\right]}
+\[
+ \begin{qmatrix}
+          \TTT{\TIT{x}} \\ \TTT{\TIT{y}}
+     \end{qmatrix}=\begin{qmatrix}
+         \TTT{\TIT{x0}} \\ \TTT{\TIT{y0}}
+    \end{qmatrix} +
+    \begin{qmatrix}
+         \TTT{\TIT{x1}} & \TTT{\TIT{x2}} \\
+         \TTT{\TIT{y1}} & \TTT{\TIT{y2}}
+    \end{qmatrix}    \begin{qmatrix}
+         \bar{\TTT{\TIT{x}}} \\ \bar{\TTT{\TIT{y}}}
+    \end{qmatrix}
+\]
+
+For example,
+\begin{Verbatim}[commandchars=\|\[\]]
+\referencesystem(1,2)(1,0)(0.5,0.5)
+\end{Verbatim}
+sets a new reference system that has its origin in the point $O(1,2)$
+and the coordinate vectors $\vec u_1=(1,0)$ and $\vec u_2=(1/2,1/2)$.
+The following pictures show this coordinate system built on the standard
+reference system
+and a Cartesian grid refered to the new reference system.
+
+\noindent
+\setlength\unitlength{1cm}%
+ \renewcommand{\Pictlabelsep}{0.2}
+\begin{Picture}(-3.1,-3.1)(3.1,3.1)
+\put(-1.5,0){\line(1,0){3}}
+\put(0,-1.5){\line(0,1){3}}
+{\makenolabels
+\cartesianaxes(-3,-3)(3,3)}
+\thicklines
+ \xVECTOR(0,0)(1,2)
+\pictcolor{red}
+\referencesystem(1,2)(1,0)(0.5,0.5)
+\Put[-45](0,0){$O$}
+\renewcommand\axescolor{red}
+\renewcommand\axeslabelcolor{red}
+\cartesianaxes(-2.1,-2.1)(2.1,2.1)
+\linethickness{1pt}
+\xVECTOR(0,0)(1,0)
+\xVECTOR(0,0)(0,1)
+\rPut{SE}(1,0){$\vec u_1$}
+\Put[SE](0,1){$\vec u_2$}
+\end{Picture}
+\hfill%
+{\referencesystem(1,2)(1,0)(0.5,0.5)
+\begin{Picture}(-3.6,-3.6)(3.5,3.5)
+\thinlines
+\cartesiangrid(-3,-3)(3,3)
+\pictcolor{red}
+\linethickness{1pt}
+\xVECTOR(0,0)(1,0)
+\xVECTOR(0,0)(0,1)
+\end{Picture}}
+
+Alternatively, you can use the \csdef{changereferencesystem} declaration:
+in the instruction
+\begin{Verbatim}[commandchars=\|\[\]]
+\changereferencesystem(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])(|TIT[x2],|TIT[y2])
+\end{Verbatim}
+point $(\TTT{\TIT{x0}},\TTT{\TIT{y0})}$ and vectors
+$(\TTT{\TIT{x1}},\TTT{\TIT{y1}})$ i $(\TTT{\TIT{x2}},\TTT{\TIT{y2}})$
+are not refered to the standard system,
+but to the \emph{active} reference system.\footnote{%
+In other words, the instruction
+\cs{referencesystem} changes from the standard reference system
+to the new one, while
+\cs{changereferencesystem} changes from the active system.}
+Moreover, as the more interesting (and frequent) reference system changes
+consist of translations of the origin, rotations of the axes
+and symmetries, \package{xpicture}
+introduces three specific commands to these special cases:
+\ttslashindex{translateorigin}
+\begin{Verbatim}[commandchars=\|\[\]]
+\translateorigin(|TIT[x0],|TIT[y0])
+\end{Verbatim}
+moves the origin to the specified coordinates.
+\ttslashindex{rotateaxes}
+\begin{Verbatim}[commandchars=\|\[\]]
+\rotateaxes{|TIT[angle]}
+\end{Verbatim}
+rotates the axes. The \TTT{\TIT{angle}}  parameter is interpreted
+as the rotation angle in radians
+(if the \csdef{radiansangles} declaration is active) or in
+sexagesimal degrees (if the \csdef{degreesangles} declaration is active).
+And\ttslashindex{symmetrize}
+\begin{Verbatim}[commandchars=\|\[\]]
+\symmetrize{|TIT[angle]}
+\end{Verbatim}
+performs a symmetry, being \TTT{\TIT{angle}}
+the angle between the $x$ axis and  the symmetry axis.
+Also here, the \csdef{radiansangles} and \csdef{degreesangles}
+declarations determine if angles are
+interpreted as radians or degrees.
+%
+These three declarations always apply to the active reference system.
+\begin{Exemple}
+\newcommand{\mypicture}{%
+{\thicklines
+\xVECTOR(-1,-1)(1,1)
+\pictcolor{red}\Circle{1}
+\pictcolor{blue}\regularPolygon{1}{4}
+\polarreference\degreesangles
+\pictcolor{green}\Polygon(1,90)(0,0)(1,-30)}}
+\centering
+\setlength{\unitlength}{1cm}
+\fbox{\begin{Picture}[black!5!white](-1.5,-6.5)(14.5,1.5)
+\cartesiangrid(-1,-1)(14,1)
+\mypicture
+{\referencesystem(3,0)(1,1)(1,0)
+\mypicture
+\changereferencesystem(0,4)(-1,1)(1,-2)
+\mypicture}
+\degreesangles
+\translateorigin(10,0)
+{\rotateaxes{45}
+\mypicture}
+\translateorigin(3,0)
+\symmetrize{45}
+\mypicture
+\referencesystem(6.5,-4)(7,0)(0,-2)\mypicture
+\end{Picture}}
+\end{Exemple}
+
+The \csdef{standardreferencesystem} declaration restores the standard 
+reference.
+
+\medskip
+
+Changes of reference system can
+be used inside or outside the \environ{Picture} environment.
+In the next sections we will see what are the effects produced in each case.
+
+\subsubsection{Polar coordinates}
+Instead of Cartesian coordinates, we can refer to a point $P$ using the 
+polar coordinates $(r,\phi)$ of this point: 
+$r$ is the distance from the origin $O$ and $\phi$ is the angle between 
+the first coordinate vector and the $OP$ segment.
+The \csdef{cartesianreference} and \csdef{polarreference} declarations
+establish the coordinates of one or the other type.
+By default, the Cartesian coordinates are used, but in some cases
+is much easier determine polar coordinates.
+Additionally, the \csdef{radiansangles} and \csdef{degreesangles}
+declarations
+sets angle measuring in radians or in degrees, respectively
+(by default, angles are measured in radians).
+
+The following example shows a typical situation in which it is more
+appropriate to use polar coordinates:
+the \emph{natural} way to enter coordinates on a circle is using 
+polar coordinates.
+
+\begin{exemple}
+\setlength{\unitlength}{3cm}
+\fbox{\begin{Picture}(-1.3,-1.3)(1.3,1.3)
+\polarreference
+\degreesangles
+
+\renewcommand{\Pictlabelsep}{0.1}
+
+\multiPut(1,0)(0,30){12}{\circle*{0.05}}
+    % Put twelve dots, one unit apart, 
+    % at 0, 30, 60, ..., 330 degrees
+
+\cPut{90}(1,90){\textsc{xii}}
+\cPut{0}(1,0){\textsc{iii}}
+\cPut{270}(1,270){\textsc{vi}}
+\cPut{180}(1,180){\textsc{ix}}
+
+\pictcolor{blue}\thicklines
+
+\arrowsize{8}{2}
+\xtrivVECTOR(0,0)(0.5,37.5)
+\xtrivVECTOR(0,0)(0.9,180)
+
+\Put(0,0){\circle*{0.1}}
+\linethickness{4pt}
+\Circle{1.3}
+\end{Picture}}
+\end{exemple}
+
+The new commands defined in the \package{xpicture} package and requiring
+some kind of coordinates support polar coordinates,
+except the \environ{Picture} and \environ{xpicture} environments
+and the \cs{cartesianaxes} and \cs{cartesiangrid} environments.
+\subsection{The \environ{Picture} (or \environ{xpicture}) environment}
+The \package{xpicture} package supports all drawing commands
+from standard \LaTeX;
+in particular, you can use the \environ{picture} environment.
+However, in the expression
+\begin{Verbatim}[commandchars=\|\[\]]
+\begin{picture}(|TIT[x],|TIT[y])(|TIT[x0],|TIT[y0])
+\end{Verbatim}
+the pairs of numbers \TTT{(\TIT x,\TIT y)} and
+\TTT{(\TIT{x0},\TIT{y0})} always denote standard coordinates,
+namely,
+the \environ{picture} environment only uses the standard reference,
+thus it defines, as drawing area, the rectangle
+\TTT{[\TIT{x0},\TIT{x-x0}]}$\times$\TTT{[\TIT{y0},\TIT{y-y0}]},
+regardless of whether this is the  active reference.
+If we want draw a picture referring coordinates to an alternative reference
+system, to determine the appropriate drawing area in absolute coordinates
+is not obvious (and often is difficult).
+However, the \environdef{Picture} environment 
+defines a working area on the active reference system: the
+\begin{Verbatim}[commandchars=\|\{\}]
+\begin|{Picture|}[|TIT{color}](|TIT{x0},|TIT{y0})(|TIT{x1},|TIT{y1})
+\end{Verbatim}
+instruction fixes the drawing area
+\TTT{[\TIT{x0},\TIT{x1}]}$\times$\TTT{[\TIT{y0},\TIT{y1}]},
+refered to the active reference system.
+Here, the \TTT{(\TIT{x0},\TIT{y0})} i \TTT{(\TIT{x1},\TIT{y1})}
+coordinates are always rectangular
+(even when reference in polar coordinates is active).
+More precisely, this environment defines a \environ{picture} box
+that circumscribes our drawing area.
+If the optional argument is used, background is colored in the given 
+\textit{color}. 
+
+\emph{Very important: note that the syntax of the 
+\environ{picture} environment is not analogous
+to the new environment \environ{Picture}}:
+Here two pairs of coordinates are required,
+\TTT{(\TIT{x0},\TIT{y0})} and \TTT{(\TIT{x1},\TIT{y1})},
+representing two opposite corners of the drawing area.\footnote{%
+Although it may seem more \emph{logical}
+preserve the syntax of \environ{picture} environment, 
+it is more natural to define the drawing area in that way.}
+Obviously, if the reference sustem is the standard, expression
+\begin{Verbatim}[commandchars=\|\[\]]
+\begin{Picture}(0,0)(|TIT[x],|TIT[y])
+\end{Verbatim}
+is equivalent to
+\begin{Verbatim}[commandchars=\|\[\]]
+\begin{picture}(|TIT[x],|TIT[y])
+\end{Verbatim}
+
+The following example shows the boxes produced by the 
+\environ{picture} and \environ{Picture} environments.
+
+\medskip
+
+\begin{Exemple}
+ \begin{center}
+  \setlength{\unitlength}{0.5cm}
+  \referencesystem(0,0)(1,-1)(1,1)
+
+  \fbox{\begin{picture}(6,6)(-3,-3)
+   \cartesiangrid(-3,-3)(3,3)
+  \end{picture}}\qquad
+  \fbox{\begin{Picture}(-3,-3)(3,3)
+   \cartesiangrid(-3,-3)(3,3)
+  \end{Picture}}
+ \end{center}
+\end{Exemple}
+
+The left picture does not fit the box.
+ In fact, some elementary geometric considerations
+shown that a square box of $ 12\times12$ units of length must be reserved,
+\begin{Verbatim}[commandchars=\|\[\]]
+\begin{picture}(12,12)(-6,-6)
+\end{Verbatim}
+The use of the \environ{Picture} environment frees us to determine the
+actual dimensions of the drawing.
+
+The new environment \environdef{xpicture} is an alias to the
+\environ{Picture} environment.
+Its sintax and its behavior are identical.
+
+On the other hand, the \csdef{draftPictures} declaration 
+disables all the instructions defined in this package, 
+replacing each picture set in a \environ{Picture} environment
+by a parallelogram circumscribed by a white rectangle (the box that shows
+the area reserved for the drawing).\footnote{If you use an instruction 
+not directly defined by \package{xpicture} (inside of a \environ{Picture}
+environment), this instruction may take effect.}
+
+\begin{center}
+\setlength{\unitlength}{1cm}
+\draftPictures
+
+\begin{minipage}{5cm}\centering
+\begin{Picture}(0,0)(5,5)
+\end{Picture}
+
+\verb+\standardreferencesystem+
+\end{minipage}\quad
+\begin{minipage}{7.5cm}\centering
+\referencesystem(0,0)(1,0)(0.5,1)
+\begin{Picture}(0,0)(5,5)
+\end{Picture}
+
+\verb+\referencesystem(0,0)(1,0)(0.5,1)+
+\end{minipage}
+\end{center}
+
+\subsection{Coordinate axes}
+Instruction\ttslashindex{cartesianaxes}
+\begin{Verbatim}[commandchars=\|\[\]]
+\cartesianaxes(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])
+\end{Verbatim}
+draws the coordinate axes corresponding to the
+\TTT{[\TIT{x0},\TIT{x1}]}$\times$\TTT{[\TIT{y0},\TIT{y1}]} rectangle.
+Arguments \TTT{\TIT{x0}}, \TTT{\TIT{y0}},
+\TTT{\TIT{x1}} and \TTT{\TIT{y1}} must satisfy the conditions
+\TTT{\TIT{x0}}$<$\TTT{\TIT{x1}} and \TTT{\TIT{y0}}$<$\TTT{\TIT{y1}}.
+Here, coordinates \TTT{(\TIT{x0},\TIT{y0})} and \TTT{(\TIT{x1},\TIT{y1})}
+are always rectangular (even when reference in polar coordinates is active).
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{0.75cm}%
+\begin{Picture}[black!10!white](-4,-3)(4,3)
+\renewcommand{\Pictlabelsep}{0.2}
+\cartesianaxes(-3.5,-2.5)(3.5,2.5)
+\Put[r](3.5,0){$x$}
+\Put[t](0,2.5){$y$}
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{exemple}
+\begin{center}
+\referencesystem(0,0)(1,0)(0.5,1)
+\setlength{\unitlength}{0.75cm}%
+\begin{Picture}[black!10!white](-4,-3)(4,3)
+\renewcommand{\Pictlabelsep}{0.2}
+\cartesianaxes(-3.5,-2.5)(3.5,2.5)
+\Put[r](3.5,0){$x$}
+\Put[t](0,2.5){$y$}
+\end{Picture}
+\end{center}
+\end{exemple}
+The following parameters control the style of the axes, the cut marks
+and labels on the axes:
+
+\subsubsection{The style of the axes}
+\begin{description}
+\item[\csdef{axescolor}] By default, the axes color is \TTT{black}, but
+we can change it by redefining the \cs{axescolor} declaration. For example,
+\begin{Verbatim}[commandchars=\|\[\]]
+\renewcommand{\axescolor}{orange}
+\end{Verbatim}
+
+We must use a color name predefined in the package \textsf{xcolor}
+or defined by the user (for example, using the \cs{definecolor} command).
+\item[\csdef{axesthickness}] Length determining the thickness of axes 
+(default \verb+1 pt+).
+You can modify it using any command that fixes a length (as \cs{setlength}
+or \cs{settowidth}).
+\item[\csdef{xunitdivisions}, \csdef{yunitdivisions}] Number of subdivisions of
+the unit (in each axis). 
+By default, 1. These arguments can also be redefined using
+the \cs{renewcommand} command (they must be positive integers).
+\end{description}
+\begin{exemple}
+\renewcommand{\xunitdivisions}{2}
+\renewcommand{\yunitdivisions}{3}
+
+\begin{center}
+\setlength{\unitlength}{1cm}%
+\begin{Picture}(-4,-4)(4,4)
+\cartesianaxes(-3.5,-3.5)(3.5,3.5)
+\end{Picture}
+\end{center}
+\end{exemple}
+\subsubsection{Axes position}
+The coordinate axes (and also tags and cut marks)
+are placed by default in the traditional way, on the $y = 0$ (the $x$ axis)
+and $x = 0$ (the $y$ axis) lines.
+However, sometimes the fact that labels are inside the graphic can be
+annoying.\footnote{And produces strange effects when the origin $(0.0)$
+is not in the drawing area.}
+Alternatively, we can place axes and tags at the 
+lower and left sides of the coordinate rectangle.
+To choose between these two options we should use the following
+declarations:
+\begin{description}
+\item[\csdef{internalaxes}, \csdef{externalaxes}]
+If the \cs{internalaxes} declaration is active, then axes lies
+on $y=0$ and $x=0$.
+
+However, if we activate the \cs{externalaxes} declaration, the axes
+produced by the instruction
+\begin{Verbatim}[commandchars=\|\[\]]
+\cartesianaxes(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])
+\end{Verbatim}
+lies on $y=\TTT{\TIT{y0}}$ and $x=\TTT{\TIT{x0}}$.
+
+By default, the \cs{internalaxes} declaration is active.
+\end{description}
+\begin{exemple}
+\renewcommand{\xunitdivisions}{2}
+\renewcommand{\yunitdivisions}{2}
+
+\begin{center}
+\externalaxes
+\setlength{\unitlength}{1cm}%
+\begin{Picture}(-4,-4)(4,4)
+\cartesianaxes(-3.5,-3.5)(3.5,3.5)
+\end{Picture}
+\end{center}
+\end{exemple}
+
+\subsubsection{Tags style}
+The numerical tags on the axes are made in math mode.
+If you need textual labels, put them in a \cs{mbox} or,
+using \package{amsmath}, a \cs{text} box.
+We can control the color, attributes and distance to the axes of these tags,
+redefining
+(with \cs{renewcommand}) the following marks:
+\begin{description}
+\item[\csdef{axeslabelcolor}] The color of the numerical tags on the axes.
+By default, this color is identical to the axes color.
+\item[\csdef{axeslabelsize}] Size of numerical tags.
+By default, \cs{small}.
+\item[\csdef{axeslabelmathversion}]
+ Mathversion of numerical tags.
+By default, \TTT{normal}.\footnote{Standard \emph{math versions}
+are \TTT{normal} and \TTT{bold}, but some packages
+define other math versions.}
+\item[\csdef{axeslabelmathalphabet}] Mathalphabet of numerical tags.
+By default, \cs{mathrm}.
+\item[\csdef{axislabelsep}] Distance between tags and cut marks,
+measured in \cs{unitlength} units;\footnote{The distance between axes and
+tags equals \cs{ticssize}$+$\cs{axislabelsep}.}
+by default, \verb+0.1+ (see later the description of \cs{makenotics}).
+\end{description}
+
+\subsubsection{Tags position}
+Position of tags is controlled by two declarations:
+\begin{description}
+\item[\cs{xlabelpos\{\TIT{position}\}}]\ttslashindex{xlabelpos}
+change the relative position of labels in $x$ axis. 
+Admissible values are those allowed in the \TTT{\TIT{position}} 
+argument of command \cs{Put} (see subsection~\ref{subsec:put}).
+Default is \verb+-90+.
+\item[\cs{ylabelpos\{\TIT{position}\}}]\ttslashindex{ylabelpos}
+change the relative position of labels in $y$ axis. 
+Default is \verb+180+.
+\end{description}
+
+\subsubsection{Style of cut marks}
+Units (and, optionally, unit fractions) are marked over axes with small
+segments,
+the style of which is controlled by the following parameters:
+\begin{description}
+\item[\csdef{ticssize}, \csdef{secundaryticssize}]
+These lengths control the size of the tics:
+\cs{ticssize} is half the length of main cuts
+(by default, \verb+4pt+)
+and \cs{secundaryticssize} is half the length of secundary cuts
+(by default, \verb+2pt+).
+\item[\csdef{ticsthickness}] Thickness of the marks on axes 
+(by default, \verb+1pt+).
+\item[\csdef{ticscolor}] Color of the marks on axes (by default, \verb+black+).
+\end{description}
+\begin{exemple}
+\renewcommand{\axescolor}{blue}
+\setlength{\axesthickness}{3pt}
+\renewcommand{\xunitdivisions}{2}
+\renewcommand{\yunitdivisions}{3}
+
+\renewcommand{\axeslabelcolor}{teal}
+\renewcommand{\axeslabelsize}{\footnotesize}
+\renewcommand{\axeslabelmathversion}{bold}
+\renewcommand{\axeslabelmathalphabet}{\mathsf}
+\renewcommand{\axislabelsep}{0.05}
+\xlabelpos{ttl}
+\ylabelpos{r}
+
+\setlength{\ticssize}{0.2cm}
+\setlength{\secundaryticssize}{0.1cm}
+\setlength{\ticsthickness}{2pt}
+\renewcommand{\ticscolor}{blue!50}
+
+\begin{center}
+\degreesangles
+\rotateaxes{-30}
+\setlength{\unitlength}{0.75cm}%
+\begin{Picture}(-5,-4)(5,4)
+\cartesianaxes(-4.5,-3.5)(4.5,3.5)
+\end{Picture}
+\end{center}
+\end{exemple}
+
+\subsubsection{Removing and directly printing cut marks and labels}
+\begin{description}
+ \item [\csdef{maketics}, \csdef{makenotics}]
+ These two declarations determine if
+ divisions on the axes should be marked or not.
+ By default the \cs{maketics} declaration is active.
+
+If divisions are not marked, the \csdef{axislabelsep}
+declaration determines the distance between axes and labels.
+\end{description}
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{0.75cm}%
+\begin{Picture}(-4.5,-2.5)(4.5,2.5)
+\makenotics
+\cartesianaxes(-4,-2)(4,2)
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{description}
+ \item [\csdef{makelabels}, \csdef{makenolabels}] Two declarations
+determining whether numerical labels on the axes must appear or not.
+By default, the \cs{makelabels} declaration is active.
+\end{description}
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{0.75cm}%
+\begin{Picture}(-4.5,-2.5)(4.5,2.5)
+\makenolabels
+\cartesianaxes(-4,-2)(4,2)
+\end{Picture}
+\end{center}
+\end{exemple}
+
+Declarations \cs{makenotics} and \cs{makenolabels}
+can be useful when you want to show only some specific coordinates, 
+when the points to be highlighted on the axes are not integers
+and when you need to print labels in some special format. In  this cases 
+you can plot tics and/or print labels using the following commands.
+\begin{description}
+\item [\cs{plotxtic\{\TIT{x-coor}\}}, \cs{plotytic\{\TIT{y-coor}\}}] 
+\ttslashindex{plotxtic}\ttslashindex{plotytic}
+plot a tic for the given \TIT{x} or \TIT{y} coordinate.
+\item [\cs{printxlabel\{\TIT{x-coor}\}\{\TIT{label}\}}, 
+       \cs{printylabel\{\TIT{y-coor}\}\{\TIT{label}\}}] 
+\ttslashindex{printxlabel}\ttslashindex{printylabel}
+print \TIT{label}
+for the given \TIT{x} or \TIT{y} coordinate. Labels are printed in math mode.
+\item [\cs{printxticlabel\{\TIT{x-coor}\}\{\TIT{label}\}}, 
+       \cs{printyticlabel\{\TIT{y-coor}\}\{\TIT{label}\}}] 
+plot a tic and print \TIT{label} for the given \TIT{x} or \TIT{y} coordinate.
+\end{description}
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{1cm}%
+\begin{Picture}(-4.5,-0.5)(4.5,3.5)
+\makenolabels
+\makenotics
+\cartesianaxes(-4,0)(4,3)
+
+\plotytic{0.5}
+\printylabel{0.5}{1/2}
+\printxticlabel{2}{2}
+
+\Polyline(2,0)(2,0.5)(0,0,5)
+\thicklines
+\SCALEfunction{0.125}{\SQUAREfunction}{\F}
+\PlotFunction[3]{\F}{-4}{4}
+\end{Picture}
+\end{center}
+\end{exemple}
+
+Multiple equally spaced tics and/or labels can be drawn simultaneously:
+\begin{description}
+\item [\cs{plotxtics\{\TIT{firstcoor}\}\{\TIT{incr}\}\{\TIT{bound}\}},
+       \cs{plotytics\{\TIT{firstcoor}\}\{\TIT{incr}\}\{\TIT{bound}\}}]
+\ttslashindex{plotxtics}\ttslashindex{plotytics}       
+plot several (\TIT{x} or \TIT{y}) tics,
+from the initial coordinate \TIT{firstcoor}; \TIT{incr} is the distance 
+between consecutive tics, and the last tic is not in a position 
+greater than \TIT{bound}.
+\item [\cs{printxlabels[\TIT{digits}]\{\TIT{firstcoor}\}\{\TIT{incr}\}%
+       \{\TIT{bound}\}}, 
+       \cs{printylabels[\TIT{digits}]\{\TIT{firstcoor}\}\{\TIT{incr}\}%
+       \{\TIT{bound}\}}] 
+\ttslashindex{printxlabels}\ttslashindex{printylabels} print several labels,
+from the initial coordinate \TIT{firstcoor}; \TIT{incr} is the distance 
+between consecutive label positions, 
+and the last position is not greater than \TIT{bound}. 
+The optional argument \TIT{digits} is the number of decimal digits to be 
+printed (by default, numbers are printed with its natural number of decimals).
+\item [\cs{printxticslabels[\TIT{digits}]\{\TIT{firstcoor}\}\{\TIT{incr}\}%
+          \{\TIT{bound}\}}]\ttslashindex{printxticslabels} 
+ plot \TIT{x} tics and labels simultaneously.
+\item [\cs{printyticslabels[\TIT{digits}]\{\TIT{firstcoor}\}\{\TIT{incr}\}%
+          \{\TIT{bound}\}}]\ttslashindex{printyticslabels}
+ plot \TIT{y} tics and labels simultaneously.      
+\end{description}
+\begin{exemple}
+\externalaxes
+\setlength{\unitlength}{1cm}
+\renewcommand{\axeslabelsize}{\tiny}
+\referencesystem(0,0)(1.5,0)(0,2)
+\begin{center}
+\begin{Picture}(-2.5,-1.5)(2.5,1.5)
+\makenotics
+\makenolabels
+\cartesianaxes(-2.25,-1.25)(2.25,1.25)
+\printxticslabels[1]{-2}{0.5}{2.25}
+\printyticslabels[4]{-1}{0.25}{1}
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{Exemple}
+\setlength{\unitlength}{1cm}
+\begin{center}
+\begin{Picture}(-7,-2.5)(7,2.5)
+{\referencesystem(0,0)(\numberHALFPI,0)(0,1)
+\renewcommand{\xunitdivisions}{2}
+\renewcommand{\yunitdivisions}{2}
+\makenolabels
+\renewcommand{\Pictlabelsep}{0.25}
+\cartesianaxes(-4.2,-2.2)(4.2,2.2)
+
+\printylabels{-2}{0.5}{2}
+
+\highestlabel{$-3\pi/2$}
+\printxlabel{-4}{-2\pi}
+\printxlabel{-3}{-3\pi/2}
+\printxlabel{-2}{-\pi}
+\printxlabel{-1}{-\pi/2}
+\printxlabel{1}{\pi/2}
+\printxlabel{2}{\pi}
+\printxlabel{3}{3\pi/2}
+\printxlabel{4}{2\pi}
+}
+\end{Picture}
+\end{center}
+\end{Exemple}
+
+\subsection{Cartesian grids}
+As an alternative to the \cs{cartesianaxes} command,
+we can use \csdef{cartesiangrid},
+to better visualize the coordinates:
+\begin{Verbatim}[commandchars=\|\[\]]
+\cartesiangrid(|begin[math]x0,y0|end[math])(|begin[math]x1,y1|end[math])
+\end{Verbatim}
+\begin{exemple}
+\definecolor{myblue}{cmyk}{1,1,0,0.5}
+\renewcommand{\gridcolor}{myblue}
+\renewcommand{\secundarygridcolor}{cyan}
+\setlength{\gridthickness}{0.5pt}
+\setlength{\secundarygridthickness}{0.1pt}
+\renewcommand{\xunitdivisions}{5}
+\renewcommand{\yunitdivisions}{5}
+\renewcommand{\axeslabelsize}{\footnotesize}
+\begin{center}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-3.5,-2.5)(3.5,2.5)
+\cartesiangrid(-3.4,-2.4)(3.4,2.4)
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{exemple}
+\definecolor{myblue}{cmyk}{1,1,0,0.5}
+\renewcommand{\gridcolor}{myblue}
+\renewcommand{\secundarygridcolor}{cyan}
+\setlength{\gridthickness}{0.5pt}
+\setlength{\secundarygridthickness}{0.1pt}
+\renewcommand{\xunitdivisions}{5}
+\renewcommand{\yunitdivisions}{5}
+\renewcommand{\axeslabelsize}{\footnotesize}
+\begin{center}
+\setlength{\unitlength}{1cm}
+\referencesystem(0,0)(1,0)(0.25,1)
+\externalaxes
+\begin{Picture}(-4,-3)(4,3)
+\cartesiangrid(-3.4,-2.4)(3.4,2.4)
+\end{Picture}
+\end{center}
+\end{exemple}
+
+\subsubsection{Grid style}
+Note that, in addition to the parameters outlined above, there are the 
+following ones, which control the style of the grid 
+(as in previous cases, these parameters are changed
+by redefining them with the \cs{renewcommand} declaration,
+or using the usual instructions when they are lengths).
+
+\begin{description}
+ \item [\csdef{gridcolor}] determines the color of main divisions in the grid
+(regardless of the axes color). By default, this color is \verb+gray+.
+ \item [\csdef{secundarygridcolor}] determines the color of secundary 
+divisions in the grid.
+By default, \verb+lightgray+).
+\item[\csdef{gridthickness}] thickness of main divisions 
+(by default, \verb+0.4pt+).
+\item[\csdef{secundarygridthickness}] thickness of secundary divisions
+(by default, \verb+0.2pt+).
+\end{description}
+\subsection{Polar grids}
+Finally, instead of Cartesian axes, we can construct a polar grid
+(obviously, this option will be interesting when we use polar coordinates).
+\ttslashindex{polargrid}
+\begin{Verbatim}[commandchars=\|\[\]]
+\polargrid{|TIT[radius]}{|TIT[circledivs]}
+\end{Verbatim}
+(\TTT{\TIT{radius}} and \TTT{\TIT{circledivs}} are, respectively,
+the radius and the number of divisions of the circle
+(\TTT{\TIT{circledivs}}must be a positive integer).
+
+This command supports the same parameters that \cs{cartesianaxes} and
+\cs{cartesiangrid} (when they makes sense), and also the following:
+\begin{description}
+\item[\csdef{runitdivisions}] Number of radial subdivisions of the unit.
+By default, $1$ (it must be a positive integer).
+\end{description}
+\begin{exemple}
+\renewcommand{\runitdivisions}{2}
+\setlength{\unitlength}{0.75cm}
+\renewcommand{\gridcolor}{magenta}
+\begin{center}
+\begin{Picture}(-4,-4)(4,4)
+\polargrid{3.5}{12}
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{exemple}
+\renewcommand{\runitdivisions}{2}
+\setlength{\unitlength}{0.75cm}
+\renewcommand{\gridcolor}{magenta}
+\referencesystem(0,0)(1,-1)(0.5,0.5)
+\begin{center}
+\begin{Picture}(-3.5,-3.5)(3.5,3.5)
+\polargrid{3.5}{12}
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{description}
+\item[\csdef{degreespolarlabels}, \csdef{radianspolarlabels}]
+Arcs are printed, by default, in  radians. 
+If you want angular units mesured in degrees,
+use the  \csdef{degreespolarlabels} declaration (obviously,
+\csdef{radianspolarlabels} recovers tags in radians).
+\end{description}
+\begin{exemple}
+\begin{center}
+\degreespolarlabels
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-4,-4)(4,4)
+\polargrid{3}{24}
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{description}
+\item[\csdef{rlabelpos}] Relative position of labels in polar axis.
+Admissible values are those allowed in the \TTT{\TIT{position}} 
+argument of command \cs{Put} (see subsection~\ref{subsec:put}).
+Default is \verb+bbr+.
+\end{description}
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-4,-4)(4,4)
+\rlabelpos{b}
+\polargrid{3.5}{10}
+\end{Picture}
+\end{center}
+\end{exemple}
+
+
+To remove tags on the polar axis and angles you can use the 
+\csdef{makenolabels} declaration.
+
+\section[Alternatives to some standard commands]{%
+             Alternatives to standard commands
+             \cs{put},\cs{multiput}, \cs{line}, and \cs{vector}}
+Standard commands used inside the \environ{picture} environment
+are not modified by this package
+(although if we include these commands in the body of a \environ{Picture}
+environment).
+In particular, there does not affect the \cs{referencesystem} declaration.
+This package introduces similar commands to those which are sensitive to the
+active reference system and give us a greater control over their behavior.
+These are the instructions described below.
+
+\subsection{Extensions of the \cs{put} command}\label{subsec:put}
+ \begin{description}
+ \item[\csdef{Put}, \csdef{cPut}, \csdef{rPut}]
+\mbox{}
+
+\begin{Verbatim}[commandchars=\|\{\}]
+\Put[|TIT{position}](|TIT{x},|TIT{y})|{|TIT{object}|}
+\Put*[|TIT{position}](|TIT{x},|TIT{y})|{|TIT{object}|}
+\cPut|{|TIT{position}|}(|TIT{x},|TIT{y})|{|TIT{object}|}
+\rPut|{|TIT{position}|}(|TIT{x},|TIT{y})|{|TIT{object}|}
+\rPut*|{|TIT{position}|}(|TIT{x},|TIT{y})|{|TIT{object}|}
+\end{Verbatim}
+place the drawing pointer in the point
+of  coordinates \verb+(+\TTT{\TIT{x}}\verb+,+\TTT{\TIT{y}}\verb+)+
+with respect to the active reference system (which may coincide or not with
+the standard system).
+These commands differ in the criteria used to determine the precise position
+of the object.
+
+Involved parameters are (see below)
+\ttslashindex{Pictlabelsep}
+\ttslashindex{defaultPut}
+\ttslashindex{highestlabel}
+\begin{Verbatim}[commandchars=\|\[\]]
+\Pictlabelsep|{|TIT[distance]|}
+\defaultPut|{c|}/\defaultPut|{r|}
+\highestlabel|{|TIT[text]|}
+\end{Verbatim}
+\medskip
+
+In the following example, the red circle (included as an argument in the
+\cs{put} command) is at the point
+of standard coordinates $(1,-1)$; however, in the case of the
+blue circle, coordinates $(1,-1)$ refer to the active reference system.
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{0.75cm}
+\referencesystem(0,0)(1,-1)(1,1)
+\begin{Picture}(-2.5,-2.5)(2.5,2.5)
+\cartesiangrid(-2,-2)(2,2)
+\pictcolor{red}
+\put(1,-1){\circle*{0.25}}
+\pictcolor{blue}
+\Put(1,-1){\circle*{0.25}}
+\end{Picture}
+\end{center}
+\end{exemple}
+
+Recall that coordinates can be rectangular or polar, and angles may
+be measured in radians or in degrees.
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-2.5,-2.5)(2.5,2.5)
+\cartesiangrid(-2,-2)(2,2)
+\polarreference
+\pictcolor{blue}
+\Put(1,\numberHALFPI){\circle*{0.25}}
+\degreesangles
+\pictcolor{red}
+\Put(1,180){\circle*{0.25}}
+\end{Picture}
+\end{center}
+\end{exemple}
+\subsubsection{Accurate positioning of the graphical object}
+The \TTT{\TIT{position}} argument allows us to fix the relative position of
+\TTT{\TIT{object}} respect to point \TTT{(\TIT{x},\TIT{y})}.
+Note that this argument is optional in \cs{Put} and \cs{Put*},
+but mandatory in the other commands we are describing.
+The purpose of this parameter is to rationalize the disposition of
+objects, especially when they are not strictly graphical objects
+(but labels, text boxes or mathematical formulas). In these cases, 
+the appropriate choice of coordinates seems a problem that is not well
+solved with standard instructions, despite the special syntax of the 
+\cs{makebox} command in the \environ{picture} environment. 
+For example, in this picture (which we made using only the standard 
+\LaTeX{} commands)
+\begin{center}
+\setlength{\unitlength}{2cm}
+
+\begin{picture}(7,3)(-0.5,-1.5)
+
+\put(0,0){\line(1,0){7}}
+\put(0,-1.5){\line(0,1){3}}
+\put(0,-1.5){\line(0,-1){0}}
+\multiput(1.570796,-0.1)(1.570796,0){4}{\line(0,1){0.2}}
+\multiput(-0.1,-1)(0,1){3}{\line(1,0){0.2}}
+
+\qbezier(0,0)(1,1)(1.570796,1)
+\qbezier(1.570796,1)(2.141593,1)(3.141593,0)
+\qbezier(3.141593,0)(4.141593,-1)(4.712389,-1)
+\qbezier(4.712389,-1)(5.283185,-1)(6.283185,0)
+
+\put(-1.570796,0){%
+   \qbezier(1.570796,1)(2.141593,1)(3.141593,0)
+   \qbezier(3.141593,0)(4.141593,-1)(4.712389,-1)
+   \qbezier(4.712389,-1)(5.283185,-1)(6.283185,0)}
+\put(4.712389,0){\qbezier(0,0)(1,1)(1.570796,1)}
+
+\put(2.356194,0.707107){$\sin x$}
+\put(6.283185,1){$\cos x$}
+\put(-0.15,-1){\makebox(0,0)[r]{$-1$}}
+\put(-0.15,0){\makebox(0,0)[r]{$0$}}
+\put(-0.15,1){\makebox(0,0)[r]{$1$}}
+\put(1.570796,-0.15){\makebox(0,0)[t]{$\pi/2$}}
+\put(3.141593,-0.15){\makebox(0,0)[t]{$\pi$}}
+\put(4.712389,-0.15){\makebox(0,0)[t]{$3\pi/2$}}
+\put(6.283185,-0.15){\makebox(0,0)[t]{$2\pi$}}
+\end{picture}
+\end{center}
+we have located numerical labels ($0$, $1$, $\pi$\ldots) at 
+\TTT{0.15\cs{unitlength}} of its \emph{natural} position over the axes,
+while the reference points of tags
+``$\sin x$'' and ``$\cos x$'' are just in points $(3\pi/4,\sin(3\pi/4))$ and 
+$(2\pi,1)$, using these instructions:
+\begin{Verbatim}
+\put(2.356194,0.707107){$\sin x$}
+\put(6.283185,1){$\cos x$}
+\put(-0.15,-1){\makebox(0,0)[r]{$-1$}}
+\put(-0.15,0){\makebox(0,0)[r]{$0$}}
+\put(-0.15,1){\makebox(0,0)[r]{$1$}}
+\put(1.570796,-0.15){\makebox(0,0)[t]{$\pi/2$}}
+\put(3.141593,-0.15){\makebox(0,0)[t]{$\pi$}}
+\put(4.712389,-0.15){\makebox(0,0)[t]{$3\pi/2$}}
+\put(6.283185,-0.15){\makebox(0,0)[t]{$2\pi$}}
+\end{Verbatim}
+
+If we change the value of \cs{unitlength}, then these values become
+inappropriate and we need to change several lines of code.
+\begin{center}
+\setlength{\unitlength}{1cm}
+
+\begin{picture}(7,3)(-0.5,-1.5)
+
+\put(0,0){\line(1,0){7}}
+\put(0,-1.5){\line(0,1){3}}
+\put(0,-1.5){\line(0,-1){0}}
+\multiput(1.570796,-0.1)(1.570796,0){4}{\line(0,1){0.2}}
+\multiput(-0.1,-1)(0,1){3}{\line(1,0){0.2}}
+
+\qbezier(0,0)(1,1)(1.570796,1)
+\qbezier(1.570796,1)(2.141593,1)(3.141593,0)
+\qbezier(3.141593,0)(4.141593,-1)(4.712389,-1)
+\qbezier(4.712389,-1)(5.283185,-1)(6.283185,0)
+
+\put(-1.570796,0){%
+   \qbezier(1.570796,1)(2.141593,1)(3.141593,0)
+   \qbezier(3.141593,0)(4.141593,-1)(4.712389,-1)
+   \qbezier(4.712389,-1)(5.283185,-1)(6.283185,0)}
+\put(4.712389,0){\qbezier(0,0)(1,1)(1.570796,1)}
+
+\put(2.356194,0.707107){$\sin x$}
+\put(6.283185,1){$\cos x$}
+\put(-0.15,-1){\makebox(0,0)[r]{$-1$}}
+\put(-0.15,0){\makebox(0,0)[r]{$0$}}
+\put(-0.15,1){\makebox(0,0)[r]{$1$}}
+\put(1.570796,-0.15){\makebox(0,0)[t]{$\pi/2$}}
+\put(3.141593,-0.15){\makebox(0,0)[t]{$\pi$}}
+\put(4.712389,-0.15){\makebox(0,0)[t]{$3\pi/2$}}
+\put(6.283185,-0.15){\makebox(0,0)[t]{$2\pi$}}
+\end{picture}
+\end{center}
+
+Note that, regarding labels along the $x$ axis, instead of aligning them to a 
+fixed distance of this axis, there would be better to align the baselines
+($\pi$ and $2\pi$ should go down);
+some of these labels should
+move slightly to the right or to the left to avoid that it cut the graph.
+Finally, the tag ``$\cos x$'' should be vertically centered
+(with respect to the curve) and slightly moved to the right.
+\medskip
+
+Using the \package{xpicture} package we construct this picture 
+in the following way:
+\begin{Exemple}
+\MULTIPLY{3}{\numberQUARTERPI}{\numberTQPI}
+\SIN{\numberTQPI}{\sinTQPI}
+
+\begin{center}
+\setlength{\unitlength}{2cm}
+\begin{Picture}(-0.5,-1.5)(6.5,1.5)
+{\referencesystem(0,0)(\numberHALFPI,0)(0,1)
+\makenolabels
+\renewcommand{\Pictlabelsep}{0.1}
+\highestlabel{$-3\pi/2$}
+\cartesianaxes(0,-1.5)(4.25,1.5)
+
+\rPut{l}(0,-1){$-1$}                           % put the y-axis labels at left
+\rPut{l}(0,0){$0$}
+\rPut{l}(0,1){$1$}
+\rPut*{bbl}(1,0){$\pi/2$}                      % put "\pi/2" at bbl
+\rPut*{b}(2,0){$\pi$}                          % put "\pi" at bottom
+\rPut*{bbr}(3,0){$3\pi/2$}                     % put "3\pi/2" at bbr
+\rPut*{b}(4,0){$2\pi$}                         % put "2\pi" at bottom
+
+\rPut*{b}(0,0){\pictcolor{gray}\xLINE(0.75,0)(4.25,0)}} % \baseline of x-labels
+
+\PlotFunction[8]{\COSfunction}{0}{\numberTWOPI}
+\PlotFunction[8]{\SINfunction}{0}{\numberTWOPI}
+
+\Put[NE](\numberTQPI,\sinTQPI){$\sin x$}       % put "\sin x" at NorthEast
+\Put[E](\numberTWOPI,1){$\cos x$}              % put "\cos x" at East
+\end{Picture}
+\end{center}
+\end{Exemple}
+Here we used several tools to draw the graphs of the functions.
+But aside from this, commands \cs{Put}, \cs{rPut} and \cs{rPut*} have allowed 
+we to determine the logical position of objects in a much more 
+reasonable way.\footnote{Regarding to labels on coordinated axes 
+a better choice would be to use other specific commands, 
+as \cs{printxlabels}. Here we have chosen \cs{rPut} because we are
+illustrating this instruction.}
+
+Argument \TTT{\TIT{position}} supports multiple values:
+\begin{description}
+\item[An integer or decimal number,] determining the angle (in degrees)
+where \TTT{\TIT{object}} is placed,
+ with respect to the reference point \TTT{(\TIT{x},\TIT{y})}.
+\end{description}
+
+\begin{Exemple}
+\begin{center}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(0,-1)(9,1)
+\makenolabels
+\renewcommand{\axescolor}{lightgray}\renewcommand{\ticscolor}{lightgray}
+\cartesiangrid(0,-1)(8,1)
+\pictcolor{blue}
+\Put[0](0,0){0}
+\Put[45](1,0){45}
+\Put[90](2,0){90}
+\Put[135](3,0){135}
+\Put[180](4,0){180}
+\Put[225](5,0){225}
+\Put[270](6,0){270}
+\Put[315](7,0){315}
+\Put[360](8,0){360}
+\end{Picture}
+\end{center}
+\end{Exemple}
+\begin{description}
+\item[Letter \TTT{c}] (from \emph{center}),
+which places the center of \TTT{\TIT{object}} at point
+\verb+(+\TTT{\TIT{x}}\verb+,+\TTT{\TIT{y}}\verb+)+.
+\end{description}
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{2cm}
+\begin{Picture}(-1,-1)(1,1)
+\cartesianaxes(-1,-1)(1,1)
+\pictcolor{blue}
+\Put[c](0,0){A CENTERED BOX}
+\end{Picture}
+\end{center}
+\end{exemple}
+Note that this option is not equivalent to the suppression of the optional 
+argument, because in that case
+the reference point of \TTT{\TIT{object}} is located
+in \verb+(+\TTT{\TIT{x}}\verb+,+\TTT{\TIT{y}}\verb+)+.
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{2cm}
+\begin{Picture}(-1,-1)(1,1)
+\cartesianaxes(-1,-1)(1,1)
+\pictcolor{blue}
+\Put(0,0){A NONCENTERED BOX}
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{description}
+\item[Letters or letter combinations \TTT N, \TTT E, \TTT S, \TTT W,
+\TTT{NE}, \TTT{SE}, \TTT{SW}, \TTT{NW},
+\TTT{NNE}, \TTT{ENE}, \TTT{ESE}, \TTT{SSE}, \TTT{SSW}, \TTT{WSW}, \TTT{WNW},
+\TTT{NNW}]\mbox{}
+
+Abbreviation of \emph{North}, \emph{East}\ldots,  \emph{North-East}\ldots,  
+\emph{North-North-East}\ldots
+
+For example, the
+\begin{Verbatim}
+\Put[NE](0,0){A}
+\end{Verbatim}
+instruction writes ``\verb+A+''  \emph{at north-east} of point \verb+(0,0)+.
+\item[Letters o letter combinations  \TTT t, \TTT  r, \TTT  b, \TTT  l,
+ \TTT{tr}, \TTT{br}, \TTT{bl}, \TTT{tl},
+ \TTT{ttr}, \TTT{rtr}, \TTT{rbr}, \TTT{bbr}, \TTT{bbl}, \TTT{lbl}, \TTT{ltl},
+ \TTT{ttl}]\mbox{}
+ 
+Abbreviation of \emph{top}, \emph{right}\ldots,  \emph{top-right}\ldots,  
+\emph{top-top-right}\ldots
+
+For example,
+\begin{Verbatim}
+\Put[tr](0,0){A}
+\end{Verbatim}
+writes ``\verb+A+''  \emph{at top and right} of point \verb+(0,0)+.
+
+Parameter \cs{Pictlabelsep} determines the distance between the graphical 
+object and the given point.
+In the following examples we have made this argument very big to clearly 
+appreciate the positioning of objects.
+\end{description}
+\begin{exemple}
+\renewcommand{\Pictlabelsep}{1}
+\begin{center}
+\setlength{\unitlength}{2.5cm}%
+
+\begin{Picture}(-1.5,-1.5)(1.5,1.5)
+\Put[N](0,0){N}
+\Put[S](0,0){S}
+\Put[E](0,0){E}
+\Put[W](0,0){W}
+\Put[NE](0,0){NE}
+\Put[SE](0,0){SE}
+\Put[SW](0,0){SW}
+\Put[NW](0,0){NW}
+%
+\Put[NNE](0,0){NNE}
+\Put[ENE](0,0){ENE}
+\Put[ESE](0,0){ESE}
+\Put[SSE](0,0){SSE}
+\Put[SSW](0,0){SSW}
+\Put[WSW](0,0){WSW}
+\Put[WNW](0,0){WNW}
+\Put[NNW](0,0){NNW}
+\Put(0,0){\Circle{1}}
+\xLINE(-1,0)(1,0)
+\xLINE(0,-1)(0,1)
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{exemple}
+\renewcommand{\Pictlabelsep}{1}
+\begin{center}
+\setlength{\unitlength}{2.5cm}%
+
+\begin{Picture}(-1.5,-1.5)(1.5,1.5)
+\Put[t](0,0){t}
+\Put[r](0,0){r}
+\Put[b](0,0){b}
+\Put[l](0,0){l}
+\Put[tr](0,0){tr}
+\Put[br](0,0){br}
+\Put[bl](0,0){bl}
+\Put[tl](0,0){tl}
+\Put[ttr](0,0){ttr}
+\Put[rtr](0,0){rtr}
+\Put[rbr](0,0){rbr}
+\Put[bbr](0,0){bbr}
+\Put[bbl](0,0){bbl}
+\Put[lbl](0,0){lbl}
+\Put[ltl](0,0){ltl}
+\Put[ttl](0,0){ttl}
+\Put(0,0){%
+   \regularPolygon[45]{\numberSQRTTWO}{4}}
+\xLINE(-1,0)(1,0)
+\xLINE(0,-1)(0,1)
+\end{Picture}
+\end{center}
+\end{exemple}
+\end{description}
+\paragraph{Rectangular o circular distance?}
+Commands \cs{rPut} and \cs{cPut} differ only in the criterion they use
+to determine the distance between the reference point and the graphical object.
+Command \cs{rPut} places the object (outside of) 
+the square centered at the reference point and side \verb+2\Pictlabelsep+, 
+while \cs{cPut} places it in the cercle of radius \verb+\Pictlabelsep+
+(letters \verb+r+ and \verb+c+ mean, respectively,
+a \emph{rectangular} and \emph{circular} layout).%
+\footnote{For the mathematicians: command \cs{cPut} uses the euclidean norm 
+(or 2-norm), while \cs{rPut} uses the infinite norm.}
+Although, for small values of the \cs{Pictlabelsep} parameter,
+the difference is subtle and usually not very significant, it is generally best
+to use the circular version (because it corresponds to the natural concept of 
+distance) and reserve the rectangular version
+to objects that are placed on horizontal or vertical lines.
+\begin{Exemple}
+\begin{center}
+\setlength{\unitlength}{1.5cm}
+\renewcommand{\Pictlabelsep}{1}
+
+\begin{Picture}(-1.5,-1.5)(2,1.5)
+\regularPolygon[45]{\numberSQRTTWO}{4}
+\Put(0,0){\circle*{0.1}}
+\rPut{45}(0,0){r}
+\xLINE(0,0)(0,-1)
+\thicklines
+\renewcommand{\Pictlabelsep}{0.1}
+\xLINE(0,0)(1,1)
+\xLINE(0,0)(1,0)
+\xtrivVECTOR(0,-1)(1,-1)
+\xtrivVECTOR(1,-1)(0,-1)
+\rPut{b}(0.5,-1){\footnotesize\textbackslash Pictlabelsep}
+\xtrivVECTOR(1,-1)(1,0)
+\xtrivVECTOR(1,0)(1,-1)
+\rPut{r}(1,-0.5){\footnotesize\textbackslash Pictlabelsep}
+\polarreference\degreesangles
+\xArc{0.3}{0}{45}
+\degreesangles
+\Put[22.5](0.3,22.5){$45^{\mathrm o}$}
+\end{Picture}
+\begin{Picture}(-1.5,-1.5)(2,1.5)
+\Put(0,0){\circle*{0.1}}
+\cPut{45}(0,0){c}
+\Circle{1}
+\thicklines
+\xLINE(0,0)(\numberCOSXLV,\numberCOSXLV)
+\xLINE(0,0)(1,0)
+\xtrivVECTOR(0,0)(0,-1)
+\xtrivVECTOR(0,-1)(0,0)
+\renewcommand{\Pictlabelsep}{0.1}
+\rPut{r}(0,-0.5){\footnotesize\textbackslash Pictlabelsep}
+\polarreference\degreesangles
+\xArc{0.3}{0}{45}
+\degreesangles
+\Put[22.5](0.3,22.5){$45^{\mathrm o}$}
+\end{Picture}
+\end{center}
+\end{Exemple}
+
+Note that if the commands we use are \cs{rPut} or \cs{cPut}, then the 
+positioners
+\verb+t, r, tr+\ldots are equivalent to the corresponding \verb+N, E, NE+\ldots
+However, the \cs{Put} command choose between rectangular or circular layout
+following this criteria:
+\begin{itemize}
+ \item Positioners of \emph{compass} type (like \verb+NE+) use the circular
+layout.
+ \item Positioners \verb+t, tr+, et cetera use the rectangular layout.
+ \item If the positioner is an angle (a number), it uses a default position
+which is set using the \cs{defaultPut} declaration:
+\verb+\defaultPut{c}+
+determines a circular distance, while
+\verb+\defaultPut{r}+
+determines the rectangular alternative.
+\end{itemize}
+\begin{exemple}
+\renewcommand{\Pictlabelsep}{1}
+\begin{center}
+\setlength{\unitlength}{2.5cm}%
+
+\begin{Picture}(-1.5,-1.5)(1.5,1.5)
+\defaultPut{c}
+\Put[45](0,0){c}
+\defaultPut{r}
+\Put[45](0,0){r}
+\regularPolygon[45]{\numberSQRTTWO}{4}
+\Put(0,0){\Circle{1}}
+\xLINE(-1,0)(1,0)
+\xLINE(0,-1)(0,1)
+\end{Picture}
+\end{center}
+\end{exemple}
+\paragraph{Alignment by the baseline}
+Starred versions \cs{Put*} and \cs{rPut*} allow us to align by the baseline
+objects positioned below the reference point.
+To use these commands, user must decide which is the higher object to be 
+positioned, and introduce it as an argument of
+the \csdef{highestlabel} declaration. For example, typing
+\begin{Verbatim}
+\highestlabel{\Huge A}
+\end{Verbatim}
+we reserve a sufficient vertical space to write the character {\Huge A}.
+
+It should be noted that starred versions behave differently
+only when the position of the object stands
+under the reference point, with positioners
+\verb+bbl+, \verb+b+ or \verb+bbr+, or with an appropiate angle
+(as \verb+-90+ or \verb+300+); otherwise (including
+\verb$S$, \verb$SSW$, et cetera),
+the \cs{Put*} and \cs{rPut*} commands are equivalent
+to the non-starred commands
+ \cs{Put} and \cs{rPut}.
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{1cm}
+
+\begin{Picture}(-3.5,-1.5)(3.5,1.5)
+\xLINE(-3.5,0)(3.5,0)
+\multiPut(-3,-0.1)(1,0){7}{\xLINE(0,0)(0,0.2)}
+\highestlabel{\Huge A}
+\renewcommand{\Pictlabelsep}{0.2}
+\Put*[bbl](-3,0){\small A}
+\Put*[b](-2,0){\normalsize A}
+\Put*[-100](-1,0){\large A}
+\Put*[-90](0,0){\Large A}
+\Put*[270](1,0){\LARGE A}
+\Put*[300](2,0){\huge A}
+\Put*[bbr](3,0){\Huge A}
+\Put*[bbl](-3.5,0){%
+   \pictcolor{gray}\xLINE(0,0)(7,0)}
+\end{Picture}
+\end{center}
+\end{exemple}
+ 
+
+When a \environ{Picture} environment starts,
+highest label is set to \verb+\normalfont\normalsize$1$+
+(i.e., the high of a \emph{normal} $1$).
+\subsection{Alternatives to the \cs{multiput} command}
+The \package{xpicture} package introduces two families of commands
+to generalize the \cs{multiput} command:
+\begin{enumerate}
+ \item The natural generalization, with all versions,
+ \ttslashindex{multiPut}\ttslashindex{multicPut}\ttslashindex{multirPut}
+\begin{Verbatim}[commandchars=\|\{\},commentchar=\%]
+\multiPut[|TIT{position}](|TIT{x0},|TIT{y0})(|TIT{|(|Delta|)x},%
+|TIT{|(|Delta|)y})|{|TIT{n}|}|{|TIT{object}|}
+\multiPut*[|TIT{position}](|TIT{x0},|TIT{y0})(|TIT{|(|Delta|)x}%
+,|TIT{|(|Delta|)y})|{|TIT{n}|}|{|TIT{object}|}
+\multicPut|{|TIT{position}|}(|TIT{x0},|TIT{y0})(|TIT{|(|Delta|)x}%
+,|TIT{|(|Delta|)y})|{|TIT{n}|}|{|TIT{object}|}
+\multirPut|{|TIT{position}|}(|TIT{x0},|TIT{y0})(|TIT{|(|Delta|)x}%
+,|TIT{|(|Delta|)y})|{|TIT{n}|}|{|TIT{object}|}
+\multirPut*|{|TIT{position}|}(|TIT{x0},|TIT{y0})(|TIT{|(|Delta|)x}%
+,|TIT{|(|Delta|)y})|{|TIT{n}|}|{|TIT{object}|}
+\end{Verbatim}
+These commands compose \TIT{n} copies of \TTT{\TIT{object}}
+in $(\TIT{x0},\TIT{y0})$, $(\TIT{x0}+\Delta x,\TIT{y0}+\Delta y)$,
+ $(\TIT{x0}+2\Delta x,\TIT{y0}+2\Delta y)$,\ldots, 
+ $(\TIT{x0}+(\TIT n-1)\Delta x,\TIT{y0}+(\TIT n-1)\Delta y)$.
+\item A new command group,
+\ttslashindex{multiPlot}\ttslashindex{multicPlot}\ttslashindex{multirPlot}
+\begin{Verbatim}[commandchars=\|\{\},commentchar=\%]
+\multiPlot[|TIT{position}]|{|TIT{object}|}(|TIT{x0},|TIT{y0})(|TIT{x1},%
+|TIT{y1})...(|TIT{xn},|TIT{yn})
+\multiPlot*[|TIT{position}]|{|TIT{object}|}(|TIT{x0},|TIT{y0})(|TIT{x1},%
+|TIT{y1})...(|TIT{xn},|TIT{yn})
+\multicPlot|{|TIT{position}|}|{|TIT{object}|}(|TIT{x0},|TIT{y0})(|TIT{x1},%
+|TIT{y1})...(|TIT{xn},|TIT{yn})
+\multirPlot|{|TIT{position}|}|{|TIT{object}|}(|TIT{x0},|TIT{y0})(|TIT{x1},%
+|TIT{y1})...(|TIT{xn},|TIT{yn})
+\multirPlot*|{|TIT{position}|}|{|TIT{object}|}(|TIT{x0},|TIT{y0})(|TIT{x1},%
+|TIT{y1})...(|TIT{xn},|TIT{yn})
+\end{Verbatim}
+These commands compose the done object in several positions, that are freely
+entered as a list of coordinate pairs.
+\end{enumerate}
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{1cm}
+\referencesystem(0,0)(1,-1)(1,1)
+\begin{Picture}(-2.5,-2.5)(2.5,2.5)
+\cartesiangrid(-2,-2)(2,2)
+\pictcolor{blue}
+\multiPut(-2,-2)(1,1){5}{\circle*{0.25}}
+\pictcolor{red}
+\multiPlot{\circle*{0.25}}(-1,-2)(2,1)(-2,2)
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{1cm}
+\referencesystem(0,0)(1,-1)(1,1)
+\begin{Picture}(-2.5,-2.5)(2.5,2.5)
+\cartesiangrid(-2,-2)(2,2)
+\pictcolor{blue}
+\multiPut[b](-2,-2)(1,1){5}{\circle*{0.25}}
+\pictcolor{red}
+\multiPlot[NE]{\circle*{0.25}}(-1,-2)(2,1)(-2,2)
+\end{Picture}
+\end{center}
+\end{exemple}
+\subsection{Alternatives to \cs{line} and \cs{vector}}
+\begin{description}
+\item[\csdef{xLINE}] This command draws line segments:
+\begin{Verbatim}[commandchars=\|\[\]]
+\xLINE(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])
+\end{Verbatim}
+draws the line segment between the two points
+\verb+(+\TIT{x0}\verb+,+\TIT{y0}\verb+)+ and
+\verb+(+\TIT{x1}\verb+,+\TIT{y1}\verb+)+
+(Cartesian or polar coordinates, in the active reference system).
+This allows us to draw any segment in any direction.
+\item[\csdef{xVECTOR}, \csdef{xtrivVECTOR}] plot arrows:
+\begin{Verbatim}[commandchars=\|\[\]]
+\xVECTOR(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])
+\xtrivVECTOR(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])
+\end{Verbatim}
+draw an arrow between points
+\verb+(+\TIT{x0}\verb+,+\TIT{y0}\verb+)+ and
+\verb+(+\TIT{x1}\verb+,+\TIT{y1}\verb+)+.
+The \cs{xtrivVECTOR} command draw an arrow
+the end of which simply consists of a pair of segments
+(\setlength{\unitlength}{1cm}%
+\begin{Picture}(0,-0.1)(0.5,0.1)\xtrivVECTOR(0,0)(0.5,0)\end{Picture}).
+length and aperture of the end of arrow are controled by the instruction
+\ttslashindex{arrowsize}
+\begin{Verbatim}[commandchars=\|\[\]]
+\arrowsize{|TIT[xlen]}{|TIT[ylen]}
+\end{Verbatim}
+where the two parameters are non-negative numbers:
+the first one for the length (in points); second
+for the half of the aperture. Default is
+\begin{Verbatim}
+\arrowsize{5}{2}
+\end{Verbatim}
+\begin{exemple}
+\setlength{\unitlength}{0.75cm}
+\referencesystem(0,0)(1,0)(0.25,0.75)
+\begin{Picture}(-4.5,-4.5)(4.5,4.5)
+\cartesiangrid(-4,-4)(4,4)
+\thicklines
+\pictcolor{blue}
+\xLINE(-4,0)(1,4)
+\Put(1,-3){\xLINE(0,0)(3,2)}
+\pictcolor{red}
+\xtrivVECTOR(0,0)(2,3)
+\xtrivVECTOR(0,0)(2,0)
+\arrowsize{10}{4}
+\xtrivVECTOR(0,0)(-2,-1)
+
+\pictcolor{magenta}
+\xVECTOR(-3,-3)(-3,3)
+\xVECTOR(-3,-3)(-2,-2)
+\end{Picture}
+\end{exemple}
+\item[\csdef{xline}, \csdef{xvector}, \csdef{xtrivvector}]
+draw lines and vectors using the standard \LaTeX{} syntax
+(but without any restriction in allowed parameters,
+that can be integer or decimal numbers, positive, negative or zero).
+\begin{Verbatim}[commandchars=\|\[\]]
+\xline(|TIT[x],|TIT[y]){|TIT[size]}
+\xvector(|TIT[x],|TIT[y]){|TIT[size]}
+\xtrivvector(|TIT[x],|TIT[y]){|TIT[size]}
+\end{Verbatim}
+\begin{exemple}
+\setlength{\unitlength}{0.75cm}
+\referencesystem(0,0)(1,0)(0.25,0.75)
+\begin{Picture}(-4.5,-4.5)(4.5,4.5)
+\cartesiangrid(-4,-4)(4,4)
+\thicklines
+\pictcolor{blue}
+\Put(-4,0){\xline(5,4){5}}
+\Put(1,-3){\xline(3,2){3}}
+\pictcolor{red}
+\Put(0,0){\xtrivvector(2,3){2}}
+\xtrivvector(1,0){2}
+\arrowsize{10}{4}
+\Put(0,0){\xtrivvector(2,1){-2}}
+
+\pictcolor{magenta}
+\Put(-3,-3){\xvector(0,1){6}}
+\Put(-3,-3){\xvector(1,1){1}}
+\end{Picture}
+\end{exemple}
+
+If you want to draw only an arrowhead (without any line)
+you can use either the
+\csdef{zerovector}/\csdef{zerotrivvector}
+or \cs{xvector}/\cs{xtrivvector} commands:
+\begin{Verbatim}[commandchars=\|\[\]]
+\zerovector(|TIT[x],|TIT[y])
+\zerotrivvector(|TIT[x],|TIT[y])
+\xvector(|TIT[x],|TIT[y]){0}
+\xtrivvector(|TIT[x],|TIT[y]){0}
+\end{Verbatim}
+\end{description}
+\subsection{Polygons anf polygonal lines}
+The \package{pict2e} and \package{curve2e} packages include
+specific instructions for drawing polygonal lines and polygons.
+We introduce new versions of these
+commands in order to refer to the active reference system.
+\begin{description}
+\item[\csdef{Polyline}] draws polygonal lines.
+Logically, we must pass the list of vertices:
+\begin{Verbatim}[commandchars=\|\[\]]
+\Polyline(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])...(|TIT[xn],|TIT[yn])
+\end{Verbatim}
+\item[\csdef{Polygon}] plots polygons, ie, closed polygonal lines:
+\begin{Verbatim}[commandchars=\|\[\]]
+\Polygon(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])...(|TIT[xn],|TIT[yn])
+\end{Verbatim}
+is equivalent to
+\begin{Verbatim}[commandchars=\|\[\],commentchar=\%]
+\Polyline(|TIT[x0],|TIT[y0])(|TIT[x1],|TIT[y1])...(|TIT[xn],|TIT[yn])%
+(|TIT[x0],|TIT[y0])
+\end{Verbatim}
+
+\begin{exemple}
+\setlength{\unitlength}{0.75cm}
+\referencesystem(0,0)(1,0)(0.25,0.75)
+\begin{Picture}(-4.5,-4.5)(4.5,4.5)
+\externalaxes
+\cartesiangrid(-4,-4)(4,4)
+\linethickness{1pt}
+\pictcolor{blue}
+\Polyline(-2,2)(-3,-1)(0,0)(2,3)(2,2)
+\pictcolor{red}
+\Polygon(0,0)(1,1)(3,1)(1,-1)
+\end{Picture}
+\end{exemple}
+\item[\csdef{regularPolygon}] draws regular polygons:
+\begin{Verbatim}[commandchars=\|\(\)]
+\regularPolygon[|TIT(initial angle)]{|TIT(radius)}{|TIT(sides)}
+\end{Verbatim}
+makes the regular polygon with the given radius and sides.
+The optional argument (zero, by default) determines
+the slope of the first vertex, always measured in degrees.
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{0.5cm}
+\begin{Picture}(-7.5,-7.5)(7.5,7.5)
+\externalaxes
+\cartesiangrid(-7,-7)(7,7)
+\pictcolor{blue}
+\regularPolygon{1}{5}
+\Put(-4,0){\regularPolygon{2}{6}}
+\Put(3,3){\regularPolygon{2}{4}}
+\Put(-4,-4){\regularPolygon[45]{2}{4}}
+\Put(4,-4){\regularPolygon[90]{2.5}{11}}
+\Put(-4,4){\regularPolygon[90]{3}{3}}
+\end{Picture}
+\end{center}
+\end{exemple}
+
+\end{description}
+\section{Drawing curves}
+This section highlights the true potentiality of the \package{xpicture} 
+package.
+We will describe the instructions that can be used to easily (and effectively) 
+represent
+several interesting curves: Firstly, conic sections and arcs.
+Then, any piecewise regular curve
+(including graphs of real variable functions, in rectangular or polar 
+coordinates,
+and ---in a more general way--- curves defined by parametric equations).
+\subsection{Conic sections}
+The \package{xpicture} package defines new commands to draw conic sections:
+ ellipses, circles, hyperbolas and parabolas.
+\subsubsection{Circles}
+We can draw the circle of implicit equation $x^2+y^2=r^2$ typing
+\ttslashindex{Circle}
+\begin{Verbatim}[commandchars=\|\[\]]
+\Circle{|TIT[r]}
+\end{Verbatim}
+Note than the standard command \cs{circle}
+requeres the diameter as mandatory argument, while here we must insert the 
+radius.
+\subsubsection{Ellipses}
+To draw the ellipse $\displaystyle\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ enter the
+following instruction:\ttslashindex{Ellipse}
+\begin{Verbatim}[commandchars=\|\[\]]
+\Ellipse{|TIT[a]}{|TIT[b]}
+\end{Verbatim}
+\begin{exemple}
+\setlength{\unitlength}{0.5cm}
+\renewcommand{\axeslabelsize}{\footnotesize}
+\begin{Picture}(-5.5,-4.5)(5.5,4.5)
+\cartesiangrid(-5,-4)(5,4)
+\pictcolor{blue}
+\Ellipse{4}{3}
+\Circle{2}
+\end{Picture}
+
+\referencesystem(0,0)(1,0)(0.5,0.5)
+\begin{Picture}(-5.5,-4.5)(5.5,4.5)
+\cartesiangrid(-5,-4)(5,4)
+\pictcolor{blue}
+\Ellipse{4}{3}
+\Circle{2}
+\end{Picture}
+\end{exemple}
+\subsubsection{Hyperbolas}
+Since the hyperbolas and parabolas are not bounded curves, to define the
+portion of the curve that we want to draw  we need to specify the
+maximum values for the $x$ and $y$ variables.\ttslashindex{Hyperbola}
+\begin{Verbatim}[commandchars=\|\[\]]
+\Hyperbola{|TIT[a]}{|TIT[b]}{|TIT[xmax]}{|TIT[ymax]}
+\end{Verbatim}
+draws the hyperbola
+$\displaystyle\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$,
+where variables $x$ and $y$ are limited, respectively,
+to the $\TTT{[-\TIT{xmax}}, \TTT{\TIT{xmax}]}$ and 
+$\TTT{[-\TIT{ymax}}, \TTT{\TIT{ymax}]}$ intervals.
+This curve is well defined if the parameter \TTT{\TIT{xmax}}
+is greater than \TTT{\TIT{a}}. Otherwise, \package{xpicture} returns an error 
+message and does not draw any curve.
+
+In the following example, we show the hyperbola 
+$\displaystyle\frac{x^2}{5^2}-\frac{y^2}{2^2}=1$
+and its asymptotes,
+using the \cs{xLINE} command (these asymptotes are lines $2x=\pm5y$,
+passing through $(\pm16,\pm6.4)$).
+\begin{Exemple}
+\begin{center}
+\setlength{\unitlength}{0.5cm}
+\begin{Picture}(-17,-9)(17,9)
+\renewcommand{\axeslabelsize}{\footnotesize}
+\cartesiangrid(-16,-8)(16,8)
+\pictcolor{blue}
+\Hyperbola{5}{2}{16}{8}
+\pictcolor{orange}
+\xLINE(16,6.4)(-16,-6.4)
+\xLINE(-16,6.4)(16,-6.4)
+\end{Picture}
+\end{center}
+\end{Exemple}
+
+Instructions \csdef{lHyperbola} and \csdef{rHyperbola} draw, respectively,
+only the \emph{left} or only the \emph{right} branch of the given hyperbola
+(here, is interpreted as \emph{right} branch this one that belongs to positive
+values of variable $x$).
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{0.5cm}
+\begin{Picture}(-5.5,-5.5)(5.5,5.5)
+\renewcommand{\axeslabelsize}{\footnotesize}
+\cartesiangrid(-5,-5)(5,5)
+\pictcolor{red}
+\lHyperbola{2}{3}{5}{5}
+\pictcolor{blue}
+\rHyperbola{2}{3}{5}{5}
+\end{Picture}
+\end{center}
+\end{exemple}
+\subsubsection{Parabolas}
+Instruction\ttslashindex{Parabola}
+\begin{Verbatim}[commandchars=\|\[\]]
+\Parabola{|TIT[a]}{|TIT[xmax]}{|TIT[ymax]}
+\end{Verbatim}
+draw the parabola $x=ay^2$, varying $x$, at most, in the interval
+$[0,\TTT{\TIT{xmax}}]$
+(if \TTT{\TIT{a}} is positive) or in $[-\TTT{\TIT{xmax}},0]$
+(for negative values of \TTT{\TIT{a}}),
+and $y$ in $[-\TTT{\TIT{ymax}},\TTT{\TIT{ymax}}]$.
+Parameters \TTT{\TIT{xmax}} and \TTT{\TIT{ymax}}
+must be positive.
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{0.5cm}
+\begin{Picture}(-5.5,-5.5)(5.5,5.5)
+\cartesiangrid(-5,-5)(5,5)
+\pictcolor{blue}
+\Parabola{2}{5}{5}
+\Parabola{0.2}{5}{5}
+\pictcolor{orange}
+\Parabola{-2}{5}{5}
+\Parabola{-0.2}{5}{5}
+\end{Picture}
+\end{center}
+\end{exemple}
+\medskip
+
+All commands drawing conic sections or arcs divide the curve in 
+\csdef{defaultplotdivs} pieces (8, by default). To obtain a greather
+accuracy, you can redefine this parameter.
+
+\medskip
+
+Note that all these commands draw conic sections centered
+at the coordinate origin, so that their
+principal axes coincide with the coordinate axes. If we
+want to move his
+center to any other point, we can do it moving in advance
+the origin of coordinates or simply
+including the command as an argument of the \cs{Put} command.
+\begin{Exemple}
+\begin{center}
+\setlength{\unitlength}{0.5cm}
+\begin{Picture}(-11,-8)(11,8)
+\renewcommand{\axeslabelsize}{\footnotesize}
+\cartesiangrid(-10,-7)(11,7)
+\pictcolor{blue}
+\Put(2,3){\Ellipse{4}{3}}
+\Put(2,3){\Circle{0.25}}
+\pictcolor{orange}
+\Put(2,-3){\Hyperbola{5}{2}{9}{3}}
+\Put(2,-3){\Circle{0.25}}
+\pictcolor{green}
+\translateorigin(-10,2)
+\Parabola{0.5}{21}{5}
+\Circle{0.25}
+\end{Picture}
+\end{center}
+\end{Exemple}
+But, if the symmetry axes of our curve are not parallel to the coordinate
+axes,\footnote{That is, in mathematical terms,
+if the eigenvectors of the underlying quadratic form are not the canonical 
+vectors.}
+then we will need a rotation of axes.
+\begin{Exemple}
+\setlength{\unitlength}{0.5cm}
+\begin{center}
+\begin{Picture}(-10.5,-7.5)(10.5,7.5)
+\renewcommand{\axeslabelsize}{\footnotesize}
+\cartesiangrid(-10,-7)(10,7)
+{%
+\pictcolor{blue}
+\translateorigin(5,3)
+\rotateaxes{\numberSIXTHPI}
+\Ellipse{4}{3}
+\xLINE(-4,0)(4,0)
+\xLINE(0,-3)(0,3)
+}
+\degreesangles
+{%
+\pictcolor{orange}
+\translateorigin(-3,0)
+\rotateaxes{110}
+\Hyperbola{3}{2}{6}{4}
+\xLINE(-6,-4)(6,4)
+\xLINE(6,-4)(-6,4)
+}
+\pictcolor{green}
+\translateorigin(5,-6)
+\rotateaxes{72}
+\Parabola{1}{4}{3}
+\xLINE(0,-2)(0,2)
+\xLINE(0,0)(4,0)
+\end{Picture}
+\end{center}
+\end{Exemple}
+Note that we made a couple of changes of local reference system (one for each
+curve) within the drawing.
+We can use the recourse to the change of coordinates also to
+draw the hyperbola $\displaystyle\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ and the
+parabola $y=ax^2$.
+Note than \verb+\referencesystem(0,0)(0,1)(1,0)+
+(or \verb+\symmetrize{\numberQUARTERPI}+)
+makes vertical the $x$ axis and horizontal the
+$y$ axis.\footnote{We will use this trick later
+to plot inverse functions.}
+\begin{exemple}
+\setlength{\unitlength}{0.5cm}
+\begin{center}
+\begin{Picture}(-5.5,-5.5)(5.5,5,5)
+\renewcommand{\axeslabelsize}{\footnotesize}
+\cartesiangrid(-5,-5)(5,5)
+\referencesystem(0,0)(0,1)(1,0)
+\pictcolor{blue}
+\Parabola{0.22}{5}{5}
+\pictcolor{red}
+\Hyperbola{2}{3}{5}{5}
+\end{Picture}
+\end{center}
+\end{exemple}
+
+\subsection{Arcs (of conic sections)}
+The instructions described above allow us to draw whole circles, ellipses
+hyperbolas and parabolas. More generally, we can represent any portion of 
+these curves, ie, circular, elliptic, hyperbolic and parabolic arcs.
+\ttslashindex{xArc}\ttslashindex{circularArc}
+\begin{Verbatim}[commandchars=\|\[\]]
+\xArc{|TIT[r]}{|TIT[angle1]}{|TIT[angle2]}
+\circularArc{|TIT[r]}{|TIT[angle1]}{|TIT[angle2]}
+\end{Verbatim}
+These two instructions are equivalent.
+They draw the arc of the circle centered at $(0,0)$
+with radius $\TIT{r}$
+and limited by the $\TTT{\TIT{angle1}}$ and $\TTT{\TIT{angle2}}$
+angles.
+\begin{exemple}
+\setlength{\unitlength}{0.5cm}
+\begin{center}
+\begin{Picture}(-5.5,-5.5)(5.5,5,5)
+\renewcommand{\axeslabelsize}{\footnotesize}
+\cartesianaxes(-5,-5)(5,5)
+\pictcolor{gray}
+\circularArc{3}{\numberPI}{\numberTWOPI}
+\pictcolor{red}
+\xLINE(-2,2)(-2,5)
+\xLINE(-2,2)(-5,2)
+\degreesangles
+\Put(-2,2){\circularArc{1}{90}{180}}
+\pictcolor{blue}
+\polarreference
+\Put(1,30){\xLINE(0,0)(4,30)}
+\Put(1,30){\xLINE(0,0)(4,60)}
+\Put(1,30){\circularArc{2}{30}{60}}
+\end{Picture}
+\end{center}
+\end{exemple}
+\begin{exemple}
+\SUBTRACT{\numberGOLD}{1}{\midaB}
+\COPY{1}{\midaA}
+\ADD{\midaA}{\midaB}{\Mida}
+\setlength{\unitlength}{5cm}
+\newcommand{\espiral}{%
+    \Put(0,0){\begin{Picture}(0,0)(0,0)
+      \translateorigin(\midaA,0)
+      \pictcolor{red}
+      \circularArc{\midaA}{\numberHALFPI}{\numberPI}
+      \pictcolor{blue}
+      \xLINE(0,0)(0,\midaA)
+   \end{Picture}
+   }
+   \COPY{\midaA}{\Mida}
+   \COPY{\midaB}{\midaA}
+   \SUBTRACT{\Mida}{\midaA}{\midaB}
+   \translateorigin(\Mida,\midaB)
+   \changereferencesystem(0,\midaA)(0,-1)(1,0)
+}
+\renewcommand{\defaultplotdivs}{2}
+
+\begin{center}
+\begin{Picture}(0,0)(\numberGOLD,1)
+   \Polygon(0,0)(\Mida,0)(\Mida,1)(0,1)
+   % Plot 8 circular arcs
+   \espiral\espiral\espiral\espiral
+   \espiral\espiral\espiral\espiral
+\end{Picture}
+
+Golden rectangles and spiral
+\end{center}
+\end{exemple}
+\ttslashindex{ellipticArc}
+\begin{Verbatim}[commandchars=\|\[\]]
+\ellipticArc{|TIT[a]}{|TIT[b]}{|TIT[angle1]}{|TIT[angle2]}
+\end{Verbatim}
+This instruction draws the arc of the ellipse centered at
+ $(0,0)$ with semiaxes $\TIT{a}$
+and $\TIT{b}$, $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$,
+limited by angles $\TTT{\TIT{angle1}}$ and $\TTT{\TIT{angle2}}$.
+\begin{exemple}
+\setlength{\unitlength}{0.5cm}
+\begin{center}
+\begin{Picture}(-0.5,-3.5)(5.5,3.5)
+\degreesangles
+\ellipticArc{2}{3}{-90}{90}
+\ellipticArc{5}{3}{-90}{90}
+\end{Picture}
+\end{center}
+\end{exemple}
+\ttslashindex{lhyperbolicArc}\ttslashindex{rhyperbolicArc}
+\begin{Verbatim}[commandchars=\|\[\]]
+\rhyperbolicArc{|TIT[a]}{|TIT[b]}{|TIT[y1]}{|TIT[y2]}
+\lhyperbolicArc{|TIT[a]}{|TIT[b]}{|TIT[y1]}{|TIT[y2]}
+\end{Verbatim}
+Draw the arc (of the right or left branch, respectively)
+of the hyperbola
+ $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ included between $y=\TTT{\TIT{y1}}$ and 
+ $y=\TTT{\TIT{y2}}$.
+\begin{exemple}
+\setlength{\unitlength}{0.5cm}
+\begin{center}
+\begin{Picture}(-5.5,-5.5)(5.5,5,5)
+\renewcommand{\axeslabelsize}{\footnotesize}
+\cartesianaxes(-5,-5)(5,5)
+\pictcolor{red}
+\lhyperbolicArc{2}{3}{-4}{0}
+\pictcolor{blue}
+\rhyperbolicArc{2}{3}{-2}{5}
+\end{Picture}
+\end{center}
+\end{exemple}
+\ttslashindex{parabolicArc}
+\begin{Verbatim}[commandchars=\|\[\]]
+\parabolicArc{|TIT[a]}{|TIT[y1]}{|TIT[y2]}
+\end{Verbatim}
+Draw the arc of the parabola
+ $x=ay^2$ included between $y=\TTT{\TIT{y1}}$ and $y=\TTT{\TIT{y2}}$.
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\begin{center}
+\begin{Picture}(-2.5,-2.5)(2.5,2,5)
+\renewcommand{\axeslabelsize}{\footnotesize}
+\cartesianaxes(-2,-2)(2,2)
+\pictcolor{red}
+\parabolicArc{-2}{-1}{0}
+\pictcolor{blue}
+\parabolicArc{0.5}{0}{2}
+\end{Picture}
+\end{center}
+\end{exemple}
+\subsection{Real variable functions}\label{subsec:real}
+The \package{xpicture} package provides us two commands
+to draw the graph of a function:
+\csdef{PlotFunction} and \csdef{PlotPointsOfFunction}.
+\begin{Verbatim}[commandchars=\|\(\)]
+\PlotFunction[|TIT(n)]{\|TIT(functionname)}{\|TIT(tzero)}{\|TIT(tone)}
+\PlotPointsOfFunction{|TIT(n)}{\|TIT(functionname)}{\|TIT(tzero)}{\|TIT(tone)}
+\end{Verbatim}
+Note that the parameter $\TTT{\TIT{n}}$ is optional in one of these 
+instructions and mandatory in the other one.
+In the case of \csdef{PlotFunction},
+if we do not use this optional parameter,
+a quadratic approximation of the function
+\cs{\TIT{functionname}}
+in the $[\cs{\TIT{tzero}},\cs{\TIT{tone}}]$ interval is drawn.
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-2.5,-0.5)(3.5,4.5)
+\cartesianaxes(-2,0)(2,4)
+\pictcolor{blue}
+\PlotFunction{\SQUAREfunction}{-2}{2}
+\Put[E](2,4){$f(t)=t^2$}
+\end{Picture}
+\end{exemple}
+Now, this almost never provides a right graphic.
+To draw curves with a greater accuracy we should use the parameter,
+\TTT{\TIT{n}},
+dividing the interval in \TTT{\TIT{n}} subintervals.
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\CUBE{1.5}{\mymax}
+\begin{Picture}(-2,-4)(2,4)
+\cartesianaxes(-1.5,-\mymax)(1.5,\mymax)
+\pictcolor{blue}
+\PlotFunction[8]{\CUBEfunction}{-1.5}{1.5}
+\Put[E](1.5,\mymax){$f(t)=t^3$}
+\end{Picture}
+\end{exemple}
+
+On the other hand, the \csdef{PlotPointsOfFunction} command
+plots $\TTT{\TIT{n}}+1$ \emph{points}, uniformly distributed
+about the $x$-axis.
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\CUBE{1.5}{\mymax}
+\begin{Picture}(-2,-4)(2,4)
+\cartesianaxes(-1.5,-\mymax)(1.5,\mymax)
+\pictcolor{blue}
+\PlotPointsOfFunction{24}{\CUBEfunction}{-1.5}{1.5}
+\Put[E](1.5,\mymax){$f(t)=t^3$}
+\end{Picture}
+\end{exemple}
+
+By default, \cs{PlotPointsOfFunction} plot \emph{points} as a filled circle
+of diameter \verb+0.1\unitlength+. But you can modifie this diameter, by 
+redefining the \csdef{pointmarkdiam} parameter.
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\CUBE{1.5}{\mymax}
+\renewcommand{\pointmarkdiam}{0.3}
+\begin{Picture}(-2,-4)(2,4)
+\cartesianaxes(-1.5,-\mymax)(1.5,\mymax)
+\pictcolor{blue}
+\PlotPointsOfFunction{24}{\CUBEfunction}{-1.5}{1.5}
+\Put[E](1.5,\mymax){$f(t)=t^3$}
+\end{Picture}
+\end{exemple}
+
+Moreover, you can select another symbol for these points, redefining 
+\csdef{pointmark}.
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\CUBE{1.5}{\mymax}
+\renewcommand{\pointmark}{$\diamond$}
+\begin{Picture}(-2,-4)(2,4)
+\cartesianaxes(-1.5,-\mymax)(1.5,\mymax)
+\pictcolor{blue}
+\PlotPointsOfFunction{24}{\CUBEfunction}{-1.5}{1.5}
+\Put[E](1.5,\mymax){$f(t)=t^3$}
+\end{Picture}
+\end{exemple}
+
+Naturally, in order to apply these commands the function must be defined.
+\package{xpicture}
+loads the \packagedef{calculus} package, which
+predefines some of the most common elementary functions
+and includes several tools to build new ones.
+The predefined functions are the following:
+\begin{center}
+\begin{tabular}{l>{$}l<{$}>{\qquad}l>{$}l<{$}}
+ \csdef{ZEROfunction} & f(t)=0 &
+ \csdef{ONEfunction}  & f(t)=1    \\
+ \csdef{IDENTITYfunction}  & f(t)=t &
+ \csdef{RECIPROCALfunction}  & f(t)=1/t \\
+ \csdef{SQUAREfunction}  & f(t)=t^2 &
+ \csdef{CUBEfunction}  & f(t)=t^3 \\
+ \csdef{SQRTfunction}  & f(t)=\sqrt t \\
+ \csdef{EXPfunction}  & f(t)=\exp t &
+ \csdef{LOGfunction} & f(t)=\log t \\
+ \csdef{COSfunction}  & f(t)=\cos t &
+ \csdef{SINfunction}  & f(t)=\sin t \\
+ \csdef{TANfunction}  & f(t)=\tan t &
+ \csdef{COTfunction}  & f(t)=\cot t \\
+ \csdef{COSHfunction}  & f(t)=\cosh t &
+ \csdef{SINHfunction}  & f(t)=\sinh t \\
+ \csdef{TANHfunction}  & f(t)=\tanh t &
+ \csdef{COTHfunction}  & f(t)=\coth t \\
+ \csdef{HEAVISIDEfunction} & f(t)=\begin{cases}
+                              0 & \text{si $t<0$} \\
+                              1 & \text{si $t\geq0$}
+                          \end{cases}
+\end{tabular}
+\end{center}
+
+\begin{Exemple}
+\setlength{\unitlength}{1cm}
+\linethickness{1.5pt}
+\centering
+\begin{Picture}(-5,-5)(6,5)
+\externalaxes\makenotics
+\cartesiangrid(-4.5,-4.5)(4.5,4.5)
+\pictcolor{red}
+\PlotFunction{\IDENTITYfunction}{-4.5}{4.5}
+\Put[tr](4.5,4.5){$y=x$}
+
+\DIVIDE{1}{4.5}{\minx}
+\pictcolor{magenta}
+\PlotFunction[10]{\RECIPROCALfunction}{\minx}{4.5}
+\PlotFunction[10]{\RECIPROCALfunction}{-\minx}{-4.5}
+\Put[r](4.5,\minx){$y=1/x$}
+
+\SQRT{4.5}{\maxx}
+\pictcolor{cyan}
+\PlotFunction[10]{\SQUAREfunction}{-\maxx}{\maxx}
+\Put[tr](\maxx,4.5){$y=x^2$}
+
+\pictcolor{blue}
+\PlotFunction[10]{\CUBEfunction}{-1.6509}{1.6509}
+\Put[t](1.6509,4.5){$y=x^3$}
+\end{Picture}
+\end{Exemple}
+
+\begin{Exemple}
+\setlength{\unitlength}{1cm}
+\linethickness{1.5pt}
+\centering
+\begin{Picture}(-7,-4.5)(7,4.5)
+{\makenolabels
+\changereferencesystem(0,0)(\numberHALFPI,0)(0,1)
+\cartesiangrid(-4,-4)(4,4)
+\highestlabel{$2\pi$}
+\printylabels{-4}{1}{4}
+\printxlabel{-4}{-2\pi}
+\printxlabel{-2}{-\pi}
+\printxlabel{2}{\pi}
+\printxlabel{4}{2\pi}}
+\pictcolor{red}
+\PlotFunction[16]{\COSfunction}{-\numberTWOPI}{\numberTWOPI}
+\pictcolor{blue}
+\PlotFunction[16]{\SINfunction}{-\numberTWOPI}{\numberTWOPI}
+\pictcolor{magenta}
+\PlotFunction[6]{\TANfunction}{-1.3258}{1.3258}
+\end{Picture}
+\end{Exemple}
+
+From these basic functions we can define many others,
+using the following \emph{operations}:
+\newcommand{\functoper}{%
+   \{\cs{\TIT{function1}}\}\{\cs{\TIT{function2}}\}\{\cs{\TIT{newfunction}}\}}
+\begin{description}
+\item[Constant function:]\mbox{}
+
+\csdef{CONSTANTfunction}\{\TIT{k}\}\{\cs{\TIT{newfunction}}\}
+
+ Example: defining the  $F(t)=5$ function:
+
+\cs{CONSTANTfunction}\{5\}\{\cs{F}\}
+
+\item[Sum function:]\mbox{}
+
+\csdef{SUMfunction}\functoper
+
+
+Example: defining the $F(t)=t^2+t^3$ function:
+
+\cs{SUMfunction}\{\cs{SQUAREfunction}\}\{\cs{CUBEfunction}\}\{\cs{F}\}
+
+\item[Difference function:]\mbox{}
+
+\csdef{SUBTRACTfunction}\functoper
+
+Example: defining the $F(t)=t^2-t^3$ function:
+
+\cs{SUBTRACTfunction}\cs{SQUAREfunction}\cs{CUBEfunction}\{\cs{F}\}
+
+\item[Product function:]\mbox{}
+
+\csdef{PRODUCTfunction}\functoper
+
+Example: defining the $F(t)=\mathrm e^t\cos t$ function:
+
+\cs{PRODUCTfunction}\cs{EXPfunction}\cs{COSfunction}\{\cs{F}\}
+
+\item[Quotient function:]\mbox{}
+
+\csdef{QUOTIENTfunction}\functoper
+
+Example: defining the $F(t)=\mathrm e^t/\cos t$ function:
+
+\cs{QUOTIENTfunction}\cs{EXPfunction}\cs{COSfunction}\{\cs{F}\}
+
+\item[Composition of two functions:]\mbox{}
+
+\csdef{COMPOSITIONfunction}\functoper
+
+Example: defining the $F(t)=\mathrm e^{\cos t}$ function:
+
+\cs{COMPOSITIONfunction}\cs{EXPfunction}\cs{COSfunction}\{\cs{F}\}
+
+\item[Scaled function:]\mbox{}
+
+\csdef{SCALEfunction}\{\TIT{k}\}\{\cs{\TIT{function}}\}%
+   \{\cs{\TIT{newfunction}}\}
+
+Example: defining the $F(t)=3{\cos t}$ function:
+
+\cs{SCALEfunction}\{3\}\cs{COSfunction}\{\cs{F}\}
+
+\item[Scaled variable:]\mbox{}
+
+\csdef{SCALEVARIABLEfunction}\{\TIT{k}\}\{\cs{\TIT{function}}\}%
+   \{\cs{\TIT{newfunction}}\}
+
+Example: defining the $F(t)=\cos 3t$ function:
+
+\cs{SCALEVARIABLEfunction}\{3\}\cs{COSfunction}\{\cs{F}\}
+
+\item[Power function:] (exponent enter positiu)\mbox{}
+
+\csdef{POWERfunction}\{\cs{\TIT{function}}\}\{\TIT{n}\}%
+   \{\cs{\TIT{newfunction}}\}
+
+Example: defining the $F(t)=t^5$ function:
+
+\cs{POWERfunction}\cs{IDENTITYfunction}\{5\}\{\cs{F}\}
+
+\item[Linear combination:]\mbox{}
+
+\csdef{LINEARCOMBINATIONfunction}\{\TIT{a}\}\{\cs{\TIT{function1}}\}%
+  \{\TIT{b}\}\{\cs{\TIT{function2}}\}\{\cs{\TIT{newfunction}}\}
+
+Example: defining the $F(t)=2t-3\cos t$ function:
+
+\cs{LINEARCOMBINATIONfunction}\{2\}\cs{IDENTITYfunction}\{-3\}%
+   \cs{COSfunction}\{\cs{F}\}
+\end{description}
+
+By combining properly these operations, we can draw graphs of many functions.
+Some examples are shown in next pages.
+\newpage
+
+First, we will draw the function $f(t)=t^3-2t$,
+dividing the interval $[-2,2]$ in ten subintervals.
+The simplest way to construct this function is as a linear combination of
+$f_1(t)=t^3$ and $f_2(t)=t$.
+
+\begin{exemple}
+\LINEARCOMBINATIONfunction
+               {1}{\CUBEfunction}
+               {-2}{\IDENTITYfunction}
+               {\Ffunction}
+\begin{center}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-2.5,-4.5)(2.5,4.5)
+\cartesianaxes(-2,-4)(2,4)
+\pictcolor{blue}
+\PlotFunction[10]{\Ffunction}{-2}{2}
+\Put[rbr](2,4){$f(t)=t^3-2t$}
+\end{Picture}
+\end{center}
+\end{exemple}
+\newpage
+
+Graph of $g(t)=t\cos t$. We multiply the identity and the cosine functions:
+
+\begin{Exemple}
+\setlength{\unitlength}{0.5cm}
+\begin{center}
+\begin{Picture}(-11,-11)(11,11)
+\cartesianaxes(-10,-10)(10,10)
+\PRODUCTfunction{\IDENTITYfunction}{\COSfunction}{\Gfunction}
+\pictcolor{red}
+\PlotFunction[30]{\Gfunction}{-10}{10}
+\end{Picture}
+\end{center}
+\end{Exemple}
+\newpage
+
+Graph of $f(t)=(\cos t)^3$.
+
+\begin{Exemple}
+\setlength{\unitlength}{1cm}
+\begin{center}
+\begin{Picture}(-7,-3)(7,3)
+\cartesianaxes(-\numberTWOPI,-2)(\numberTWOPI,2)
+\POWERfunction{\COSfunction}{3}{\Ffunction}
+\pictcolor{blue}
+\PlotFunction[50]{\Ffunction}{-\numberTWOPI}{\numberTWOPI}
+\end{Picture}
+\end{center}
+\end{Exemple}
+\newpage
+
+Graph of $g(t)=t\cos t\sin t$.
+Note that in this case we have two operations:
+First, we define the $f(t)=t \cos t$, multiplying the identity and cosine 
+functions; then, we multiply by the sine function.
+\begin{Exemple}
+\begin{center}
+\setlength{\unitlength}{0.75cm}
+ \begin{Picture}(-11,-6)(11,6)
+\cartesianaxes(-10,-5)(10,5)
+\PRODUCTfunction{\IDENTITYfunction}{\COSfunction}{%
+                            \Ffunction}
+\PRODUCTfunction{\Ffunction}{\SINfunction}{\Gfunction}
+\pictcolor{red}
+\PlotFunction[40]{\Gfunction}{-10}{10}
+\end{Picture}
+\end{center}
+\end{Exemple}
+
+Graph of $g(t)=\arcsin t$. The \package{calculus} package
+not support, for now, the inverse trigonometric functions; but we can plot
+these functions (or any other inverse function)
+swapping coordinated axes.
+
+\begin{exemple}
+\begin{center}
+\setlength{\unitlength}{2cm}
+\begin{Picture}(-1.5,-2)(1.5,2)
+\makenolabels\makenotics
+\cartesianaxes
+     (-1,-\numberHALFPI)(1,\numberHALFPI)
+\printxticslabels{-1}{0.5}{1}
+\printyticlabel{-\numberHALFPI}{-\pi/2}
+\printyticlabel{-\numberQUARTERPI}{-\pi/4}
+\printyticlabel{\numberQUARTERPI}{\pi/4}
+\printyticlabel{\numberHALFPI}{\pi/2}
+\pictcolor{red}
+\symmetrize{\numberQUARTERPI}
+\PlotFunction[4]{\SINfunction}
+     {-\numberHALFPI}{\numberHALFPI}
+\end{Picture}
+\end{center}
+\end{exemple}
+\subsubsection{Polynomial functions}
+Although polynomial functions can be easily defined as
+linear combinations of power functions,
+to facilitate our work, the \package{calculus} package predefines
+polynomials of
+1, 2, and 3 degrees by these commands:
+\cs{newlpoly} (new \emph{linear} polynomial), \cs{newqpoly}
+(new \emph{quadratic} polynomial),
+and \cs{newcpoly} (new \emph{cubic} polynomial):
+\begin{description}
+\item[\csdef{newlpoly}\{\cs{\TIT{newfunction}}\}\{\TIT a\}\{\TIT b\}]
+stores the
+$p(t)=\TTT{\TIT{a}}+\TTT{\TIT{b}}t$
+function in the
+ \cs{\TIT{newfunction}} command.
+\item[\csdef{newqpoly}%
+   \{\cs{\TIT{newfunction}}\}\{\TIT a\}\{\TIT b\}\{\TIT c\}]
+stores the
+$p(t)=\TTT{\TIT{a}}+\TTT{\TIT{b}}t+\TTT{\TIT{c}}t^2$
+function in the
+\cs{\TIT{newfunction}} command.
+\item[\csdef{newcpoly}%
+\{\cs{\TIT{newfunction}}\}\{\TIT a\}\{\TIT b\}\{\TIT c\}\{\TIT d\}]
+stores the
+$p(t)=\TTT{\TIT{a}}+\TTT{\TIT{b}}t+\TTT{\TIT{c}}t^2+\TTT{\TIT{d}}t^3$
+function in the
+\cs{\TIT{newfunction}} command.
+\end{description}
+\begin{exemple}
+% F(t)=-1+2t
+   \newlpoly{\poliF}{-1}{2}
+% G(t)=-1+2t+t^2
+   \newqpoly{\poliG}{-1}{2}{1}
+% H(t)=-1+2t+t^2-0,5t^3
+   \newcpoly{\poliH}{-1}{2}{1}{-0.5}
+
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-4.5,-5.5)(4.5,5.5)
+\cartesianaxes(-4,-5)(4,5)
+\pictcolor{blue}
+\PlotFunction{\poliF}{-2}{3}
+\pictcolor{red}
+\PlotFunction{\poliG}{-3.5}{1.5}
+\pictcolor{orange}
+\PlotFunction[10]{\poliH}{-2}{3.5}
+\end{Picture}
+\end{exemple}
+
+\subsubsection{Possible errors}
+In many cases you get a fairly accurate graph dividing the domain into several 
+subintervals.
+But an indiscriminate use of this method can produce erroneous results.
+For example, if inside a subinterval there is
+a discontinuity or a point where the function is not differentiable.
+Look at the following example.
+\medskip
+
+\begin{exemple}
+\SUBTRACTfunction{\SQUAREfunction}{\ONEfunction}
+                            {\Ffunction}
+\QUOTIENTfunction{\IDENTITYfunction}{\Ffunction}
+                            {\Gfunction}
+
+\setlength{\unitlength}{0.5cm}
+
+\begin{Picture}(-8,-6)(8,6)
+\def\xunitdivisions{2}
+\def\yunitdivisions{2}
+\renewcommand{\axeslabelsize}{\scriptsize}
+\cartesianaxes(-7,-5)(7,5)
+\Put(3,3){%
+   $\boxed{\displaystyle g(t)=\frac{t}{t^ 2-1}}$}
+\pictcolor{red}
+\PlotFunction[10]{\Gfunction}{-7}{7}
+\end{Picture}
+\end{exemple}
+
+Where is the problem?
+Our function is $g(t)=t/(t^2-1)$;
+this function has a pair of vertical asymptotes
+at $t=\pm1$ (the two zeros of denominator).
+
+We made 10 subdivisions of the $[-7,7]$ interval.
+Do, we compute the function in points $-7+(14/10)k=-7+(7/5)k$,
+$0\leq k\leq10$, ie,
+\[
+   -7\quad -\frac{28}{5}\quad -\frac{21}{5}\quad -\frac{14}{5}\quad
+    -\frac{7}{5}\quad  0\quad  \frac{7}{5}\quad  \frac{14}{5}\quad
+     \frac{21}{5}\quad  \frac{28}{5}\quad 7
+\]
+
+Singularities are between $-7/5$ and $0$, and between $0$ and $7/5$,
+So, the graph is not correct in these intervals.
+\medskip
+
+To avoid this problem, we will
+draw the function in three intervals, excluding the points where it is
+undefined:
+\medskip
+\begin{exemple}
+\SUBTRACTfunction{\SQUAREfunction}{\ONEfunction}
+                            {\Ffunction}
+\QUOTIENTfunction{\IDENTITYfunction}{\Ffunction}
+                            {\Gfunction}
+\renewcommand{\axeslabelsize}{\scriptsize}
+\setlength{\unitlength}{0.5cm}
+\begin{Picture}(-8,-6)(8,6)
+\def\xunitdivisions{2}
+\def\yunitdivisions{2}
+\cartesianaxes(-7,-5)(7,5)
+\pictcolor{red}
+\PlotFunction[5]{\Gfunction}{-7}{-1.105}
+\PlotFunction[5]{\Gfunction}{-0.905}{0}
+\PlotFunction[5]{\Gfunction}{0}{0.905}
+\PlotFunction[5]{\Gfunction}{1.105}{7}
+\end{Picture}
+\end{exemple}
+
+(To determine the ends of the ranges of variation
+$\pm1.105$ and $\pm0.905$, we solved the equation
+$g(t)=5$, to ensure that asymtotic branches are interrupted
+at the border of the drawing area).
+
+\subsubsection{Accurate graphs}
+In general, to obtain fairly reliable results we must make
+ a careful analysis of the behavior of the function,
+determining the points where it is undefined or not differentiable,
+ the intervals where it is increasing, its extreme values,
+points where graph cuts the coordinate axes and, in general,
+ all points where the behavior of
+function is significant.
+From this information, we can chose the appropriate
+drawing intervals.
+A careful choice of the partition
+subintervals in the domain ensures us
+that the graph accurately reflects the behavior of the function.
+
+We will see a couple of examples.
+First, we draw the sine function in $[-\pi,\pi]$.
+This function ant its derivative have no discontinuities,
+but it is convenient to choose a number of partitions
+being multiple of $4$, to carefully draw
+function at the
+$k\pi/2$ points.
+In fact, a good choice are 24 subdivisions,
+to ensure also the well known values of this function
+for angles
+multiple of $\pi/6$ and $\pi/4$.
+\begin{Exemple}
+\setlength{\unitlength}{2cm}%
+
+\highestlabel{\normalfont\normalsize$3\pi/2$}
+\begin{center}
+\begin{Picture}(-3.5,-1.5)(3.5,1.5)
+{\referencesystem(0,0)(\numberHALFPI,0)(0,1)
+\makenolabels
+\cartesianaxes(-2.2,-1.2)(2.2,1.2)}
+\printylabels{-1}{1}{1}
+\printxlabel{-\numberPI}{-\pi}
+\printxlabel{-\numberHALFPI}{-\pi/2}
+\printxlabel{\numberHALFPI}{\pi/2}
+\printxlabel{\numberPI}{\pi}
+\pictcolor{red}
+   \PlotFunction[24]{\SINfunction}{-\numberPI}{\numberPI}
+\renewcommand{\axeslabelcolor}{red}
+\printxlabel{\numberSIXTHPI}{\pi/6}
+\printylabel{0.5}{1/2}
+\Polyline(\numberSIXTHPI,0)(\numberSIXTHPI,0.5)(0,0.5)
+\end{Picture}
+\end{center}
+\end{Exemple}
+
+Our second example is more complex. Let's graph the function
+\[
+f(t)=(t^3/3-t^2/2-2t+3)/3
+\]
+
+This function has three roots, at
+$t=3/2$ and $t=\pm\sqrt{6}$.
+Its derivative, $f'(t)=(t^2-t-2)/3$, equals zero at
+$t=-1$ and $t=2$, where the function has, respectively,
+a relative maximum and a relative minimum.
+ The second derivative, $f''(t)=(2t-1)/3$,
+ is zero at $t=1/2$, which is an inflexion point.
+Interesting points are, then, the following:
+\[
+     -\sqrt{6},-1,0,1/2,3/2,2,\sqrt{6}
+\]
+
+We will plot this function in the
+ $[-3,4]$ interval (because it includes all these points),
+ but we divide it as
+\[
+      [-3,-\sqrt{6}]\cup
+      [-\sqrt{6},-1]\cup
+      [-1,0]\cup
+      [0,1/2]\cup
+      [1/2,3/2]\cup
+      [3/2,2]\cup
+      [2,\sqrt{6}]\cup
+      [\sqrt{6},4]
+\]
+\begin{Exemple}
+\SQRT{6}{\SQRTSIX}
+\newcpoly{\functionf}{1}{-0.66667}{-0.16667}{0.11111}
+\setlength{\unitlength}{2cm}
+\begin{center}
+ \begin{Picture}(-3.5,-2.5)(4.5,3.5)
+\renewcommand{\xunitdivisions}{10}
+\renewcommand{\yunitdivisions}{10}
+\cartesiangrid(-3,-2)(4,3)
+\pictcolor{red}
+\PlotFunction{\functionf}{-3}{-\SQRTSIX}
+\PlotFunction[4]{\functionf}{-\SQRTSIX}{-1}
+\PlotFunction[4]{\functionf}{-1}{0}
+\PlotFunction[4]{\functionf}{0}{0.5}
+\PlotFunction[4]{\functionf}{0.5}{1.5}
+\PlotFunction[4]{\functionf}{1.5}{2}
+\PlotFunction[4]{\functionf}{2}{\SQRTSIX}
+\PlotFunction{\functionf}{\SQRTSIX}{4}
+\functionf{-1}{\tempf}{\tempDf}
+\xLINE(-1,0)(-1,\tempf)
+\functionf{2}{\tempf}{\tempDf}
+\xLINE(2,0)(2,\tempf)
+\functionf{0.5}{\tempf}{\tempDf}
+\xLINE(0.5,0)(0.5,\tempf)
+\end{Picture}
+\end{center}
+\end{Exemple}
+
+\subsection{Polar coordinates curves}
+To draw a curve defined in polar form as $\rho =f(t)$, we must
+declare it as a polar curve, using the \csdef{POLARfunction}
+declaration: writing
+\begin{Verbatim}[commandchars=\|\[\]]
+\POLARfunction{\|TIT[functionname]}{\|TIT[polarfunction]}
+\end{Verbatim}
+we declare the new polar curve \cs{\TIT{polarfunction}}
+$\rho=\cs{\TIT{functionname}}(t)$.
+For example, the \emph{cardioide} curve, $\rho=1+\cos t$,
+can be defined in the following way:
+\begin{Verbatim}
+\SUMfunction{\ONEfunction}{\COSfunction}{\ffunction} % (y=1 + cos t)
+\POLARfunction{\ffunction}{\cardioide}
+\end{Verbatim}
+
+Curves defined in such a way can be plotted using the
+\csdef{PlotParametricFunction} command,
+which syntax is analogous to that of \cs{PlotFunction}.
+
+\begin{exemple}
+% Cardioide: r = 1+cos t
+\SUMfunction{\ONEfunction}{\COSfunction}
+            {\ffunction}
+\POLARfunction{\ffunction}{\cardioide}
+\begin{center}
+\def\runitdivisions{2}
+\setlength{\unitlength}{1.5cm}
+\begin{Picture}(-2.5,-2.5)(2.5,2.5)
+\polargrid{2}{24}
+\pictcolor{blue}\linethickness{1pt}
+ \PlotParametricFunction[20]{%
+         \cardioide}{0}{\numberTWOPI}
+\end{Picture}
+$\rho=1+\cos\phi$
+\end{center}
+\end{exemple}
+
+\begin{exemple}
+% Eight petal rose: r = cos(4t)
+\SCALEVARIABLEfunction{4}{\COSfunction}
+                      {\ffunction}
+\POLARfunction{\ffunction}{\rose}
+\begin{center}
+\def\runitdivisions{3}
+\MULTIPLY{2}{\numberTWOPI}{\numberFOURPI}
+\setlength{\unitlength}{2.5cm}
+
+\begin{Picture}(-1.5,-1.5)(1.5,1.5)
+\polargrid{1}{16}
+\pictcolor{red}\linethickness{1pt}
+\PlotParametricFunction[16]\rose{0}{\numberTWOPI}
+\end{Picture}
+$\rho=\cos 4\phi$
+\end{center}
+\end{exemple}
+
+\begin{exemple}
+% Archimedean spiral: r=0,5t
+\SCALEfunction{0.5}{\IDENTITYfunction}{\ffunction}
+\POLARfunction{\ffunction}{\archimedes}
+
+\MULTIPLY{2}{\numberTWOPI}{\numberFOURPI}
+\setlength{\unitlength}{0.5cm}
+\begin{center}
+\begin{Picture}(-7,-7)(7,7)
+\pictcolor{red}
+\PlotParametricFunction[16]{%
+                \archimedes}{0}{\numberFOURPI}
+\end{Picture}
+$2\rho=\phi$
+\end{center}
+\end{exemple}
+
+\begin{exemple}
+\SCALEVARIABLEfunction{3.2}{\SINfunction}{\ffunction}
+\SCALEfunction{0.2}{\ffunction}{\gfunction}
+\SUMfunction{\ONEfunction}{\gfunction}{\myfunction}
+\POLARfunction{\myfunction}{\Rfunction}
+\MULTIPLY{10}{\numberPI}{\numberTENPI}
+\setlength{\unitlength}{3cm}
+\linethickness{2pt}
+\begin{center}
+\begin{Picture}(-1.2,-1.2)(1.2,1.2)
+\pictcolor{orange}
+\PlotParametricFunction[120]\Rfunction{0}{\numberTENPI}
+\end{Picture}
+$\rho=1+2\sin 3.2\phi$
+\end{center}
+\end{exemple}
+\subsection{Parametrically defined curves}\label{subsec:param}
+Polar curves are a particular case of parametrically defined curves,
+$x=f(t), y=g(t)$. These curves are declared by the
+ \csdef{PARAMETRICfunction} command:
+\begin{Verbatim}[commandchars=\|\[\],commentchar=\%]
+\PARAMETRICfunction{\|TIT[Xfunction]}{\|TIT[Yfunction]}%
+{\|TIT[parametricfunction]}
+\end{Verbatim}
+
+Once we have defined it,
+to draw this curve, we use the \csdef{PlotParametricFunction} as described 
+above.
+\begin{Exemple}
+\POWERfunction{\IDENTITYfunction}{5}{\xfunction}
+\PARAMETRICfunction{\xfunction}{\CUBEfunction}{\myparfunction}
+\centering
+\setlength{\unitlength}{0.75cm}
+\begin{Picture}(-11,-6)(11,6)
+\cartesiangrid(-10,-5)(10,5)
+\pictcolor{blue}
+\PlotParametricFunction[10]{\myparfunction}{-1.5849}{0}
+\PlotParametricFunction[10]{\myparfunction}{0}{1.5849}
+\Put[E](10,4){$\begin{matrix}x=t^5\\y=t^3\end{matrix}$}
+\end{Picture}
+\end{Exemple}
+\begin{exemple}
+% A Lissanjous curve: x=sin 3t, y=sin 4t
+\SCALEVARIABLEfunction{3}{\SINfunction}{\ffunction}
+\SCALEVARIABLEfunction{4}{\SINfunction}{\gfunction}
+\PARAMETRICfunction{\ffunction}{\gfunction}{\myfunction}
+\MULTIPLY{10}{\numberPI}{\numberTENPI}
+\setlength{\unitlength}{3cm}
+\linethickness{2pt}
+\begin{center}
+\begin{Picture}(-1.2,-1.2)(1.2,1.2)
+\pictcolor{red}
+\PlotParametricFunction[24]\myfunction{0}{\numberTWOPI}
+\end{Picture}
+
+$x=\sin 3t,\ y=\sin 4t$
+\end{center}
+\end{exemple}
+
+Here, we should also take into account the characteristics of the curve
+in order to choose appropriate intervals for
+the parameter (typically, the points where the function is not defined,
+singularities, cuts with axes,
+points where some of the derivatives $x',x'',\ldots$ or $y',y''\ldots$) is 
+zero\ldots
+In the following example, to represent the curve $x=t^2-1$, $y=t^3-t$,
+we see that $x$ or $y$ equals zero when $t$ is
+$0$, $1$ or $-1$; the first derivatives $x'=2t$, $y'=3t^2-1$,
+in $t=0$ and $t=\pm\sqrt3/3$, and second derivative of $y$ in $t=0$.
+Thus, we choose an interval containing these values of $t$, such $[-2.2]$,
+and this partition of it:
+\[
+   [-2,2]=[-2,-1]\cup[-1,-\sqrt3/3]\cup[-\sqrt3/3,0]\cup[0,\sqrt3/3]\cup[\sqrt3/3,1]\cup[1,2]
+\]
+
+This same curve was depicted with a single instruction
+\cs{PlotParametricFunction} dividing
+the interval $[-2.2]$ into five subintervals.
+Note that the obtained picture is almost identical, but the fact that
+partition not includes zero
+conceals the fact that the vertical tangent occurs at the point
+ $(-1,0)$.
+So, one of the most significant features of the curve is not correctly 
+displayed.
+\begin{Exemple}
+\SUBTRACTfunction{\SQUAREfunction}{\ONEfunction}{\Xpart}
+\SUBTRACTfunction{\CUBEfunction}{\IDENTITYfunction}{\Ypart}
+\PARAMETRICfunction{\Xpart}{\Ypart}{\myparfunction}
+\centering
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-3.5,-6.5)(3.5,6.5)
+\cartesiangrid(-3,-6)(3,6)
+\pictcolor{blue}
+\PlotParametricFunction\myparfunction{-2}{-1}
+\PlotParametricFunction\myparfunction{-1}{-0.57735}
+\PlotParametricFunction\myparfunction{-0.57735}{0}
+\PlotParametricFunction\myparfunction{0}{0.57735}
+\PlotParametricFunction\myparfunction{0.57735}{1}
+\PlotParametricFunction\myparfunction{1}{2}
+\Put[E](3,6){$\begin{matrix}x=t^2-1\\y=t^3-t\end{matrix}$}
+\end{Picture}
+\qquad
+\begin{Picture}(-3.5,-6.5)(3.5,6.5)
+\cartesiangrid(-3,-6)(3,6)
+\pictcolor{orange}
+\PlotParametricFunction[5]\myparfunction{-2}{2}
+\Put[E](3,6){$\begin{matrix}x=t^2-1\\y=t^3-t\end{matrix}$}
+\end{Picture}
+\end{Exemple}
+\subsubsection{The curve of the front page}
+To conclude this section we will study in detail the example
+of the front page of this manual.
+This example shows the power,
+while the simplicity of the package \package{xpicture}.
+
+It is the transcendent curve named \emph{butterfly},
+\begin{gather*}
+        x=\sin t \left(\mathrm e^{\cos t} - 2 \cos 4t 
+                       + \sin^5\left(\frac t{12}\right)\right) \\
+        y=\cos t \left(\mathrm e^{\cos t} - 2 \cos 4t 
+                       + \sin^5\left(\frac t{12}\right)\right)
+\end{gather*}
+
+We analyze step by step the code we used:
+\begin{itemize}
+\item First, we calculated some numbers we'll use later:
+\begin{inparaenum}[(a)]
+\item $1/12$, that appears in the definition of functions $x$ and $y$;
+\item $12\times2\pi$, to plot the curve in $[0,24\pi]$ (twelve laps); and
+\item$12\times64$, the number of subdivisions we will use
+(64 subintervals for each lap).
+\VerbatimInput[numbers=left,firstline=3,lastline=5]{xpicture1.tex}
+\end{inparaenum}
+\item In the next block we do the important work:
+the curve is defined step by step.
+
+\begin{compactitem}
+\item Define the function $A(t)=\mathrm e^{\cos t}$
+\VerbatimInput[numbers=left,firstline=7,lastline=7]{xpicture1.tex}
+\item Define  $B(t)=\cos 4t$
+\VerbatimInput[numbers=left,firstline=8,lastline=8]{xpicture1.tex}
+\item Define $c(t)=\sin t/12$
+\VerbatimInput[numbers=left,firstline=9,lastline=9]{xpicture1.tex}
+\item Define $C(t)=\sin^5 t/12$
+\VerbatimInput[numbers=left,firstline=10,lastline=10]{xpicture1.tex}
+\item Define  $AB(t)=\mathrm e^{\cos t}-2\cos 4t$
+\VerbatimInput[numbers=left,firstline=11,lastline=11]{xpicture1.tex}
+\item Define $ABC(t)=\mathrm e^{\cos t}-2\cos 4t+\sin^5 t/12$
+\VerbatimInput[numbers=left,firstline=12,lastline=12]{xpicture1.tex}
+\item Define the $x$ and $y$ functions
+\VerbatimInput[numbers=left,firstline=13,lastline=16]{xpicture1.tex}
+\item And, finally, we declare the parametric curve:
+\VerbatimInput[numbers=left,firstline=17,lastline=17]{xpicture1.tex}
+\end{compactitem}
+
+\item Now, the picture composition is trivial
+(note the use of constants
+\cs{divisions} and \cs{phione} we previously calculated):
+\VerbatimInput[numbers=left,firstline=19,lastline=21]{xpicture1.tex}
+\end{itemize}
+
+\subsection{Drawing curves from a table of values}
+All instructions to draw curves described here use the
+\csdef{qCurve} command, which draws quadratic B\'ezier curves:
+\begin{Verbatim}[commandchars=\|\[\],commentchar=\%]
+\qCurve(|TIT[x0],|TIT[y0])(|TIT[u0],|TIT[v0])(|TIT[x1],|TIT[y1])(|TIT[u1],%
+|TIT[v1])
+\end{Verbatim}
+draw a smooth curve between the points $(\TTT{\TIT{x0}},\TTT{\TIT{y0}})$
+and $(\TTT{\TIT{x1}},\TTT{\TIT{y1}})$, with tangent vectors
+$(\TTT{\TIT{u0}},\TTT{\TIT{v0}})$ and $(\TTT{\TIT{u1}},\TTT{\TIT{v1}})$,
+respectively.
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-0.5,-0.5)(5.5,5.5)
+\cartesianaxes(0,0)(5,5)
+\pictcolor{blue}
+\qCurve(1,2)(1,2)(4,3)(-1,1)
+\pictcolor{gray}
+\Put(1,2){\xtrivVECTOR(0,0)(1,2)}
+\Put(4,3){\xtrivVECTOR(0,0)(-1,1)}
+\Polyline(1,0)(1,2)(0,2)
+\Polyline(4,0)(4,3)(0,3)
+\end{Picture}
+\end{exemple}
+
+The \csdef{PlotQuadraticCurve} command generalizes \cs{qCurve}
+to an arbitrary number of points. 
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-0.5,-0.5)(5.5,3.5)
+\cartesianaxes(0,0)(5,3)
+\pictcolor{blue}
+\PlotQuadraticCurve(0,0)(1,0)%
+                   (1,1)(1,2)%
+                   (3,2)(-1,1)%
+                   (5,2)(0,-1)
+\end{Picture}
+\end{exemple}
+This command supports two alternative syntaxes:
+\begin{enumerate}[(a)]
+\item
+\begin{Verbatim}[commandchars=\|\[\],commentchar=\%]
+\PlotQuadraticCurve(|TIT[x0],|TIT[y0])(|TIT[u0],|TIT[v0])(|TIT[x1],|TIT[y1])%
+(|TIT[u1],|TIT[v1])...(|TIT[xn],|TIT[yn])(|TIT[un],|TIT[vn])
+\end{Verbatim}
+draws a curve through the points
+$(\TTT{\TIT{x0}},\TTT{\TIT{y0}})$,
+ $(\TTT{\TIT{x1}},\TTT{\TIT{y1}})$\ldots
+ $(\TTT{\TIT{xn}},\TTT{\TIT{yn}})$
+with tangent vectors
+$(\TTT{\TIT{u0}},\TTT{\TIT{v0}})$, $(\TTT{\TIT{u1}},\TTT{\TIT{v1}})$\dots
+$(\TTT{\TIT{un}},\TTT{\TIT{vn}})$.%
+\footnote{This command draws a
+quadratic curve between each pair of adjacent points.
+
+The \cs{Curve} command, introduced by the
+\package{curve2e} package, does a similar job,
+but using cubic approximations, instead of quadratic.}
+
+\begin{exemple}
+\setlength{\unitlength}{2cm}
+\begin{center}
+\begin{Picture}(1,1)(-1,-1)
+\pictcolor{red}
+\PlotQuadraticCurve(1,0)(1,0)(0,1)(0,1)%
+                   (-1,0)(-1,0)(0,-1)(0,-1)%
+                   (1,0)(1,0)
+\pictcolor{blue}
+\referencesystem(0,0)%
+                (\numberCOSXLV,\numberCOSXLV)%
+                (-\numberCOSXLV,\numberCOSXLV)
+\PlotQuadraticCurve(1,0)(1,0)(0,1)(0,1)%
+                   (-1,0)(-1,0)(0,-1)(0,-1)%
+                   (1,0)(1,0)
+\end{Picture}
+\end{center}
+\end{exemple}
+\item
+\begin{Verbatim}[commandchars=\|\[\],commentchar=\%]
+\PlotQuadraticCurve(|TIT[x0],|TIT[y0]){|TIT[angle0]}(|TIT[x1],|TIT[y1])%
+{|TIT[angle1]}...(|TIT[xn],|TIT[yn]){|TIT[anglen]}
+\end{Verbatim}
+draws a curve through the points
+$(\TTT{\TIT{x0}},\TTT{\TIT{y0}})$,
+ $(\TTT{\TIT{x1}},\TTT{\TIT{y1}})$\ldots
+ $(\TTT{\TIT{xn}},\TTT{\TIT{yn}})$
+the inclination angles of which, with respect to the $x$ axis,
+are \TTT{\TIT{angle0}}, \TTT{\TIT{angle1}}\dots,
+  \TTT{\TIT{angle0}} (always measured in degrees).
+\begin{exemple}
+\setlength{\unitlength}{2cm}
+\begin{center}
+\begin{Picture}(1,1)(-1,-1)
+\pictcolor{red}
+\PlotQuadraticCurve(1,0){0}(0,1){90}
+                   (-1,0){180}(0,-1){270}
+                   (1,0){360}
+\pictcolor{blue}
+\referencesystem(0,0)%
+                (\numberCOSXLV,\numberCOSXLV)%
+                (-\numberCOSXLV,\numberCOSXLV)
+\PlotQuadraticCurve(1,0){0}(0,1){90}
+                   (-1,0){180}(0,-1){270}
+                   (1,0){360}
+\end{Picture}
+\end{center}
+\end{exemple}
+\end{enumerate}
+With the \cs{PlotQuadraticCurve} command you can approximate any smooth curve
+passing through a list of points when you know the tangent vectors.
+A particular case, particularly interesting (at least in a calculus course)
+is the drawing of the graph a function of real variable knowing a table of 
+values of the function and its derivative.
+To facilitate this work \package{xpicture}
+includes the \csdef{PlotxyDyData} command:
+\begin{Verbatim}[commandchars=\|\[\],commentchar=\%]
+\PlotxyDyData(|TIT[x0],|TIT[y0],|TIT[Dy0])(|TIT[x1],|TIT[y1],|TIT[Dy1])...%
+(|TIT[xn],|TIT[yn],|TIT[Dyn])
+\end{Verbatim}
+plots the graph of a function $y=f(x)$  passing through points
+$(\TTT{\TIT{x0}},\TTT{\TIT{y0}})$,
+$(\TTT{\TIT{x1}},\TTT{\TIT{y1}})$\ldots
+$(\TTT{\TIT{xn}},\TTT{\TIT{yn}})$
+with derivatives $\TTT{\TIT{Dy0}}$, $\TTT{\TIT{Dy1}}$\ldots
+$\TTT{\TIT{Dyn}}$.
+\begin{exemple}
+\setlength{\unitlength}{1cm}
+\begin{Picture}(-1,-1)(5.5,5.5)
+\cartesianaxes(0,0)(5,5)
+\pictcolor{blue}
+\PlotxyDyData(0,0,2)(1,1,0)(2,2,3)
+                          (3,4,0)(5,1,-2)
+\pictcolor{gray}
+\Put(0,0){\xtrivVECTOR(0,0)(1,2)}
+\Put(1,1){\xtrivVECTOR(0,0)(1,0)}
+\Put(2,2){\xtrivVECTOR(0,0)(1,3)}
+\Put(3,4){\xtrivVECTOR(0,0)(1,0)}
+\Put(5,1){\xtrivVECTOR(0,0)(1,-2)}
+\end{Picture}
+\end{exemple}
+\section{Package options and configuration file}
+This package is loaded as usual, using the instruction
+\cs{usepackage\{\TIT{list of options}\}\{xpicture\}}.
+Then, packages \packagedef{pict2e}, \packagedef{curve2e}, \packagedef{xcolor},
+\packagedef{calculator}, and \packagedef{calculus} are automatically loaded.
+This package is compatible with any system that supports 
+\packagedef{xcolor} and \packagedef{pict2e} packages.
+
+The only specific option for this package is \optiondef{draft},
+which disables all the instructions defined in this package, 
+replacing each picture set in a \environ{Picture} environment
+by a parallelogram circumscribed by a white rectangle (the box that shows
+the area reserved for the picture).\footnote{This option is equivalent to
+a global use of
+the \texttt{\textbackslash draftPictures} declaration.}
+This option is very useful throughout the production 
+of the document, 
+since the composition of the drawings slows considerably
+the compilation time. 
+
+All other options are passed directly to packages 
+\packagedef{pict2e}, \packagedef{curve2e}, and \packagedef{xcolor}.
+The most interesting option (from package \package{pict2e})
+is \optiondef{pstarrows}; 
+if used, arrowheads in vectors are drawn in PSTricks style (instead of the
+standard \LaTeX{} style). 
+Do not use the \optiondef{hide} or \optiondef{original}
+options (from package \package{pict2e}).
+
+You can include your preferred values for configurable \package{xpicture}
+parameters 
+(like axes or labels style, radians or degrees measure for angles,
+radians or degrees labels in polar grids, et cetera)
+using the file \texttt{xpicture.cfg}\ttindex{xpicture.cfg}, because,
+if exists, this local configuration file is loaded.
+If you want to use it, copy the file 
+\texttt{xpicture.cfgxmpl}\ttindex{xpicture.cfgxmpl}
+(which is distributed along with package \package{xpicture}),
+call your copy as \texttt{xpicture.cfg} and put it in your local
+\texttt{texmf} tree.
+Initially, this file contains the default values for all parameters, but
+you edit it to modify everything agreed.
+\section{Compatibility with related packages}
+As mentioned earlier, this package loads packages 
+\packagedef{pict2e}, \packagedef{curve2e}, \packagedef{xcolor},
+\packagedef{calculator}, and \packagedef{calculus}. Every command defined in
+these packages works fine within a \environ{Picture} environment. The only
+restriction to take in account is that colors must be selected with the
+\cs{pictcolor} command, because commands \cs{color} and \cs{textcolor}
+may cause the appearance of unwanted spaces. Picture commands defined 
+in \packagedef{pict2e} and \packagedef{curve2e} can be freely used 
+(had in mind, however, that in this case coordinates 
+are interpreted as standard), 
+and you can use all the techniques for defining and manipulating colors
+from \packagedef{color} and \packagedef{xcolor} packages.
+
+Although guidelines for defining and operating with functions
+explained in subsections~\ref{subsec:real}--\ref{subsec:param} 
+may be enough to compose a lot of graphics, 
+in order to take full advantage of this package you must known
+packages \packagedef{calculator} and \packagedef{calculus}
+with certain depth. Package \package{calculator} 
+will set you free of many tedious calculations.
+\medskip
+
+On the other hand, \package{xpicture} is widely compatible with other packages
+related to the graphics inclusion, composition or modification.
+This fact gives us a lot of flexibility when using them together. 
+
+For example, a picture drawn by \package{xpicture} can include external images 
+loaded with packages \packagedef{graphics}/\packagedef{graphicx}, 
+and you can also manipulate the whole picture with the aid of these packages.
+In a similar way, \texttt{pgf/tikz}\ttindex{pgf}\ttindex{tikz} 
+pictures can be included inside a 
+\package{xpicture} draw. If you use \LaTeX{} and \TTT{dvips} to compile your 
+document, you can combine \package{xpicture} with \packagedef{pstricks}.
+
+\printindex
+\end{document}
diff --git a/Master/texmf-dist/doc/latex/xpicture/xpicture.pdf b/Master/texmf-dist/doc/latex/xpicture/xpicture.pdf
new file mode 100644
index 00000000000..eee47e12be5
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/xpicture/xpicture.pdf
diff --git a/Master/texmf-dist/source/latex/xpicture/xpicture.dtx b/Master/texmf-dist/source/latex/xpicture/xpicture.dtx
new file mode 100644
index 00000000000..65aab3c5fca
--- /dev/null
+++ b/Master/texmf-dist/source/latex/xpicture/xpicture.dtx
@@ -0,0 +1,3570 @@
+% \iffalse meta-comment
+%<*internal>
+\begingroup
+\input docstrip.tex
+\keepsilent
+\declarepreamble\packagepreamble
+********************************************************************
+The xpicture package
+Copyright (C) 2010, 2011, 2012 by Robert Fuster <rfuster@mat.upv.es>
+All rights reserved
+
+This file may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+
+   http://www.latex-project.org/lppl.txt
+
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+********************************************************************
+\endpreamble
+\declarepreamble\cfgpreamble
+************************************************************************
+This is xpicture.cfgxmpl, part of the xpicture distribution
+Copyright (C) 2010, 2011, 2012 by Robert Fuster <rfuster@mat.upv.es>
+All rights reserved
+
+        This is a model for the xpicture configuration file
+
+You should not modify this file.
+To costumize your xpicture installation, make a copy of this file,
+save it as 'xpicture.cfg' and modify this new file at your convenience.
+************************************************************************
+
+\endpreamble
+\postamble
+\endpostamble
+
+\askforoverwritefalse
+\generate{\usepreamble\packagepreamble
+             \file{xpicture.sty}{\from{xpicture.dtx}{xpicture,defaults}}
+          \usepreamble\cfgpreamble
+             \file{xpicture.cfgxmpl}{\from{xpicture.dtx}{defaults,cfg}}
+   }
+
+\def\tmpa{plain}
+\ifx\tmpa\fmtname\endgroup\expandafter\bye\fi
+\endgroup
+%</internal>
+%
+% Copyright (C) 2010, 2011, 2012 by Robert Fuster <rfuster@mat.upv.es>
+%
+% This file may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%
+%   http://www.latex-project.org/lppl.txt
+%
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% \fi
+% \CheckSum{2978}
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\ProvidesFile{xpicture.dtx}
+   [2012/12/17 v.1.2a documented xpicture package]
+\GetFileInfo{xpicture.dtx}
+\usepackage[lmargin=5cm,rmargin=2cm]{geometry}
+
+\usepackage{xpicture}
+
+\newcommand{\environ}[1]{\textnormal{\texttt{#1}}}
+\newcommand{\package}[1]{\textnormal{\texttt{#1}}}
+\newcommand{\option}[1]{\textnormal{\texttt{#1}}}
+\newcommand{\optionindex}[1]{%
+    \index{#1=\texttt{#1} (package option)|usage}%
+    \index{options:>#1=\texttt{#1}|usage}}
+
+\newcommand{\starred}{\textnormal{\texttt{*}}}
+\newcommand{\Parg}[1]{\textnormal{\texttt(\textit{#1}\texttt)}}
+\makeatletter
+\newcommand{\myDescribeMacro}{\@ifstar
+      \xpct@myDescribeMacrostar
+      \xpct@myDescribeMacro
+      }
+\newcommand{\xpct@myDescribeMacro}[1]{\smallskip\par\DescribeMacro{#1}}
+\newcommand{\xpct@myDescribeMacrostar}[1]{\myDescribeMacro{#1}{ }}
+\newcommand{\myDescribeEnv}[1]{\smallskip\par
+   \DescribeEnv{#1}{ }\cs{begin}\{\texttt{#1}\}}
+\makeatother
+
+\def\fileversion{1.2a}
+\def\filedate{2012/12/17}
+\title{The \textsf{xpicture} package\thanks{This document
+       corresponds to \textsf{xpicture}~\fileversion, dated \filedate.}\\
+       (\texttt{http://www.upv.es/\~{}rfuster/xpicture}) \\
+       Several extensions of the \textsf{picture} standard environment\\
+       Reference manual and documented source}
+\author{Robert Fuster\\
+        Universitat Polit\`ecnica de Val\`encia \\
+        \texttt{rfuster@mat.upv.es}}
+\date{\filedate}
+\EnableCrossrefs         
+\CodelineIndex
+
+\begin{document}
+  \DocInput{xpicture.dtx}
+  \newpage
+  
+  \PrintIndex
+\end{document}
+%</driver>
+%
+% \fi
+%
+%
+% \DoNotIndex{\NeedsTeXFormat}
+% \DoNotIndex{\RequirePackage,\ProcessOptions,\ProvidesPackage}
+% \DoNotIndex{\CurrentOption,\DeclareOption}
+% \DoNotIndex{\MessageBreak,\PackageError,\PackageInfo,\PackageWarning}
+% \DoNotIndex{\PassOptionsToPackage,\InputIfFileExists}
+% \DoNotIndex{\begingroup,\endgroup,\begin,\end}
+% \DoNotIndex{\def,\let,\edef,\xdef,\newcommand,\newenvironment}
+% \DoNotIndex{\if,\ifx,\ifnum,\ifdim,\else,\fi,\@whilenum,\@whiledim,\value}
+% \DoNotIndex{\@ifnextchar,\@ifstar,\@ifundefined,\@killglue,\do,\newif}
+% \DoNotIndex{\undefined,\newcounter,\newdimen,\stepcounter}
+% \DoNotIndex{\setcounter,\setlength,\unitlength,\settoheight,\settowidth}
+% \DoNotIndex{\p@,\z@}
+% \DoNotIndex{\noexpand,\ignorespaces}
+% \DoNotIndex{\normalfont,\normalsize,\small}
+% \DoNotIndex{\circle,\line,\linethickness,\makebox,\put,\multiput,\qbezier}
+% \DoNotIndex{\ensuremath,\mathrm,\mathversion}
+% \DoNotIndex{\scshape}
+% \DoNotIndex{\color,\textcolor,\colorlet}
+% \DoNotIndex{\moveto,\lineto,\closepath,\fillpath}
+% \DoNotIndex{\LINE,\VECTOR,\segment}
+% \DoNotIndex{\x,\Dx,\y,\Dy,\t,\Dt}
+% \DoNotIndex{\Picture,\endPicture}
+% \DoNotIndex{\ADD,\COPY,\GLOBALCOPY}
+% \DoNotIndex{\COS,\RADtoDEG,\COSH,\COTAN,\COTANH,\CUBE,\DIVIDE,\EXP,\LOG}
+% \DoNotIndex{\MULTIPLY,\POWER,\SIN,\SINH,\SQRT,\SQUARE,\SUBTRACT,\TAN,\TANH}
+% \DoNotIndex{\ABSVALUE,\DEGREESCOS,\DEGREESSIN,\DEGREESTAN,\DEGREESCOT}
+% \DoNotIndex{\COS,\SIN,\TAN,\COT,\pi}
+% \DoNotIndex{\DETERMINANT,\MATRIXVECTORPRODUCT,\SCALARVECTORPRODUCT}
+% \DoNotIndex{\MAX,\MIN,\ROUND,\TRUNCATE}
+% \DoNotIndex{\FLOOR,\FRACTIONSIMPLIFY,\LENGTHDIVIDE,\SQUAREROOT}
+% \DoNotIndex{\numberTWOPI,\newvectorfunction}
+% \DoNotIndex{\UNITVECTOR,\VECTORADD,\VECTORCOPY,\VECTORNORM,\VECTORSUB}
+
+% \maketitle
+% \begin{abstract}
+% The \package{xpicture} package extends the graphic abilities 
+% of the \environ{picture} standard environment and packages \package{pict2e}
+% and \package{curve2e}, adding the ability to work with arbitrary 
+% In addition to other utilities,
+% the greater interest of \package{xpicture} 
+% lies in its capacity to draw function graphs,
+% conic sections and arcs, and parametrically defined curves.
+
+% This is the technical documentation and reference manual 
+% of package \package{xpicture}, but not its user manual.
+% User manual is on file \texttt{xpicture-doc.pdf}, 
+% distributed together with the package.
+% \end{abstract}
+% \tableofcontents
+% \newpage
+%
+% \section{Introduction}
+% The \package{xpicture} package introduces several new graphical 
+% instructions,
+% and some enriched versions of standard
+% instructions used inside the \environ{picture} environment.
+% All these new instructions can be classified as follows:
+% \begin{enumerate}
+%  \item Reference systems and coordinates:
+% \begin{itemize}
+% \item Declaration and use of different reference systems,
+% with Cartesian or polar coordinates.
+% \item Instructions to show Cartesian or polar reference systems.
+% \end{itemize}
+%  \item  An alternative to the \environ{picture} environment,
+% compatible with the new reference systems.
+%  \item Alternative instructions or extensions of the standard
+%  \environ{picture} commands and those defined by the packages
+%  \package{pict2e} and \package{curve2e}:
+% \begin{itemize}
+%  \item Enriched versions of marks \cs{put} and \cs{multiput},
+%  providing an adequate control of the precise position 
+% in which objects are composed
+% (this functionality is especially useful in the composition
+% of not strictly graphical objects, such as formulas or labels).
+% \item Instructions for drawing straight segments, vectors
+% (in any direction and using any reference system), polylines,
+% polygons, regular and arbitrary polygons .
+% \end{itemize}
+% \item Regular curves:
+% \begin{itemize}
+% \item Instructions for drawing conic sections (circles, ellipses,
+% hyperbolas and parabolas) and arcs of these curves.
+% \item Instructions to graph functions and parametrically defined curves
+% (this is the most interesting feature of this package).
+% \end{itemize}
+% \end{enumerate}
+%
+% To enjoy this package you need to have an adequate knowledge of the commands
+% defined in packages \package{calculator} and \package{calculus}, 
+% especially concerning to the definition of 
+% functions and operations with functions.
+% 
+% 
+% \setlength{\marginparsep}{0pt}
+% \setlength{\parindent}{0pt}
+% \section{Usage}
+% This package is loaded as usual, using the instruction
+% \cs{usepackage}\oarg{list of options}|{xpicture}|.
+% Then, packages \package{pict2e}, \package{curve2e}, \package{xcolor},
+% \package{calculator}, and \package{calculus} are automatically loaded.
+% This package is compatible with any system that supports 
+% \package{xcolor} and \package{pict2e} packages.\footnote{%
+% Earlier versions supports \option{dvi} option, 
+% which was compatible with a pure \texttt{dvi} output, 
+% but this possibility has been eliminated in version 2.1a, 
+% because it was too expensive and probably unhelpful.}
+%
+% Options are passed directly to packages 
+% \package{pict2e}, \package{curve2e}, and \package{xcolor}, excerpt option
+% \option{draft}\optionindex{draft},
+% which disables all the instructions defined in this package, 
+% replacing each picture set in a \environ{Picture} environment
+% by a blank rectangle.\footnote{If you use an instruction 
+% not directly defined by \package{xpicture}, 
+% this instruction may take effect.} 
+% Using this option is very convenient throughout the production 
+% of the document, 
+% since the composition of the drawings slows considerably
+% the compilation time.
+% The |\draftPictures| declaration performs a similar work,
+% allowing the user to locally disable |Picture| commands.
+% 
+% An interesting option (from package \package{pict2e}) is 
+% \option{pstarrows};\optionindex{pstarrows} 
+% if used, arrowheads in vectors are drawn in PSTricks style (instead of the
+% standard \LaTeX{} style).
+% 
+% If exists, the local configuration file \texttt{xpicture.cfg} is loaded.
+% This file allows the user to customize all configurable
+% \package{xpicture} parameters;
+% if you want to use it, copy the file \texttt{xpicture.cfgxmpl}, 
+% which is distributed along with package \package{xpicture},
+% call your copy as \texttt{xpicture.cfg}, put it in your local
+% \texttt{texmf} tree
+% and edit this file to modify everything agreed. 
+% 
+% \section{The user interface}
+% \subsection{Color selection}
+%
+% \myDescribeMacro\pictcolor\marg{color}
+% select a color without spurious spaces.
+%
+% Example: |\pictcolor{blue}|
+%
+% \subsection{Reference systems}
+% \myDescribeMacro\referencesystem\parg{x0,y0}\parg{x1,y1}\parg{x2,y2}
+% selects the affine reference system with origin in point
+% (\textit{x0},\textit{y0}) and coordinate vectors (\textit{x1},\textit{y1})
+% and (\textit{x2},\textit{y2}). 
+%
+% Coordinates are refered to the standard reference system. 
+%
+% Example: |\referencesystem(0,0)(1,-1)(1,1)|
+%
+% \myDescribeMacro\changereferencesystem\parg{x0,y0}\parg{x1,y1}\parg{x2,y2}
+% selects the affine reference system with origin in point
+% (\textit{x0},\textit{y0}) and coordinate vectors (\textit{x1},\textit{y1})
+% and (\textit{x2},\textit{y2}).
+%
+% Coordinates are refered to the active reference system.
+%
+% Example: |\changereferencesystem(0,0)(1,-1)(1,1)|
+%
+% \myDescribeMacro\translateorigin\parg{x0,y0}
+% translates origin to the given point.
+%
+% Coordinates are refered to the active reference system.
+%
+% Example: |\translateorigin(2,-3)|
+%
+% \myDescribeMacro\rotateaxes\marg{angle}
+% rotates the axes. 
+% The angle parameter is interpreted as the rotation angle in radians 
+% (if the \cs{radiansangles} declaration is active) 
+% or in sexagesimal degrees (if the \cs{degreesangles} declaration is active).
+%
+% Coordinates are refered to the active reference system.
+%
+% Example: |\rotateaxes{\numberQUARTERPI}|
+%
+% \myDescribeMacro\symmetrize\marg{angle}
+% performs a symmetry, being \textit{angle}
+% the angle between the symmetry axis and the $x$ axis.
+% The \cs{radiansangles} and \cs{degreesangles} declarations determine 
+% if angles are interpreted as radians or degrees.
+%
+% Coordinates are refered to the active reference system.
+%
+% Example: |\symmetrize{\numberPI}|
+%
+% \myDescribeMacro*\radiansangles
+% declares that angles are measured in radians (default).
+%
+% \myDescribeMacro*\degreesangles
+% declares that angles are measured in degrees.
+% 
+% \myDescribeMacro*\cartesianreference
+% declares Cartesian coordinates (default).
+% 
+% \myDescribeMacro*\polarreference
+% declares polar coordinates.
+%
+% \myDescribeMacro\polarcoor\parg{radius,angle}\parg{x,y}
+% changes from polar to Cartesian coordinates.
+%
+% \subsection{The \environ{Picture} environment}
+%
+% \myDescribeEnv{Picture}\oarg{color}\parg{x0,y0}\parg{x1,y1}
+% starts a picture, refered to rectangle 
+% $[\textit{x0},\textit{y0}]\times[\textit{x1},\textit{y1}]$.
+% If optional argument is present, background is colored with 
+% this \textit{color}. By default, background is not colored.
+% 
+% Coordinates are refered to the active reference system and are always 
+% Cartesian coordinates.
+%
+% Example: |\begin{Picture}[black!10!white](-3.5,-4)(3.5,4)|
+%
+% \myDescribeEnv{xpicture}
+% is an alias for \cs{begin\{Picture\}}.
+%
+% Example: |\begin{xpicture}[black!10!white](-3.5,-4)(3.5,4)|
+%
+% \myDescribeMacro*{\draftPictures}
+% disables |Picture| commands, showing only the picture area.
+%
+% Example: |\begin{xpicture}[black!10!white](-3.5,-4)(3.5,4)|
+%
+% \subsection{Cartesian and polar coordinate axes and grids}
+%
+% \myDescribeMacro{\cartesianaxes}\parg{x0,y0}\parg{x1,y1}
+% draws the coordinate axes corresponding to the
+% $[\textit{x0},\textit{y0}]\times[\textit{x1},\textit{y1}]$ rectangle.
+%
+% Example: |\cartesianaxes(-3.25,-4.5)(3.25,4.25)|
+%
+% \myDescribeMacro{\cartesiangrid}\parg{x0,y0}\parg{x1,y1}
+% draws a coordinate grid corresponding to the
+% $[\textit{x0},\textit{y0}]\times[\textit{x1},\textit{y1}]$ rectangle.
+%
+% Example: |\cartesiangrid(-3.25,-4.5)(3.25,4.25)|
+%
+% \myDescribeMacro{\polargrid}\marg{radius}\marg{circledivs}
+% draws a polar grid. |radius| is the radius of the circle and |circledivs|
+% (an integer) the number of angular divisions.
+%
+% Example: |\polargrid{3.5}{16}|
+%
+% \subsubsection{The style of the axes}
+%
+% \myDescribeMacro*{\axescolor} User can change the axes color
+% by redefining the \cs{axescolor} declaration.
+% 
+% Example: |\renewcommand{\axescolor}{orange}| (default is \texttt{black}).
+%
+% \myDescribeMacro*{\axesthickness} Length determining the thickness of axes 
+% (default \verb+1 pt+).
+% 
+% Example: |\setlength{\axesthickness}{1mm}|
+%
+% \myDescribeMacro*{\xunitdivisions} Number of subdivisions of
+% the unit in the $x$ axis (must a  positive integer).
+% 
+% Example:|\renewcommand{\xunitdivisions}{5}|
+% (default is \texttt{1}).
+%
+% \myDescribeMacro*{\yunitdivisions} Number of subdivisions of
+% the unit in the $y$ axis (must a  positive integer).
+% 
+% Example:|\renewcommand{\yunitdivisions}{3}|
+% (default is \texttt{1}).
+% 
+% \myDescribeMacro*{\runitdivisions} Number of subdivisions of
+% the unit in the polar axis (must a  positive integer).
+% 
+% Example:|\renewcommand{\runitdivisions}{3}|
+% (default is \texttt{1}).
+% 
+% \subsubsection{Axes position}
+% 
+% \myDescribeMacro*{\internalaxes}
+% Cartesian axes lies on $y=0$ and $x=0$ (default).
+%
+% \myDescribeMacro*{\externalaxes}
+% Cartesian axes lies on $y=\textit{y0}$ and $x=\textit{x0}$.
+% 
+% \subsubsection{Style of numerical labels}
+%
+% \myDescribeMacro*{\axeslabelcolor} 
+% User can change the color of labels by redefining the 
+% \cs{axeslabelcolor} declaration.
+% 
+% Example: |\renewcommand{\axeslabelcolor}{red}| 
+% (default is equal to the axes color).
+%
+% \myDescribeMacro*{\axeslabelsize} 
+% User can change the size of labels by redefining the 
+% \cs{axeslabelsize} declaration.
+% 
+% Example: |\renewcommand{\axeslabelsize}{\tiny}| 
+% (default is |\small|).
+%
+% \myDescribeMacro*{\axeslabelmathversion} 
+% User can change the mathversion of labels by redefining the 
+% \cs{axeslabelmathversion} declaration.
+% 
+% Example: |\renewcommand{\axeslabelmathversion}{bold}| 
+% (default is |normal|).
+%
+% \myDescribeMacro*{\axeslabelmathalphabet} 
+% User can change the math alphabet of labels by redefining the 
+% \cs{axeslabelmathalphabet} declaration.
+% 
+% Example: |\renewcommand{\axeslabelmathalphabet}{\mathsf}| 
+% (default is |\mathrm|).
+%
+% \myDescribeMacro*{\radianspolarlabels}
+% when this declaration is active, angular labels in polar grids are printed
+% in radians (default).
+%
+% \myDescribeMacro*{\degreespolarlabels}
+% when this declaration is active, angular labels in polar grids are printed
+% in degrees.
+% 
+% \myDescribeMacro*{\axislabelsep}
+% Distance between tags and cut marks, measured in \cs{unitlength} units;
+% the distance between axes and tags equals \cs{ticssize}$+$\cs{axislabelsep}.
+% (see description of \cs{makenotics}).
+% 
+% Example: |\renewcommand{\axislabelsep}{0.3}| 
+% (default is |0.1|).
+%
+% \subsubsection{Position of numerical labels}
+%
+% \myDescribeMacro{\xlabelpos}\marg{position}
+% Relative position of labels in $x$ axis.
+% 
+% Example: |\xlabelpos{t}| 
+% (default is |-90|).
+%
+% \myDescribeMacro{\ylabelpos}\marg{position}
+% Relative position of labels in $y$ axis.
+% 
+% Example: |\ylabelpos{tl}| 
+% (default is |180|).
+%
+% \subsubsection{Style of cut marks}
+%
+% \myDescribeMacro*{\ticssize}
+% half the length of main axes cuts.
+% 
+% Example: |\setlength{\ticssize}{3mm}|
+% (default is |4pt|)
+%
+% \myDescribeMacro*{\secundaryticssize}
+% half the length of secundary axes cuts.
+% 
+% Example: |\setlength{\secunadryticssize}{1mm}|
+% (default is |2pt|)
+%
+% \myDescribeMacro*{\ticsthickness}
+% thickness of the marks on axes.
+% 
+% Example: |\setlength{\ticsthickness}{0.5pt}|
+% (default is |1pt|)
+%
+% \myDescribeMacro*{\ticscolor}
+% User can change the color of tics by redefining the 
+% \cs{ticscolor} declaration.
+% 
+% Example: |\renewcommand{\ticscolor}{lightgray}|
+% (default is |black|)
+%
+% \subsubsection{Grid style}
+%
+% \myDescribeMacro*{\gridthickness}
+% thickness of the main grid lines.
+% 
+% Example: |\setlength{\gridthickness}{1pt}|
+% (default is |0.4pt|)
+%
+% \myDescribeMacro*{\secundarygridthickness}
+% thickness of the secundary grid lines.
+% 
+% Example: |\setlength{\gridthickness}{0.25pt}|
+% (default is |0.2pt|)
+%
+% \myDescribeMacro*{\gridcolor}
+% User can change the color of main grid lines by redefining the 
+% \cs{ticscolor} declaration.
+% 
+% Example: |\renewcommand{\gridcolor}{blue}|
+% (default is |gray|)
+%
+% \myDescribeMacro*{\secundarygridcolor}
+% User can change the color of secundary grid lines by redefining the 
+% \cs{ticscolor} declaration.
+% 
+% Example: |\renewcommand{\secundarygridcolor}{blue}|
+% (default is |lightgray|)
+%
+% \subsubsection{Removing cut marks, labels and grids}
+% \myDescribeMacro*{\maketics}
+% when this declaration is active, divisions of axes are marked (default).
+% 
+% \myDescribeMacro*{\makenotics}
+% when this declaration is active, divisions of axes are not marked.
+%
+% In this case, the distance between axes and tags equals \cs{axislabelsep}.
+%
+% \myDescribeMacro*{\makelabels}
+% when this declaration is active, numerical labels are printed (default).
+%
+% \myDescribeMacro*{\makenolabels}
+% when this declaration is active, numerical labels are not printed.
+%
+% \myDescribeMacro*{\makenogrid}
+% If the \cs{makenogrid} declaration is active,
+% then \cs{cartesianaxes} plots only the axes (default).
+%
+% \myDescribeMacro*{\makegrid}
+% If the \cs{makegrid} declaration is active,
+% then \cs{cartesianaxes} plots a Cartesian grid.
+% 
+% In this case, \cs{cartesianaxes} is equivalent to \cs{cartesiangrid}.
+% 
+% \subsection{Directly printing cuts and labels}
+%
+% \myDescribeMacro{\plotxtic}\marg{x-coor} 
+% plot a tic for the given $x$ coordinate.
+%
+% \myDescribeMacro{\plotytic}\marg{y-coor} 
+% plot a tic for the given $y$ coordinate.
+%
+% \myDescribeMacro{\printxlabel}\marg{x-coor}\marg{label} 
+% print the required label at the given $x$ coordinate.
+%
+% \myDescribeMacro{\printylabel}\marg{y-coor}\marg{label} 
+% print the required label at the given $y$ coordinate.
+%
+% \myDescribeMacro{\printxticlabel}\marg{x-coor}\marg{label} 
+% print a tic and the required label at the given $x$ coordinate.
+%
+% \myDescribeMacro{\printyticlabel}\marg{y-coor}\marg{label} 
+% print a tic and  the required label at the given $y$ coordinate.
+%
+% \myDescribeMacro{\plotxtics}\marg{firstcoor}\marg{incr}\marg{bound} 
+% plot several $x$ tics, from the initial coordinate \textit{firstcoor}; 
+% \textit{incr} is the distance between consecutive tics, 
+% and the last tic is not in a position greater than \textit{bound}.
+%
+% \myDescribeMacro{\plotytics}\marg{firstcoor}\marg{incr}\marg{bound} 
+% plot several $y$ tics, from the initial coordinate \textit{firstcoor}; 
+% \textit{incr} is the distance between consecutive tics, 
+% and the last tic is not in a position greater than \textit{bound}.
+%
+% \myDescribeMacro{\printxlabels}%
+% \oarg{digits}\marg{firstcoor}\marg{incr}\marg{bound} 
+% print several $x$ labels, from the initial coordinate \textit{firstcoor}; 
+% \textit{incr} is the distance between consecutive label positions, 
+% and the last position is not greater than \textit{bound}. 
+% The optional argument \textit{digits} is the number of decimal 
+% digits to be printed 
+% (by default, numbers are printed with its natural number of decimals).
+% \myDescribeMacro{\printylabels}%
+% \oarg{digits}\marg{firstcoor}\marg{incr}\marg{bound}
+% print several $x$ labels, from the initial coordinate \textit{firstcoor}; 
+% \textit{incr} is the distance between consecutive label positions, 
+% and the last position is not greater than \textit{bound}. 
+% The optional argument \textit{digits} is the number of decimal 
+% digits to be printed 
+% (by default, numbers are printed with its natural number of decimals).
+%
+% \myDescribeMacro{\printxticslabels}%
+% \oarg{digits}\marg{firstcoor}\marg{incr}\marg{bound}
+% print $x$ tics and labels simultaneously.
+%
+% \myDescribeMacro{\printyticslabels}%
+% \oarg{digits}\marg{firstcoor}\marg{incr}\marg{bound} 
+% print $y$ tics and labels simultaneously.
+%
+% \subsection{\cs{put} and \cs{multiput} extensions}
+% 
+% \myDescribeMacro{\cPut}\marg{position}\parg{x,y}\marg{object}
+% \myDescribeMacro{\rPut}\starred\marg{position}\parg{x,y}\marg{object}
+% \myDescribeMacro{\Put}\starred\oarg{position}\parg{x,y}\marg{object}
+%
+% draw \textit{object} in point \Parg{x,y}.
+% Argument \textit{position} fixes the precise position of \textit{object}
+% with respect \Parg{x,y}.
+%
+% In starred versions objects positioned below the reference point
+% are aligned at a fixed vertical distance (normally, by the baseline).
+% User must decide which is that amount (normally the higher object 
+% to be positioned), and introduce it as an argument of
+% the \cs{highestlabel} declaration.
+%
+% Example: |\Put*[SSE](1,2){\Ellipse{2}{3}}|
+% 
+% \medskip
+%
+% Argument \textit{position} supports the following values:
+% \begin{description}
+% \item[An integer or decimal number,] determining the angle (in degrees)
+% where \textit{object} is placed,
+% (with respect to the reference point \Parg{x,y}).
+% \item[Letter \texttt{c}]
+% which places the center of \textit{object} at
+% \Parg{x,y}).
+% \item[Letter or letter combinations \texttt N, \texttt E, \texttt S, 
+% \texttt W,
+% \texttt{NE}, \texttt{SE}, \texttt{SW}, \texttt{NW},
+% \texttt{NNE}, \texttt{ENE}, \texttt{ESE}, \texttt{SSE}, \texttt{SSW},%
+% \texttt{WSW}, \texttt{WNW}, 
+% \texttt{NNW}]
+% Abbreviation of \emph{North}, \emph{East}\ldots,  \emph{North-East}\ldots,  
+% \emph{North-North-East}\ldots
+% \item[Letter o letter combinations  \texttt t, \texttt  r, \texttt  b,%
+% \texttt  l,
+% \texttt{tr}, \texttt{br}, \texttt{bl}, \texttt{tl},
+% \texttt{ttr}, \texttt{rtr}, \texttt{rbr}, \texttt{bbr}, \texttt{bbl},% 
+% \texttt{lbl}, \texttt{ltl}, 
+% \texttt{ttl}]
+% Abbreviation of \emph{top}, \emph{right}\ldots,  \emph{top-right}\ldots,  
+% \emph{top-top-right}\ldots 
+% 
+% \end{description}
+% Without optional argument \textit{position} (in command \cs{Put})
+% the reference point of \textit{object} is placed at 
+% \Parg{x,y})
+% (in a similar way to the \cs{put} command).
+%
+% \myDescribeMacro*{\Pictlabelsep} 
+% determines the distance between the graphical object and the given point.
+% User can redefine this declaration by typing
+% \cs{renewcommand}\cs{Pictlabelsep}\marg{number}.
+% This number is interpreted as an amount of |\unitlength|.
+%
+% Example: |\renewcommand{\Pictlabelsep}{1}| (default is |0.1|).
+%
+% This distance is understood either as the Euclidean (circular) distance, 
+% derived from the $2$-norm,
+% or as the distance derived from the $\infty$-norm (rectangular distance),
+% following these rules:
+% \begin{itemize}
+% \item If argument \textit{position} is a \textit{compass} argument 
+% (like \texttt N or \texttt{SSW}), then circular distance is used.
+% \item If argument \textit{position} is like \texttt t, \texttt{bbl},\ldots
+% then rectangular distance is used.
+% In all other cases, |\cPut| uses circular distance, 
+% |\rPut| uses rectangular distance and |\Put| uses distance established
+% by \cs{defaultPut}.
+% \end{itemize}
+%
+% \myDescribeMacro{\defaultPut}\marg{position}
+% fixes the default position for \cs{Put}, \cs{multiPut} and \cs{multiPlot}
+% commands. Argument \textit{position} can be \texttt c or \texttt r.
+%
+% Example: |\defaultPut{r}| (default is \texttt c).
+%
+% \myDescribeMacro{\highestlabel}\marg{text} declares the highest label to be
+% equal to height of \textit{text}.
+%
+% Example: |\highestlabel{\Huge A}| (default is |\normalfont\normalsize$1$|)
+% 
+% \myDescribeMacro{\multicPut}
+% \marg{position}\parg{x,y}\parg{$\Delta$x,$\Delta$y}\marg{n}\marg{object}
+% \myDescribeMacro{\multirPut}\starred
+% \marg{position}\parg{x,y}\parg{$\Delta$x,$\Delta$y}\marg{n}\marg{object}
+% \myDescribeMacro{\multiPut}\starred
+% \oarg{position}\parg{x,y}\parg{$\Delta$x,$\Delta$y}\marg{n}\marg{object}
+%
+% put \textit{n} copies of \textit{object} in \textit{position}
+% at points 
+% $(\textit{x0},\textit{y0})$, $(\textit{x0}+\Delta x,\textit{y0}+\Delta y)$,
+% $(\textit{x0}+2\Delta x,\textit{y0}+2\Delta y)$, \ldots, 
+% $(\textit{x0}+(\textit n-1)\Delta x,\textit{y0}+(\textit n-1)\Delta y)$.
+%  
+% Example: |\multicPut{c}(1,2)(1,-1){4}{\xVECTOR(0,0)(1,1)}|
+% 
+% \myDescribeMacro{\multicPlot}
+% \marg{position}\marg{object}\parg{x0,y0}\parg{x1,y1}\ldots\parg{xn,yn}
+% 
+% \myDescribeMacro{\multirPlot}\starred
+% \marg{position}\marg{object}\parg{x0,y0}\parg{x1,y1}\ldots\parg{xn,yn}
+% 
+% \myDescribeMacro{\multiPlot}\starred
+% \oarg{position}\marg{object}\parg{x0,y0}\parg{x1,y1}\ldots\parg{xn,yn}
+% 
+% put $\textit{n}+1$ copies of \textit{object} at points 
+% \Parg{x0,y0},
+% \Parg{x1,y1},\ldots,
+% \Parg{xn,yn}
+%  
+% Example: |\multirPlot{c}{\xVECTOR(0,0)(1,1)}(1,2)(2,1)(3,0)(4,-1)|
+% 
+% \subsection{Drawing lines, vectors and polylines}
+% 
+% \subsubsection{Lines and vectors}
+% 
+% \myDescribeMacro{\xLINE}\parg{x0,y0}\parg{x1,y1}
+% draws a stright line between points \Parg{x0,y0}
+% and  \Parg{x1,y1}.
+%
+% Example: |\xLINE(1,-2)(0,3)|.
+% 
+% \myDescribeMacro{\xVECTOR}\parg{x0,y0}\parg{x1,y1}
+% draws an arrow from point \Parg{x0,y0}
+% to point \Parg{x1,y1}.
+%
+% Example: |\xVECTOR(1,-2)(0,3)|.
+% 
+% \myDescribeMacro{\xtrivVECTOR}\parg{x0,y0}\parg{x1,y1}
+% draws an arrow from point \Parg{x0,y0}
+% to point \Parg{x1,y1}.
+% The arrowhead consists of two lines, controled by the |\arrowsize| 
+% declaration.
+%
+% Example: |\xtrivVECTOR(1,-2)(0,3)|.
+% 
+% \myDescribeMacro{\xline}\parg{x,y}\marg{size}
+% \myDescribeMacro{\xvector}\parg{x,y}\marg{size}
+% \myDescribeMacro{\xtrivvector}\parg{x,y}\marg{size}
+%
+% draw lines, vectors and triv vectors with the standard \LaTeX{} syntax,
+% but without any restriction.
+% 
+% Example: |\Put(1,-2){\xline(-1,5){1}}|
+% 
+% \myDescribeMacro{\zerovector}\parg{x,y}
+% \myDescribeMacro{\zerotrivvector}\parg{x,y}
+% 
+% draw a zero-length vector (an arrowhead) in direction 
+% \Parg{x,y}.
+% 
+% Example: |\Put(0,3){\zerovector(-1,5)}|
+%
+% \myDescribeMacro\arrowsize\marg{xlen}\marg{ylen}
+% declares dimensions of triv arrowhead: |xlen|\,pt is its length, and
+%  |ylen|\,pt is half of its aperture.
+% 
+% Example: |\arrowsize{4}{2}| (default is |xlen=5|, |ylen=2|)
+% 
+% \subsubsection{Polylines and polygons}
+% 
+% \myDescribeMacro{\Polyline}\parg{x0,y0}\parg{x1,y1}\ldots\parg{xn,yn}
+% draws a polyline with vertices 
+% \Parg{x0,y0}\Parg{x1,y1}\ldots\Parg{xn,yn}.
+% 
+% Example: |\Polyline(1,1)(2,0)(0,-1)|
+% 
+% \myDescribeMacro{\Polygon}\parg{x0,y0}\parg{x1,y1}\ldots\parg{xn,yn}
+% draws a polygon with vertices 
+% \Parg{x0,y0}\Parg{x1,y1}\ldots\Parg{xn,yn}.
+% 
+% Example: |\Polygon(1,1)(2,0)(0,-1)|
+% 
+% \myDescribeMacro{\regularPolygon}\oarg{angle}\marg{radius}\marg{sides}
+% draws a regular polygon with the given \textit{radius} and \textit{sides}.
+% The optional argument (zero, by default) determines the inclination angle 
+% of the first vertex, always measured in degrees.
+% 
+% Example: |\regularPolygon[90]{4}{7}|
+% 
+% \subsection{Drawing curves}
+% \subsubsection{Conic sections and arcs}
+% 
+% \myDescribeMacro{\Circle}\marg{r}
+% draws the circle $x^2+y^2=\textit{r}^2$.
+% 
+% Example: |\Circle{2.5}|
+% 
+% \myDescribeMacro{\Ellipse}\marg{a}\marg{b}
+% draws the ellipse 
+% $\displaystyle\frac{x^2}{\textit{a}^2}+\frac{y^2}{\textit{b}^2}=1$.
+% 
+% Example: |\Ellipse{2}{3}|
+% 
+% \myDescribeMacro{\Hyperbola}\marg{a}\marg{b}\marg{xmax}\marg{ymax}
+% draws the hyperbola 
+% $\displaystyle\frac{x^2}{\textit{a}^2}-\frac{y^2}{\textit{b}^2}=1$.
+% 
+% Variables $x$ and $y$ are limited, respectively,
+% to the $[-\textit{xmax},\textit{xmax}]$ and 
+% $[-\textit{ymax},\textit{ymax}]$  intervals.
+% This curve is well defined if the parameter \textit{xmax}
+% is greater than \textit{a}. Otherwise, \package{xpicture} returns an error 
+% message and does not draw any curve.
+%
+% Example: |\Hyperbola{2}{3}{5}{5}|
+% 
+% \myDescribeMacro{\rHyperbola}\marg{a}\marg{b}\marg{xmax}\marg{ymax}
+% draws the \emph{right} branch of hyperbola 
+% $\displaystyle\frac{x^2}{\textit{a}^2}-\frac{y^2}{\textit{b}^2}=1$.
+%
+% (parameters are restricted as in |\Hyperbola|). 
+%
+% Example: |\rHyperbola{2}{3}{5}{5}|
+% 
+% \myDescribeMacro{\lHyperbola}\marg{a}\marg{b}\marg{xmax}\marg{ymax}
+% draws the \emph{left} branch of hyperbola 
+% $\displaystyle\frac{x^2}{\textit{a}^2}-\frac{y^2}{\textit{b}^2}=1$.
+%
+% (parameters are restricted as in |\Hyperbola|). 
+%
+% Example: |\rHyperbola{2}{3}{5}{5}|
+% 
+% \myDescribeMacro{\Parabola}\marg{a}\marg{xmax}\marg{ymax}
+% draws the parabola $x=ay^2$.
+% 
+% Variable $x$ is limited, respectively,
+% to the $[0,\textit{xmax}]$ (if \textit{a} is positive) 
+% or $[-\textit{xmax},0]$ (if negative) interval.
+% $[-\textit{ymax},\textit{ymax}]$  intervals.
+%
+% Example: |\Parabola{2}{5}{5}|
+% 
+% \myDescribeMacro{\circularArc}\marg{r}\marg{angle1}\marg{angle2}
+% draws the arc of circle 
+% $x=r\cos t,y=r\sin t,\ t\in[\textit{angle1},\textit{angle2}]$
+% (the arc of the circle centered at $(0,0)$ with radius $\textit{r}$
+% and limited between $\textit{angle1}$ and $\textit{angle2}$).
+%
+% Example: |\circularArc{3}{0}{\numberSIXTHPI}|
+% 
+% \myDescribeMacro*{\xArc} is an alias for \cs{circularArc}.
+%
+% Example: |\xArc{3}{0}{\numberSIXTHPI}|
+%  
+% \myDescribeMacro{\ellipticArc}\marg{a}\marg{b}\marg{angle1}\marg{angle2}
+% draws the arc of ellipse 
+% $x=a\cos t,y=b\sin t,\ t\in[\textit{angle1},\textit{angle2}]$
+% (the arc of the ellipse centered at $(0,0)$ with semiaxes 
+% $\textit{a}$ and $\textit{b}$
+% and limited between $\textit{angle1}$ and $\textit{angle2}$).
+%
+% Example: |\ellipticArc{2}{3}{-\numberSIXTHPI}{\numberSIXTHPI}|
+%  
+% \myDescribeMacro{\rhyperbolicArc}\marg{a}\marg{b}\marg{y0}\marg{y1}
+% draws the right arc of hyperbola
+% $\displaystyle\frac{x^2}{\textit{a}^2}-\frac{y^2}{\textit{b}^2}=1$
+% included between
+% $\textit{y}=\textit{y0}$ and $\textit{y}=\textit{y1}$.
+%
+% Example: |\rhyperbolicArc{2}{3}{-2}{2}|
+%   
+% \myDescribeMacro{\lhyperbolicArc}\marg{a}\marg{b}\marg{y0}\marg{y1}
+% draws the left arc of hyperbola
+% $\displaystyle\frac{x^2}{\textit{a}^2}-\frac{y^2}{\textit{b}^2}=1$
+% included between $\textit{y}=\textit{y0}$ and $\textit{y}=\textit{y1}$.
+%
+% Example: |\lhyperbolicArc{2}{3}{-2}{2}|
+%   
+% \myDescribeMacro{\parabolicArc}\marg{a}\marg{y0}\marg{y1}
+% Draw the arc of the parabola $x=ay^2$ included between 
+% $\textit{y}=\textit{y0}$ and $\textit{y}=\textit{y1}$.
+%
+% Example: |\parabolicArc{2}{-2}{2}|
+%
+% \myDescribeMacro{\defaultplotdivs}\marg{divisions} 
+% declares the number of subintervals we divide the domain of curves 
+% when plotting conic arcs.
+% 
+% Example: |\defaultplotdivs{16}| (default is |8|).
+% 
+% \subsubsection{Real variable functions}
+% 
+% \myDescribeMacro{\PlotFunction}
+% \oarg{n}\marg{\textbackslash functionname}\marg{t0}\marg{t1}
+% draws the graph of function \cs{functionname}$(t)$, 
+% $t\in[\textit{t0},\textit{t1}]$.
+% This interval is partitioned in \textit{n} subintervals (default for
+% \textit{n} is |2|).
+% 
+% Example: |\PlotFunction[16]{\COSfunction}{-\numberTWOPI}{\numberTWOPI}|
+% 
+% \myDescribeMacro{\PlotPointsOfFunction}
+% \marg{n}\marg{\textbackslash functionname}\marg{t0}\marg{t1}
+% draws $\textit{n}+1$ points of the graph of function \cs{functionname}$(t)$,
+% $t\in[\textit{t0},\textit{t1}]$.
+% 
+% Example: |\PlotPointsOfFunction{20}{\SQRTfunction}{0}{4}|
+% 
+% \myDescribeMacro*{\pointmarkdiam}
+% is the size of points printed by |\PlotPointsOfFunction|, measured in
+% |\unitlength| units. It may be
+% redefined with a |\renewcommand| declaration.
+% 
+% Example: |\renewcommand{\pointmarkdiam}{0.3}|
+% 
+% \myDescribeMacro*{\pointmark}
+% is the symbol printed at every point by |\PlotPointsOfFunction|. It may be
+% redefined with a |\renewcommand| declaration.
+% 
+% Example: |\renewcommand{\pointmark}{$\diamond$}|
+% 
+% \subsubsection{Parametrically defined curves}
+% 
+% \myDescribeMacro{\PlotParametricFunction}
+% \oarg{n}\marg{\textbackslash functionname}\marg{t0}\marg{t1}
+% draws the graph of parametric curve \cs{functionname}$(t)$, 
+% $t\in[\textit{t0},\textit{t1}]$.
+% This interval is partitioned in \textit{n} subintervals (default for
+% \textit{n} is |2|).
+% 
+% Example: |\ParametricFunction{\F}{\SQUAREfunction}{CUBEfunction}|
+% \\
+% \phantom{Example:} |\PlotParametricFunction[15]{\F}{-2}{2}|
+% 
+% \subsubsection{Drawing curves from a table of values}
+% 
+% \myDescribeMacro{\qCurve}\parg{x0,y0}\parg{u0,v0}\parg{x1,y1}\parg{u1,v1}
+% draws the quadratic curve between points \textit{x0,y0} and \textit{x1,y1}
+% with tangent vectors \textit{u0,v0} nd \textit{u1,v1}. 
+% 
+% Example: |\qCurve(1,2)(1,2)(4,3)(-1,1)|
+%
+% \myDescribeMacro{\PlotQuadraticCurve}
+% \parg{x0,y0}\parg{u0,v0}\parg{x1,y1}\parg{u1,v1}\ldots%
+% \parg{xn,yn}\parg{un,vn}
+%
+% draws a curve through the points
+% \parg{x0,y0}, \parg{x1,y1},\ldots, \parg{xn,yn}
+% with tangent vectors
+% \parg{u0,v0}, \parg{u1,v1},\ldots, \parg{un,vn}.
+% 
+% Example:
+% |\PlotQuadraticCurve(1,0)(1,0)(0,1)(0,1)(-1,0)(-1,0)(0,-1)(0,-1)|
+% 
+% \myDescribeMacro{\PlotQuadraticCurve}
+% \parg{x0,y0}\marg{angle0}\parg{x1,y1}\marg{angle1}\ldots
+% \parg{xn,yn}\marg{anglen}
+% 
+% draws a curve through the points
+% \parg{x0,y0}, \parg{x1,y1},\ldots, \parg{xn,yn}
+% the inclination angles of which, with respect to the $x$ axis,
+% are \textit{{angle0}, \textit{angle1}}\dots,
+% \textit{anglen} (always measured in degrees).
+%
+% Example:
+% |\PlotQuadraticCurve(1,0){0}(0,1){90}(-1,0){180}(0,-1){270}}|
+% \StopEventually{} 
+%
+% \myDescribeMacro{\PlotxyDyData}
+% \parg{x0,y0,Dy0}\parg{x1,y1,Dy1}\ldots\parg{xn,yn,Dyn}
+% draws a curve through the points
+% \parg{x0,y0}, \parg{x1,y1},\ldots, \parg{xn,yn} 
+% with derivatives \textit{Dy0}, \textit{Dy1}, \ldots, \textit{Dyn}.
+% \section{Implementation}
+%    \begin{macrocode}
+%<*xpicture>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{xpicture}[2012/12/17 v.1.2a picture environment extensions]
+%    \end{macrocode}
+% \subsection{Package options}
+% If the |draft| option is selected, 
+% |Picture| environments are shown
+% as a rectangular frame and |xpicture| commands are ignored
+% (Boolean |draft| controls whether this option has been selected).
+%    \begin{macrocode}
+\newif\ifdraft\draftfalse
+\DeclareOption{draft}{\drafttrue}
+%    \end{macrocode}
+% All other options are passed to packages |curve2e| and |xcolor|
+% (Old options |dvi|, |pict2e| and |curve2e| have been removed in 
+% version 1.2a).
+%    \begin{macrocode}
+\DeclareOption*{%
+   \PassOptionsToPackage{\CurrentOption}{curve2e}
+    \PassOptionsToPackage{\CurrentOption}{xcolor}}
+\ProcessOptions
+%    \end{macrocode}
+% \subsection{Booleans for some command options}
+% Booleans used by several declarations  
+% controlling the behavior of some |xpicture| commands.
+% \begin{macro}{\ifpolar}
+% True: polar coordinates. False: Cartesian coordinates.
+%    \begin{macrocode}
+\newif\ifpolar\polarfalse
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ifrputstar}
+% True: |\rPut| starred.
+%    \begin{macrocode}
+\newif\ifrputstar\rputstarfalse
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ifdegrees}
+%  True: angles mesured in degrees. False: arcs mesured in radians.
+%    \begin{macrocode}
+\newif\ifdegrees\degreesfalse
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\iftics}
+% True: coordinate axes include tic marks.
+%    \begin{macrocode}
+\newif\iftics\ticstrue
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\iflabels}
+% True: coordinate axes include numeric labels.
+%    \begin{macrocode}
+\newif\iflabels\labelstrue
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ifgrid}
+%  True: Cartesian grids.
+%    \begin{macrocode}
+\newif\ifgrid\gridfalse
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ifticslabelsgrid}
+% True: Tics, labels or grid must be printed.
+%    \begin{macrocode}
+\newif\ifticslabelsgrid\ticslabelsgridfalse
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ifinzeroaxes}
+% True: Representation of axes passes through the origin (internal axes). 
+% False: external axes.
+%    \begin{macrocode}
+\newif\ifinzeroaxes\inzeroaxestrue
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ifbg}
+% True: Background will be colored. 
+%    \begin{macrocode}
+\newif\ifbg\bgfalse
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Required packages}
+%    \begin{macrocode}
+\RequirePackage{curve2e}
+\RequirePackage{xcolor}
+\RequirePackage{calculus}
+%    \end{macrocode}
+% \subsection{Error, Warning and Info messages}
+%    \begin{macrocode}
+\def\xpct@Warnbadpos{%
+      \PackageWarning{xpicture}%
+        {Argument in \noexpand\defaultPut command must be either
+        'c' or 'r'\MessageBreak
+         I will no change the default position for 
+         \noexpand\Put commands}}
+\def\xpct@Infopos#1{%
+      \PackageInfo{xpicture}%
+        {Default position for \noexpand\Put commands changed to #1}}                  
+\def\xpct@WarnIncSys(#1,#2)(#3,#4){%
+      \PackageWarning{xpicture}{%
+           Incompatible linear system!\MessageBreak
+           Tangent lines are parallel}}                                            
+\def\xpct@ErrHypCons{%
+       \PackageError{xpicture}{%
+        Inconsistent parameters in \noexpand\Hyperbola command}{%
+        The first and second parameters in a \noexpand\Hyperbola 
+        command\MessageBreak
+        must be, respectively, lesser than the third and 
+        the fourth ones.}}                          
+\def\xpct@Infocfg{\PackageInfo{xpicture}{%
+          Loading local configuration file xpicture.cfg}}
+\def\xpct@Infonocfg{\PackageInfo{xpicture}{%
+          Local configuration file xpicture.cfg does not exists}}
+%    \end{macrocode}
+% \subsection{Internal counters and lengths and a special number}
+% Counters |xpct@counta| and |xpct@countb| will be used by several
+% internal commands (mainly in |while| clauses).
+% |xpct@step| is used when iterating functions plots, and
+% |multiput| by commands extending the |\multiput| command.
+%    \begin{macrocode}
+\newcounter{xpct@counta}
+\newcounter{xpct@countb}
+\newcounter{xpct@step}
+\newcounter{multiput}
+%    \end{macrocode}
+% \begin{macro}{\xpct@bxw}
+% \begin{macro}{\xpct@bxh}
+% Width and height of certain boxes. 
+%    \begin{macrocode}
+\newdimen\xpct@bxw
+\newdimen\xpct@bxh
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@maxnum}
+% The largest \TeX{} number. 
+%    \begin{macrocode}
+\def\xpct@maxnum{16383.99998}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Declarations and parameters controlling axes style}
+% \begin{macro}{\makenotics}
+% \begin{macro}{\maketics}
+% \begin{macro}{\makenolabels}
+% \begin{macro}{\makelabels}
+% \begin{macro}{\makegrid}
+% \begin{macro}{\makenogrid}
+% \begin{macro}{\externalaxes}
+% \begin{macro}{\internalaxes}
+% Four pairs of alternative declarations, switching booleans
+% |\iftics|, |\iflabels|, |\ifgrid|, and |\ifinzeroaxes|.
+% Defaults are |\maketics|,  |\makelabels|, |\makenogrid|,
+% and  |\internalaxes|.
+%    \begin{macrocode}
+\def\makenotics{\ticsfalse}
+\def\maketics{\ticstrue}
+\def\makenolabels{\labelsfalse}
+\def\makelabels{\labelstrue}
+\def\makenogrid{\gridfalse}
+\def\makegrid{\gridtrue}
+\def\externalaxes{\inzeroaxesfalse}
+\def\internalaxes{\inzeroaxestrue}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\axesthickness}
+% Thickness of axes (it is a length).
+%    \begin{macrocode}
+\newdimen\axesthickness
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@axeslabelattrib}
+% Attributes of labels. It is a private declaration, because you can select
+% attributes (size, color and mathversion) of labels independently.
+%    \begin{macrocode}
+\def\xpct@axeslabelattrib{\axeslabelsize%
+       \pictcolor{\axeslabelcolor}%
+       \mathversion{\axeslabelmathversion}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ticsthickness}
+% \begin{macro}{\ticssize}
+% \begin{macro}{\secundaryticssize}
+% \begin{macro}{\gridthickness}
+% \begin{macro}{\secundarygridthickness}
+% Thickness and size of tics and grid lines.
+%    \begin{macrocode}
+\newdimen\ticsthickness
+\newdimen\ticssize
+\newdimen\secundaryticssize
+\newdimen\gridthickness
+\newdimen\secundarygridthickness
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \subsection{Color selection}
+% \begin{macro}{\pictcolor}
+% Declaration |\pictcolor| supresses  spureus spaces when selecting color.
+%    \begin{macrocode}    
+\def\pictcolor{\@killglue\color}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Reference systems}
+% \begin{macro}{\standardreferencesystem}
+% Declaration to select the standard reference system.
+%    \begin{macrocode}
+\def\standardreferencesystem{\referencesystem(0,0)(1,0)(0,1)}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\referencesystem}
+% \begin{macro}{\changereferencesystem}
+% \begin{macro}{\xpct@xorigin}
+% \begin{macro}{\xpct@yorigin}
+% \begin{macro}{\xpct@xI}
+% \begin{macro}{\xpct@yI}
+% \begin{macro}{\xpct@xII}
+% \begin{macro}{\xpct@yII}
+% |\referencesystem| changes to the affine reference centered
+% in P|(#1,#2)| with directions |(#3,#4)| and |(#5,#6)|.
+% These six numbers are stored in 
+% |\xpct@xorigin|, |\xpct@yorigin|, 
+% |\xpct@xI|, |\xpct@yI|, |\xpct@xII|, and |\xpct@yII|.
+%    \begin{macrocode}
+\def\referencesystem(#1,#2)(#3,#4)(#5,#6){%
+       \COPY{#1}\xpct@xorigin
+       \COPY{#2}\xpct@yorigin
+       \COPY{#3}\xpct@xI
+       \COPY{#4}\xpct@yI
+       \COPY{#5}\xpct@xII
+       \COPY{#6}\xpct@yII}
+%    \end{macrocode}
+% The |\changereferencesystem| changes from the active reference system.
+%    \begin{macrocode} 
+\def\changereferencesystem(#1)(#2)(#3){%
+       \refsysPoint(#1)(\xpct@newx,\xpct@newy)
+       \refsysVector(#2)(\xpct@newux,\xpct@newuy)
+       \refsysVector(#3)(\xpct@newvx,\xpct@newvy)
+       \referencesystem(\xpct@newx,\xpct@newy)(\xpct@newux,\xpct@newuy)%
+       (\xpct@newvx,\xpct@newvy)}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\translateorigin}
+% \begin{macro}{\rotateaxes}
+% \begin{macro}{\symmetrize}
+% Translations and orthogonal changes (rotations and symmetries)
+% of reference system.
+%    \begin{macrocode}
+\def\translateorigin(#1){\changereferencesystem(#1)(1,0)(0,1)}
+\def\rotateaxes#1{%
+       \ifdegrees\DEGREESCOS{#1}\xpct@cosine\DEGREESSIN{#1}\xpct@sine
+       \else\COS{#1}\xpct@cosine\SIN{#1}\xpct@sine\fi
+       \changereferencesystem%
+          (0,0)(\xpct@cosine,\xpct@sine)(-\xpct@sine,\xpct@cosine)}
+%    \end{macrocode}
+%    \begin{macrocode}
+\def\symmetrize#1{%
+       \MULTIPLY{2}{#1}{\xpct@sym}
+       \ifdegrees
+          \DEGREESCOS{\xpct@sym}\xpct@cosine\DEGREESSIN{\xpct@sym}\xpct@sine
+       \else
+          \COS{\xpct@sym}\xpct@cosine\SIN{\xpct@sym}\xpct@sine\fi
+       \changereferencesystem%
+          (0,0)(\xpct@cosine,\xpct@sine)(\xpct@sine,-\xpct@cosine)}
+%    \end{macrocode}
+% \end{macro} 
+% \end{macro} 
+% \end{macro} 
+% \subsection{Coordinates}
+% \begin{macro}{\refsysxyVector}
+% \begin{macro}{\refsysxyPoint}
+% Canonical coordinates of a point or vector given in Cartesian coordinates
+% (change from the active r.s. to the standard one).
+%    \begin{macrocode}    
+\def\refsysxyVector(#1)(#2,#3){%
+       \MATRIXVECTORPRODUCT%
+          (\xpct@xI,\xpct@xII;\xpct@yI,\xpct@yII)(#1)(#2,#3)}
+\def\refsysxyPoint(#1)(#2,#3){%
+       \MATRIXVECTORPRODUCT(\xpct@xI,\xpct@xII;\xpct@yI,\xpct@yII)(#1)(#2,#3)
+       \VECTORADD(#2,#3)(\xpct@xorigin,\xpct@yorigin)(#2,#3)} 
+%    \end{macrocode}
+% \end{macro} 
+% \end{macro}
+% \begin{macro}{\refsyspVector}
+% \begin{macro}{\refsyspPoint}
+% Canonical coordinates of a point or vector given in polar coordinates.
+%    \begin{macrocode}
+\def\refsyspVector(#1,#2)(#3,#4){%
+      \polarcoor(#1,#2)(\xpct@polarx,\xpct@polary)
+      \refsysxyVector(\xpct@polarx,\xpct@polary)(#3,#4)}
+\def\refsyspPoint(#1,#2)(#3,#4){%
+      \polarcoor(#1,#2)(\xpct@polarx,\xpct@polary)
+      \refsysxyPoint(\xpct@polarx,\xpct@polary)(#3,#4)}
+%    \end{macrocode}
+% \end{macro} 
+% \end{macro}
+% \begin{macro}{\cartesianreference}
+% \begin{macro}{\polarreference}
+% Alternative declarations to switch between Cartesian or polar coordinates.
+% 
+% \noindent In fact, they define |\refsysVector|/|\refsysPoint| to be
+%  |\refsysxyVector|/|\refsysxyPoint| or  |\refsyspVector|/|\refsyspPoint|.
+%    \begin{macrocode}
+\def\cartesianreference{%
+       \def\refsysVector{\refsysxyVector}%
+       \def\refsysPoint{\refsysxyPoint}\polarfalse}
+\def\polarreference{%
+       \def\refsysVector{\refsyspVector}%
+       \def\refsysPoint{\refsyspPoint}\polartrue}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\polarcoor}
+% |\polarcoor| changes from polar to rectangular coordinates.
+%    \begin{macrocode}
+\def\polarcoor(#1,#2)(#3,#4){%
+       \ifdegrees\DEGREESCOS{#2}{\xpct@Px}\DEGREESSIN{#2}{\xpct@Py}
+       \else\COS{#2}{\xpct@Px}\SIN{#2}{\xpct@Py}\fi
+       \MULTIPLY{\xpct@Px}{#1}{#3}
+       \MULTIPLY{\xpct@Py}{#1}{#4}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\degreesangles}
+% \begin{macro}{\radiansangles}
+% Switches to measure angles in degrees or radians.
+%    \begin{macrocode}
+\def\degreesangles{\degreestrue}
+\def\radiansangles{\degreesfalse}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \subsection{The \texttt{Picture} environment}
+% \begin{environment}{Picture}
+% |Picture| is an extension of |picture| to refer points to the
+% active reference system. 
+% It can take an optional argument (background color).
+%    \begin{macrocode}
+\def\Picture{\@ifnextchar[{\xpct@@Picture}{\xpct@Picture}}
+%    \end{macrocode}
+% \end{environment}
+% \begin{macro}{\xpct@Picture}
+% Compute the surrounding box and call |picture| with the appropriate 
+% parameters. 
+%    \begin{macrocode}
+\def\xpct@Picture(#1,#2)(#3,#4){%
+%    \end{macrocode}
+% First, we determine the standard coordinates of the four vertices
+%    \begin{macrocode}
+       \refsysxyPoint(#1,#2)(\xpct@xzero,\xpct@yzero)
+       \refsysxyPoint(#3,#4)(\xpct@xone,\xpct@yone)
+       \refsysxyPoint(#1,#4)(\xpct@xtwo,\xpct@ytwo)
+       \refsysxyPoint(#3,#2)(\xpct@xthree,\xpct@ythree)
+%    \end{macrocode}
+% Now we calculate the maximum and minimum |x| and |y| coordinates.
+%    \begin{macrocode}       
+       \MIN{\xpct@xzero}{\xpct@xone}{\xpct@xmin}
+       \MIN{\xpct@xmin}{\xpct@xtwo}{\xpct@xmin}
+       \MIN{\xpct@xmin}{\xpct@xthree}{\xpct@xmin}
+       \MIN{\xpct@yzero}{\xpct@yone}{\xpct@ymin}
+       \MIN{\xpct@ymin}{\xpct@ytwo}{\xpct@ymin}
+       \MIN{\xpct@ymin}{\xpct@ythree}{\xpct@ymin}
+       \MAX{\xpct@xzero}{\xpct@xone}{\xpct@xmax}
+       \MAX{\xpct@xmax}{\xpct@xtwo}{\xpct@xmax}
+       \MAX{\xpct@xmax}{\xpct@xthree}{\xpct@xmax}
+       \MAX{\xpct@yzero}{\xpct@yone}{\xpct@ymax}
+       \MAX{\xpct@ymax}{\xpct@ytwo}{\xpct@ymax}
+       \MAX{\xpct@ymax}{\xpct@ythree}{\xpct@ymax}
+%    \end{macrocode}
+% Width and height (|xmax-xmin| and |ymax-ymin|) of the sorrounding box.
+%    \begin{macrocode}
+       \SUBTRACT{\xpct@xmax}{\xpct@xmin}{\xpct@pictwidth}
+       \SUBTRACT{\xpct@ymax}{\xpct@ymin}{\xpct@pictheight}
+%    \end{macrocode}
+% Call |picture|.
+%    \begin{macrocode}
+          \begin{picture}(\xpct@pictwidth,\xpct@pictheight)(%
+             \xpct@xmin,\xpct@ymin)
+%    \end{macrocode}
+% Fix highest label to normal 1.
+%    \begin{macrocode}
+          \highestlabel{\normalfont\normalsize$1$}
+%    \end{macrocode}
+% If option |draft| was selected, background is colored, 
+% a surrounding rectangle is drawn and a centered label is printed.
+%    \begin{macrocode}
+          \ifdraft
+            \colorlet{backgroundcolor}{lightgray}
+            \xpct@backgrd
+            \put(\xpct@xmin,\xpct@ymin){\line(1,0){\xpct@pictwidth}}
+            \put(\xpct@xmin,\xpct@ymin){\line(0,1){\xpct@pictheight}}
+            \put(\xpct@xmin,\xpct@ymax){\line(1,0){\xpct@pictwidth}}
+            \put(\xpct@xmax,\xpct@ymin){\line(0,1){\xpct@pictheight}}
+            \VECTORADD(\xpct@xmax,\xpct@ymax)(\xpct@xmin,\xpct@ymin)(%
+            \xpct@xmed,\xpct@ymed)
+            \SCALARVECTORPRODUCT{0.5}(\xpct@xmed,\xpct@ymed)(%
+            \xpct@xmed,\xpct@ymed)
+            \put(\xpct@xmed,\xpct@ymed){\makebox(0,0){\scshape xpicture}}
+         \else
+%    \end{macrocode}
+% Finally, if required, we color the background.
+%    \begin{macrocode}
+            \ifbg\xpct@backgrd\fi
+         \fi}
+%    \end{macrocode}
+% \end{macro}     
+% \begin{macro}{\xpct@@Picture}
+% Set background color to |#1|, swich boolean |\ifbg| 
+% to true and call |\xpct@Picture|.
+%    \begin{macrocode}
+\def\xpct@@Picture[#1](#2,#3)(#4,#5){%
+         \colorlet{backgroundcolor}{#1}%
+         \bgtrue\xpct@Picture(#2,#3)(#4,#5)}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@backgrd}
+% Fill background with |backgroundcolor|. We use |pict2e| path commands.
+%    \begin{macrocode}
+\def\xpct@backgrd{\begingroup
+                \pictcolor{backgroundcolor}
+                \moveto(\xpct@xzero,\xpct@yzero)
+                \lineto(\xpct@xthree,\xpct@ythree)
+                \lineto(\xpct@xone,\xpct@yone)
+                \lineto(\xpct@xtwo,\xpct@ytwo)
+                \closepath\fillpath
+            \endgroup}         
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\endPicture}
+% Close |picture| environment.
+%    \begin{macrocode}         
+\def\endPicture{\end{picture}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{environment}{xpicture}
+% |xpicture| is an alias for |Picture|.
+%    \begin{macrocode}
+\newenvironment{xpicture}{\begin{Picture}}{\end{Picture}}
+%    \end{macrocode}
+% \end{environment}
+% \subsection{\cs{put} extensions}
+% User's commands are |\cPut|, |\rPut|, and |\Put|. 
+% |\rPut| and |\Put| have starred versions. Related commands are
+% |\highestlabel| and |\defaultPut|.
+% \begin{macro}{\cPut}
+% |\cPut| puts the |#4| object in the |(#2,#3)| point at the |#1| position
+% (circular version).
+%    \begin{macrocode}
+\def\cPut#1(#2,#3)#4{%
+%    \end{macrocode}
+% Select circular trigonometry and call |\xpct@PUT|.
+%    \begin{macrocode}
+       \COPY{0}{\xpct@CorRput}
+       \xpct@PUT{#1}(#2,#3){#4}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\rPut} 
+% \begin{macro}{\rPut*}
+% |\rPut| puts the |#4| object in the |(#2,#3)| point at the |#1| position
+% (rectangular version). 
+% Call |\xpct@rPut| (ordinary) or |\xpct@rPutstar| (starred).
+%    \begin{macrocode}
+\def\rPut{\@ifstar
+             \xpct@rPutstar%
+             \xpct@rPut%
+             }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\Put}
+% \begin{macro}{\Put*}
+% |\Put| is equivalent to |\cPut| or |\rPut|, and has a starred form.
+% Call |\xpct@Put| (ordinary) or |\xpct@Putstar| (starred).
+%    \begin{macrocode} 
+\def\Put{\@ifstar
+            \xpct@Putstar%
+            \xpct@Put%
+        }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\defaultPut} 
+% \begin{macro}{\xpct@defaultPut}
+% |\defaultPut| is a declaration to fix default position (|c| or |r|) 
+% for the |\Put| command. It defines |\xpct@defaultPut| to be
+% |\rPut| or |\cPut|.
+%    \begin{macrocode}
+\def\defaultPut#1{\def\xpct@tempa{#1}\def\xpct@tempb{r}
+       \ifx\xpct@tempa\xpct@tempb
+          \xpct@Infopos#1
+          \def\xpct@defaultPut{\rPut}
+       \else
+          \xpct@Infopos#1
+          \def\xpct@tempc{c}
+          \ifx\xpct@tempa\xpct@tempc
+             \def\xpct@defaultPut{\cPut}
+          \else
+             \xpct@Warnbadpos
+       \fi\fi}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\highestlabel}
+% The highest label for the starred |\Put| and |\rPut| commands.
+% First we mesure the label, then we convert this length to |\unitlength|.
+% This number is stored in |\xpct@rputmxhg|.
+%    \begin{macrocode}
+\def\highestlabel#1{\settoheight{\xpct@bxh}{#1}%
+       \LENGTHDIVIDE{\xpct@bxh}{\unitlength}{\xpct@rputmxhg}}
+%    \end{macrocode}
+% \end{macro}
+% Private commands. Main command is |\xpct@PUT|, all other commands are 
+% intended to select appropiate geometry.
+% \begin{macro}{\xpct@rPut}
+% \begin{macro}{\xpct@rPutstar}
+% We give the appropriate value to boolean |\rputstar|, select rectangular
+% trigonometry and call |\xpct@PUT|.
+%    \begin{macrocode}
+\def\xpct@rPutstar{\rputstartrue\COPY{1}{\xpct@CorRput}\xpct@PUT}
+\def\xpct@rPut{\rputstarfalse\COPY{1}{\xpct@CorRput}\xpct@PUT}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@Putstar}
+% \begin{macro}{\xpct@Put}
+% |\Put| can take an optional argument.
+%    \begin{macrocode}
+\def\xpct@Putstar{\@ifnextchar[{\xpct@@Putstar}{\xpct@@Put}}
+\def\xpct@Put{\@ifnextchar[{\xpct@@@Put}{\xpct@@Put}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@@Putstar}
+% \begin{macro}{\xpct@@Put}
+% \begin{macro}{\xpct@@@Put}
+% |\Put[pos]| is |\rPut*{pos}|  (for ``bl'' like pos),
+%                   |\cPut{pos}| (for ``SW'' like pos) and
+%                   |\defaultPut| pos otherwise.
+% 
+% |\Put*[pos]| is |\rPut*{pos}|  
+%                   or |\cPut{pos}| (only for ``SW'' like pos).
+%    \begin{macrocode}
+\def\xpct@@Put(#1){\refsysPoint(#1)(\xpct@abscoorx,\xpct@abscoory)
+       \put(\xpct@abscoorx,\xpct@abscoory)}
+\def\xpct@@Putstar[#1](#2)#3{\xpct@convtoang{#1}{\xpct@putpos}{\xpct@CorR}
+       \if\xpct@CorR c
+          \cPut{#1}(#2){#3}
+       \else
+          \rPut*{#1}(#2){#3}
+       \fi}
+\def\xpct@@@Put[#1](#2)#3{\xpct@convtoang{#1}{\xpct@putpos}{\xpct@CorR}
+       \if\xpct@CorR c
+          \cPut{#1}(#2){#3}
+       \else
+          \if\xpct@CorR r
+             \rPut{#1}(#2){#3}
+          \else
+             \xpct@defaultPut{#1}(#2){#3}
+       \fi\fi}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@PUT}
+% This command puts object |#4| in |(#2,#3)| (active reference),
+% according to |#1| position.
+%    \begin{macrocode}
+\def\xpct@PUT#1(#2,#3)#4{%
+%    \end{macrocode}
+% Call |\xpct@alphaput| to compute |(\xpct@xPictsep,\xpct@yPictsep)|,
+% displacement of |\Pictlabelsep| units in direction |#1|.
+% Then, apply |\refsysxyVector| to get |(\xpct@Posx,\xpct@Posy)|,
+% standard coordinates of vector |(\xpct@xPictsep,\xpct@yPictsep)|.
+%    \begin{macrocode}
+       \xpct@alphaput{#1}{\xpct@CorRput}
+       \refsysxyVector(\xpct@xPictsep,\xpct@yPictsep)(\xpct@Posx,\xpct@Posy)
+%    \end{macrocode}
+% Compute |(\xpct@posx,\xpct@posy)|, standard coordinates of point |(#2,#3)|.
+%    \begin{macrocode}
+       \refsysPoint(#2,#3)(\xpct@posx,\xpct@posy)
+%    \end{macrocode}
+% Call |\xpct@alphamove| to adjust |(\xpct@Posx,\xpct@Posy)|
+% according to dimensions of |#4|.
+% Then add |(\xpct@posx,\xpct@posy)| to |(\xpct@Posx,\xpct@Posy)|.
+%    \begin{macrocode}
+       \xpct@alphamove{#4}{\xpct@CorRput}
+       \VECTORADD(\xpct@posx,\xpct@posy)(\xpct@Posx,\xpct@Posy)(%
+          \xpct@Posx,\xpct@Posy)
+%    \end{macrocode}
+% Now |(\xpct@Posx,\xpct@Posy)| is the absolute position where |#4|
+% must go.
+%    \begin{macrocode}
+       \put(\xpct@Posx,\xpct@Posy){#4}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@alphaput}
+% Computes displacement vector required by |#1| and stores it in
+%  |(\xpct@xPictsep},\xpct@yPictsep)|.
+%    \begin{macrocode}
+\def\xpct@alphaput#1#2{\def\xpct@tempa{#1}\def\xpct@tempb{c}%
+       \ifx\xpct@tempa\xpct@tempb
+%    \end{macrocode}
+% If |#1=c|, no displacement is required: 
+%|(\xpct@xPictsep},\xpct@yPictsep)=(0,0)|.
+%    \begin{macrocode}
+          \COPY{0}{\xpct@xPictsep}\COPY{0}{\xpct@yPictsep}
+       \else
+%    \end{macrocode}
+% Else, call |\xpct@convtoang| to translate |#1| to a number (of degrees),
+%    \begin{macrocode}
+          \xpct@convtoang{#1}{\xpct@putpos}{\xpct@CorR}
+%    \end{macrocode}
+% and compute |(\xpct@xPictsep},\xpct@yPictsep)|.
+%    \begin{macrocode}
+          \ifnum #2=0
+             \DEGREESCOS{\xpct@putpos}{\xpct@cosine}
+             \DEGREESSIN{\xpct@putpos}{\xpct@sine}
+          \else
+             \qCOS{\xpct@putpos}{\xpct@cosine}
+             \qSIN{\xpct@putpos}{\xpct@sine}
+          \fi          
+          \MULTIPLY{\Pictlabelsep}{\xpct@cosine}{\xpct@xPictsep}
+          \MULTIPLY{\Pictlabelsep}{\xpct@sine}{\xpct@yPictsep}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@alphamove}
+% Adjust |(\xpct@Posx,\xpct@Posy)| to required position, according to
+% |#1| dimensions. If |#2| equals |0|, it uses circular trigonometry, else
+% it uses square trigonometry. 
+%    \begin{macrocode}
+\def\xpct@alphamove#1#2{%
+%    \end{macrocode}
+% Computes half of dimensions of |#1|,
+%    \begin{macrocode}
+       \xpct@halfbox{#1}{\xpct@amplada}{\xpct@altura}
+       \ifx\xpct@tempa\xpct@tempb
+       \else
+%    \end{macrocode}
+% If required position is not centered, move |(\xpct@Posx,\xpct@Posy)|
+% (circular or square cases). First, compute a unitary vector in
+% |(\xpct@Posx,\xpct@Posy)| direction.
+%    \begin{macrocode}
+          \ifnum #2=0
+             \UNITVECTOR(\xpct@Posx,\xpct@Posy)(\xpct@xdir,\xpct@ydir)
+          \else
+             \qUNITVECTOR(\xpct@Posx,\xpct@Posy)(\xpct@xdir,\xpct@ydir)
+%    \end{macrocode}
+% If starred, change height to half |\xpct@rputmxhg|.
+%    \begin{macrocode}
+             \ifrputstar
+                \ifdim\xpct@ydir\p@=-1\p@
+                   \DIVIDE{\xpct@rputmxhg}{2}{\xpct@altura}
+                \fi
+             \fi
+             \fi
+%    \end{macrocode}
+% Adjust |(\xpct@xdir,\xpct@ydir)| to |#1| dimensions.
+%    \begin{macrocode}            
+             \MULTIPLY{\xpct@ydir}{\xpct@altura}{\xpct@ydir}
+             \MULTIPLY{\xpct@xdir}{\xpct@amplada}{\xpct@xdir}
+             \VECTORADD(\xpct@Posx,\xpct@Posy)(\xpct@xdir,\xpct@ydir)%
+                       (\xpct@Posx,\xpct@Posy)
+       \fi
+%    \end{macrocode}
+% Move |(\xpct@Posx,\xpct@Posy)| according to |#1| dimensions.
+%    \begin{macrocode}        
+       \VECTORSUB(\xpct@Posx,\xpct@Posy)(\xpct@amplada,\xpct@altura)(%
+          \xpct@Posx,\xpct@Posy)}
+%    \end{macrocode}
+% \end{macro}     
+% \begin{macro}{\xpct@convtoang}
+% Literal specifiers in |\Put|-like commands must be converted to angles.
+% |c| or |r| (circular or rectangular) distance is also selected.
+%    \begin{macrocode}    
+\def\xpct@convtoang#1#2#3{%
+     \def\xpct@tempc{#1}
+     \def\xpct@tempd{r}\ifx\xpct@tempc\xpct@tempd\COPY{0}{#2}\def#3{r}\else
+     \def\xpct@tempd{tr}\ifx\xpct@tempc\xpct@tempd\COPY{45}{#2}\def#3{r}\else
+     \def\xpct@tempd{t}\ifx\xpct@tempc\xpct@tempd\COPY{90}{#2}\def#3{r}\else
+     \def\xpct@tempd{tl}\ifx\xpct@tempc\xpct@tempd\COPY{135}{#2}\def#3{r}\else
+     \def\xpct@tempd{l}\ifx\xpct@tempc\xpct@tempd\COPY{180}{#2}\def#3{r}
+     \else
+     \def\xpct@tempd{bl}\ifx\xpct@tempc\xpct@tempd\COPY{-135}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{b}\ifx\xpct@tempc\xpct@tempd\COPY{-90}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{br}\ifx\xpct@tempc\xpct@tempd\COPY{-45}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{rtr}\ifx\xpct@tempc\xpct@tempd\COPY{22.5}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{ttr}\ifx\xpct@tempc\xpct@tempd\COPY{67.5}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{ttl}\ifx\xpct@tempc\xpct@tempd\COPY{112.5}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{ltl}\ifx\xpct@tempc\xpct@tempd\COPY{157.5}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{lbl}\ifx\xpct@tempc\xpct@tempd\COPY{-157.5}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{bbl}\ifx\xpct@tempc\xpct@tempd\COPY{-112.5}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{bbr}\ifx\xpct@tempc\xpct@tempd\COPY{-67.5}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{rbr}\ifx\xpct@tempc\xpct@tempd\COPY{-22.5}{#2}
+     \def#3{r}\else
+     \def\xpct@tempd{E}\ifx\xpct@tempc\xpct@tempd\COPY{0}{#2}\def#3{c}\else
+     \def\xpct@tempd{NE}\ifx\xpct@tempc\xpct@tempd\COPY{45}{#2}\def#3{c}\else
+     \def\xpct@tempd{N}\ifx\xpct@tempc\xpct@tempd\COPY{90}{#2}\def#3{c}\else
+     \def\xpct@tempd{NW}\ifx\xpct@tempc\xpct@tempd\COPY{135}{#2}\def#3{c}\else
+     \def\xpct@tempd{W}\ifx\xpct@tempc\xpct@tempd\COPY{180}{#2}\def#3{c}\else
+     \def\xpct@tempd{SW}\ifx\xpct@tempc\xpct@tempd\COPY{-135}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{S}\ifx\xpct@tempc\xpct@tempd\COPY{-90}{#2}\def#3{c}\else
+     \def\xpct@tempd{SE}\ifx\xpct@tempc\xpct@tempd\COPY{-45}{#2}\def#3{c}\else
+     \def\xpct@tempd{ENE}\ifx\xpct@tempc\xpct@tempd\COPY{22.5}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{NNE}\ifx\xpct@tempc\xpct@tempd\COPY{67.5}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{NNW}\ifx\xpct@tempc\xpct@tempd\COPY{112.5}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{WNW}\ifx\xpct@tempc\xpct@tempd\COPY{157.5}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{WSW}\ifx\xpct@tempc\xpct@tempd\COPY{-157.5}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{SSW}\ifx\xpct@tempc\xpct@tempd\COPY{-112.5}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{SSE}\ifx\xpct@tempc\xpct@tempd\COPY{-67.5}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{ESE}\ifx\xpct@tempc\xpct@tempd\COPY{-22.5}{#2}
+     \def#3{c}\else
+     \def\xpct@tempd{c}\ifx\xpct@tempc\xpct@tempd\COPY{0}{#2}\def#3{c}\else
+     \COPY{#1}{#2}\def#3{a}
+\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@halfbox}
+% Half of dimensions of a box.
+%    \begin{macrocode}
+\def\xpct@halfbox#1#2#3{%
+        \settowidth\xpct@bxw{#1}%
+        \settoheight\xpct@bxh{#1}%
+        \LENGTHDIVIDE{\xpct@bxw}{\unitlength}{#2}
+        \LENGTHDIVIDE{\xpct@bxh}{\unitlength}{#3}
+        \MULTIPLY{0.5}{#2}{#2}
+        \MULTIPLY{0.5}{#3}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\qCOS}
+% \begin{macro}{\qSIN}
+% \begin{macro}{\qUNITVECTOR}
+% Square versions of |\DEGREESCOS|, |\DEGREESSIN| and |\UNITVECTOR|.
+%    \begin{macrocode}
+\def\qCOS#1#2{%
+    \ifdim #1\p@<-135\p@ 
+         \ADD{360}{#1}{\xpct@angles}\qCOS{\xpct@angles}{#2}
+    \else
+       \ifdim #1\p@>225\p@ \SUBTRACT{#1}{360}{\xpct@angles}
+                           \qCOS{\xpct@angles}{#2}
+       \else
+          \ifdim #1\p@<-45\p@ \DEGREESCOT{#1}{#2}\MULTIPLY{-1}{#2}{#2}
+          \else
+             \ifdim #1\p@<45\p@ \COPY{1}{#2}
+             \else
+                \ifdim #1\p@<135\p@ \DEGREESCOT{#1}{#2}
+                \else
+                   \COPY{-1}{#2}
+                \fi           
+             \fi             
+          \fi
+       \fi
+    \fi
+}
+\def\qSIN#1#2{%
+    \ifdim #1\p@<-135\p@ 
+         \ADD{360}{#1}{\xpct@angles}\qSIN{\xpct@angles}{#2}
+    \else
+       \ifdim #1\p@>225\p@ \SUBTRACT{#1}{360}{\xpct@angles}
+                           \qSIN{\xpct@angles}{#2}
+       \else
+          \ifdim #1\p@<-45\p@ \COPY{-1}{#2}
+          \else
+             \ifdim #1\p@<45\p@ \DEGREESTAN{#1}{#2}
+             \else
+                \ifdim #1\p@<135\p@ \COPY{1}{#2}
+                \else
+                   \DEGREESTAN{#1}{#2}\MULTIPLY{-1}{#2}{#2}
+                \fi           
+             \fi             
+          \fi
+       \fi
+    \fi
+}
+\def\qUNITVECTOR(#1,#2)(#3,#4){%
+          \VECTORCOPY(#1,#2)(#3,#4)
+          \ABSVALUE{#4}{\xpct@Ydir}
+          \ifdim \xpct@Ydir\p@ < 0.00005\p@
+          \COPY{\xpct@maxnum}{\xpct@tan} 
+          \else
+             \DIVIDE{#3}{#4}{\xpct@tan}
+          \fi
+          \ifdim #3\p@ > 0\p@
+             \ifdim #4\p@ > 0\p@ 
+                \ifdim #3\p@ > #4\p@
+                   \COPY{1}{#3}\DIVIDE{#4}{\xpct@tan}{#4}
+                \else    
+                   \COPY{1}{#4}\COPY{\xpct@tan}{#3}
+                \fi
+                \else
+                   \ifdim #3\p@ > -#4\p@
+                      \COPY{1}{#3}\DIVIDE{-#4}{\xpct@tan}{#4}
+                   \else
+                      \COPY{-1}{#4}\MULTIPLY{-1}{\xpct@tan}{#3}
+                   \fi
+                \fi
+             \else
+                \ifdim #4\p@ > 0\p@ 
+                   \ifdim -#3\p@ > #4\p@
+                      \COPY{-1}{#3}\DIVIDE{-#4}{\xpct@tan}{#4}
+                   \else    
+                      \COPY{1}{#4}\COPY{\xpct@tan}{#3} 
+                   \fi
+                \else
+                   \ifdim #3\p@ > #4\p@
+                      \COPY{-1}{#4}\COPY{-\xpct@tan}{#3}
+                   \else
+                      \COPY{-1}{#3}\DIVIDE{#4}{\xpct@tan}{#4}
+                   \fi
+                \fi
+             \fi
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \subsection{\cs{multiput} extensions}
+% User commands: |\multicPut|, |\multirPut|, |\multiPut|; 
+% |\multicPlot|, |\multirPlot|, |\multiPlot|. 
+% |\multirPut|, |\multiPut|, |\multirPlot|, and |\multiPlot|
+% have starred versions.
+% \begin{macro}{\multicPut}
+% Define |\xpct@mPut| as |\cPut{#1}| and call |\xpct@@mPut|.
+%    \begin{macrocode}
+\def\multicPut#1{\def\xpct@mPut{\cPut{#1}}\xpct@@mPut}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\multirPut}
+% \begin{macro}{\multirPut*}
+% Call |\xpct@multirPut| or |\xpct@multirPutstar| (if starred).
+%    \begin{macrocode}
+\def\multirPut{\@ifstar
+       \xpct@multirPutstar%
+       \xpct@multirPut%
+       }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\multiPut}
+% \begin{macro}{\multiPut*}
+% Call |\xpct@multiPut| or |\xpct@multiPutstar| (if starred).
+%    \begin{macrocode}
+\def\multiPut{\@ifstar
+       \xpct@multiPutstar%
+       \xpct@multiPut%
+       }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@multirPutstar}
+% \begin{macro}{\xpct@multirPut}
+% Define |\xpct@mPut| as |\rPut*{#1}| or |\rPut{#1}| and call |\xpct@@mPut|.
+%    \begin{macrocode}
+\def\xpct@multirPutstar#1{\def\xpct@mPut{\rPut*{#1}}\xpct@@mPut}
+\def\xpct@multirPut#1{\def\xpct@mPut{\rPut{#1}}\xpct@@mPut}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@multiPut}
+% \begin{macro}{\xpct@multiPutstar}
+% |\multiPut| can take an optional argument.
+%    \begin{macrocode}
+\def\xpct@multiPut{\@ifnextchar[{\xpct@@@multiPut}{\xpct@@multiPut}}
+\def\xpct@multiPutstar{\@ifnextchar[{\xpct@@@multiPutstar}{\xpct@@multiPutstar}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@@multiPut}
+% \begin{macro}{\xpct@@multiPutstar}
+% Define |\xpct@mPut| as |\Put| or |\Put*| and call |\xpct@@mPut|.
+%    \begin{macrocode}
+\def\xpct@@multiPut{\def\xpct@mPut{\Put}\xpct@@mPut}     
+\def\xpct@@multiPutstar{\def\xpct@mPut{\Put*}\xpct@@mPut}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@@@multiPut}
+% \begin{macro}{\xpct@@@multiPutstar}
+% Define |\xpct@mPut| as |\Put[#1]| or |\Put*[#1]| and call |\xpct@@mPut|.
+%    \begin{macrocode}
+\def\xpct@@@multiPut[#1]{\def\xpct@mPut{\Put[#1]}\xpct@@mPut}
+\def\xpct@@@multiPutstar[#1]{\def\xpct@mPut{\Put*[#1]}\xpct@@mPut}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@@mPut}
+% \begin{macro}{\xpct@mPut}
+% |\xpct@@mPut| is the main macro about |\multiPut|-like commands.
+% |\xpct@mPut| is already defined as the appropiate |\Put| command.
+%    \begin{macrocode}
+\def\xpct@@mPut(#1,#2)(#3,#4)#5#6{%
+%    \end{macrocode}
+% Use counter |multiput| to count iterations.
+% |(\xpct@@abscoorx,\xpct@@abscoory)| is the point to be ploted in each 
+% iteration.
+%    \begin{macrocode}
+       \COPY{#1}\xpct@@abscoorx\COPY{#2}\xpct@@abscoory
+       \setcounter{multiput}{0}%
+       \@whilenum\value{multiput}<#5 \do
+%    \end{macrocode}
+% Plot the point, translate it, and update conter.
+%    \begin{macrocode}
+          {\xpct@mPut(\xpct@@abscoorx,\xpct@@abscoory){#6}
+           \ADD{#3}\xpct@@abscoorx\xpct@@abscoorx
+           \ADD{#4}\xpct@@abscoory\xpct@@abscoory
+           \stepcounter{multiput}}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\multicPlot}
+% Execute |\cPut| and iterates itself while next character be |(|.
+%    \begin{macrocode}
+\def\multicPlot#1#2(#3){\cPut{#1}(#3){#2}\@ifnextchar({\multicPlot{#1}{#2}}{}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\multirPlot}
+% \begin{macro}{\multirPlot*}
+% |\multirPlot| can take a starred form. Call |\xpct@multirPlot| or,
+% if starred, |\xpct@multirPlotstar|.
+%    \begin{macrocode}
+\def\multirPlot{\@ifstar
+       \xpct@multirPlotstar%
+       \xpct@multirPlot%
+       }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\multiPlot}
+% \begin{macro}{\multiPlot*}
+% |\multiPlot| can take a starred form. Call |\xpct@multiPlot| or,
+% if starred, |\xpct@multiPlotstar|.
+%    \begin{macrocode}
+\def\multiPlot{\@ifstar
+             \xpct@multiPlotstar%
+             \xpct@multiPlot%
+             }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@multirPlotstar}
+% \begin{macro}{\xpct@multirPlot}
+% Execute |\rPut*| or |\rPut| and iterates itself while next character be |(|.
+%    \begin{macrocode}
+\def\xpct@multirPlotstar#1#2(#3){\rPut*{#1}(#3){#2}
+       \@ifnextchar({\xpct@multirPlotstar{#1}{#2}}{}}
+\def\xpct@multirPlot#1#2(#3){\rPut{#1}(#3){#2}
+       \@ifnextchar({\xpct@multirPlot{#1}{#2}}{}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@multiPlotstar}
+% \begin{macro}{\xpct@multiPlot}
+% |\multiPlot| (and |\multiPlot*|) can take an optional argument. 
+% We have four cases: (starred or not) and (optional argument or not).
+%    \begin{macrocode}
+\def\xpct@multiPlotstar{%
+   \@ifnextchar[{\xpct@@@multiPlotstar}{\xpct@@multiPlotstar}}
+\def\xpct@multiPlot{\@ifnextchar[{\xpct@@@multiPlot}{\xpct@@multiPlot}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@@multiPlot}
+% \begin{macro}{\xpct@@@multiPlot}
+% \begin{macro}{\xpct@@multiPlotstar}
+% \begin{macro}{\xpct@@@multiPlotstar}
+% Execute |\Put| (or |\Put*|) and iterates itself while next character be |(|.
+%    \begin{macrocode}
+\def\xpct@@multiPlot#1(#2){\Put(#2){#1}\@ifnextchar({\xpct@@multiPlot{#1}}{}}
+\def\xpct@@@multiPlot[#1]#2(#3){\Put[#1](#3){#2}
+       \@ifnextchar({\xpct@@@multiPlot[#1]{#2}}{}}
+\def\xpct@@multiPlotstar#1(#2){\Put*(#2){#1}
+       \@ifnextchar({\xpct@@multiPlotstar{#1}}{}}
+\def\xpct@@@multiPlotstar[#1]#2(#3){\Put*[#1](#3){#2}
+       \@ifnextchar({\xpct@@@multiPlotstar[#1]{#2}}{}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \subsection{Strigth lines and vectors}
+% \begin{macro}{\xLINE}
+% \begin{macro}{\strline}
+% Compute standard coordinates of two points and call |\xpct@strline|
+% to plot a line.
+%    \begin{macrocode}
+\def\xLINE(#1)(#2){%        
+         \refsysPoint(#1)(\xpct@xzero,\xpct@yzero)
+         \refsysPoint(#2)(\xpct@xone,\xpct@yone)
+         \xpct@strline(\xpct@xzero,\xpct@yzero)(\xpct@xone,\xpct@yone)}
+\let\strline\xLINE
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@strline}
+% This command calls the |\segment| command from |curve2e|
+% (or |\LINE|, for old versions of |curve2e|).
+%    \begin{macrocode}
+\def\xpct@strline{\@killglue\@ifundefined{segment}{\LINE}{\segment}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xVECTOR}
+% Compute standard coordinates of two points and call |\VECTOR|
+% to plot a vector.
+%    \begin{macrocode}
+\def\xVECTOR(#1)(#2){%
+       \refsysPoint(#1)(\xpct@xzero,\xpct@yzero)
+       \refsysPoint(#2)(\xpct@xone,\xpct@yone)
+       \VECTOR(\xpct@xzero,\xpct@yzero)(\xpct@xone,\xpct@yone)}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xtrivVECTOR}
+% Compute standard coordinates of two points and call |\xpct@xtrivVECTOR|
+% to plot a  `triv' vector.
+%    \begin{macrocode}
+\def\xtrivVECTOR(#1)(#2){%
+       \refsysPoint(#1)(\xpct@xzeropoint,\xpct@yzeropoint)
+       \refsysPoint(#2)(\xpct@xonepoint,\xpct@yonepoint)
+       \xpct@xtrivVECTOR(\xpct@xzeropoint,\xpct@yzeropoint)(%
+                         \xpct@xonepoint,\xpct@yonepoint)}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\arrowsize}
+% Store dimensions of triv arrows. 
+% to plot a vector.
+%    \begin{macrocode}
+\def\arrowsize#1#2{\COPY{#1}{\xpct@xarrowlen}
+                   \COPY{#2}{\xpct@yarrowlen}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@xtrivVECTOR}
+% Plot a stright line, compute size of arrowhead and call |\xpct@arrow|
+% to plot it.
+%    \begin{macrocode}        
+\def\xpct@xtrivVECTOR(#1)(#2){%
+         \xpct@strline(#1)(#2)
+         \VECTORSUB(#2)(#1)(\xpct@xarrow,\xpct@yarrow)
+         \VECTORNORM(\xpct@xarrow,\xpct@yarrow){\xpct@xarrowunit}
+         \DIVIDE{\xpct@xarrow}{\xpct@xarrowunit}{\xpct@xarrow}
+         \DIVIDE{\xpct@yarrow}{\xpct@xarrowunit}{\xpct@yarrow}
+         \xpct@arrow(#2){\xpct@xarrow}{\xpct@yarrow}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@arrow}
+% Make an arrowhead as a small picture.
+%    \begin{macrocode} 
+\def\xpct@arrow(#1)#2#3{\begingroup%
+             \referencesystem(#1)(#2,#3)(-#3,#2)
+             \Put(0,0){\setlength{\unitlength}{1pt}%
+                \begin{Picture}(0,0)(0,0)\cartesianreference
+                         \xLINE(-\xpct@xarrowlen,\xpct@yarrowlen)(0,0)
+                         \xLINE(0,0)(-\xpct@xarrowlen,-\xpct@yarrowlen)
+                \end{Picture}}\endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\zerovector}
+% \begin{macro}{\zerotrivvector}
+% To have an arrowhead, draw a very short vector (of |0.01\unitlength|).
+%    \begin{macrocode}
+\def\zerovector(#1){%
+   \UNITVECTOR(#1)(\xpct@dirx,\xpct@diry)
+   \SCALARVECTORPRODUCT{0.01}(\xpct@dirx,\xpct@diry)(\xpct@dirx,\xpct@diry)
+    \xVECTOR(0,0)(\xpct@dirx,\xpct@diry)}
+\def\zerotrivvector(#1){%
+   \UNITVECTOR(#1)(\xpct@dirx,\xpct@diry)
+   \SCALARVECTORPRODUCT{0.01}(\xpct@dirx,\xpct@diry)(\xpct@dirx,\xpct@diry)
+    \xtrivVECTOR(0,0)(\xpct@dirx,\xpct@diry)}    
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xline}
+% \begin{macro}{\xvector}
+% \begin{macro}{\xtrivvector}
+% Standard syntax strigth lines and vectors.
+% Call |\xpct@xline| to compute adequate coordinates of line or vector ends.
+% Then call |\xLINE|, |\xVECTOR| or |\xtrivVECTOR| command.
+%    \begin{macrocode}
+\def\xline(#1,#2)#3{%
+       \xpct@xline(#1,#2){#3}
+   \xLINE(0,0)(\xpct@@xdir,\xpct@@ydir)}
+
+\def\xvector(#1,#2)#3{%
+   \ifdim #3 pt = 0 pt \zerovector(#1,#2)
+   \else 
+       \xpct@xline(#1,#2){#3}
+   \xVECTOR(0,0)(\xpct@@xdir,\xpct@@ydir)
+   \fi}
+
+\def\xtrivvector(#1,#2)#3{%
+   \ifdim #3 pt = 0 pt \zerotrivvector(#1,#2)
+   \else 
+       \xpct@xline(#1,#2){#3}
+   \xtrivVECTOR(0,0)(\xpct@@xdir,\xpct@@ydir)
+   \fi}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@xline}
+% Calculate the coordinates of the endpoint of |\xline(#1,#2){#3}| and stores
+% them in |(\xpct@@xdir,\xpct@@ydir)|.
+%    \begin{macrocode}
+\def\xpct@xline(#1,#2)#3{%
+         \ABSVALUE{#1}{\xpct@modx}
+         \ifdim \xpct@modx pt < 0.0001 pt  
+              \COPY{0}{\xpct@@xdir}
+              \ifdim #2\p@>\z@ \COPY{#3}{\xpct@@ydir}
+              \else \MULTIPLY{-1}{#3}{\xpct@@ydir}
+              \fi
+         \else 
+              \DIVIDE{#1}{\xpct@modx}{\xpct@@xdir}
+              \DIVIDE{#2}{\xpct@modx}{\xpct@@ydir}
+              \SCALARVECTORPRODUCT{#3}(\xpct@@xdir,\xpct@@ydir)(%
+                                       \xpct@@xdir,\xpct@@ydir)
+        \fi}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Polygons and polylines}
+% \begin{macro}{\Polyline}
+% This command plots a line between the two first points and, if next
+% character is |(|, supresses first point and iterates itself.
+%    \begin{macrocode}
+\def\Polyline(#1)(#2){%
+         \xLINE(#1)(#2)\@ifnextchar({\Polyline(#2)}{}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\Polygon}
+% Store the first point in |(\xpct@firstx,\xpct@firsty)| and call
+% |\xpct@Polygon|.
+%    \begin{macrocode}
+\def\Polygon(#1,#2)(#3){% 
+       \COPY{#1}{\xpct@firstx}\COPY{#2}{\xpct@firsty}
+                  \xpct@Polygon(#1,#2)(#3)}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@Polygon}
+% This command plots a line between the two first points and, if next
+% character is |(|, supresses first point and iterates itself. 
+% When finished, adds a closing line to the previously stored first point.
+%    \begin{macrocode}
+\def\xpct@Polygon(#1)(#2){%
+       \xLINE(#1)(#2)\@ifnextchar({\xpct@Polygon(#2)}{%
+       \xLINE(#2)(\xpct@firstx,\xpct@firsty)}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\regularPolygon}
+% |\regularPolygon| can take an optional argument.
+%    \begin{macrocode}
+\def\regularPolygon{%
+       \@ifnextchar[{\xpct@regPolygon}{\xpct@@regPolygon}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@@regPolygon}
+% Default for optional argument is |0|.
+%    \begin{macrocode}
+\def\xpct@@regPolygon#1#2{\xpct@regPolygon[0]{#1}{#2}}                                               
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@regPolygon}
+% |\xpct@regPolygon[#1]{#2}{#3}| uses the |xpct@counta| counter to
+% plot |#3| lines, in polar coordinates with |#2| radius, 
+% startint with angle |#1| and using $360/|#3|$ to
+% incrementing angle in each step. 
+%    \begin{macrocode}
+\def\xpct@regPolygon[#1]#2#3{\begingroup%
+       \polarreference\degreesangles
+       \setcounter{xpct@counta}{0}%
+       \setcounter{xpct@countb}{#3}%
+       \DIVIDE{360}{#3}{\xpct@angles}
+       \COPY{#1}{\xpct@anglea}
+       \@whilenum\value{xpct@counta}<\value{xpct@countb} \do {% 
+          \ADD{\xpct@anglea}{\xpct@angles}{\xpct@angleb}
+          \xLINE(#2,\xpct@anglea)(#2,\xpct@angleb)
+          \COPY{\xpct@angleb}{\xpct@anglea}\stepcounter{xpct@counta}}
+       \endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Quadratic curves}
+% \begin{macro}{\xpct@ctrlpoint}
+% The main command in this section is |\xpct@ctrlpoint|.
+% It computes the control point in a quadratic Bezier curve
+% from the coordinates and direction vectors of ending points.
+%    \begin{macrocode}
+\def\xpct@ctrlpoint(#1,#2)(#3,#4)(#5,#6)(#7,#8){%
+       \DETERMINANT(#3,#4;#7,#8)\xpct@detA
+       \DETERMINANT(#1,#2;#3,#4)\xpct@detB
+       \DETERMINANT(#5,#6;#7,#8)\xpct@detC
+       \DETERMINANT(#3,#7;\xpct@detB,\xpct@detC)\xpct@detD
+       \DETERMINANT(#4,#8;\xpct@detB,\xpct@detC)\xpct@detE
+       \ABSVALUE{\xpct@detA}{\xpct@@detA}
+       \ABSVALUE{\xpct@detD}{\xpct@@detD}
+       \ABSVALUE{\xpct@detE}{\xpct@@detE}
+       \ifdim \xpct@@detA pt<0.00005 pt 
+%    \end{macrocode}       
+% If |\xpct@detA| approaches zero, matrix is singular or close to singular.
+% Then tangent lines may be parallel or coincide.
+%    \begin{macrocode}       
+          \ifdim \xpct@@detD pt<0.00005 pt %\xpct@detD pt=0 pt
+             \ifdim \xpct@@detE pt<0.00005 pt %\xpct@detE pt=0 pt 
+%    \end{macrocode}       
+% Indeterminate system. The curve is a straight line.
+% We take (as reference point) middle point between end points.
+%    \begin{macrocode} 
+                \ADD{#1}{#5}{\xpct@solx}\DIVIDE{\xpct@solx}{2}{\xpct@solx}
+                \ADD{#2}{#6}{\xpct@soly}\DIVIDE{\xpct@soly}{2}{\xpct@soly}
+             \fi\else
+%    \end{macrocode}       
+% Inconsistent case. Return a warning and undefine control point.
+%    \begin{macrocode} 
+             \xpct@WarnIncSys(#1,#2)(#5,#6)
+             \let\xpct@solx\undefined\let\xpct@soly\undefined
+          \fi
+       \else 
+%    \end{macrocode}       
+% This is the regular case.
+%    \begin{macrocode} 
+          \DIVIDE{\xpct@detD}{\xpct@detA}{\xpct@solx}
+          \DIVIDE{\xpct@detE}{\xpct@detA}{\xpct@soly}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\qCurve}
+% This macro accepts two alternative syntax (directions given by a vector
+% or by an angle).
+%    \begin{macrocode}
+\def\qCurve(#1){\@ifnextchar({\xpct@@qCurve(#1)}{\xpct@@@qCurve(#1)}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@@qCurve}
+% Compute standard coordinates of points and vectors and call |\xpct@qCurve|.
+%    \begin{macrocode}                     
+\def\xpct@@qCurve(#1)(#2)(#3)(#4){%
+       \refsysPoint(#1)(\xpct@@xzero,\xpct@@yzero)
+       \refsysPoint(#3)(\xpct@@xone,\xpct@@yone)
+       \refsysVector(#2)(\xpct@@dxzero,\xpct@@dyzero)
+       \refsysVector(#4)(\xpct@@dxone,\xpct@@dyone)
+       \xpct@qCurve(\xpct@@xzero,\xpct@@yzero)(\xpct@@dxzero,\xpct@@dyzero)(%
+                    \xpct@@xone,\xpct@@yone)%
+          (\xpct@@dxone,\xpct@@dyone)}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@@@qCurve}
+% Translate direction angles to vectors and call |\qCurve|.
+%    \begin{macrocode}       
+\def\xpct@@@qCurve(#1)#2(#3)#4{%
+             \ifpolar
+                 \qCurve(#1)(1,#2)(#3)(1,#4)
+             \else
+             \DEGREESCOS{#2}{\xpct@angxz}
+             \DEGREESSIN{#2}{\xpct@angyz}
+             \DEGREESCOS{#4}{\xpct@angxo}
+             \DEGREESSIN{#4}{\xpct@angyo}
+             \qCurve(#1)(\xpct@angxz,\xpct@angyz)(#3)%
+                (\xpct@angxo,\xpct@angyo)\fi}      
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@qCurve}
+% Call |\xpct@ctrlpoint| to compute control point; then, use |\qbezier|
+% to plot the curve. If the control point is undefined, nothing is drawn.
+%    \begin{macrocode} 
+\def\xpct@qCurve(#1)(#2)(#3)(#4){%
+       \xpct@ctrlpoint(#1)(#2)(#3)(#4)
+       \ifx\xpct@solx\undefined
+       \else   
+          \qbezier(#1)(\xpct@solx,\xpct@soly)(#3)\fi\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\PlotQuadraticCurve}
+% Try between the two alternative sintax.
+%    \begin{macrocode}
+\def\PlotQuadraticCurve(#1){%
+       \@ifnextchar({\xpct@PlotQuadraticCurve(#1)}{%
+                     \xpct@@PlotQuadraticCurve(#1)}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@PlotQuadraticCurve}
+% \begin{macro}{\xpct@@PlotQuadraticCurve}
+% Call |\qCurve| and iterate |\PlotQuadraticCurve|.
+%    \begin{macrocode}
+\def\xpct@PlotQuadraticCurve(#1)(#2)(#3)(#4){%
+       \qCurve(#1)(#2)(#3)(#4)
+       \@ifnextchar({\PlotQuadraticCurve(#3)(#4)}{}}
+\def\xpct@@PlotQuadraticCurve(#1)#2(#3)#4{%
+       \qCurve(#1){#2}(#3){#4}
+       \@ifnextchar({\PlotQuadraticCurve(#3){#4}}{}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \subsection{Conic sections and arcs}
+% \begin{macro}{\xpct@circulararc}
+% \begin{macro}{\xpct@hyperbolicarc}
+% \begin{macro}{\xpct@parabolicarc}
+% Parametric equations of circular, hyperbolic and parabolic arcs
+% defined as vector functions. 
+%    \begin{macrocode}        
+\newvectorfunction{\xpct@circulararc}{%
+%    \end{macrocode}
+% Unit circle equation $x^2+y^2=1$ can be parameterized as
+% $f(t)=(\cos t,\sin t)$.
+% If the angles are measured in degrees, the derivative is not correct.
+% Should be multiplied by  $\pi/180$, but because what we want is the
+% direction of the derivative, we will not do.
+%    \begin{macrocode} 
+    \ifdegrees
+       \DEGREESCOS{\t}{\x}
+       \DEGREESSIN{\t}{\y}
+       \COPY{\x}{\Dy}
+       \MULTIPLY{-1}{\y}{\Dx}
+    \else
+       \COS{\t}{\x}
+       \SIN{\t}{\y}
+       \COPY{\x}{\Dy}
+       \MULTIPLY{-1}{\y}{\Dx}
+    \fi}
+\newvectorfunction{\xpct@hyperbolicarc}{%
+%    \end{macrocode}
+% Hyperbola $x^2-y^2=1$, parameterized as $f(t)=\frac12(t+1/t,t-1/t)$.
+% This derivative is not correct. 
+% We should divide it by $t$, but that did not change direction.
+%    \begin{macrocode} 
+       \DIVIDE{1}{\t}{\xpct@invt}
+       \ADD{\t}{\xpct@invt}{\x}
+       \SUBTRACT{\t}{\xpct@invt}{\y}
+       \MULTIPLY{0.5}{\x}{\x}
+       \MULTIPLY{0.5}{\y}{\y}
+       \COPY{\x}{\Dy}
+       \COPY{\y}{\Dx}}
+%    \end{macrocode}
+% Parabola $x=y^2$ (or $f(t)=(t^2,t)$).
+%    \begin{macrocode} 
+\newvectorfunction{\xpct@parabolicarc}{%
+        \COPY{\t}{\y}
+        \COPY{1}{\Dy}
+        \SQUARE{\t}{\x}
+        \MULTIPLY{2}{\t}{\Dx}}
+%    \end{macrocode}         
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\circularArc}
+% \begin{macro}{\xArc}
+% A circular arc is an elliptic arc with equal semiaxes.
+%    \begin{macrocode} 
+\def\circularArc#1#2#3{\ellipticArc{#1}{#1}{#2}{#3}}
+\let\xArc\circularArc
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\ellipticArc}
+% To draw an arc of ellipse of semiaxes |#1| and |#2|, 
+% scale the axes and draw a circular arc.
+% |\defaultplotdivs| is the number of subintervals we divide  |[#3,#4]|.
+%    \begin{macrocode}
+\def\ellipticArc#1#2#3#4{%
+    \begingroup
+      \cartesianreference
+       \changereferencesystem(0,0)(#1,0)(0,#2)
+       \PlotParametricFunction[\defaultplotdivs]{\xpct@circulararc}{#3}{#4}
+    \endgroup\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\Circle}
+% \begin{macro}{\Ellipse}
+% A circle (or ellipse) is a circular (elliptic) arc of amplitude $2\pi$.
+%    \begin{macrocode}
+\def\Circle#1{\begingroup\radiansangles
+                     \circularArc{#1}{0}{\numberTWOPI}\endgroup\ignorespaces}
+\def\Ellipse#1#2{\begingroup\radiansangles
+                         \ellipticArc{#1}{#2}{0}{\numberTWOPI}
+                         \endgroup\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\lhyperbolicArc}
+% Change $x$-axis to $-x$, then draw a right hyperbolic arc.
+%    \begin{macrocode}
+\def\lhyperbolicArc#1#2#3#4{%
+            \begingroup
+               \changereferencesystem(0,0)(-1,0)(0,1)  
+               \rhyperbolicArc{#1}{#2}{#3}{#4}        
+           \endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\rhyperbolicArc}
+% Call |\xpct@hypluy| to compute extreme variables, then draw a
+% normalized arc of hyperbola.
+%    \begin{macrocode}
+\def\rhyperbolicArc#1#2#3#4{%
+              \xpct@hypluy{#2}{#3}{\xpct@uone}
+              \xpct@hypluy{#2}{#4}{\xpct@utwo}
+              \xpct@hyperbolicArc{#1}{#2}{\xpct@uone}{\xpct@utwo}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@hyperbolicArc}
+% To draw an arc of (right branch of) hyperbola of semiaxes |#1| and |#2|, 
+% scale the axes and draw a normalized arc of hyperbola.
+% |\defaultplotdivs| is the number of subintervals we divide  |[#3,#4]|.
+%    \begin{macrocode}
+\def\xpct@hyperbolicArc#1#2#3#4{%
+    \begingroup
+      \cartesianreference
+      \changereferencesystem(0,0)(#1,0)(0,#2)
+       \PlotParametricFunction[\defaultplotdivs]{\xpct@hyperbolicarc}{#3}{#4}
+    \endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\lHyperbola}
+% Change $x$-axis to $-x$, then draw a right hyperbola branch.
+%    \begin{macrocode}
+\def\lHyperbola#1#2#3#4{%
+          \begingroup
+          \changereferencesystem(0,0)(-1,0)(0,1)
+          \rHyperbola{#1}{#2}{#3}{#4}
+          \endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\rHyperbola}
+% Use |\xpct@hypconsist| to ensure parameters consistency,
+% call |\xpct@hyperbolalastu| to compute extreme variable,
+% then plot the right hyperbola branch. 
+% Divide the curve into two arcs to ensure that 
+% it includes point |(#1,0)|.
+%    \begin{macrocode}
+\def\rHyperbola#1#2#3#4{%
+       \def\xpct@hycons{}\xpct@hypconsist{#1}{#3}%
+          \ifx\xpct@hycons\undefined
+          \else
+              \xpct@hyperbolalastu{#1}{#2}{#3}{#4}
+              \DIVIDE{1}{\xpct@umax}{\xpct@umin}
+              \xpct@hyperbolicArc{#1}{#2}{\xpct@umin}{1}
+               \xpct@hyperbolicArc{#1}{#2}{1}{\xpct@umax}
+          \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\Hyperbola}
+% Use |\xpct@hypconsist| to ensure parameters consistency,
+% call |\xpct@hyperbolalastu| to compute extreme variable,
+% then plot the two branches.
+%    \begin{macrocode}
+\def\Hyperbola#1#2#3#4{%
+       \begingroup
+       \def\xpct@hycons{}\xpct@hypconsist{#1}{#3}%
+          \ifx\xpct@hycons\undefined
+          \else
+              \xpct@hyperbolalastu{#1}{#2}{#3}{#4}
+              \DIVIDE{1}{\xpct@umax}{\xpct@umin}
+               \xpct@hyperbolicArc{#1}{#2}{\xpct@umin}{1}
+               \xpct@hyperbolicArc{#1}{#2}{1}{\xpct@umax}
+             \changereferencesystem(0,0)(-1,0)(0,1)
+              \xpct@hyperbolicArc{#1}{#2}{\xpct@umin}{1}
+               \xpct@hyperbolicArc{#1}{#2}{1}{\xpct@umax}
+          \fi\endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@hypconsist}
+% Ensures consistency of parameters in |\Hyperbola|-like commands.
+% This curve is not defined for $x<a$ values. 
+%    \begin{macrocode}
+\def\xpct@hypconsist#1#2{% 
+       \ifnum #1<#2\else\xpct@ErrHypCons
+                            \let\xpct@hycons\undefined\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@hyperbolalastu}
+% Compute the max value of parameter ensuring restrictions
+% |x<#3| and |y<#4|. 
+%    \begin{macrocode}
+\def\xpct@hyperbolalastu#1#2#3#4{%
+      \xpct@hyplux{#1}{#3}{\xpct@umaxx}
+      \xpct@hypluy{#2}{#4}{\xpct@umaxy}
+       \MIN{\xpct@umaxx}{\xpct@umaxy}{\xpct@umax}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@hyplux}
+% To compute the max value of parameter ensuring restriction
+% |x<=#2|, solve equation |#2=(1/2)#1(u+1/u)| (|u=#3|).
+%    \begin{macrocode}
+\def \xpct@hyplux#1#2#3{%
+       \DIVIDE{#2}{#1}{\xpct@xa}
+       \SQUARE{\xpct@xa}{#3}
+       \SUBTRACT{#3}{1}{#3}
+       \SQUAREROOT{#3}{\xpct@@umaxx}
+       \ADD{\xpct@xa}{\xpct@@umaxx}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@hypluy}
+% To compute the max value of parameter ensuring restriction
+% |y<#2|, solve equation |#2=(1/2)#1(u-1/u)| (|u=#3|).
+%    \begin{macrocode}
+\def \xpct@hypluy#1#2#3{%
+       \DIVIDE{#2}{#1}{\xpct@xa}
+       \SQUARE{\xpct@xa}{#3}
+       \ADD{#3}{1}{#3}
+       \SQUAREROOT{#3}{\xpct@@umaxx}
+       \ADD{\xpct@xa}{\xpct@@umaxx}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\parabolicArc}
+% To draw an arc of parabola
+%  scale the $x$-axis and draw a normalized arc of parabola. 
+% |\defaultplotdivs| is the number of subintervals we divide |[#2,#3]|.
+%    \begin{macrocode}
+\def\parabolicArc#1#2#3{%
+    \begingroup
+       \changereferencesystem(0,0)(#1,0)(0,1)
+       \PlotParametricFunction[\defaultplotdivs]{\xpct@parabolicarc}{#2}{#3}
+    \endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\Parabola}
+% Call |\xpct@parabolalasty| to compute extreme variable, then plot 
+% the parabola. Divide the curve into two arcs to
+% ensure that it includes point |(0,0)|.
+%    \begin{macrocode}
+\def\Parabola#1#2#3{%
+              \xpct@parabolalasty{#1}{#2}{#3} 
+              \parabolicArc{#1}{-\xpct@maxy}{0}
+              \parabolicArc{#1}{0}{\xpct@maxy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@parabolalasty}
+% Ensure restrictions |x<=#2|, |y<=#3|: solve equation |#2=#1 y^2|.
+% Then, |\xpct@maxy=min(y,#3)|.
+%    \begin{macrocode}
+\def\xpct@parabolalasty#1#2#3{%
+       \ABSVALUE{#1}{\xpct@@maxy}
+       \DIVIDE{#2}{\xpct@@maxy}{\xpct@@maxy}
+       \SQUAREROOT{\xpct@@maxy}{\xpct@maxy}
+       \MIN{\xpct@maxy}{#3}{\xpct@maxy}}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Graphing functions}
+% \begin{macro}{\PlotFunction}
+% This command can take an optional argument.
+%    \begin{macrocode} 
+\def\PlotFunction{%
+       \@ifnextchar[{\xpct@iterateplotfunction}{\xpct@plotfunction}}
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\xpct@iterateplotfunction}
+% Compute |\xpct@step| as |(#4-#3)/#1| and iterate |\xpct@plotfunction|
+% |#1| times.
+%    \begin{macrocode} 
+\def\xpct@iterateplotfunction[#1]#2#3#4{%
+\setcounter{xpct@step}{0}%
+\COPY{#3}{\xpct@oldt}
+\SUBTRACT{#4}{#3}{\xpct@step}
+\DIVIDE{\xpct@step}{#1}{\xpct@step}
+\@whilenum \value{xpct@step}<#1 \do
+   {\ADD{\xpct@oldt}{\xpct@step}{\xpct@newt}
+   \xpct@plotfunction{#2}{\xpct@oldt}{\xpct@newt}
+   \stepcounter{xpct@step}%
+   \COPY\xpct@newt\xpct@oldt
+}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@plotfunction}
+% Draw graph of |#1| function between |#2| and |#3|.
+%    \begin{macrocode} 
+\def\xpct@plotfunction#1#2#3{\@killglue%
+%    \end{macrocode}
+% Compute $f$ and $f'$ in |#2| and |#3|, and apply |\PlotxyDyData|.
+%    \begin{macrocode}
+       #1{#2}{\yzero}{\Dyzero}%
+       #1{#3}{\yone}{\Dyone}%
+       \PlotxyDyData(#2,\yzero,\Dyzero)(#3,\yone,\Dyone)
+       \ifx\xpct@solx\undefined
+%    \end{macrocode}
+% If tangent vectors are parallel, divide the interval into two halves
+% and recall |\xpct@plotfunction|.
+%    \begin{macrocode}       
+       \ADD{#2}{#3}{\xpct@middt}
+       \MULTIPLY{0.5}{\xpct@middt}{\xpct@middt}
+       \xpct@plotfunction{#1}{#2}{\xpct@middt}
+       \xpct@plotfunction{#1}{\xpct@middt}{#3}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\PlotPointsOfFunction}
+% The |\PlotPointsOfFunction| command is essentialy equal to 
+% |\xpct@iterateplotfunction|,
+% but instead of a curve between two adjacent points,
+% plots a |\pointmark| (user can redefine |\pointmark|).
+%    \begin{macrocode}
+\def\PlotPointsOfFunction#1#2#3#4{%
+   \setcounter{xpct@step}{0}%
+\COPY{#3}{\xpct@oldt}
+\SUBTRACT{#4}{#3}{\xpct@step}
+\DIVIDE{\xpct@step}{#1}{\xpct@step}
+\ADD{#1}{1}{\xpct@lastt}
+\@whilenum \value{xpct@step}<\xpct@lastt \do 
+   {\ADD{\xpct@oldt}{\xpct@step}{\xpct@newt}
+   #2{\xpct@oldt}{\xpct@oldy}{\xpct@oldDy}
+   \Put[c](\xpct@oldt,\xpct@oldy){\pointmark}
+   \stepcounter{xpct@step}%
+   \COPY\xpct@newt\xpct@oldt
+}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\PlotxyDyData}
+% |\PlotxyDyData(x0,y0,y0')(x1,y1,y1')(x2,y2,y2')...|
+% uses |\qCurve| to draw a curve between |(x0,y0)| and |(x1,y1)|
+% with tangent vectors |(1,y0')| and |(1,y1')|, then iterates itself.
+%    \begin{macrocode}  
+\def\PlotxyDyData(#1,#2,#3)(#4,#5,#6){%
+       \qCurve(#1,#2)(1,#3)(#4,#5)(1,#6)
+       \@ifnextchar({\PlotxyDyData(#4,#5,#6)}{}}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Graphing parametric curves}
+% \begin{macro}{\PlotParametricFunction}
+% Plot vectorial function |#2| between the parameter values |#3| and |#4|.
+% It can take an optional argument |#1|.
+%    \begin{macrocode}  
+\def\PlotParametricFunction{%
+    \@ifnextchar[{\xpct@iterateplotpfunction}{\xpct@plotpfunction}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@iterateplotpfunction}
+% Divide |[#3,#4]| in |#1| pieces, then iterate |\xpct@plotpfunction| |#1|
+% times.
+%    \begin{macrocode}
+\def\xpct@iterateplotpfunction[#1]#2#3#4{%
+\setcounter{xpct@step}{0}%
+\COPY{#3}{\xpct@oldt}
+\SUBTRACT{#4}{#3}{\xpct@step}
+\DIVIDE{\xpct@step}{#1}{\xpct@step}
+\@whilenum \value{xpct@step}<#1 \do
+   {\ADD{\xpct@oldt}{\xpct@step}{\xpct@newt}
+   \xpct@plotpfunction{#2}{\xpct@oldt}{\xpct@newt}
+   \stepcounter{xpct@step}%
+   \COPY\xpct@newt\xpct@oldt}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@plotpfunction}
+% Compute function (and derivative of) |#1| in |#2| and |#3|, then
+% call |\qCurve|.
+%    \begin{macrocode}
+\def\xpct@plotpfunction#1#2#3{%
+    \begingroup
+       #1{#2}\xzero\Dxzero\yzero\Dyzero
+       #1{#3}\xone\Dxone\yone\Dyone
+       \cartesianreference
+       \qCurve(\xzero,\yzero)(\Dxzero,\Dyzero)(\xone,\yone)(\Dxone,\Dyone)
+    \endgroup\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Cartesian axes and grids}
+% Main commands: |\cartesianaxes| and |\cartesiangrid|. 
+% \begin{macro}{\cartesiangrid}
+% Put |\ifgrid| to true, then call |\cartesianaxes|.
+%    \begin{macrocode} 
+\def\cartesiangrid(#1,#2)(#3,#4){%
+       \begingroup\gridtrue\cartesianaxes(#1,#2)(#3,#4)\endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\cartesianaxes}
+% \begin{macro}{\xpct@XZero}
+% \begin{macro}{\xpct@XOne}
+% \begin{macro}{\xpct@YZero}
+% \begin{macro}{\xpct@YOne}
+% |\cartesianaxes| makes axes and, optionally, grid, tics, and/or labels.
+% Cartesian rectangle limits are stored in 
+% |\xpct@XZero|, |\xpct@XOne|, |\xpct@YZero|, and |\xpct@YOne|.
+%    \begin{macrocode}
+\def\cartesianaxes(#1,#2)(#3,#4){%
+%    \end{macrocode}
+% In this command, coordinates are Cartesian.
+%    \begin{macrocode}
+       \begingroup\cartesianreference
+          \GLOBALCOPY{#1}{\xpct@XZero}\GLOBALCOPY{#2}{\xpct@YZero}
+          \GLOBALCOPY{#3}{\xpct@XOne}\GLOBALCOPY{#4}{\xpct@YOne}
+%    \end{macrocode}
+% There shall be cuts, labels or grid?
+%    \begin{macrocode}
+          \iftics
+             \ticslabelsgridtrue
+          \else
+             \iflabels
+                \ticslabelsgridtrue
+             \else
+                \ifgrid
+                   \ticslabelsgridtrue
+          \fi\fi\fi
+          \ifticslabelsgrid
+             \xpct@plotticslabels
+          \fi
+%    \end{macrocode}
+% Call |\xpct@plotaxes| to plot axes.
+%    \begin{macrocode}          
+          \xpct@plotaxes\endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\plotxtic}
+% \begin{macro}{\plotytic}
+% Put |\iftics| boolean to true, adjust tics lengths and position,
+% and call |\xpct@printtic|.
+%    \begin{macrocode}   
+\def\plotxtic#1{%
+          \maketics
+          \xpct@adjticssize
+          \xpct@adjxorytics{#1}{0}
+          \xpct@printtic}
+\def\plotytic#1{%
+          \maketics
+          \xpct@adjticssize
+          \xpct@adjxorytics{#1}{1}
+          \xpct@printtic}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\printxlabel}
+% \begin{macro}{\printylabel}
+% Adjust tics lengths and position, and call |\xpct@printlabel|.
+%    \begin{macrocode}  
+\def\printxlabel#1#2{%
+          \xpct@adjticssize
+          \xpct@adjxorytics{#1}{0}
+          \xpct@printlabel{0}{#2}}
+\def\printylabel#1#2{%
+          \xpct@adjticssize
+          \xpct@adjxorytics{#1}{1}
+          \xpct@printlabel{1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\printxticlabel}
+% \begin{macro}{\printyticlabel}
+% Print tic and label.
+%    \begin{macrocode} 
+\def\printxticlabel#1#2{\plotxtic{#1}\printxlabel{#1}{#2}}       
+\def\printyticlabel#1#2{\plotytic{#1}\printylabel{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\plotxtics}
+% \begin{macro}{\plotytics}
+% Call |\xpct@plottics{0}}| or |\xpct@plottics{1}|.
+%    \begin{macrocode} 
+\def\plotxtics{\xpct@plottics{0}}
+\def\plotytics{\xpct@plottics{1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\printxlabels}
+% \begin{macro}{\printylabels}
+% Call |\xpct@printlabels{0}| or |\xpct@printlabels{1}|.
+% By default, optional argument must be |-1|.
+%    \begin{macrocode}
+\def\printxlabels{%
+   \@ifnextchar[{\xpct@printlabels{0}}{\xpct@printlabels{0}[-1]}}
+\def\printylabels{%
+   \@ifnextchar[{\xpct@printlabels{1}}{\xpct@printlabels{1}[-1]}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\printxticslabels}
+% \begin{macro}{\printyticslabels}
+% Call |\xpct@printxticslabels| or |\xpct@printyticslabels|.
+% By default, optional argument must be |-1|.
+%    \begin{macrocode}
+\def\printxticslabels{%
+   \@ifnextchar[{\xpct@printxticslabels}{\xpct@printxticslabels[-1]}}
+\def\printyticslabels{%
+   \@ifnextchar[{\xpct@printyticslabels}{\xpct@printyticslabels[-1]}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+
+
+
+% \begin{macro}{\xpct@plotaxes}
+% Axes are simple lines, but its position depends on boolean |\inzeroaxes|.
+%    \begin{macrocode}
+\def\xpct@plotaxes{\linethickness{\axesthickness}%
+               \pictcolor{\axescolor}
+               \ifinzeroaxes
+                  \xLINE(\xpct@XZero,0)(\xpct@XOne,0)
+                  \xLINE(0,\xpct@YZero)(0,\xpct@YOne)
+               \else   
+                   \xLINE(\xpct@XZero,\xpct@YZero)(\xpct@XOne,\xpct@YZero)
+                   \xLINE(\xpct@XZero,\xpct@YZero)(\xpct@XZero,\xpct@YOne)
+               \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@plotticslabels}
+% Adjust tics sizes to axes lengths
+% and call |\xpct@plotxticslabels| and |\xpct@plotyticslabels|.
+%    \begin{macrocode}
+\def\xpct@plotticslabels{%
+       \xpct@adjticssize
+       \xpct@plotxticslabels\xpct@plotyticslabels}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@plotxticslabels}
+% Grid, tics and labels on the |x| axis.
+% If secundary divisions are required, this command iterates itself.
+%    \begin{macrocode}
+\def\xpct@plotxticslabels{%
+%    \end{macrocode}
+% If required, plot grid (in both directions, |x| and |y|). 
+%    \begin{macrocode}
+       \ifgrid\xpct@plotgrid\fi
+       \begingroup
+          \ifnum\xunitdivisions=1
+%    \end{macrocode}
+% Call |\xpct@ticsinterval| to compute integer interval extremes
+% and number of tics;
+% then plot |x| tics. 
+%    \begin{macrocode}        
+             \xpct@ticsinterval{\xpct@XZero}{\xpct@XOne}
+             \xpct@plotxtics
+          \else
+%    \end{macrocode}
+% Secundary tics.
+%    \begin{macrocode}
+             \begingroup
+%    \end{macrocode}
+% Secundary tics. Change the reference system to the small unities,
+% and ajust tics sizes, thickness and colors.
+%    \begin{macrocode}
+                \xpct@adjstics
+                \MULTIPLY{\secundaryyticssize}{\yunitdivisions}{\yticssize}
+%    \end{macrocode}
+% At secundary level one must not print labels. 
+%    \begin{macrocode}
+                \makenolabels
+%    \end{macrocode}
+% Print secundary tics. 
+%    \begin{macrocode}
+                \def\xunitdivisions{1}
+                \xpct@plotxticslabels
+             \endgroup
+%    \end{macrocode}
+% Print primary tics and (perhaps) labels. 
+%    \begin{macrocode}                                   
+             \def\xunitdivisions{1}
+             \xpct@plotxticslabels
+          \fi
+       \endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@plotyticslabels}
+% Tics and labels on the |y| axis.
+% If secundary divisions are required, this command iterates itself.
+%    \begin{macrocode}
+\def\xpct@plotyticslabels{%
+       \begingroup
+          \ifnum\yunitdivisions=1
+%    \end{macrocode}
+% Call |\xpct@ticsinterval| to compute integer interval extremes
+% and number of tics;
+% then plot |y| tics. 
+%    \begin{macrocode} 
+             \xpct@ticsinterval{\xpct@YZero}{\xpct@YOne}
+             \xpct@plotytics
+          \else
+%    \end{macrocode}
+% Secundary tics.
+%    \begin{macrocode}
+             \begingroup
+%    \end{macrocode}
+% Secundary tics. Change the reference system to the small unities,
+% and ajust tics sizes, thickness and colors.
+%    \begin{macrocode}
+                \xpct@adjstics
+                \MULTIPLY{\secundaryxticssize}{\xunitdivisions}{\xticssize}
+%    \end{macrocode}
+% At secundary level one must not print labels. 
+%    \begin{macrocode}
+                \makenolabels
+%    \end{macrocode}
+% Print secundary tics. 
+%    \begin{macrocode}
+                \def\yunitdivisions{1}
+                \xpct@plotyticslabels
+             \endgroup
+%    \end{macrocode}
+% Print primary tics and (perhaps) labels. 
+%    \begin{macrocode} 
+             \def\yunitdivisions{1}
+             \xpct@plotyticslabels
+          \fi
+       \endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@adjstics}
+% Adjust length, color and thickness for secundary tics.
+%    \begin{macrocode}
+\def\xpct@adjstics{%
+                \MULTIPLY{\xpct@XZero}{\xunitdivisions}{\xpct@XZero}
+                \MULTIPLY{\xpct@YZero}{\yunitdivisions}{\xpct@YZero}
+                \MULTIPLY{\xpct@XOne}{\xunitdivisions}{\xpct@XOne}
+                \MULTIPLY{\xpct@YOne}{\yunitdivisions}{\xpct@YOne}
+                \DIVIDE{1}{\xunitdivisions}{\xpct@xunit}
+                \DIVIDE{1}{\yunitdivisions}{\xpct@yunit}
+                \changereferencesystem(0,0)(\xpct@xunit,0)(0,\xpct@yunit)
+                \def\gridthickness{\secundarygridthickness}
+                \def\gridcolor{\secundarygridcolor}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@plotxtics}
+% \begin{macro}{\xpct@plotytics}
+% Call |\xpct@maketics| to make tics and/or labels (on |x| and |y| axes). 
+%    \begin{macrocode}
+\def\xpct@plotxtics{\xpct@maketics{\xpct@firstint}{\xpct@numtics}{0}}
+\def\xpct@plotytics{\xpct@maketics{\xpct@firstint}{\xpct@numtics}{1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@maketics}
+% Makes tics and/or labels (|#2| points, begining in |#1|;
+% |#3=0| means |x| axis, |#3=1| means |y| axis).
+%    \begin{macrocode}
+\def\xpct@maketics#1#2#3{%
+%    \end{macrocode}
+% Call |\xpct@adjxorytics| to compute coordinates of extreme points of first 
+% tic and translation vector from one tic to the next one.
+%    \begin{macrocode}
+   \xpct@adjxorytics{#1}{#3}
+%    \end{macrocode}
+% Use counter |xpct@counta| for tics and |xpct@countb| for labels
+% (number to print in each label).
+%    \begin{macrocode}
+       \setcounter{xpct@counta}{0}%
+       \iflabels\setcounter{xpct@countb}{#1}\fi
+%    \end{macrocode}
+% Main loop: |#2| steps, begining in |#1|.
+%    \begin{macrocode}
+       \@whilenum \value{xpct@counta}<#2 \do {%
+          \iftics
+%    \end{macrocode}
+% If required, print tic.
+%    \begin{macrocode}
+           \xpct@printtic
+           \fi
+           \iflabels
+%    \end{macrocode}
+% If labels are to be printed, adjust |\Pictlabelsep|; then print label
+% and step label (|xpct@countb| counter).
+%    \begin{macrocode}
+              \highestlabel{\xpct@axeslabelattrib%
+                            $\axeslabelmathalphabet{1}$}%
+              \xpct@printlabel{#3}{\thexpct@countb}
+              \stepcounter{xpct@countb}%
+           \fi
+%    \end{macrocode}
+% Step tics counter and move coordinates to next point.
+%    \begin{macrocode}
+           \stepcounter{xpct@counta}%
+           \VECTORADD(\xpct@@xzero,\xpct@@yzero)(\xpct@@xincr,\xpct@@yincr)%
+           (\xpct@@xzero,\xpct@@yzero)
+           \VECTORADD(\xpct@@xone,\xpct@@yone)(\xpct@@xincr,\xpct@@yincr)%
+           (\xpct@@xone,\xpct@@yone)
+       }}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@adjxorytics}
+% Compute coordinates of extreme points of first tic 
+% and translation vector from one tic to the next one.
+% There are four cases: |x| or |y| axis, and external or internal axes.  
+%    \begin{macrocode}     
+\def\xpct@adjxorytics#1#2{%
+      \ifnum #2=0 
+                \COPY{#1}{\xpct@@xzero}
+                \COPY{-\yticssize}{\xpct@@yzero}
+                \COPY{#1}{\xpct@@xone}
+                \COPY{\yticssize}{\xpct@@yone}
+                \COPY{1}{\xpct@@xincr}
+                \COPY{0}{\xpct@@yincr}
+                \ifinzeroaxes\else
+                   \ADD{\xpct@YZero}{\xpct@@yzero}{\xpct@@yzero}
+                   \ADD{\xpct@YZero}{\xpct@@yone}{\xpct@@yone}
+                \fi  
+           \else 
+                \COPY{#1}{\xpct@@yzero}
+                \COPY{-\xticssize}{\xpct@@xzero}
+                \COPY{#1}{\xpct@@yone}
+                \COPY{\xticssize}{\xpct@@xone}
+                \COPY{1}{\xpct@@yincr}
+                \COPY{0}{\xpct@@xincr}
+                \ifinzeroaxes\else
+                   \ADD{\xpct@XZero}{\xpct@@xzero}{\xpct@@xzero}
+                   \ADD{\xpct@XZero}{\xpct@@xone}{\xpct@@xone}
+                \fi  
+       \fi}       
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@printtic}
+% Plot a tic.
+%    \begin{macrocode}
+\def\xpct@printtic{\pictcolor{\ticscolor}
+             \linethickness{\ticsthickness}
+             \xLINE(\xpct@@xzero,\xpct@@yzero)(\xpct@@xone,\xpct@@yone)}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@adjticssize}
+% Adjust size of tics according to axes length.
+%    \begin{macrocode}
+\def\xpct@adjticssize{%
+%    \end{macrocode}
+% First, convert absolute lenghts |\ticssize| and |\secundaryticssize| to 
+% the |\unitlength| unity.
+%    \begin{macrocode}
+       \LENGTHDIVIDE{\ticssize}{\unitlength}{\xpct@ticssize}
+       \LENGTHDIVIDE{\secundaryticssize}{\unitlength}{\xpct@sticssize}
+%    \end{macrocode}
+% Calculate the size of vector |(1,0)|, converting it to standard coordinates 
+% and computing its norm. 
+% Then we adjust |\xticssize| and |\secundaryxticssize|; this ensures 
+% the desired sizes.
+%    \begin{macrocode}
+       \refsysxyVector(1,0)(\xpct@a,\xpct@b)
+          \VECTORNORM(\xpct@a,\xpct@b){\xpct@norm}
+          \DIVIDE{\xpct@ticssize}{\xpct@norm}{\xticssize}
+          \DIVIDE{\xpct@sticssize}{\xpct@norm}{\secundaryxticssize}
+          \DIVIDE{\axislabelsep}{\xpct@norm}{\xpct@xaxislabelsep}
+%    \end{macrocode}
+% Repeat calculations for vector $(0,1)$, 
+% adjusting |\yticssize| and |\secundaryyticssize|.
+%    \begin{macrocode}
+       \refsysxyVector(0,1)(\xpct@a,\xpct@b)
+          \VECTORNORM(\xpct@a,\xpct@b){\xpct@norm}
+          \DIVIDE{\xpct@ticssize}{\xpct@norm}{\yticssize}
+          \DIVIDE{\xpct@sticssize}{\xpct@norm}{\secundaryyticssize}
+          \DIVIDE{\axislabelsep}{\xpct@norm}{\xpct@yaxislabelsep}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@printlabel}
+% Adjust highest label (for horizontal labels); 
+% then print value of |#2|.
+% Four cases: |x| or |y|, external or internal.
+%    \begin{macrocode}
+\def\xpct@printlabel#1#2{%
+       \iftics
+          \ifnum #1=0
+             \ADD{\yticssize}{\xpct@yaxislabelsep}{\Pictlabelsep}
+          \else
+             \ADD{\xticssize}{\xpct@xaxislabelsep}{\Pictlabelsep}
+          \fi
+       \else
+          \ifnum #1=0
+             \COPY{\xpct@yaxislabelsep}{\Pictlabelsep}
+          \else
+             \COPY{\xpct@xaxislabelsep}{\Pictlabelsep}
+          \fi          
+       \fi
+    \ifinzeroaxes
+       \ifnum\thexpct@countb=0
+       \else
+          \ifnum #1=0
+             \rPut*{\xpct@xlblpos}(\xpct@@xzero,0){%
+                \xpct@axeslabelattrib%
+                \ensuremath{\axeslabelmathalphabet{#2}}}
+          \else                         
+             \rPut*{\xpct@ylblpos}(0,\xpct@@yzero){%
+                \xpct@axeslabelattrib%
+                \ensuremath{\axeslabelmathalphabet{#2}}}
+          \fi
+       \fi
+    \else
+       \ifnum #1=0
+          \rPut*{\xpct@xlblpos}(\xpct@@xzero,\xpct@YZero){%
+             \xpct@axeslabelattrib%
+             \ensuremath{\axeslabelmathalphabet{#2}}}
+       \else                         
+          \rPut*{\xpct@ylblpos}(\xpct@XZero,\xpct@@yzero){%
+             \xpct@axeslabelattrib%
+             \ensuremath{\axeslabelmathalphabet{#2}}}
+       \fi
+    \fi}
+%    \end{macrocode}
+% \end{macro}   
+% \begin{macro}{\xlabelpos}
+% \begin{macro}{\ylabelpos}
+% Default position for labels on axes. Call |\xpct@convtoang| to define
+% |\xpct@xlblpos| or |\xpct@ylblpos|.
+%    \begin{macrocode}
+\def\xlabelpos#1{\xpct@convtoang{#1}{\xpct@xlblpos}{\xpct@CorR}}
+\def\ylabelpos#1{\xpct@convtoang{#1}{\xpct@ylblpos}{\xpct@CorR}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@printxticslabels}
+% \begin{macro}{\xpct@printyticslabels}
+% Print tics and labels.
+%    \begin{macrocode}
+\def\xpct@printxticslabels[#1]#2#3#4{%
+       \plotxtics{#2}{#3}{#4}\printxlabels[#1]{#2}{#3}{#4}}
+\def\xpct@printyticslabels[#1]#2#3#4{%
+       \plotytics{#2}{#3}{#4}\printylabels[#1]{#2}{#3}{#4}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@plottics}
+% Plot |x| or |y| tics (if |#1| equals |0| or |1|),
+% starting an |#2|. Distance between two consecutive tics is |#3|, and 
+% position of last tic is not greather than |#4|. 
+%    \begin{macrocode}
+\def\xpct@plottics#1#2#3#4{%
+      \COPY{#2}{\xpct@ticcoor}
+%    \end{macrocode}
+% |\xpct@ticcoor| is the position of next tic.
+%    \begin{macrocode}
+      \@whiledim\xpct@ticcoor\p@<#4\p@ \do {%
+%    \end{macrocode}
+% Make a tic while |\xpct@ticcoor<#4|
+%    \begin{macrocode}
+      \ifnum #1=0 
+         \plotxtic{\xpct@ticcoor} 
+      \else 
+         \plotytic{\xpct@ticcoor}
+      \fi
+      \ADD{#3}{\xpct@ticcoor}{\xpct@ticcoor}
+      }
+%    \end{macrocode}
+% If |\xpct@ticcoor=#4| then this is the last tic position.
+%    \begin{macrocode}
+      \ifdim\xpct@ticcoor\p@>#4\p@
+      \else
+         \ifnum #1=0 
+            \plotxtic{\xpct@ticcoor} 
+         \else 
+            \plotytic{\xpct@ticcoor}
+         \fi
+      \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@printlabels}
+% Print |x| or |y| labels (if |#1| equals |0| or |1|),
+% starting an |#3|. Distance between two consecutive tics is |#4|, and 
+% position of last tic is not greather than |#5|. 
+% |#2| is the number of decimal digits to be printed
+% (default is |#2=-1|, meaning no control of digits in number printing).
+%    \begin{macrocode}
+\def\xpct@printlabels#1[#2]#3#4#5{%
+      \COPY{#3}{\xpct@ticcoor}
+%    \end{macrocode}
+% |\xpct@ticcoor| is the position of next label.
+%    \begin{macrocode}
+      \@whiledim\xpct@ticcoor\p@<#5\p@ \do {%
+%    \end{macrocode}
+%  Print a label while |\xpct@ticcoor<#5|
+% |\xpct@Ticcoor| is the label with adjusted number of digits.
+%    \begin{macrocode}
+         \ifnum #2=-1 
+            \COPY{\xpct@ticcoor}{\xpct@Ticcoor}
+         \else
+            \ROUND[#2]{\xpct@ticcoor}{\xpct@Ticcoor}
+         \fi
+         \xpct@prtlbl{#1}
+         \ADD{#4}{\xpct@ticcoor}{\xpct@ticcoor}}
+      \ifdim\xpct@ticcoor\p@>#5\p@
+%    \end{macrocode}
+% If |\xpct@ticcoor=#5| then this is the last label position.
+%    \begin{macrocode}
+      \else
+         \ifnum #2=-1 
+            \COPY{\xpct@ticcoor}{\xpct@Ticcoor}
+         \else
+            \ROUND[#2]{\xpct@ticcoor}{\xpct@Ticcoor}
+         \fi
+         \xpct@prtlbl{#1}
+      \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@prtlbl}
+% Print the |x| or |y| label (for |#1=0| or |1|)
+% |\xpct@Ticcoor| at |\xpct@ticcoor|. 
+% When |\ifinzeroaxes| is true label at |0| position is not printed. 
+%    \begin{macrocode}
+\def\xpct@prtlbl#1{%
+        \ifinzeroaxes
+        \ifdim \xpct@ticcoor\p@=\z@\else
+            \xpct@adjticssize
+            \xpct@adjxorytics{\xpct@ticcoor}{#1}
+            \xpct@printlabel{#1}{\xpct@Ticcoor}
+         \fi
+         \else
+            \xpct@adjticssize
+            \xpct@adjxorytics{\xpct@ticcoor}{#1}
+            \xpct@printlabel{#1}{\xpct@Ticcoor}\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@plotgrid}
+% Plot a grid in a Cartesian rectangle.
+%    \begin{macrocode}
+\def\xpct@plotgrid{%
+%    \end{macrocode}
+% Call |\xpct@ticsinterval| to compute integer interval extremes
+% and number of tics;
+% then plot grid lines (for |x| axis). 
+%    \begin{macrocode}
+       \xpct@ticsinterval{\xpct@XZero}{\xpct@XOne}
+       \begingroup\setcounter{xpct@counta}{0}%
+          \pictcolor{\gridcolor}\linethickness{\gridthickness}
+          \COPY{\xpct@firstint}{\xpct@grid}
+          \@whilenum\value{xpct@counta}<\xpct@numtics\do{
+             \xLINE(\xpct@grid,\xpct@YZero)(\xpct@grid,\xpct@YOne)
+             \ADD{1}{\xpct@grid}{\xpct@grid}
+             \stepcounter{xpct@counta}}\endgroup
+%    \end{macrocode}
+% Call |\xpct@ticsinterval| to compute integer interval extremes
+% and number of tics;
+% then plot grid lines (for |y| axis).
+%    \begin{macrocode}
+       \xpct@ticsinterval{\xpct@YZero}{\xpct@YOne}
+       \begingroup\setcounter{xpct@counta}{0}%
+          \pictcolor{\gridcolor}\linethickness{\gridthickness}
+          \COPY{\xpct@firstint}{\xpct@grid}
+          \@whilenum\value{xpct@counta}<\xpct@numtics\do{
+             \xLINE(\xpct@XZero,\xpct@grid)(\xpct@XOne,\xpct@grid)
+             \ADD{1}{\xpct@grid}{\xpct@grid}
+             \stepcounter{xpct@counta}}\endgroup}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@ticsinterval}
+% Truncate extremes to integers, then compute the number of tics
+% (|\xpct@firstint-\xpct@lastint+1|).
+%    \begin{macrocode}
+\def\xpct@ticsinterval#1#2{\TRUNCATE[0]{#1}{\xpct@firstint}
+                       \TRUNCATE[0]{#2}{\xpct@lastint}
+                       \SUBTRACT{\xpct@lastint}{\xpct@firstint}{\xpct@numtics}
+                       \ADD{\xpct@numtics}{1}{\xpct@numtics}}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Polar grids}
+% \begin{macro}{\polargrid}
+% Plot a polar grid of radius |#1| and |#2| divisions of circle. 
+%    \begin{macrocode}
+\def\polargrid#1#2{%
+       \begingroup
+       \polarreference
+%    \end{macrocode}
+% Compute integer part of radius, number of circles and distance
+% between circles.
+%    \begin{macrocode}
+       \FLOOR{#1}{\xpct@rint}
+       \MULTIPLY{\xpct@rint}{\runitdivisions}{\xpct@rdivs}
+       \DIVIDE{1}{\runitdivisions}{\rincr}
+%    \end{macrocode}
+% Use counter |xpct@counta| to control the number of printed circles
+% and |\xpct@radius| as radius of the current circle.
+%    \begin{macrocode}       
+       \COPY{0}{\xpct@radius}
+       \setcounter{xpct@counta}{1}%
+%    \end{macrocode}
+% Plot |\xpct@rdivs| circles.
+%    \begin{macrocode}   
+       \begingroup
+          \pictcolor{\gridcolor}
+          \linethickness{\gridthickness}
+          \@whilenum \value{xpct@counta}<\xpct@rdivs\do {%
+             \ADD{\rincr}{\xpct@radius}{\xpct@radius}
+             \Ellipse{\xpct@radius}{\xpct@radius}
+             \stepcounter{xpct@counta}}%
+%    \end{macrocode}
+% Plot external circle.
+%    \begin{macrocode} 
+          \pictcolor{\axescolor}
+          \linethickness{\axesthickness}
+          \Ellipse{\xpct@rint}{\xpct@rint}
+       \endgroup
+%    \end{macrocode}
+% Use counter |xpct@counta| to control the number of printed lines and
+% |\xpct@angle| as arc (in radians) of the current line.
+% |\xpct@angincr| is the gap between two adjacent lines.
+%    \begin{macrocode}
+       \COPY{0}{\xpct@angle}
+       \DIVIDE{\numberTWOPI}{#2}{\xpct@angincr}
+       \setcounter{xpct@counta}{0}%
+%    \end{macrocode}
+% Plot |#2| lines.
+%    \begin{macrocode}
+       \pictcolor{\gridcolor}
+       \linethickness{\gridthickness}
+       \@whilenum \value{xpct@counta}<#2 \do {%
+          \xLINE(0,0)(#1,\xpct@angle)
+%    \end{macrocode}
+% If required, print angular label: evaluate the number |\xpct@arc|
+% such that angle is |(\xpct@arc/#2) pi| and call |\xpct@polarlabel|.
+%    \begin{macrocode}
+          \iflabels
+             \COPY{\axislabelsep}{\Pictlabelsep}
+             \MULTIPLY{2}{\thexpct@counta}{\xpct@arc}
+             \xpct@polarlabel{#1}{\xpct@arc}{#2}\fi
+          \ADD{\xpct@angincr}{\xpct@angle}{\xpct@angle}
+          \stepcounter{xpct@counta}}%
+%    \end{macrocode}
+% Plot the polar line.
+%    \begin{macrocode}
+        \pictcolor{\axescolor}
+        \linethickness{\axesthickness}
+        \xLINE(0,0)(#1,0)
+%    \end{macrocode}
+% If required, print radial labels.
+%    \begin{macrocode}
+       \iflabels
+          \highestlabel{\xpct@axeslabelattrib$\axeslabelmathalphabet{1}$}  
+          \multiPut*[\xpct@rlblpos](1,0)(1,0){\xpct@rint}{%
+             \ADD{\value{multiput}}{1}{\xpct@lbl}
+             \xpct@axeslabelattrib%
+             \ensuremath{\axeslabelmathalphabet{\xpct@lbl}}}%
+       \fi
+       \endgroup}
+%    \end{macrocode}
+% \end{macro}
+
+% \begin{macro}{\rlabelpos}
+% Default position for labels on polar axis. Call |\xpct@convtoang| to define
+% |\xpct@rlblpos|.
+%    \begin{macrocode}
+\def\rlabelpos#1{\xpct@convtoang{#1}{\xpct@rlblpos}{\xpct@CorR}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\degreespolarlabels}
+% \begin{macro}{\radianspolarlabels}
+% Define |\xpct@polarlabel| to be |\xpct@degreeslabel| or |\xpct@radianslabel|
+% (print polar label as degrees or radians).
+%    \begin{macrocode}
+\def\degreespolarlabels{\def\xpct@polarlabel{\xpct@degreeslabel}}
+\def\radianspolarlabels{\def\xpct@polarlabel{\xpct@radianslabel}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\xpct@degreeslabel}
+% Print the angle label |(#2/#3) pi| converted to degrees.
+%    \begin{macrocode}
+\def\xpct@degreeslabel#1#2#3{%
+%    \end{macrocode}
+% Adjust label position.
+%    \begin{macrocode}
+%    \end{macrocode}
+% Simplify |#2/#3|. Then convert |(#2/#3) pi| to degrees
+% (evaluate |(#2 180)/#3|).
+%    \begin{macrocode}
+       \FRACTIONSIMPLIFY{#2}{#3}\xpct@num\xpct@den
+       \MULTIPLY{\xpct@num}{180}{\xpct@degangle}
+       \DIVIDE{\xpct@degangle}{\xpct@den}{\xpct@degangle}
+%    \end{macrocode}
+% Print label.
+%    \begin{macrocode}
+       \cPut{\xpct@degangle}(#1,\xpct@angle){%
+          \xpct@axeslabelattrib%
+          \ensuremath{\axeslabelmathalphabet{\xpct@degangle^\mathrm{o}}}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@radianslabel}
+% Print the angle label |(#2/#3) pi|.
+%    \begin{macrocode}
+\def\xpct@radianslabel#1#2#3{%
+%    \end{macrocode}
+% Adjust label position and call |\xpct@prtfracrad|.
+%    \begin{macrocode}
+          \RADtoDEG{\xpct@angle}{\xpct@angles}
+          \cPut{\xpct@angles}(#1,\xpct@angle){%
+             \xpct@axeslabelattrib%
+             \ensuremath{\axeslabelmathalphabet
+                 {\xpct@prtfracrad{#2}{#3}}}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xpct@prtfracrad}
+% Pretty print |(#1/#2)pi|
+%    \begin{macrocode}
+\def\xpct@prtfracrad#1#2{%
+       \FRACTIONSIMPLIFY{#1}{#2}\xpct@num\xpct@den
+          \ifnum \xpct@num = 0 0
+          \else
+             \ifnum \xpct@num = 1 
+                \ifnum \xpct@den = 1 \pi
+                \else \pi/\xpct@den
+                \fi
+             \else \xpct@num\pi/\xpct@den
+             \fi
+          \fi}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Configurable parameters}
+% These are the parameters the user can customize.
+% Default values ​​are written to |xpicture.sty| and |xpicture.cfgxmpl|.
+%    \begin{macrocode}
+%</xpicture>
+%<*defaults>
+%<+cfg>%%
+%<+cfg>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%<+cfg>% xpicture configurable parameters %
+%<+cfg>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%<+cfg>%%
+%<+cfg>%%%%% Cartesian and polar axes
+%<+cfg>    % Thickness and color of axes
+\axesthickness=1pt
+\def\axescolor{black}
+%<+cfg>    % Color, size, mathversion and mathalphabet of numeric labels
+\def\axeslabelcolor{\axescolor}
+\def\axeslabelsize{\small}
+\def\axeslabelmathversion{normal}
+\def\axeslabelmathalphabet{\mathrm}
+%<+cfg>    % Relative position of numeric labels on x- y- and r- axes
+\xlabelpos{-90}
+\ylabelpos{180}
+\rlabelpos{bbr}
+%<+cfg>    % Distance between tags and cut marks,
+%<+cfg>    % is is a number (not a lenght) of \unitlength units
+\def\axislabelsep{0.1}
+%<+cfg>    % Color, thickness and size of tics
+\def\ticscolor{\axescolor}
+\ticsthickness=1pt
+\ticssize=4pt
+%<+cfg>    % Size of secundary tics
+\secundaryticssize=2pt
+%<+cfg>    % Thickness and color of Cartesian or polar grid
+\gridthickness=0.4pt
+\def\gridcolor{gray}
+%<+cfg>    % Thickness and color of Cartesian or polar secundary grid
+\secundarygridthickness=0.2pt
+\def\secundarygridcolor{lightgray}
+%<+cfg>    % Number of divisions of unity in x- y- and r-axis
+\def\xunitdivisions{1}
+\def\yunitdivisions{1}
+\def\runitdivisions{1}
+%<+cfg>    % Arc labels in radians (\xpct@radianslabel)
+%<+cfg>    %            or degrees (\xpct@degreeslabel)
+\def\xpct@polarlabel{\xpct@radianslabel}
+%<+cfg>%%%%% \put and \multiput extensions
+%<+cfg>    % Distance from label to reference point,
+%<+cfg>    % is is a number (not a lenght) of \unitlength units
+\def\Pictlabelsep{0.1}
+%<+cfg>    % Default layout for distance (\defaultPut{c} or \defaultPut{r})
+\defaultPut{c}
+%<+cfg>%%%%% Reference systems
+%<+cfg>    % Default reference system
+\referencesystem(0,0)(1,0)(0,1)
+%<+cfg>    % Cartesian or polar reference
+\cartesianreference
+%<+cfg>%%%%% Arrow size in \xtrivVECTOR
+\arrowsize{5}{2}
+%<+cfg>%%%%% Default interval divisions
+%<+cfg>    % (used when plotting conic sections and arcs)
+\def\defaultplotdivs{8}
+%<+cfg>%%%%% Size to be used by \pointmark
+\def\pointmarkdiam{0.1}
+%<+cfg>%%%%% Point mark used by \PlotPointsOfFunction
+\def\pointmark{\circle*{\pointmarkdiam}}
+%</defaults>
+%<*xpicture>
+%    \end{macrocode}
+% \subsection{Commands to be ignored if draft option or \cs{draftPicture} 
+%             declaration is active}
+% \begin{macro}{\draftPictures}
+% This declaration allow user to locally disable |Picture| drawns.
+%    \begin{macrocode}
+\def\draftPictures{%
+       \drafttrue
+       \def\cPut##1(##2,##3)##4{}
+       \def\xpct@@Put(##1)##2{}
+       \def\xpct@@Putstar[##1](##2)##3{}
+       \def\xpct@@@Put[##1](##2)##3{}
+       \def\defaultPut##1{\def\xpct@defaultPut{\cPut}}
+       \def\xpct@@mPut(##1,##2)(##3,##4)##5##6{}
+       \def\xpct@PUT##1(##2,##3)##4{}
+       \def\xLINE(##1)(##2){}
+       \def\xtrivVECTOR(##1)(##2){}
+       \def\xVECTOR(##1)(##2){}
+       \def\zerovector(##1){}
+       \def\zerotrivvector(##1){}
+       \def\xline(##1,##2)##3{}
+       \def\xvector(##1,##2)##3{}
+       \def\xtrivvector(##1,##2)##3{}
+       \def\xpct@regPolygon[##1]##2##3{}
+       \def\xpct@@qCurve(##1)(##2)(##3)(##4){}
+       \def\xpct@PlotQuadraticCurve(##1)(##2)(##3)(##4){%
+           \@ifnextchar({\PlotQuadraticCurve(##3)(##4)}{}}
+       \def\xpct@@PlotQuadraticCurve(##1)##2(##3)##4{%
+           \@ifnextchar({\PlotQuadraticCurve(##3){##4}}{}}
+       \def\circularArc##1##2##3{}
+       \def\ellipticArc##1##2##3##4{}
+       \def\Ellipse##1##2{}
+       \def\Circle##1{}
+       \def\xpct@hyperbolicArc##1##2##3##4{}
+       \def\lHyperbola##1##2##3##4{}
+       \def\rHyperbola##1##2##3##4{}
+       \def\Hyperbola##1##2##3##4{}
+       \def\rhyperbolicArc##1##2##3##4{}
+       \def\lhyperbolicArc##1##2##3##4{}
+       \def\parabolicArc##1##2##3{}
+       \def\Parabola##1##2##3{}
+       \def\PlotPointsOfFunction##1##2##3##4{}
+       \def\xpct@iterateplotfunction[##1]##2##3##4{}
+       \def\xpct@plotfunction##1##2##3{}
+       \def\xpct@iterateplotpfunction[##1]##2##3##4{}
+       \def\xpct@plotpfunction##1##2##3{}
+       \def\cartesianaxes(##1,##2)(##3,##4){}
+       \def\cartesiangrid(##1,##2)(##3,##4){}
+       \def\plotxtic##1{}
+       \def\plotytic##1{}
+       \def\printxlabel##1##2{}
+       \def\printylabel##1##2{}
+       \def\printxticlabel##1##2{}
+       \def\printyticlabel##1##2{}
+       \def\plotxtics##1##2##3{}
+       \def\plotytics##1##2##3{}
+       \def\xpct@printlabels##1[##2]##3##4##5{}
+       \def\polargrid##1##2{}
+}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ifdraft}
+% If |draft| option is active |\draftPictures| is executed. 
+% Then all |Picture| commands are disabled.
+%    \begin{macrocode}
+\ifdraft
+   \draftPictures
+\fi
+%    \end{macrocode}
+% \end{macro}
+% Input local defaults (file |xpicture.cfg|).
+%    \begin{macrocode}
+\InputIfFileExists{xpicture.cfg}{\xpct@Infocfg}{\xpct@Infonocfg}
+%</xpicture>
+%    \end{macrocode}
+% \section{Change history}
+% \begin{description}
+% \item[v1.2a] (2012/11/17)
+% 
+% Documented source.\par
+% Many internal c.s. renamed and/or rewrited.\par
+% dvi/pict2e/curve2e options supressed.\par
+% draft option added.\par
+% Background color added to Picture environment.\par
+% \cs{Pictlabelsep} is set to \verb+\normalfont\normalsize$1$+
+% when a \verb+Picture+ environment starts.\par
+% New commands: \cs{draftPictures},\cs{symmetrize}, 
+% \cs{xlabelpos}, \cs{ylabelpos},
+% \cs{plotxtic}, \cs{plotytic}, \cs{plotxtics}, \cs{plotytics},
+% \cs{printxlabel}, \cs{printylabel}, \cs{printxlabels}, \cs{printylabels},
+% \cs{printxticlabel}, \cs{printyticlabel},
+% \cs{printxticslabels}, \cs{printyticslabels},
+% \cs{makegrid}, \cs{makenogrid}, 
+% \cs{PlotPointsOfFunction}, \cs{pointmark}, \cs{pointmarkdiam}.
+% 
+% \item[v1.2] (2012/04/25) 
+% 
+% First public version. 
+% \end{description}
+% \Finale
+%
\ No newline at end of file
diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check
index b2f7bef2d15..c41efa6deb8 100755
--- a/Master/tlpkg/bin/tlpkg-ctan-check
+++ b/Master/tlpkg/bin/tlpkg-ctan-check
@@ -462,7 +462,7 @@ my @TLP_working = qw(
     xetexref xfor xgreek xhfill
     xifthen xits
     xkeyval xlop xltxtra xmpincl xnewcommand
-    xoptarg xpatch xpeek xpinyin xpunctuate
+    xoptarg xpatch xpeek xpicture xpinyin xpunctuate
     xq xskak xstring xtab xunicode
     xwatermark xyling xypic xypic-tut-pt xytree
   yafoot yagusylo yannisgr yax ydoc yfonts york-thesis youngtab yplan ytableau
diff --git a/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc b/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc
index 2ae31bc9efa..58a42b760a0 100644
--- a/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc
+++ b/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc
@@ -99,5 +99,6 @@ depend tkz-tab
 depend tsemlines
 depend tufte-latex
 depend venndiagram
+depend xpicture
 depend xypic
 depend collection-basic
diff --git a/Master/tlpkg/tlpsrc/xpicture.tlpsrc b/Master/tlpkg/tlpsrc/xpicture.tlpsrc
new file mode 100644
index 00000000000..e69de29bb2d
--- /dev/null
+++ b/Master/tlpkg/tlpsrc/xpicture.tlpsrc