curve2e (12nov10)

git-svn-id: svn://tug.org/texlive/trunk@20420 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 742 insertions, 247 deletions

diff --git a/Master/texmf-dist/source/latex/curve2e/curve2e.dtx b/Master/texmf-dist/source/latex/curve2e/curve2e.dtx
index d1dd0a41b16..91d53920373 100644
--- a/Master/texmf-dist/source/latex/curve2e/curve2e.dtx
+++ b/Master/texmf-dist/source/latex/curve2e/curve2e.dtx
@@ -1,38 +1,75 @@
 % \iffalse
+%<*internal>
+\begingroup
+\input docstrip.tex
+\keepsilent
+\preamble
+  ______________________________________________________
+  The curve2e package for LaTeX and XeLATeX
+  Copyright (C) 2010 Claudio Beccari 
+  All rights reserved
+
+  License information appended
+
+\endpreamble
+\postamble
+
+Copyright 2005-2010 Claudio Beccari
+
+Distributable under the LaTeX Project Public License,
+version 1.3c or higher (your choice). The latest version of
+this license is at: http://www.latex-project.org/lppl.txt
+
+This work is "author-maintained"
+
+This work consists of this file curve2e.dtx, a README file
+and the derived files curve2e.sty and curve2e.pdf.
+
+\endpostamble
+\askforoverwritefalse
+
+\generate{\file{curve2e.sty}{\from{curve2e.dtx}{package}}}
+
+\def\tmpa{plain}
+\ifx\tmpa\fmtname\endgroup\expandafter\bye\fi
+\endgroup
+%</internal>
+%
 %%
 %% File `curve2e.dtx'.
-%% Copyright (C)  2005--2006 Claudio Beccari  all rights reserved.
+%% Copyright (C)  2005--2010 Claudio Beccari  all rights reserved.
 %%
 % What follows is the usual trick that is not typeset in the documentation
 % dvi file that is produced by LaTeX. It is used to define the date, the version
 % and the short description that characterizes both this file and the package;
 % the point is that |\ProvidesFile| is being read only by the driver, while
-% |\ProvidePackage| goes to the stripped package file; It must be done before
+% |\ProvidePackage| goes to the stripped package file; it must be done before
 % starting the documentation otherwise |\GetFileInfo|  can't get the necessary
 % information.
 % \fi
+%
+% \iffalse
 %<*package>
-%    \begin{macrocode}
-\NeedsTeXFormat{LaTeX2e}
+%<package>\NeedsTeXFormat{LaTeX2e}
 %</package>
 %<*driver>
 \ProvidesFile{curve2e.dtx}%
 %</driver>
 %<+package>\ProvidesPackage{curve2e}%
-        [2008/05/04 v.1.01 Extension package for pict2e]
 %<*package>
-%    \end{macrocode}
+        [2010/11/08 v.1.30 Extension package for pict2e]
 %</package>
-% \iffalse
 %<*driver>
 \documentclass{ltxdoc}
 \hfuzz 10pt
 \usepackage{multicol}
 \usepackage[ansinew]{inputenc}
+\usepackage{curve2e}
 \GetFileInfo{curve2e.dtx}
 \title{The extension package \textsf{curve2e}\thanks{Version number
 \fileversion; last revised \filedate.}}
 \author{Claudio Beccari}
+\date{}
 \begin{document}
  \maketitle
 \begin{multicols}{2}
@@ -43,12 +80,17 @@
 %</driver>
 % \fi
 %
-% \CheckSum{2222}
+% \CheckSum{2304}
 % \begin{abstract}
 % This file documents the |curve2e| extension package to the recent
 % implementation of the |pict2e| bundle that has been described by Lamport
 % himself in the second edition of his \LaTeX\ handbook.
 %
+% Please take notice that in August 2009 a new updated version of the package 
+% |pict2e| has been released that incorporates some of the commands defined in
+% this package; apparently there are no conflicts, but only the advanced features
+% of |curve2e| remain available for extending the above package.
+%
 % This extension redefines a couple of commands and introduces some more drawing
 % facilities that allow to draw circular arcs and arbitrary curves with the
 % minimum of user intervention. This beta version is open to the contribution of
@@ -70,27 +112,30 @@
 % environment; specifically:
 % \begin{enumerate}
 % \item the line and vector slopes were limited to the ratios of relatively
-% prime one digit integers of magnitude not exceeding 6 for lines and 4 for
+% prime one-digit integers of magnitude not exceeding 6 for lines and 4 for
 % vectors;
 % \item filled and unfilled full circles were limited by the necessarily
-% bounded number of specific glyphs contained in the special \LaTeX\
+% limited number of specific glyphs contained in the special \LaTeX\
 % \texttt{picture} fonts;
 % \item quarter circles were also limited in their radii for the same reason;
 % \item ovals (rectangles with rounded corners) could not be too small because
 % of the unavailability of small radius quarter circles, nor could be too
 % large, in the sense that after a certain radius the rounded corners remained
 % the same and would not increase proportionally to the oval size.
-% \item vector arrows had only one possible shape besides matching the limited
+% \item vector arrows had only one possible shape and matched the limited
 % number of vector slopes;
-% \item for circles and inclined lines and vectors there were available just
-% two possible thicknesses.
+% \item for circles and inclined lines and vectors just two possible thicknesses
+%  were available.
 % \end{enumerate}
 %
 % The package \texttt{pict2e} removes most if not all the above limitations:
 % \begin{enumerate}
 % \item line and vector slopes are virtually unlimited; the only remaining
 % limitation is that the direction coefficients must be three-digit integer
-% numbers; they need not be relatively prime;
+% numbers; they need not be relatively prime; with the 2009 upgrade even this
+% limitation was removed and now slope coefficients can be any fractional number
+% whose magnitude does not exceed 16\,384, the maximum dimension in points that
+% \TeX\ can handle;
 % \item filled and unfilled circles can be of any size;
 % \item ovals can be designed with  any specified corner curvature and there is
 % virtually no limitation to such curvatures; of course corner radii should not
@@ -104,26 +149,44 @@
 %  This specific extension adds the following features
 % \begin{enumerate}
 % \item commands for setting the line terminations are introduced; the user can
-% chose between square or rounded caps; the default is set to rounded caps;
+% chose between square or rounded caps; the default is set to rounded caps (now
+% available also with |pict2e|); 
+% \item commands for specifying the way two lines or curves join to one nanother;
+% ^^A
 % \item the |\line| macro is redefined so as to allow integer and fractional
 % direction coefficients, but maintaining the same syntax as in the original
-% \texttt{picture} environment;
-% \item a new macro |\Line| is defined so as to avoid the need to specify the
-% horizontal projection of inclined lines;
-% \item a new macro |\LINE| joins two points specified with their coordinates;
-% of course there is no need to use the |\put| command with this line
-% specification;
+% \texttt{picture} environment (now available also with |pict2e|);
+% ^^A
+% \item a new macro |\Line| was defined so as to avoid the need to specify the
+% horizontal projection of inclined lines (now available also with |pict2e|);
+% this conflicts with |pict2e| 2009 version; therefore its name is changed to
+% |\LIne| and supposedly it will not be used very often, if ever used; 
+% ^^A
+% \item a new macro |\LINE| was defined in order to join two points specified with
+% their coordinates; this is now the normal behavior of the |\Line| macro of
+% |pict2e| so that |\LINE| is now renamed |\segment|; of course there is no need
+% to use the |\put| command with this line specification;
+% ^^A
+% \item a new macro |\DLine| is defined in order to draw dashed lines joining any
+% two given points; the dash length and gap (equal to one another) must be
+% specified;
+% ^^A
 % \item similar macros are redefined for vectors; |\vector| redefines the
-% original macro but with the vector slope limitation removed; |\Vector| gets
+% original macro but with the vector slope limitations removed; |\Vector| gets
 % specified with its two horizontal and vertical components; |\VECTOR|
 % joins two specified points (without using the |\put| command) with  the arrow
 % pointing to the second point;
 % \item a new macro |\polyline| for drawing polygonal lines is defined that
 % accepts from two vertices up to an arbitrary (reasonably limited) number of
-% them;
+% them (available now also in |pict2e|);
 % \item a new macro |\Arc| is defined in order to draw an arc with arbitrary
 % radius and arbitrary angle amplitude; this amplitude is specified in
-% sexagesimal degrees, not in radians;
+% sexagesimal degrees, not in radians; the same functionality is now achieved with
+% the |\arc| macro of |pict2e|, which provides also the strar version |\arc*| that
+% fills up the interior of the generated circular arc. It must be noticed that
+% the syntax is slighltly different, so that it's reasonable that both commands,
+% in spite  of producing identical arcs, might be more comfortable with this or that
+% syntax.
 % \item two new macros are defined in order to draw circular arcs with one
 % arrow at one or both ends;
 % \item a new macro |\Curve| is defined so as to draw arbitrary curved lines
@@ -132,10 +195,10 @@
 % \end{enumerate}
 %
 % In order to make the necessary calculations many macros have been defined so
-% as to use complex number to manipulate point coordinates, directions,
+% as to use complex number arithmetics to manipulate point coordinates, directions,
 % rotations and the like. The trigonometric functions have also been defined in
-% a way that the author believes to be more efficient that that implied by the
-%  \texttt{trig} package; in any case the macro names are sufficiently
+% a way that the author believes to be more efficient than that implied by the
+% \texttt{trig} package; in any case the macro names are sufficiently
 % different to accommodate both definitions in the same \LaTeX\ run.
 %
 % Many aspects of this extension could be fine tuned for better performance;
@@ -148,14 +211,347 @@
 % Gäßlein and Niepraschk  who are the prime maintainers of \texttt{pict2e};
 % they only can decide whether or not to incorporate new macros in their package.
 %
+% \section{Summary of modifications and new commands}
+% This package \texttt{curve2e} extends the power of \texttt{pict2e} with the
+% following modifications and the following new commands.
+% \begin{enumerate}
+% \item This package |curve2e| calls directly the \LaTeX\ packages |color| and 
+% |pict2e| to whom it passes any possible option that the latter can receive;
+% actually the only options that make sense are those concerning the arrow tips,
+% either \LaTeX\ or PostScript styled, because it is assumed that if you use this
+% package you are not interested in using the original \LaTeX\ commands. See the
+% |pict2e| documentation in order to use the correct options |pict2e| can receive.
+% \item New commands are offered the user in order to control the line terminators
+% and the line joins; specifically:
+% \begin{itemize}
+% \item |\roundcap|: the line is terminated with a semicircle;
+% \item |\squarecap|: the line is terminated with a half square;
+% \item |\roundjoin|: two lines are joined with a rounded join;
+% \item |\beveljoin|: two lines are joined with a bevel join;
+% \item |\miterjoin|: two lines are terminated with a miter join.
+% \end{itemize}
+% All the above commands should respect the intended range; but since they act at
+% the PostScript or PDF level, not at \TeX\ level, it might be necessary to issue
+% the necessary command in order to restore the previous terminator or join.
+% \item The commands |\linethickness|, |\thicklines|, |\thinlines| together with
+% |\defaultlinethickness| always redefine the internal |\@wholewidth| and
+% |\@halfwidth|
+% so that the latter always refer to a full width and to a half of it in this
+% way: if you issue the command |\defaultlinewidth{2pt}| all thin lines will be
+% drawn with a thickenes of 1\,pt while if a drawing command directly refers to the
+% internal value |\@wholewidth|, its line will be drawn with a thickness of 2\,pt.
+% If one issues the declaration |\thinlines| all lines will be drawn with a  1\,pt
+% width, but if a command refers to the internal value |\@halfwidth| the line will
+% be drawn with a thickness of 0.5\,pt. The command |\linethickness| redefines the
+% above internals but does not change the default width value; all these width
+% specifications apply to all lines, straight ones, curved ones, circles, ovals,
+% vectors, dashed, et cetera. It's better to recall that |thinlines| and
+% |thicklines| are declarations that do not take arguments; on the opposite the
+% other two commands follow the standard syntax:
+% \begin{flushleft}
+% |\linethickness|\marg{dimensioned value}\\
+% |\defaultlinewidth|\marg{dimensioned value}
+% \end{flushleft}
+% where \meta{dimensioned value} means a length specification complete of its units
+% or a dimensional expression.
+% \item Straight lines and vectors are redefined in such a way that fractional slope
+% coefficients may be specified; the zero length line does not produce errors and is
+% ignored; the zero length vectors draw only the arrow tips.
+% \item New line and vector macros are defined that avoid the necessity of
+% specifying the horizontal component |\put(3,4){\LIne(25,15)}| specifies a segment
+% that starts at point $(3,4)$ and goes to point $(3+25,4+15)$; the command
+% |\segment(3,4)(28,19)| achieves the same result without the need of the using
+% command |\put|.
+% The same applies to the vector commands |\Vector| and |\VECTOR|. Experience has
+% shown that the commands intended to joint two specified coordinates are
+% particularly useful.
+% \item The |\polyline| command has been introduced: it accepts an unlimited list of 
+% point coordinates enclosed within round parentheses; the command draws a sequence
+% of connected segments that joins in sequence the specified points; the syntax is:
+%	\begin{flushleft}
+%	\cs{polyline[}\marg{optional join style}\texttt{](}\meta{$P_1$}\texttt{)(}%
+%	\meta{$P_2$}\texttt{)...(}\meta{$P_n$}\texttt{)}
+%	\end{flushleft}
+% See figure~\ref{fig:polyline} where a pentagon is designed..
+%
+%	\begin{figure}[!ht]
+%	\begin{minipage}{.48\linewidth}
+%	\begin{verbatim}
+%	\unitlength=.5mm
+%	\begin{picture}(40,32)(-20,0)
+%	\polyline(0,0)(19.0211,13,8197)(11.7557,36.1803)%
+%	(-11.7557,36.1803)(-19.0211,13,8197)(0,0)
+%	\end{picture}
+%	\end{verbatim}
+%	\end{minipage}
+%   \hfill
+%	\begin{minipage}{.48\linewidth}\raggedleft
+%   \unitlength=.5mm
+%	\begin{picture}(40,32)(-20,0)
+%	\polyline(0,0)(19.0211,13,8197)(11.7557,36.1803)%
+%	(-11.7557,36.1803)(-19.0211,13,8197)(0,0)
+%	\end{picture}\hspace*{2em}
+%	\end{minipage}
+%	\caption{Polygonal line obtained by means of the \texttt{\string\polyline}
+%   command}	\label{fig:polyline}
+%	\end{figure}
+%
+% Although you can draw polygons with |\polyline|, as it was done in 
+% figure~\ref{fig:polyline}, do not confuse this command with the command |\polygon|
+% defined in |pict2e| 2009; the latter automatically joins the last specified
+% coordinate to the first one, therefore closing the path. |pict2e| defines also the 
+% starred command that fills up the inside of the generated polygon.
+% \item The new command
+% \begin{flushleft}
+% |\Dline(|\textit{first point}|)(|\textit{second point}|)(|\textit{dash length}|)|
+% \end{flushleft}
+% draws a dashed line containing as many dashes as possible, long as specified, and
+% separated by a gap exactly the same size; actually, in order to make an even
+% gap-dash sequence, the desired dash length is used to do some computations in
+% order to find a suitable length, close to the one specified, such that the
+% distance of the end points is evenly divided in equally sized dashes and gaps.
+% The end points may be anywhere in
+% the drawing area, without any constraint on the slope of the joining segment. The
+% desired dash length is specified as a fractional multiple of |\unitlength|; see
+% figure~\ref{fig:dashline}.
+%	\begin{figure}[!ht]
+%	\begin{minipage}{.48\textwidth}
+%	\begin{verbatim}
+%	\unitlength.5mm
+%	\begin{picture}(40,40)
+%	\put(0,0){\GraphGrid(40,40)}
+%	\Dline(0,0)(40,10){4}
+%	\put(0,0){\circle*{2}}
+%	\Dline(40,10)(0,25){4}
+%	\put(40,10){\circle*{2}}
+%	\Dline(0,25)(20,40){4}
+%	\put(0,25){\circle*{2}}
+%	\put(20,40){\circle*{2}}
+%	\end{picture}
+%	\end{verbatim}
+%	\end{minipage}
+%	\hfill
+%	\begin{minipage}{.48\textwidth}\centering
+%	\unitlength.5mm
+%	\begin{picture}(40,40)
+%	\put(0,0){\GraphGrid(40,40)}
+%	\Dline(0,0)(40,10){4}
+%	\put(0,0){\circle*{2}}
+%	\Dline(40,10)(0,25){4}
+%	\put(40,10){\circle*{2}}
+%	\Dline(0,25)(20,40){4}
+%	\put(0,25){\circle*{2}}
+%	\put(20,40){\circle*{2}}
+%	\end{picture}
+%	\end{minipage}
+%	\caption{Dashed lines and graph grid}\label{fig:dashline}
+%	\end{figure}
+% \item |\GraphGrid| is a command that draws a red grid over the drawing area with
+% lines separated |10\unitlength|s; it is described only with a comma separated
+% couple of numbers, representing the base and the height of the grid, see
+% figure~\ref{fig;dashline}; it's better to specify multiples of ten and the grid
+% can be placed anywhere in the drawing plane by means of |\put|, whose coordinates
+% are multiples of 10; nevertheless the grid line distance is rounded to the
+% nearest multiple of 10, while the point coordinates specified to |\put| are not
+% rounded at all; therefore some care should be used to place the working grid in
+% the drawing plane. This grid is intended as an aid in drawing; even if you sketch
+% your drawing on millimeter paper, the drawing grid turns out to be very useful;
+% one must only delete or comment out the command when the drawing is finished.
+% \item New trigonometric function macros have been implemented; possibly they are
+% not better than the corresponding macros of the |trig| package, but they are
+% supposed to be more accurate at least they were intended to be so. The other
+% difference is that angles are specified in sexagesimal degrees ($360^\circ$ to one
+% revolution), so that reduction to the fundamental quadrant is supposed to be more
+% accurate; the tangent of odd multiples of $90^\circ$ are approximated with a
+% ``\TeX\ infinity'', that is the signed value 16383.99999. This will possibly
+% produce computational errors in the subsequent calculations, but at least it does
+% not stop the tangent computation. In order to avoid overflows or underflows in the
+% computation of small angles (reduced to the first quadrant), the sine and the
+% tangent of angles smaller than $1^\circ$ are approximated by the first term of the
+% McLaurin series, while for the cosine the approximation is given by the first two
+% terms of the McLaurin series. In both cases theoretical errors are smaller
+% than what \TeX\ arithmetics can handle.
+%
+% These trigonometric functions are used within the complex number macros; but if
+% the user wants to use them the syntax is the following:
+%\begin{flushleft}
+%      \texttt{\char92SinOf}\meta{angle}\texttt{to}\meta{control sequence}
+%\\
+%      \texttt{\char92CosOf}\meta{angle}\texttt{to}\meta{control sequence}
+%\\
+%      \texttt{\char92TanOf}\meta{angle}\texttt{to}\meta{control sequence}
+%\end{flushleft}
+% The \meta{control sequence} may then be used as a multiplying factor of a length.
+% \item Arcs can be drawn as simple circular arcs, or with one or two arrows at
+% their ends (curved vectors);  the syntax is:
+%\begin{flushleft}
+% \texttt{\char92Arc(}\meta{center}\texttt{)(}\meta{starting point}\texttt{)}\marg{angle}\\
+% \texttt{\char92VectorArc(}\meta{center}\texttt{)(}\meta{starting point}\texttt{)}\marg{angle}\\
+% \texttt{\char92VectorARC(}\meta{center}\texttt{)(}\meta{starting point}\texttt{)}\marg{angle}\\
+%\end{flushleft}
+% If the angle is specified numerically it must be enclosed in braces, while if it
+% is specified with a control sequence the braces (curly brackets) are not
+% necessary. The above macro |\Arc| draws a simple circular arc without arrows;
+% |\VectorArc| draws an arc with an arrow tip at the ending point; |\VectorARC|
+% draws an arc with arrow tips at both ends; see figure~\ref{fig:arcs}.
+%	\begin{figure}
+%	\begin{minipage}{.48\textwidth}
+%	\begin{verbatim}
+%	\unitlength=0.5mm
+%	\begin{picture}(60,40)
+%	\put(0,0){\GraphGrid(60,40)}
+%	\Arc(0,20)(30,0){60}
+%	\VECTOR(0,20)(30,0)\VECTOR(0,20)(32.5,36)
+%	\VectorArc(0,20)(15,10){60}
+%	\put(20,20){\makebox(0,0)[l]{$60^\circ$}}
+%	\VectorARC(60,20)(60,0){-180}
+%	\end{picture}
+%	\end{verbatim}
+%	\end{minipage}
+%	\hfill
+%	\begin{minipage}{.48\textwidth}\centering
+%	\unitlength=0.5mm
+%	\begin{picture}(60,40)
+%	\put(0,0){\GraphGrid(60,40)}
+%	\Arc(0,20)(30,0){60}
+%	\VECTOR(0,20)(30,0)\VECTOR(0,20)(32.5,36)
+%	\VectorArc(0,20)(15,10){60}
+%	\put(20,20){\makebox(0,0)[l]{$60^\circ$}}
+%	\VectorARC(60,20)(60,0){-180}
+%	\end{picture}
+%	\end{minipage}
+%	\caption{Arcs and curved vectors}\label{fig:arcs}
+%	\end{figure}
+% \item A multitude of commands have been defined in order to manage complex
+% numbers; actually complex numbers are represented as a comma separated pair of
+% fractional numbers. They are used to point to specific points in the drawing
+% plane, but also as operators so as to scale and rotate other objects. In the
+% following \meta{vector} means a comma separated pair of fractional numbers,
+% possibly stored in macros; \meta{argument} means a brace delimiteded numeric
+% value, possibly a macro; \textit{macro} is a valid macro name, a backslash
+% followed by letters, or anything else that can receive a definition.
+%
+% {\footnotesize\begin{itemize}
+% \item |\MakeVectorFrom|\meta{two arguments}|to|\meta{vector}
+% \item |\CopyVect|\meta{first vector}|to|\meta{second vector}
+% \item |\ModOfVect|\meta{vector}|to|\meta{macro}
+% \item |\DirOfvect|\meta{vector}|to|\meta{macro}
+% \item |\DmodAndDirOfVect|\meta{vector}|to|\meta{first macro}|and|\meta{second macro}
+% \item |\DistanceAndDirOfVect|\meta{first vector}|minus|\meta{second vector}|to|\meta{first macro}|and|\meta{second macro}
+% \item |\XpartOfVect|\meta{vector}|to|\meta{macro}
+% \item |\YpartOfVect|\meta{vector}|to|\meta{macro}
+% \item |\DirFromAngle|\meta{angle}|to|\meta{macro}
+% \item |\ScaleVect|\meta{vector}|by|\meta{scaling factor}|to|\meta{macro}
+% \item |\ConjVect|\meta{vector}|to|\meta{conjugate vector}
+% \item |\SubVect|\meta{first vector}|from|\meta{second vector}|to|\meta{vector}
+% \item |\AddVect|\meta{first vector}|and|\meta{second vector}|to|\meta{vector}
+% \item |\MultVect|\meta{first vector}|by|\meta{second vector}|to|\meta{vector}
+% \item |\MultVect|\meta{first vector}|by*|\meta{second vector}|to|\meta{vector}
+% \item |\DivVect|\meta{first vector}|by|\meta{second vector}|to|\meta{vector}
+% \end{itemize}}
+%
+% \item General curves can be drawn with the |pict2e| macro |\curve| but it requires
+% the specification of the Bézier third order spline control points; sometimes it's
+% better to be very specific with the control points and there is no other means to
+% do a decent graph; sometimes the curves to be drawn are not so tricky and a
+% general set of macros can be defined so as to compute the control points, while
+% letting the user specify only the nodes through which the curve must pass, and the
+% tangent direction of the curve in such nodes. This macro is |\Curve| and must be
+% followed by an ``unlimited" sequence of node-direction coordinates as a quadruple
+% defined as
+%\[
+% \texttt{(}\meta{node coordinates}\texttt{)<}\meta{direction vector}\texttt{>}
+%\]
+% Possibly if a sudden change of direction has to be performed (cusp) another item
+% can be inserted after one of those quadruples in the form
+%\[
+% \texttt{...(...)<...>[}\meta{new direction vector}\texttt{](...)<...>...}
+%\]
+% The |\Curve| macro does not (still) have facilities for cycling the path, that is
+% to close the path from the last specified node-direction to the first specified
+% node-direction.
+% The tangent direction need not be specified with a unit vector, although only its
+% direction is relevant; the scaling of the specified direction vector to a unit
+% vector is performed by the macro itself. Therefore one cannot specify the fine
+% tuning of the curve convexity as it can be done with other programs, as for
+% example with METAFONT or the |pgf/tikz| package and environment.
+% See figure~\ref{fig:curve} for an example.
+% \end{enumerate}
+%	\begin{figure}
+%	\begin{minipage}{.48\textwidth}
+%   \begin{verbatim}
+%	\unitlength=8mm
+%	\begin{picture}(5,5)
+%	\put(0,0){\framebox(5,5){}}\thicklines\roundcap
+%	\Curve(2.5,0)<1,1>(5,3.5)<0,1>%
+%	      (2.5,3.5)<-.5,-1.2>[-.5,1.2]%
+%	      (0,3.5)<0,-1>(2.5,0)<1,-1>
+%	\end{picture}
+%   \end{verbatim}
+%	\end{minipage}
+%	\hfill
+%	\begin{minipage}{.48\textwidth}\raggedleft
+%	\unitlength=8mm
+%	\begin{picture}(5,5)
+%	\put(0,0){\framebox(5,5){}}\thicklines\roundcap
+%	\Curve(2.5,0)<1,1>(5,3.5)<0,1>(2.5,3.5)<-0.5,-1.2>[-0.5,1.2](0,3.5)<0,-1>(2.5,0)<1,-1>
+%	\end{picture}
+%	\end{minipage}
+%	\caption{A heart shaped curve with cusps drawn with \texttt{\string\Curve}}
+%	\label{fig:curve}
+%	\end{figure}
+%
+% In spite of the relative simplicity of the macros contained in this package, the
+% described macros, as well as the original macros included in the |pict2e| package,
+% allow to produce fine drawings that were inconceivable of with the original \LaTeX\ 
+% picture environment. Leslie Lamport himself announced an extension to his
+% environment when \LaTeXe\ was first issued in 1994; in the |latexnews| news letter
+% of December 2003; the first implementation appeared; the first version of this
+% package was issued in 2006. It was time to have a better drawing environment; this
+% package is a simple attempt to follow the initial path while extending the drawing
+% facilities; but Till Tantau's |pgf| package has gone much farther.
+%
+% \section{Notice}
+% There are other packages in the \textsc{ctan} archives that deal with tracing
+% curves of various kinds. |PSTricks| and |tikz/pgf| are the most powerful ones. But
+% there are also the package |curves| that is intended to draw almost anything by
+% using little dots or other symbols partially superimposed to one another. It used
+% only quadratic Bézier curves and the curve tracing is eased by specifying only the
+% curve nodes, without specifying the control nodes; with a suitable option to the
+% package call it is possible to reduce the memory usage by using short straight
+% segments drawn with the PostScript facilities offered by the |dvips| driver.
+%
+% Another package |ebezier| performs about the same as |curve2e| but draws its
+% Bézier curves by using little dots partially superimposed to one another. The
+% documentation is quite interesting but since it explains very clearly what exactly
+% are the Bézier splines, it appears that |ebezier| should be used only for dvi
+% output without recourse to PostScript machinery.
+%
 % \section{Acknowledgements}
 % I wish to express my deepest thanks to Michel Goosens who spotted some errors
 % and very kindly submitted them to me so that I was able to correct them.
 %
+% Josef Tkadlec and the author collaborated extensively in order to make a better
+% real long division so as to get the fractional part and to avoid as much as
+% possible any numeric overflow; many Josef's ideas are incorporated in the macro
+% that is implemented in this package, although the macro used by Josef is slightly
+% different from this one. Both versions aim at a better accuracy and at widening
+% the operand ranges.
+%
+% Daniele Degiorgi spotted a fault in the kernel definition of |\linethickness|
+% that heavily influenced also |curve2e|; see below.
+%
+% Thanks also to Jin-Hwan Cho and Juho Lee who suggested a small but crucial modification
+% in order to have \texttt{curve2e} work smoothly also with XeTeX (XeLaTeX).
+% Actually if version 0.2x or later, dated 2009/08/05 or later, of |pict2e| is being used,
+% such modification is not necessary, but it's true that it becomes imperative if older
+% versions are used.
+%
 % \StopEventually{%
 % \begin{thebibliography}{9}
-% \bibitem{pict2e} Gäßlein H.\ and Niepraschk R., \emph{The \texttt{pict2e}
-% package}, PDF document attached to the ``new'' \texttt{pict2e} bundle; the
+% \bibitem{pict2e} Gäßlein H.,  Niepraschk R., and Tkadlec J.
+% \emph{The \texttt{pict2e}
+% package}, 2009, PDF document attached to the ``new'' \texttt{pict2e} bundle; the
 % bundle may be downloaded from any CTAN archive or one of their mirrors.
 % \end{thebibliography}
 % }
@@ -171,20 +567,25 @@
 %    \end{macrocode}
 %  Next we define the line terminators and joins; the following definitions work
 % correctly  if the \texttt{dvips} or the \texttt{pdftex} driver are specified;
-% probably other modes should be added so as to be consistent with
-% \texttt{pict2e}.
+% probably other modes should be added so as to be consistent with \texttt{pict2e}:
+% |\providecommand| is used instead of the low level command |\def| in order to
+% avoid redefinitions of |pict2e| macros.
 %    \begin{macrocode}
 \ifcase\pIIe@mode\relax
 \or %Postscript
- \def\roundcap{\special{ps:: 1 setlinecap}}%
- \def\squarecap{\special{ps:: 0 setlinecap}}%
- \def\roundjoin{\special{ps:: 1 setlinejoin}}%
- \def\beveljoin{\special{ps:: 2 setlinejoin}}%
+ \providecommand\roundcap{\special{ps:: 1 setlinecap}}%
+ \providecommand\squarecap{\special{ps:: 0 setlinecap}}%
+ \newcommand\roundjoin{\special{ps:: 1 setlinejoin}}%
+ \providecommand\beveljoin{\special{ps:: 2 setlinejoin}}%
+ \providecommand\miterjoin{\special{ps:: 0 setlinejoin}}%
 \or %pdf
- \def\roundcap{\pdfliteral{1 J}}%
- \def\squarecap{\pdfliteral{0 J}}%
- \def\roundjoin{\pdfliteral{1 j}}%
- \def\beveljoin{\pdfliteral{2 j}}%
+ \@ifundefined{XeTeXrevision}{}
+          {\def\pdfliteral#1{\special{pdf: literal #1}}}%
+ \providecommand\roundcap{\pdfliteral{1 J}}%
+ \providecommand\squarecap{\pdfliteral{0 J}}%
+ \providecommand\roundjoin{\pdfliteral{1 j}}%
+ \providecommand\beveljoin{\pdfliteral{2 j}}%
+ \providecommand\miterjoin{\pdfliteral{0 j}}%
 \fi
 %    \end{macrocode}
 %
@@ -217,10 +618,10 @@
 % 1pt, thick lines will be 1pt thick and thin lines will be 0.5pt thick.  The
 % default whole width of thick lines is 0,8pt, but this is specified in the
 % kernel of \LaTeX\ and\slash or in \texttt{pict2e}. On the opposite it is
-% necessary to redefine |\linethickness| because the \LaTeX\ kernel global definition
-% does not hide the space after the closed brace when you enter something such as
-% |\linethickness{1mm}| followed by a space or a new line.\footnote{Thanks to
-% Daniele Degiorgi (\texttt{degiorgi@inf.ethz.ch}).}
+% necessary to redefine |\linethickness| because the \LaTeX\ kernel global
+% definition does not hide the space after the closed brace when you enter something
+% such as |\linethickness{1mm}| followed by a space or a new line.\footnote{Thanks
+% to Daniele Degiorgi (\texttt{degiorgi@inf.ethz.ch}).}
 %    \begin{macrocode}
 \gdef\linethickness#1{\@wholewidth#1\@halfwidth.5\@wholewidth\ignorespaces}%
 \newcommand\defaultlinethickness[1]{\defaultlinewidth=#1\relax
@@ -234,27 +635,36 @@
 % eliminate.
 %
 % \subsubsection{Improved line and vector macros}
-% The new macro |\Line| allows to draw an arbitrary inclination line as if it
-% was a polygon with just two vertices. This line should be set by means of a
+% The new macro |\LIne| allows to draw an arbitrary inclination line as if it
+% was a polygonal with just two vertices. This line should be set by means of a
 % |\put| command so that its starting point is always at a relative 0,0
 % coordinate point. The two arguments define the horizontal and the
 % vertical component respectively.
 %    \begin{macrocode}
-\def\Line(#1,#2){\pIIe@moveto\z@\z@
+\def\LIne(#1,#2){\pIIe@moveto\z@\z@
       \pIIe@lineto{#1\unitlength}{#2\unitlength}\pIIe@strokeGraph}%
 %    \end{macrocode}
 %
-% A similar macro |\LINE| operates between two explicit points with absolute
+% A similar macro |\segment| operates between two explicit points with absolute
 % coordinates, instead of relative to the position specified by a |\put|
 % command; it resorts to the |\polyline| macro that is to be defined in a while.
-% The |\@killglue|command might be unnecessary, but it does not harm; it eliminates any
-% explicit or implicit spacing that might precede this command.
-%    \begin{macrocode}
-\def\LINE(#1)(#2){\@killglue\polyline(#1)(#2)}%
-%    \end{macrocode}
-%
-%  The |\line| macro is redefined by making use of a new division routine that
-%  receives in input two dimensions and yields on output their fractional ratio.
+% The |\@killglue|command might be unnecessary, but it does not harm; it eliminates
+% any explicit or implicit spacing that might precede this command.
+%    \begin{macrocode}
+\def\segment(#1)(#2){\@killglue\polyline(#1)(#2)}%
+%    \end{macrocode}
+% By passing its ending points coordinates to the |\polyline| macro, both macro
+% arguments are a pair of coordinates, not their components; in other words, if
+% $P_1=(x_1, y_2)$ and $P_2=(x_2, y_2)$, then the first argument is the couple
+% $x_1, y_1$ and likewise the second argument is $x_2, y_2$. Please remember that
+% the decimal separator is the decimal \emph{point}, while the \emph{comma} acts
+% as coordinate separator. This recommendation is particularly important for
+% non-English speaking users, since the ISO regulations allow the decimal point
+% only for English speaking countries, while in all other countries the comma
+% must be used as the decimal separator.
+%
+% The |\line| macro is redefined by making use of a new division routine that
+% receives in input two dimensions and yields on output their fractional ratio.
 % The beginning of the macro definition is the same as that of \texttt{pict2e}:
 %    \begin{macrocode}
 \def\line(#1)#2{\begingroup
@@ -262,7 +672,8 @@
   \ifdim\@linelen<\z@\@badlinearg\else
 %    \end{macrocode}
 % but as soon as it is verified that the line length is not negative, things
-% change remarkably; in facts the machinery for complex numbers is invoked:
+% change remarkably; in facts the machinery for complex numbers is invoked.
+% This makes the code muche simpler, not necessarily more efficient; nevertheless
 % |\DirOfVect| takes the only macro argument (that actually contains a comma
 % separated pair of fractional numbers) and copies it to |\Dir@line| (an
 % arbitrarily named control sequence) after re-normalizing to unit magnitude;
@@ -285,7 +696,8 @@
       \@linelen=\sc@lelen\@linelen
     \fi
 %    \end{macrocode}
-%  Finally the \texttt{moveto}, \texttt{lineto} and \texttt{stroke} language
+% Of course, it the line is vertical this division must not take place.
+% Finally the \texttt{moveto}, \texttt{lineto} and \texttt{stroke} language
 % keywords are invoked by means of the internal \texttt{pict2e} commands in
 % order to draw the line. Notice that even vertical lines are drawn with the
 % ``PostScript'' commands instead of resorting to the dvi low level language
@@ -297,9 +709,50 @@
     \pIIe@moveto\z@\z@
     \pIIe@lineto{\d@mX\@linelen}{\d@mY\@linelen}%
     \pIIe@strokeGraph
-\fi
+  \fi
 \endgroup\ignorespaces}%
 %    \end{macrocode}
+% The new definition of the command |\line|, besides tha ease with which is
+% readable, does not do different things from the definition of |pict2e| 2009, but
+% it did preform in a better way whith the 2004 version that was limited to integer
+% direction coefficients up to 999 in magnitude.
+%
+% Another usefull line-type macro creates a dashed line between two given points
+% with a dash length that must be specified; actually the specified dash length is a
+% desired dash length; the actual length is computed by integer division between
+% the distance of the given points and the desired dash length; this integer is
+% tested in order to see if it's odd; if it's not, it is increased by one. Then the
+% actual dash length is obtained by dividing the above distance by this odd number.
+% Another vector is created from $P_1-P_0$ by dividing it by the magic odd number;
+% then it is multiplied by two in order to have the increment from one dash to the
+% next, and finally the number of patterns is obtained by integer dividing the magic
+% odd number by 2 and increasing it by 1. A simple |\multiput| completes the job,
+% but in order to use the various vectors and numbers within a group and to throw the result outside the group while restoring all the intermediate counters and registers, a service macro is
+% created with an expanded definition and then this service macro is executed.
+%    \begin{macrocode}
+\ifx\Dline\undefined
+\def\Dline(#1,#2)(#3,#4)#5{%
+\begingroup
+   \countdef\NumA254\countdef\NumB252\relax
+   \MakeVectorFrom{#1}{#2}to\V@ttA 
+   \MakeVectorFrom{#3}{#4}to\V@ttB 				
+   \SubVect\V@ttA from\V@ttB to\V@ttC 			
+   \ModOfVect\V@ttC to\DlineMod 				
+   \DividE\DlineMod\p@ by#5\p@ to\NumD 			
+   \NumA\expandafter\Integer\NumD?? 	
+   \ifodd\NumA\else\advance\NumA\@ne\fi 		
+   \NumB=\NumA \divide\NumB\tw@ 				
+   \DividE\DlineMod\p@ by\NumA\p@  to\D@shMod 	
+   \DividE\p@ by\NumA\p@ to \@tempa 			
+   \MultVect\V@ttC by\@tempa,0 to\V@ttB	
+   \MultVect\V@ttB by 2,0 to\V@ttC
+   \advance\NumB\@ne			
+   \edef\@mpt{\noexpand\endgroup
+   \noexpand\multiput(\V@ttA)(\V@ttC){\number\NumB}{\noexpand\LIne(\V@ttB)}}%
+   \@mpt\ignorespaces}%
+\fi
+%    \end{macrocode}
+%
 % The new macro |\GetCoord| splits a vector (or complex number) specification
 % into its components:
 %    \begin{macrocode}
@@ -313,11 +766,13 @@
 %
 % The redefinitions and the new definitions for vectors are a little more
 % complicated than with segments, because each vector is drawn as a filled
-% contour; the original \texttt{pict2e} macro checks if the slopes are
+% contour; the original \texttt{pict2e} 2004  macro checks if the slopes are
 % corresponding to the limitations specified by Lamport (integer three digit
 % signed numbers) and sets up a transformation in order to make it possible to
 % draw each vector as an horizontal left-to-right arrow and then to rotate it by
-% its angle about its tail point; actually there are two macros for tracing the
+% its angle about its tail point; with |pict2e| 2009, possibly this redefinition
+% of |\vector| is not necessary, but we do it as well and for the same reasons
+% we had for redefining |\line|; actually there are two macros for tracing the
 % contours that are eventually filled by the principal macro; each contour
 % macro draws the vector with a \LaTeX\ or a PostScript arrow whose parameters
 % are specified by default or may be taken from the parameters taken from the
@@ -349,14 +804,14 @@
 %    \begin{macrocode}
       \ifdim\@linelen<\z@ \@linelen=-\@linelen\fi
 %    \end{macrocode}
-% We now make a vector with the slope direction even if one or the other is
+% We now make a vector with the slope coefficients even if one or the other is
 % zero and we determine its direction; the real and imaginary parts of the
 % direction vector are also the values we need for the subsequent rotation.
 %    \begin{macrocode}
       \MakeVectorFrom\d@mX\d@mY to\@Vect
       \DirOfVect\@Vect to\Dir@Vect
 %    \end{macrocode}
-% In order to be compatible with the original \texttt{pict2e} I need to
+% In order to be compatible with the original \texttt{pict2e} we need to
 % transform the components of the vector direction in lengths with the specific
 % names |\@xdim| and |\@ydim|
 %    \begin{macrocode}
@@ -425,7 +880,7 @@
 %
 % On the opposite the next macro specifies a vector by means of the coordinates
 % of its end points; the first point is where the vector starts, and the second
-% point is  the arrow tip side. We need the difference as these two coordinates,because % it  represents the actual vector.
+% point is  the arrow tip side. We need the difference of these two coordinates, because % it  represents the actual vector.
 %    \begin{macrocode}
 \def\VECTOR(#1)(#2){\begingroup
 \SubVect#1from#2to\@tempa
@@ -436,13 +891,39 @@
 % The \texttt{pict2e} documentation says that if the vector length is zero the
 % macro designs only the arrow tip; this may work with macro |\vector|,
 % certainly not with |\Vector| and |\VECTOR|. This might be useful for adding
-% an arrow tip to a circular arc
+% an arrow tip to a circular arc. See examples in figure~\ref{fig:vectors}.
+%
+%	\begin{figure}
+%	\begin{minipage}{.48\textwidth}
+%	\begin{verbatim}
+%	\unitlength=.5mm
+%	\begin{picture}(60,20)
+%	\put(0,0){\GraphGrid(60,20)}
+%	\put(0,0){\vector(1.5,2.3){10}}
+%	\put(20,0){\Vector(10,15.33333)}
+%	\VECTOR(40,0)(50,15.33333)
+%	\end{picture}
+%	\end{verbatim}
+%	\end{minipage}
+%	\hfill
+%	\begin{minipage}{.48\textwidth}\centering
+%	\unitlength=.5mm
+%	\begin{picture}(60,20)
+%	\put(0,0){\GraphGrid(60,20)}
+%	\put(0,0){\vector(1.5,2.3){10}}
+%	\put(20,0){\Vector(10,15.33333)}
+%	\VECTOR(40,0)(50,15.33333)
+%	\end{picture}
+%	\end{minipage}
+%   \caption{Three (displaced) identical vectors obtained with the three vector
+%            macros.}\label{fig:vectors}
+%	\end{figure}
 %
 % \subsubsection{Polygonal lines}
 % We now define the polygonal line macro; its syntax is very simple
-% \begin{flushleft}\ttfamily
-% \cs{polygonal}(\rmfamily{P}$_0$)(\rmfamily{P}$_1$)\rmfamily{P}$_2$)\dots
-% (\rmfamily{P}$_n$)
+% \begin{flushleft}
+% \cs{polygonal}\texttt{(}$P_0$\texttt{)(}$P_1$\texttt{)(}$P_2$)%
+%  \texttt{\dots(}$P_n$\texttt{)}
 % \end{flushleft}
 % In order to write a recursive macro we need aliases for the parentheses;
 % actually we need only the left parenthesis, but some editors complain about
@@ -457,18 +938,27 @@
 % preceded by spaces that are ignored by the |\@ifnextchar| macro) then a
 % warning message is output together with the line number where the missing
 % parenthesis causes the warning: beware, this line number might point to
-% several lines further on along the source file! In any case it's necessary to insert
-% a |\@killglue| command, because |\polyline| refers to absolute coordinates
+% several lines further on along the source file! In any case it's necessary to
+% insert a |\@killglue| command, because |\polyline| refers to absolute coordinates
 % not necessarily is put in position through a |\put| command that provides to
 % eliminate any spurious spaces preceding this command.
+%
+% Remember: |\polyline| has been incorporated into |pict2e| 2009, but we redefine it so as to allow an optional argument to allow the line join specification.
+%
+% In order to allow a specification for the joints of the various segements of
+% a polygonal line it is necessary to allow for an optional parameter; the default
+% join is the bevel join.
 %    \begin{macrocode}
-\def\polyline(#1){\@killglue\beveljoin\GetCoord(#1)\d@mX\d@mY
+\providecommand*\polyline[1][\beveljoin]{\p@lylin@[#1]}
+
+\def\p@lylin@[#1](#2){\@killglue#1\GetCoord(#2)\d@mX\d@mY
     \pIIe@moveto{\d@mX\unitlength}{\d@mY\unitlength}%
     \@ifnextchar\lp@r{\p@lyline}{%
     \PackageWarning{curve2e}%
     {Polygonal lines require at least two vertices!\MessageBreak
      Control your polygonal line specification\MessageBreak}%
     \ignorespaces}}
+
 %    \end{macrocode}
 % But if there is a second or further point coordinate the recursive macro
 % |\p@lyline| is called; it works on the next point and checks for a further
@@ -487,7 +977,7 @@
 % aid and the user should know what he/she is doing; nevertheless it is
 % advisable to displace the grid by means of a |\put| command so that its grid
 % lines coincide with the graph coordinates multiples of 10. Missing to do so
-% the readings become cumbersome. The |\RoundUp| macros provide to increase the
+% the readings become cumbersome. The |\RoundUp| macro provides to increase the
 % grid dimensions to integer multiples of ten.
 %    \begin{macrocode}
 \def\GraphGrid(#1,#2){\begingroup\textcolor{red}{\linethickness{.1\p@}%
@@ -523,74 +1013,97 @@
 %
 % \subsection{The new division macro}
 % Now comes one of the most important macros in the whole package: the division
-% macro; it takes two lengths as input values ant computes their fractional
-% ratio.
+% macro; it takes two lengths as input values and computes their fractional
+% ratio into a control sequence.
 % It must take care of the signs, so that it examines the operand signs and
 % determines the result sign separately conserving this computed sign in the
 % macro |\segno|; this done, we are sure that both operands are or are
 % made positive; should the
 % numerator be zero it directly issues the zero quotient; should the
-% denominator be zero it outputs a signed ``infinity'', that is the maximum
-% allowable length measured in points that \TeX\ can deal with.
+% denominator be zero it outputs  ``infinity'' (|\maxdimen| in points), that is
+% the maximum allowable length measured in points that \TeX\ can deal with.
 % Since the result is assigned a value, the calling statement must pass as the
 % third argument either a control sequence or an active character. Of course the
 % first operand is the dividend, the second the divisor and the third the
 % quotient.
+%
+% Since |curve2e| is supposed to be an extension of |pic2e| and this macro package
+% already contains a division maro, we do not define any other division macro;
+% nevetheless, since the macro in |pic2e| may not be so efficient as it might be
+% if the |e-tex| extensions of the interpreter program were available, here we
+% check and eventually provide a more efficient macro. The latter exploits the
+% scaling mechanism embedded in |pdftex| since 2007, if the extended mode is
+% enabled, that is used to scale a dimension by a fraction: $L\times N/D$, where
+% $L$ is a dimension, and $N$ and $D$ are the numerator an denominator of the
+% scaling factor; these might be integers, but it's better they represent the
+% numbers of scaled points another two dimensions correspond to, in the philosophy
+% that floating point numbers are represented by the measures of lengths in points.
+%
+% Therefore first we test if the macro is already defined:
 %    \begin{macrocode}
 \ifx\DividE\undefined
-  \def\DividE#1by#2to#3{%
-      \begingroup
-      \dimendef\Numer=254\relax \dimendef\Denom=252\relax
-      \countdef\Num 254\relax
-      \countdef\Den 252\relax
-      \countdef\I=250\relax
-      \Numer #1\relax \Denom #2\relax
-      \ifdim\Denom<\z@ \Denom -\Denom \Numer -\Numer\fi
-      \def\segno{}\ifdim\Numer<\z@ \def\segno{-}\Numer -\Numer\fi
-      \ifdim\Denom=\z@
-        \ifdim\Numer>\z@\def\Q{16383.99999}\else\def\Q{-16383.99999}\fi
-      \else
-        \Num=\Numer \Den=\Denom \divide\Num\Den
-        \edef\Q{\number\Num.}%
-        \advance\Numer -\Q\Denom \I=6\relax
-        \@whilenum \I>\z@ \do{\DividEDec\advance\I\m@ne}%
-      \fi
-      \xdef#3{\segno\Q}\endgroup
-  }%
-%    \end{macrocode}
-%  The |\DividEDec| macro takes the remainder of the previous division,
-% multiplies it by 10, computes a one digit quotient that postfixes to the
-% previous overall quotient, and computes the next remainder; all operations
-% are done on integer registers to whom the dimensional operands are assigned
-%  so that the mentioned registers acquire the measures of the dimensions in
-% scaled points; \TeX\ is called to perform integer arithmetics, but the long
-% division takes care of the decimal separator and of the suitable number of
-% fractional digits.
-%    \begin{macrocode}
-  \def\DividEDec{\Numer=10\Numer \Num=\Numer \divide\Num\Den
-              \edef\q{\number\Num}\edef\Q{\Q\q}\advance\Numer -\q\Denom}%
-\fi
 %    \end{macrocode}
-% In the above code the |\begingroup|\dots|\endgroup| maintain all registers
-% local so that only the result must be globally defined. The |\ifx|\dots|\fi|
-% construct assures the division machinery is not redefined; I use it in so
-% many packages that its better not to mix up things even with slightly
-% different definitions.
+%then we test if the extended mode exists and/or is enabled:
+%    \begin{macrocode}
+\ifx\dimexpr\undefined\else
+%    \end{macrocode}
+% Notice that |\dimexpr| is the specific extended mode control sequence we are going
+% to use in order to perform our task; if the interpeter program is too old and/or
+% it is a recent version, but it was compiled without activating the extended mode,
+% the macro |\dimexpr| is undefined.
+%
+% The macro, creates a group where the names of two counters and a
+% dimensional register are defined; the numbers of these integer and dimension
+% registers are expressly above the value 255, because one of the extensions is
+% the possibility of using a virtually unlimited number of registers; moreover
+% even if these registers were used within other macros, their use within a group
+% does not damage the other macros; we just have to use a dirty trick to throw
+% the result beyond the end-group command.
+%
+% The efficiency of this macro is contained in the extended command |\dimexpr|; both
+% the |\@DimA| and |\Num| registers are program words of 32\,bits; the result is
+% stored into an internal register of 64\,bits; the final division by a factor
+% stored into a register of 32 bits, so that in terms of scaled points a division by
+% 1\,pt = $1\times 2^{16}$, scales down the result by 16 bits, and if the total
+% length of the result is smaller than $2^{30}$, the result can be correctly
+% assigned to a dimension register. In any other case the extended features imply
+% suitable error messages end the termination of the program. During the division a
+% scaling down by 16 bits, the result is not simply truncated, but it is rounded to
+% the nearest integer (in scaled points)
+%
+%    \begin{macrocode}
+	\def\DividE#1by#2to#3{%
+	\begingroup
+		\countdef\Num2254\relax \countdef\Den2252\relax
+		\dimendef\@DimA 2254
+		\Num=\p@ \@DimA=#2\relax \Den=\@DimA
+		\ifnum\Den=\z@
+			\edef\x{\noexpand\endgroup\noexpand\def\noexpand#3{\strip@pt\maxdimen}}%
+		\else
+			\@DimA=#1\relax
+			\@DimA=\dimexpr\@DimA*\Num/\Den\relax
+			\edef\x{\noexpand\endgroup\noexpand\def\noexpand#3{\strip@pt\@DimA}}%
+		\fi
+	\x}
+%    \end{macrocode}
+%    \begin{macrocode}
+\fi\fi
+%    \end{macrocode}
 %
 % The next two macros are one of the myriad variants of the dirty trick used by
 % Knuth for separating a measure from its units that \textit{must} be points,
-% ``\texttt{pt}''; One has to call |\Numero| with a control sequence and a
+% ``\texttt{pt}''. One has to call |\Numero| with a control sequence and a
 % dimension; the dimension value in points is assigned to the control sequence.
 %    \begin{macrocode}
-\ifx\undefined\@Numero%                         s
+\ifx\undefined\@Numero%                         
   {\let\cc\catcode \cc`p=12\cc`t=12\gdef\@Numero#1pt{#1}}%
 \fi
 \ifx\undefined\Numero
-  \def\Numero#1#2{\dimen254
-#2\edef#1{\expandafter\@Numero\the\dimen254}\ignorespaces}%
+  \def\Numero#1#2{\dimen254#2\relax
+  \edef#1{\expandafter\@Numero\the\dimen254}\ignorespaces}%
 \fi
 %    \end{macrocode}
-% For both macros the |\ifx|\dots|\fi| constructs avoids messing up the
+% For both macros the |\ifx|\dots|\fi| constructs avoid messing up the
 % definitions I have in several packages.
 %
 % \subsection{Trigonometric functions}
@@ -599,7 +1112,7 @@
 % not appear so essential) by means of the parametric formulas that require the
 % knowledge of the tangent of the half angle. We want to specify the angles
 % in sexagesimal degrees, not in radians, so we can make accurate reductions to
-% the main quadrants. we use the formulas
+% the main quadrants. We use the formulas
 % \begin{eqnarray*}
 % \sin\theta &=& \frac{2}{\cot x + \tan x}\\
 % \cos\theta &=& \frac{\cot x - \tan x}{\cot x + \tan x}\\
@@ -628,11 +1141,11 @@
 %
 % The first macro is the service routine that computes the tangent and the
 % cotangent of the half angle in radians; since we have to use always the
-% reciprocal if this value, we call it |\X| but ins spite of the similarity it
+% reciprocal of this value, we call it |\X@| but in spite of the similarity it
 % is the reciprocal of $x$. Notice that parameter \texttt{\#1} must be a length.
 %    \begin{macrocode}
 \def\g@tTanCotanFrom#1to#2and#3{%
-\DividE 114.591559\p@ by#1to\X \@tdB=\X\p@
+\DividE 114.591559\p@ by#1to\X@ \@tdB=\X@\p@
 %    \end{macrocode}
 % Computations are done with the help of counter |\I|, of the length |\@tdB|,
 % and the auxiliary control sequences |\Tan| and |\Cot| whose meaning is
@@ -661,9 +1174,16 @@
 % half angle, we can compute the real trigonometric functions we are interested
 % in. The sine value is computed after reducing the sine argument to the
 % interval $0^\circ< \theta<180^\circ$; actually special values such as
-% $0^\circ$,$90^\circ$, $180^\circ$, et cetera, are taken care separately, so
+% $0^\circ$, $90^\circ$, $180^\circ$, et cetera, are taken care separately, so
 % that CPU time is saved for these special cases. The sine sign is taken care
 % separately according to the quadrant of the sine argument.
+%
+% Since all computations are done within a group, a trick is necessary in order to
+% extract the sine value from the group; this is done by defining within the group
+% a macro (in this case |\endSinOf|) with the expanded definition of the result,
+% but in charge of of closing the group, so that when the group is closed the
+% auxiliary function is not defined any more, although its expansion keeps getting
+% executed so that the expanded result is thrown beyond the group end.
 %    \begin{macrocode}
 \def\SinOf#1to#2{\begingroup%
 \@tdA=#1\p@%
@@ -672,7 +1192,7 @@
 \else%
   \@whiledim\@tdA<-180\p@\do{\advance\@tdA 360\p@}%
 \fi \ifdim\@tdA=\z@
-  \gdef#2{0}%
+  \def\@tempA{0}%
 \else
   \ifdim\@tdA>\z@
     \def\Segno{+}%
@@ -684,26 +1204,29 @@
     \@tdA=-\@tdA \advance\@tdA 180\p@
   \fi
   \ifdim\@tdA=90\p@
-    \xdef#2{\Segno1}%
+    \def\@tempA{\Segno1}%
   \else
     \ifdim\@tdA=180\p@
-      \gdef#2{0}%
+      \def\@tempA{0}%
     \else
       \ifdim\@tdA<\p@
         \@tdA=\Segno0.0174533\@tdA
-        \DividE\@tdA by\p@ to#2%
+        \DividE\@tdA by\p@ to \@tempA%
       \else
         \g@tTanCotanFrom\@tdA to\T and\Tp
         \@tdA=\T\p@ \advance\@tdA \Tp\p@
-        \DividE \Segno2\p@ by\@tdA to#2%
+        \DividE \Segno2\p@ by\@tdA to \@tempA%
       \fi
     \fi
   \fi
 \fi
-\endgroup\ignorespaces}%
+\edef\endSinOf{\noexpand\endgroup
+  \noexpand\def\noexpand#2{\@tempA}\noexpand\ignorespaces}%
+\endSinOf}%
 %    \end{macrocode}
 %
-% For the computation of the cosine we behave in a similar way.
+% For the computation of the cosine we behave in a similar way using also the identical
+% trick for throwing the result beyond the group end.
 %    \begin{macrocode}
 \def\CosOf#1to#2{\begingroup%
 \@tdA=#1\p@%
@@ -724,31 +1247,33 @@
   \@tdA=-\@tdA \advance\@tdA 180\p@
 \fi
 \ifdim\@tdA=\z@
-  \gdef#2{\Segno1}%
+  \def\@tempA{\Segno1}%
 \else
   \ifdim\@tdA<\p@
     \@tdA=0.0174533\@tdA \Numero\@tempA\@tdA
     \@tdA=\@tempA\@tdA \@tdA=-.5\@tdA
     \advance\@tdA \p@
-    \DividE\@tdA by\p@ to#2%
+    \DividE\@tdA by\p@ to\@tempA%
   \else
     \ifdim\@tdA=90\p@
-      \gdef#2{0}%
+      \def\@tempA{0}%
     \else
       \g@tTanCotanFrom\@tdA to\T and\Tp
       \@tdA=\Tp\p@ \advance\@tdA-\T\p@
       \@tdB=\Tp\p@ \advance\@tdB\T\p@
-      \DividE\Segno\@tdA by\@tdB to#2%
+      \DividE\Segno\@tdA by\@tdB to\@tempA%
     \fi
   \fi
 \fi
-\endgroup\ignorespaces}%
+\edef\endCosOf{\noexpand\endgroup
+    \noexpand\def\noexpand#2{\@tempA}\noexpand\ignorespaces}%
+\endCosOf}%
 %    \end{macrocode}
 %
 % For the tangent computation we behave in a similar way, except that we
 % consider the fundamental interval as $0^\circ<\theta<90^\circ$; for the odd
 % multiples of $90^\circ$ we assign the result a \TeX\ infinity value, that is
-% the maximum number in points a dimension can be.
+% the maximum a dimension can be.
 %    \begin{macrocode}
 \def\TanOf#1to#2{\begingroup%
 \@tdA=#1\p@%
@@ -758,7 +1283,7 @@
   \@whiledim\@tdA<-90\p@\do{\advance\@tdA 180\p@}%
 \fi%
 \ifdim\@tdA=\z@%
-  \gdef#2{0}%
+  \def\@tempA{0}%
 \else
   \ifdim\@tdA>\z@
     \def\Segno{+}%
@@ -767,29 +1292,38 @@
     \@tdA=-\@tdA
   \fi
   \ifdim\@tdA=90\p@
-    \xdef#2{\Segno16383.99999}%
+    \def\@tempA{\Segno16383.99999}%
   \else
     \ifdim\@tdA<\p@
         \@tdA=\Segno0.0174533\@tdA
-        \DividE\@tdA by\p@ to#2%
+        \DividE\@tdA by\p@ to\@tempA%
     \else
       \g@tTanCotanFrom\@tdA to\T and\Tp
       \@tdA\Tp\p@ \advance\@tdA -\T\p@
-      \DividE\Segno2\p@ by\@tdA to#2%
+      \DividE\Segno2\p@ by\@tdA to\@tempA%
     \fi
   \fi
 \fi
-\endgroup\ignorespaces}%
+\edef\endTanOf{\noexpand\endgroup
+   \noexpand\def\noexpand#2{\@tempA}\noexpand\ignorespaces}%
+\endTanOf}%
 %    \end{macrocode}
 %
 % \subsection{Arcs and curves preliminary information}
 % We would like to define now a macro for drawing circular arcs of any radius
 % and any angular aperture; the macro should require the arc center, the
-% arc starting point and the angular aperture. The command should have the
-% following syntax:
+% arc starting point and the angular aperture. The arc has its reference point in
+% its center, therefore it does not need to be put in place by the command |\put|;
+% nevertheless if |\put| is used, it may displace the arc into another position.
+% The command should have the following syntax:
 % \begin{flushleft}\ttfamily
 % \cs{Arc}(\meta{{\rmfamily center}})(\meta{{\rmfamily starting
-%                 point}}){\meta{{\rmfamily angle}}}
+%                 point}}){\marg{{\rmfamily angle}}}
+% \end{flushleft}
+% which is totally equivalent to:
+% \begin{flushleft}\ttfamily
+% \string\put(\meta{\rmfamily center})\string{\string\Arc(0,0)(\meta{\rmfamily starting
+% point})\marg{\rmfamily angle}\string}
 % \end{flushleft}
 %  If the \meta{angle} is positive the arc runs counterclockwise from the
 % starting point; clockwise if it's negative.
@@ -808,12 +1342,12 @@
 % We need therefore macros for summing, subtracting, multiplying, dividing
 % complex numbers, for determining they directions (unit vectors); a unit vector
 % is the complex number divided by its magnitude so that the result is the
-% Cartesian form of the Euler's equation
+% Cartesian form of the Euler's formula
 % \[
 % \mathrm{e}^{\mathrm{j}\phi} = \cos\phi+\mathrm{j}\sin\phi
 % \]
 %
-% The magnitude of a vector id determined by taking a clever square root of a
+% The magnitude of a vector is determined by taking a clever square root of a
 % function of the real and the imaginary parts; see further on.
 %
 % It's better to represent each complex number with one control sequence; this
@@ -840,9 +1374,9 @@
 % then taken as the reference one so that, if $a$ is larger than $b$, the
 % square root of the sum of their squares is computed as such:
 % \[
-% M = \sqrt{a^2+b^2} = a\sqrt{1+(b/a)^2}
+% M = \sqrt{a^2+b^2} = \vert a\vert\sqrt{1+(b/a)^2}
 % \]
-% In this way the radicand never exceeds 2 and its is quite easy taking its
+% In this way the radicand never exceeds 2 and it is quite easy to get its
 % square root by means of the Newton iterative process; due to the quadratic
 % convergence, five iterations are more than sufficient. When one of the
 % components is zero, the Newton iterative process is skipped. The overall
@@ -858,9 +1392,10 @@
    \DividE\@tempdima by\@tempdimb to\@T
    \@tempdimc=\@tempdimb
 \fi
-\ifdim\@T\p@>\z@
+\ifdim\@T\p@=\z@
+\else
    \@tempdima=\@T\p@ \@tempdima=\@T\@tempdima
-   \advance\@tempdima\p@ %
+   \advance\@tempdima\p@%
    \@tempdimb=\p@%
    \@tempcnta=5\relax
    \@whilenum\@tempcnta>\z@\do{\DividE\@tempdima by\@tempdimb to\@T
@@ -885,8 +1420,8 @@
 \ifdim\@tempdimc=\z@\else
    \DividE\t@X\p@ by\@tempdimc to\t@X
    \DividE\t@Y\p@ by\@tempdimc to\t@Y
-   \MakeVectorFrom\t@X\t@Y to#2\relax
-\fi\ignorespaces}%
+\fi
+\MakeVectorFrom\t@X\t@Y to#2\ignorespaces}%
 %    \end{macrocode}
 %
 % A cumulative macro uses the above ones for determining with one call both the
@@ -899,7 +1434,10 @@
 \def\ModAndDirOfVect#1to#2and#3{%
 \GetCoord(#1)\t@X\t@Y
 \ModOfVect#1to#2%
-\DividE\t@X\p@ by\@tempdimc to\t@X \DividE\t@Y\p@ by\@tempdimc to\t@Y
+\ifdim\@tempdimc=\z@\else
+  \DividE\t@X\p@ by\@tempdimc to\t@X 
+  \DividE\t@Y\p@ by\@tempdimc to\t@Y
+\fi
 \MakeVectorFrom\t@X\t@Y to#3\ignorespaces}%
 %    \end{macrocode}
 % The next macro computes the magnitude and the direction of the difference of
@@ -910,25 +1448,25 @@
 % and is described further on.
 %    \begin{macrocode}
 \def\DistanceAndDirOfVect#1minus#2to#3and#4{%
-\SubVect#2from#1to\@tempa \ModAndDirOfVect\@tempa to#3and#4\relax
-\ignorespaces}%
+\SubVect#2from#1to\@tempa 
+\ModAndDirOfVect\@tempa to#3and#4\ignorespaces}%
 %    \end{macrocode}
 % We now have two macros intended to fetch just the real or, respectively, the
 % imaginary part of the input complex number.
 %    \begin{macrocode}
 \def\XpartOfVect#1to#2{%
-\GetCoord(#1)#2\@tempa
-\ignorespaces}%
+\GetCoord(#1)#2\@tempa\ignorespaces}%
 %
 \def\YpartOfVect#1to#2{%
-\GetCoord(#1)\@tempa#2\relax
-\ignorespaces}%
+\GetCoord(#1)\@tempa#2\ignorespaces}%
 %    \end{macrocode}
 % With the next macro we create a direction vector (second argument) from a
 % given angle (first argument).
 %    \begin{macrocode}
-\def\DirFromAngle#1to#2{\CosOf#1to\t@X%
-\SinOf#1to\t@Y\MakeVectorFrom\t@X\t@Y to#2\ignorespaces}%
+\def\DirFromAngle#1to#2{%
+\CosOf#1to\t@X
+\SinOf#1to\t@Y
+\MakeVectorFrom\t@X\t@Y to#2\ignorespaces}%
 %    \end{macrocode}
 %
 % Sometimes it is necessary to scale a vector by an arbitrary real factor; this
@@ -953,17 +1491,17 @@
 % addition:
 %    \begin{macrocode}
 \def\AddVect#1and#2to#3{\GetCoord(#1)\tu@X\tu@Y
-\GetCoord(#2)\td@X\td@Y \@tempdima\tu@X\p@
-\advance\@tempdima\td@X\p@ \Numero\t@X\@tempdima \@tempdima\tu@Y\p@
-\advance\@tempdima\td@Y\p@ \Numero\t@Y\@tempdima
+\GetCoord(#2)\td@X\td@Y 
+\@tempdima\tu@X\p@\advance\@tempdima\td@X\p@ \Numero\t@X\@tempdima 
+\@tempdima\tu@Y\p@\advance\@tempdima\td@Y\p@ \Numero\t@Y\@tempdima
 \MakeVectorFrom\t@X\t@Y to#3\ignorespaces}%
 %    \end{macrocode}
 % Then the subtraction:
 %    \begin{macrocode}
 \def\SubVect#1from#2to#3{\GetCoord(#1)\tu@X\tu@Y
-\GetCoord(#2)\td@X\td@Y \@tempdima\td@X\p@
-\advance\@tempdima-\tu@X\p@ \Numero\t@X\@tempdima \@tempdima\td@Y\p@
-\advance\@tempdima-\tu@Y\p@ \Numero\t@Y\@tempdima
+\GetCoord(#2)\td@X\td@Y 
+\@tempdima\td@X\p@\advance\@tempdima-\tu@X\p@ \Numero\t@X\@tempdima 
+\@tempdima\td@Y\p@\advance\@tempdima-\tu@Y\p@ \Numero\t@Y\@tempdima
 \MakeVectorFrom\t@X\t@Y to#3\ignorespaces}%
 %    \end{macrocode}
 %
@@ -971,18 +1509,18 @@
 % that we want to multiply by the second operand or by the complex conjugate of
 % the second operand; it would be nice if we could use the usual
 % postfixed asterisk notation for the complex conjugate, but I could not find
-%  a simple means for doing so; therefore I use the prefixed notation, that is
+% a simple means for doing so; therefore I use the prefixed notation, that is
 % I put the asterisk before the second operand. The first part of the
 % multiplication macro just takes care of the multiplicand and then checks for
 % the asterisk; if there is no asterisk it calls a second service macro that
-%  performs a regular complex multiplication, otherwise it calls a third
+% performs a regular complex multiplication, otherwise it calls a third
 % service macro that executes the conjugate multiplication.
 %    \begin{macrocode}
 \def\MultVect#1by{\@ifstar{\@ConjMultVect#1by}{\@MultVect#1by}}%
 %
 \def\@MultVect#1by#2to#3{\GetCoord(#1)\tu@X\tu@Y
-\GetCoord(#2)\td@X\td@Y \@tempdima\tu@X\p@
-\@tempdimb\tu@Y\p@
+\GetCoord(#2)\td@X\td@Y 
+\@tempdima\tu@X\p@ \@tempdimb\tu@Y\p@
 \@tempdimc=\td@X\@tempdima\advance\@tempdimc-\td@Y\@tempdimb
 \Numero\t@X\@tempdimc
 \@tempdimc=\td@Y\@tempdima\advance\@tempdimc\td@X\@tempdimb
@@ -1013,12 +1551,13 @@
 % \subsubsection{Arcs}
 % We start with tracing
 % a circular arc of arbitrary center, arbitrary starting point and arbitrary
-% aperture; The first macro checks the aperture; if this is not zero it
+% aperture; the first macro checks the aperture; if this is not zero it
 % actually proceeds with the necessary computations, otherwise it does
 % nothing.
 %    \begin{macrocode}
 \def\Arc(#1)(#2)#3{\begingroup
-\@tdA=#3\p@ \ifdim\@tdA=\z@\else
+\@tdA=#3\p@ 
+\ifdim\@tdA=\z@\else
   \@Arc(#1)(#2)%
 \fi
 \endgroup\ignorespaces}%
@@ -1039,7 +1578,7 @@
 % If the rotation angle is larger than $360^\circ$ a message is issued that
 % informs the user that the angle will be reduced modulo $360^\circ$; this
 % operation is performed by successive subtractions rather than with modular
-%  arithmetics on the assumption that in general one subtraction suffices.
+% arithmetics on the assumption that in general one subtraction suffices.
 %    \begin{macrocode}
 \Numero\@gradi\@tdA
 \ifdim\@tdA>360\p@
@@ -1143,16 +1682,16 @@
 % |\VerctorArc| draws an arrow at the ending point of the arc; the second macro
 % |\VectorARC| draws arrows at both ends; the arrows have the same shape as
 % those for vectors; actually they are drawn by putting a vector of zero
-% length at the proper arc end(s), therefore they are styled as traditional or
-% PostScript arrows according to the option of the \texttt{pict2e} package.
+% length at the proper arc end(s), therefore they are styled as traditional \LaTeX\
+% or PostScript arrows according to the option of the \texttt{pict2e} package.
 %
 % But the specific drawing done here shortens the arc so as not to overlap on
-% the arrow(s); the only or both arrows are also lightly tilted in order to
+% the arrow(s); the only arrow (or both ones) are also lightly tilted in order to
 % avoid the impression of a corner where the arc enters the arrow tip.
 %
 %  All these operations require a lot of ``playing'' with vector directions,
 % but even if the operations are numerous, they do not do anything else but:
-% (a) determining the end point and its direction ; (b) determining the arrow
+% (a) determining the end point and its direction; (b) determining the arrow
 % length as an angular quantity, i.e. the arc amplitude that must be subtracted
 % from the total arc to be drawn; (c) the direction of the arrow should be
 % corresponding to the tangent to the arc at the point where the arrow tip is
@@ -1179,19 +1718,20 @@
 \fi
 \endgroup\ignorespaces}%
 %    \end{macrocode}
-%  The single arrowed arc is defined with the following long macro where all the
+%
+% The single arrowed arc is defined with the following long macro where all the
 % described operations are performed more or less in the described succession;
 % probably the macro requires a little cleaning, but since it works fine I did
 % not try to optimize it for time or number of tokens. The final part of the
 % macro is almost identical to that of the plain arc; the beginning also is
 % quite similar. The central part is dedicated to the positioning of the arrow
 % tip and to the necessary calculations for determining the tip tilt and the
-% reduction of the total arc length;pay attention that the arrow length, stored in 
+% reduction of the total arc length; pay attention that the arrow length, stored in 
 % |\@tdE| is a real length, while the radius stored in |\@Raggio| is just a multiple
-% of the |\unitlength|, so that the division (that yields a good angular approximation
-% to the arrow length as seen from the center of the arc) must be done with real
-% lengths. The already defined |\@@Arc| macro actually draws the curved vector
-% stem without stroking it.
+% of the |\unitlength|, so that the division (that yields a good angular
+% approximation to the arrow length as seen from the center of the arc) must be done
+% with real lengths. The already defined |\@@Arc| macro actually draws the curved
+% vector stem without stroking it.
 %    \begin{macrocode}
 \def\@VArc(#1)(#2){%
 \ifdim\@tdA>\z@
@@ -1253,7 +1793,7 @@
 \@tdD=\DeltaGradi\p@ \@tdD=57.29578\@tdD \Numero\DeltaGradi\@tdD
 \@tdD=\ifx\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD
 \DirFromAngle\@tempa to\@Dir
-\MultVect\@V by\@Dir to\@sPun
+\MultVect\@V by\@Dir to\@sPun% corrects the end point
 \edef\@tempA{\ifx\Segno-\m@ne\else\@ne\fi}%
 \MultVect\@sPun by 0,\@tempA to\@vPun
 \DirOfVect\@vPun to\@Dir
@@ -1264,7 +1804,7 @@
 \DirFromAngle\@tempB to\@Dird
 \MultVect\@Dir by*\@Dird to\@Dir
 \GetCoord(\@Dir)\@xnum\@ynum
-\put(\@tdX,\@tdY){\vector(\@xnum,\@ynum){0}}%
+\put(\@tdX,\@tdY){\vector(\@xnum,\@ynum){0}}% arrow tip at the end point
 \@tdE =\DeltaGradi\p@
 \advance\@tdA -2\@tdE \Numero\@gradi\@tdA
 \CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
@@ -1274,9 +1814,9 @@
 \@tdE\ifx\Segno--\fi\DeltaGradi\p@
 \Numero\@tempB{0.5\@tdE}%
 \DirFromAngle\@tempB to\@Dird
-\MultVect\@vPun by\@Dird to\@vPun
+\MultVect\@vPun by\@Dird to\@vPun% corrects the starting point
 \DirOfVect\@vPun to\@Dir\GetCoord(\@Dir)\@xnum\@ynum
-\put(\@pPunX,\@pPunY){\vector(\@xnum,\@ynum){0}}
+\put(\@pPunX,\@pPunY){\vector(\@xnum,\@ynum){0}}% arrow tip at the starting point
 \edef\@tempa{\ifx\Segno--\fi\DeltaGradi}%
 \DirFromAngle\@tempa to \@Dir
 \SubVect\@Cent from\@pPun to\@V
@@ -1301,7 +1841,7 @@
 % to draw almost anything. It traces a single Bézier spline from a first point
 % where the tangent direction is specified to a second point where again it is
 % specified the tangent direction. Actually this is a special (possibly useless)
-% case where the general |\Curve| macro could do the same or a better job. In
+% case where the general |\curve| macro could do the same or a better job. In
 % any case\dots
 %    \begin{macrocode}
 \def\CurveBetween#1and#2WithDirs#3and#4{%
@@ -1309,7 +1849,7 @@
 \CurveTo#2WithDir{#4}\CurveFinish}%
 %    \end{macrocode}
 %
-%  Actually the above macro is a special case of concatenation of the triplet
+% Actually the above macro is a special case of concatenation of the triplet
 % formed by macros |\StartCurve|, |\CurveTo| and|\CurveFinish|; the second of
 % which can be repeated an arbitrary number of times.
 %
@@ -1452,8 +1992,7 @@
   \fi
 %    \end{macrocode}
 % \dots\ from when the ``left'' direction is not perpendicular to the chord; it
-% might
-% be  parallel and we must distinguish the cases for the other direction~\dots
+% might be  parallel and we must distinguish the cases for the other direction~\dots
 %    \begin{macrocode}
 \else
   \ifdim\@Xpuno\p@=\z@
@@ -1464,9 +2003,7 @@
      \ifdim\@Ypzero\p@=\z@
        \@tdA=0.333333\p@
        \Numero\@Mcpzero{\@Chord\@tdA}%
-       \ifdim\@Ypuno\p@=\z@
-            \edef\@Mcpuno{\@Mcpzero}%
-       \fi
+       \edef\@Mcpuno{\@Mcpzero}% 
 %    \end{macrocode}
 % \dots\ from when the left direction is oblique and the other direction is
 % either parallel to the chord~\dots
@@ -1491,7 +2028,7 @@
          \fi
 %    \end{macrocode}
 % The control sequence |\@Dwpuno| contains the right direction for forming the
-% triangle; we cam make the weighed subdivision of the chord according to the
+% triangle; we can make the weighed subdivision of the chord according to the
 % horizontal components of the directions; we eventually turn negative values
 % to positive ones since we are interested in the magnitudes of the control
 % vectors.
@@ -1506,7 +2043,7 @@
          \@tdD=\p@ \advance\@tdD-\@Fact\p@
          \ifdim\@tdD<\z@ \@tdD=-\@tdD\fi
 %    \end{macrocode}
-%  before dividing by the denominator we have to check the directions, although
+% Before dividing by the denominator we have to check the directions, although
 % oblique to the chord are not parallel to one another; in this case there is
 % no question of a weighed subdivision of the chord
 %    \begin{macrocode}
@@ -1531,7 +2068,7 @@
 % Now we have all data we need and we determine the positions of the control
 % points; we do not work any more on the rotated diagram of the horizontal
 % chord, but we operate on the original points and directions; all we had to
-% compute, after all, were the distances of the control point along the
+% compute, after all, were the distances of the control points along the
 % specified directions; remember that the ``left'' control point is along the
 % positive ``left'' direction, while the ``right'' control point precedes the
 % curve node along the ``right'' direction, so that a vector subtraction must
@@ -1581,15 +2118,15 @@
 % regular parentheses while direction components are grouped within angle
 % brackets. The first call of the macro initializes the drawing process and
 % checks for the next node and direction; if a second node is missing, it issues
-% a warning message and does not draw anything. The second macro defines the
-% path to the next point and checks for another node; if the next list item is
-% a square bracket delimited argument, it interprets it as a change of
-% direction, while if it is another parenthesis delimited argument it interprets
-% it as a new node-direction specification;
-% if the node and direction list is terminated, it issues the stroking command
-% and exits the recursive process. The |@ChangeDir| macro is just an interface
-% for executing the regular |\ChangeDir| macro, but also for recursing again by
-% recalling |\@Curve|.
+% a warning message and does not draw anything. It does not check for a change in
+% direction, because it would be meaningless at the beginning of a curve.
+% The second macro defines the path to the next point and checks for another node;
+% if the next list item is a square bracket delimited argument, it interprets it as
+% a change of direction, while if it is another parenthesis delimited argument it
+% interprets it as a new node-direction specification; if the node and direction
+% list is terminated, it issues the stroking command and exits the recursive
+% process. The |@ChangeDir| macro is just an interface for executing the regular
+% |\ChangeDir| macro, but also for recursing again by recalling |\@Curve|.
 %    \begin{macrocode}
 \def\Curve(#1)<#2>{%
     \StartCurveAt#1WithDir{#2}%
diff --git a/Master/texmf-dist/source/latex/curve2e/curve2e.ins b/Master/texmf-dist/source/latex/curve2e/curve2e.ins
deleted file mode 100644
index b16bd21a1c0..00000000000
--- a/Master/texmf-dist/source/latex/curve2e/curve2e.ins
+++ /dev/null
@@ -1,42 +0,0 @@
-%%

-%% --------------- start of docstrip commands ------------------

-%%

-\def\batchfile{curve2e.ins}

-\input docstrip.tex

-\preamble

-

-Copyright 2005 Claudio Beccari All rights reserved.

-

- This system is distributed in the hope that it will be useful,

- but WITHOUT ANY WARRANTY; without even the implied warranty of

- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

-

-

-IMPORTANT NOTICE:

-

-This work may be distributed and/or modified under the

-conditions of the LaTeX Project Public License, either version 1.3

-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 1.3 or later is part of all distributions of LaTeX

-version 2003/12/01 or later.

-

-This work has the LPPL maintenance status "author-maintained".

-

-This work consists of all files listed in manifest.txt.

-

-

-If you receive only some of these files from someone, complain!

-

-\endpreamble

-\def\batchfile{curve2e.dst}      % ignored in distribution

-\input docstrip.tex           % ignored in distribution

-

-\keepsilent

-

-\Msg{*** Generating package curve2e ***}

-

-\generateFile{curve2e.sty}{t}{\from{curve2e.dtx}{package}}

-

-\endinput