curve2e (29jun15)

git-svn-id: svn://tug.org/texlive/trunk@37708 c570f23f-e606-0410-a88d-b1316a301751

5 files changed, 680 insertions, 187 deletions

diff --git a/Master/texmf-dist/doc/latex/curve2e/README b/Master/texmf-dist/doc/latex/curve2e/README
index a1390fa48ec..3a0800ebf63 100644
--- a/Master/texmf-dist/doc/latex/curve2e/README
+++ b/Master/texmf-dist/doc/latex/curve2e/README
@@ -1,6 +1,6 @@
 Curve2e.sty
-version: 1.50
-filedate: 19 June 2015
+version: 1.54
+filedate: 27 June 2015
 
 This file is an extension of the package pict2e.sty which extends the standard  picture LaTeX environment according to what Leslie Lamport specified in the second edition of his LaTeX manual.
 
diff --git a/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf b/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf
index aa8c5dd79ff..23b401b7417 100644
--- a/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf
+++ b/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf
diff --git a/Master/texmf-dist/doc/latex/curve2e/manifest.txt b/Master/texmf-dist/doc/latex/curve2e/manifest.txt
index 04b8fefba5d..b717de9f259 100644
--- a/Master/texmf-dist/doc/latex/curve2e/manifest.txt
+++ b/Master/texmf-dist/doc/latex/curve2e/manifest.txt
@@ -21,7 +21,7 @@ Therefore, according to the licence, you are entitled to modify this package,
 as long as you fulfil the few conditions set forth by the Licence.
 
 Nevertheless this package is an extension to the standard LaTeX package pict2e 
-(2011). Therefore  any change must be controlled  against the parent package 
+(2014). Therefore  any change must be controlled  against the parent package 
 pict2e so as to avoid redefining what has already been incorporated in the 
 official package. 
 
diff --git a/Master/texmf-dist/source/latex/curve2e/curve2e.dtx b/Master/texmf-dist/source/latex/curve2e/curve2e.dtx
index 7e5e7bae80f..55ef4c3f96b 100644
--- a/Master/texmf-dist/source/latex/curve2e/curve2e.dtx
+++ b/Master/texmf-dist/source/latex/curve2e/curve2e.dtx
@@ -57,7 +57,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 %</driver>
 %<+package>\ProvidesPackage{curve2e}%
 %<*package>
-        [2015/06/19 v.1.50 Extension package for pict2e]
+        [2015/06/27 v.1.54 Extension package for pict2e]
 %</package>
 %<*driver>
 \documentclass{ltxdoc}\errorcontextlines=9
@@ -76,16 +76,28 @@ and the derived files curve2e.sty and curve2e.pdf.
 \renewcommand\marg[1]{\texttt{\{\meta{#1}\}}}
 \providecommand\oarg{}
 \renewcommand\oarg[1]{\texttt{[\meta{#1}]}}
+\providecommand\aarg{}
+\renewcommand*\aarg[1]{\texttt{<\meta{#1}>}}
 \providecommand\parg{}
-\renewcommand\parg[1]{\texttt{(#1)}}
+\renewcommand\parg[1]{\texttt{(\meta{#1})}}
 \makeatletter
+
 \newcommand*\Pall[1][1.5]{\def\circdiam{#1}\@Pall}
    \def\@Pall(#1){\put(#1){\circle*{\circdiam}}}
+
 \def\legenda(#1,#2)#3{\put(#1,#2){\setbox3333\hbox{$#3$}%
    \dimen3333\dimexpr\wd3333*\p@/\unitlength +3\p@\relax
    \edef\@tempA{\strip@pt\dimen3333}%
    \framebox(\@tempA,7){\box3333}}}
-\def\Zbox(#1)[#2]#3{\put(#1){\makebox(0,0)[#2]{$#3$}}}
+   
+\def\Zbox(#1){\bgroup\edef\@tempA{#1}\@Zbox}
+
+\newcommand*\@Zbox[2][]{\fboxrule\z@\fboxsep=0.75ex\relax
+\setbox2575\hbox{\fbox{$\relax\rule[-0.5ex]{0pt}{2.5ex}#2\relax$}}\relax
+\ifx\@tempB\empty
+\put(\@tempA){\makebox(0,0){\box2575}}\else
+\put(\@tempA){\makebox(0,0)[#1]{\box2575}}\fi\egroup\ignorespaces}
+
 \begin{document}
 \maketitle
 \columnseprule=0.4pt
@@ -97,7 +109,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 %</driver>
 % \fi
 %
-% \CheckSum{2756}
+% \CheckSum{3078}
 % \begin{abstract}
 % This file documents the |curve2e| extension package to the recent
 % implementation of the |pict2e| bundle that has been described by Lamport
@@ -242,7 +254,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % version fills up the interior of the curve with the currently specified color.
 %^^A
 % \item |\Curve| is a recursive macro that can draw an unlimited (reasonably
-% low) number of connecter Bézier spline arcs with continuos tangents except
+% low) number of connected Bézier spline arcs with continuos tangents except
 % for cusps; these arcs require only the specification of te tangent
 % direction at the interpolation nodes. It is possible to use a lower level
 % macro |\CbezierTo| that does the same but lets the user specify the control
@@ -333,8 +345,8 @@ and the derived files curve2e.sty and curve2e.pdf.
 % 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
+% 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}\\
@@ -353,7 +365,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % command |\segment(3,4)(28,19)| achieves the same result without the need of
 % 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
+% shown that the commands intended to join two specified coordinates are
 % particularly useful.
 %^^A
 % \item The |\polyline| command has been introduced: it accepts an unlimited
@@ -361,8 +373,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % draws a sequence of connected segments that joins in order the specified
 % points; the syntax is:
 %	\begin{flushleft}
-%\cs{polyline}\texttt{[}\marg{optional join style}\texttt{]%
-%(}\meta{$P_1$}\texttt{)(}\meta{$P_2$}\texttt{)...(}\meta{$P_n$}\texttt{)}
+%\cs{polyline}\oarg{optional join style}\parg{$P_1$}\parg{$P_2$}\texttt{...}\parg{$P_n$}
 %	\end{flushleft}
 % See figure~\ref{fig:polyline} where a regular pentagon is drawn; usage of polar
 % coordinates is also shown.
@@ -397,7 +408,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 %^^A
 % \item The new command |\Dashline| (alias: |\Dline| for backwards compatibility)
 % \begin{flushleft}
-% |\Dashline(|\meta{first point}|)(|\meta{second point}|){|\meta{dash length}|}|
+% |\Dashline|\parg{first point}\parg{second point}\marg{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
@@ -446,7 +457,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 %\item Analogous to |\Dashline|, a new command |\Dotline| draws a dotted line with
 % the syntax:
 % \begin{flushleft}
-% |\Dotline(|\meta{first point}|)(|\meta{end point}|){|\meta{dot gap}|}|
+% |\Dotline|\parg{first point}\parg{end point}\marg{dot gap}
 % \end{flushleft}
 % See figures~\ref{fig:dashline} and~\ref{fig:dottedlines} for  examples.
 %^^A
@@ -482,11 +493,11 @@ and the derived files curve2e.sty and curve2e.pdf.
 % 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}
+%      \cs{SinOf}\meta{angle}\texttt{to}\meta{control sequence}
 %\\
-%      \texttt{\char92CosOf}\meta{angle}\texttt{to}\meta{control sequence}
+%      \cs{CosOf}\meta{angle}\texttt{to}\meta{control sequence}
 %\\
-%      \texttt{\char92TanOf}\meta{angle}\texttt{to}\meta{control sequence}
+%      \cs{TanOf}\meta{angle}\texttt{to}\meta{control sequence}
 %\end{flushleft}
 % The \meta{control sequence} may then be used as a multiplying factor of a
 % length.
@@ -494,12 +505,9 @@ and the derived files curve2e.sty and curve2e.pdf.
 % \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}\\
+% \cs{Arc}\parg{center}\parg{starting point}\marg{angle}\\
+% \cs{VectorArc}\parg{center}\parg{starting point}\marg{angle}\\
+% \cs{VectorARC}\parg{center}\parg{starting point}\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
@@ -543,11 +551,12 @@ and the derived files curve2e.sty and curve2e.pdf.
 % \meta{vector macro} means a macro the contains a comma separated pair of
 % fractional numbers; \meta{angle macro} means a macro that contains the angle
 % of a vector in sexagesimal degrees; \meta{argument} means a brace delimited
-% numeric value, possibly a macro; \textit{macro} is a valid macro name, that
+% numeric value, even a macro; \textit{macro} is a valid macro name, that
 % is a backslash followed by letters, or anything else that can receive a
 % definition. A `direction' of a vector is its versor; the angle of a vector
-% is the angle between the vector and the positive $x$ axis, generally directly
-% used in the Euler formula $ \vec{v} = Me^{\mathrm{j}\varphi}$.
+% is the angle between the vector and the positive $x$ axis in counterclockwise
+% direction, generally directly used in the Euler formula $ \vec{v} =
+% Me^{\mathrm{j}\varphi}$.
 %
 % {\footnotesize\begin{itemize}
 % \item |\MakeVectorFrom|\meta{two arguments}|to|\meta{vector macro}
@@ -579,12 +588,12 @@ and the derived files curve2e.sty and curve2e.pdf.
 % nodes. This macro is |\Curve| and must be followed by an ``unlimited''
 % sequence of node-direction coordinates as a quadruple defined as
 %\[
-% \texttt{(}\meta{node coordinates}\texttt{)<}\meta{direction vector}\texttt{>}
+% \parg{node coordinates}\aarg{direction vector}
 %\]
 % 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
 %\[
-% \texttt{...(...)<...>[}\meta{new direction vector}\texttt{](...)<...>...}
+% \mbox{\dots\parg{...}\aarg{...}\oarg{new direction vector}\parg{...}\aarg{...}\dots}
 %\]
 % 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
@@ -719,8 +728,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % \begin{thebibliography}{9}
 % \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.
+% package}, 2014, PDF documentation of \texttt{pict2e} is part of any modern complete distribution of the \TeX\ system. In case of a basic or partial system installation, the package may be installed by means of the specific facilities of the distribution. It may be read by means of the line command \texttt{texdoc pict2e}.
 % \end{thebibliography}
 % }
 %
@@ -809,7 +817,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % $x_1, y_1$ 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  in all other languages the comma
+% non-English speaking users, since in all other languages the comma
 % must be used as the decimal separator.
 %
 % The |\line| macro is redefined by making use of a new division routine that
@@ -968,7 +976,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 %\label{fig:dashedlines}
 %\end{figure}
 %
-% A simpler |\Dotline| macro can draw a dotted line between to given points; 
+% A simpler |\Dotline| macro can draw a dotted line between two given points; 
 % the dots are rather small, therefore the inter dot distance is computed in
 % such a way as to have the first and the last dot at the exact position of
 % the dotted-line end-points; again the specified dot distance is nominal in
@@ -1283,29 +1291,30 @@ and the derived files curve2e.sty and curve2e.pdf.
 % \subsection{Polylines}
 % We now define the polygonal line macro; its syntax is very simple
 % \begin{flushleft}
-% \cs{polygonal}\texttt{(}$P_0$\texttt{)(}$P_1$\texttt{)(}$P_2$)%
+% \cs{polygonal}\oarg{join}\texttt{(}$P_0$\texttt{)(}$P_1$\texttt{)(}$P_2$)%
 %  \texttt{\dots(}$P_n$\texttt{)}
 % \end{flushleft}
+% Remember: |\polyline| has been incorporated into |pict2e| 2009, but we
+% redefine it so as to allow an optional argument to specify the line join type.
+%
 % 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
 % unmatched delimiters, so we define an alias also for the right parenthesis.
 %    \begin{macrocode}
 \let\lp@r( \let\rp@r)
 %    \end{macrocode}
-% The first call to |\polyline| examines the first point coordinates and moves
-% the drawing position to this point; afterwards it looks for the second point
-% coordinates; they start with a left parenthesis; if this is found the
-% coordinates should be there, but if the left parenthesis is missing (possibly
-% 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 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 specify the line join type.
+% The first call to |\polyline|, besides setting the line joints, examines
+% the first point coordinates and moves the drawing position to this point;
+% afterwards it looks for the second point coordinates; they start with a
+% left parenthesis; if this is found the coordinates should be there, but
+% if the left parenthesis is missing (possibly 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 not necessarily
+% is put in position through a |\put| command that provides to eliminate any
+% spurious spaces preceding this command.
 %
 % In order to allow a specification for the joints of the various segments of
 % a polygonal line it is necessary to allow for an optional parameter; the default
@@ -1397,7 +1406,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % 32-bit word contains the dimension in \emph{scaled points}, where 1\,pt
 % equals $2^{16}$\,sp.
 %
-% Since the number of digits of the fractional part is constant (16) it is said
+% Since the number of bits of the fractional part is constant (16) it is said
 % that the number representation is in \emph{fixed radix}. This is much
 % different form the scientific approach to fractional numbers where
 % a 32-bit word reserves 24 bits to the significant digits, one bit for the sign,
@@ -1430,7 +1439,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % would require a lot of time for their execution; this is a serious problem
 % with package |pgfplots| with which it is possible to draw beautiful 2D and
 % 3D color diagrams, but at the expense of even dozens of seconds of computation
-% time instead of microseconds.
+% time instead of milliseconds.
 %
 % \subsection{The new division macro}
 % The most important macro in the whole package is the division
@@ -1491,9 +1500,9 @@ and the derived files curve2e.sty and curve2e.pdf.
 % 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 and the termination of the program. During the division
-% and a scaling down by 16 bits, the result is not simply truncated, but it is
-% rounded to the nearest integer (in scaled points). The first two operands
+% suitable error messages but not the termination of the program. During the
+% division and a scaling down by 16 bits, the result is not simply truncated, but
+% it is rounded to the nearest integer (in scaled points). The first two operands
 % are lengths and the third is a macro.
 %
 %    \begin{macrocode}
@@ -1535,6 +1544,7 @@ and the derived files curve2e.sty and curve2e.pdf.
            \noexpand\egroup\noexpand\def\noexpand#3{%
              \strip@pt\dimexpr\@DimA*\@DimB/\p@\relax}}%
         \x\ignorespaces}%
+        \let\MultiplyFN\MultiplY
     \fi
 \fi
 %    \end{macrocode}
@@ -1585,7 +1595,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % converted to radians) is so small (about 0.017) that the sine and tangent
 % can be freely approximated with $y$ itself (the error being smaller than
 % approximately $10^{-6}$), while the cosine can be freely approximated with
-% the formula $1-0.5y^2$ (the error being smaller than about $\cdot10^{-6}$).
+% the formula $1-0.5y^2$ (the error being smaller than about $10^{-6}$).
 %
 % We keep using grouping so that internal variables are local to these groups
 % and do not mess up other things.
@@ -1602,7 +1612,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % Computations are done with the help of counter |\I|, of the length |\@tdB|,
 % and the auxiliary control sequences |\Tan| and |\Cot| whose meaning is
 % transparent. The iterative process controlled by |\@whilenum| implements the
-% (truncated) continued fraction expansion of the tangent function.
+% (truncated) continued fraction expansion of the tangent function:
 % \[
 % \tan x = \frac{1}{\displaystyle \frac{1\mathstrut}{\displaystyle x}
 %     -\frac{1}{\displaystyle \frac{3\mathstrut}{\displaystyle x}
@@ -1795,9 +1805,8 @@ and the derived files curve2e.sty and curve2e.pdf.
 %
 % The results obtainable with equation~\eqref{equ:tanfimezzi} are possibly
 % acceptable, but the square that must be computed in it tends to go in
-% underflow if too many iterations are performed and the algorythim crashes;
-% therefore it's virtually impossibile to get more than three correct digits
-% after the decimal separator.
+% underflow if too many iterations are performed and the algorithm crashes;
+% therefore it's virtually impossibile to get an absolute error lower than 0.0005.
 % 
 % It is probably better to refer to the Newton iterations for solving the
 % equation:
@@ -1805,39 +1814,40 @@ and the derived files curve2e.sty and curve2e.pdf.
 % \tan\theta -\tan\theta_\infty= 0
 %\end{equation}
 % in the unknown $\theta$ given the value $t=\tan\theta_\infty$; see
-% figure~\ref{fig:tangenti}.
-%
-%\begin{figure}\centering\unitlength=0.007\textwidth
-%\begin{picture}(100,60)
+% figure~\ref{fig:tangenti}%
+%\begin{figure}[!htb]\centering\unitlength=0.01\textwidth
+%\begin{picture}(100,80)
 %\legenda(15,73){y=\tan\theta}
-%\legenda(35,73){t=\tan\theta_\infty}
-%\put(0,0){\vector(1,0){100}}\Zbox(100,1)[br]{\theta}
-%\put(0,0){\vector(0,1){80}}\Zbox(1,80)[tl]{y}
-%\Dashline(75,0)(75,80){2.5}
-%\put(76,1){\makebox(0,0)[bl]{$\pi/2$}}
+%\legenda(37,73){t=\tan\theta_\infty}
+%\put(0,0){\vector(1,0){100}}\Zbox(100,0)[br]{\theta}
+%\put(0,0){\vector(0,1){80}}\Zbox(0,80)[tl]{y}
+%\Dashline(90,0)(90,80){2.5}
+%\Zbox(90,0)[br]{\pi/2}
+%\Pall[2](28.8,11)\Line(0,11)(80,11)%\Dashline(28.8,0)(28.8,11){2.5}
+%\Zbox(0,11)[bl]{t}\Zbox(28.8,0)[br]{\theta_\infty}
+%
+%\Dashline(34,0)(34,11){1.5}\Zbox(34,0)[bl]{\theta_{i+1}}
+%
+%\Pall[2](47.5,21.83)\Dashline(47.5,0)(47.5,21.83){2.5}
+%\Dashline(0,21.83)(47.5,21.83){2.5}
+%\Zbox(0,20.83)[bl]{y_i}\Zbox(47.5,0)[bl]{\theta_{i}}
+%
+%\Pall[2](61.2,36.38)\Dashline(61.2,0)(61.2,36.38){2.5}
+%\Dashline(0,36.38)(61.2,36.38){2.5}
+%\Zbox(0,36.38)[bl]{y_{i-1}}\Zbox(61.2,0)[bl]{\theta_{i-1}}
+%
+%\Pall[2](72,61.55367)\Dashline(72,0)(72,61.55367){2.5}
+%\Dashline(0,61.55367)(72,61.55367){2.5}
+%\Zbox(0,61.55367)[bl]{y_{i-2}}\Zbox(72,0)[bl]{\theta_{i-2}}
+%
 %\put(0,0){\linethickness{1pt}
-%\Curve(0,0)<1,0.8>(24,20)<1,0.90>(51,49.5)<17,29,5>(60,70)<1,5>(62,80)<1,8>}
-%\put(51,49.5){\circle*{2}}
-%\Dashline(51,0)(51,49.5){2.5}
-%\put(52,1){\makebox(0,0)[bl]{$\theta_{i-1}$}}
-%\Dashline(0,49.5)(51,49.5){2.5}
-%\put(1,51){\makebox(0,0)[bl]{$y_{i-1}$}}
-%\put(0,20){\line(1,0){70}}\put(1,21){\makebox(0,0)[bl]{$t$}}
-%\Line(34,20)(51,49.25)
-%\Line(60.15,70)(51,20)
-%\put(51,20){\circle*{2}}\put(60,70){\circle*{2}}
-%\Dashline(60,0)(60,70){2.5}
-%\put(61,1){\makebox(0,0)[bl]{$\theta_{i-2}$}}
-%\Dashline(0,70)(60,70){2.5}
-%\put(1,71){\makebox(0,0)[bl]{$y_{i-2}$}}
-%\put(34,20){\circle*{2}}\put(34,29.5){\circle*{2}}
-%\Dashline(34,0)(34,29.5){2.5}
-%\Dashline(0,29.5)(34,29.5){2.5}
-%\put(1,30.5){\makebox(0,0)[bl]{$y_i$}}
-%\put(35,1){\makebox(0,0)[bl]{$\theta_{i}$}}
-%\put(24,20){\circle*{2}}
-%\Dashline(24,0)(24,20){2.5}
-%\put(25,1){\makebox(0,0)[bl]{$\theta_\infty$}}
+%\Curve%(0,0)<1,0.34907>(28.8,11)<1,0.45456>(47.5,21.83)<1,0.76479>%
+%(61.2,36.38)<1,1.91499>(72,61.55367)<1,4.65428>(74.4,71.6)<1,6.14571>
+%}%
+%
+%\Line(34,11)(47.5,21.83)
+%\Line(61.2,36.38)(47.5,11)
+%\Line(72,61.55367)(61.2,11)
 %\end{picture}
 %\caption{Newton's method of tangents}\label{fig:tangenti}
 %\end{figure}
@@ -1859,18 +1869,28 @@ and the derived files curve2e.sty and curve2e.pdf.
 % already have the algorithms for computing both the tangent and the cosine;
 % such Newton iterative method does not set forth any problem, especially if we
 % use the properties of the trigonometric functions and we confine the
-% computations to the first quadrant.
+% computations to the first quadrant; possibly we limit the computations
+% to the first octant and we resort to the cotangent when the tangent exceeds
+% one; in this case we use the same algorithm, but we have to get the 
+% complementary angle; in order to make computations with positive numbers,
+% we save the initial tangent sign and we restore it to the result.
 %    \begin{macrocode}
 \def\ArcTanOf#1to#2{\bgroup
+\countdef\Inverti 4444\Inverti=0
+\def\Segno{}
 \edef\@tF{#1}\@tdF=\@tF\p@ \@tdE=57.295778\p@
-\@tdD=\ifdim\@tdF>\z@ \@tdF\else -\@tdF\fi
+\@tdD=\ifdim\@tdF<\z@ -\@tdF\def\Segno{-}\else\@tdF\fi
+\ifdim\@tdD>\p@ 
+\Inverti=\@ne
+\@tdD=\dimexpr\p@*\p@/\@tdD\relax 
+\fi
 \unless\ifdim\@tdD>0.02\p@
-    \def\@tX{\strip@pt\dimexpr57.295778\@tdF\relax}%
+    \def\@tX{\strip@pt\dimexpr57.295778\@tdD\relax}%
 \else
     \edef\@tX{45}\relax
-    \countdef\I 2523 \I=8\relax
+    \countdef\I 2523 \I=9\relax
     \@whilenum\I>0\do{\TanOf\@tX to\@tG
-    \edef\@tG{\strip@pt\dimexpr\@tG\p@-\@tdF\relax}\relax
+    \edef\@tG{\strip@pt\dimexpr\@tG\p@-\@tdD\relax}\relax
     \MultiplY\@tG by57.295778to\@tG
     \CosOf\@tX to\@tH
     \MultiplY\@tH by\@tH to\@tH
@@ -1878,7 +1898,10 @@ and the derived files curve2e.sty and curve2e.pdf.
     \edef\@tX{\strip@pt\dimexpr\@tX\p@ - \@tH\p@\relax}\relax
     \advance\I\m@ne}%
 \fi
-\edef\x{\egroup\noexpand\edef\noexpand#2{\@tX}}\x\ignorespaces}%
+\ifnum\Inverti=\@ne
+\edef\@tX{\strip@pt\dimexpr90\p@-\@tX\p@\relax}
+\fi
+\edef\x{\egroup\noexpand\edef\noexpand#2{\Segno\@tX}}\x\ignorespaces}%
 %    \end{macrocode} 
 %
 % \subsection{Arcs and curves preliminary information}
@@ -1938,7 +1961,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % roto-amplification operator that scales its operand and rotates it about
 % a pivot point; besides the usual conventional representation used by the
 % mathematicians where the ordered pair is enclosed in round parentheses
-% (which is in perfect agreement with the standard code use by the |picture|
+% (which is in perfect agreement with the standard code used by the |picture|
 % environment) there is the other conventional representation used by the
 % engineers that stress the roto-amplification nature of a complex number:
 %\[
@@ -2049,7 +2072,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 \MakeVectorFrom\t@X\t@Y to#2\ignorespaces}%
 %    \end{macrocode}
 %
-% A cumulative macro uses the above ones for determining with one call both the
+% A cumulative macro uses the above ones to determine with one call both the
 % magnitude and the direction of a complex number. The first argument is the
 % input complex number, the second its magnitude, and the third is again a
 % complex number normalized to unit magnitude (unless the input was the null
@@ -2148,43 +2171,12 @@ and the derived files curve2e.sty and curve2e.pdf.
 \edef\x{\noexpand\egroup\noexpand\edef\noexpand#2{\ArcTan}}%
 \x\ignorespaces}
 %    \end{macrocode}
-%^^A  \begin{tabular}{ll}
-%^^A  0		& \ArcTanOf 0 to\Res \Res\\
-%^^A  0.01		& \ArcTanOf 0.01 to\Res \Res\\
-%^^A  0.02		& \ArcTanOf 0.02 to\Res \Res\\
-%^^A  0.04		& \ArcTanOf 0.04 to\Res \Res\\
-%^^A  0.05		& \ArcTanOf 0.05 to\Res \Res\\
-%^^A  0.06		& \ArcTanOf 0.06 to\Res \Res\\
-%^^A  0.09		& \ArcTanOf 0.09 to\Res \Res\\
-%^^A  0.1		& \ArcTanOf 0.1 to\Res \Res\\
-%^^A  0.2		& \ArcTanOf 0.2 to\Res \Res\\
-%^^A  0.4		& \ArcTanOf 0.4 to\Res \Res\\
-%^^A  0.5		& \ArcTanOf 0.5 to\Res \Res\\
-%^^A  0.6		& \ArcTanOf 0.6 to\Res \Res\\
-%^^A  0.8		& \ArcTanOf 0.8 to\Res \Res\\
-%^^A  0.707	& \ArcTanOf 0.707 to\Res \Res\\
-%^^A  1		& \ArcTanOf 1 to\Res \Res\\
-%^^A  2		& \ArcTanOf 2 to\Res \Res\\
-%^^A  \end{tabular}
-% 
-% \bigskip
-%
-%^^A \begin{tabular}{rl}
-%^^A 0,0		& \ArgOfVect0,0to\Res \Res\\
-%^^A 1,0		& \ArgOfVect1,0to\Res \Res\\
-%^^A -1,0		& \ArgOfVect-1,0to\Res \Res\\
-%^^A 0,1		& \ArgOfVect0,1to\Res \Res\\
-%^^A 0,-1		& \ArgOfVect0,-1to\Res \Res\\
-%^^A 1,1		& \ArgOfVect1,1to\Res \Res\\
-%^^A 1,-1		& \ArgOfVect1,-1to\Res \Res\\
-% ^^A-1,1		& \ArgOfVect-1,1to\Res \Res\\
-% ^^A-1,-1		& \ArgOfVect-1,-1to\Res \Res\\
-%^^A \end{tabular}
-% It is worth noting that the absolute error in these computations is lower
-% than 0.0001°; pretty satisfactory since the typesetting engines work in
-% fixed radix notation with 16 fractional binary digits, and an error on
-% the fifth fractional decimal digit is almost the best it can be expected
-% from this kind of arithmetics. 
+%
+% It is worth noting that the absolute average error in these computations is 
+% much lower than 0.0001°; pretty satisfactory since the typesetting engines work
+% in fixed radix notation with 16 fractional binary digits, and an error on
+% the fourth  or fifth fractional decimal digit is almost the best it can be
+% expected from this kind of arithmetics. 
 %
 % Sometimes it is necessary to scale a vector by an arbitrary real factor; this
 % implies scaling both the real and imaginary part of the input given vector.
@@ -2312,7 +2304,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 \CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
 %    \end{macrocode}
 % From now on it's better to define a new macro that will be used also in the
-% subsequent macros that trace arcs; here we already have the starting point
+% subsequent macros that draw arcs; here we already have the starting point
 % coordinates and the angle to draw the arc, therefore we just call the new
 % macro, stroke the line and exit.
 %    \begin{macrocode}
@@ -2320,7 +2312,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 \strokepath\ignorespaces}%
 %    \end{macrocode}
 % And the new macro |\@@Arc| starts with moving the drawing point to the first
-% point and does everything needed for tracing the requested arc, except
+% point and does everything needed for drawing the requested arc, except
 % stroking it; I leave the \texttt{stroke} command to the completion of the
 % calling macro and nobody forbids to use the |\@@Arc| macro for other purposes.
 %    \begin{macrocode}
@@ -2604,31 +2596,87 @@ and the derived files curve2e.sty and curve2e.pdf.
 % straight arrow tip if this one is large in comparison to the arc radius.
 %
 % \subsection{General curves}
+% The most used method to draw curved lines with computer programs is to
+% connect several simple curved lines, general ``arcs'', one to another
+% generally maintaining the same tangent at the junction. I the direction
+% changes we are dealing with a cusp.
+%
+% The simple general arcs that are directly implemented in every program that
+% display typeset documents, are those drawn with the parametri curves called
+% \emph{Béźier splines}; given a sequence of points in the $x,y$ plane, say
+% $P_0, P_1, P_2, p_3, \dots$ (represented as coordinate pairs, i.e. by complex
+% numbers), the most common Bézier splines are the following ones:
+% \begin{align}
+% \mathcal{B}_1 &= P_0(1-t) + P_1t               \label{equ:B-1}      \\
+% \mathcal{B}_2 &= P_0(1-t)^2 + P_1 2(1-t)t + P_2t^2 \label{equ:B-2}  \\
+% \mathcal{B}_3 &= P_0(1-t)^3 + P_1 3(1-t)^2t +P_2 3(1-t)t^2 +P_3t^3
+% \label{equ:B-3}
+% \end{align}
+%
+% All these splines depend on parameter $t$; they have the property that for
+% $t=0$ each line starts at the first point, while for $t=1$ they reach the
+% last point; in each case the generic point $P$ on each curve takes off
+% with a direction that points to the next point, while it reaches the
+% destination point with a direction coming from the penultimate point;
+% moreover, when $t$ varies from 0 to 1, the curve arc is completely
+% contained within the convex hull formed by the polygon that has the
+% spline points as vertices. Last but not least first order splines implement
+% just straight lines and they are out of question for what concerns maxima,
+% minima, inflection points and the like. Quadratic splines draw just
+% parabolas, therefore they draw arcs that have the concavity just on one
+% side of the path; therefore no inflection points. Cubic splines are
+% extremely versatile and can draw lines with maxima, minima and inflection
+% points. Virtually a multi-arc curve may be drawn by a set of cubic splines
+% as well as a set of quadratic splines (fonts are a good example: Adobe
+% Type~1 fonts have their contours described by cubic splines, while TrueType
+% fonts have their contours described with quadratic splines; with a naked
+% eye it is impossible to notice the difference).
+%
+% Each program that processes the file to be displayed is capable of drawing
+% first order Bézier splines (segments) and third order Bézier splines, for
+% no other reason, at least, because they have to draw vector fonts whose
+% contours are described by Bézier splines; sometimes they have also the
+% program commands to draw second order Bézier splines, but not always these
+% machine code routines are available to the user for general use. For what
+% concerns |pdftex|, |xetex| and |luatex|, they have the user commands for
+% straight lines and cubic arcs. At least with |pdftex|, quadratic arcs must
+% be simulated with a clever use of third order Bézier splines.
+%
+% Notice that \LaTeXe\ environment |picture| by itself is capable of drawing
+% both cubic and quadratic Bézier splines as single arcs; but it resorts to
+% ``poor man'' solutions. The |pict2e| package removes all the old limitations
+% and implements the interface macros for sending the driver the
+% necessary drawing information, including the transformation from
+% typographical points (72.27\,pt/inch) to PostScript big points (72\,bp/inch).
+% But for what concerns the quadratic spline it resorts to the clever use of a
+% cubic spline.
+%
+% Therefore here we treat first the drawings that can be made with cubic
+% splines; then we describe the approach to quadratic splines.
+%
+%\subsection{Cubic splines}
 % Now we define a macro for tracing a general, not necessarily circular, arc.
 % This macro resorts to a general triplet of macros with which it is possible
 % 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
-% any case\dots
+% case where the general |\curve| macro of |pict2e| could do the same or a
+% better job. In any case\dots
 %    \begin{macrocode}
 \def\CurveBetween#1and#2WithDirs#3and#4{%
 \StartCurveAt#1WithDir{#3}\relax
 \CurveTo#2WithDir{#4}\CurveFinish\ignorespaces}%
 %    \end{macrocode}
-% For backwards compatibility the old command with lower case |and| is made
-% to do the same as this macro |\CurveBetween| with capitalised |And|.
 %
 % 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.
 %In any case the directions specified with the direction arguments, both here
 % and with the more general macro|\Curve|, the angle between the indicated
-% tangent and the arc chord  should never exceed 90° in absolute value;
-% strange error messages may be issued by the interpreter. Some control is
-% exercised on these values, but some tests might fail if the angle derives
-% from computations; this is a good place to use polar forms for the direction
-% vectors.
+% tangent and the arc chord may give raise to some little problems when they
+% are very close to 90° in absolute value. Some control is exercised on these
+% values, but some tests might fail if the angle derives from computations;
+% this is a good place to use polar forms for the direction vectors.
 %
 %\begin{figure}\centering\unitlength=0.004\textwidth
 %\begin{picture}(220,120)(-50,-20)
@@ -2708,7 +2756,8 @@ and the derived files curve2e.sty and curve2e.pdf.
 \pIIe@moveto{\@tempa\unitlength}{\@tempb\unitlength}%
 \GetCoord(#2)\@tempa\@tempb
 \CopyVect\@tempa,\@tempb to\@Dzero
-\DirOfVect\@Dzero to\@Dzero}
+\DirOfVect\@Dzero to\@Dzero
+\ignorespaces}
 %    \end{macrocode}
 % And this re-initializes the direction to create  a cusp:
 %    \begin{macrocode}
@@ -2754,14 +2803,16 @@ and the derived files curve2e.sty and curve2e.pdf.
 % be therefore:
 %\begin{flushleft}
 %\cs{CbezierTo}\meta{end
-% point}|WithDir|\meta{direction}|AndDist|\meta{$K_0$}|And|\meta{$K_1$}
+% point}|WithDir|\meta{direction}|AndDists|\meta{$K_0$}|And|\meta{$K_1$}
 %\end{flushleft}
 % where \meta{end point} is a vector macro or a comma separated pair of values;
 % again \meta{direction} is another vector macro or a comma separated pair of
 % values, that not necessarily indicate a unit vector, since the macro provides
 % to normalise it to unity; \meta{$K_0$} and\meta{$K_1$} are the distances of
 % the control point from their respective node points; they must be positive
-% integers or fractional numbers.
+% integers or fractional numbers. If \meta{$K_1$} is a number must be enclosed
+% in curly braces, while if it is a macro name (containing the desired fractional
+% or integer value) there is no need for braces.
 %
 % This macro uses the input information to use the internal |pict2e| macro
 % |\pIIe@curveto| with the proper arguments, and to save the final direction
@@ -2797,13 +2848,13 @@ and the derived files curve2e.sty and curve2e.pdf.
 %
 % An example of use is shown in figure~\ref{fig:Cbezier}; notice that the
 % tangents at the end points are the same for the black curve drawn with
-% |\CurveBetween| and the four red curves drawn with |\CbezierBetween|; the
+% |\CurveBetween| and the five red curves drawn with |\CbezierBetween|; the
 % five red curves differ only for the distance of their control point $C_0$
 % from the starting  point; the differences are remarkable and the topmost
 % curve even presents a slight inflection close to the end point. These
 % effects cannot be obtained with the ``smarter'' macro |\CurveBetween|. But
-% certainly this simpler macro is more difficult to use because of the
-% distances of the control point are sort of unpredictable and require a
+% certainly this simpler macro is more difficult to use because the
+% distances of the control point are difficult to estimate and require a
 % number of cut-and-try experiments.
 %
 %\begin{figure}[!tb]
@@ -2849,12 +2900,80 @@ and the derived files curve2e.sty and curve2e.pdf.
 % along the arc.
 %
 % The strategy I devised consists in determining each control point as if it
-% were the control point of a circular arc, precisely an arc of an
-% osculating circle, a circle tangent to the curve at that node. The ambiguity
+% were the control point of a circular arc, precisely an arc of an osculating
+% circle, i.e. a circle tangent to the curve at that node. The ambiguity
 % of the stated problem may be solved by establishing that the chord of the
 % osculating circle has the same direction as the chord of the arc being drawn,
 % and that the curve chord is divided into two equal parts each of which should be
 % interpreted as half the chord of the osculating circle. 
+% This makes the algorithm a little rigid; sometimes the path drawn is very
+% pleasant, while in other circumstances the determined curvatures are too
+% large or too small. We therefore add some optional information that lets
+% us have some control over the curvatures; the idea is based on the concept
+% of \emph{tension}, similar but not identical to the one used in the drawing
+% programs \MF\ and \MP. We add to the direction information, with which the
+% control nodes of the osculating circle arcs are determined, a scaling factor
+% that should be intuitively related to the tension of the arc: the smaller
+% this number, the closer the arc resembles a straight line as a rope subjected
+% to a high tension; value zero is allowed, while a value of 4 is close to
+% ``infinity'' and turns a quarter circle into a line with an unusual loop;
+% a value of 2 turns a quarter circle almost into a polygonal line
+% with rounded corner. Therefore these tension factors should
+% be used only for fine tuning the arcs, not as the first time a path is drawn.
+%
+% We devised a syntax for specifying direction and tensions:
+%\begin{flushleft}
+% \meta{direction\texttt{\upshape;}tension factors}
+%\end{flushleft}
+% where \emph{direction} contains a pair of fractional number that not
+% necessarily refer to the components of a unit vector direction, but simply
+% to a vector with the desired orientation; the information contained from
+% the semicolon (included) to the rest of the specification is optional; if
+% it is present, the \emph{tension factors} is simply a comma separated pair
+% of fractional or integer numbers that represent respectively the tension
+% at the starting or the ending node of a path arc.
+%
+% We therefor need a macro to extract the mandatory and optional parts:
+%    \begin{macrocode}
+\def\@isTension#1;#2!!{\def\@tempA{#1}%
+\def\@tempB{#2}\unless\ifx\@tempB\empty\strip@semicolon#2\fi}
+\def\strip@semicolon#1;{\def\@tempB{#1}}
+%    \end{macrocode}
+% By changing the tension values we can achieve different results: see
+% figure~\ref{fig:tensions}.
+%\begin{figure}[!htb]\centering
+%\begin{minipage}{0.48\textwidth}\small
+%\begin{verbatim}
+%\raggedleft\unitlength=0.01\textwidth
+%\begin{picture}(70,70)
+%\put(0,0){\color{blue}\frame(70,70){}}
+%\put(0,0){\color{red}\Curve(0,0)<1,1>(70,0)<1,-1>}
+%\Curve(0,0)<1,1>(70,0)<1,-1;0,0>
+%\Curve(0,0)<1,1>(70,0)<1,-1;0.2,0.2>
+%\Curve(0,0)<1,1>(70,0)<1,-1;2,2>
+%\Curve(0,0)<1,1>(70,0)<1,-1;4.5,4.5>
+%\Curve(0,0)<1,1>(70,0)<1,-1;0,3>
+%\Curve(0,0)<1,1>(70,0)<1,-1;3,0>
+%\end{picture}
+%\end{verbatim}
+%\end{minipage}
+%\hfill
+%\begin{minipage}{0.46\textwidth}
+%\raggedleft\unitlength=0.01\textwidth
+%\begin{picture}(70,70)
+%\put(0,0){\color{blue}\framebox(70,70){}}
+%\put(0,0){\color{red}\Curve(0,0)<1,1>(70,0)<1,-1>}
+%\Curve(0,0)<1,1>(70,0)<1,-1;0,0>
+%\Curve(0,0)<1,1>(70,0)<1,-1;0.2,0.2>
+%\Curve(0,0)<1,1>(70,0)<1,-1;2,2>
+%\Curve(0,0)<1,1>(70,0)<1,-1;4.5,4.5>
+%\Curve(0,0)<1,1>(70,0)<1,-1;0,3>
+%\Curve(0,0)<1,1>(70,0)<1,-1;3,0>
+%\end{picture}
+%\end{minipage}
+%\caption{The effects of tension factors}\label{fig:tensions}
+%\end{figure}
+%
 %
 % We use the formula we got for arcs~\eqref{equ:corda}, where the half chord is
 % indicated with $s$,  and we derive the necessary distances:
@@ -2869,7 +2988,10 @@ and the derived files curve2e.sty and curve2e.pdf.
 % chord and its direction:
 %    \begin{macrocode}
 \def\CurveTo#1WithDir#2{%
-\def\@Puno{#1}\def\@Duno{#2}\DirOfVect\@Duno to\@Duno
+\def\@Tuno{1}\def\@Tzero{1}\relax
+\edef\@Puno{#1}\@isTension#2;!!%
+\expandafter\DirOfVect\@tempA to\@Duno
+\bgroup\unless\ifx\@tempB\empty\GetCoord(\@tempB)\@Tzero\@Tuno\fi
 \DistanceAndDirOfVect\@Puno minus\@Pzero to\@Chord and\@DirChord
 %    \end{macrocode}
 % Then we rotate everything about the starting point so as to bring the chord on
@@ -2912,10 +3034,11 @@ and the derived files curve2e.sty and curve2e.pdf.
     \edef\@SinDzero{\ifdim\@DYpzero\p@<\z@ -\fi\@DYpzero}%
     \@tdA=\@semichord\p@ \@tdA=1.333333\@tdA
     \DividE\@tdA by\@SinDzero\p@ to \@KCzero
-    \@tdA=\dimexpr(\p@-\@CosDzero\p@)
+    \@tdA=\dimexpr(\p@-\@CosDzero\p@)\relax
     \DividE\@KCzero\@tdA by\@SinDzero\p@ to \@KCzero
   \fi
 \fi
+\MultiplyFN\@KCzero by \@Tzero to \@KCzero
 \ScaleVect\@Dzero by\@KCzero to\@CPzero
 \AddVect\@Pzero and\@CPzero to\@CPzero
 %    \end{macrocode}
@@ -2940,22 +3063,23 @@ and the derived files curve2e.sty and curve2e.pdf.
     \edef\@SinDuno{\ifdim\@DYpuno\p@<\z@ -\fi\@DYpuno}%
     \@tdA=\@semichord\p@ \@tdA=-1.333333\@tdA
     \DividE\@tdA by \@SinDuno\p@ to \@KCuno
-    \@tdA=\dimexpr(\p@-\@CosDuno\p@)
+    \@tdA=\dimexpr(\p@-\@CosDuno\p@)\relax
     \DividE\@KCuno\@tdA by\@SinDuno\p@ to \@KCuno
   \fi
 \fi
+\MultiplyFN\@KCuno by \@Tuno to \@KCuno
 \ScaleVect\@Duno by\@KCuno to\@CPuno
 \AddVect\@Puno and\@CPuno to\@CPuno
 %    \end{macrocode}
 % Now we have the four points and we can instruct the internal \texttt{pict2e}
-% macros to do the path tracing.
+% macros to do the path drawing.
 %    \begin{macrocode}
 \GetCoord(\@Puno)\@XPuno\@YPuno
 \GetCoord(\@CPzero)\@XCPzero\@YCPzero
 \GetCoord(\@CPuno)\@XCPuno\@YCPuno
 \pIIe@curveto{\@XCPzero\unitlength}{\@YCPzero\unitlength}%
              {\@XCPuno\unitlength}{\@YCPuno\unitlength}%
-             {\@XPuno\unitlength}{\@YPuno\unitlength}%
+             {\@XPuno\unitlength}{\@YPuno\unitlength}\egroup
 %    \end{macrocode}
 %  It does not have to stroke the curve because other Bézier splines might still
 %  be added to the path. On the opposite it memorises the final point as the
@@ -3005,7 +3129,7 @@ and the derived files curve2e.sty and curve2e.pdf.
 % As a concluding remark, please notice that the |\Curve| macro is certainly the
 % most comfortable to use, but it is sort of frozen in its possibilities. The
 % user may certainly use the |\StartCurve|, |\CurveTo|, |\ChangeDir|, and
-% |\CurveFinish| or  |FillCurve| for a more versatile set of drawing macros;
+% |\CurveFinish| or  |\FillCurve| for a more versatile set of drawing macros;
 % evidently nobody forbids to exploit the full power of the |\cbezier| original
 % macro for cubic splines; we made available macros |\CbezierTo| and the
 % isolated arc macro |\CbezierBetween| in order to use the general internal
@@ -3015,24 +3139,20 @@ and the derived files curve2e.sty and curve2e.pdf.
 %\unitlength=0.01\textwidth
 %\begin{picture}(100,50)(0,-25)
 %\put(0,0){\VECTOR(0,0)(45,0)\VECTOR(0,-25)(0,25)
-%\Zbox(45,1)[br]{x}\Zbox(1,25)[tl]{y}
-%\Curve(0,0)<1,3.927>%
-%(5,14.14)<1,2.776>%
-%(10,20)<1,0>%
-%(15,14.14)<1,-2.776>%
-%(20,0)<1,-3.927>%
-%(25,-14.14)<1,-2.776>%
-%(30,-20)<1,0>%
-%(35,-14.14)<1,2.776>%
-%(40,0)<1,3.927>%
+%\Zbox(45,0)[br]{x}\Zbox(0,26)[tl]{y}
+%\Curve(0,0)<77:1>(10,20)<1,0;2,0.4>(30,-20)<1,0;0.4,0.4>(40,0)<77:1;0.4,2>
 %}
-%\put(50,0){\VECTOR(0,0)(45,0)\VECTOR(0,-25)(0,25)
-%\Zbox(45,1)[br]{x}\Zbox(1,25)[tl]{y}
+%\put(55,0){\VECTOR(0,0)(45,0)\VECTOR(0,-25)(0,25)
+%\Zbox(45,0)[br]{x}\Zbox(0,26)[tl]{y}
 %\CbezierBetween0,0And20,0WithDirs77:1And-77:1UsingDists28And{28}
 %\CbezierBetween20,0And40,0WithDirs-77:1And77:1UsingDists28And{28}}
 %\end{picture}
-%\caption{A sequence of arcs; the left figure has been drawn with the \cs{Curve} command with a sequence of nine couples of point-direction arguments; the right figure has been drawn with two commands \cs{CbezierBetween} that include also the specification of the control points}
-%\label{fig:sinewawe}
+%\caption{A sequence of arcs; the left figure has been drawn with the
+% \cs{Curve} command with a sequence of four couples of point-direction
+% arguments; the right figure has been drawn with two commands
+% \cs{CbezierBetween} that include also the specification of the control
+% points}
+%\label{fig:sinewave}
 %\end{figure}
 %
 % As it can be seen in figure~\ref{fig:sinewave} the two diagrams should
@@ -3041,14 +3161,297 @@ and the derived files curve2e.sty and curve2e.pdf.
 % it is  only possible to approximate it. It is evident that the approximation
 % obtained with full control on the control points requires less arcs and
 % it is more accurate than the approximation obtained with the recursive
-% |\Curve| macro; this macro requires almost three times as many pieces of
+% |\Curve| macro; this macro requires almost two times as many pieces of
 % information in order to minimise the effects of the lack of control on the
 % control points, and even with this added information the macro approaches
 % the sine wave with less accuracy. At the same time for many applications
-% the |\Curve| recursive macro proves to be far much easier to use than with
+% the |\Curve| recursive macro proves to be much easier to use than with
 % single arcs drawn with the |\CbezierBetween| macro.
 %
-% I believe that the set of new macrosprovided by this package  can really
+% \subsection{Quadratic splines}
+% We want to create a recursive macro with the same properties as the above
+% described |\Curve| macro, but that uses quadratic splines; we call it
+% |\Qurve| so that the initial macro name letter reminds us of the nature
+% of the splines being used. For the rest they have an almost identical
+% syntax; with quadratic spline it is not possible to specify the distance
+% of the control points from the extrema, since quadratic spline have just
+% one control point that must lay at the intersection of the two tangent
+% directions therefore with quadratic splines the tangents at each point
+% cannot have the optional part that starts with a semicolon. The syntax, therefore, is just:
+%\begin{flushleft}
+%\cs{Qurve}\parg{first point}\aarg{direction}...\parg{any point}\aarg{direction}...\parg{last point}\aarg{direction}
+%\end{flushleft}
+% As with |\Curve|, also with |\Qurve| there is no limitation on the number
+% of points, except for the computer memory size; it is advisable not to use
+% many arcs otherwise it might become very difficult to find errors.
+% 
+% The first macros that set up the recursion are very similar to those we
+% wrote for |\Curve|:
+%    \begin{macrocode}
+\def\Qurve{\@ifstar{\let\fillstroke\fillpath\Qurve@}%
+{\let\fillstroke\strokepath\Qurve@}}
+
+\def\Qurve@(#1)<#2>{%
+    \StartCurveAt#1WithDir{#2}%
+    \@ifnextchar\lp@r\@Qurve{%
+    \PackageWarning{curve2e}{%
+      Quadratic curve specifications must contain at least 
+      two nodes!\Messagebreak
+      Please, control your Qurve specifications\MessageBreak}}}%
+\def\@Qurve(#1)<#2>{\QurveTo#1WithDir{#2}%
+    \@ifnextchar\lp@r\@Qurve{%
+    \@ifnextchar[\@ChangeQDir\CurveEnd}}%
+\def\@ChangeQDir[#1]{\ChangeDir<#1>\@Qurve}%
+%    \end{macrocode}
+% Notice that in case of long paths it might be better to use the single
+% macros |\StartCurveAt|, |\QurveTo|, |\ChangeDir| and |\CurveFinish|
+% (or |\FillCurve|), with their respective syntax, in such a way that a long list 
+% of node-direction specifications passed to |\Qurve| may be split into
+% shorter input lines in order to edit the input data in a more comfortable way.
+%
+%
+% The macro that does everything is |\QurveTo|. it start with reading its
+% arguments received through the calling macro |\@Qurve|
+%    \begin{macrocode}
+\def\QurveTo#1WithDir#2{%
+\edef\@Puno{#1}\DirOfVect#2to\@Duno\bgroup
+\DistanceAndDirOfVect\@Puno minus\@Pzero to\@Chord and\@DirChord
+%    \end{macrocode}
+% It verifies if |\@Dpzero| and |\@Dpuno|, the directions at the two extrema
+% of the arc, are parallel or anti-parallel by taking their
+% ``scalar'' product (|\@Dpzero| times |\@Dpuno*|); if  the imaginary
+% component  of the scalar product vanishes the two directions are parallel;
+% in this case we produce an error message, but we continue skipping this arc
+% destination point; evidently the drawing will not be the desired one, but
+% the job should not abort.
+%    \begin{macrocode}
+\MultVect\@Dzero by*\@Duno to \@Scalar
+\YpartOfVect\@Scalar to \@YScalar
+\ifdim\@YScalar\p@=\z@
+\PackageWarning{curve2e}%
+   {Quadratic Bezier arcs cannot have their starting\MessageBreak
+   and ending directions parallel or antiparallel with\MessageBreak
+   each other. This arc is skipped and replaced with 
+   a dotted line.\MessageBreak}%
+   \Dotline(\@Pzero)(\@Puno){2}\relax
+\else
+%    \end{macrocode}
+% Otherwise we rotate everything about the starting point so as to bring the
+% chord on the real axis; we get also the components of the two directions that,
+% we should remember, are unit vectors, not generic vectors, although the user
+% can use the vector specifications that are more understandable to him/her:
+%    \begin{macrocode}
+\MultVect\@Dzero by*\@DirChord to \@Dpzero
+\MultVect\@Duno by*\@DirChord to \@Dpuno
+\GetCoord(\@Dpzero)\@DXpzero\@DYpzero
+\GetCoord(\@Dpuno)\@DXpuno\@DYpuno
+%    \end{macrocode}
+% We check if the two directions point to the same half plane; this implies
+% that these rotated directions point to different sides of the chord vector;
+% all this  is equivalent that the two direction Y components have opposite
+% signs, and therefore their product is strictly negative, and that the two
+% X components product is not negative.
+%    \begin{macrocode}
+\MultiplyFN\@DXpzero by\@DXpuno to\@XXD
+\MultiplyFN\@DYpzero by\@DYpuno to\@YYD
+\unless\ifdim\@YYD\p@<\z@\ifdim\@XXD\p@<\z@
+\PackageWarning{curve2e}%
+   {Quadratic Bezier arcs cannot have inflection points\MessageBreak
+   Therefore the tangents to the starting and ending arc\MessageBreak
+   points cannot be directed to the same half plane.\MessageBreak
+   This arc is skipped and replaced by a dotted line\MessageBreak}%
+   \Dotline(\@Pzero)(\@Puno){2}\fi
+\else
+%    \end{macrocode}
+%
+% After these tests we should be in a ``normal'' situation.We first copy
+% the expanded input information into new macros that have more explicit
+% names: macros stating wit `S' denote the sine of the direction angle,
+% while those starting with `C' denote the cosine of that angle. We will
+% use these expanded definitions as we know we are working with the actual
+% values. These directions are those relative to the arc chord.
+%    \begin{macrocode}
+\edef\@CDzero{\@DXpzero}\relax
+\edef\@SDzero{\@DYpzero}\relax
+\edef\@CDuno{\@DXpuno}\relax
+\edef\@SDuno{\@DYpuno}\relax
+%    \end{macrocode}
+% Suppose we write the parametric equations of a straight line that departs
+% from the beginning of the chord with direction angle $\phi_0$ and the
+% corresponding equation of the straight line departing from the end of the
+% chord (of length $c$) with direction angle $\phi_1$. We have to find the
+% coordinates of the intersection point of these two straight lines.
+%\begin{subequations}
+%\begin{align}
+% t \cos\phi_0 - s \cos\phi_1 &=  c\\
+% t \sin\phi_0 - s \sin\phi_1 &= 0
+%\end{align}
+%\end{subequations}
+% The parameters $t$ and $s$ are just the running parameters; we have
+% to solve those simultaneous equations in the unknown variables $t$ and $s$;
+% these values let us comupte the coordinates of the intersection point:
+%\begin{subequations}\begin{align}
+% X_C &=\dfrac{c\cos\phi_0\sin\phi_1}{\sin\phi_0\cos\phi_1 - \cos\phi_0\sin\phi_1} \\
+% Y_C &=\dfrac{c\sin\phi_0\sin\phi_1}{\sin\phi_0\cos\phi_1 - \cos\phi_0\sin\phi_1}
+%\end{align}\end{subequations}
+%
+% Having performed the previous tests we are sure that the denominator is not
+% vanishing (direction are not parallel or anti-parallel) and that it lays at
+% the same side as the direction with angle $\phi_0$ with respect to the chord.
+% The coding then goes on like this:
+%    \begin{macrocode}
+\MultiplyFN\@SDzero by\@CDuno to\@tempA 
+\MultiplyFN\@SDuno by\@CDzero to\@tempB 
+\edef\@tempA{\strip@pt\dimexpr\@tempA\p@-\@tempB\p@}\relax
+\@tdA=\@SDuno\p@ \@tdB=\@Chord\p@ \@tdC=\@tempA\p@
+\edef\@tempC{\strip@pt\dimexpr \@tdA*\@tdB/\@tdC}\relax
+\MultiplyFN\@tempC by\@CDzero to \@XC 
+\MultiplyFN\@tempC by\@SDzero to \@YC 
+\ModOfVect\@XC,\@YC to\@KC            
+%    \end{macrocode}
+% We eventually computed the coordinates and the module  of the intersection
+% point vector taking into account the rotation of the real axis; getting
+% back to the original coordinates before rotation we get:
+%    \begin{macrocode}
+\ScaleVect\@Dzero by\@KC to\@CP       
+\AddVect\@Pzero and\@CP to\@CP       
+\GetCoord(\@Pzero)\@XPzero\@YPzero    
+\GetCoord(\@Puno)\@XPuno\@YPuno      
+\GetCoord(\@CP)\@XCP\@YCP             
+%    \end{macrocode}
+% We have now the coordinates of the two extrema point of the quadratic arc
+% and of the control point. Keeping in mind that the symbols $P_0$, $P_1$
+% and $C$ denote geometrical points but also their coordinates as ordered
+% pairs of real numbers (i.e. they are complex numbers) we have to determine
+% the smart cubic arc nodes and control points; we should determine the
+% values of $P_a$ and $P_b$ such that
+%\[
+% P_0(1-t)^3 +3P_a(1-t)^2t +3P_b(1-t)t^2 +P_1t^3
+%\]
+% is equivalent to
+%\[
+% P_0(1-t)^2 + 2C(1-t)t + P_1t^2
+%\]
+% It turns out that the solution is given by
+%\begin{equation}
+%P_a= C+(P_0-C)/3 \qquad \text{and}\qquad P_b = C+(P_1- C)/3
+%\label{equ:spline3}
+%\end{equation}
+%
+% The transformations implied by equations~\eqref{equ:spline3} are performed
+% by the following macros already available from the |pict2e| package; we
+% use them here with the actual arguments used for this task:
+%    \begin{macrocode}
+\@ovxx=\@XPzero\unitlength \@ovyy=\@YPzero\unitlength
+\@ovdx=\@XCP\unitlength \@ovdy=\@YCP\unitlength
+\@xdim=\@XPuno\unitlength \@ydim=\@YPuno\unitlength
+      \pIIe@bezier@QtoC\@ovxx\@ovdx\@ovro
+      \pIIe@bezier@QtoC\@ovyy\@ovdy\@ovri
+      \pIIe@bezier@QtoC\@xdim\@ovdx\@clnwd
+      \pIIe@bezier@QtoC\@ydim\@ovdy\@clnht
+      \pIIe@moveto\@ovxx\@ovyy
+%    \end{macrocode}
+%
+% We call the basic |pict2e| macro to draw a cubic spline and we finish
+% the conditional statements with which we started these calculations;
+% eventually we close the group we opened at the beginning and we copy
+% the terminal node information (position and direction) into the
+% 0-labelled macros that indicate the starting point of the next arc.
+%    \begin{macrocode}
+      \pIIe@curveto\@ovro\@ovri\@clnwd\@clnht\@xdim\@ydim
+\fi\fi\egroup
+\CopyVect\@Puno to\@Pzero
+\CopyVect\@Duno to\@Dzero
+\ignorespaces}
+%    \end{macrocode}
+%
+% An example of usage is shown at the left in figure~\ref{fig:quadratic-arcs}\footnote{The commands \cs{legenda}, \cs{Pall} and
+% \cs{Zbox} are specifically defined in the preamble of this document; they must
+% be used within a \texttt{picture} environment. \cs{legenda} draws a framed
+% legend made up of a single (short) math formula; \cs{Pall} is just a shorthand
+% to put a filled small circle at a specified position' \cs{Zbox} puts a
+% symbol in math mode a little displaced in the proper direction relative to
+% a specified position. They are just handy to label certain objects in a
+% \texttt{picture} diagram, but they are not part of the \texttt{curve2e}
+% package.}.
+% created with the following code:
+%\begin{verbatim}
+%\begin{figure}[!htp]
+%\unitlength=0.0045\textwidth
+%\begin{picture}(100,100)
+%\put(0,0){\framebox(100,100){}}
+%\put(50,50){\Qurve(0,-50)<1,0>(50,0)<0,1>(0,50)<-1,0>%
+%(-50,0)<0,-1>(0,-50)<1,0>\color{green}%
+%\Qurve*(0,-50)<0,1>(50,0)<1,0>[-1,0](0,50)<0,1>[0,-1]
+%(-50,0)<-1,0>[1,0](0,-50)<0,-1>}
+%\Qurve(0,0)<1,4>(50,50)<1,0>(100,100)<1,4>
+%\put(5,50){\Qurve(0,0)<1,1.5>(22.5,20)<1,0>(45,0)<1,-1.5>%
+%(67.5,-20)<1,0>(90,0)<1,1.5>}
+%\Zbox(0,0)[tl]{0,0}\Zbox(100,0)[tr]{100,0}
+%\Zbox(100,100)[br]{100,100}\Zbox(0,100)[bl]{0,100}
+%\end{picture}
+%\end{figure}
+%\end{verbatim}
+%
+%\begin{figure}[!tb]
+%\unitlength=0.0045\textwidth
+%\begin{picture}(100,100)
+%\put(0,0){\framebox(100,100){}}
+%\put(50,50){\Qurve(0,-50)<1,0>(50,0)<0,1>(0,50)<-1,0>(-50,0)<0,-1>(0,-50)<1,0>\color{green}%
+%\Qurve*(0,-50)<0,1>(50,0)<1,0>[-1,0](0,50)<0,1>[0,-1](-50,0)<-1,0>[1,0](0,-50)<0,-1>}
+%\Qurve(0,0)<1,4>(50,50)<1,0>(100,100)<1,4>
+%\put(5,50){\Qurve(0,0)<1,1.5>(22.5,20)<1,0>(45,0)<1,-1.5>(67.5,-20)<1,0>(90,0)<1,1.5>}
+%\Zbox(0,0)[tl]{0,0}\Zbox(100,0)[tr]{100,0}
+%\Zbox(100,100)[br]{100,100}\Zbox(0,100)[bl]{0,100}
+%\Pall[2](0,0)\Pall[2](100,0)\Pall[2](100,100)\Pall[2](0,100)
+%\end{picture}
+%\hfill
+%\begin{picture}(100,100)
+%\put(0,0){\framebox(100,100){}}
+%\put(50,50){\Qurve(0,-50)<1,0>(50,0)<0,1>(0,50)<-1,0>(-50,0)<0,-1>(0,-50)<1,0>
+%\Curve(0,-50)<1,0>(50,0)<0,1>(0,50)<-1,0>(-50,0)<0,-1>(0,-50)<1,0>}
+%\Zbox(50,50)[t]{O}\Pall[2](50,50)\put(50,50){\Vector(45:50)}\Zbox(67,70)[tl]{R}
+%\end{picture}
+%
+%\caption{\rule{0pt}{4ex}Several graphs drawn with quadratic Bézier splines}
+%\label{fig:quadratic-arcs}
+%\end{figure}
+%
+% Notice the green filled path: that result is not expected, but the filling
+% operation is controlled by the inner workings of the typesetting program,
+% where it fills what \emph{it} considers the interior of a path, not what
+% \emph{we} think it is the interior of a path.Knowing this feature it is not
+% difficult to fill the external lozenge with green, and then fill the internal
+% path with white; the result would be to cover with white the external part of
+% the interior path. Sort of odd way of getting the result, but this is not due
+% to the quadratic splines but to the internal workings of |pdftex| and its
+% companion typesetting engines, that consider ``interior'' the concave side of
+% the closed path, not the convex one.
+% 
+% Notice also that the inflexed line is made with two arcs that meet at the
+% inflection point; the same is true for the line that resembles a sine wave.
+% The cusps of the inner border of the green area are obtained with the usual
+% optional argument already used also with the |\Curve| recursive macro.
+%
+% The ``circle'' inside the square frame is visibly different from a real
+% circle, in spite of the fact that the maximum deviation from the true
+% circle is just about 6\% relative to the radius; a quarter circle obtained
+% with a single parabola is definitely a poor approximation of a real quarter
+% circle; possibly by splitting each quarter circle in three or four partial
+% arcs the approximation of a real quarter circle would be much better. On the
+% right of figure~\ref{fig:quadratic-arcs} it is possible to compare a
+% ``circle'' obtained with quadratic arcs with the the internal circle
+% obtained with cubic arcs; the difference is easily seen even with a naked eye.
+%
+% With quadratic arcs we decided to avoid defining specific macros similar
+% to |\CurveBetween| and |\CbezierBetween|; the first macro would not save
+% any typing to the operator; furthermore it may be questionable if it was
+% really useful even with cubic splines; the second macro with quadratic
+% arcs is meaningless, since with quadratic arcs there is just one control
+% point and there is no choice on its position.
+%
+% \section{Conclusion}
+% I believe that the set of new macros provided by this package  can really
 % help the user to draw his/her diagrams with more agility; it will be the
 % accumulated experience to decide if this is true.
 %\iffalse
diff --git a/Master/texmf-dist/tex/latex/curve2e/curve2e.sty b/Master/texmf-dist/tex/latex/curve2e/curve2e.sty
index db002fd2a51..818c1e986c1 100644
--- a/Master/texmf-dist/tex/latex/curve2e/curve2e.sty
+++ b/Master/texmf-dist/tex/latex/curve2e/curve2e.sty
@@ -17,7 +17,7 @@
 %%
 \NeedsTeXFormat{LaTeX2e}[2014/05/01]
 \ProvidesPackage{curve2e}%
-        [2015/06/19 v.1.50 Extension package for pict2e]
+        [2015/06/27 v.1.54 Extension package for pict2e]
 
 
 \RequirePackage{color}
@@ -221,6 +221,7 @@
            \noexpand\egroup\noexpand\def\noexpand#3{%
              \strip@pt\dimexpr\@DimA*\@DimB/\p@\relax}}%
         \x\ignorespaces}%
+        \let\MultiplyFN\MultiplY
     \fi
 \fi
 
@@ -346,15 +347,21 @@
    \noexpand\def\noexpand#2{\@tempA}\noexpand\ignorespaces}%
 \endTanOf}%
 \def\ArcTanOf#1to#2{\bgroup
+\countdef\Inverti 4444\Inverti=0
+\def\Segno{}
 \edef\@tF{#1}\@tdF=\@tF\p@ \@tdE=57.295778\p@
-\@tdD=\ifdim\@tdF>\z@ \@tdF\else -\@tdF\fi
+\@tdD=\ifdim\@tdF<\z@ -\@tdF\def\Segno{-}\else\@tdF\fi
+\ifdim\@tdD>\p@
+\Inverti=\@ne
+\@tdD=\dimexpr\p@*\p@/\@tdD\relax
+\fi
 \unless\ifdim\@tdD>0.02\p@
-    \def\@tX{\strip@pt\dimexpr57.295778\@tdF\relax}%
+    \def\@tX{\strip@pt\dimexpr57.295778\@tdD\relax}%
 \else
     \edef\@tX{45}\relax
-    \countdef\I 2523 \I=8\relax
+    \countdef\I 2523 \I=9\relax
     \@whilenum\I>0\do{\TanOf\@tX to\@tG
-    \edef\@tG{\strip@pt\dimexpr\@tG\p@-\@tdF\relax}\relax
+    \edef\@tG{\strip@pt\dimexpr\@tG\p@-\@tdD\relax}\relax
     \MultiplY\@tG by57.295778to\@tG
     \CosOf\@tX to\@tH
     \MultiplY\@tH by\@tH to\@tH
@@ -362,7 +369,10 @@
     \edef\@tX{\strip@pt\dimexpr\@tX\p@ - \@tH\p@\relax}\relax
     \advance\I\m@ne}%
 \fi
-\edef\x{\egroup\noexpand\edef\noexpand#2{\@tX}}\x\ignorespaces}%
+\ifnum\Inverti=\@ne
+\edef\@tX{\strip@pt\dimexpr90\p@-\@tX\p@\relax}
+\fi
+\edef\x{\egroup\noexpand\edef\noexpand#2{\Segno\@tX}}\x\ignorespaces}%
 \def\MakeVectorFrom#1#2to#3{\edef#3{#1,#2}\ignorespaces}%
 \def\CopyVect#1to#2{\edef#2{#1}\ignorespaces}%
 \def\ModOfVect#1to#2{\GetCoord(#1)\t@X\t@Y
@@ -679,7 +689,8 @@
 \pIIe@moveto{\@tempa\unitlength}{\@tempb\unitlength}%
 \GetCoord(#2)\@tempa\@tempb
 \CopyVect\@tempa,\@tempb to\@Dzero
-\DirOfVect\@Dzero to\@Dzero}
+\DirOfVect\@Dzero to\@Dzero
+\ignorespaces}
 \def\ChangeDir<#1>{%
 \GetCoord(#1)\@tempa\@tempb
 \CopyVect\@tempa,\@tempb to\@Dzero
@@ -707,8 +718,14 @@
 \StartCurveAt#1WithDir{#3}\relax
 \CbezierTo#2WithDir#4AndDists#5And{#6}\CurveFinish}
 
+\def\@isTension#1;#2!!{\def\@tempA{#1}%
+\def\@tempB{#2}\unless\ifx\@tempB\empty\strip@semicolon#2\fi}
+\def\strip@semicolon#1;{\def\@tempB{#1}}
 \def\CurveTo#1WithDir#2{%
-\def\@Puno{#1}\def\@Duno{#2}\DirOfVect\@Duno to\@Duno
+\def\@Tuno{1}\def\@Tzero{1}\relax
+\edef\@Puno{#1}\@isTension#2;!!%
+\expandafter\DirOfVect\@tempA to\@Duno
+\bgroup\unless\ifx\@tempB\empty\GetCoord(\@tempB)\@Tzero\@Tuno\fi
 \DistanceAndDirOfVect\@Puno minus\@Pzero to\@Chord and\@DirChord
 \MultVect\@Dzero by*\@DirChord to \@Dpzero
 \MultVect\@Duno by*\@DirChord to \@Dpuno
@@ -729,10 +746,11 @@
     \edef\@SinDzero{\ifdim\@DYpzero\p@<\z@ -\fi\@DYpzero}%
     \@tdA=\@semichord\p@ \@tdA=1.333333\@tdA
     \DividE\@tdA by\@SinDzero\p@ to \@KCzero
-    \@tdA=\dimexpr(\p@-\@CosDzero\p@)
+    \@tdA=\dimexpr(\p@-\@CosDzero\p@)\relax
     \DividE\@KCzero\@tdA by\@SinDzero\p@ to \@KCzero
   \fi
 \fi
+\MultiplyFN\@KCzero by \@Tzero to \@KCzero
 \ScaleVect\@Dzero by\@KCzero to\@CPzero
 \AddVect\@Pzero and\@CPzero to\@CPzero
 \ifdim\@DXpuno\p@=\z@
@@ -749,10 +767,11 @@
     \edef\@SinDuno{\ifdim\@DYpuno\p@<\z@ -\fi\@DYpuno}%
     \@tdA=\@semichord\p@ \@tdA=-1.333333\@tdA
     \DividE\@tdA by \@SinDuno\p@ to \@KCuno
-    \@tdA=\dimexpr(\p@-\@CosDuno\p@)
+    \@tdA=\dimexpr(\p@-\@CosDuno\p@)\relax
     \DividE\@KCuno\@tdA by\@SinDuno\p@ to \@KCuno
   \fi
 \fi
+\MultiplyFN\@KCuno by \@Tuno to \@KCuno
 \ScaleVect\@Duno by\@KCuno to\@CPuno
 \AddVect\@Puno and\@CPuno to\@CPuno
 \GetCoord(\@Puno)\@XPuno\@YPuno
@@ -760,7 +779,7 @@
 \GetCoord(\@CPuno)\@XCPuno\@YCPuno
 \pIIe@curveto{\@XCPzero\unitlength}{\@YCPzero\unitlength}%
              {\@XCPuno\unitlength}{\@YCPuno\unitlength}%
-             {\@XPuno\unitlength}{\@YPuno\unitlength}%
+             {\@XPuno\unitlength}{\@YPuno\unitlength}\egroup
 \CopyVect\@Puno to\@Pzero
 \CopyVect\@Duno to\@Dzero
 \ignorespaces}%
@@ -777,6 +796,77 @@
     \@ifnextchar\lp@r\@Curve{%
     \@ifnextchar[\@ChangeDir\CurveEnd}}
 \def\@ChangeDir[#1]{\ChangeDir<#1>\@Curve}
+\def\Qurve{\@ifstar{\let\fillstroke\fillpath\Qurve@}%
+{\let\fillstroke\strokepath\Qurve@}}
+
+\def\Qurve@(#1)<#2>{%
+    \StartCurveAt#1WithDir{#2}%
+    \@ifnextchar\lp@r\@Qurve{%
+    \PackageWarning{curve2e}{%
+      Quadratic curve specifications must contain at least
+      two nodes!\Messagebreak
+      Please, control your Qurve specifications\MessageBreak}}}%
+\def\@Qurve(#1)<#2>{\QurveTo#1WithDir{#2}%
+    \@ifnextchar\lp@r\@Qurve{%
+    \@ifnextchar[\@ChangeQDir\CurveEnd}}%
+\def\@ChangeQDir[#1]{\ChangeDir<#1>\@Qurve}%
+\def\QurveTo#1WithDir#2{%
+\edef\@Puno{#1}\DirOfVect#2to\@Duno\bgroup
+\DistanceAndDirOfVect\@Puno minus\@Pzero to\@Chord and\@DirChord
+\MultVect\@Dzero by*\@Duno to \@Scalar
+\YpartOfVect\@Scalar to \@YScalar
+\ifdim\@YScalar\p@=\z@
+\PackageWarning{curve2e}%
+   {Quadratic Bezier arcs cannot have their starting\MessageBreak
+   and ending directions parallel or antiparallel with\MessageBreak
+   each other. This arc is skipped and replaced with
+   a dotted line.\MessageBreak}%
+   \Dotline(\@Pzero)(\@Puno){2}\relax
+\else
+\MultVect\@Dzero by*\@DirChord to \@Dpzero
+\MultVect\@Duno by*\@DirChord to \@Dpuno
+\GetCoord(\@Dpzero)\@DXpzero\@DYpzero
+\GetCoord(\@Dpuno)\@DXpuno\@DYpuno
+\MultiplyFN\@DXpzero by\@DXpuno to\@XXD
+\MultiplyFN\@DYpzero by\@DYpuno to\@YYD
+\unless\ifdim\@YYD\p@<\z@\ifdim\@XXD\p@<\z@
+\PackageWarning{curve2e}%
+   {Quadratic Bezier arcs cannot have inflection points\MessageBreak
+   Therefore the tangents to the starting and ending arc\MessageBreak
+   points cannot be directed to the same half plane.\MessageBreak
+   This arc is skipped and replaced by a dotted line\MessageBreak}%
+   \Dotline(\@Pzero)(\@Puno){2}\fi
+\else
+\edef\@CDzero{\@DXpzero}\relax
+\edef\@SDzero{\@DYpzero}\relax
+\edef\@CDuno{\@DXpuno}\relax
+\edef\@SDuno{\@DYpuno}\relax
+\MultiplyFN\@SDzero by\@CDuno to\@tempA
+\MultiplyFN\@SDuno by\@CDzero to\@tempB
+\edef\@tempA{\strip@pt\dimexpr\@tempA\p@-\@tempB\p@}\relax
+\@tdA=\@SDuno\p@ \@tdB=\@Chord\p@ \@tdC=\@tempA\p@
+\edef\@tempC{\strip@pt\dimexpr \@tdA*\@tdB/\@tdC}\relax
+\MultiplyFN\@tempC by\@CDzero to \@XC
+\MultiplyFN\@tempC by\@SDzero to \@YC
+\ModOfVect\@XC,\@YC to\@KC
+\ScaleVect\@Dzero by\@KC to\@CP
+\AddVect\@Pzero and\@CP to\@CP
+\GetCoord(\@Pzero)\@XPzero\@YPzero
+\GetCoord(\@Puno)\@XPuno\@YPuno
+\GetCoord(\@CP)\@XCP\@YCP
+\@ovxx=\@XPzero\unitlength \@ovyy=\@YPzero\unitlength
+\@ovdx=\@XCP\unitlength \@ovdy=\@YCP\unitlength
+\@xdim=\@XPuno\unitlength \@ydim=\@YPuno\unitlength
+      \pIIe@bezier@QtoC\@ovxx\@ovdx\@ovro
+      \pIIe@bezier@QtoC\@ovyy\@ovdy\@ovri
+      \pIIe@bezier@QtoC\@xdim\@ovdx\@clnwd
+      \pIIe@bezier@QtoC\@ydim\@ovdy\@clnht
+      \pIIe@moveto\@ovxx\@ovyy
+      \pIIe@curveto\@ovro\@ovri\@clnwd\@clnht\@xdim\@ydim
+\fi\fi\egroup
+\CopyVect\@Puno to\@Pzero
+\CopyVect\@Duno to\@Dzero
+\ignorespaces}
 
 %% 
 %% Copyright 2005-2015 Claudio Beccari