ellipse (6dec15)

git-svn-id: svn://tug.org/texlive/trunk@39025 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 1309 insertions, 0 deletions

diff --git a/Master/texmf-dist/source/latex/ellipse/ellipse.dtx b/Master/texmf-dist/source/latex/ellipse/ellipse.dtx
new file mode 100644
index 00000000000..c22bfe2a58f
--- /dev/null
+++ b/Master/texmf-dist/source/latex/ellipse/ellipse.dtx
@@ -0,0 +1,1238 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 2015 Daan Leijen
+% -------------------------------------------------------
+% 
+% This file may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.2
+% 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 1.2 or later is part of all distributions of LaTeX 
+% version 1999/12/01 or later.
+%
+% \fi
+%
+% \iffalse
+%<*driver>
+\ProvidesFile{ellipse.dtx}
+%</driver>
+%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
+%<package>\ProvidesPackage{ellipse}
+%<*package>
+    [2004/11/05 v1.0 .dtx ellipse file]
+%</package>
+%<package>\RequirePackage{pict2e}
+%
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{graphicx}
+\usepackage{ellipse}[2004/11/05]
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{hyperref}
+\usepackage{lmodern}
+\usepackage{xcolor}
+\usepackage{wrapfig}
+\newcommand\kk[1]{\iota_{#1}}
+\newcommand\sk[1]{\rho_{#1}}
+\newcommand\sint[1]{\textit{sint}_{#1}}
+\newcommand\cost[1]{\textit{cost}_{#1}}
+\newcommand\sign[1]{\pm_{#1}}
+\newcommand\csqrt{\textit{csqrt}}
+\renewcommand\cos{\textit{cos}}\renewcommand\sin{\textit{sin}}
+\renewcommand\arctan{\textit{arctan}}\renewcommand\tan{\textit{tan}}
+\renewcommand\max{\textit{max}}\renewcommand\sin{\textit{sin}}
+\providecolor{teal}{HTML}{008080}
+\providecolor{purple}{HTML}{800080}
+\providecolor{navy}{HTML}{000080}
+\providecolor{maroon}{HTML}{800000}
+\providecolor{floralwhite}{HTML}{FFFAF0}
+\providecolor{ivory}{HTML}{FFFFF0}
+\providecolor{white}{HTML}{FFFFFF}
+\providecolor{transparent}{named}{white}
+\providecolor{gainsboro}{HTML}{DCDCDC}
+\hypersetup{colorlinks=true,citecolor=navy,linkcolor=navy,urlcolor=navy,filecolor=navy,bookmarksdepth=3,bookmarksopenlevel=1}
+\makeatletter
+\DeclareRobustCommand*\package[2][]{%
+  \def\@tempa{#1}%
+  \ifx\@tempa\@empty
+    \textsf{#2}%
+  \else
+    \href{http://mirrors.ctan.org/macros/latex/#1}{\textsf{#2}}%
+  \fi
+}%
+\DeclareRobustCommand*\pkgpicte{\package[contrib/pict2e/pict2e.pdf]{pict2e}}
+\newsavebox{\@ebox}
+\newcommand*\@unit[1]{\strip@pt\dimexpr#1\relax}%
+\newcommand*\ellipbox[1]{%
+  \begingroup
+  \savebox{\@ebox}{#1}%
+  \setlength{\unitlength}{1pt}%
+  \hspace*{0.8ex}%
+  \begin{picture}(0,0)%
+   \put(\@unit{0.5\wd\@ebox},\@unit{0.5\ht\@ebox - 0.5\dp\@ebox}){%
+     \ellipse{\@unit{0.8ex + 0.5\wd\@ebox}}{\@unit{0.8ex + 0.5\ht\@ebox}}%
+  }%
+  \end{picture}%
+  \usebox{\@ebox}%
+  \hspace{0.8ex}%
+  \endgroup%
+}
+\makeatother
+\EnableCrossrefs         
+\CodelineIndex
+\RecordChanges
+\begin{document}
+  \setlength\emergencystretch{3em}  
+  \DocInput{ellipse.dtx}
+  \PrintChanges
+  \setcounter{IndexColumns}{2}%
+  \PrintIndex
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{0}
+%
+% \CharacterTable
+%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%   Digits        \0\1\2\3\4\5\6\7\8\9
+%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%   Dollar        \$     Percent       \%     Ampersand     \&
+%   Acute accent  \'     Left paren    \(     Right paren   \)
+%   Asterisk      \*     Plus          \+     Comma         \,
+%   Minus         \-     Point         \.     Solidus       \/
+%   Colon         \:     Semicolon     \;     Less than     \<
+%   Equals        \=     Greater than  \>     Question mark \?
+%   Commercial at \@     Left bracket  \[     Backslash     \\
+%   Right bracket \]     Circumflex    \^     Underscore    \_
+%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%   Right brace   \}     Tilde         \~}
+%
+%
+% \changes{v1.0}{2015/03/24}{Initial version}
+%
+% \GetFileInfo{ellipse.dtx}
+%
+% \DoNotIndex{\newcommand,\renewcommand,\newenvironment,\renewenvironment}
+% \DoNotIndex{\providecommand,\def,\edef,\let,\gdef,\xdef,\global,\newtoks}
+% \DoNotIndex{\RequirePackage,\DeclareOption,\ProcessOptions,\ExecuteOptions}
+% \DoNotIndex{\input,\InputIfFileExists}
+% \DoNotIndex{\@ifdefinable,\@ifundefined,\@percentchar}
+% \DoNotIndex{\AtBeginDocument,\AtEndOfPackage}
+% \DoNotIndex{\PackageError,\PackageWarning,\PackageWarningNoLine,\PackageInfo}
+% \DoNotIndex{\MessageBreak,\typeout}
+%
+% \DoNotIndex{\z@,\z@skip,\p@,\@ne,\tw@,\thr@@,\@iv,\two@fourteen,\strip@pt}
+% \DoNotIndex{\the,\if,\else,\or,\fi,\ifnum,\ifdim,\ifcase,\ifodd}
+% \DoNotIndex{\advance,\multiply,\divide}
+% \DoNotIndex{\@tfor,\do}
+% \DoNotIndex{\csname,\endcsname,\begingroup,\endgroup}
+% \DoNotIndex{\expandafter,\afterassignment,\noexpand}
+% \DoNotIndex{\@ovxx,\@ovyy,\@ovdx,\@ovdy}
+% \DoNotIndex{\undefined,\dimexpr,\relax,\space,\protect,\begin}
+% \DoNotIndex{\@tempdima,\@tempdimb,\@tempdimc,\@tempdimd,\dimen@,\@tempa}
+% \DoNotIndex{\@tempswafalse,\@tempswatrue,\if@tempswa,\iffalse,\ifx,\ignorespaces}
+%
+% \title{The {\linethickness{0.6pt}\ellipbox{\textsf{ellipse}}} package}
+% \author{Daan Leijen \\ \texttt{daan@microsoft.com}}
+%
+% \maketitle
+%  
+% \newcommand\pictexample[1]{%
+%   \setlength{\unitlength}{10pt}%
+%   \raisebox{-30pt}{\begin{picture}(6,8)%
+%   \linethickness{0.4pt}\roundjoin%
+%   \color{gainsboro}%
+%   \put(0,0){\multiput(0,0)(1,0){9}{\line(0,1){6}}%
+%    \multiput(0,0)(0,1){7}{\line(1,0){8}}%  
+%   }%
+%   \put(0,0){\color{gray}%
+%     {\vector(1,0){8}}\put(-0.5,6.5){$y$}%
+%     {\vector(0,1){6}}\put(8.5,-0.5){$x$}%
+%   }%
+%   \color{black}%
+%   \linethickness{0.8pt}%
+%   #1\end{picture}}%
+% } 
+% 
+% \section{Introduction}
+%
+% \LaTeX{} has many advanced graphics packages now, the most extensive are 
+% \href{https://www.ctan.org/pkg/pgf}{\textsf{tikz}}
+% and \href{https://www.ctan.org/pkg/pstricks-base}{\textsf{pstricks}}.
+% However, these are also large packages that take long to load and
+% may not always work on all drivers. The standard \pkgpicte{} package removes many of the previous
+% limitations of the `old' \LaTeX{} |picture| environment and makes it a \emph{lean
+% and portable} alternative to the more full featured packages. However, even though it can
+% draw circles and circle arcs well, it lacks the ability to draw ellipses and elliptical
+% arcs. This package adds these functions on top of the standard \pkgpicte{} primitives 
+% (i.e. the |\cbezier| command).
+%
+% \section{Drawing ellipses}
+%
+% \noindent
+% \DescribeMacro\ellipse
+% \DescribeMacro{\ellipse*}
+% \marg{x-radius}\marg{y-radius}\\
+% \strut\\
+% These commands draw an ellipse with the specified radi\"\i. The |\ellipse| command draws
+% a stroked ellipse with the current |\linethickness| while |\ellipse*| draws a filled
+% ellipse with the current |\color|. For example:
+%
+% \noindent\begin{minipage}{0.7\linewidth}%
+% \begin{verbatim}
+% \setlength{\unitlength}{10pt}%
+% \begin{picture}(6,8)
+%   \linethickness{0.8pt}%
+%   \put(6,3){\color{teal}\ellipse*{2}{3}}%
+%   \put(3,3){\color{blue}\ellipse{3}{2}}%
+% \end{picture}
+% \end{verbatim}\end{minipage}
+% \pictexample{%
+%   \put(6,3){\color{teal}\ellipse*{2}{3}}%
+%   \put(3,3){\color{blue}\ellipse{3}{2}}%
+% }\\[2ex]
+%
+% \noindent
+% \DescribeMacro\earc
+% \DescribeMacro{\earc*}
+% \oarg{start-angle$\rangle$|,|$\langle$end-angle}\marg{x-radius}\marg{y-radius}\\
+% \strut\\
+% These commands draw part of an ellipse with the specified radi\"\i. 
+% The |\earc| command draws
+% a stroked elliptical arc with the current |\linethickness| while |\earc*| draws a filled
+% elliptical `pie slice' with the current |\color|. The optional argument specifies a start and 
+% end-angle in degrees which must be between $-720$ and $720$ (but can be fractional).
+% The endings of the arcs are determined by the \emph{cap} setting: |\buttcap| (default),
+% |\roundcap| (add half disc), or |\squarecap| (add half square).
+%
+% \noindent\begin{minipage}{0.7\linewidth}%
+% \begin{verbatim}
+% \put(3,3){%
+%   \color{blue}\roundcap\earc[135,330]{3}{2}}%
+% \put(6,3){%
+%   \color{teal}\earc*[-45,90]{2}{3}}%
+% \end{verbatim}
+% \end{minipage}
+% \pictexample{%
+%   \put(3,3){\color{blue}\roundcap\earc[135,330]{3}{2}}%
+%   \put(6,3){\color{teal}\earc*[-45,90]{2}{3}}%
+% }\\[2ex]
+%
+% \noindent
+% \DescribeMacro\elliparc
+% \oarg{initial}\marg{center-x}\marg{center-y}\marg{x-rad}\marg{y-rad}\marg{start-angle}\marg{end-angle}\\
+%
+% \noindent The core elliptical arc routine. These are to be used with path commands, like
+% |\lineto|, |\moveto|, |\strokepath|, etc, and can draw an elliptical arc at any center point. 
+% The optional argument specifies the initial drawing
+% action: the default is $0$ (|\lineto|) which draws a line to the arc starting point,
+% the value $1$
+% (|\moveto|) just moves to the starting point, and $2$ does nothing as an initial action. 
+% If the start angle is larger than the end angle, the arc is drawn clockwise, and otherwise
+% anti-clockwise.\\[1ex]
+%
+% \noindent\begin{minipage}{0.7\linewidth}%
+% \begin{verbatim}
+% \elliparc[1]{3}{3}{3}{2}{90}{270}%
+% \elliparc{5}{3}{2}{2}{-90}{90}%
+% \closepath\strokepath
+% \color{teal}%
+% \moveto(1,3)
+% \elliparc{3}{3}{2}{1}{-135}{135}%
+% \closepath
+% \fillpath
+% \end{verbatim}\end{minipage}
+% \pictexample{%
+%   \elliparc[1]{3}{3}{3}{2}{90}{270}%
+%   \elliparc{5}{3}{2}{2}{-90}{90}%
+%   \closepath\strokepath
+%   \color{teal}%
+%   \moveto(1,3)
+%   \elliparc{3}{3}{2}{1}{-135}{135}%
+%   \closepath
+%   \fillpath
+% }\\[2ex]
+%
+% \noindent Note how the two initial arcs are automatically connected by a line
+% segment from $(3,1)$ to $(5,1)$ (due to the default optional argument of $0$ that
+% uses a |\lineto| command to the starting point of the arc). Similarly, we use
+% such initial line segment and a |\closepath| to draw the triangular side of the
+% inner ellipse.
+%
+% \subsection{Rotated ellipses}
+%
+% There is no direct command to rotate an ellipse but you can use the
+% standard |\rotatebox| command from the \package[required/graphics/grfguide.pdf]{graphicx} package. For example:
+%
+% \noindent\begin{minipage}{0.7\linewidth}%
+% \begin{verbatim}
+% \put(3,3){%
+%   \rotatebox[origin=c]{45}{\ellipse{3}{2}}%
+% }%
+% \end{verbatim}\end{minipage}
+% \pictexample{%
+% \put(3,3){\rotatebox[origin=c]{45}{\ellipse{3}{2}}%
+% }%
+% }\\[2ex]
+%
+% \subsection{Using the picture environment inline}
+%
+% The standard \LaTeX{} |picture| environment is nowadays quite
+% powerful and convenient. Read the latest \pkgpicte{} documentation
+% and ``The unknown \emph{picture} environment'' \cite{picture} for more information. 
+% One particularly nice feature is that we
+% can create a picture as |\begin{picture}(0,0)| to give it zero
+% space. This can be used for example to define an |\ellipbox| command
+% like:\\[1ex]
+%
+% \noindent\begin{minipage}{0.6\linewidth}%
+% \begin{verbatim}
+% Boxed numbers: 
+%   \ellipbox{1}, \ellipbox{123}.  
+% \end{verbatim}
+% \end{minipage}
+% \begin{minipage}{0.38\linewidth}%
+% Boxed numbers: \ellipbox{1}, \ellipbox{123}.
+% \end{minipage}\\[1ex]
+%
+% \noindent We also used this command to draw the ellipse in the title
+% of this article, and it is defined as:
+% \begin{verbatim}
+%\newsavebox{\@ebox}
+%\newcommand*\@unit[1]{\strip@pt\dimexpr#1\relax}%
+%\newcommand*\ellipbox[1]{%
+%  \begingroup
+%  \savebox{\@ebox}{#1}%
+%  \setlength{\unitlength}{1pt}%
+%  \hspace*{0.8ex}%
+%  \begin{picture}(0,0)%
+%   \put(\@unit{0.5\wd\@ebox},\@unit{0.5\ht\@ebox - 0.5\dp\@ebox}){%
+%     \ellipse{\@unit{0.8ex + 0.5\wd\@ebox}}{\@unit{0.8ex + 0.5\ht\@ebox}}%
+%  }%
+%  \end{picture}%
+%  \usebox{\@ebox}\hspace{0.25ex}\endgroup}
+% \end{verbatim}
+% \noindent This is not the best code possible but it hopefully gives you a good
+% idea on how to implement your own boxes. Note the use of the |\@unit| macro
+% to convert dimensions to units, which is also why we need to set the |\unitlength|
+% to |1pt| here.
+%
+% \StopEventually{}
+%
+% \begin{thebibliography}{9}
+% \raggedright
+%
+% \bibitem{abst} M.~Abramowitz and I.A.~Stegun: \textit{Handbook of Mathematical Functions},
+%  \url{people.math.sfu.ca/~cbm/aands}, 1964
+%
+% \bibitem{picture} Claudio Beccari: \emph{The unknown \emph{picture} environment},
+%   TUGBoat, vol. 33(1), 2012. \url{tug.org/TUGboat/tb33-1/tb103becc-picture.pdf}
+%
+% \bibitem{ellipse} Luc Maisonobe: \textit{Drawing an elliptical arc using polylines, quadratic or cubic B\'ezier lines.}
+%    \url{www.spaceroots.org/documents/ellipse/elliptical-arc.pdf}, 2003
+%
+% \bibitem{rajan:atan} S.~Rajan, Sichun Wang, R.~Inkol, and A.~Joyal: \textit{Efficient approximations for the arctangent function}. 
+%  In Signal Processing Magazine, vol. 23(3), pages 108--111, May 2006
+%
+% \end{thebibliography}
+%
+% \clearpage
+%
+% \newcommand\abs[1]{\lvert #1\rvert}
+% \newcommand\rarg[1]{$\langle$\textit{#1}$\rangle$}
+% \newcommand\xellipse{\mathcal{E}}
+%
+% \section{Elliptical arcs as B\'ezier curves}
+% \begin{figure}\begin{center}
+% \setlength\unitlength{18pt}
+% \begin{picture}(12,9)(-1.5,-0.5)%
+%   \linethickness{0.4pt}\roundjoin%
+%   \iffalse
+%    \color{gainsboro}%
+%    \put(0,0){%
+%      \multiput(-2,-1)(1,0){13}{\line(0,1){9}}%
+%      \multiput(-2,-1)(0,1){10}{\line(1,0){12}}%
+%    }%
+%   \fi
+%   \color{black}%
+%   \put(0,0){%
+%     \put(0,-0.5){\vector(0,1){8}}\put(8.5,-0.5){$x$}%
+%     \put(-1.5,0){\vector(1,0){11}}\put(-0.5,6.5){$y$}%
+%   }%
+%   \put(4,3.3){\color{navy}\earc{5}{3}
+%     \put(3,-2){$\xellipse$}%%  
+%     \color{teal}%
+%     \put(-5.5,0){\line(1,0){11}}%
+%     \put(0,-3.5){\line(0,1){8}}%
+%     \put(3,0){\vector(-1,0){3}\vector(1,0){2}\raisebox{0.3ex}{$a$}}%
+%     \put(0,-1.5){\vector(0,1){1.5}\vector(0,-1){1.5}$\,b$}%
+%     \color{maroon}%
+%     \put(0,0){\moveto(0,0)\elliparc{0}{0}{5}{3}{30}{120}\closepath\strokepath}%
+%     {\linethickness{2pt}\earc[30,120]{5}{3}}%
+%     \put(3.7,2.2){$p_1$}\put(-2,3.1){$p_2$}%
+%     \put(2.25,2.92){\moveto(0,0)\lineto(1.35,-0.84)\strokepath\circle*{0.1}$\;q_1$}%
+%     \put(-0.075,3.22){\moveto(0,0)\lineto(-1.56,-0.39)\strokepath\circle*{0.1}$\,q_2$}%
+%     \color{black}
+%     \linethickness{0.2pt}\arc[0,30]{1}\arc[0,120]{2}%
+%     \put(1,0.2){$\alpha_1$}\put(1,1.8){$\alpha_2$}%
+%   }%
+%   \color{navy}\put(4,-0.3){$\,c_x$}\put(0,2.9){$\,c_y$}%
+%   %
+% \end{picture}\end{center}
+% \caption{Approximating an elliptical arc with a cubic B\'ezier curve. The center of the ellipse
+%  is at $(c_x,c_y)$ with a horizontal radius of $a$ and a vertical one $b$. The elliptical arc goes
+%  from $\alpha_1$ to $\alpha_2$ and is approximated with a thick red cubic B\'ezier curve. The curve
+%  starts at $p_1$ and ends in $p_2$ with two control points $q_1$ and $q_2$. The curve was drawn
+%  using the command \texttt{\textbackslash{}elliparc\{4\}\{3.3\}\{5\}\{3\}\{30\}\{120\}}.}
+% \label{fig:ellipse}
+% \end{figure}
+% \begin{figure}
+% \setlength\unitlength{20pt}\begin{center}
+% \begin{picture}(12,8)(-1.5,-0.5)%
+%   \linethickness{0.4pt}\roundjoin%
+%   \iffalse
+%   \put(0,0){\color{gainsboro}%
+%     \multiput(-2,-1)(1,0){13}{\line(0,1){8}}%
+%     \multiput(-2,-1)(0,1){9}{\line(1,0){12}}%
+%   }%
+%   \fi
+%   \put(4,3){\color{navy}\earc{5}{3}\put(-4,1){$\xellipse$}\color{teal}%
+%     \put(-5.5,0){\line(1,0){11}}%
+%     \put(0,-3.5){\line(0,1){7}}%
+%     \put(-2,0){\vector(-1,0){3}\vector(1,0){2}\raisebox{0.3ex}{$a$}}%
+%     \put(0,-1.5){\vector(0,1){1.5}\vector(0,-1){1.5}$\,b$}%
+%     \color{black}%
+%     \put(0,0){\circle{6}}%
+%     \put(0,0){\vector(3.6,2.08){3.6}\vector(2.16,2.08){2.16}}%
+%     \put(0,0){\color{maroon}%
+%      \put(3.6,0){\line(0,1){2.08}\circle*{0.1}}%
+%      \put(3.2,-0.5){$a\cos(t_1)$}%
+%      \put(2.16,0){\line(0,1){2.08}\circle*{0.1}}%
+%      \put(1.3,-0.5){$\cos(t_1)$}%
+%     }%
+%     \linethickness{0.2pt}\arc[0,30]{1}\arc[0,43.9]{2}%
+%     \put(1,0.2){$\alpha_1$}\put(1.65,1.25){$t_1$}%
+%   }%
+%   %
+% \end{picture}\end{center}
+% \caption{The relation between the parametric angle $t_1$ and the angle $\alpha_1$ to the point on the ellipse.
+%   All points on the ellipse are defined by the parametric equation $\xellipse(t) = (c_x + a\cdot\cos(t), c_y + b\cdot\sin(t))$}
+% \label{fig:parametric}
+% \end{figure}
+% %
+% %
+% Drawing an ellipse or part of an ellipse (\emph{elliptical arc}) using B\'ezier
+% curves requires some math to determine the right control points of the B\'ezier curve.
+% Figure~\ref{fig:ellipse} establishes some notation. We do not consider rotated
+% ellipses here and always use $a$ for the $x$-radius and $b$ for the $y$-radius.
+% We are interested in finding the B\'ezier curve between the $\alpha_1$ and
+% $\alpha_2$ angles, which implies finding the starting 
+% point $p_1$, the end point $p_2$ and the control points $q_1$ and $q_2$. 
+%
+% Each point on an ellipse is determined by the following parametric equation:
+% \[ \xellipse(t) = (c_x + a\cdot\cos(t), c_y + b\cdot\sin(t)) \]
+% where $t$ is the
+% parametric angle. The parametric angle $t$ is just a property of the ellipse and has no
+% `real' counterpart. Figure~\ref{fig:parametric} gives some helpful intuition how
+% the $\alpha$ angles and $t$ angles are related: we can imagine drawing a unit circle inside
+% an ellipse where for every $t$ angle on the unit circle we have a corresponding point
+% and angle $\alpha$ on the ellipse. From the definition of $\xellipse$ it 
+% is straightforward to derive a parametric angle $t_i$ for some $\alpha_i$: 
+% \[ t_i = \arctan_2(\frac{\sin(\alpha_i)}{b},\frac{\cos(\alpha_i)}{a}) \]
+%
+% \noindent Given this relation, the start and end points of our curve are simply:
+% \begin{align*}
+% p_1 &= \xellipse(t_1)\\
+% p_2 &= \xellipse(t_2)
+% \end{align*}
+%
+% \noindent To be able to calculate optimal control points $q$ we need to also determine the 
+% tangent of each point on the ellipse, which is given by the derivative of $\xellipse$:
+% \[ \xellipse'(t) = (-a\cdot\sin(t), b\cdot\cos(t)) \]
+% 
+% \noindent 
+% The derivation of the optimal B\'ezier control points for an ellipse is quite involved, 
+% see~\cite{ellipse} for a nice overview. 
+% For a quadratic B\'ezier curve, it turns out the optimal control points are determined as:
+% \begin{align*}
+% q_1 &= p_1 + \tan(\frac{t_2 - t_1}{2})\cdot\xellipse'(t_1)\\
+%     &= p_2 - \tan(\frac{t_2 - t_1}{2})\cdot\xellipse'(t_2)
+% \end{align*}
+% %
+% \noindent while for a cubic B\'ezier curve, one solution for optimal control points is:
+% %
+% \begin{align*}
+% q_1 &= p_1 + \kappa\cdot\xellipse'(t_1)\\
+% q_2 &= p_2 - \kappa\cdot\xellipse'(t_2)\\
+% \kappa &= \sin(t_2 - t_1)\frac{\sqrt{4 + 3\tan^2(\frac{t_2 - t_1}{2})}-1}{3}
+% \end{align*}
+% \noindent We will use cubic bezier curves since they look best. However, a na\"\i{}ve implementation
+% may be too expensive in \LaTeX: if we count the expensive operations, we need about 11 $\cos$/$\sin$ 
+% operations, plus a $\sqrt{}$ and 2 $\arctan$ operations.
+% %
+% \subsection{Optimizing elliptic arc equations} 
+% Fortunately, we can improve upon this. First we note:
+% \begin{flalign*}
+% t_i &= \arctan_2(\frac{\sin(\alpha_i)}{b},\frac{\cos(\alpha_i)}{a}) & \hfill\\ 
+%     &= \arctan(\frac{a}{b}\tan(\alpha_i)) \\
+%     &= \arctan(\kk{i}) & \mbox{(introducing $\kk{i}$ for $\frac{a}{b}\tan(\alpha_i)$)}
+% \end{flalign*}
+% \noindent where we write $\kk{i}$ for $\frac{a}{b}\tan(\alpha_i)$. Now, 
+% \begin{flalign*}
+% \cost{i} &= \cos(t_i)\\
+%           &= \cos(\arctan(\kk{i})) & \mbox{(geometry and pythagorean theorem)}\\
+%           &= \sign{i}\frac{1}{\sqrt{1 + \kk{i}^2}} \\
+% \mbox{with}\\
+% \sign{i} &= \textsf{if}\; \cos(\alpha_i) < 0\; \textsf{then}\; -\; \textsf{else}\; + 
+% \end{flalign*}
+% Later we will see how we can efficiently calculate the square root term, but first 
+% do the same derivation for the $\sin$ function:
+% \begin{flalign*}
+% \sint{i}&= \sin(t_i) \\
+%         &= \sin(\arctan(\frac{a}{b}\tan(\alpha_i))) & \\
+%           &= \sin(\arctan(\kk{i})) \\
+%           &= \sign{i}\frac{\kk{i}}{\sqrt{1 + \kk{i}^2}}  
+% \end{flalign*}
+% \noindent Note that the interaction between the $\sin$ and $\kk{i}$ term (whose sign is determined by $\tan(\alpha_i)$) allows us to reuse the sign function used for $\cost{i}$. 
+% %
+% Using the previous equalities we can restate the parametric equations in terms of $\sint{i}$
+% and $\cost{i}$:
+% \begin{flalign*}
+% \xellipse_i &= (c_x + a\cdot\cost{i}), c_y + b\cdot\sint{i}) \\
+% \xellipse'_i &= (-a\cdot\sint{i}, b\cdot\cost{i})
+% \end{flalign*}
+% %
+% \noindent This takes care of $p_1$ and $p_2$. The control points $q$ still need $\sin(t_2 - t_1)$ and $\tan(\frac{t_2 - t_1}{2})$.
+% The halving rule on $\tan$ gives us:
+% \[
+% \tan(\frac{t_2 - t_1}{2}) = \frac{1 - \cos(t_2 - t_1)}{\sin(t_2 - t_1)} \mbox{\quad(\cite[page 71, 4.3.20]{abst})}
+% \]
+% \noindent So that leaves $\sin(t_2 - t_1)$ and $\cos(t_2 - t_1)$. Using the addition laws it follows:
+% \begin{flalign*}
+% \sin(t_2 - t_1) = \sint2\cost1 - \cost2\sint1 & \mbox{\quad(\cite[page 72, 4.3.16]{abst})}\\
+% \cos(t_2 - t_1) = \cost2\cost1 + \sint2\sint1 & \mbox{\quad(\cite[page 72, 4.3.17]{abst})}
+% \end{flalign*}
+%
+% \subsection{Circular square roots}
+% \noindent Now, we only need two $\tan$ operations to calculate the initial $\kk{1}$ and $\kk{2}$ terms but we still have
+% three square roots: $\sqrt{1 + \kk{i}^2}$ and $\sqrt{4 + 3\tan^2(\frac{t_2 - t_1}{2})}$. 
+% Fortunately, both have the form $\sqrt{x^2 + y^2}$. For this form, we can make a very good 
+% \begin{wrapfigure}[10]{o}{0.3\textwidth}
+% \setlength\unitlength{3pt}
+% \begin{picture}(30,30)(-15,-15)%
+%   \linethickness{0.4pt}\roundjoin%
+%   \iffalse
+%   \put(0,0){\color{gainsboro}%
+%     \multiput(-15,-15)(1,0){31}{\line(0,1){30}}%
+%     \multiput(-15,-15)(0,1){31}{\line(1,0){30}}%
+%   }%
+%   \fi
+%   \color{gainsboro}%
+%   \put(0,0){\put(0,-15){\line(0,1){30}}%
+%     \put(-15,0){\line(1,0){30}}%
+%   }%
+%   \color{black}%
+%   \put(0,0){\circle{20}\put(-9,3){$\,x^2 + y^2$}%
+%     \color{maroon}\moveto(14.14,0)\lineto(0,14.14)\lineto(-14.14,0)\lineto(0,-14.14)
+%     \closepath\strokepath
+%     \put(3,13){$\frac{1}{\sqrt{2}}(x+y)$}%
+%     \color{navy}\moveto(10,10)\lineto(-10,10)\lineto(-10,-10)\lineto(10,-10)
+%     \closepath\strokepath
+%     \put(6,-12){$\,\max(x,y)$}%
+%   }
+%   %
+% \end{picture}\iffalse\caption{Estimating an initial value for $\sqrt{x^2+y^2}$}\fi
+% \end{wrapfigure}
+% initial guess for the square root, since this is the parametric equation for a circle.
+% The two good initial guesses form a `square' and `diamond' around this circle, namely
+% $\max(\abs{x},\abs{y})$ and $\frac{1}{\sqrt{2}}\abs{x+y}$. Each one can be superior depending if $x$ and $y$
+% are close or not, but it can be shown that the best choice is always the largest of these.
+% Using this guess as an initial seed, we can do a standard Newton-Raphson iteration to 
+% find a the square root where we only need 2 or 3 steps to achieve the desired precision. 
+% Let's define a `circular square root' function $\csqrt$ such that
+% $\csqrt(x,y) \approx \sqrt{x^2 + y^2}$ as:
+% \begin{align*}
+% \csqrt(x,y) = &\textsf{let} & sqr & = x^2 + y^2 & \hfill \\
+%             &               & x_0 & = \max(\abs{x},\abs{y},\frac{1}{\sqrt{2}}\abs{x+y}) & \\
+%             &               & x_1 & = (x_0 + \frac{sqr}{x_0})/2 & \hspace{\textwidth}\\
+%             &               & x_2 & = (x_1 + \frac{sqr}{x_1})/2 &\\
+%             &  \textsf{in} & x_2 & 
+% \end{align*}
+% 
+% \subsection{The optimized elliptical B\'ezier equations}
+% \noindent Taking it all together, we get the following equations for a cubic B\'ezier curve approximation of an elliptical arc,
+% where we assume as input the center point $(c_x,c_y)$, the $x$- and $y$-radius $(a,b)$, and a start and end angle
+% $\alpha_1$ and $\alpha_2$. % It is assumed that $\alpha_1 \ne \alpha_2$ and $a \ge 0, b \ge 0$. Of course,
+% with bezier curves one should build a full ellipse of parts where for each part $\rvert\alpha_1 - \alpha_2\lvert \le 90$.
+% Given these parameters, the start and end point $p_1$ and $p_2$, and the control points $q_1$ and $q_2$ are
+% defined as:
+% \begin{flalign*}
+% p_1 &= \xellipse_1 & \\
+% p_2 &= \xellipse_2\\
+% q_1 &= p_1 + \kappa\cdot\xellipse'_1\\
+% q_2 &= p_2 - \kappa\cdot\xellipse'_2\\
+% \xellipse_i &= (c_x + a\cdot\cost{i}, c_y + b\cdot\sint{i})\\
+% \xellipse'_i &= (-a\cdot\sint{i}, b\cdot\cost{i})
+% \end{flalign*}
+% The $\cost{i}$ and $\sint{i}$ are calculated as:
+% \begin{flalign*}
+% \sint{i} & = \sign{i}\frac{\kk{i}}{\sk{i}} & \\
+% \cost{i} & = \sign{i}\frac{1}{\sk{i}} 
+% \end{flalign*}
+% with
+% \begin{flalign*}
+% \kk{i} &= \frac{a}{b}\tan(\alpha_i) & \\
+% \sk{i} &= \csqrt(1,\kk{i}) \;\;(\approx \sqrt{1 + \kk{i}^2}) \\
+% \sign{i} &= \textsf{if}\; \cos(\alpha_i) < 0\; \textsf{then}\; -\; \textsf{else}\; + 
+% \end{flalign*}
+% And finally, the $\kappa$ term can be defined as:
+% \begin{flalign*}
+% \kappa    &= \sint{21}\frac{\kappa_{sqrt}-1}{3} & 
+% \end{flalign*}
+% with
+% \begin{flalign*}
+% \sint{21} & = \sint2\cost1 - \cost2\sint1 \;\;(=\sin(t_2 - t_1)) & \\
+% \cost{21} & = \cost2\cost1 + \sint2\sint1 \;\;(=\cos(t_2 - t_1))\\
+% \kappa_{tan} &= \frac{1 - \cost{21}}{\sint{21}} \;\;\mbox{(note: divides by zero if $\alpha_1 = \alpha_2$)}\\
+% \kappa_{sqrt} &= \csqrt(\sqrt{4},\sqrt{3}\cdot\kappa_{tan}) \;\;(\approx \sqrt{4 + 3\kappa_{tan}^2})
+% \end{flalign*}
+%
+%\section{Implementation}
+%
+% Generally, we use e-\TeX{} division to divide dimensions, where we 
+% divide \rarg{dim$_1$} by \rarg{dim$_2$} using:
+% |\dimexpr 1pt * |\rarg{dim$_1$}|/|\rarg{dim$_2$}|\relax| 
+% since it keeps a 64-bit intermediate result for such `scaling' expressions. 
+% Note that both \rarg{dim}
+% expressions occur in an integer context and \TeX{} will convert
+% them to numbers automatically (i.e. in |sp| units).
+%
+
+% \subsection{Generic math and trigonometry routines}
+%
+% \begin{macro}{\pIIe@csedef}
+% \marg{csname}\textit{pattern}\marg{body}\\
+% Define a macro by a \textit{csname}. Just like the |\csedef| function 
+% from  \textsf{etoolbox} package 
+%    \begin{macrocode}
+\providecommand*\pIIe@csedef[1]{\expandafter\edef\csname #1\endcsname}
+%    \end{macrocode}
+% \end{macro}
+%
+%\begin{macro}{\pIIe@ellip@csqrt}
+% \marg{dimen$_x$}\marg{dimen$_y$}\marg{dimreg$_{res}$}\\
+% Calculates $res \approx \sqrt{x^2 + y^2}$ and caches previous results
+% for efficiency.
+%
+% Overwrites |\@ovxx|,|\@ovyy|,|\@ovdx|,|\@ovdy|,|\@tempa|, and |\dimen@|.
+%    \begin{macrocode}
+\newcommand*\pIIe@ellip@csqrt[3]{%
+  \@ovxx=#1\relax
+  \ifdim\@ovxx<\z@\@ovxx-\@ovxx\fi
+  \@ovyy=#2\relax
+  \ifdim\@ovyy<\z@\@ovyy-\@ovyy\fi
+  \edef\pIIe@csname{@csqrt(\number\@ovxx,\number\@ovyy)}%
+  \expandafter\ifx\csname\pIIe@csname\endcsname\relax
+    \pIIe@ellip@csqrt@%    
+    \pIIe@csedef{\pIIe@csname}{\the\dimen@}%
+    #3\dimen@
+  \else
+    #3\dimexpr\csname\pIIe@csname\endcsname\relax
+  \fi
+}
+%    \end{macrocode}
+%\end{macro}
+%\begin{macro}{\pIIe@ellip@csqrt@}
+% Internal routine: calculates |\dimen@| $\approx \sqrt{x^2 + y^2}$.
+% where $x \ge 0$ and $y \ge 0$, and |\@ovxx| $=x$ and |\@ovyy| $=y$.
+% 
+% Overwrites |\@ovdx|,|\@ovdy|, and |\@tempa|.
+%    \begin{macrocode}
+\newcommand*\pIIe@ellip@csqrt@{%
+%    \end{macrocode}
+% First determine $\max(x,y,\frac{1}{\sqrt{2}}(x+y))$ in |\dimen@|.
+% Put the sum $x+y$ in |\@ovdx|.
+%    \begin{macrocode}  
+  \@ovdx\@ovxx
+  \advance\@ovdx by \@ovyy
+%    \end{macrocode}
+% Put initial guess in |\dimen@| $=\max(\abs{x},\abs{y},\frac{1}{\sqrt{2}}(x+y))$.
+%    \begin{macrocode}  
+  \dimen@0.7071067\@ovdx
+  \ifdim\dimen@<\@ovyy\dimen@\@ovyy\fi
+  \ifdim\dimen@<\@ovxx\dimen@\@ovxx\fi
+%    \end{macrocode}
+% To prevent overflowing \TeX{} dimensions we only do
+% a further Newton-Raphson approximation if the sum $x+y$ is less than 128pt.
+% Otherwise, for our application, the initial guess is still very precise since $x \ll y$ in that case.
+%    \begin{macrocode}  
+  \ifdim\@ovdx<128\p@    
+%    \end{macrocode}
+% Set |\@ovxx| to $x^2 + y^2$
+%    \begin{macrocode}  
+    \edef\@tempa{\strip@pt\@ovxx}%
+    \@ovxx\@tempa\@ovxx
+    \edef\@tempa{\strip@pt\@ovyy}%
+    \@ovyy\@tempa\@ovyy
+    \advance\@ovxx by \@ovyy
+%    \end{macrocode}
+% Do two steps of Newton-Raphson (should we do three?)
+%    \begin{macrocode}    
+    \advance\dimen@ by \dimexpr1pt * \@ovxx/\dimen@\relax
+    \divide\dimen@ by 2%
+    \advance\dimen@ by \dimexpr1pt * \@ovxx/\dimen@\relax
+    \divide\dimen@ by 2%
+  \fi
+%    \end{macrocode}
+% Result is |\dimen@|.
+%    \begin{macrocode}    
+}
+%    \end{macrocode}
+% \end{macro}
+%
+
+
+% \begin{macro}{\pIIe@atan@}
+%
+% Approximate the $\arctan$ using 
+% \[x\cdot\frac{\pi}{4} - x \cdot (\abs{x} - 1) \cdot (0.2447 + 0.0663\cdot\abs{x})\]
+% This approximation was described by Rajan et al.~\cite{rajan:atan}.
+%
+% The \cmd{pIIe@atan@} computes the arctan of |\dimen@| which must be between $-1$ and $1$, and stores it in |\dimen@| again.
+% Overwrites |\@tempdim|(|a|,|b|,|c|,|d|),|\@tempa|, and |\dimen@|.
+%    \begin{macrocode}
+\newcommand*\pIIe@atan@{%
+%    \end{macrocode}
+% |\dimen@| contains $x$.
+%    \begin{macrocode}  
+  \@tempdima\dimen@
+%    \end{macrocode}
+% Set |\@dimtmpb| to $\abs{x}$
+%    \begin{macrocode}  
+  \@tempdimb\@tempdima
+  \ifdim\@tempdimb<\z@\@tempdimb-\@tempdimb\fi
+  \dimen@0.0663\@tempdimb
+  \advance\dimen@ 0.2447pt\relax
+  \advance\@tempdimb -1pt\relax
+  \edef\@tempa{\strip@pt\@tempdimb}%
+  \dimen@\@tempa\dimen@
+  \edef\@tempa{\strip@pt\@tempdima}%
+  \dimen@\@tempa\dimen@
+  \dimen@-\dimen@
+%    \end{macrocode}
+% Add $x\cdot\frac{\pi}{4}$ ($\approx 0.7853\cdot x$).
+%    \begin{macrocode}   
+  \advance\dimen@ 0.7853\@tempdima
+}
+%    \end{macrocode}
+% \end{macro}
+
+% \begin{macro}{\pIIe@atantwo}
+% \marg{dimen$_y$}\marg{dimen$_x$}\marg{dimreg$_{res}$}\\
+% Calculate \rarg{res} $= \arctan_2(y,x)$ and caches the result for later use.
+%
+% Overwrites |\@tempdim|(|a|,|b|,|c|,|d|),|\@tempa|, and |\dimen@|.
+% Both $y$ and $x$ must be dimensions.
+%    \begin{macrocode}
+\newcommand*\pIIe@atantwo[3]{%
+  \edef\pIIe@csname{@atan2(\number\dimexpr#1\relax,\number\dimexpr#2\relax)}%
+  \expandafter\ifx\csname\pIIe@csname\endcsname\relax
+    \pIIe@atantwo@{#1}{#2}{#3}%    
+    \pIIe@csedef{\pIIe@csname}{\the\dimexpr#3\relax}%
+  \else
+    #3\dimexpr\csname\pIIe@csname\endcsname\relax
+  \fi
+}
+%    \end{macrocode}
+% \end{macro}
+
+% \begin{macro}{\pIIe@atantwo@}
+% \marg{dimen$_y$}\marg{dimen$_x$}\marg{dimreg$_{res}$}\\
+% Calculate \rarg{res} $= \arctan_2(y,x)$.
+% Overwrites |\@tempdim|(|a|,|b|,|c|,|d|),|\@tempa|, and |\dimen@|.
+% Both $y$ and $x$ must be dimensions.
+%    \begin{macrocode}
+\newcommand*\pIIe@atantwo@[3]{%
+  \@tempdima\dimexpr#2\relax
+  \@tempdimb\dimexpr#1\relax
+%    \end{macrocode}
+% Handle extremes
+%    \begin{macrocode}  
+  \ifdim\@tempdima=\z@\relax
+    \ifdim\@tempdimb>\z@\relax\dimen@90\p@
+    \else\ifdim\@tempdimb<\z@\relax\dimen@-90\p@
+    \else\dimen@0\p@
+    \fi\fi
+  \else
+%    \end{macrocode}
+% Save angle adjustment term in |\@tempdimd|.
+%    \begin{macrocode}  
+    \@tempdimd\z@
+    \ifdim\@tempdima<\z@\relax
+      \ifdim\@tempdimb<\z@\relax\@tempdimd-180\p@
+      \else\@tempdimd180\p@
+      \fi
+    \fi
+%    \end{macrocode}
+% Divide $\frac{y}{x}$ and check if $-1 \le \frac{y}{x} \le 1$.
+%    \begin{macrocode}  
+    \dimen@\dimexpr1pt * \@tempdimb/\@tempdima\relax
+    \@tempdimc\dimen@
+    \ifdim\@tempdimc<\z@\relax\@tempdimc-\@tempdimc\fi
+    \ifdim\@tempdimc>\p@\relax
+%    \end{macrocode}
+% Use the equality $\arctan(x) = \pm\frac{1}{2}\pi - \arctan(\frac{1}{x})$ 
+% to stay within the valid domain of |\pIIe@atan@|. The sign $\pm$ is
+% positive when $x \ge 0$ and negative otherwise.
+%    \begin{macrocode}
+      \dimen@\dimexpr1pt * \@tempdima/\@tempdimb\relax
+      \ifdim\dimen@<\z@\relax\def\@tempsign{-}\else\def\@tempsign{}\fi
+      \pIIe@atan@
+      \dimen@-\dimen@
+      \advance\dimen@ by \@tempsign1.5707pt\relax
+    \else
+      \pIIe@atan@
+    \fi
+%    \end{macrocode}
+% And convert back to degrees ($\frac{180}{\pi} \approx 57.29578$)
+%    \begin{macrocode}
+    \dimen@57.29578\dimen@
+%    \end{macrocode}
+% Apply angle adjustment 
+%    \begin{macrocode}    
+    \advance\dimen@ by \@tempdimd
+  \fi
+  #3\dimen@%
+}
+%    \end{macrocode}
+% \end{macro}
+
+% \subsection{Sub routines for drawing an elliptical arc}
+%
+%
+% \begin{macro}{\pIIe@noneto}
+% \marg{dimen$_x$}\marg{dimen$_y$}\\
+% Ignores its arguments. Used as a no-op instead of |\pIIe@lineto| or |pIIe@moveto|.
+%    \begin{macrocode}
+\newcommand*\pIIe@noneto[2]{}
+%    \end{macrocode}
+% \end{macro}
+%
+%\begin{macro}{\pIIe@ellip@sincost@}
+% \marg{$\alpha_i$}\marg{$i$ = |one| or |two|}\\
+% Calculate $\sint{i}$ and $\cost{i}$ into the |\@ellip|(|sin|/|cos|)$i$.
+% Assumes |\@ellipratio| $=\frac{a}{b}$.
+%    \begin{macrocode}
+\newcommand*\pIIe@ellip@sincost@[2]{%
+%    \end{macrocode}
+% Put the $\sin(\alpha_i)$ and $\cos(\alpha_i)$ into |\@tempdima| and |\@tempdimb|.
+%    \begin{macrocode}    
+  \CalculateSin{#1}%
+  \CalculateCos{#1}% 
+  \@tempdima\UseSin{#1}\p@   
+  \@tempdimb\UseCos{#1}\p@
+%    \end{macrocode}
+% Check for extremes where $\tan = \pm\infty$.
+%    \begin{macrocode}    
+  \ifdim\@tempdima=\p@\relax
+    \pIIe@csedef{@ellipsin#2}{1}%
+    \pIIe@csedef{@ellipcos#2}{0}%
+  \else\ifdim\@tempdima=-\p@\relax
+    \pIIe@csedef{@ellipsin#2}{-1}%
+    \pIIe@csedef{@ellipcos#2}{0}%
+  \else
+%    \end{macrocode}
+% Calculate $\kk{i}$ in |\@tempdimc| and $\sqrt{1 + \kk{i}^2}$ in |\@tempdimd|, 
+% and derive $\sint{i}$ and $\cost{i}$.
+%    \begin{macrocode}    
+    \@tempdimc\@ellipratio\dimexpr1pt * \@tempdima/\@tempdimb\relax
+    %\typeout{ i#2=\the\@tempdimc, sin(#1)=\the\@tempdima}%
+    \pIIe@ellip@csqrt{\p@}{\@tempdimc}\@tempdimd
+    \ifdim\@tempdimb<\z@\relax\@tempdimd-\@tempdimd\fi
+    \pIIe@csedef{@ellipsin#2}{\strip@pt\dimexpr1pt * \@tempdimc/\@tempdimd\relax}%
+    \pIIe@csedef{@ellipcos#2}{\strip@pt\dimexpr1pt * \p@/\@tempdimd\relax}%
+  \fi\fi
+}
+%    \end{macrocode}
+% \end{macro}
+
+%\begin{macro}{\pIIe@ellip@sincost}
+% \marg{$\alpha_1$}\marg{$\alpha_2$}\\
+% Calculate $\sint{i}$ and $\cost{i}$ into the |\@ellip|(|sin|/|cos|)(|one|/|two|).
+% Assumes |\@ovro|$=a$ and |\@ovri|$=b$ with $b \ne 0$.
+%    \begin{macrocode}
+\newcommand*\pIIe@ellip@sincost[2]{%
+%    \end{macrocode}
+% Set |\@ellipratio| to the ratio $\frac{a}{b}$.
+%    \begin{macrocode}    
+  %\typeout{ calc sin cos: angles (#1,#2), radii: (\the\@ovro,\the\@ovri)}%
+  \edef\@ellipratio{\strip@pt\dimexpr1pt * \@ovro/\@ovri\relax}%
+%    \end{macrocode}
+% And calculate $\sint{i}$ and $\cost{i}$
+%    \begin{macrocode} 
+  \pIIe@ellip@sincost@{#1}{one}%
+  \pIIe@ellip@sincost@{#2}{two}%
+  %\typeout{ sincos(a=#1)=(\@ellipsinone,\@ellipcosone), sincos(a=#2)=(\@ellipsintwo,\@ellipcostwo), }%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%\begin{macro}{\pIIe@omega}
+% \marg{$i$ = |one| or |two|}\\
+% Calculates $\xellipse_i$ into |\@tempdima| and |\@tempdimb|.
+% Assumes |\@ovro|$=a$ and |\@ovri|$=b$.
+%    \begin{macrocode}
+\newcommand*\pIIe@omega[3]{%
+  \@tempdima\csname @ellipcos#3\endcsname\@ovro
+  \advance\@tempdima by #1\relax
+  \@tempdimb\csname @ellipsin#3\endcsname\@ovri
+  \advance\@tempdimb by #2\relax
+}
+%    \end{macrocode}
+% \end{macro}
+
+%\begin{macro}{\pIIe@omegai}
+% \marg{$i$ = |one| or |two|}\\
+% Calculates $\xellipse'_i$ into |\@tempdimc| and |\@tempdimd|.
+% Assumes |\@ovro|$=a$ and |\@ovri|$=b$.
+%    \begin{macrocode}
+\newcommand*\pIIe@omegai[1]{%
+  \@tempdimc\csname @ellipsin#1\endcsname\@ovro
+  \@tempdimc-\@tempdimc
+  \@tempdimd\csname @ellipcos#1\endcsname\@ovri
+}
+%    \end{macrocode}
+% \end{macro}
+
+%\begin{macro}{\pIIe@ellip@kappa}
+% Calculates $\kappa$, expects |\@ellip|(|sin|/|cos|)(|one|/|two|) to be defined.
+%    \begin{macrocode}
+\newcommand*\pIIe@ellip@kappa{%
+%    \end{macrocode}
+% Calculate $\sint{21}$ and $\cost{21}$ in |\@tempdima| and |\@tempdimb|.
+%    \begin{macrocode}  
+  \@ovyy\@ellipsinone\p@
+  \@ovxx\@ellipcosone\p@
+  \@tempdima\@ellipcostwo\@ovyy
+  \@tempdima-\@tempdima
+  \advance\@tempdima by \@ellipsintwo\@ovxx
+  \@tempdimb\@ellipcostwo\@ovxx
+  \advance\@tempdimb by \@ellipsintwo\@ovyy
+%    \end{macrocode}
+% First test if $\sint{21} = 0$ to prevent division by zero. In that
+% case, it must have been that $\alpha_1 = \alpha_2$ and we set $\kappa$ to zero
+% so it the control points become equal to the start and end point.
+%    \begin{macrocode}  
+  \ifdim\@tempdima=\z@\relax
+    \edef\@ellipkappa{0}%
+  \else
+%    \end{macrocode}
+% Calculate $\kappa_{tan}$ in |\dimen@|
+%    \begin{macrocode}  
+    \dimen@\dimexpr1pt - \@tempdimb\relax
+    \dimen@\dimexpr1pt * \dimen@/\@tempdima\relax
+%    \end{macrocode}
+% Calculate $\kappa_{sqrt}$ in |\dimen@|
+%    \begin{macrocode}  
+    \pIIe@ellip@csqrt{2\p@}{1.73205\dimen@}{\dimen@}%
+%    \end{macrocode}
+% Calculate $\kappa$ in |\dimen@|
+%    \begin{macrocode}  
+    \advance\dimen@ by -\p@
+    \divide\dimen@ by 3%
+    \edef\@tempa{\strip@pt\@tempdima}%
+    \dimen@\@tempa\dimen@
+    \edef\@ellipkappa{\strip@pt\dimen@}%
+  \fi
+  %\typeout{ calculated kappa: \@ellipkappa}%
+}
+%    \end{macrocode}
+% \end{macro}
+
+% \subsection{Core routines for drawing elliptical arcs}
+%
+%\begin{macro}{\pIIe@elliparc@}
+% \oarg{start}\marg{$c_x$}\marg{$c_y$}\marg{$\alpha_1$}\marg{$\alpha_2$}\\
+% Assumes that the radii are set as |\@ovro|$=a$ and |\@ovri|$=b$.
+% This is the main routine for drawing an elliptic arc, where $\abs{\alpha_2 - \alpha_1}\,\le 90$.
+%    \begin{macrocode}
+\newcommand*\pIIe@elliparc@[5]{%
+  %\typeout{elliparc: #1, center: (#2, #3), radius (\the\@ovro, \the\@ovri),angle (#4, #5)}%
+%    \end{macrocode}
+% Define initial action: 0 (lineto), 1(moveto), or 2 (nothing)
+%    \begin{macrocode}    
+  \ifcase #1\relax
+      \let\@ellip@startto\pIIe@lineto
+  \or \let\@ellip@startto\pIIe@moveto
+  \or \let\@ellip@startto\pIIe@noneto%
+  \else\PackageWarning{ellipse}{Illegal initial action in \protect\elliparc: %
+          must be one of 0 (lineto), 1 (moveto) or 2 (do nothing) but I got: #1}%
+  \fi
+%    \end{macrocode}
+% Perform just the start action if the radii are zero
+%    \begin{macrocode}    
+  \ifdim\@ovro=\z@\relax\@ovri\z@\fi
+  \ifdim\@ovri=\z@\relax
+    \@ellip@startto{#2}{#3}%
+  \else
+%    \end{macrocode}
+% Calculate $\sint{i}$ and $\cost{i}$ first into the |\@ellip|(|sin|/|cos|)(|one|/|two|) registers.
+%    \begin{macrocode}    
+    \pIIe@ellip@sincost{#4}{#5}%
+%    \end{macrocode}
+% And draw..
+%    \begin{macrocode}
+    \pIIe@elliparc@draw{#2}{#3}%
+  \fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%\begin{macro}{\pIIe@elliparc@t}
+% \oarg{start}\marg{$c_x$}\marg{$c_y$}\marg{$t_1$}\marg{$t_2$}\\
+% Assumes that the radii are set as |\@ovro|$=a$ and |\@ovri|$=b$.
+% Moreover, this routine take $t_1$ and $t_2$ as the angles of the ellipse equation (instead of real angles $\alpha_i$).
+% This routine is mainly for other libraries that may already have computed the $t$ angles
+% and need a bit more efficiency.
+%    \begin{macrocode}
+\newcommand*\pIIe@elliparc@t[5]{%
+%    \end{macrocode}
+% Define initial action: 0 (lineto), 1(moveto), or 2 (nothing)
+%    \begin{macrocode}    
+  \ifcase #1\relax
+      \let\@ellip@startto\pIIe@lineto
+  \or \let\@ellip@startto\pIIe@moveto
+  \or \let\@ellip@startto\pIIe@noneto%
+  \else\PackageWarning{ellipse}{Illegal initial action in \protect\elliparc: %
+          must be one of 0 (lineto), 1 (moveto) or 2 (do nothing) but I got: #1}%
+  \fi
+%    \end{macrocode}
+% Perform just the start action if the radii are zero
+%    \begin{macrocode}    
+  \ifdim\@ovro=\z@\relax\@ovri\z@\fi
+  \ifdim\@ovri=\z@\relax
+    \@ellip@startto{#2}{#3}%
+  \else
+%    \end{macrocode}
+% Calculate $\sint{i}$ and $\cost{i}$ first into the |\@ellip|(|sin|/|cos|)(|one|/|two|) registers.
+%    \begin{macrocode}    
+    \CalculateSin{#4}\CalculateCos{#4}%
+    \edef\@ellipsinone{\UseSin{#4}}%
+    \edef\@ellipcosone{\UseCos{#4}}%
+    \CalculateSin{#5}\CalculateCos{#5}%
+    \edef\@ellipsintwo{\UseSin{#5}}%
+    \edef\@ellipcostwo{\UseCos{#5}}%
+%    \end{macrocode}
+% And draw..
+%    \begin{macrocode}
+    \pIIe@elliparc@draw{#2}{#3}%
+  \fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{pIIe@elliparc@draw}
+% \marg{$c_x$}\marg{$c_y$}\\
+% Expects $a =$|\@ovro|, $b$ = |\@ovri|, and  |\@ellip|(|sin|/|cos|)(|one|/|two|) defined.
+% |\@ellipstarto| should contain the initial drawing action and is called with an initial
+% $x$ and $y$ coordinate (usually equal to |\pIIe@lineto|,|\pIIe@moveto|, or |pIIe@noneto|).
+%    \begin{macrocode}
+\newcommand*\pIIe@elliparc@draw[2]{%
+% Calculate $\kappa$.
+%    \begin{macrocode}    
+  \pIIe@ellip@kappa%
+%    \end{macrocode}
+% Now we are ready to compute the control points. First $p_1$.
+%    \begin{macrocode}
+  \pIIe@omega{#1}{#2}{one}%
+  %\typeout{ point one: (\the\@tempdima,\the\@tempdimb)}%
+%    \end{macrocode}
+% The coordinates are added to the path if and how necessary:
+%    \begin{macrocode}
+  \@ellip@startto\@tempdima\@tempdimb
+%    \end{macrocode}
+% Add control point $q_1$
+%    \begin{macrocode}
+  \pIIe@omegai{one}%
+  \advance\@tempdima by \@ellipkappa\@tempdimc
+  \advance\@tempdimb by \@ellipkappa\@tempdimd
+  \pIIe@add@nums\@tempdima\@tempdimb
+  %\typeout{ control one: (\the\@tempdima,\the\@tempdimb)}%
+%    \end{macrocode}
+% Calculate $p_2$
+%    \begin{macrocode}
+  \pIIe@omega{#1}{#2}{two}%
+%    \end{macrocode}
+% Add control point $q_1$
+%    \begin{macrocode}
+  \pIIe@omegai{two}%
+  \@tempdimc\@ellipkappa\@tempdimc
+  \@tempdimd\@ellipkappa\@tempdimd
+  \@tempdimc-\@tempdimc
+  \@tempdimd-\@tempdimd
+  \advance\@tempdimc by \@tempdima
+  \advance\@tempdimd by \@tempdimb
+  \pIIe@add@nums\@tempdimc\@tempdimd
+  %\typeout{ control two: (\the\@tempdimc,\the\@tempdimd)}%
+%    \end{macrocode}
+% And finally add $p_2$ to the path
+%    \begin{macrocode}
+  \pIIe@add@CP\@tempdima\@tempdimb
+  %\typeout{ point two: (\the\@tempdima,\the\@tempdimb)}%
+  \pIIe@addtoGraph\pIIe@curveto@op
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Normalizing elliptical arcs}
+%
+% \begin{macro}{pIIe@elliparc}
+% \begin{macro}{pIIe@@elliparc}
+% \oarg{start}\marg{$c_x$}\marg{$c_y$}\marg{a}\marg{b}\marg{$\alpha_1$}\marg{$\alpha_2$}\\
+% \strut\\
+% These two macros check the arguments and normalize the angles.
+%    \begin{macrocode}
+\newcommand*\pIIe@elliparc[7][0]{%
+%    \end{macrocode}
+% Store the radii in registers, where |\@ovro|$=a$ and |\@ovri|$=b$.
+%    \begin{macrocode}  
+  \@ovro #4\relax
+  \@ovri #5\relax
+  \iffalse%dim\@ovro=\@ovri
+%    \end{macrocode}
+% Call the circular arc routine if the x- and y-radius are equal
+%    \begin{macrocode}  
+    \pIIe@arc[#1]{#2}{#3}{#4}{#6}{#7}
+  \else
+%    \end{macrocode}
+% Normalize angles such that the arc angle $\abs{\alpha_2 - \alpha_1}\,\le 720$.
+% Store the arc angle in |\@arclen|.
+%    \begin{macrocode}  
+    \ifdim \@ovro<\z@ \pIIe@badcircarg\else
+      \ifdim \@ovri<\z@ \pIIe@badcircarg\else
+        \@arclen #7\p@ \advance\@arclen -#6\p@
+        \ifdim \@arclen<\z@ \def\@tempsign{-}\else\def\@tempsign{}\fi
+        \ifdim \@tempsign\@arclen>720\p@
+          \PackageWarning {ellipse}{The arc angle is reduced to -720..720}%
+          \@whiledim \@tempsign\@arclen>720\p@ \do {\advance\@arclen-\@tempsign360\p@}%
+          \@tempdima #6\p@ \advance\@tempdima \@arclen
+          \edef\@angleend{\strip@pt\@tempdima}%
+          \pIIe@@elliparc{#1}{#2}{#3}{#6}{\@angleend}%
+        \else
+          \pIIe@@elliparc{#1}{#2}{#3}{#6}{#7}%
+        \fi
+      \fi
+    \fi
+  \fi
+}
+%    \end{macrocode}
+% |\pIIe@@elliparc| divides the total angle in parts of at most $90$ degrees.
+% Assumes |\@ovro|$=a$ and |\@ovri|$=b$, and |\@arclen| the arc angle, with |\@tempsign| 
+% sign of the arc angle.
+%    \begin{macrocode}  
+\newcommand*\pIIe@@elliparc[5]{%
+  \begingroup
+  \ifdim \@tempsign\@arclen>90\p@
+%    \end{macrocode}
+% If the arc angle is too large, the arc is recursively
+% divided into 2 parts until the arc angle is at most 90~degrees.
+%    \begin{macrocode}
+    \divide\@arclen 2%
+    \@tempdima #4\p@\advance\@tempdima by \@arclen
+    \edef\@anglemid{\strip@pt\@tempdima}%
+    \def\@tempa{\pIIe@@elliparc{#1}{#2}{#3}{#4}}%
+    \expandafter\@tempa\expandafter{\@anglemid}%
+    \def\@tempa{\pIIe@@elliparc{2}{#2}{#3}}%
+    \expandafter\@tempa\expandafter{\@anglemid}{#5}%
+  \else
+%    \end{macrocode}
+% The arc angle is smaller than 90 degrees.
+%    \begin{macrocode}
+    \pIIe@elliparc@{#1}{#2}{#3}{#4}{#5}%
+  \fi
+  \endgroup
+}%
+%    \end{macrocode}
+% \end{macro}
+%\end{macro}
+
+% \subsection{Drawing elliptical arcs}
+%
+%\begin{macro}{\elliparc}
+%\begin{macro}{\pIIeelliparc}
+% \oarg{start}\marg{center-x}\marg{center-y}\marg{radius-x}\marg{radius-y}\marg{start-angle}\marg{end-angle}\\
+% \strut\\
+% The main elliptical arc drawing routine. We start with |\pIIeelliparc| to avoid conflicts with
+% other packages.
+%    \begin{macrocode}
+\newcommand*\pIIeelliparc[7][0]{%
+  \@killglue
+  \pIIe@elliparc[#1]{#2\unitlength}{#3\unitlength}{#4\unitlength}{#5\unitlength}{#6}{#7}%
+  \ignorespaces%
+}
+\ifx\undefined\elliparc\else
+  \PackageWarning{ellipse}{\protect\elliparc\space is redefined}%
+\fi
+\let\elliparc\pIIeelliparc
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+
+% \begin{macro}{\earc}
+% \begin{macro}{\earc*}
+% |[|\rarg{$\alpha_0$}|,|\rarg{$\alpha_1$}|]|\marg{radius-x}\marg{radius-y}\\
+% \strut\\
+% The \cmd{\earc} command generalizes the standard \cmd{\arc} with both
+% a $x$- and $y$-radius. The |\earc*| version draws a filled elliptical arc while
+% |\earc| only strokes the elliptical arc. Both take an optional comma separated pair of 
+% angles which specify the initial and final angle ($0$ and $360$ by default). 
+% We start with \cmd{\pIIeearc} to avoid conflicts with otherpackages.
+%    \begin{macrocode}
+\newcommand*\pIIeearc
+  {\@ifstar{\@tempswatrue\pIIe@earc@}{\@tempswafalse\pIIe@earc@}}
+\newcommand*\pIIe@earc@[3][0,360]{\pIIe@earc@@(#1){#2}{#3}}
+\def\pIIe@earc@@(#1,#2)#3#4{%
+  \if@tempswa
+    \pIIe@moveto\z@\z@
+    \pIIe@elliparc{\z@}{\z@}{#3\unitlength}{#4\unitlength}{#1}{#2}%
+    \pIIe@closepath\pIIe@fillGraph
+  \else
+    \pIIe@elliparc[1]{\z@}{\z@}{#3\unitlength}{#4\unitlength}{#1}{#2}%
+    \pIIe@strokeGraph
+  \fi}
+\ifx\undefined\earc\else
+  \PackageWarning{ellipse}{\protect\earc\space is redefined}%
+\fi
+\let\earc\pIIeearc
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+
+% \begin{macro}{\ellipse}
+% \begin{macro}{\ellipse*}
+% \marg{radius-x}\marg{radius-y}\\
+% \strut\\
+% The \cmd{\ellipse} draws an ellipse with the specified $x$- and $y$-radius. 
+% The |\ellipse*| version draws a filled ellipse. 
+% We start with \cmd{\pIIeellipse} to avoid conflicts with other packages.
+% The implementation redirects immediately to |earc| which generalized this command.
+%    \begin{macrocode}
+\newcommand*\pIIeellipse
+  {\@ifstar{\@tempswatrue\pIIe@earc@}{\@tempswafalse\pIIe@earc@}}
+\let\ellipse\pIIeellipse
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+
+%
+% \Finale
+\endinput
+  
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/ellipse/ellipse.ins b/Master/texmf-dist/source/latex/ellipse/ellipse.ins
new file mode 100644
index 00000000000..51abc729e9a
--- /dev/null
+++ b/Master/texmf-dist/source/latex/ellipse/ellipse.ins
@@ -0,0 +1,71 @@
+%%
+%% Copyright (C) 2015
+%% Daan Leijen
+%%
+%% This file is part of the LaTeX `ellipse' package.
+%% ------------------------------------------------
+%%
+%% 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".
+%%
+%% In particular, NO PERMISSION is granted to modify the contents of this
+%% file since it contains the legal notices that are placed in the files
+%% it generates.
+%%
+%% This work consists of all files listed in manifest.txt.
+%%
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+
+\input docstrip
+
+\preamble
+
+Copyright (C) 2015
+Daan Leijen
+
+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".
+
+\endpreamble
+
+\keepsilent
+\askforoverwritefalse
+
+\usedir{tex/latex/pict2e}
+
+\generate{\file{ellipse.sty}{\from{ellipse.dtx}{package}}}
+
+%\usepreamble\empty
+%\usepostamble\empty
+
+
+\Msg{***********************************************************}
+\Msg{*}
+\Msg{* To finish the installation you have to move the following}
+\Msg{* files into a directory searched by TeX:}
+\Msg{*}
+\Msg{* All the files with extension `.sty' and `.def'}
+\Msg{*}
+\Msg{* To produce the documentation run the .dtx files through LaTeX.}
+\Msg{*}
+\Msg{* Happy TeXing}
+\Msg{***********************************************************}
+
+
+\endbatchfile
\ No newline at end of file