% \iffalse meta-comment
%
% Copyright (C) 2016, 2021 by Paul Gaborit
% -----------------------------------
%
% 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
% 2005/12/01 or later.
% 
% This work has the LPPL maintenance status “maintained”.
% 
% The Current Maintainer of this work is Paul Gaborit.
% 
% This work consists of the files sankey.dtx, sankey.ins and the derived
% files sankey.sty, tikzlibrarydubins.code.tex, sankey-doc-preamble.sty,
% sankey-example1.tex, sankey-example2.tex, sankey-example3.tex,
% sankey-example3-variation.tex, sankey-example4.tex,
% sankey-example-energy.tex
%
%
% \fi
%
% \iffalse
%
%<*driver>
\documentclass[a4paper,10pt,draft]{ltxdoc}
\usepackage{sankey-doc-preamble}
\EnableCrossrefs
\CodelineIndex
\RecordChanges
\begin{document}
\DocInput{sankey.dtx}
\end{document}
%</driver>
% \fi
%
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%  {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
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%   Digits        \0\1\2\3\4\5\6\7\8\9
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%   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     \\
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%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%   Right brace   \}     Tilde         \~}
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% \GetFileInfo{\jobname.dtx}
%
% \DoNotIndex{\newcommand,\newenvironment}
% \DoNotIndex{\#,\$,\%,\&,\@,\\,\{,\},\^,\_,\~,\ }
% \DoNotIndex{\begingroup,\endgroup,\begin,\end}
% \DoNotIndex{\def,\edef,\gdef,\xdef,\ifx,\else,\string,\relax}
% \DoNotIndex{\csname,\endcsname,\ifcsdef,\expandafter,\ifnumgreater}
% \DoNotIndex{\NewDocumentCommand,\NewDocumentEnvironment,\IfBooleanTF}
% \DoNotIndex{\NeedsTeXFormat,\ProvidesPackage,\RequirePackage,\PackageError,\PackageWarning}
% \DoNotIndex{\newtoggle,\toggletrue,\togglefalse,\iftoggle,\ifdefempty,\ifundef,\ifdefstrequal}
% \DoNotIndex{\ifbool,\ifdef,\ifnumequal,\colorlet,\fpeval,\inteval,\newbool}
% \DoNotIndex{\pgfmathsetmacro,\pgfdeclarelayer,\pgfdeclareshape,\pgfkeys,\pgfset,\usetikzlibrary}
% \DoNotIndex{\the,\pgf@x,\pgf@y,\tikz@scan@one@point,\pgfutil@firstofone}
% \DoNotIndex{\pgfsetlayers,\inheritsavedanchors,\inheritanchor,\inheritanchorborder,\anchor,\pgf@process,\northeast,\southwest}
% \DoNotIndex{\pgfmathresult,\pgfinterruptpath,\endpgfinterruptpath,\pgfkeysvalueof,\pgfmathtruncatemacro,\pgfmathparse}
% \DoNotIndex{\tikzset,\pgfextra,\pgflinewidth,\foreach,\coordinate}
% \DoNotIndex{\path,\node,\pgfmathprintnumber,\n,\p,\x,\y}
% \DoNotIndex{\tiny,\ttfamily,\space}
%
% \title{The \textsf{sankey} package\\
% Draw Sankey diagrams via TikZ}
%
% \author{Paul Gaborit
% (\href{mailto:paul.gaborit@gmail.com}{\texttt{paul.gaborit@gmail.com}})}
% \date{\fileversion{} -- \filedate{}}
%
% \GetFileInfo{sankey.sty}
%
% \def\manualparts{
% \begin{quote}
%   This manual contains three parts:
%   \nameref{usermanual} (p.\pageref{usermanual}),
%   \nameref{examples} (p.\pageref{examples})
%   and \nameref{implementation} (p.\pageref{implementation}).
% \end{quote}
% }
%
% \maketitle
%
% \hypersetup{
%  pdftitle=How to use the sankey package to build Sankey diagrams (\fileversion),
%  pdfauthor=Paul Gaborit,
% }
%
%
%
% \begin{abstract}
%   The \texttt{sankey} package provides macros and environments to
%   build \emph{Sankey
%   diagrams}\footnote{\url{https://en.wikipedia.org/wiki/Sankey_diagram}},
%   i.e.  \emph{flow diagrams} in which the width of the arrows is
%   proportional to the flow rate.  The initial idea for the first
%   implementation came out from
%   \href{https://tex.stackexchange.com/q/40159/14500}{this question} on
%   \href{https://tex.stackexchange.com/}{TeX.StackExchange}.
%   
%
% \end{abstract}
%
% \manualparts
%
% \begin{quote}
%   {\footnotesize Note: the \code{sankey.dtx} and \code{sankey.ins}
%   files are attachments of the current PDF document.\par}
% \end{quote}
% 
%^^A % ------------------------------------------------------------
% \part{User manual}
% \label{usermanual}
%^^A % ------------------------------------------------------------
%
% {
%   \setlength{\parskip}{0pt}
%   \localtableofcontents
% }
%
%^^A % ------------------------------------------------------------
% \section{Preamble}
%^^A % ------------------------------------------------------------
%
% To use the \code{sankey} package, insert the following line in your preamble:
%
% \begin{lstlisting}[style=LaTeXsmall]
% \usepackage{sankey}
% \end{lstlisting}
%
% {\small Note: the
% \code{sankey} package requires automatically the
% \code{xparse}, \code{etoolbox}, \code{xfp} and
% \code{tikz} packages, and the \code{calc},
% \code{decorations.markings} and
% \code{dubins} (cf. \vref{sec:dubins}) TikZ libraries.\par}
%
%
%^^A % ------------------------------------------------------------
% \section{The \texttt{sankeydiagram} environment}
%^^A % ------------------------------------------------------------
%
% \DescribeEnv{sankeydiagram} %
% A \code{sankeydiagram} environment nested in a \code{tikzpicture}
% environment activates the sankey macros:
%
% \begin{lstlisting}[style=LaTeXsmall]
% \begin{tikzpicture}
%   \begin{sankeydiagram}[... options ...]
%     ... sankey macros ...
%   \end{sankeydiagram}  
% \end{tikzpicture}
% \end{lstlisting}
%
%^^A % ------------------------------------------------------------
% \section{Sankey diagram options}
%^^A % ------------------------------------------------------------
%
% The \code{sankey} package uses \code{pgfkeys} to set options via
% \emph{key=value} pairs with default path \texttt{/sankey} (and
% \texttt{/sankey/node parameters} for Sankey node parameters).
%
% The options can be defined via the optional argument of the
% \code{sankeydiagram} environment:
%
% \begin{lstlisting}[style=LaTeXsmall]
% \begin{sankeydiagram}[debug=true]
%   \sankeynode{name=a,quantity=1,angle=0,at={0,0}}
% \end{sankeydiagram}
% \end{lstlisting}
%
% \DescribeMacro{\sankeyset} %
% The options can also be modified via the \code{\sankeyset} macro:
%
% \begin{lstlisting}[style=LaTeXsmall]
% \begin{sankeydiagram}
%   \sankeyset{debug=true}
%   \sankeynode{name=a,quantity=1,angle=0,at={0,0}}
% \end{sankeydiagram}
% \end{lstlisting}
%
% The options can be  temporarily modified for a single macro:
% \begin{lstlisting}[style=LaTeXsmall]
% \begin{sankeydiagram}
%   \sankeynode[debug=true]{name=a,quantity=1,angle=0,at={0,0}}
% \end{sankeydiagram}
% \end{lstlisting}
%
% At the begining of each Sankey diagram, all options are initialized
% with initial values then the \code{every diagram} style is applied.
%
% \begin{sankeyoption}{every diagram}{}{}{empty}
%   This style is installed at beginning of each Sankey diagram.
% \end{sankeyoption}
%
% For instance, to use a ratio of 5mm/10 by default (instead of 1cm/10)
% for all Sankey diagrams, add the following line:
%
% \begin{lstlisting}[style=LaTeXsmall]
% \sankeyset{every diagram/.style={ratio=5mm/10}}
% \end{lstlisting}
%
%^^A % ------------------------------------------------------------
% \subsection{Keys to choose the scale}
%^^A % ------------------------------------------------------------
%
% The scale or ratio of the Sankey diagram is the ratio between the %
% \code{ratio length} and the \code{ratio quantity}.
%
% \begin{sankeyoption}{ratio quantity}{\VAR{number}}{}{10}
%   Quantity (in units of flow) to define ratio. The \VAR{number} can be
%   any math expression.
% \end{sankeyoption}
%
% \begin{sankeyoption}{ratio length}{\VAR{distance}}{}{1cm}
%   Distance (a graphical distance) to define scale.
% \end{sankeyoption}
%
% \begin{sankeyoption}{ratio}{\VAR{distance}/\VAR{number}}{}{1cm/10}
%   Fix the ratio to \VAR{distance}\texttt{/}\VAR{number}.
% \end{sankeyoption}
%
% The initial ratio is 1\,cm/10 units.
%
%
% \textbf{Note:} the \code{sankey} package uses the \code{xfp} package to
% evaluate all math expressions that use quantities (in units of
% flow). You can therefore use quantities of a very large or very small
% order of magnitude. In contrast, for graphic distances, the sankey
% package uses the \code{pgfmath} package (all calculations must not
% exceed $\pm 16383.99999$).
%
%^^A % ------------------------------------------------------------
% \subsection{Keys to define rotate offset}
%^^A % ------------------------------------------------------------
%
% \begin{sankeyoption}{rotate}{\VAR{angle}}{}{0}
%
%   The \code{rotate} key stores an offset angle applied to all Sankey
%   nodes.  This is useful when using the \code{rotate} option within a
%   \code{tikzpicture} or a \code{scope}. This TikZ option is only
%   applied to coordinates and not to TikZ nodes (remember that Sankey
%   nodes are TikZ nodes). It's up to the author to keep the
%   \code{rotate} option of the \code{tikzpicture} and that of the
%   \code{sankeydiagram} synchronous.
%   
% \end{sankeyoption}
%
%^^A % ------------------------------------------------------------
% \subsection{Keys to define drawing parameters}
%^^A % ------------------------------------------------------------
%
% \begin{sankeyoption}{minimum radius}{\VAR{distance}}{}{5mm}
%   The minimum radius used by \code{\sankeyturn} and
%   \code{\sankeydubins}.
% \end{sankeyoption}
%
% \begin{sankeyoption}{outin steps}{\VAR{integer}}{}{10}
%   Number of steps used by the \code{\sankeyoutin} macro to simulate flow
%   lanes with constant width.
% \end{sankeyoption}
%
%^^A % ------------------------------------------------------------
% \subsection{Keys to choose drawing styles}
%^^A % ------------------------------------------------------------
%
% \begin{sankeyoption}{fill/.style}{\VAR{style}}{}{{line width=0pt,fill=white}}
%   This TikZ style is used to \emph{fill} all sankey paths.
% \end{sankeyoption}
%
% \begin{sankeyoption}{draw/.style}{\VAR{style}}{}{draw=black,line width=.4pt}
%   This TikZ style is used to \emph{draw} all sankey paths.
% \end{sankeyoption}
%
% \begin{sankeyoption}{start style}{\VAR{style name}}{}{none}
%   There are three predefined \emph{start} styles: \constant{none},
%   \constant{simple}, \constant{arrow}.
% \end{sankeyoption}
%
% \begin{sankeyoption}{end style}{\VAR{style name}}{}{none}
%   There are three predefined \emph{end} styles: \constant{none},
%   \constant{simple}, \constant{arrow}.
% \end{sankeyoption}
%
%^^A % ------------------------------------------------------------
% \subsection{Keys to define new \emph{start} and \emph{end} styles}
%^^A % ------------------------------------------------------------
%
% \begin{sankeyoption}{new start style}{\{\VAR{name}\}\{\VAR{fill
%       path}\}\{\VAR{draw path}\}}{}{}
%   Define the new start style named \VAR{name} with its \VAR{fill
%     path} and its \VAR{draw path}.
% \end{sankeyoption}
%
% \begin{sankeyoption}{new end style}{\{\VAR{name}\}\{\VAR{fill
%       path}\}\{\VAR{draw path}\}}{}{}
%   Define the new end style named \VAR{name} with its \VAR{fill
%     path} and its \VAR{draw path}.
% \end{sankeyoption}
%
% The \VAR{fill path} and the \VAR{draw path} are build in a TikZ scope
% where the origin is the center of the current Sankey node (its name is
% accessible via \code{\name}) and the coordinate system is rotated by
% its orientation.
%
%^^A % ------------------------------------------------------------
% \subsection{The \emph{debug} key}
%^^A % ------------------------------------------------------------
%
% \begin{sankeyoption}{debug}{\VAR{boolean}}{true}{false}
%   To debug a sankey diagram.
% \end{sankeyoption}
%
%^^A % ------------------------------------------------------------
% \section{Sankey nodes and flows}
%^^A % ------------------------------------------------------------
%
%^^A % ------------------------------------------------------------
% \subsection{Create Sankey nodes}
%^^A % ------------------------------------------------------------
%
%^^A % ------------------------------------------------------------
%
% \begin{miniblock}
% \MACRO\code{\sankeynode}\OPTARG{\VAR{options}}\ARG{\VAR{node parameters}}
%
% \DescribeMacro{\sankeynode} %
% The \code{\sankeynode} macro defines a Sankey node. The \VAR{options}
% can be any Sankey diagram keys. To define a Sankey node, you must
% provide a \emph{name}, a \emph{quantity} and an \emph{angle} as
% \VAR{node parameters}.
%
% \begin{sankeyoption}[/sankey/node parameters]{name}{\VAR{name}}{}{}
%   The \VAR{name} of the new Sankey node (and the associated TikZ node).
% \end{sankeyoption}
%
% \begin{sankeyoption}[/sankey/node parameters]{quantity}{\VAR{quantity}}{}{}
%   The quantity (in flow unit) of the new Sankey node. The \VAR{quantity}
%   can be any math expression.
% \end{sankeyoption}
%
% \begin{sankeyoption}[/sankey/node parameters]{angle}{\VAR{angle}}{}{}
%   The orientation of the flow (0 points to the right) of the new Sankey
%   node.
% \end{sankeyoption}
%
% \begin{sankeyoption}[/sankey/node parameters]{at}{\VAR{at}}{}{0,0}
%   The position of the new Sankey node (a TikZ coordinate \emph{without}
%   round brackets or parentheses).
% \end{sankeyoption}
%
% \begin{sankeyoption}[/sankey/node parameters]{anchor}{\VAR{anchor}}{}{center}
%   Specify the anchor of the Sankey node. Possible values are
%   \constant{center}, \constant{left} or \constant{right}.
% \end{sankeyoption}
%
% \begin{sankeyoption}[/sankey/node parameters]{as}{\VAR{name}}{}{}
%   Copy the \emph{name}, the \emph{quantity}, the \emph{angle} and the
%   \emph{position} of the Sankey node named \VAR{name}.
% \end{sankeyoption}
%
% A Sankey node is also a Tikz node but with only three anchors:
% \code{left}, \code{center} and \code{right}\footnote{In fact, to be
% able to use the TikZ \code{fit} library, the %
% \code{north}, \code{north east} and \code{north west} anchors exist
% and are equal to \code{left}, %
% the \code{east} and \code{west} anchors exist and are equal to
% \code{center} and %
% the \code{south}, \code{south east} and \code{south west} anchors
% exist and are equal to \code{right}.}:
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[debug]
%     \sankeynode{name=a,quantity=10}
%     \sankeynode{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeynode{name=c,quantity=20,angle=-90,at={5,1},anchor=right}
%
%     \foreach \nodename/\pos in {a/left,b/below left,c/above}{
%       \foreach \ancname in {left,center,right}{
%         \node[node font=\ttfamily\footnotesize,\pos=1mm of \nodename.\ancname,
%         inner sep=0pt,rotate=\sankeygetnodeorient{\nodename},anchor=east]
%         {\ancname\vphantom{g}};
%         \fill[black] (\nodename.\ancname) circle(1pt);
%       }
%     }
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%^^A % ------------------------------------------------------------
% \subsubsection{Choose default parameters}
%^^A % ------------------------------------------------------------
%
% \begin{sankeyoption}{every node/.style}{\{\VAR{node parameters}\}}{}{empty}
%   The \VAR{node parameters} defined by the
%   \code{every node} style is installed at the creation of every Sankey node.
% \end{sankeyoption}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Create starting and ending nodes via macros}
%^^A % ------------------------------------------------------------
%
% \begin{miniblock}
% \MACRO\code{\sankeynodestart}\OPTARG{\VAR{options}}\ARG{\VAR{node parameters}}
%
% \DescribeMacro{\sankeynodestart} %
% The \code{\sankeynodestart} creates and fills/draws a starting Sankey
% node:
%
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,fill/.style={fill=orange!20}]
%     \sankeynodestart{name=a,quantity=10}
%     \sankeynodestart{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeynodestart{name=c,quantity=20,angle=-90,at={5,1},anchor=right}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%^^A % ------------------------------------------------------------
%
%
% \begin{miniblock}
%   \MACRO\code{\sankeynodeend}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   parameters}}
%   
%   \DescribeMacro{\sankeynodeend} %
%   The \code{\sankeynodeend} creates and fills/draws an ending Sankey
%   node:
%   
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[end style=simple,fill/.style={fill=orange!20}]
%     \sankeynodeend{name=a,quantity=10}
%     \sankeynodeend{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeynodeend{name=c,quantity=20,angle=-90,at={5,1},anchor=right}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Create starting and ending nodes via options}
%^^A % ------------------------------------------------------------
%
% \begin{miniblock}
%   \begin{sankeyoption}[/sankey/node parameters]{start}{\VAR{boolean}}{true}{false}
%     The \code{\sankeynode} macro acts as the
%     \code{\sankeynodestart} macro if you add the
%     \code{start} option to its options.
%   \end{sankeyoption}
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,fill/.style={fill=orange!20}]
%     \sankeynode{name=a,quantity=10,start}
%     \sankeynode{name=b,quantity=5,angle=45,at={2,1},anchor=left,start}
%     \sankeynode{name=c,quantity=20,angle=-90,at={5,1},anchor=right,start}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \begin{sankeyoption}[/sankey/node parameters]{end}{\VAR{boolean}}{true}{false}
%     The \code{\sankeynode} macro acts as the \code{\sankeynodeend}
%     macro if you add the \code{end} option to its options.
%   \end{sankeyoption}
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[end style=simple,fill/.style={fill=orange!20}]
%     \sankeynode{name=a,quantity=10,end}
%     \sankeynode{name=b,quantity=5,angle=45,at={2,1},anchor=left,end}
%     \sankeynode{name=c,quantity=20,angle=-90,at={5,1},anchor=right,end}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%
% \begin{miniblock}
%   Although rarely necessary, you can mix these two parameters:
%
%   \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}
%     \sankeyset{
%       end style=arrow,
%       start style=arrow,
%       fill/.style={fill=orange!20}
%     }
%     \sankeynode{name=a,quantity=10,start,end}
%     \sankeynode{name=b,quantity=5,angle=45,at={2,1},anchor=left,start,end}
%     \sankeynode{name=c,quantity=20,angle=-90,at={5,1},anchor=right,start,end}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% % 
% {\centering\input{\samplecodename}\par}
% % 
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
%
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \subsection{Retrieve information from Sankey nodes}
%^^A % ------------------------------------------------------------
%
% \MACRO\code{\sankeygetnodeqty}\ARG{\VAR{node name}}
%
% \DescribeMacro{\sankeygetnodeqty} %
% The expandable command \code{\sankeygetnodeqty} returns the quantity
% assigned to the Sankey node named \VAR{node name}.
%
% \MACRO\code{\sankeyqtytolen}\ARG{\VAR{quantity}}
%
% \DescribeMacro{\sankeyqtytolen} %
% The expandable \code{\sankeyqtytolen} macro converts \VAR{quantity} to
% graphical length using the current ratio.
%
% \MACRO\code{\sankeygetnodeorient}\ARG{\VAR{node name}}
%
% \DescribeMacro{\sankeygetnodeorient} %
% The expandable command \code{\sankeygetnodeorient} returns the angle
% (orientation) assigned to the Sankey node named \VAR{node name}.
%
%^^A % ------------------------------------------------------------
% \subsection{Move nodes}
%^^A % ------------------------------------------------------------
%
% All the macros of this section move a Sankey node and fill/draw a
% portion of the Sankey flow. Then the previous position of the Sankey
% node is accessible via the \code{-old} suffix (i.e. if you move the
% \code{a} node, its previous position is the \code{a-old} node).
%
% The starred version of each of these macros moves in the opposite
% direction to their non-starred version.
%
% Except for the \code{\sankeyturn} macro, a negative value (distance or
% angle) moves in the opposite direction (the \code{\sankeyturn} macro
% is an exception: a negative angle turns right while a positive value
% turns left).
%
% {\centering
% \begin{tikzpicture}
%   \begin{sankeydiagram}
%     \tikzset{com/.style={node font=\ttfamily\scriptsize,
%     fill=bgcode,fill opacity=1,text opacity=1}}
%     \sankeyset{end style=simple,start style=simple}
%     \sankeynode{name=ac,quantity=5}
%     \sankeynode{name=al,quantity=5,at={[yshift=2mm]ac.left},anchor=right}
%     \sankeynode{name=ar,quantity=5,at={[yshift=-2mm]ac.right},anchor=left}
%     \sankeyturnleft{al}{60}
%     \sankeyadvance{ac}{1cm}
%     \sankeyturnright{ar}{60}
%     \sankeyturnleft*{al-old}{60}
%     \sankeyadvance*{ac-old}{1cm}
%     \sankeyturnright*{ar-old}{60}
%     \sankeystart{al-old}
%     \sankeystart{ac-old}
%     \sankeystart{ar-old}
%     \sankeyend{al}
%     \sankeyend{ac}
%     \sankeyend{ar}
%     \draw[red,very thick]
%     (al-old-old.left) -- node[com]{n} (al-old-old.right) 
%     (ac-old-old.left) -- node[com]{n} (ac-old-old.right)
%     (ar-old-old.left) -- node[com]{n} (ar-old-old.right);
%     \path
%     (al) ++(2mm,2mm) node[com,anchor=south west,align=left] {
%       \string\sankeyturnleft\{n\}\{angle>0\}\\
%       \string\sankeyturnleftbackward\{n\}\{angle<0\}\\
%       \string\sankeyturnleft*\{n\}\{angle<0\}\\
%       \string\sankeyturnleftbackward*\{n\}\{angle>0\}\\
%       \string\sankeyturn\{n\}\{angle>0\}
%     };
%     \path
%     (al-old) ++(-2mm,2mm) node[com,anchor=south east,align=right] {
%       \string\sankeyturnleftbackward\{n\}\{angle>0\}\\
%       \string\sankeyturnleft\{n\}\{angle<0\}\\
%       \string\sankeyturnleft*\{n\}\{angle>0\}\\
%       \string\sankeyturnleftbackward*\{n\}\{angle<0\}\\
%       \string\sankeyturn*\{n\}\{angle>0\}
%     };
%     \path
%     (ac) ++(2mm,0) node[com,anchor=west,align=left] {
%       \string\sankeyadvance\{n\}\{distance>0\}\\
%       \string\sankeyadvance*\{n\}\{distance<0\}
%     };
%     \path
%     (ac-old) ++(-2mm,0) node[com,anchor=east,align=right] {
%       \string\sankeyadvance\{n\}\{distance<0\}\\
%       \string\sankeyadvance*\{n\}\{distance>0\}
%     };
%     \path
%     (ar) ++(2mm,-2mm) node[com,anchor=north west,align=left] {
%       \string\sankeyturnright\{n\}\{angle>0\}\\
%       \string\sankeyturnrightbackward\{n\}\{angle<0\}\\
%       \string\sankeyturnright*\{n\}\{angle<0\}\\
%       \string\sankeyturnrightbackward*\{n\}\{angle>0\}\\
%       \string\sankeyturn\{n\}\{angle<0\}
%     };
%     \path
%     (ar-old) ++(-2mm,-2mm) node[com,anchor=north east,align=right] {
%       \string\sankeyturnrightbackward\{n\}\{angle>0\}\\
%       \string\sankeyturnright\{n\}\{angle<0\}\\
%       \string\sankeyturnright*\{n\}\{angle>0\}\\
%       \string\sankeyturnrightbackward*\{n\}\{angle<0\}\\
%       \string\sankeyturn*\{n\}\{angle<0\}
%     };
%     \end{sankeydiagram}
%   \end{tikzpicture}
% \par}
%^^A % ------------------------------------------------------------
% \subsubsection{Macro to move straight (forward or backward)}
%^^A % ------------------------------------------------------------
%
%
% \begin{miniblock}
%   \MACRO\code{\sankeyadvance}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{distance}}
%   
%   \DescribeMacro{\sankeyadvance} The \code{\sankeyadvance} moves the
%   sankey node straight ahead and fills/draws this portion of the
%   sankey path. A positive \VAR{distance} moves forward while a
%   negative \VAR{distance} moves backward.
%   
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,fill/.style={fill=orange!20}]
%     \sankeynodestart{name=a,quantity=10}
%     \sankeyadvance{a}{1cm}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeynodestart{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeyadvance{b}{1cm}
%     \sankeynodestart{name=c,quantity=10,angle=-90,at={5,1},anchor=right}
%     \sankeyadvance{c}{5mm}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeyadvance*}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{distance}}
%   
%   \DescribeMacro{\sankeyadvance*} The \code{\sankeyadvance*} moves
%   the sankey node straight back and fills/draws this portion of the
%   sankey path. A positive \VAR{distance} moves backward while a
%   negative \VAR{distance} moves forward.
%   
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[end style=arrow,fill/.style={fill=orange!20}]
%     \sankeynodeend{name=a,quantity=10}
%     \sankeyadvance*{a}{1cm}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeynodeend{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeyadvance*{b}{1cm}
%     \sankeynodeend{name=c,quantity=10,angle=-90,at={5,1},anchor=right}
%     \sankeyadvance*{c}{5mm}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Macro to turn forward or backward}
%^^A % ------------------------------------------------------------
%
%\begin{miniblock}
%   \MACRO\code{\sankeyturn}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturn} The \code{\sankeyturn} macro moves the
%   sankey node by turning to one side or the other and fills/draws
%   this portion of the sankey path. A \emph{positive} \VAR{angle}
%   turns left while a \emph{negative} \VAR{angle} turns right.
%   
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,fill/.style={fill=orange!20}]
%     \sankeynodestart{name=a,quantity=10}
%     \sankeyturn{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeynodestart{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeyturn[minimum radius=1cm]{b}{-45}
%     \sankeynodestart{name=c,quantity=10,angle=-90,at={5,1},anchor=right}
%     \sankeyturn{c}{180}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturn*}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturn*} The \code{\sankeyturn*} macro moves the
%   sankey node backward by turning right or left and fills/draws this
%   portion of the sankey path. A \emph{positive} \VAR{angle} turns left
%   while a \emph{negative} \VAR{angle} turns right.
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[end style=simple,fill/.style={fill=orange!20}]
%     \sankeynodeend{name=a,quantity=10}
%     \sankeyturn*{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeynodeend{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeyturn*[minimum radius=1cm]{b}{-45}
%     \sankeynodeend{name=c,quantity=10,angle=-90,at={3,1},anchor=right}
%     \sankeyturn*{c}{180}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Macros to turn left (forward or backward)}
%^^A % ------------------------------------------------------------
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturnleft}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturnleft} The
%   \code{\sankeyturnleft} macro moves the sankey node by turning left
%   and fills/draws this portion of the sankey path. A \emph{positive}
%   \VAR{angle} turns forward while a \emph{negative} \VAR{angle} turns backward.
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodestart{name=a,quantity=10}
%     \sankeyturnleft{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeyset{fill/.style={fill=lime!20}}
%     \sankeynodeend{name=b,quantity=5,angle=-135,at={1,2},anchor=left}
%     \sankeyturnleft[minimum radius=1cm]{b}{-225}
% \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturnleft*}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturnleft*} The
%   \code{\sankeyturnleft*} macro moves the sankey node backward
%   by turning left and fills/draws this portion of the sankey path.
%   A \emph{positive} \VAR{angle} turns backward while a
%   \emph{negative} \VAR{angle} turns forward.
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodeend{name=a,quantity=10}
%     \sankeyturnleft*{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeyset{fill/.style={fill=lime!20}}
%     \sankeynodestart{name=b,quantity=5,angle=-135,at={1,2},anchor=left}
%     \sankeyturnleft*[minimum radius=.75cm]{b}{-225}
% \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturnleftbackward}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturnleftbackward} The
%   \code{\sankeyturnleftbackward} macro moves the sankey node backward
%   by turning left and fills/draws this portion of the sankey path.
%   A \emph{positive} \VAR{angle} turns backward while a
%   \emph{negative} \VAR{angle} turns forward.
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodeend{name=a,quantity=10}
%     \sankeyturnleftbackward{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeyset{fill/.style={fill=lime!20}}
%     \sankeynodestart{name=b,quantity=5,angle=-135,at={1,2},anchor=left}
%     \sankeyturnleftbackward[minimum radius=.75cm]{b}{-225}
% \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturnleftbackward*}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturnleftbackward*} The
%   \code{\sankeyturnleftbackward*} macro moves the sankey node by turning left
%   and fills/draws this portion of the sankey path. A \emph{positive}
%   \VAR{angle} turns forward while a \emph{negative} \VAR{angle} turns backward.
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodestart{name=a,quantity=10}
%     \sankeyturnleftbackward*{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeyset{fill/.style={fill=lime!20}}
%     \sankeynodeend{name=b,quantity=5,angle=-135,at={1,2},anchor=left}
%     \sankeyturnleftbackward*[minimum radius=1cm]{b}{-225}
% \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% 
%^^A % ------------------------------------------------------------
% \subsubsection{Macros to turn right (forward or backward)}
%^^A % ------------------------------------------------------------
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturnright}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturnright} The \code{\sankeyturnright} macro
%   moves the sankey node by turning right and fills/draws this portion
%   of the sankey path. A \emph{positive} \VAR{angle} turns forward
%   while a \emph{negative} \VAR{angle} turns backward.
%   
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodestart{name=a,quantity=10}
%     \sankeyturnright[fill/.style={fill=orange!20}]{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeyset{fill/.style={fill=lime!20}}
%     \sankeynodeend{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeyturnright[minimum radius=.75cm]{b}{-225}
% \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturnright*}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturnright*} The \code{\sankeyturnright*} macro
%   moves the sankey node backward by turning right and fills/draws
%   this portion of the sankey path. A \emph{positive} \VAR{angle} turns
%   backward while a \emph{negative} \VAR{angle} turns forward.
%   
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodeend{name=a,quantity=10}
%     \sankeyturnright*[fill/.style={fill=orange!20}]{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeyset{fill/.style={fill=lime!20}}
%     \sankeynodestart{name=b,quantity=5,angle=45,at={1,1},anchor=left}
%     \sankeyturnright*[minimum radius=.75cm]{b}{-225}
% \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturnrightbackward}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturnrightbackward}
%   The \code{\sankeyturnrightbackward} macro
%   moves the sankey node backward by turning right and fills/draws
%   this portion of the sankey path. A \emph{positive} \VAR{angle} turns
%   backward while a \emph{negative} \VAR{angle} turns forward.
%   
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodeend{name=a,quantity=10}
%     \sankeyturnrightbackward[fill/.style={fill=orange!20}]{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeyset{fill/.style={fill=lime!20}}
%     \sankeynodestart{name=b,quantity=5,angle=45,at={1,1},anchor=left}
%     \sankeyturnrightbackward[minimum radius=.75cm]{b}{-225}
% \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeyturnrightbackward*}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   name}}\ARG{\VAR{angle}}
%   
%   \DescribeMacro{\sankeyturnrightbackward*} The
%   \code{\sankeyturnrightbackward*} macro  moves the sankey
%   node forward by turning right and fills/draws this portion
%   of the sankey path. A \emph{positive} \VAR{angle} turns forward
%   while a \emph{negative} \VAR{angle} turns backward.
%   
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=arrow,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodestart{name=a,quantity=10}
%     \sankeyturnrightbackward*[fill/.style={fill=orange!20}]{a}{90}
%     \sankeynode[debug]{as=a}
%     \sankeynode[debug]{as=a-old}
%     \sankeyset{fill/.style={fill=lime!20}}
%     \sankeynodeend{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeyturnrightbackward*[minimum radius=.75cm]{b}{-225}
% \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
%
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%
%^^A % ------------------------------------------------------------
% \subsection{Links between nodes}
%^^A % ------------------------------------------------------------
%
% The macros described in this section fill/draw a lane between two
% Sankey nodes.
%
% Note: since Sankey nodes are oriented, linking \code{A} node to
% \code{B} node does not produce the same result as linking \code{B}
% node to \code{A} node!
%
% \begin{miniblock}
%   \MACRO\code{\sankeyoutin}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   A}}\ARG{\VAR{node B}}
%   
%   \DescribeMacro{\sankeyoutin} The \code{\sankeyoutin} macro
%   fills/draws a lane from \VAR{node A} to \VAR{node B} using a
%   Bézier curve with regular steps (10 steps by default) to
%   simulate constant width lane.
%   
%   The constant width and the minimum curvature are \emph{not} guaranteed!
% \end{miniblock}
%
% \begin{miniblock}
%   \MACRO\code{\sankeydubins}\OPTARG{\VAR{options}}\ARG{\VAR{node
%   A}}\ARG{\VAR{node B}}
%   
%   \DescribeMacro{\sankeydubins} %
%   The \code{\sankeydubins} macro fills/draws a lane between
%   \VAR{node A} and \VAR{node B} using a Dubins
%   path\footnote{\url{https://en.wikipedia.org/wiki/Dubins_path}}.
%   
%   The constant width and the minimum curvature are guaranteed.
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Comparison between \texttt{outin} and \texttt{dubins}
%   paths}
%^^A % ------------------------------------------------------------
%
% The following diagrams compare \texttt{outin} path with
% 10 steps (orange), \texttt{outin} path with 2 steps (red)
% and \texttt{dubins} path (lime) in various positions.
%
% \begin{miniblock}
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=simple,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodestart{name=a,quantity=5}
%     \sankeynodeend{name=b,at={4,3},quantity=5}
%     \sankeyoutin{a}{b}
%
%     \sankeyset{fill/.style={fill=red!20}}
%     \sankeynodestart{name=a,at={2,0},quantity=5}
%     \sankeynodeend{name=b,at={6,3},quantity=5}
%     \sankeyoutin[outin steps=2]{a}{b}
%
%     \sankeyset{fill/.style={fill=lime!40}}
%     \sankeynodestart{name=a,at={4,0},quantity=5}
%     \sankeynodeend{name=b,at={(8,3},quantity=5}
%     \sankeydubins[minimum radius=5mm]{a}{b}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=simple,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodestart{name=a,quantity=5}
%     \sankeynodeend{name=b,at={2,3},quantity=5}
%     \sankeyoutin{a}{b}
%
%     \sankeyset{fill/.style={fill=red!20}}
%     \sankeynodestart{name=a,at={2,0},quantity=5}
%     \sankeynodeend{name=b,at={4,3},quantity=5}
%     \sankeyoutin[outin steps=2]{a}{b}
%
%     \sankeyset{fill/.style={fill=lime!40}}
%     \sankeynodestart{name=a,at={4,0},quantity=5}
%     \sankeynodeend{name=b,at={(6,3},quantity=5}
%     \sankeydubins[minimum radius=5mm]{a}{b}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
% \begin{miniblock}
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=simple,end style=arrow]
%     \sankeyset{fill/.style={fill=orange!20}}
%     \sankeynodestart{name=a,quantity=5}
%     \sankeynodeend{name=b,at={0,3},quantity=5}
%     \sankeyoutin{a}{b}
%
%     \sankeyset{fill/.style={fill=red!20}}
%     \sankeynodestart{name=a,at={2,0},quantity=5}
%     \sankeynodeend{name=b,at={2,3},quantity=5}
%     \sankeyoutin[outin steps=2]{a}{b}
%
%     \sankeyset{fill/.style={fill=lime!40}}
%     \sankeynodestart{name=a,at={4,0},quantity=5}
%     \sankeynodeend{name=b,at={(4,3},quantity=5}
%     \sankeydubins[minimum radius=5mm]{a}{b}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Examples of \texttt{dubins} paths}
%^^A % ------------------------------------------------------------
%
% \begin{miniblock}
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}[start style=simple,end style=arrow]
%     \sankeyset{
%       fill/.style={fill=lime!40},
%       draw/.style={draw=green!50!black,line width=2pt},
%     }
%
%     \sankeynodestart{name=a,quantity=5}
%     \sankeynodeend{name=b,at={0,2},quantity=5}
%     \sankeydubins[minimum radius=2mm]{a}{b}
%
%     \fill[green!50!black] (2,0) coordinate (c) circle(2pt);
%     \sankeynodestart{name=a,at={[shift={(c)}]90:5mm},quantity=5}
%     \sankeynodeend{name=b,at={[shift={(c)}]150:5mm},angle=60,quantity=5}
%     \sankeydubins[minimum radius=2.5mm]{a}{b}
%
%     \sankeynodestart{name=a,at={3.5,0},quantity=5}
%     \sankeynodeend{name=b,at={3.5,.75},angle=-180,quantity=5}
%     \sankeydubins[minimum radius=5mm]{a}{b}
%
%     \sankeynodestart{name=a,at={7,1},quantity=5}
%     \sankeynodeend{name=b,at={7,1.75},quantity=5}
%     \sankeydubins[minimum radius=2.5mm]{a}{b}
%
%     \sankeynodestart{name=a,at={9,0},quantity=5}
%     \sankeynodeend{name=b,at={9,2},angle=180,quantity=5}
%     \sankeydubins[minimum radius=2.5mm]{a}{b}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \subsection{Pure filling/drawing macros}
%^^A % ------------------------------------------------------------
%
% \begin{miniblock}
% \MACRO\code{\sankeystart}\OPTARG{\VAR{options}}\ARG{\VAR{name}}
%
% \DescribeMacro{\sankeystart} %
% The \code{\sankeystart} fills/draws a starting extremity attached to
% the preexisting Sankey node \VAR{name}:
%
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}
%     [start style=arrow,fill/.style={fill=cyan!20},draw/.style={draw=blue}]
%     \sankeynode{name=a,quantity=10}
%     \sankeystart{a}
%     \sankeynode{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeystart{b}
%     \sankeynode{name=c,quantity=20,angle=-90,at={5,1},anchor=right}
%     \sankeystart{c}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% %
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%^^A % ------------------------------------------------------------
%
%
% \begin{miniblock}
%   \MACRO\code{\sankeyend}\OPTARG{\VAR{options}}\ARG{\VAR{name}}
%
%   \DescribeMacro{\sankeyend} %
%   The \code{\sankeyend} fills/draws an ending extremity attached to
%   the preexisting Sankey node \VAR{name}:
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}
%     [end style=simple,fill/.style={fill=cyan!20},draw/.style={draw=blue}]
%     \sankeynode{name=a,quantity=10}
%     \sankeyend{a}
%     \sankeynode{name=b,quantity=5,angle=45,at={2,1},anchor=left}
%     \sankeyend{b}
%     \sankeynode{name=c,quantity=20,angle=-90,at={5,1},anchor=right}
%     \sankeyend{c}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% % 
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% % 
% {\centering\input{\samplecodename}\par}
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \subsection{Forked node}
%^^A % ------------------------------------------------------------
%
%^^A % ------------------------------------------------------------
% \subsubsection{Create and fork a Sankey node}
%^^A % ------------------------------------------------------------
%
% \changes{v3.0}{2021/03/14}{add keys to fork a Sankey node during its
% creation}
%
% \begin{miniblock}
%   When creating a new Sankey node, the \code{forked} and %
%   \code{fork anchor} keys allow to fork the node directly \emph{and} to
%   anchor it on an anchor of a forked subnode.
%
% \begin{sankeyoption}[/sankey/node parameters]{forked}{\{\VAR{quantity/name pairs}\}}{}{}
%   The \VAR{quantity/name pairs} is a comma separated list of
%   \emph{quantity/name} pairs (one for each subnode, from left to
%   right). The sum of all quantities \emph{must} be equal to the quantity
%   of the new node to fork.
% \end{sankeyoption}
%
% \begin{sankeyoption}[/sankey/node parameters]{fork anchor}{\VAR{node.anchor}}{}{}
%   An anchor belonging to the new node \emph{or} belonging to a subnode
%   (the anchor name must be prefixed by the name of the
%   node). \emph{Note:} when a \code{fork anchor} key is supplied, the
%   \code{anchor} key is ignored (with a \emph{warning} message).
% \end{sankeyoption}
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}
%     \sankeyset{
%       start style=arrow,end style=arrow,
%       fill/.style={fill=yellow!10,line width=0pt,draw=yellow!10}
%     }
%
%     \sankeynode[debug]{
%       name=a,quantity=40,angle=-80,
%       forked={25/b,10/c,5/d},
%       fork anchor=c.right,
%     }
%
%     \sankeyadvance*{b}{1cm}
%     \sankeyturn*[minimum radius=2cm]{c}{-30}
%     \sankeyturn*[minimum radius=2cm]{c}{30}
%     \sankeyturn*[minimum radius=5mm]{d}{-90}
%     \sankeyadvance{a}{1.5cm}
%     \foreach \nodename in {b,c,d}{ \sankeystart{\nodename} }
%     \sankeyend{a}
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% % 
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%
%^^A % ------------------------------------------------------------
% \subsubsection{Fork a Sankey node}
%^^A % ------------------------------------------------------------
% \begin{miniblock}
%   \MACRO\code{\sankeyfork}\OPTARG{\VAR{options}}\ARG{\VAR{name}}\ARG{\VAR{quantity/name pairs}}
%
%   \DescribeMacro{\sankeyfork} %
%   The \code{\sankeyfork} macro splits the preexisting Sankey node
%   named \VAR{name} in a list of new Sankey subnodes. The
%   \VAR{quantity/name pairs} is a comma separated list of
%   \emph{quantity/name} pairs, one for each subnode from left to
%   right. The sum of all quantities \emph{must} be equal to the
%   quantity of the node to fork.
%
% \begin{VerbatimOut}[gobble=2]{\samplecodename}
% \begin{tikzpicture}
%   \begin{sankeydiagram}
%     \sankeynode{name=a,quantity=40,angle=-45}
%     \sankeyfork[debug]{a}{25/b,10/c,5/d}
%     \path (a.left) rectangle (a.right); %^^A create a bounding box
%   \end{sankeydiagram}
% \end{tikzpicture}
% \end{VerbatimOut}
% % 
% {\centering\input{\samplecodename}\par}
% %
% \lstinputlisting[style=LaTeXsmall]{\samplecodename}
% \end{miniblock}
%
%^^A % ------------------------------------------------------------
% \section{Miscellaneous}
%^^A % ------------------------------------------------------------
%
%^^A % ------------------------------------------------------------
% \subsection{The \texttt{debug} layer}
%^^A % ------------------------------------------------------------
%
% The options \code{debug} key uses the \code{sankeydebug} layer to draw
% above the \code{main} TikZ layer (via \code{\pgfsetlayers}, the
% \code{sankey} package installs four layers: \code{background},
% \code{main}, \code{foreground}, \code{sankeydebug}).
%
% The four following styles define how to display debug information:
%
% \begin{lstlisting}[style=LaTeXsmall]
% \sankeyset{
%   debug color/.style={/utils/exec={\colorlet{debug color}{#1}}},
%   % debug color used by all debug macros
%   debug color=red!75!black,
%   % debug line between left and right anchors
%   debug line/.style={overlay,draw=debug color,|-|},
%   % debug line between center and label
%   debug normal/.style={overlay,draw=debug color},
%   % debug node label
%   debug label/.style={
%     overlay,
%     draw,
%     font=\ttfamily\tiny,
%     text=debug color,text opacity=1,
%     inner sep=.1em,
%     fill=white,fill opacity=1,
%     rounded corners=.1em,
%     node contents={\name},
%   },
% }
% \end{lstlisting}
%
%^^A % ------------------------------------------------------------
% \subsection{The \texttt{dubins} TikZ library}
% \label{sec:dubins}
%^^A % ------------------------------------------------------------
%
% The \code{sankey} package uses the \code{dubins} TikZ library (the
% \code{tikzlibrarydubins.code.tex} file) to compute Dubins paths. The
% documentation for this library does not yet exist.
%
%^^A % ------------------------------------------------------------
% \subsection{How to duplicate a Sankey node}
%^^A % ------------------------------------------------------------
%
% \MACRO\code{\sankeynodealias}\ARG{\VAR{origname}}\ARG{\VAR{clonename}}
%
% \DescribeMacro{\sankeynodealias} %
% The \code{\sankeynodealias} macro clones the Sankey node named
% \VAR{origname} into the Sankey node named \VAR{clonename}.
%
% So, you can clone a Sankey node via two methods:
%
% \begin{lstlisting}[style=LaTeXsmall]
% \sankeynode{name=a,quantity=10}
% \sankeynode{as=a,name=b}
% \end{lstlisting}
%
% \begin{lstlisting}[style=LaTeXsmall]
% \sankeynode{name=a,quantity=10}
% \sankeynodealias{a}{b}
% \end{lstlisting}
%
%^^A % ------------------------------------------------------------
% \subsection{How to define new start and end styles}
%^^A % ------------------------------------------------------------
%
% Here are the definitions of the \code{arrow} styles:
%
% \begin{lstlisting}[style=LaTeXsmall]
% \sankeyset{
%   %% arrow style
%   new start style={arrow}{
%     (\name.left) -- ++(-10pt,0)
%     -- ([xshift=-10pt/6]\name.center)
%     -- ([xshift=-10pt]\name.right)
%     -- (\name.right) -- cycle
%   }{
%     (\name.left) -- ++(-10pt,0)
%     -- ([xshift=-10pt/6]\name.center)
%     -- ([xshift=-10pt]\name.right)
%     -- (\name.right)
%   },
%   new end style={arrow}{
%     (\name.left) -- ([yshift=1mm]\name.left)
%     -- ([xshift=10pt]\name.center)
%     -- ([yshift=-1mm]\name.right) -- (\name.right) -- cycle
%   }{
%     (\name.left) -- ([yshift=1mm]\name.left)
%     -- ([xshift=10pt]\name.center)
%     -- ([yshift=-1mm]\name.right) -- (\name.right)
%   },
% }
% \end{lstlisting}
%
%^^A % ------------------------------------------------------------
% \section{Todo}
%^^A % ------------------------------------------------------------
%
% \begin{itemize}
% \item Document the \code{dubins} TikZ library.
% \item Add a tutorial.
% \item Add examples with cycle(s).
% \end{itemize}
%
% ^^A % ------------------------------------------------------------
% \clearpage
%
% \manualparts
%
% \part{Examples}
% \label{examples}
%^^A % ------------------------------------------------------------
% {
%   \setlength{\parskip}{0pt}
%   \localtableofcontents
%   \listoffigures
% }
%
% \tikzset{every picture/.style={}}
%^^A % ------------------------------------------------------------
%
%^^A % ------------------------------------------------------------
% \clearpage
% \section{Simple example}
%^^A % ------------------------------------------------------------
%
% \embedfile[mimetype=text/plain]{sankey-example1.tex}
%
% \begin{figure}
%   \centering
%   {\MakePercentComment\input{sankey-example1.tex}}
%   \caption{Simple example}
%   \label{fig:simple-example}
% \end{figure}
%
% See figure~\vref{fig:simple-example}. The \code{sankey-example1.tex}
% file contains the following code and is an attachement of the current
% PDF document.
%
% \lstinputlisting[style=LaTeXsmall]{sankey-example1.tex}
%
% \iffalse
%<*example1>
\begin{tikzpicture}
  \begin{sankeydiagram}%[debug]
    \colorlet{cold}[rgb]{cyan!75!blue!50!white}
    \colorlet{hot}[rgb]{red!50!orange!75!white}
    \sankeyset{
      ratio=90pt/6,minimum radius=15pt,
      start style=simple,end style=simple,
      draw/.style={
        draw=blue!50!cyan,
        line width=1pt,line cap=round,line join=round,
      },
      cold/.style={
        fill/.style={
          draw=cold,line width=0pt,fill=cold,
        },
      },
      cold to hot/.style={
        fill/.style={
          fill=none,top color=cold,
          bottom color=hot,middle color=yellow,
        },
      },
      hot/.style={
        fill/.style={
          draw=hot,line width=0pt,fill=hot,
        },
      },
    }

    \sankeyset{cold}
    \sankeynodestart{name=p0,at={100,0},angle=-90,quantity=6}
    \sankeyadvance{p0}{50pt}
    \sankeyfork{p0}{3/p1,3/p2}
    \sankeyturnleft{p1}{90}
    \sankeyadvance{p1}{20pt}
    \sankeyadvance{p2}{60pt}
    \sankeyfork{p2}{2/p3,1/p4}
    \sankeyturnleft{p3}{90}
    \sankeyadvance{p3}{50pt}
    \sankeyfork{p3}{1/p5,1/p6}
    \sankeyadvance{p5}{70pt}
    \sankeyfork{p1}{1/p7,1/p8,1/p9}
    \sankeyadvance{p7}{50pt}
    \sankeyadvance{p9}{50pt}
    \sankeyadvance{p4}{40pt}
    \sankeyturnleft{p4}{90}
    \sankeyadvance{p4}{65pt}
    \sankeyadvance{p7}{40pt}
    \sankeynode{
      name=p11,at={[shift={(50pt,-15pt)}]p7},quantity=3,
      forked={1/p7a,1/p9a,1/p5a},
    }
    \sankeyoutin{p7}{p7a}
    \sankeyoutin{p9}{p9a}
    \sankeyoutin{p5}{p5a}
    \sankeyadvance{p11}{30pt}
    \sankeyend{p11}
    \sankeyturnright{p8}{90}
    \sankeyturnright{p6}{90}
    \sankeyturnright{p4}{90}
    \sankeyset{hot}
    \sankeyadvance[cold to hot]{p8}{40pt}
    \sankeynode{
      name=p10,at={[shift={(-15pt,-60pt)}]p8},angle=-90,quantity=3,
      forked={1/p8a,1/p6a,1/p4a},
    }
    \sankeyoutin[cold to hot]{p4}{p4a}
    \sankeyoutin[cold to hot]{p6}{p6a}
    \sankeyoutin{p8}{p8a}
    \sankeyadvance{p10}{30pt}
    \sankeyend{p10}
  \end{sankeydiagram}
\end{tikzpicture}
%</example1>
% \fi
% 
%^^A % ------------------------------------------------------------
% \clearpage
% \section{Energy diagram}
%^^A % ------------------------------------------------------------
%
% \embedfile[mimetype=text/plain]{sankey-example-energy.tex}
%
% \begin{figure}
%   \centering
%   {\MakePercentComment\input{sankey-example-energy.tex}}
%   \caption{Energy diagram}
%   \label{fig:very-simple-example}
% \end{figure}
%
% This example comes from
% \href{https://ibphysicsblog.wordpress.com/2015/10/23/sankey-diagrams/}{IB
% Pysics Blog} by Kyu Won Shim.
%
% See figure~\vref{fig:very-simple-example}. The \code{sankey-example-energy.tex}
% file contains the following code and is an attachement of the current
% PDF document.
%
% \lstinputlisting[style=LaTeXsmall]{sankey-example-energy.tex}
%
% \iffalse
%<*example-energy>
\begin{tikzpicture}
  % font choice
  \renewcommand\rmdefault{txr}\rmfamily\footnotesize
  \sisetup{
    round-mode=places,
    round-precision=1,
    add-decimal-zero,
    round-pad=true,
  }
  \begin{sankeydiagram}
    \colorlet{energy}{blue!30!cyan!80!black}
    \colorlet{lost energy}{red!50!orange!90!black}
    \sankeyset{
      ratio=13em/100,
      minimum radius=1em,
      start style=simple,end style=simple,
      draw/.style={draw=none,line width=0},
      energy/.style={
        fill/.style={
          draw=energy,
          line width=0,
          fill=energy,
        }
      },
      lost energy/.style={
        fill/.style={
          draw=lost energy,
          line width=0,
          fill=lost energy,
        }
      }
    }

    \newcommand\abovelabel[2]{ % valname, label
      \node[anchor=south east,align=center,inner xsep=0] at (#1.left) {#2};
    }
    
    \newcommand\energylabel[1]{ % valname
      \node[anchor=north east,text=energy,inner xsep=0] at (#1.right)
      {\num{\sankeygetnodeqty{#1}}};
    }

    \newcommand\lostenergylabel[2]{ % valname, label
      \node[anchor=north,text=lost energy] at ([yshift=-2.5mm]#1.center)
      (value)
      {\num{\sankeygetnodeqty{#1}}};
      \node[anchor=north,inner sep=0,align=center] at (value.south) {#2};
    }
    
    \newcommand\lostenergylabelbottom[2]{ % valname, label
      \draw[draw=lost energy,dashed,thick]
      ([yshift=-3mm]#1.center) coordinate (#1) -- ([yshift=-3mm]#1.center);
      \lostenergylabel{#1}{#2}
    }
    
    \sankeynode{name=Co,quantity=100.0}
    \path (Co.right) ++(0,-7mm) coordinate (c);
    
    \newcommand\turnandstop[2]{ % valname, label
      \begingroup
      \sankeyset{lost energy}
      \sankeyturnright{#1}{90}
      \sankeynode{as=#1,name=#1-stop,at={#1 |- c}}
      \sankeyoutin{#1}{#1-stop}
      \sankeynode{as=#1-stop,name=#1}
      \sankeyend{#1}
      \lostenergylabel{#1}{#2}
      \endgroup
    }    

    \newcommand\turnandstopbottom[2]{ % valname, label
      \begingroup
      \sankeyset{lost energy}
      \sankeyturnright{#1}{90}
      \sankeynode{as=#1,name=#1-stop,at={#1 |- c}}
      \sankeyoutin{#1}{#1-stop}
      \sankeynode{as=#1-stop,name=#1}
      \sankeyend{#1}
      \lostenergylabelbottom{#1}{#2}
      \endgroup
    }    

    \def\hshift{6.25em}
    
    \sankeyadvance[energy]{Co}{1.2*\hshift}
    \abovelabel{Co}{\textbf{Coal}\\(Primary energy)}
    \energylabel{Co}
    \sankeyfork{Co}{35/El1,65/Pg}
    \turnandstop{Pg}{Power generation}

    \sankeyadvance[energy]{El1}{1.8*\hshift}
    \abovelabel{El1}{\textbf{Electricity}\\(Secondary energy)}
    \energylabel{El1}
    \sankeyfork{El1}{33.5/El2,1.5/Tr}
    \turnandstopbottom{Tr}{Transmission}
    
    \sankeyadvance[energy]{El2}{.65*\hshift}
    \energylabel{El2}
    \sankeyfork{El2}{31.5/El3,2.0/Di}
    \turnandstop{Di}{Distribution}
    
    \sankeyadvance[energy]{El3}{.65*\hshift}
    \energylabel{El3}
    \sankeyfork{El3}{31.0/El4,0.5/Wi}
    \turnandstopbottom{Wi}{Wiring}
    
    \sankeyadvance[energy]{El4}{.65*\hshift}
    \abovelabel{El4}{\textbf{Electricity}\\(Final energy)}
    \energylabel{El4}
    \sankeyfork{El4}{3.0/Lr1,28.0/Lb}
    \turnandstop{Lb}{Lightbulb}
    
    \sankeyadvance[energy]{Lr1}{1.1*\hshift}
    \abovelabel{Lr1}{\textbf{Light radiation}\\(Useful energy)}
    \energylabel{Lr1}
    \sankeyfork{Lr1}{2.0/Lr2,1.0/Ls}
    \turnandstopbottom{Ls}{Lampshade}
    
    \sankeyadvance[energy]{Lr2}{.6*\hshift}
    \energylabel{Lr2}
    \sankeyfork{Lr2}{1.0/Il,1.0/Id}
    \turnandstop{Id}{Idle}

    \sankeyadvance[energy]{Il}{.6*\hshift}
    \abovelabel{Il}{\textbf{Illumination}\\(Energy services)}
    \energylabel{Il}
    \sankeyend[energy]{Il}
  \end{sankeydiagram}
\end{tikzpicture}
%</example-energy>
% \fi
%^^A % ------------------------------------------------------------
% \clearpage
% \section{Example from question on TeX.se}
%^^A % ------------------------------------------------------------
%
% \changes{v3.0}{2021/03/14}{fix bad names in second example}
%
% \embedfile[mimetype=text/plain]{sankey-example2.tex}
%
% \begin{figure}
%   \centering
%   {\MakePercentComment\input{sankey-example2}}
%   \caption{Example from TeX.se question}
%   \label{fig:texse-example}
% \end{figure}
%
% This example came from
% \href{https://tex.stackexchange.com/q/40159/14500}{this question} on
% \href{https://tex.stackexchange.com/}{TeX.StackExchange}.
%
% See figure~\vref{fig:texse-example}. The \code{sankey-example2.tex}
% file contains the following code and is an attachement of the current
% PDF document.
% 
% \lstinputlisting[style=LaTeXsmall]{sankey-example2}
%
% \iffalse
%<*example2>
\begin{tikzpicture}
  \renewcommand*\sfdefault{txss}

  \begin{sankeydiagram}%[debug]
    \sankeyset{
      ratio=4cm/524.3,
      minimum radius=3mm,
      start style=arrow,
      end style=arrow,
      fill/.style={
        line width=0pt,
        fill=cyan!50!blue!50!black,
        draw=cyan!50!blue!50!black,
      },
      draw/.style={draw=none},
      every node/.style={angle=-90},
    }

    \sankeynodestart{name=B,at={-.5,0},quantity=7.2}
    \coordinate[below=1mm of B.center] (B label);
    \sankeyadvance{B}{5mm}
    \sankeynodestart{name=GI,at={1,0},quantity=137.3}
    \coordinate[below=1mm of GI.center] (GI label);
    \sankeyadvance{GI}{5mm}
    \sankeynodestart{name=I,at={4,0},quantity=397.8}
    \coordinate[below=1mm of I.center] (I label);
    \sankeynode{
      name=EI,at={2.86,-3},quantity=542.3,
      forked={397.8/Ia,137.3/GIa,7.2/Ba}
    }
    \sankeydubins[minimum radius=1.2cm]{I}{Ia}
    \sankeyoutin{GI}{GIa}
    \sankeyoutin{B}{Ba}
    \sankeyadvance{EI}{5mm}
    \coordinate (EI label) at (EI);
    \sankeyadvance{EI}{5mm}
    \sankeyfork{EI}{63.1/EB,479.2/P}

    \sankeyturnleft{EB}{90}
    \sankeyadvance{EB}{4cm}
    \coordinate (EB label) at ($(EB)!.5!(EB-old)$);
    \sankeyend{EB}

    \sankeyadvance{P}{10mm}
    \coordinate (P label) at (P);
    \sankeyadvance{P}{5mm}

    \sankeyfork{P}{33.5/NV,445.7/P-NV}

    {
      \colorlet{NV color}{cyan!80!lime!50!gray}
      \sankeyset{fill/.append style={fill=NV color,draw=NV color}}
      \sankeyturnleft{NV}{90}
      \sankeynode{as=NV,name=NV2,at=NV -| EB}
      \sankeyoutin{NV}{NV2}
      \coordinate (NV label) at (NV -| EB label);
      \sankeyend{NV2}
    }

    \sankeyadvance{P-NV}{10mm}
    \sankeyfork{P-NV}{118.1/U,327.6/P-NV-U}

    {
      \sankeyset{
        fill/.style={fill=orange!70!gray!50,draw=orange!70!gray!50}
      }
      \sankeyturnleft{U}{90}
      \sankeynode{as=U,name=U2,at=U -| EB}
      \sankeyoutin{U}{U2}
      \coordinate (U label) at (U -| EB label);
      \sankeyend{U2}
    }

    \sankeyadvance{P-NV-U}{10mm}
    \sankeyfork{P-NV-U}{327.2/P-NV-U-SD,0.4/SD}

    {
      \sankeyturnright{SD}{90}
      \sankeyadvance{SD}{15mm}
      \coordinate (SD label) at (SD);
      \sankeyadvance{SD}{15mm}
      \sankeyend{SD}
    }

    \sankeyadvance{P-NV-U-SD}{8mm}
    \sankeyfork{P-NV-U-SD}{18.8/VE,308.4/E}

    {
      \sankeyset{fill/.append style={orange!70!gray!30}}
      \sankeyturnleft{VE}{90}
      \sankeynode{as=VE,name=VE2,at=VE -| EB}
      \sankeyoutin{VE}{VE2}
      \coordinate (VE label) at (VE -| EB label);
      \sankeyend{VE2}
    }

    \sankeyadvance{E}{8mm}
    \coordinate (E label) at (E);
    \sankeyadvance{E}{20mm}
    \sankeyfork{E}{135.1/H+GHD,87.2/V,86.1/In}

    \sankeyturnright{In}{90}
    \sankeyadvance{In}{10mm}
    \sankeyturnleft{In}{90}
    \sankeyadvance{In}{5mm}
    \coordinate (In label)  at (In);
    \sankeyadvance{In}{10mm}
    \sankeyend{In}

    \sankeynode{as=V,name=V2,at=V|-In label}
    \sankeyoutin{V}{V2}
    \coordinate (V label) at (V2);
    \sankeyadvance{V2}{10mm}
    \sankeyend{V2}

    \sankeyturnleft{H+GHD}{90}
    \sankeyadvance{H+GHD}{5mm}
    \sankeyfork{H+GHD}{47.0/GHD,88.1/H}

    \sankeyturnright{H}{90}
    \sankeynode{as=H,name=H2,at=H|-In label}
    \sankeyoutin{H}{H2}
    \coordinate (H label) at (H2);
    \sankeyadvance{H2}{10mm}
    \sankeyend{H2}

    \sankeyadvance{GHD}{30mm}
    \sankeyturnright{GHD}{90}
    \sankeynode{as=GHD,name=GHD2,at=GHD|-In label}
    \sankeyoutin{GHD}{GHD2}
    \coordinate (GHD label) at (GHD2);
    \sankeyadvance{GHD2}{10mm}
    \sankeyend{GHD2}
  \end{sankeydiagram}

  % labels
  \tikzset{
    label/.style={
      fill=white,fill opacity=.8,text opacity=1,
      inner sep=1mm,
      text=cyan!50!blue!50!black,
      inner xsep=2mm,
      font=\sffamily\bfseries\footnotesize,
      align=center,
    },
  }
  \node[label,anchor=north] (B label) at (B label) {7.2};
  \node[label,left=1mm of B label] {Bestands-\\entnahme};
  \node[label,anchor=north] at (GI label) {137.3};
  \node[label,above=5mm of GI label] {Gewinnung\\im Inland};
  \node[label,anchor=north] at (I label) {397.8};
  \node[label,above=5mm of I label] {Import};

  \node[label] at (EI label) {542.3\\Energieaufkommen im Inland};

  \node[label,anchor=center] (EB label) at (EB label) {63.1};
  \node[label,above=1mm of EB label] {Export und\\Bunkerung};

  \node[label] at (P label) {479.2\\Primärenergieverbrauch};

  \node[label,anchor=center] (NV label) at (NV label) {33.5};
  \node[label,above=0mm of NV label] {Nichtenergetischer Verbrauch};

  \node[label,anchor=center] (U label) at (U label) {118.1};
  \node[label,below=3mm of U label] {Umwandlungsverluste};

  \node[label,anchor=center] (SD label) at (SD label) {0.4};
  \node[label,above=0mm of SD label] {Statistische\\Differenzen};

  \node[label,anchor=center] (VE label) at (VE label) {18.8};
  \node[label,below=0mm of VE label] {Verbrauch in den\\Energiesktoren};

  \node[label,anchor=north] (E label) at (E label)
  {308.4\\Endenergieverbrauch};

  \node[label,anchor=north] (In label) at (In label) {86.1};
  \node[label,anchor=north,below=1cm of In label] {Industrie};

  \node[label,anchor=north] (V label) at (V label) {87.2};
  \node[label,anchor=north,below=1cm of V label] {Verkehr};

  \node[label,anchor=north] (H label) at (H label) {88.1};
  \node[label,anchor=north,below=1cm of H label] {Haushalte};

  \node[label,anchor=north] (GHD label) at (GHD label) {47.0};
  \node[label,anchor=north,below=1cm of GHD label]
  {Gewerbe, Handel\\Diensleistungen};
\end{tikzpicture}
%</example2>
% \fi
%
%^^A % ------------------------------------------------------------
% \clearpage
% \section{Reproduction of an example from Google Charts documentation}
%^^A % ------------------------------------------------------------
%
% \changes{v3.0}{2021/03/14}{add the reproduction of an example from
% Google Charts documentation}
%
% \embedfile[mimetype=text/plain]{sankey-example3.tex}
%
% This example is a reproduction of an example of Google
% Charts Documentation\footnote{\url{https://developers.google.com/chart/interactive/docs/gallery/sankey}}.
%
% See figure \vref{fig:google-example}. The \code{sankey-example3.tex}
% file contains the following code and is an attachement of the current
% PDF document.
%
% \begin{figure}
%   \centering
%   {\MakePercentComment\input{sankey-example3}}
%   \caption{Reproduction of an example from Google Charts
%   documentation}
%   \label{fig:google-example}
% \end{figure}
%
% \lstinputlisting[style=LaTeXsmall]{sankey-example3}
%
% \iffalse
%<*example3>
\begin{tikzpicture}
  \begin{sankeydiagram}%[debug]
    \sffamily
    \sankeyset{
      ratio=1cm/10,
      outin steps=2,
      draw/.style={draw=none,line width=0pt},
      color/.style={fill/.style={fill=#1,fill opacity=.75}},
      shade/.style 2 args={fill/.style={left color=#1,
          right color=#2,fill opacity=.5}},
      % colors
      @define HTML color/.code args={#1/#2}{\definecolor{#1}{HTML}{#2}},
      @define HTML color/.list={
        cyan/a6cee3,lime/b2df8a,red/fb9a99,orange/fdbf6f,
        violet/cab2d6,yellow/ffff99,blue/1f78b4,green/33a02c
      },
      % colors of countries
      @let country color/.code args={#1/#2}{\colorlet{#1}[rgb]{#2}},
      @let country color/.list={
        CA/red,US/orange,MX/orange,BR/cyan,FR/lime,GB/red,
        SP/lime,PT/cyan,ML/blue,SN/violet,MA/yellow,
        AO/violet,ZA/yellow,IN/green,JP/green,CN/blue
      },
    }
    \def\vdist{5mm}
    \def\hwidth{.5em}
    \def\hdist{4.1cm}
    
    \sankeynode{name=CA,quantity=7}
    \sankeynode{name=US,quantity=8,at={[yshift=\vdist]CA.left},anchor=right}
    \sankeynode{name=MX,quantity=8,at={[yshift=\vdist]US.left},anchor=right}
    \sankeynode{name=BR,quantity=8,at={[yshift=\vdist]MX.left},anchor=right}

    \foreach \country in {CA,US,MX,BR}{
      \sankeyadvance[color=\country]{\country}{\hwidth}
    }

    \sankeyfork{CA}{1/CA-to-PT,1/CA-to-GB,5/CA-to-FR}
    \sankeyfork{US}{1/US-to-PT,1/US-to-SP,5/US-to-GB,1/US-to-FR}
    \sankeyfork{MX}{1/MX-to-PT,5/MX-to-SP,1/MX-to-GB,1/MX-to-FR}
    \sankeyfork{BR}{5/BR-to-PT,1/BR-to-SP,1/BR-to-GB,1/BR-to-FR}

    \sankeynode{name=FR,quantity=11,
      at={[xshift=\hdist]CA.right},anchor=right}
    \sankeynode{name=GB,quantity=11,
      at={[yshift=\vdist]FR.left},anchor=right}
    \sankeynode{name=SP,quantity=7,
      at={[yshift=\vdist]GB.left},anchor=right}
    \sankeynode{name=PT,quantity=8,
      at={[yshift=\vdist]SP.left},anchor=right}

    \sankeyfork{FR}
    {1/FR-from-BR,1/FR-from-MX,1/FR-from-US,5/FR-from-CA,3/FR-from-00}
    \sankeyfork{GB}
    {1/GB-from-BR,1/GB-from-MX,5/GB-from-US,1/GB-from-CA,3/GB-from-00}
    \sankeyfork{SP}{1/SP-from-BR,5/SP-from-MX,1/SP-from-US}
    \sankeyfork{PT}{5/PT-from-BR,1/PT-from-MX,1/PT-from-US,1/PT-from-CA}

    \foreach \country in {FR,GB,SP,PT}{
      \sankeyadvance[color=\country]{\country}{\hwidth}
    }

    \sankeyfork{FR}{1/FR-to-ZA,1/FR-to-AO,3/FR-to-MA,3/FR-to-SN,3/FR-to-ML}
    \sankeyfork{GB}{7/GB-to-ZA,1/GB-to-AO,2/GB-to-MA,1/GB-to-SN}
    \sankeyfork{SP}{1/SP-to-ZA,3/SP-to-MA,1/SP-to-SN,2/SP-to-00}
    \sankeyfork{PT}{3/PT-to-ZA,2/PT-to-AO,1/PT-to-MA,1/PT-to-SN,1/PT-to-00}

    \sankeynode{name=ML,quantity=9,
      at={[xshift=\hdist]FR.right},anchor=right}
    \sankeynode{name=SN,quantity=9,
      at={[yshift=\vdist]ML.left},anchor=right}
    \sankeynode{name=MA,quantity=9,
      at={[yshift=\vdist]SN.left},anchor=right}
    \sankeynode{name=AO,quantity=9,
      at={[yshift=\vdist]MA.left},anchor=right}
    \sankeynode{name=ZA,quantity=12,
      at={[yshift=\vdist]AO.left},anchor=right}

    \sankeyfork{ML}{3/ML-from-FR,6/Mail-from-00}
    \sankeyfork{SN}
    {1/SN-from-PT,1/SN-from-SP,1/SN-from-GB,3/SN-from-FR,3/SN-from-00}
    \sankeyfork{MA}{1/MA-from-PT,3/MA-from-SP,2/MA-from-GB,3/MA-from-FR}
    \sankeyfork{AO}{2/AO-from-PT,1/AO-from-GB,1/AO-from-FR,5/AO-from-00}
    \sankeyfork{ZA}{3/ZA-from-PT,1/ZA-from-SP,7/ZA-from-GB,1/ZA-from-FR}
    
    \foreach \country in {ML,SN,MA,AO,ZA}{
      \sankeyadvance[color=\country]{\country}{\hwidth}
    }

    \sankeyfork{ML}{5/ML-to-CN,3/ML-to-JP,1/ML-to-IN}
    \sankeyfork{SN}{5/SN-to-CN,3/SN-to-JP,1/SN-to-IN}
    \sankeyfork{MA}{5/MA-to-CN,3/MA-to-JP,1/MA-to-IN}
    \sankeyfork{AO}{5/AO-to-CN,3/AO-to-JP,1/AO-to-IN}
    \sankeyfork{ZA}{5/ZA-to-CN,3/ZA-to-JP,1/ZA-to-IN,3/ZA-to-00}

    \sankeynode{name=IN,quantity=5,
      at={[xshift=\hdist]ML.right},anchor=right}
    \sankeynode{name=JP,quantity=15,
      at={[yshift=\vdist]IN.left},anchor=right}
    \sankeynode{name=CN,quantity=25,
      at={[yshift=\vdist]JP.left},anchor=right}
    
    \sankeyfork{IN}
    {1/IN-from-ZA,1/IN-from-AO,1/IN-from-MA,1/IN-from-SN,1/IN-from-ML}
    \sankeyfork{JP}
    {3/JP-from-ZA,3/JP-from-AO,3/JP-from-MA,3/JP-from-SN,3/JP-from-ML}
    \sankeyfork{CN}
    {5/CN-from-ZA,5/CN-from-AO,5/CN-from-MA,5/CN-from-SN,5/CN-from-ML}

    \foreach \country in {IN,JP,CN}{
      \sankeyadvance[color=\country]{\country}{\hwidth}
    }
    
    \foreach \startcountry/\countries in {
      CA/{PT,GB,FR},    US/{PT,SP,GB,FR},    MX/{PT,SP,GB,FR},
      BR/{PT,SP,GB,FR}, FR/{ML,SN,MA,AO,ZA}, GB/{SN,MA,AO,ZA},
      SP/{SN,MA,ZA},    PT/{SN,MA,AO,ZA},    ML/{IN,JP,CN},
      SN/{IN,JP,CN},    MA/{IN,JP,CN},       AO/{IN,JP,CN},
      ZA/{IN,JP,CN}}
    {
      \foreach \endcountry in \countries {
        \sankeyoutin[shade={\startcountry}{\endcountry}]
        {\startcountry-to-\endcountry}{\endcountry-from-\startcountry}
      }
    }

    \foreach \country/\countryname in {CA/Canada, US/USA, MX/Mexico,
      BR/Brazil, FR/France, GB/England, SP/Spain, PT/Portugal}
    {
      \node[anchor=west,inner sep=.1em,font=\small]
      at (\country) {\countryname\vphantom{Ag}};
    }

    \foreach \country/\countryname in {
      ML/Mali, SN/Senegal, MA/Morocco, AO/Angola,
      ZA/South Africa, IN/India, JP/Japan, CN/China}
    {
      \node[anchor=east,inner sep=.1em,font=\small]
      at (\country-old) {\countryname\vphantom{Ag}};
    }
  \end{sankeydiagram}
\end{tikzpicture}
%</example3>
% \fi
%
%^^A % ------------------------------------------------------------
% \subsection{Variation}
%^^A % ------------------------------------------------------------
%
% Here is a variation of the previous example using the \code{rotate}
% key.
%
% See figure \vref{fig:google-example-variation}. The
% \code{sankey-example3-variation.tex} file contains the following code
% and is an attachement of the current PDF document.
%
% \begin{figure}
%   \centering
%   {\MakePercentComment\input{sankey-example3-variation}}
%   \caption{Reproduction of an example from Google Charts documentation
%   -- variation using the \protect\texttt{rotate} key.}
%   \label{fig:google-example-variation}
% \end{figure}
%
% \lstinputlisting[style=LaTeXsmall]{sankey-example3-variation}
%
% \iffalse
%<*example3-variation>
\begin{tikzpicture}[rotate=-90]
  \begin{sankeydiagram}[rotate=-90]
    \sffamily
    \sankeyset{
      ratio=1.7cm/10,
      outin steps=2,
      start style=arrow,
      end style=simple,
      draw/.style={draw=white,line width=.4pt},
      color/.style={fill/.style={fill=#1,fill opacity=.75}},
      shade/.style 2 args={fill/.style={
          fill=none,line width=0,
          top color=#1,bottom color=#2,
          middle color=#1!50!#2!50!white,
          fill opacity=.75}},
      % colors
      @define HTML color/.code args={#1/#2}{\definecolor{#1}{HTML}{#2}},
      @define HTML color/.list={
        cyan/a6cee3,lime/b2df8a,red/fb9a99,orange/fdbf6f,
        violet/cab2d6,yellow/ffff99,blue/1f78b4,green/33a02c
      },
      % colors of countries
      @let country color/.code args={#1/#2}{\colorlet{#1}[rgb]{#2}},
      @let country color/.list={
        CA/red,US/orange,MX/lime,BR/violet,FR/yellow,GB/blue,
        SP/green,PT/cyan,ML/cyan,SN/red,MA/orange,
        AO/violet,ZA/lime,IN/blue,JP/yellow,CN/green
      },
    }
    \def\vdist{5mm}
    \def\hwidth{1em}
    \def\hdist{6cm}

    \sankeynode{name=CA,quantity=7}
    \sankeynode{name=US,quantity=8,at={[yshift=\vdist]CA.left},anchor=right}
    \sankeynode{name=MX,quantity=8,at={[yshift=\vdist]US.left},anchor=right}
    \sankeynode{name=BR,quantity=8,at={[yshift=\vdist]MX.left},anchor=right}

    \foreach \country in {CA,US,MX,BR}{
      \sankeystart[color=\country]{\country}
      \sankeyadvance[color=\country]{\country}{\hwidth}
    }

    \sankeyfork{CA}{1/CA-to-PT,1/CA-to-GB,5/CA-to-FR}
    \sankeyfork{US}{1/US-to-PT,1/US-to-SP,5/US-to-GB,1/US-to-FR}
    \sankeyfork{MX}{1/MX-to-PT,5/MX-to-SP,1/MX-to-GB,1/MX-to-FR}
    \sankeyfork{BR}{5/BR-to-PT,1/BR-to-SP,1/BR-to-GB,1/BR-to-FR}

    \sankeynode{name=FR,quantity=11,
      at={[xshift=\hdist]CA.right},anchor=right}
    \sankeynode{name=GB,quantity=11,
      at={[yshift=\vdist]FR.left},anchor=right}
    \sankeynode{name=SP,quantity=7,
      at={[yshift=\vdist]GB.left},anchor=right}
    \sankeynode{name=PT,quantity=8,
      at={[yshift=\vdist]SP.left},anchor=right}

    \sankeyfork{FR}
    {1/FR-from-BR,1/FR-from-MX,1/FR-from-US,5/FR-from-CA,3/FR-from-00}
    \sankeyfork{GB}
    {1/GB-from-BR,1/GB-from-MX,5/GB-from-US,1/GB-from-CA,3/GB-from-00}
    \sankeyfork{SP}{1/SP-from-BR,5/SP-from-MX,1/SP-from-US}
    \sankeyfork{PT}{5/PT-from-BR,1/PT-from-MX,1/PT-from-US,1/PT-from-CA}

    \foreach \country in {FR,GB,SP,PT}{
      \sankeyadvance[color=\country]{\country}{\hwidth}
    }

    \sankeyfork{FR}{1/FR-to-ZA,1/FR-to-AO,3/FR-to-MA,3/FR-to-SN,3/FR-to-ML}
    \sankeyfork{GB}{7/GB-to-ZA,1/GB-to-AO,2/GB-to-MA,1/GB-to-SN}
    \sankeyfork{SP}{1/SP-to-ZA,3/SP-to-MA,1/SP-to-SN,2/SP-to-00}
    \sankeyfork{PT}{3/PT-to-ZA,2/PT-to-AO,1/PT-to-MA,1/PT-to-SN,1/PT-to-00}

    \sankeynode{name=ML,quantity=9,
      at={[xshift=\hdist]FR.right},anchor=right}
    \sankeynode{name=SN,quantity=9,
      at={[yshift=\vdist]ML.left},anchor=right}
    \sankeynode{name=MA,quantity=9,
      at={[yshift=\vdist]SN.left},anchor=right}
    \sankeynode{name=AO,quantity=9,
      at={[yshift=\vdist]MA.left},anchor=right}
    \sankeynode{name=ZA,quantity=12,
      at={[yshift=\vdist]AO.left},anchor=right}

    \sankeyfork{ML}{3/ML-from-FR,6/Mail-from-00}
    \sankeyfork{SN}
    {1/SN-from-PT,1/SN-from-SP,1/SN-from-GB,3/SN-from-FR,3/SN-from-00}
    \sankeyfork{MA}{1/MA-from-PT,3/MA-from-SP,2/MA-from-GB,3/MA-from-FR}
    \sankeyfork{AO}{2/AO-from-PT,1/AO-from-GB,1/AO-from-FR,5/AO-from-00}
    \sankeyfork{ZA}{3/ZA-from-PT,1/ZA-from-SP,7/ZA-from-GB,1/ZA-from-FR}

    \foreach \country in {ML,SN,MA,AO,ZA}{
      \sankeyadvance[color=\country]{\country}{\hwidth}
    }

    \sankeyfork{ML}{5/ML-to-CN,3/ML-to-JP,1/ML-to-IN}
    \sankeyfork{SN}{5/SN-to-CN,3/SN-to-JP,1/SN-to-IN}
    \sankeyfork{MA}{5/MA-to-CN,3/MA-to-JP,1/MA-to-IN}
    \sankeyfork{AO}{5/AO-to-CN,3/AO-to-JP,1/AO-to-IN}
    \sankeyfork{ZA}{5/ZA-to-CN,3/ZA-to-JP,1/ZA-to-IN,3/ZA-to-00}

    \sankeynode{name=IN,quantity=5,
      at={[xshift=\hdist]ML.right},anchor=right}
    \sankeynode{name=JP,quantity=15,
      at={[yshift=\vdist]IN.left},anchor=right}
    \sankeynode{name=CN,quantity=25,
      at={[yshift=\vdist]JP.left},anchor=right}

    \sankeyfork{IN}
    {1/IN-from-ZA,1/IN-from-AO,1/IN-from-MA,1/IN-from-SN,1/IN-from-ML}
    \sankeyfork{JP}
    {3/JP-from-ZA,3/JP-from-AO,3/JP-from-MA,3/JP-from-SN,3/JP-from-ML}
    \sankeyfork{CN}
    {5/CN-from-ZA,5/CN-from-AO,5/CN-from-MA,5/CN-from-SN,5/CN-from-ML}

    \foreach \country in {IN,JP,CN}{
      \sankeyadvance[color=\country]{\country}{\hwidth}
      \sankeyend[color=\country]{\country}
    }

    \foreach \startcountry/\countries in {
      CA/{PT,GB,FR},    US/{PT,SP,GB,FR},    MX/{PT,SP,GB,FR},
      BR/{PT,SP,GB,FR}, FR/{ML,SN,MA,AO,ZA}, GB/{SN,MA,AO,ZA},
      SP/{SN,MA,ZA},    PT/{SN,MA,AO,ZA},    ML/{IN,JP,CN},
      SN/{IN,JP,CN},    MA/{IN,JP,CN},       AO/{IN,JP,CN},
      ZA/{IN,JP,CN}}
    {
      \foreach \endcountry in \countries {
        \sankeyoutin[shade={\startcountry}{\endcountry}]
        {\startcountry-to-\endcountry}{\endcountry-from-\startcountry}
      }
    }

    
    \foreach \country/\countryname in {CA/Canada, US/USA, MX/Mexico,
      BR/Brazil, FR/France, GB/England, SP/Spain, PT/Portugal}
    {
      \node[anchor=south,inner sep=.1em,font=\small]
      at (\country) {\countryname\vphantom{Ag}};
    }

    \foreach \country/\countryname in {
      ML/Mali, SN/Senegal, MA/Morocco, AO/Angola,
      ZA/South Africa, IN/India, JP/Japan, CN/China}
    {
      \node[anchor=south,inner sep=.1em,font=\small]
      at (\country) {\countryname\vphantom{Ag}};
    }
  \end{sankeydiagram}
\end{tikzpicture}
%</example3-variation>
% \fi
%
%^^A % ------------------------------------------------------------
% \clearpage
% \section{Very nice example -- Nadieh Bremer creation}
%^^A % ------------------------------------------------------------
%
% \embedfile[mimetype=text/plain]{sankey-example4.tex}
%
% \begin{figure}
%   \centering
%   {\MakePercentComment\input{sankey-example4}}
%   \caption{Very nice example -- Nadieh Bremer's creation}
%   (from
%   \href{https://www.visualcinnamon.com/portfolio/adyen-report-2019/}{Adyen's
%     Shareholder Report})
%   \label{fig:nice-example}
% \end{figure}
%
% Graphic designer Nadieh Bremer created this very nice Sankey
% diagram\footnote{\url{https://www.visualcinnamon.com/portfolio/adyen-report-2019/}}
% for Adyen's second half 2018 report to shareholders. It is coded here
% with her kind permission.
%
% You can change the data values between lines 28 and 53.
%
% See figure~\vref{fig:nice-example}. The \code{sankey-example4.tex}
% file contains the following code and is an attachement of the current
% PDF document.
%
% \lstinputlisting[numbers=left,style=LaTeXsmall]{sankey-example4}
%
% \iffalse
%<*example4>
\begin{tikzpicture}
  \renewcommand*\sfdefault{txss}
  \sffamily
  \sisetup{
    detect-all=true,
    group-separator={,},
    group-minimum-digits=4,
  }
  % storage of labels
  \newcommand\LabSet[2]{% node name, label
    \expandafter\edef\csname#1@Lab\endcsname{#2}}
  \newcommand\Lab[1]{% node name
    \csname#1@Lab\endcsname}
  % storage of quantities
  \newcommand\QtySet[2]{% node name, quantity
    \expandafter\edef\csname#1@Qty\endcsname{\fpeval{#2}}}
  \newcommand\Qty[1]{% node name
    \csname#1@Qty\endcsname}
  % all nodes with their name, label and quantity
  \sankeyset{
    def data/.code args={#1/#2/#3}{% node name/label/values
      \LabSet{#1}{#2}
      \QtySet{#1}{#3}
      \typeout{#1: \Qty{#1}€ (\Lab{#1})}
    },
    def data/.list={
      {Pf/Processing\\fees/71713},
      {Sog/Sales of\\good/4547},
      {Sf/Settlement\\fees/842075},
      {Os/Other\\services/37532},
      {R/Revenues/\Qty{Pf}+\Qty{Sog}+\Qty{Sf}+\Qty{Os}},
      {Coi/Cost of Inventory/5151},
      {Ciffi/Cost insecure from financial institutions/758234},
      {Nr/Net revenue/\Qty{R}-\Qty{Coi}-\Qty{Ciffi}},
      {Aadotaifa/Amortization and\\depreciation of tangible and\\
        intangible fixed assets/4688},
      {Ssapc/Social securities and\\pension costs/7860},
      {Was/Wages and salaries/35627},
      {Ooe/Other operating expenses/37346},
      {Nr2/-/\Qty{Nr}-\Qty{Aadotaifa}-\Qty{Ssapc}-\Qty{Was}-\Qty{Ooe}},
      {Oi/Other income/47},
      {Ibiiieait/Income before interest income,\\interest expense and
        income taxes/\Qty{Nr2}+\Qty{Oi}},
      {Fe/Finance expense/561},
      {Ofr/Other financial results/2533},
      {Ibiiieait2/-/\Qty{Ibiiieait}-\Qty{Fe}-\Qty{Ofr}},
      {Fi/Finance income/204},
      {Ibit/Income before income taxes/\Qty{Ibiiieait2}+\Qty{Fi}},
      {It/Income taxes/21134},
      {Niftp/Net income for the period/\Qty{Ibit}-\Qty{It}},
      {Octa/Other currency\\translation adjustments/785},
      {Tci/Total comprehensive income/\Qty{Niftp}+\Qty{Octa}}
    },
  }

  \definecolor{mygreen}{RGB}{9,192,82}
  \tikzset{
    cost node/.style={
      overlay,
      align=flush center,
      node font=\footnotesize\sffamily\bfseries,
      inner sep=0,
      node contents={%
        {\mdseries€\,\num{\Qty{#1}}}\\
        \Lab{#1}\vphantom{g}%
      },
    },
    white hash/.style={
      draw=none,fill=none,
      pattern={Lines[angle=60,line width=2pt,distance=4pt]},
      pattern color=white,
    },
    line sep/.style={draw=white,line width=1pt},
    left label/.style={left=#1,align=flush right,anchor=north east},
    right label/.style={right=#1,align=flush left},
    right label hashed/.style={
      right=1mm of $(#1.left)!.5!(#1-old.left)$,align=flush left,
    },
    left label hashed/.style={
      left=1mm of $(#1.right)!.5!(#1-old.right)$,align=flush right,
    },
  }

  \newcommand\turnandstop[1]{
    \sankeyturn[green to greenwhite]{#1}{-90}
    \sankeynode{as=#1,name=#1-e,at={#1 -| Coi}}
    \sankeyoutin[greenwhite to white]{#1}{#1-e}
    \node[cost node=#1,left label={1mm of #1-e.right}];
  }

  \begin{sankeydiagram}%[debug]
    \sankeyset{
      ratio=28em/1000000,
      minimum radius=2cm,
      start style=none,
      every node/.style={angle=-90},
      % default fill and draw styles
      fill/.style={
        line width=0pt,
        fill=mygreen,
      },
      draw/.style={draw=none},
      % specific fill and draw styles
      green to greenwhite/.style={
        fill/.style={
          line width=0pt,
          right color=mygreen,
          left color=mygreen!20!white,
        }
      },
      greenwhite to white/.style={
        fill/.style={
          line width=0pt,
          right color=mygreen!20!white,
          left color=mygreen!5!white,
        }
      },
      dashed/.style={draw/.style={draw=mygreen,dashed}},
    }

    \coordinate (top) at (0,2em);

    \sankeynodestart{name=Pf,quantity=\Qty{Pf}}
    \node[cost node=Pf,above=.5em of Pf.center];

    \sankeynodestart{name=Sog,quantity=\Qty{Sog},
      at={[xshift=4em]Pf.left},anchor=right}
    \node[cost node=Sog,above=.5em of Sog.center];

    \sankeynodestart{name=Sf,quantity=\Qty{Sf},
      at={[xshift=2em]Sog.left},anchor=right}
    \node[cost node=Sf,above=.5em of Sf.center];

    \sankeynodestart{name=Os,quantity=\Qty{Os},
      at={[xshift=2em]Sf.left},anchor=right}
    \node[cost node=Os,above=.5em of Os.center];

    \sankeynode{
      name=R,quantity=\Qty{R},at={[yshift=-10em]Sf.center},
      forked={\Qty{Os}/Os-a,\Qty{Sf}/Sf-a,\Qty{Sog}/Sog-a,\Qty{Pf}/Pf-a},
    }

    \foreach \nodename in {Pf,Sog,Sf,Os}{
      \sankeyoutin[fill/.style={top color=white,bottom color=mygreen}]
      {\nodename}{\nodename-a}
    }

    \sankeyadvance{R}{1em}
    \node[cost node=R,right label hashed=R];

    \sankeyfork{R}{\Qty{Ciffi}/Ciffi,\Qty{Nr}/Nr,\Qty{Coi}/Coi}

    \sankeyturnleft[minimum radius=1.cm]{Ciffi}{90}
    \node[cost node=Ciffi,at={([shift={(1mm,0)}]Ciffi.center)},rotate=-90,
    anchor=south,align=flush left,node font=\scriptsize\sffamily\bfseries];

    \sankeyturnright[green to greenwhite]{Coi}{90}
    \sankeyadvance[greenwhite to white]{Coi}{1em}
    \node[cost node=Coi,left={1mm of [yshift=.75ex]Coi.left},
    align=flush right,anchor=north east,overlay];

    \sankeyadvance{Nr}{9em}
    \sankeyadvance{Nr}{1em}
    \node[cost node=Nr,left label hashed=Nr,
    node font=\large\sffamily\bfseries];

    \sankeyfork{Nr}{\Qty{Nr2}/Nr2,\Qty{Ooe}/Ooe,
      \Qty{Was}/Was,\Qty{Ssapc}/Ssapc,\Qty{Aadotaifa}/Aadotaifa}

    \turnandstop{Aadotaifa}

    \sankeyadvance{Ssapc}{5em}
    \turnandstop{Ssapc}

    \sankeyadvance{Was}{9em}
    \turnandstop{Was}

    \sankeyadvance{Ooe}{12em}
    \turnandstop{Ooe}

    \sankeyadvance{Nr2}{15em}
    \sankeynode{name=Ibiiieait,quantity=\Qty{Ibiiieait},
      anchor=right,at={Nr2.right},
      forked={\Qty{Oi}/Oi,\Qty{Nr2}/Nr2-e}}

    \sankeyturnleftbackward[minimum radius=1cm,dashed]{Oi}{90}
    \node[cost node=Oi,right label=1mm of Oi.left];

    \sankeyadvance{Ibiiieait}{1em}
    \node[cost node=Ibiiieait,right label hashed=Ibiiieait];

    \sankeyfork{Ibiiieait}
    {\Qty{Ibiiieait2}/Ibiiieait2,\Qty{Ofr}/Ofr,\Qty{Fe}/Fe}

    \turnandstop{Fe}

    \sankeyadvance{Ofr}{3em}
    \turnandstop{Ofr}

    \sankeyadvance{Ibiiieait2}{6em}
    \sankeynode{name=Ibit,quantity={\Qty{Ibiiieait2}+\Qty{Fi}},
      anchor=right,at={Ibiiieait2.right},
      forked={\Qty{Fi}/Fi,\Qty{Ibiiieait2}/Ibiiieait2-e}}

    \sankeyturnleftbackward[minimum radius=1cm,dashed]{Fi}{90}
    \node[cost node=Fi,right label=1mm of Fi.left];

    \sankeyadvance{Ibit}{1em}
    \node[cost node=Ibit,right label hashed=Ibit];

    \sankeyfork{Ibit}{\Qty{Niftp}/Niftp,\Qty{It}/It}

    \turnandstop{It}

    \sankeyadvance{Niftp}{6em}

    \sankeyadvance{Niftp}{1em}
    \node[cost node=Niftp,right label hashed=Niftp];

    \sankeynode{name=Tci,quantity=\Qty{Niftp}+\Qty{Octa},
      anchor=right,at={[yshift=-6em]Niftp.right},
      forked={\Qty{Octa}/Octa,\Qty{Niftp}/Niftp-e}}
    \sankeyoutin{Niftp}{Niftp-e}

    \sankeyturnleftbackward[minimum radius=1cm]{Octa}{90}
    \node[cost node=Octa,right label=1mm of Octa.left];

    \sankeyadvance{Tci}{1em}
    \node[cost node=Tci,right label hashed=Tci];

    \newcommand\hashband[1]{
      \draw[line sep] (#1-old.right) -- (#1-old.left);
      \draw[line sep] (#1.right) -- (#1.left);
      \path[white hash] (#1-old.right) rectangle (#1.left);
    }

    \foreach \nodename in {R,Nr,Nr,Ibiiieait,Ibit,Niftp,Tci}{
      \hashband{\nodename}
    }

  \end{sankeydiagram}
\end{tikzpicture}
%</example4>
% \fi
%
% \clearpage
%
% \StopEventually{}
%^^A % ------------------------------------------------------------
%
% \manualparts
%
% \part{Installation \& Implementation}
% \label{implementation}
%^^A % ------------------------------------------------------------
%
% {
%   \setlength{\parskip}{0pt}
%   \localtableofcontents
% }
%
%
% \changes{v3.0.1}{2022/02/04}{fix options used by the new version of siunitx}
%
%^^A % ------------------------------------------------------------
% \section{Compiling \texttt{sankey}}
%^^A % ------------------------------------------------------------
%
% \changes{v3.0.1}{2022/02/04}{instructions for compiling and installing the
% package}
%
% To produce the \code{sankey} package:
%
% \begin{lstlisting}[style=bashsmall]
% pdflatex sankey.ins # or 'latex sankey.ins'
% \end{lstlisting}
%
% To finish the installation you have to move the
% \code{tikzlibrarydubins.code.tex} and
% \code{sankey.sty} files into a directory searched by \LaTeX.
% 
% To compile the \code{sankey} documentation (the
% \code{sankey.pdf} file):
%
% \begin{lstlisting}[style=bashsmall]
% pdflatex sankey.dtx
% makeindex -s gind.ist -o sankey.ind sankey.idx
% pdflatex sankey.dtx
% makeindex -s gind.ist -o sankey.ind sankey.idx
% pdflatex sankey.dtx
% pdflatex sankey.dtx
% \end{lstlisting}
%
%
%^^A % ------------------------------------------------------------
% \section{The \texttt{sankey.sty} file}
%^^A % ------------------------------------------------------------
%
% Poorly commented source code...
%
% \changes{v1.0}{2016/03/06}{first version}
% \changes{v2.0}{2021/01/27}{first public version (on \CTAN)}
% \changes{v3.0}{2021/03/14}{better naming rule}
% \changes{v3.0}{2021/03/14}{use .ins and .dtx files}
%
% \iffalse
%<*sankey>
% \fi
%
% Version information:
%
%    \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}[2015/10/01]
\ProvidesPackage{sankey}[2022/02/04 v3.0.1 to draw Sankey diagrams]
%    \end{macrocode}
%
% All required packages and TikZ libraries:
%    \begin{macrocode}
\RequirePackage{xparse}
\RequirePackage{etoolbox}
\RequirePackage{xfp}
\RequirePackage{tikz}
\usetikzlibrary{
  calc,
  decorations.markings,
  dubins
}
%    \end{macrocode}
% 
% Declarations of PGF layers (to debug Sankey diagrams):
%
%    \begin{macrocode}
%% add a new layer to debug sankey diagrams
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfdeclarelayer{sankeydebug}
\pgfsetlayers{background,main,foreground,sankeydebug}
%    \end{macrocode}
%
%
%^^A % ------------------------------------------------------------
% \subsection{Fields}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@newfield}
%
% The \code{sankeynewfield} macro defines
% setter and getter macros for \emph{key}/\emph{value} pairs.
% It requires five parameters: the \emph{def} macro used to
% store a new value, the \emph{setter} macro name, the \emph{getter} macro name,
% the \emph{cs name} used by the new field (including a \texttt{\#1}
% parameter -- the \emph{key}) and the \emph{error message} (used by the getter
% macro if the key is not defined).
%
% The \emph{setter} macro requires
% two parameters: the key and the value.
% The \emph{getter} macro requires
% one parameter: the key.
%
%    \begin{macrocode}
\def\snk@newfield#1#2#3#4#5{
  % setter
  \def#2##1##2{\expandafter#1\csname #4\endcsname{##2}}
  % getter
  \def#3##1{%
    \ifcsdef{#4}{%
      \csname#4\endcsname%
    }{%
      \PackageError{sankey}{#5}{unknown key with \string#3}%
    }%
  }
}
%    \end{macrocode}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Definition of \emph{global} and \emph{expanded} fields (using
% \texttt{\protect\string\xdef})}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@setnodeqty}
% \begin{macro}{\sankeygetnodeqty}
% The setter and getter macros to store and retrieve
% the \emph{quantity} field associated with
% each Sankey node (the key is the name of the Sankey node).
%    \begin{macrocode}
\snk@newfield\xdef\snk@setnodeqty\sankeygetnodeqty%
{@snk@node@qty@#1}{Unknown sankey node '#1'}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% 
% \begin{macro}{\snk@setnodeorient}
% \begin{macro}{\sankeygetnodeorient}
% The setter and getter macros to store and retrieve
% the \emph{angle} (or orientation) field
% associated with each Sankey node (the key is the name of the Sankey node).
%    \begin{macrocode}
\snk@newfield\xdef\snk@setnodeorient\sankeygetnodeorient%
{@snk@node@orient@#1}{Unknown sankey node '#1'}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Definitions of \emph{local} fields (using \texttt{\protect\string\def})}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@setstartfill}
% \begin{macro}{\snk@getstartfill}
% \begin{macro}{\snk@setstartdraw}
% \begin{macro}{\snk@getstartdraw}
% The setter and getter macros to store and retrieve the starting fill/draw
% paths (the key is the style name).
%    \begin{macrocode}
\snk@newfield\def\snk@setstartfill\snk@getstartfill%
{@snk@start@fill@#1}{Unknown sankey start fill path #1}

\snk@newfield\def\snk@setstartdraw\snk@getstartdraw%
{@snk@start@draw@#1}{Unknown sankey start draw path #1}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% 
% \begin{macro}{\snk@setendfill}
% \begin{macro}{\snk@getendfill}
% \begin{macro}{\snk@setenddraw}
% \begin{macro}{\snk@getenddraw}
% The setter and getter macros to store and retrieve the ending fill/draw
% paths (the key is the style name).
%    \begin{macrocode}
\snk@newfield\def\snk@setendfill\snk@getendfill%
{@snk@end@fill@#1}{Unknown sankey end fill path #1}

\snk@newfield\def\snk@setenddraw\snk@getenddraw%
{@snk@end@draw@#1}{Unknown sankey end draw path #1}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Check if a sankey node is defined}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@ifnodedefined}

% The \code{\snk@ifnodedefined} macro checks if a Sankey
% node is defined by checking if its name is associated to
% a \emph{quantity}.
%    \begin{macrocode}
\newcommand\snk@ifnodedefined[3]{%
  \ifcsdef{@snk@node@qty@#1}{#2}{#3}%
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\snk@errorifnotdefined}
% The \code{\snk@errorifnotdefined} macro generares
% an error message if the Sankye node is not defined.
%    \begin{macrocode}
\newcommand\snk@errorifnotdefined[1]{%
  \snk@ifnodedefined{#1}{}%
  {\PackageError{sankey}{Unknown sankey node '#1'}{}}%
}
%    \end{macrocode}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsection{The \texttt{sankey node} shape}
%^^A % ------------------------------------------------------------
%
%
% A \code{sankey node} is defined as a TikZ node
% with a particular \emph{shape}: its width is null and its
% height matches the associated \emph{quantity}.
% This shape requires only three anchors: \code{center}, \code{left}
% and \code{right}.
% These threee anchors are sufficient to use the
% \code{sankey} package. But the \code{fit} library needs
% anchors defined by rectangular node.
%
%    \begin{macrocode}
\pgfdeclareshape{sankey node}{
  \inheritsavedanchors[from=rectangle]
  \inheritanchor[from=rectangle]{center}
  \inheritanchorborder[from=rectangle]
  \anchor{left}{\pgf@process{\northeast}}
  \anchor{right}{\pgf@process{\southwest}}
  % compatibility with 'fit' library
  \inheritanchor[from=rectangle]{west}
  \inheritanchor[from=rectangle]{east}
  \inheritanchor[from=rectangle]{north}
  \inheritanchor[from=rectangle]{south}
  \inheritanchor[from=rectangle]{north west}
  \inheritanchor[from=rectangle]{south east}
  \inheritanchor[from=rectangle]{north east}
  \inheritanchor[from=rectangle]{south west}
}
%    \end{macrocode}
%
%^^A % ------------------------------------------------------------
% \subsection{Keys}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\sankeyset}
% The \code{sankey} package uses \code{pgfkeys} to set options via
% \emph{key=value} pairs using the \texttt{/sankey} path
% (for Sankey diagram options) and using the
% \texttt{/sankey/node parameters} path (for Sankey node parameters).
%
% The \code{\sankeyset} macro processes
% its parameter as a list of comma separated pairs of the form
% \emph{key=value} with \texttt{/sankey} as default path.
%
%    \begin{macrocode}
\pgfkeys{/sankey/.is family}
\NewDocumentCommand\sankeyset{m}{\pgfkeys{sankey,#1}}
%    \end{macrocode}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Keys to define the scale}
%^^A % ------------------------------------------------------------
% \begin{macro}{\snk@totalqty}
% \begin{macro}{\snk@totallen}
% 
% The \code{ratio quantity}, \code{ratio length} and
% \code{ratio} keys define the ratio between
% \emph{flow quantity} and \emph{graphic length} (the scale).
% The \code{\snk@totalqty} and \code{\snk@totallen} macros store the values.
% All \emph{quantities} are processed by \code{\fpeval} and
% all \emph{lengths} are processed by \code{pgfmath}.
%    \begin{macrocode}
\sankeyset{
  ratio quantity/.code={\edef\snk@totalqty{\fpeval{#1}}},
  ratio quantity/.value required,
  ratio length/.code={
    \pgfmathsetmacro\snk@totallen{#1}
    \edef\snk@totallen{\snk@totallen pt}
  },
  ratio length/.value required,
  ratio/.style args={#1/#2}{
    ratio length=#1,
    ratio quantity=#2,
  },
  ratio/.value required,
}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Rotate offset}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@rotate}
%
% The \code{rotate} key stores an offset angle applied to all Sankey
% nodes.  This is useful when using the \code{rotate} option within a
% \code{tikzpicture} or a \code{scope}. This TikZ option is only
% applied to coordinates and not to TikZ nodes (remember that Sankey
% nodes are TikZ nodes). It's up to the author to keep the
% \code{rotate} option of the \code{tikzpicture} and that of the
% \code{sankeydiagram} synchronous.
% 
%    \begin{macrocode}
\sankeyset{
  rotate/.code={\edef\snk@rotate{\fpeval{#1}}},
  rotate/.value required,
}
%    \end{macrocode}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Minimum radius}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@minradius}
%
% The \code{minimum radius} key processes the minimum radius
% of curvature by \code{pgfmath} then stores it in
% the \code{\snk@minradius} macro.
%    \begin{macrocode}
\sankeyset{
  minimum radius/.code={
    \pgfmathsetmacro\snk@minradius{#1}
    \edef\snk@minradius{\snk@minradius pt}
  },
  minimum radius/.value required,
}
%    \end{macrocode}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Outin step}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@stepoutin}
% The \code{outin} key stores its value in
% the \code{\snk@stepoutin} macro.
%
%    \begin{macrocode}
\sankeyset{
  outin steps/.estore in=\snk@stepoutin,
  outon steps/.value required,
}
%    \end{macrocode}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Sankey debug}
%^^A % ------------------------------------------------------------
%
%
% The \code{debug} key drives the \code{sankey debug} toggle.
%
%    \begin{macrocode}
\newtoggle{sankey debug}
\sankeyset{
  debug/.is choice,
  debug/true/.code={\toggletrue{sankey debug}},
  debug/false/.code={\togglefalse{sankey debug}},
  debug/.default=true,
}
%    \end{macrocode}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Start and end styles}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@startstyle}
% \begin{macro}{\snk@endstyle}
% The \code{start style} and \code{end style} keys are choices.
%
% The \code{new start style} and \code{new end style} keys
% add new option to these choices.
% They use the \code{startfill}, \code{startdraw} fields
% or the \code{endfill} and \code{enddraw}
% fields (using the style \emph{name} as key) to store the fill and draw
% paths then create a new option to install the new
% start (\code{\snk@startstyle}) or end (\code{\snk@endstyle}) style.
%
%    \begin{macrocode}
\sankeyset{
  start style/.is choice,
  end style/.is choice,
  % to define new start and end styles
  new start style/.code n args={3}{% name, fill path, draw path
    \snk@setstartfill{#1}{#2}
    \snk@setstartdraw{#1}{#3}
    \sankeyset{start style/#1/.code={\def\snk@startstyle{#1}}}
  },
  new end style/.code n args={3}{% name, fill path, draw path
    \snk@setendfill{#1}{#2}
    \snk@setenddraw{#1}{#3}
    \sankeyset{end style/#1/.code={\def\snk@endstyle{#1}}}
  },
}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Initial parameters}
%^^A % ------------------------------------------------------------
%
% The \code{@initial options} style defines default values for
% options of Sankey diagram.  The \code{every diagram} style (initially
% empty) allows the user to choose its own default values.
%
% The \code{@initial options} and the \code{every diagram} styles are
% applied (in this order) at the beginning of each Sankey diagram.
%
%    \begin{macrocode}
\sankeyset{
  debug color/.style={/utils/exec={\colorlet{debug color}{#1}}},
  @initial options/.style={
    ratio=1cm/10,
    minimum radius=5mm,%
    outin steps=10,
    debug=false,
    start style=none,
    end style=none,
    rotate=0,
    % default fill/draw styles,
    fill/.style={line width=0pt,fill=white},
    draw/.style={draw=black,line width=.4pt},
    % debug color used by all debug macros
    debug color=red!75!black,
    % debug line between left and right anchors
    debug line/.style={overlay,draw=debug color,|-|},
    % debug line between center and label
    debug normal/.style={overlay,draw=debug color},
    % debug node label
    debug label/.style={
      overlay,
      draw,
      font=\ttfamily\tiny,
      text=debug color,text opacity=1,
      inner sep=.1em,
      fill=white,fill opacity=1,
      rounded corners=.1em,
      node contents={\name},
    },
    every node/.style={},
  },
  every diagram/.style={},
}

%    \end{macrocode}
%
%^^A % ------------------------------------------------------------
% \subsubsection{Sankey node parameters}
%^^A % ------------------------------------------------------------
%
% The \code{/sankey/node parameters} family defines all parameters during
% creation of Sankey node.
%
%    \begin{macrocode}
\sankeyset{node parameters/.is family}
%    \end{macrocode}
% \begin{macro}{\name}
% \begin{macro}{\qty}
% \begin{macro}{\orient}
% \begin{macro}{\pos}
%
% The \code{name}, \code{quantity}, \code{angle} and \code{at} keys use the
% \code{\name}, \code{\qty}, \code{\orient} and \code{\pos} macros
% to store the \emph{name}, the \emph{quantity}, the \emph{orientation} (or
% \emph{angle}) and the \emph{position} of a Sankey node during its
% creation.
%
% The \emph{quantity} is processed via \code{\fpeval}. The
% \emph{orientation} is normalized.
%
%    \begin{macrocode}
\sankeyset{node parameters,
  name/.estore in=\name,
  name/.value required,
  quantity/.code={\edef\qty{\fpeval{#1}}},
  quantity/.value required,
  angle/.code={\edef\orient{\snk@normalize@angle{#1}}},
  angle/.value required,
  at/.code={\snk@getpos\pos{#1}},
  at/.value required,
}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
% The \code{as} key is just a shortcut to define the four current node
% parameters by copying them from an existing Sankey node.
%
%    \begin{macrocode}
\sankeyset{node parameters,
  as/.style={
    name=#1,
    quantity=\sankeygetnodeqty{#1},
    angle=\sankeygetnodeorient{#1},
    at={#1.center},
  },
  as/.value required,
}
%    \end{macrocode}
%
% \begin{macro}{\snk@anchor}
%
% The \code{anchor} key stores in the \code{\snk@anchor} macro
% the anchor name to use to create the new current Sankey node
%
%    \begin{macrocode}
\sankeyset{node parameters,
  anchor/.is choice,
  anchor/left/.code={\def\snk@anchor{left}},
  anchor/right/.code={\def\snk@anchor{right}},
  anchor/center/.code={\def\snk@anchor{center}},
  anchor/.value required,
}
%    \end{macrocode}
% \end{macro}
%
% The \code{start} and \code{end} keys drive the
% \code{sankey node start} and \code{sankey node end}
% toggles.
%
%    \begin{macrocode}
\newtoggle{sankey node start}
\newtoggle{sankey node end}
\sankeyset{node parameters,
  start/.is choice,
  start/true/.code={\toggletrue{sankey node start}},
  start/false/.code={\togglefalse{sankey node start}},
  start/.default=true,
  % 
  end/.is choice,
  end/true/.code={\toggletrue{sankey node end}},
  end/false/.code={\togglefalse{sankey node end}},
  end/.default=true,
}
%    \end{macrocode}
% \begin{macro}{\snk@listofforks}
% \begin{macro}{\snk@forkanchor}
%
% The \code{forked} and \code{fork anchor} keys store their value in the
% \code{\snk@listofforks} and \code{\snk@forkanchor} macros.
%
%    \begin{macrocode}
\sankeyset{node parameters,
  forked/.estore in=\snk@listofforks,
  forked/.value required,
  fork anchor/.estore in=\snk@forkanchor,
  fork anchor/.value required,
}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% The \code{@initial parameters} style initialises all Sankey node
% parameters at the start of the creation of a new Sankey node.
%
%    \begin{macrocode}
\sankeyset{node parameters,
  @initial parameters/.style={
    start=false,
    end=false,
    forked=,
    fork anchor=,
    anchor=center,
    at={0,0},
    angle=0,
  },
}
%    \end{macrocode}
% 
%
%^^A % ------------------------------------------------------------
% \subsubsection{Internal Tikz style}
%^^A % ------------------------------------------------------------
%
% To apply this style with Tikz, use absolute key name
% (\texttt{/sankey/@sankey node}). This style is used to create the Tikz
% node assoicated to a Sankey node.
%
%    \begin{macrocode}
\sankeyset{
  % sankey node TikZ style
  @sankey node/.style n args={3}{% name, pos, anchor
    shape=sankey node,
    inner sep=0,
    minimum height={\sankeyqtytolen{\sankeygetnodeqty{#1}}},
    minimum width=0,
    draw=none,
    line width=0pt,
    fill=none,
    node contents={},
    rotate=\sankeygetnodeorient{#1}+\snk@rotate,
    at={(#2)},
    name=#1,
    anchor=#3,
  },
}
%    \end{macrocode}
%
%^^A % ------------------------------------------------------------
% \subsection{The \texttt{sankeydiagram} environment}
% ^^A % ------------------------------------------------------------
%
% \begin{environment}{sankeydiagram}
%   
%   The \code{sankeydiagram} environment defines locally all the macros
%   used by a Sankey diagram. Then it applies the %
%   \code{@initial options} and \code{every diagram} styles (in this
%   order) and applies all the keys provided in its optional argument.
%
%    \begin{macrocode}
\NewDocumentEnvironment{sankeydiagram}{O{}}{
%    \end{macrocode}
% 
%^^A % ------------------------------------------------------------
% \subsection{Internal macros}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\snk@getpos}
%
% The \code{\snk@getpos} macro extracts the position of a TikZ
% node\footnote{Thanks to Andrew Stacey \url{https://tex.stackexchange.com/a/33765/14500}}.
%
%    \begin{macrocode}
  \def\snk@getpos##1##2{%
    \tikz@scan@one@point\pgfutil@firstofone(##2)\relax%
    \edef##1{\the\pgf@x,\the\pgf@y}%
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\snk@modulo}
% 
% The \code{\snk@modulo} macro evaluates \#1 modulo \#2 using \code{\fpeval}.
% 
%    \begin{macrocode}
  \def\snk@modulo##1##2{\fpeval{##1-(floor((##1)/(##2),0)*##2)}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\snk@normalize@angle}
%
% The \code{\snk@normalize@angle} macro normalizes \#1 (an angle) between
% $-180$ and $180$ (using \code{\fpeval}).
%
%    \begin{macrocode}
  \def\snk@normalize@angle##1{%
    \fpeval{\snk@modulo{(##1)+180}{360}-180}%
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\snk@show@debug}
%
% The \code{snk@show@debug} macro draws debug information
% of the Sankey node named \#1 but only if the \code{sankey debug}
% toogle is true. Everything is drawn on the \code{sankeydebug}
% layer. It uses the \code{/sankey/debug line},
% \code{/sankey/debug normal} and \code{/sankey/debug label} Tikz styles.
%
%    \begin{macrocode}
  \def\snk@show@debug##1{% node name
    \iftoggle{sankey debug}{
      \begingroup
      \edef\name{##1}
      \edef\qty{\sankeygetnodeqty{\name}}
      \edef\orient{\sankeygetnodeorient{\name}}
      \begin{pgfonlayer}{sankeydebug}
        \path[/sankey/debug line] (\name.left) -- (\name.right);
        \pgfmathsetmacro{\snk@len}{\sankeyqtytolen{\qty}/3}
        \path[/sankey/debug normal] (\name.center)
        -- ($(\name.center)!\snk@len pt!90:(\name.right)$)
        node[/sankey/debug label,rotate=\orient+90+\snk@rotate,anchor=north];
      \end{pgfonlayer}
      \endgroup
    }{}
  }
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\snk@makeforkednode}
% \begin{macro}{\snk@tot}
% \begin{macro}{\snk@subnodeqty}
% \begin{macro}{\snk@subnodename}
% \begin{macro}{\snk@added@values}
%
% The \code{\snk@makeforkednode} forks a Sankey node.
%
%    \begin{macrocode}
  \def\snk@makeforkednode{
    \begingroup
    \ifdefempty{\snk@listofforks}{
      \ifdefempty{\snk@forkanchor}{}{
        \PackageWarning{sankey}%
        {Can't use 'fork anchor' key without 'forked' key}
      }
    }{
      \def\snk@tot{0}
      \def\snk@added@values{}
      \sankeyset{
        @add forked node/.code args={####1/####2}{
          \coordinate (####2) at ($(\name.left)%
          !\fpeval{(\snk@tot+.5*(####1))/\qty}%
          !(\name.right)$);
          \edef\snk@orient{\orient}
          \sankeynode[debug=false]
          {name=####2,quantity=####1,at=####2,angle=\snk@orient}
          \edef\snk@tot{\fpeval{\snk@tot+####1}}
          \edef\snk@added@values{\snk@added@values+####1}
        },
        @add forked node/.list/.expand once=\snk@listofforks,
      }
      \edef\snk@diff{\fpeval{abs(\qty-\snk@tot)}}
      \ifnumequal{\snk@diff}{0}{}{
        \PackageWarning{sankey}%
        {^^J*** Warning: bad sankey fork: %
          \qty\space!=\space\snk@added@values(=\snk@tot)%
          ^^J\snk@listofforks}
      }
      \ifdefempty{\snk@forkanchor}{
        \edef\snk@forkanchor{\name.\snk@anchor}
      }{}
      \snk@getpos\snk@c{$(\snk@forkanchor) - (\pos)$}
      \sankeynode{as=\name,at={$(\name) - (\snk@c)$}}
      \foreach \snk@subnodeqty/\snk@subnodename in \snk@listofforks {
        \sankeynode{as=\snk@subnodename,at={$(\snk@subnodename) - (\snk@c)$}}
      }
    }
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \begin{macro}{\snk@makenode}
%
% The \code{\snk@makenode} macro creates a new Sankey node named
% \code{\name} with \code{\qty} quantity, oriented at
% \code{\orient} degrees (but modified by the \code{\snk@rotate}
% angle offset), anchored by its \code{\anchor} (or its \emph{center}
% by default) at \code{\pos} position.
%
%    \begin{macrocode}
  \def\snk@makenode{
    \begingroup
    \snk@setnodeqty{\name}{\qty}
    \edef\orient{\snk@normalize@angle{\orient}}
    \snk@setnodeorient{\name}{\orient}
    \ifundef{\snk@anchor}{\def\snk@anchor{center}}{}
    \node[/sankey/@sankey node={\name}{\pos}{\snk@anchor}];
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\snk@filldrawstart}
%
% The \code{\snk@filldrawstart} macro fills
% (with the \code{/sankey/fill} TikZ style) then draws
% (with the \code{/sankey/draw} TikZ style)
% a start of flow using paths from style \code{\snk@startstyle} on
% the Sankey node named \code{\name}.
%
%    \begin{macrocode}
  \def\snk@filldrawstart{
    \begin{scope}[shift={(\name)},rotate=\orient]
      \path[/sankey/fill] \snk@getstartfill{\snk@startstyle};
      \path[/sankey/draw] \snk@getstartdraw{\snk@startstyle};
    \end{scope}
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\snk@filldrawend}
%
% The \code{\snk@filldrawend} macro fills
% (with the \code{/sankey/fill} TikZ style) then draws
% (with the \code{/sankey/draw} TikZ style)
% a end of flow using paths from style \code{\snk@endstyle} on
% the Sankey node named \code{\name}.
%
%    \begin{macrocode}
  \def\snk@filldrawend{
    \begin{scope}[shift={(\name)},rotate=\sankeygetnodeorient{\name}]
      \path[/sankey/fill] \snk@getendfill{\snk@endstyle};
      \path[/sankey/draw] \snk@getenddraw{\snk@endstyle};
    \end{scope}
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\snk@checkquantities}
% \begin{macro}{\snk@qtyi}
% \begin{macro}{\snk@qtyii}
% The \code{\snk@checkquantities} compares quantities
% from Sankey nodes \code{#1} and \code{#2} and emits
% an error message if they differ (\code{#3}  is the name
% of the macro which requested the verification).
%
%    \begin{macrocode}
  \def\snk@checkquantities##1##2##3{
    \begingroup
    \edef\snk@qtyi{\sankeygetnodeqty{##1}}
    \edef\snk@qtyii{\sankeygetnodeqty{##2}}
    \ifdefstrequal{\snk@qtyi}{\snk@qtyii}{}{
      \PackageError{sankey}%
      {^^J*** \string##3: quantities differ between %
        ##1 (\snk@qtyi) and ##2 (\snk@qtyii)%
        ^^J}%
      {The quantities of the two Sankey nodes must be equal.}
    }
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsection{User macros}
%^^A % ------------------------------------------------------------
%
% \begin{macro}{\sankeydubins}
%
% The \code{\sankeydubins} macro links two Sankey nodes via 
% a Dubins path. First, it computes the Dubins path between
% centers (left and right radii are the same) and stores the
% result in \code{sankey}. Then it uses the stored result
% to fill and draw the lane (left border and right borders
% use Dubins paths with asymmetric radii).
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeydubins{O{}mm}{% options, sn, en
    \snk@errorifnotdefined{##2}
    \snk@errorifnotdefined{##3}
    \snk@checkquantities{##2}{##3}{\sankeydubins}
    \begingroup
    \sankeyset{##1}
    \pgfmathsetmacro\qty{\sankeygetnodeqty{##2}}
    \dubinspathset{
      sankey/.style={
        start point=##2.center,start angle=\sankeygetnodeorient{##2},
        end point=##3.center,end angle=\sankeygetnodeorient{##3},
        minimum radius=\snk@minradius + .5 * \sankeyqtytolen{\qty} pt,
      },
    }
    \dubinspathcalc{sankey,store=sankey}
    \dubinspathset{
      left border/.style={
        sankey, use store=sankey,
        left and right minimum radii={\snk@minradius}
        and {\snk@minradius + \sankeyqtytolen{\qty} pt},
      },
      right border/.style={
        sankey, use store=sankey,
        left and right minimum radii=
        {\snk@minradius + \sankeyqtytolen{\qty} pt}
        and {\snk@minradius},
      },
    }
    % fill the region
    \path[/sankey/fill] (##2.left)  \dubinspath{left border}
    -- (##3.left) -- (##3.right) \dubinspath{right border,reverse}
    -- (##2.right) -- cycle;
    % draw left and right borders
    \path[/sankey/draw] (##2.left) \dubinspath{left border}
    (##2.right) \dubinspath{right border};
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sankeyoutin}
%
% The \code{\sankeyoutin} macro links two Sankey nodes via a Bézier curve.
% First, to simulate constant width, it creates \code{\snk@stepoutin}
% intermediate Sankey nodes along the Bézier curve. Then, the lane is
% filled and drawn linking all the intermediate Sankey node via smaller
% Bézier curves.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyoutin{O{}mm}{% options, sn, en
    \snk@errorifnotdefined{##2}
    \snk@errorifnotdefined{##3}
    \snk@checkquantities{##2}{##3}{\sankeyoutin}
    \begingroup
    \sankeyset{##1}
    \edef\qty{\sankeygetnodeqty{##2}}
    \pgfmathsetmacro\snk@len{\sankeyqtytolen{\qty}/2}
    \edef\snk@step{\fpeval{1/\snk@stepoutin}}
    \edef\snk@laststep{\inteval{\snk@stepoutin-1}}
    \path[overlay,decorate,decoration={
      markings,
      mark=between positions \snk@step and {\fpeval{1-.5*\snk@step}}
      step \snk@step with {
        \edef\snk@outinmidptname{%
          snk@outinmidpt-%
          \pgfkeysvalueof{/pgf/decoration/mark info/sequence number}%
        }
        \path
        (0,0) coordinate(\snk@outinmidptname)
        (0,-\snk@len pt) coordinate (\snk@outinmidptname-r)
        (0,\snk@len pt) coordinate (\snk@outinmidptname-l)
        ;
      }
    }]
    (##2.center)
    to[out=\sankeygetnodeorient{##2},in=\sankeygetnodeorient{##3}+180]
    (##3.center);
    \foreach \snk@ptnum in {1,...,\snk@laststep}{
      \edef\snk@outinmidptname{snk@outinmidpt-\snk@ptnum}
      \dbp@anglebetween\snk@outinmidptangle%
      {\snk@outinmidptname-r}{\snk@outinmidptname-l}
      \sankeynode[debug=false]{%
        name=\snk@outinmidptname,
        quantity=\qty,
        angle=\snk@outinmidptangle-90,%
        at=\snk@outinmidptname%
      }
    }
    \sankeynode[debug=false]{%
      name={snk@outinmidpt-0},
      quantity=\sankeygetnodeqty{##2},
      angle=\sankeygetnodeorient{##2},%
      at={##2}%
    }
    \sankeynode[debug=false]{%
      name={snk@outinmidpt-\snk@stepoutin},
      quantity={\sankeygetnodeqty{##3}},
      angle={\sankeygetnodeorient{##3}},%
      at={##3}%
    }
    \path[/sankey/fill,looseness=1]
    (snk@outinmidpt-0.left)
    \foreach \snk@curpt
    [remember=\snk@curpt as \snk@prevpt (initially 0)]
    in {1,...,\snk@stepoutin}{
      to[out=\sankeygetnodeorient{snk@outinmidpt-\snk@prevpt},
      in=\sankeygetnodeorient{snk@outinmidpt-\snk@curpt}+180]
      (snk@outinmidpt-\snk@curpt.left)
    }
    --
    (snk@outinmidpt-\snk@stepoutin.right)
    \foreach \snk@curpt
    [remember=\snk@curpt as \snk@prevpt (initially \snk@stepoutin)]
    in {\snk@laststep,...,0}{
      to[out=\sankeygetnodeorient{snk@outinmidpt-\snk@prevpt}+180,
      in=\sankeygetnodeorient{snk@outinmidpt-\snk@curpt}]
      (snk@outinmidpt-\snk@curpt.right)
    }
    -- cycle;
    \path[/sankey/draw,looseness=1]
    (snk@outinmidpt-0.left)
    \foreach \snk@curpt
    [remember=\snk@curpt as \snk@prevpt (initially 0)]
    in {1,...,\snk@stepoutin}{
      to[out=\sankeygetnodeorient{snk@outinmidpt-\snk@prevpt},
      in=\sankeygetnodeorient{snk@outinmidpt-\snk@curpt}+180]
      (snk@outinmidpt-\snk@curpt.left)
    }
    (snk@outinmidpt-\snk@stepoutin.right)
    \foreach \snk@curpt
    [remember=\snk@curpt as \snk@prevpt (initially \snk@stepoutin)]
    in {\snk@laststep,...,0}{
      to[out=\sankeygetnodeorient{snk@outinmidpt-\snk@prevpt}+180,
      in=\sankeygetnodeorient{snk@outinmidpt-\snk@curpt}]
      (snk@outinmidpt-\snk@curpt.right)
    };
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\sankeynodealias}
%
% The \code{\sankeynodealias} macro clones the Sankey node
% named \code{#1} into a Sankey node named \code{#2}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeynodealias{mm}{%name, alias
    \snk@errorifnotdefined{##1}
    \path[late options={name=##1,alias=##2}];
    \snk@setnodeqty{##2}{\sankeygetnodeqty{##1}}
    \snk@setnodeorient{##2}{\sankeygetnodeorient{##1}}
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sankeynode}
%
% The \code{\sankeynode} macro creates the new Sankey
% node named \code{#2}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeynode{O{}m}{% options, node parameters
    \begingroup
    \sankeyset{##1}
    \sankeyset{node parameters,@initial parameters,/sankey/every node,##2}
    \snk@makenode{}
    \snk@makeforkednode{}
    \iftoggle{sankey node start}{\snk@filldrawstart}{}
    \iftoggle{sankey node end}{\snk@filldrawend}{}
    \snk@show@debug{\name}
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sankeystart}
%
% The \code{\sankeystart} macro fills and draws a starting lane
% attached to the Sankey node named \code{#2}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeystart{O{}m}{% options, name
    \snk@errorifnotdefined{##2}
    \begingroup
    \sankeyset{##1}
    \edef\name{##2}
    \edef\orient{\sankeygetnodeorient{##2}}
    \edef\qty{\sankeygetnodeqty{##2}}
    \snk@filldrawstart
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sankeynodestart}
%
% The \code{\sankeynodestart} macro creates the new Sankey
% node named \code{#2} then fills and draws a starting lane
% attached to this new Sankey node.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeynodestart{O{}m}{% option, node parameters
    \sankeynode[##1]{start,##2}
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sankeyend}
%
% The \code{\sankeyend} macro fills and draws an ending lane
% attached to the Sankey node named \code{#2}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyend{O{}m}{%options, name
    \snk@errorifnotdefined{##2}
    \begingroup
    \sankeyset{##1}
    \edef\name{##2}
    \edef\orient{\sankeygetnodeorient{##2}}
    \edef\qty{\sankeygetnodeqty{##2}}
    \snk@filldrawend
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sankeynodeend}
%
% The \code{\sankeynodeend} macro creates the new Sankey
% node named \code{#2} then fills and draws an ending lane
% attached to this new Sankey node.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeynodeend{O{}m}{% options, node parameters
    \sankeynode[##1]{end,##2}
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sankeyadvance}
% \begin{macro}{\sankeyadvance*}
%
% The \code{\sankeyadvance} macro moves toward (or backward if
% \emph{starred} calls -- \code{#1}) the Sankey node named \code{#3}.
% \code{#4} is a distance. The previous position is keeped
% by a Sankey node named \code{#3-old}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyadvance{sO{}mm}{%
    %params: *(reverse), options, name, distance
    \snk@errorifnotdefined{##3}
    \begingroup
    \sankeyset{##2}
    \edef\name{##3}
    \edef\snk@oldname{##3-old}
    \sankeynodealias{\name}{\snk@oldname}
    \IfBooleanTF{##1}{
      % move backward
      \sankeynode{
        at={$(\snk@oldname.center)!##4!90:(\snk@oldname.left)$},
        angle=\sankeygetnodeorient{\snk@oldname},
        quantity=\sankeygetnodeqty{\snk@oldname},
        name=\name,
      }
      \path[/sankey/fill]
      (\name.left) -- (\snk@oldname.left)
      -- (\snk@oldname.right) -- (\name.right) -- cycle;
      \path[/sankey/draw]
      (\name.left) -- (\snk@oldname.left)
      (\snk@oldname.right) -- (\name.right);
    }{
      % move forward
      \sankeynode{
        at={$(\snk@oldname.center)!##4!-90:(\snk@oldname.left)$},
        angle=\sankeygetnodeorient{\snk@oldname},
        quantity=\sankeygetnodeqty{\snk@oldname},
        name=\name,
      }
      \path[/sankey/fill]
      (\snk@oldname.left) -- (\name.left)
      -- (\name.right) -- (\snk@oldname.right) -- cycle;
      \path[/sankey/draw]
      (\snk@oldname.left) -- (\name.left)
      (\name.right) -- (\snk@oldname.right);
    }
    \snk@show@debug{\name}
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\sankeyturnright}
% \begin{macro}{\sankeyturnright*}
%
% \changes{v3.0}{2021/03/14}{new macro}
%
% The \code{sankeyturnright} macro moves forward the Sankey node
% named \code{#3} by turning right. The angle is \code{#4} (the starred
% version uses the opposite of \code{#4}). If the angle is \emph{negative}, the
% macro calls the \code{\sankeyturnrightbackward} macro to move backward else
% the macro fills/draws the lane between the previous position and the new
% position. The previous position is keeped by a Sankey
% node named \code{#3-old}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyturnright{sO{}mm}{
    % *(reverse), options, name, angle
    \snk@errorifnotdefined{##3}
    \begingroup
    \IfBooleanTF{##1}
    {\edef\snk@angle{\fpeval{-1*##4}}}
    {\edef\snk@angle{\fpeval{1*##4}}}
    \edef\snk@anglesign{\fpeval{sign(\snk@angle)}}
    \ifnumgreater{\snk@anglesign}{-1}{
      \sankeyset{##2}
      \edef\name{##3}
      \edef\snk@oldname{##3-old}
      \sankeynodealias{\name}{\snk@oldname}
      \edef\qty{\sankeygetnodeqty{\name}}
      \edef\orient{\snk@normalize@angle{\sankeygetnodeorient{\name}-\snk@angle}}
      \snk@getpos\snk@c{$(\name.right)!-\snk@minradius!(\name.left)$}
      \snk@getpos\pos{$(\snk@c)!1!-\snk@angle:(\name.center)$}
      \snk@makenode{}
      % fill the region
      \path[/sankey/fill] let
      \p1=(\snk@oldname.left),\p2=(\snk@oldname.right),
      \p3=(\name.left),\p4=(\name.right),
      \n1={\sankeyqtytolen{\qty}},
      \n{maxr}={\snk@minradius+\n1},
      \n{minr}={\snk@minradius}
      in
      (\p1) arc(\orient+\snk@angle+90:\orient+90:\n{maxr}) -- (\p3) --
      (\p4) arc(\orient+90:\orient+\snk@angle+90:\n{minr}) -- (\p2) -- cycle;
      % draw left and right borders
      \path[/sankey/draw] let
      \p1=(\snk@oldname.left),\p2=(\snk@oldname.right),
      \p3=(\name.left),\p4=(\name.right),
      \n1={\sankeyqtytolen{\qty}},
      \n{maxr}={\snk@minradius+\n1},
      \n{minr}={\snk@minradius}
      in
      (\p1) arc(\orient+\snk@angle+90:\orient+90:\n{maxr}) 
      (\p4) arc(\orient+90:\orient+\snk@angle+90:\n{minr});
      \snk@show@debug{\name}
    }{
      \sankeyturnrightbackward[##2]{##3}{-1*\snk@angle}
    }
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\sankeyturnrightbackward}
% \begin{macro}{\sankeyturnrightbackward*}
%
% \changes{v3.0}{2021/03/14}{new macro}
%
% The \code{sankeyturnrightbackward} macro moves backward the Sankey node
% named \code{#3} by turning right. The angle is \code{#4} (the starred
% version uses the opposite of \code{#4}). If the angle is \emph{negative}, the
% macro calls the \code{\sankeyturnright} macro to move forward else
% the macro fills/draws the lane between the previous position and the new
% position. The previous position is keeped by a Sankey
% node named \code{#3-old}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyturnrightbackward{sO{}mm}{
    % *(reverse), options, name, angle
    \snk@errorifnotdefined{##3}
    \begingroup
    \IfBooleanTF{##1}
    {\edef\snk@angle{\fpeval{-1*##4}}}
    {\edef\snk@angle{\fpeval{1*##4}}}
    \edef\snk@anglesign{\fpeval{sign(\snk@angle)}}
    \ifnumgreater{\snk@anglesign}{-1}{
      \sankeyset{##2}
      \edef\name{##3}
      \edef\snk@oldname{##3-old}
      \sankeynodealias{\name}{\snk@oldname}
      \edef\qty{\sankeygetnodeqty{\name}}
      \edef\orient{\snk@normalize@angle{\sankeygetnodeorient{\name}+\snk@angle}}
      \snk@getpos\snk@c{$(\name.right)!-\snk@minradius!(\name.left)$}
      \snk@getpos\pos{$(\snk@c)!1!\snk@angle:(\name.center)$}
      \snk@makenode{}
      % fill the region
      \path[/sankey/fill] let
      \p1=(\name.left),\p2=(\name.right),
      \p3=(\snk@oldname.left),\p4=(\snk@oldname.right),
      \n1={\sankeyqtytolen{\qty}},
      \n{maxr}={\snk@minradius+\n1}, \n{minr}={\snk@minradius}
      in
      (\p1) arc(\orient+90:\orient-\snk@angle+90:\n{maxr}) -- (\p3) --
      (\p4) arc(\orient-\snk@angle+90:\orient+90:\n{minr}) -- (\p2) -- cycle;
      % draw left and right borders
      \path[/sankey/draw] let
      \p1=(\name.left),\p2=(\name.right),
      \p3=(\snk@oldname.left),\p4=(\snk@oldname.right),
      \n1={\sankeyqtytolen{\qty}},
      \n{maxr}={\snk@minradius+\n1}, \n{minr}={\snk@minradius}
      in
      (\p1) arc(\orient+90:\orient-\snk@angle+90:\n{maxr}) 
      (\p4) arc(\orient-\snk@angle+90:\orient+90:\n{minr});
      \snk@show@debug{\name}
    }{
      \sankeyturnright[##2]{##3}{-1*\snk@angle}
    }
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\sankeyturnleft}
% \begin{macro}{\sankeyturnleft*}
%
% \changes{v3.0}{2021/03/14}{new macro}
%
% The \code{sankeyturnleft} macro moves forward the Sankey node
% named \code{#3} by turning left. The angle is \code{#4} (the starred
% version uses the opposite of \code{#4}). If the angle is \emph{negative}, the
% macro calls the \code{\sankeyturnleftbackward} macro to move backward else
% the macro fills/draws the lane between the previous position and the new
% position. The previous position is keeped by a Sankey
% node named \code{#3-old}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyturnleft{sO{}mm}{
    % *(reverse), options, name, angle
    \snk@errorifnotdefined{##3}
    \begingroup
    \IfBooleanTF{##1}
    {\edef\snk@angle{\fpeval{-1*##4}}}
    {\edef\snk@angle{\fpeval{1*##4}}}
    \edef\snk@anglesign{\fpeval{sign(\snk@angle)}}
    \ifnumgreater{\snk@anglesign}{-1}{
      \sankeyset{##2}
      \edef\name{##3}
      \edef\snk@oldname{##3-old}
      \sankeynodealias{\name}{\snk@oldname}
      \edef\qty{\sankeygetnodeqty{\name}}
      \edef\orient{\snk@normalize@angle{\sankeygetnodeorient{\name}+\snk@angle}}
      \snk@getpos\snk@c{$(\name.left)!-\snk@minradius!(\name.right)$}
      \snk@getpos\pos{$(\snk@c)!1!\snk@angle:(\name.center)$}
      \snk@makenode{}
      % fill the region
      \path[/sankey/fill] let
      \p1=(\snk@oldname.left),\p2=(\snk@oldname.right),
      \p3=(\name.left),\p4=(\name.right),
      \n1={\sankeyqtytolen{\qty}},
      \n{maxr}={\snk@minradius+\n1}, \n{minr}={\snk@minradius}
      in
      (\p1) arc(\orient-\snk@angle-90:\orient-90:\n{minr}) -- (\p3) --
      (\p4) arc(\orient-90:\orient-\snk@angle-90:\n{maxr}) -- (\p2) -- cycle;
      % draw left and right borders
      \path[/sankey/draw] let
      \p1=(\snk@oldname.left),\p2=(\snk@oldname.right),
      \p3=(\name.left),\p4=(\name.right),
      \n1={\sankeyqtytolen{\qty}},
      \n{maxr}={\snk@minradius+\n1}, \n{minr}={\snk@minradius}
      in
      (\p1) arc(\orient-\snk@angle-90:\orient-90:\n{minr}) 
      (\p4) arc(\orient-90:\orient-\snk@angle-90:\n{maxr});
      \snk@show@debug{\name}
    }{
      \sankeyturnleftbackward[##2]{##3}{-1*\snk@angle}
    }
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\sankeyturnleftbackward}
% \begin{macro}{\sankeyturnleftbackward*}
%
% \changes{v3.0}{2021/03/14}{new macro}
%
% The \code{sankeyturnleftbackward} macro moves backward the Sankey node
% named \code{#3} by turning left. The angle is \code{#4} (the starred
% version uses the opposite of \code{#4}). If the angle is \emph{negative}, the
% macro calls the \code{\sankeyturnleft} macro to move forward else
% the macro fills/draws the lane between the previous position and the new
% position. The previous position is keeped by a Sankey
% node named \code{#3-old}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyturnleftbackward{sO{}mm}{
    % *(reverse), options, name, angle
    \snk@errorifnotdefined{##3}
    \begingroup
    \IfBooleanTF{##1}
    {\edef\snk@angle{\fpeval{-1*##4}}}
    {\edef\snk@angle{\fpeval{1*##4}}}
    \edef\snk@anglesign{\fpeval{sign(\snk@angle)}}
    \ifnumgreater{\snk@anglesign}{-1}{
      \sankeyset{##2}
      \edef\name{##3}
      \edef\snk@oldname{##3-old}
      \sankeynodealias{\name}{\snk@oldname}
      \edef\qty{\sankeygetnodeqty{\name}}
      \edef\orient{\snk@normalize@angle{\sankeygetnodeorient{\name}-\snk@angle}}
      \snk@getpos\snk@c{$(\name.left)!-\snk@minradius!(\name.right)$}
      \snk@getpos\pos{$(\snk@c)!1!-\snk@angle:(\name.center)$}
      \snk@makenode{}
      % fill the region
      \path[/sankey/fill] let
      \p1=(\name.left),\p2=(\name.right),
      \p3=(\snk@oldname.left),\p4=(\snk@oldname.right),
      \n1={\sankeyqtytolen{\qty}},
      \n{maxr}={\snk@minradius+\n1}, \n{minr}={\snk@minradius}
      in
      (\p1) arc(\orient-90:\orient+\snk@angle-90:\n{minr}) -- (\p3) --
      (\p4) arc(\orient+\snk@angle-90:\orient-90:\n{maxr}) -- (\p2) -- cycle;
      % draw left and right borders
      \path[/sankey/draw] let
      \p1=(\name.left),\p2=(\name.right),
      \p3=(\snk@oldname.left),\p4=(\snk@oldname.right),
      \n1={\sankeyqtytolen{\qty}},
      \n{maxr}={\snk@minradius+\n1}, \n{minr}={\snk@minradius}
      in
      (\p1) arc(\orient-90:\orient+\snk@angle-90:\n{minr}) 
      (\p4) arc(\orient+\snk@angle-90:\orient-90:\n{maxr});
      \snk@show@debug{\name}
    }{
      \sankeyturnleft[##2]{##3}{-1*\snk@angle}
    }
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\sankeyturn}
% \begin{macro}{\sankeyturn*}
%
% \changes{v3.0}{2021/03/14}{simplification by using new \emph{turn} macros}
%
% The \code{\sankeyturn} macro moves toward (or backward if
% \emph{starred} calls -- \code{#1}) the Sankey node named 
% \code{#3} by turning left (angle \code{#4} is positive)
% or right (angle \code{#4} is negative).
% The previous position is keeped by a Sankey node named
% \code{#3-old}.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyturn{sO{}mm}{%
    % *(reverse), options, name, angle
    \snk@errorifnotdefined{##3}
    \begingroup
    \edef\snk@anglesign{\fpeval{sign(##4)}}
    \IfBooleanTF{##1}{
      \ifnumgreater{\snk@anglesign}{-1}
      {\sankeyturnleftbackward[##2]{##3}{##4}}
      {\sankeyturnrightbackward[##2]{##3}{-1*##4}}
    }{
      \ifnumgreater{\snk@anglesign}{-1}
      {\sankeyturnleft[##2]{##3}{##4}}
      {\sankeyturnright[##2]{##3}{-1*##4}}
    }
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\sankeyfork}
%
% The \code{\sankeyfork} macro forks the Sankey node named
% \code{#2} to the list of subnodes given by \code{#3}.
% The subnodes are cloned to take into account
% the \code{debug} option.
%
%    \begin{macrocode}
  \NewDocumentCommand\sankeyfork{O{}mm}{%options, name, list of forks
    \snk@errorifnotdefined{##2}
    \begingroup
    \sankeyset{##1}
    \sankeynode[debug=false]{as={##2},forked={##3}}
    \foreach \qty/\snk@subnodename in {##3}{\sankeynode{as={\snk@subnodename}}}
    \endgroup
  }
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\sankeyqtytolen}
%
% The \code{\sankeyqtytolen} macro converts quantity
% to length using \code{\fpeval} and the ratio determined
% by \code{\snk@totalqty} and \code{\snk@totallen}.
%
%    \begin{macrocode}
  \def\sankeyqtytolen##1{\fpeval{(##1)/\snk@totalqty*\snk@totallen}}
%    \end{macrocode}
% \end{macro}
%
%^^A % ------------------------------------------------------------
% \subsection{The \protect\texttt{sankeydiagram} environment (the end)}
%^^A % ------------------------------------------------------------
%
% Here is the end of the definition of the \code{sankeydiagram}
% environment. The \code{@initial options} style and the %
% \code{every diagram} style are applied before options provided by
% user.
%
%    \begin{macrocode}
  \sankeyset{
    @initial options,
    every diagram,
    % user values
    #1}
}
{} % empty but mandatory ! :-)
%    \end{macrocode}
% \end{environment}
%
%^^A % ------------------------------------------------------------
% \subsection{Predefined start and end styles}
%^^A % ------------------------------------------------------------
%
% The \code{none} style.
%
%    \begin{macrocode}
\sankeyset{
  new start style={none}{}{},
  new end style={none}{}{},
}
%    \end{macrocode}
%
% The \code{simple} style.
%
%    \begin{macrocode}
\sankeyset{
  new start style={simple}{
    (\name.left) -- ([xshift=-.5\pgflinewidth]\name.left)
    -- ([xshift=-.5\pgflinewidth]\name.right) -- (\name.right) -- cycle
  }{
    (\name.left) -- ([xshift=-.5\pgflinewidth]\name.left)
    -- ([xshift=-.5\pgflinewidth]\name.right) -- (\name.right)
  },
  new end style={simple}{
    (\name.left) -- ([xshift=2mm]\name.center)
    -- (\name.right) -- cycle
  }{
    (\name.left)  -- ([xshift=2mm]\name.center) -- (\name.right)
  },
}
%    \end{macrocode}
%
% The \code{arrow} style.
%
%    \begin{macrocode}
\sankeyset{
  new start style={arrow}{
    (\name.left) -- ++(-10pt,0) -- ([xshift=-10pt/6]\name.center)
    -- ([xshift=-10pt]\name.right) -- (\name.right) -- cycle
  }{
    (\name.left) -- ++(-10pt,0) -- ([xshift=-10pt/6]\name.center)
    -- ([xshift=-10pt]\name.right) -- (\name.right)
  },
  new end style={arrow}{
    (\name.left) -- ([yshift=1mm]\name.left)
    -- ([xshift=10pt]\name.center) -- ([yshift=-1mm]\name.right)
    -- (\name.right) -- cycle
  }{
    (\name.left) -- ([yshift=1mm]\name.left)
    -- ([xshift=10pt]\name.center) -- ([yshift=-1mm]\name.right)
    -- (\name.right)
  },
}
%    \end{macrocode}
% \iffalse
%</sankey>
% \fi
%
%^^A % ------------------------------------------------------------
% \section{\texttt{tikzlibrarydubins.code.tex}}
%^^A % ------------------------------------------------------------
%
% Not yet documented nor commented...
%
% \iffalse
%<*tikzlibrarydubins.code.tex>
% \fi
% \begin{macro}{\tikzlibrarydubins@version}
% \begin{macro}{\tikzlibrarydubins@date}
%    \begin{macrocode}
\def\tikzlibrarydubins@version{v3.0.1}
\def\tikzlibrarydubins@date{2022/02/04}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% 
%    \begin{macrocode}
\usetikzlibrary{calc}
\RequirePackage{etoolbox}
\RequirePackage{xfp}

\newbool{dubinspathreverse}
%    \end{macrocode}
%
% \begin{macro}{\ifpgfmathcond}
%    \begin{macrocode}
\def\ifpgfmathcond#1{%
  \pgfmathparse{(#1)?1:0}%
  \ifnumequal{\pgfmathresult}{1}%
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@getxy}
%    \begin{macrocode}
\def\dbp@getxy#1#2#3{%
  \tikz@scan@one@point\pgfutil@firstofone(#3)\relax%
  \edef#1{\the\pgf@x}%
  \edef#2{\the\pgf@y}%
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@anglebetween}
%    \begin{macrocode}
\def\dbp@anglebetween#1#2#3{%macro, s, t
  \dbp@getxy\dbp@ax\dbp@ay{#2}
  \dbp@getxy\dbp@bx\dbp@by{#3}
  \pgfmathsetmacro#1{atan2(\dbp@by-\dbp@ay,\dbp@bx-\dbp@ax)}
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@distancebetween}
%    \begin{macrocode}
\def\dbp@distancebetween#1#2#3{%macro, s, t
  \dbp@getxy\dbp@ax\dbp@ay{#2}
  \dbp@getxy\dbp@bx\dbp@by{#3}
  \edef#1{\fpeval{sqrt(%
      (\dbp@bx-\dbp@ax)*(\dbp@bx-\dbp@ax)%
      +(\dbp@by-\dbp@ay)*(\dbp@by-\dbp@ay)%
      )}}%
}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\dbp@rsr}
%    \begin{macrocode}
\newcommand\dbp@rsr{% s, sa, t, ta, as, len, at, r
  let
  \p{tr}=([shift={(\dbp@angb-90:\dbp@radius pt)}]\dbp@b),
  \n1={\dbp@anga+90},
  \n2={\dbp@angb+90},
  \n3={\n2+\dbp@lastangle}
  in
  arc(\n1:\n1-\dbp@firstangle:\dbp@rradius pt)
  -- ([shift={(\p{tr})}]\n3:\dbp@rradius pt)
  arc(\n3:\n2:\dbp@rradius pt)
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@lsl}
%    \begin{macrocode}
\newcommand\dbp@lsl{% s, sa, t, ta, as, len, at, r
  let
  \p{tl}=([shift={(\dbp@angb+90:\dbp@radius pt)}]\dbp@b),
  \n1={\dbp@anga-90},\n2={\n1+\dbp@firstangle},
  \n3={\dbp@angb-90},\n4={\n3-\dbp@lastangle}
  in
  arc(\n1:\n2:\dbp@lradius pt)
  -- ([shift={(\p{tl})}]\n4:\dbp@lradius pt)
  arc(\n4:\n3:\dbp@lradius pt)
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@rsl}
%    \begin{macrocode}
\newcommand\dbp@rsl{% s, sa, t, ta, as, len, at, r
  let
  \p{tl}=([shift={(\dbp@angb+90:\dbp@radius pt)}]\dbp@b),
  \n1={\dbp@anga+90},\n2={\n1-\dbp@firstangle},
  \n3={\dbp@angb-90},\n4={\n3-\dbp@lastangle}
  in
  arc(\n1:\n2:\dbp@rradius pt)
  -- ([shift={(\p{tl})}]\n4:\dbp@lradius pt)
  arc(\n4:\n3:\dbp@lradius pt)
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@lsr}
%    \begin{macrocode}
\newcommand\dbp@lsr{% s, sa, t, ta, as, len, at, r
  let
  \p{tr}=([shift={(\dbp@angb-90:\dbp@radius pt)}]\dbp@b),
  \n1={\dbp@anga-90},\n2={\n1+\dbp@firstangle},
  \n3={\dbp@angb+90},\n4={\n3+\dbp@lastangle}
  in
  arc(\n1:\n2:\dbp@lradius pt)
  -- ([shift={(\p{tr})}]\n4:\dbp@rradius pt)
  arc(\n4:\n3:\dbp@rradius pt)
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@lrl}
%    \begin{macrocode}
\newcommand\dbp@lrl{% s, sa, t, ta, as, ai, at, r
  let
  \n1={\dbp@anga-90},\n2={\n1+\dbp@firstangle},
  \n3={\dbp@angb-90},\n4={\n3-\dbp@lastangle}
  in
  arc(\n1:\n2:\dbp@lradius pt)
  arc(\n2+180:\n2+180-\dbp@midparam:\dbp@rradius pt)
  arc(\n4:\n3:\dbp@lradius pt)
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@rlr}
%    \begin{macrocode}
\newcommand\dbp@rlr{% s, sa, t, ta, as, ai, at, r
  let
  \n1={\dbp@anga+90},\n2={\n1-\dbp@firstangle},
  \n3={\dbp@angb+90},\n4={\n3+\dbp@lastangle}
  in
  arc(\n1:\n2:\dbp@rradius pt)
  arc(\n2+180:\n2+180+\dbp@midparam:\dbp@lradius pt)
  arc(\n4:\n3:\dbp@rradius pt)
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@rev@lsl}
%    \begin{macrocode}
\newcommand\dbp@rev@lsl{\dbp@rsr}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@rev@rsr}
%    \begin{macrocode}
\newcommand\dbp@rev@rsr{\dbp@lsl}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@rev@lsr}
%    \begin{macrocode}
\newcommand\dbp@rev@lsr{\dbp@lsr}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@rev@rsl}
%    \begin{macrocode}
\newcommand\dbp@rev@rsl{\dbp@rsl}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@rev@lrl}
%    \begin{macrocode}
\newcommand\dbp@rev@lrl{\dbp@rlr}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@rev@rlr}
%    \begin{macrocode}
\newcommand\dbp@rev@rlr{\dbp@lrl}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dubinspath}
%    \begin{macrocode}
\newcommand\dubinspath[1]{%
  \pgfextra{
    \dubinspathset{#1}
    \ifbool{dubinspathreverse}{
      \edef\dbp@newa{\dbp@b}
      \edef\dbp@newb{\dbp@a}
      \pgfmathsetmacro\dbp@newanga{180+\dbp@angb}
      \pgfmathsetmacro\dbp@newangb{180+\dbp@anga}
      \edef\dbp@newfirstangle{\dbp@lastangle}
      \edef\dbp@newlastangle{\dbp@firstangle}
      \edef\dbp@newmethod{rev@\dbp@method}
      \edef\dbp@newlradius{\dbp@rradius}
      \edef\dbp@newrradius{\dbp@lradius}
      \dubinspathset{
        start point=\dbp@newa,
        end point=\dbp@newb,
        start angle=\dbp@newanga,
        end angle=\dbp@newangb,
        first angle=\dbp@newfirstangle,
        last angle=\dbp@newlastangle,
        left and right minimum radii=\dbp@newlradius pt and \dbp@newrradius pt,
        method=\dbp@newmethod,
      }
    }{}
  }
  \csname dbp@\dbp@method\endcsname%
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\dbp@store}
% \begin{macro}{\dbp@get}
%    \begin{macrocode}
\def\dbp@store#1#2{%
  \expandafter\xdef\csname dbp@store@#1@#2\endcsname%
  {\csname dbp@#2\endcsname}%
}
\def\dbp@get#1#2{%
  \csname dbp@store@#1@#2\endcsname%
}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\dbp@setparams}
%    \begin{macrocode}
\def\dbp@setparams#1#2#3#4#5{%
  % method, length, fisrt angle, middle param, last angle
  \edef\dbp@method{#1}
  \edef\dbp@length{#2}
  \edef\dbp@firstangle{#3}
  \edef\dbp@middleparam{#4}
  \edef\dbp@lastangle{#5}
  \ifdef{\dbp@storename}{
    \foreach \p in {method,length,firstangle,middleparam,lastangle}{
      \dbp@store{\dbp@storename}{\p}
    }
  }{}
}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\dbp@updateparams}
%    \begin{macrocode}
\def\dbp@updateparams#1#2#3#4#5{
  \ifpgfmathcond{#2<\dbp@length}{
    \dbp@setparams{#1}{#2}{#3}{#4}{#5}
  }{}
}
%    \end{macrocode}
% \end{macro}
%
%    \begin{macrocode}
\tikzset{
  dubins path/.is family,
  dubins path,
  start point/.store in=\dbp@a,
  start angle/.store in=\dbp@anga,
  end point/.store in=\dbp@b,
  end angle/.store in=\dbp@angb,
  store/.store in=\dbp@storename,
  use store/.style={
    method=\dbp@get{#1}{method},
    first angle=\dbp@get{#1}{firstangle},
    last angle=\dbp@get{#1}{lastangle},
    middle param=\dbp@get{#1}{middleparam},
  },
  minimum radius/.code={
    \pgfmathsetmacro\dbp@radius{#1}
    \pgfmathsetmacro\dbp@rradius{#1}
    \pgfmathsetmacro\dbp@lradius{#1}
  },
  left and right minimum radii/.code args={#1 and #2}{
    \pgfmathsetmacro\dbp@lradius{#1}
    \pgfmathsetmacro\dbp@rradius{#2}
    \pgfmathsetmacro\dbp@radius{(\dbp@lradius + \dbp@rradius)/2}
  },
  method/.store in=\dbp@method,
  first angle/.store in=\dbp@firstangle,
  last angle/.store in=\dbp@lastangle,
  middle param/.store in=\dbp@midparam,
  reverse/.is if=dubinspathreverse,
}
%    \end{macrocode}
%
% \begin{macro}{\dubinspathset}
%    \begin{macrocode}
\newcommand\dubinspathset[1]{\tikzset{dubins path,#1}}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\dubinspathcalc}
%    \begin{macrocode}
\newcommand\dubinspathcalc[1]{%
  \begingroup
  \dubinspathset{#1}
  \tikzset{
    declare function={
      angtodist(\dbp@a,\dbp@r)={abs(\dbp@a)*.01745329*\dbp@r};
      modangr(\dbp@a,\dbp@b)={
        (
        Mod(\dbp@a,360)<Mod(\dbp@b,360)
        ?
        Mod(\dbp@a,360)
        :
        Mod(\dbp@a,360)-360)+\dbp@b-Mod(\dbp@b,360
        )
      };
      modangl(\dbp@a,\dbp@b)={
        (
        Mod(\dbp@a,360)<Mod(\dbp@b,360)
        ?
        Mod(\dbp@a,360)+360
        :
        Mod(\dbp@a,360))+(\dbp@b)-Mod(\dbp@b,360)
      };
    },
  }
  
  \pgfmathsetmacro\dbp@radius{\dbp@rradius}
  \pgfmathsetmacro\dbp@anga{mod((\dbp@anga)+180,360)-180}
  \pgfmathsetmacro\dbp@angb{mod((\dbp@angb)+180,360)-180}
  \path
  let
  \p{a}=(\dbp@a),
  \p{b}=(\dbp@b),
  \p{ar}=($(\p{a}) + (\dbp@anga-90:\dbp@radius pt)$),
  \p{al}=($(\p{a}) + (\dbp@anga+90:\dbp@radius pt)$),
  \p{br}=($(\p{b}) + (\dbp@angb-90:\dbp@radius pt)$),
  \p{bl}=($(\p{b}) + (\dbp@angb+90:\dbp@radius pt)$)
  in \pgfextra{
    \pgfinterruptpath

    % RSR (ar and br)
    \dbp@anglebetween\dbp@rsrarbr{\p{ar}}{\p{br}}
    \dbp@distancebetween\dbp@rsrdarbr{\p{ar}}{\p{br}}
    \pgfmathsetmacro\dbp@rsrangone{Mod(\dbp@anga-\dbp@rsrarbr,360)}
    \pgfmathsetmacro\dbp@rsrangtwo{Mod(\dbp@rsrarbr-\dbp@angb,360)}
    \pgfmathsetmacro\dbp@rsrlen{\dbp@rsrdarbr}
    \pgfmathsetmacro\dbp@rsrdist{
      angtodist(\dbp@rsrangone,\dbp@radius)
      +\dbp@rsrlen
      +angtodist(\dbp@rsrangtwo,\dbp@radius)
    }
    \dbp@setparams{rsr}{\dbp@rsrdist}{\dbp@rsrangone}{\dbp@rsrlen}{\dbp@rsrangtwo}
    
    % LSL (al and bl)
    \dbp@anglebetween\dbp@lslalbl{\p{al}}{\p{bl}}
    \dbp@distancebetween\dbp@lsldalbl{\p{al}}{\p{bl}}
    \pgfmathsetmacro{\dbp@lslangone}{mod(\dbp@lslalbl-\dbp@anga+720,360)}
    \pgfmathsetmacro{\dbp@lslangtwo}{mod(\dbp@angb-\dbp@lslalbl+720,360)}
    \pgfmathsetmacro\dbp@lsllen{\dbp@lsldalbl}
    \pgfmathsetmacro\dbp@lsldist{
      angtodist(\dbp@lslangone,\dbp@radius)
      +\dbp@lsllen
      +angtodist(\dbp@lslangtwo,\dbp@radius)
    }
    \dbp@updateparams%
    {lsl}{\dbp@lsldist}{\dbp@lslangone}{\dbp@lsllen}{\dbp@lslangtwo}
    
    % RSL (ar and bl)
    \dbp@distancebetween\dbp@rsldarbl{\p{ar}}{\p{bl}}
    \pgfmathtruncatemacro\dbp@rslok{(\dbp@rsldarbl>=2*\dbp@radius)?1:0}
    \ifnumequal{\dbp@rslok}{1}{
      \dbp@anglebetween\dbp@rslarbl{\p{ar}}{\p{bl}}
      \pgfmathsetmacro\dbp@rslanglesup{
        asin(\dbp@radius/\dbp@rsldarbl*2)}
      \pgfmathsetmacro\dbp@rslangone
      {Mod(\dbp@anga-\dbp@rslarbl+\dbp@rslanglesup,360)}
      \pgfmathsetmacro\dbp@rslangtwo
      {Mod(\dbp@angb-\dbp@rslarbl+\dbp@rslanglesup,360)}
      \pgfmathsetmacro\dbp@rsllen{veclen(\dbp@rsldarbl,\dbp@radius)}
      \pgfmathsetmacro\dbp@rsldist{
        angtodist(\dbp@rslangone,\dbp@radius)
        +\dbp@rsllen
        +angtodist(\dbp@rslangtwo,\dbp@radius)
      }

      \dbp@updateparams%
      {rsl}{\dbp@rsldist}{\dbp@rslangone}{\dbp@rsllen}{\dbp@rslangtwo}
    }{}

    % LSR (al and br)
    \dbp@distancebetween\dbp@lsrdalbr{\p{al}}{\p{br}}
    \pgfmathtruncatemacro\dbp@lsrok{(\dbp@lsrdalbr>=2*\dbp@radius)?1:0}
    \ifnumequal{\dbp@lsrok}{1}{
      \dbp@anglebetween\dbp@lsralbr{\p{al}}{\p{br}}
      \pgfmathsetmacro\dbp@lsranglesup{
        asin(\dbp@radius/\dbp@lsrdalbr*2)}
      \pgfmathsetmacro\dbp@lsrangone
      {Mod(\dbp@lsralbr+\dbp@lsranglesup-\dbp@anga,360)}
      \pgfmathsetmacro\dbp@lsrangtwo
      {Mod(\dbp@lsralbr+\dbp@lsranglesup-\dbp@angb,360)}
      \pgfmathsetmacro\dbp@lsrlen{veclen(\dbp@lsrdalbr,\dbp@radius)}
      \pgfmathsetmacro\dbp@lsrdist{
        angtodist(\dbp@lsrangone,\dbp@radius)
        +\dbp@lsrlen
        +angtodist(\dbp@lsrangtwo,\dbp@radius)
      }
      \dbp@updateparams%
      {lsr}{\dbp@lsrdist}{\dbp@lsrangone}{\dbp@lsrlen}{\dbp@lsrangtwo}
    }{}
    
    % LRL (al and bl)
    \dbp@distancebetween\dbp@lrldalbl{\p{al}}{\p{bl}}
    \pgfmathtruncatemacro\dbp@lrlok{(\dbp@lrldalbl<=4*\dbp@radius)?1:0}
    \ifnumequal{\dbp@lrlok}{1}{
      \dbp@anglebetween\dbp@lrlalbl{\p{al}}{\p{bl}}
      \pgfmathsetmacro\dbp@lrlangsup{acos(\dbp@lrldalbl/\dbp@radius/4)}
      \pgfmathsetmacro\dbp@lrlangone{
        modangl(\dbp@lrlalbl+\dbp@lrlangsup,\dbp@anga-90)-(\dbp@anga-90)}
      \pgfmathsetmacro\dbp@lrlangtwo{%
        (\dbp@angb-90)-modangr(\dbp@lrlalbl+180-\dbp@lrlangsup,\dbp@angb-90)}
      \pgfmathsetmacro\dbp@lrlangthree{360-2*(90-\dbp@lrlangsup)}
      \pgfmathsetmacro\dbp@lrldist{
        angtodist(\dbp@lrlangone,\dbp@radius)
        +angtodist(\dbp@lrlangthree,\dbp@radius)
        +angtodist(\dbp@lrlangtwo,\dbp@radius)
      }
      \dbp@updateparams%
      {lrl}{\dbp@lrldist}{\dbp@lrlangone}{\dbp@lrlangthree}{\dbp@lrlangtwo}
    }{}

    % RLR (ar and br)
    \dbp@distancebetween\dbp@rlrdarbr{\p{ar}}{\p{br}}
    \pgfmathtruncatemacro\dbp@rlrok{(\dbp@rlrdarbr<=4*\dbp@radius)?1:0}
    \ifnumequal{\dbp@rlrok}{1}{
      \dbp@anglebetween\dbp@rlrarbr{\p{ar}}{\p{br}}
      \pgfmathsetmacro\dbp@rlrangsup{acos(\dbp@rlrdarbr/\dbp@radius/4)}
      \pgfmathsetmacro\dbp@rlrangone{
        (\dbp@anga+90)-modangr(\dbp@rlrarbr-\dbp@rlrangsup,\dbp@anga+90)}
      \pgfmathsetmacro\dbp@rlrangtwo{%
        modangl(\dbp@rlrarbr+180+\dbp@rlrangsup,\dbp@angb+90)-(\dbp@angb+90)}
      \pgfmathsetmacro\dbp@rlrangthree{360-2*(90-\dbp@rlrangsup)}
      \pgfmathsetmacro\dbp@rlrdist{
        angtodist(\dbp@rlrangone,\dbp@radius)
        +angtodist(\dbp@rlrangthree,\dbp@radius)
        +angtodist(\dbp@rlrangtwo,\dbp@radius)
      }
      \dbp@updateparams%
      {rlr}{\dbp@rlrdist}{\dbp@rlrangone}{\dbp@rlrangthree}{\dbp@rlrangtwo}
    }{}

    \endpgfinterruptpath
  };
  \endgroup
}
%    \end{macrocode}
% \end{macro}
% \iffalse
%</tikzlibrarydubins.code.tex>
% \fi
%
% \PrintChanges
%
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% \PrintIndex
%
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%
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\renewcommand*{\DescribeMacro}[2][]{%
  \@bsphack%
  \@ifundefined{@captype}{% not float?
    \leavevmode%
    \marginpar{%
      \hbadness=10000%
      \hfuzz=5em%
      \raggedleft%
      \ifblank{#1}{}{{\scriptsize\textsf{[#1]}} }% class
      \MacroFont\cmd{#2}% name
    }% marginpar
  }{}% not float?
  \begingroup%
  \DTXD@origwrindex{%
    \DTXD@macroname{#2}\actualchar\DTXD@verbatimcmd{#2}% name
    \ifblank{#1}{}{\levelchar[#1]}% class
    \encapchar usage}%
  \ifblank{#1}%
  {}% no class
  {% class given
    \begingroup%
    \DTXD@origwrindex{%
      #1\actualchar[#1]:\levelchar%
      \DTXD@macroname{#2}\actualchar\DTXD@verbatimcmd{#2}%
      \encapchar usage}%
  }% class given
  \@esphack%
  \ignorespaces%
}

%</sankeydocpreamble>
% \fi
\endinput

% Local Variables:
% mode: doctex
% LaTeX-verbatim-macros-with-braces-local: ("code")
% TeX-master: t
% End: