path: root/graphics/pgf/contrib/pgf-blur/pgf-blur.dtx

% \iffalse meta-comment -*-mode:Latex;tex-command:"pdflatex"-*-
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\preamble
Copyright 2012 Martin Giese, martingi@ifi.uio.no
Copyright 2012 Andrew Stacey
Copyright 2018 Norbert Preining, norbert@preining.info

This file is under the LaTeX Project Public License 
See CTAN archives in directory macros/latex/base/lppl.txt.

DESCRIPTION:
  `pgf-blur' adds blurred/faded/fuzzy shadows to TikZ/PGF

\endpreamble
\generate{\file{tikzlibraryshadows.blur.code.tex}{\from{pgf-blur.dtx}{texfile}}}
\Msg{************************************************************}
\Msg{ }
\Msg{  To finish the installation you have to move the file}
\Msg{  `tikzlibraryshadows.blur.code.tex' into a directory}
\Msg{  searched by TeX.}
\Msg{ }
\Msg{  To type-set the documentation, including instructions,}
\Msg{  run the file `pgf-blur.dtx' through LaTeX.}
\Msg{ }
\Msg{***********************************************************}
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\documentclass{ltxdoc}
\usepackage{tikz}
\usepackage{textcomp}
\usepackage{url}
\usetikzlibrary{shadows.blur}
\usetikzlibrary{shapes.symbols}
\usetikzlibrary{shapes.multipart}
\AtBeginDocument{
%  \OnlyDescription % comment out for implementation details
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%\AtEndDocument{
%  \PrintChanges
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\DocInput{pgf-blur.dtx}
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% \CheckSum{475}
%
% \CharacterTable
%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%   Digits        \0\1\2\3\4\5\6\7\8\9
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%   Acute accent  \'     Left paren    \(     Right paren   \)
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%   Minus         \-     Point         \.     Solidus       \/
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%   Equals        \=     Greater than  \>     Question mark \?
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%
%
% \changes{v1.00}{2012/04/20}{First public release. (mg)}
% \changes{v1.01}{2012/04/24}{Remove antialiasing/clipping artefacts (mg)}
% \changes{v1.02}{2018/08/21}{Fix multiple shadows, support inversion (as), changed maintainer (np)}
%
% \DoNotIndex{\!,\",\#,\$,\%,\&,\',\(,\+,\*,\,,\-,\.,\/,\:,\;,\<,\=,\>,\?}
% \setcounter{IndexColumns}{2}
%
% \title{\textsf{pgf-blur} package \\ version \fileversion}
% \author{Martin Giese}
% \date{\filedate}
% \maketitle
%
%\def\tikzname{Ti\emph{k}Z}
%
%\begin{center}
%  Currently maintained by Norbert Preining\footnote{\protect\url{https://github.com/norbusan/pgf-blur}}
%\end{center}
%
%\begin{center}
%  \small \textbf{Acknowledgement}\\ This package evolved from a discussion
%  on \url{http://tex.stackexchange.com/}.  In particular, the author received 
%  invaluable help from Andrew Stacey.
%\end{center}
%
%\section{Introduction}
% The ability to paint shadows on arbitrary shapes is a standard 
% feature of TikZ/PGF.  However, these shadows are usually `sharp':
%
%\newcommand\examplepath{
%  (0,0) -- (0,1) -- (1.5,1) -- (1,0.5) [rounded corners=2mm] -- (1,0) [sharp corners]-- cycle
%  (0.5,0.5) circle (0.3)
%  }
%
%\begin{center}
% \begin{tikzpicture}
%   \filldraw[drop shadow,draw=black,fill=white] \examplepath ;
%    \node[starburst,very thick,rounded corners=2pt,fill=white,draw=red,
%          drop shadow] at (5,0.5) 
%         {\sffamily\bfseries SPLAT!};
% \end{tikzpicture}
%\end{center}
%
% Such shadows are often optically too intrusive.  A more pleasing effect
% is achieved if the edges of the shadow are `blurred,' i.e., getting
% gradually lighter and more transparent toward the outside.
% This effect can be achieved in TikZ/PGF with the |circular drop shadow|
% key, but that works only with ellipses and circles.
%
% The |pgf-blur| package provides blurred shadows that can be
% added to any closed path, including node borders:
%
%\begin{center}
% \begin{tikzpicture}
%   \filldraw[blur shadow={shadow blur steps=8,shadow blur extra rounding},draw=black,fill=white] \examplepath ;
%    \node[starburst,very thick,rounded corners=2pt,fill=white,draw=red,
%         blur shadow={shadow blur steps=8,shadow blur extra rounding}] at (5,0.5) 
%         {\sffamily\bfseries SPLAT!};
% \end{tikzpicture}
%\end{center}
%
% \medskip
%
% The new TikZ options provided by the package
% are described in section 2 of this document.  Section 3, if present, documents the 
% implementation consisting of a generic \TeX\ file.  
%
%\section{Package Usage}
%
% To use the package, the document needs to say |\usepackage{tikz}| and
% \begin{verbatim}
%  \usetikzlibrary{shadows.blur}
% \end{verbatim}
% in the preamble.
%
% \DescribeMacro{blur shadow}
% \noindent A blurred shadow is added to a path or node by the option
% |blur shadow|, e.g.
%\begin{verbatim}
%  \begin{tikzpicture}
%    \filldraw[fill=white, draw=black, blur shadow] (0,0) circle (1);
%    \node[fill=white, draw=black, blur shadow] at (4,0.5) {\Large Node};
%  \end{tikzpicture}
%\end{verbatim}
% which gives
%\begin{center}
%  \begin{tikzpicture}
%    \filldraw[fill=white, draw=black, blur shadow] (0,0) circle (0.5);
%    \node[fill=white, draw=black, blur shadow] at (2,0) {\Large Node};
%  \end{tikzpicture}
%\end{center}
% Note that this usually makes sense only with closed paths that are filled
% (otherwise the shadow is visible through the path, and one wonders 
% what is throwing the shadow) and often looks best if used with 
% a drawn outline.
% 
% The appearance of the shadow can be fine-tuned by giving arguments
% to the |blur shadow| options.  These options do not have any effect
% if given outside of the argument of either |blur shadow| or |every shadow| 
% (described later)
%
% \DescribeMacro{shadow xshift}
% \DescribeMacro{shadow yshift}
% \DescribeMacro{shadow scale}
% \noindent The shadow is based on a shifted, and possibly scaled copy of the original path.
% These options are described in the \tikzname/PGF user manual, and they work in
% the same way for blurred shadows.  See also Fig.~\ref{fig:geometry}.  The default 
% values are 3ex for |shadow xshift|, \textminus3ex for |shadow yshift|, and
% 1 for |shadow scale|.
%
%\begin{figure}
%\begin{center}
%  \begin{tikzpicture}
%\begin{scope}
%  \clip (0,1) rectangle (8,5);
%
%  \filldraw[fill=white, draw=black, ultra thick,
%           blur shadow={
%           shadow xshift=2cm,shadow yshift=-1cm,
%           shadow blur radius=0.75cm, shadow blur steps=10}] (-4,3) rectangle (4,9);
%  \draw[xshift=2cm,yshift=-1cm,thin,dotted,red] 
%      (4,3) circle (0.75)
%      (-4,3) rectangle (4,9)
%      (-4.75,3.75) rectangle (3.25,9.75)
%      [rounded corners=0.75cm] (-3.25,2.25) rectangle (4.75,8.25);
%\end{scope}
%      
%  \draw[-stealth, thin] (4,3) -- (6,2)
%        node[pos=0.6,left=0.7em] {\footnotesize (|shadow xshift|,\,|shadow yshift|)};
%
%  \draw[stealth-stealth, thin] (6,2) -- + (-60:0.75)
%        node[pos=0.4,right=0.4em] {\footnotesize |shadow blur radius|};
%  \end{tikzpicture}
%\end{center}
%  \caption{Shadow geometry}
%  \label{fig:geometry}
%\end{figure}
%
% Here is an example for the usage of these options:
%\begin{verbatim}
%  \begin{tikzpicture}
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow xshift=1ex,
%                            shadow yshift=1ex,
%                            shadow scale=1.2}] 
%        (0,0) circle (0.5);
%  \end{tikzpicture}
%\end{verbatim}
% Which gives:
%\begin{center}
%  \begin{tikzpicture}
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow xshift=1ex,
%                            shadow yshift=1ex,
%                            shadow scale=1.2}] 
%        (0,0) circle (0.5);
%  \end{tikzpicture}
%\end{center}
%
% \DescribeMacro{shadow blur radius}
% \noindent Fig.~\ref{fig:geometry} shows how the blur shadow spreads out 
% the boundary of the path over a circular region.  The intent is
% to mimic the effect of a circular light source over the shape. 
% the radius of the ``blurring'' can be set with the 
% |shadow blur radius| option, which has a default value of 
% \csname pgfbs@radius\endcsname.
%
% Here is an example of a drastically enlarged blur radius:
%\begin{verbatim}
%  \begin{tikzpicture}
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow blur radius=1.5ex}]
%        (0,0) circle (0.5);
%  \end{tikzpicture}
%\end{verbatim}
% Which gives:
%\begin{center}
%  \begin{tikzpicture}
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow blur radius=1.5ex}]
%        (0,0) circle (0.5);
%  \end{tikzpicture}
%\end{center}
%
% \DescribeMacro{shadow opacity}
% \noindent Shadows are transparent.  They are always black since a shadow is the
% absence of light.  The opacity of the interior of the shadow, i.e.~the
% darkest region can be controlled with the |shadow opacity| option.  It
% is given as a percentage, i.e.~a number between 0 and 100.  The default
% is \csname pgfbs@opacity\endcsname.
%
% Here are examples of lighter and darker shadows:
%\begin{verbatim}
%  \begin{tikzpicture}
%     \draw[help lines,step=0.5] (-1,-1) grid (3,1);
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow opacity=20}]
%        (0,0) circle (0.5);
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow opacity=60}]
%        (2,0) circle (0.5);
%  \end{tikzpicture}
%\end{verbatim}
% Which gives:
%\begin{center}
%  \begin{tikzpicture}
%     \draw[help lines,step=0.5] (-1,-1) grid (3,1);
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow opacity=20}]
%        (0,0) circle (0.5);
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow opacity=60}]
%        (2,0) circle (0.5);
%  \end{tikzpicture}
%\end{center}
%
% \DescribeMacro{shadow blur extra rounding}
% A close inspection of the shadow in Fig.~\ref{fig:geometry}
% reveals that if the original path has a corner, then 
% the ``lines of equal opacity'' in the inner part of the shadow will
% also have corners.  This is a consequence of the way the shadows are
% rendered by default.  It gives the impression of the darkest part
% of the shadow extruding a little too much into the faded part.
% This effect can be reduced by adding the option |shadow extra rounding|,
% which has the effect of rounding all corners of the path before rendering 
% the shadow.  The rounding inset can be given as an argument; it
% defaults to the current value of the blur radius.
%
% Several points should be remembered when using this option:
% \begin{itemize}
% \item It uses the mechanism that \tikzname\ also uses for the
%       |rounded corners| option.  This works badly, distorting the
%       path in strange ways, if the individual segments of the path
%       are too short to be rounded with the given inset.  If the
%       shadows look strange, try reducing the inset, or drop this
%       option altogether.
% \item Rounding many complex paths can slow \TeX\ down considerably.
% \item The ideal rounding inset depends on the angle the path has
%       at each corner.  This is not taken into account,  the same
%       inset is used everywhere.  The default value is the one that
%       works best with 90\textdegree\ angles, but it also looks
%       fairly good with other angles.
% \item With or without this option, the shadows will not be
%       photorealistic.
% \end{itemize}
% Here is an example of squares without and with extra rounding applied:
%\begin{verbatim}
%  \begin{tikzpicture}
%     \filldraw[fill=white, draw=black,
%               blur shadow]
%        (0,0) rectangle (1,1);
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow blur extra rounding}]
%        (2,0) rectangle (3,1);
%  \end{tikzpicture}
%\end{verbatim}
% Which gives:
%\begin{center}
%  \begin{tikzpicture}
%     \filldraw[fill=white, draw=black,
%               blur shadow]
%        (0,0) rectangle (1,1);
%     \filldraw[fill=white, draw=black,
%               blur shadow={shadow blur extra rounding}]
%        (2,0) rectangle (3,1);
%  \end{tikzpicture}
%\end{center}
%
% \DescribeMacro{shadow blur steps}
% \noindent The transition of opacity in these shadows is actually not
% smooth, but proceeds in a finite number of discrete steps.
% Specifically, there is a number $n$, such that the (shifted and
% scaled) original path fades outward to complete transparency in $n$
% steps and within the selected |shadow blur radius|, and inward to
% the maximum opacity of the shadow, also within $n$ steps and the
% |shadow blur radius|.  This number of steps $n$ can be selected
% using the |shadow blur steps| option.  It defaults to 
% \csname pgfbs@steps\endcsname, which is
% enough e.g.~for inconspicuous shadows in presentations that nobody
% examines with a magnifying glass.  The examples in the introduction
% use 8, under the assumption that readers will have a close look.
% Fig.~\ref{fig:geometry} uses 10 because the blur radius is so large.
%
% A large number of steps will slow down both the \TeX\ processing and the 
% PDF rendering, usually with very little visible impact.
%
% \DescribeMacro{every shadow}
% To apply the same set of options to every shadow, it is possible to
% define the \emph{style} |every shadow|, which is taken from the
% standard shadow library.  For instance, in the following, darker
% shadows with more steps are selected for several shapes:
%\begin{verbatim}
%  \begin{tikzpicture}
%    [every shadow/.style={shadow opacity=60,
%                          shadow blur steps=7}]
%     \filldraw[fill=white, draw=black, blur shadow]
%        (0,0) rectangle (1,1);
%     \node[cloud,shape aspect=2,fill=white, draw=black,
%               blur shadow]
%        at (2.5,0.5) {Rain};
%  \end{tikzpicture}
%\end{verbatim}
% Which gives:
%\begin{center}
%  \begin{tikzpicture}
%    [every shadow/.style={shadow opacity=60,
%                          shadow blur steps=7}]
%     \filldraw[fill=white, draw=black, blur shadow]
%        (0,0) rectangle (1,1);
%     \node[cloud,shape aspect=2,fill=white, draw=black,
%               blur shadow]
%        at (2.5,0.5) {Rain};
%  \end{tikzpicture}
%\end{center}

%
% \StopEventually{}
%
% \subsection{A Note on Nodes}
%

% While this library plays nicely with most closed paths, it doesn't
% like paths with non-closed parts.  This is particularly annoying
% when used with standard node shapes, where you can't do much about
% the paths.  Take the |rectangle split| shape for instance:  
%
%\begin{verbatim}
% \begin{tikzpicture}
%     \node[rectangle split, rectangle split parts=3, draw, fill=white, 
%       blur shadow={shadow xshift=1em}] {...};
% \end{tikzpicture}
%\end{verbatim}
%
%\begin{center}
% \begin{tikzpicture}
%     \node[rectangle split, rectangle split parts=3, draw, fill=white, 
%       blur shadow={shadow xshift=1em}]
%       {Cake \nodepart{two} icing: Icing \nodepart{three} getIcing()};
% \end{tikzpicture}
%\end{center}
%
% Note how the part separation lines produce white bars in the shadow.
% This is really hard to avoid in general.  There are two simple
% workarounds: a) choosing a very small |shadow xshift| so most the 
% ``bar'' gets hidden behind the shape, or b) putting
% the node inside a simple rectangle node and add a shadow to the latter.
% For solution b) to work, the inner padding of the outer node has to
% be removed.  This in turn requires it to be reinstated for the inner
% node.  Here's the example showing both workarounds: 
%
%\begin{verbatim}
% \begin{tikzpicture}
% \node[rectangle split, rectangle split parts=3,
%       draw, fill=white,
%       blur shadow={shadow xshift=0.25ex}] at (-2,0) {...};
% \node[blur shadow={shadow xshift=1em},inner sep=0pt] at (2,0) {
%       \tikz\node[rectangle split, rectangle split parts=3,
%                  draw, fill=white, inner sep=0.333em] {...};};
% \end{tikzpicture}
%\end{verbatim}
%
%\begin{center}
% \begin{tikzpicture}
% \node[rectangle split, rectangle split parts=3,
%       draw, fill=white,
%       blur shadow={shadow xshift=0.25ex}] at (-2,0)
%                 {Cake \nodepart{two} icing: Icing \nodepart{three} getIcing()};
% \node[blur shadow={shadow xshift=1em},inner sep=0pt] at (2,0) {
%       \tikz\node[rectangle split, rectangle split parts=3,
%                  draw, fill=white, inner sep=0.333em]
%                 {Cake \nodepart{two} icing: Icing \nodepart{three} getIcing()};};
% \end{tikzpicture}
%\end{center}
%
% Solution b) is fine for rectangular outlines, but it wont work for e.g.~the
% |cylinder| shape.
%
% \section{Implementation}
%
%\begin{macro}{\fileversion}
%  \begin{macro}{\filedate}
% We define the file version and date, and
% import the original shadow code for the offset and scale parameters.
%    \begin{macrocode}
%<*texfile>
\def\fileversion{1.02}
\def\filedate{2012/12/09}
\message{ v\fileversion, \filedate}
\usetikzlibrary{shadows}
\usetikzlibrary{calc}
%    \end{macrocode}
%  \end{macro}
%\end{macro}
%\begin{macro}{\ifpgfbs@invert@fading}
% An |\if| to control whether to invert the fading or not.
%    \begin{macrocode}
\newif\ifpgfbs@invert@fading
%    \end{macrocode}
%\end{macro}
%\begin{macro}{\pgfbs@fading@count}
% A |count| to make the names unique
%    \begin{macrocode}
\newcount\pgfbs@fading@count
\pgfbs@fading@count=0\relax
%    \end{macrocode}
%\end{macro}
%\begin{macro}{shadow blur radius}
%\begin{macro}{shadow blur extra rounding}
%\begin{macro}{shadow blur steps}
%\begin{macro}{shadow opacity}
% Next we define the various \tikzname\ options, with their default values.
% The options |shadow xshift|, |shadow yshift|, |shadow scale| are imported
% from the standard \tikzname\ shadow library, so we don't need to do
% anything for them.
% Note how the default value of |shadow blur extra rounding| is by default
% set to the blur radius.  This works because the value of this key is 
% evaluated before it is used.  All other options just store values
% in a couple of macros.
%    \begin{macrocode}
\tikzset{
  /tikz/shadow blur radius/.store in=\pgfbs@radius,
  /tikz/shadow blur radius=.4ex,
  /tikz/shadow blur extra rounding/.store in=\pgfbs@extra@rounding,
  /tikz/shadow blur extra rounding=\pgfutil@empty,
  /tikz/shadow blur extra rounding/.default=\pgfbs@radius,
  /tikz/shadow blur steps/.store in=\pgfbs@steps,
  /tikz/shadow blur steps=4,
  /tikz/shadow blur invert/.is if=pgfbs@invert@fading,
  /tikz/shadow opacity/.store in=\pgfbs@opacity,
  /tikz/shadow opacity=40,
%    \end{macrocode}
%\end{macro}
%\end{macro}
%\end{macro}
%\end{macro}
%\begin{macro}{blur shadow}
% The user level option |blur shadow| sets the 
% |shadow xshift|, |shadow yshift|, |shadow scale| options to
% more useful defaults than the ones inherited from the shadows library.
% It includes any options set in the |every shadow| style, and the
% argument to |blur shadow|.  Rendering the shadow is declared as a
% |.preaction| on the path.  \tikzname\ will take care of saving the
% path for us.
%    \begin{macrocode}
  /tikz/blur shadow/.style={
    shadow scale=1,
    shadow xshift=.5ex,
    shadow yshift=-.5ex,
    preaction=render blur shadow,
    every shadow,
    #1,
  },
%    \end{macrocode}
%\end{macro}
% \begin{macro}{render blur shadow}
% The following does the actual shadow rendering.  After some preliminary
% computation of dimensions, shifting and scaling is done using a
% canvas transform.  The actual blurring effect is done using a special fading.
% Since PGF insists on centering every fading when it's constructed,
% it has to be shifted back again when it's installed.
% The shadow is painted by filling a large black rectangle using the 
% constructed fading.
%    \begin{macrocode}
  /tikz/render blur shadow/.code={
    \pgfbs@savebb
    \global\advance\pgfbs@fading@count by 1\relax
    \pgfsyssoftpath@getcurrentpath{\pgfbs@input@path}%
    \pgfbs@compute@shadow@bbox
    \pgfbs@process@rounding{\pgfbs@input@path}{\pgfbs@fadepath}%
    \pgfbs@apply@canvas@transform
    \colorlet{pstb@shadow@color}{white!\pgfbs@opacity!black}%
    \ifpgfbs@invert@fading
    \pgfdeclarefading{shadowfading-\the\pgfbs@fading@count}{\pgfbs@paint@invert@fading}%
    \else
    \pgfdeclarefading{shadowfading-\the\pgfbs@fading@count}{\pgfbs@paint@fading}%
    \fi
    \pgfsetfillcolor{black}%
    \pgfsetfading{shadowfading-\the\pgfbs@fading@count}%
       {\pgftransformshift{\pgfpoint{\pgfbs@midx}{\pgfbs@midy}}}%
    \pgfbs@usebbox{fill}%
    \pgfbs@restorebb
  },
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\pgfbs@savebb}
% Shadow rendering works with a fading.  For a fading to contain PGF code,
% it must contain a |pgfpicture|.  And nested |pgfpicture|s mess up the
% bounding box of the surrounding picture.  Which is why we save the
% current picture bounding box at the beginning of the shadow code
% and restore it at the end.  Thanks go to Andrew Stacey for this!
%    \begin{macrocode}
\def\pgfbs@savebb{%
  \edef\pgfbs@restorebb{%
    \global\pgf@picminx=\the\pgf@picminx\relax
    \global\pgf@picmaxx=\the\pgf@picmaxx\relax
    \global\pgf@picminy=\the\pgf@picminy\relax
    \global\pgf@picmaxy=\the\pgf@picmaxy\relax
  }%
}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\pgfbs@restorebb}
% Executing |\pgfbs@savebb| sets this bounding box restoring macro
% to something useful.
%    \begin{macrocode}
\def\restorebb{}%
%    \end{macrocode}
% \end{macro}
%\begin{macro}{\pgfbs@process@rounding}
% This macro prepares the path by taking care of all things having to do
% with rounding.  First, it applies extra rounding to the path if requested
% by the |shadow blur extra rounding| option.  Second, it removes all
% rounding tokens in the path by calling the |\pgfprocessround| macro.
% This is because rounding tokens don't work well with the fading code
% for some reason or other.
% |#1| must be a PGF soft path.  |#2| must be a macro into which the resulting
% soft path will be stored.
%    \begin{macrocode}
\def\pgfbs@process@rounding#1#2{
  \expandafter\ifx\pgfbs@extra@rounding\pgfutil@empty%
    \pgfprocessround{#1}{#2}%
  \else%
    \pgfmathsetmacro\pgfbs@exrd@val{\pgfbs@extra@rounding}%
    \pgfbs@roundpath{#1}{\pgfbs@exrd@val pt}%
    \pgfsyssoftpath@getcurrentpath{\pgfbs@extraroundedpath}%
    \pgfprocessround{\pgfbs@extraroundedpath}{#2}%
  \fi%
}
%    \end{macrocode}
%\end{macro}
% \begin{macro}{\pgfbs@roundpath}
% |\pgfbs@roundpath{#1}{#2}| rounds every potential corner in path |#1| 
% with an inset of at least |#2|.
% Corners that are already rounded in |#1| are either left intact if
% their insets are $\geq$|#2|, or the insets are increased to |#2|.
% Any rectangle tokens are resolved into moveto/lineto/closepath with rounding.
% The result is appended to PGF's ``current path.''
%
% The code works by giving an appropriate definition for each of the PGF
% soft path tokens and then executing the path.
%    \begin{macrocode}
\def\pgfbs@roundpath#1#2{%
  {%
    \def\pgfbs@rp@skipround{%
      \let\pgfbs@rp@possibleround\pgfbs@rp@insertround}%
    \def\pgfbs@rp@insertround{\pgfsyssoftpath@specialround{#2}{#2}}%
    \let\pgfbs@rp@possibleround\pgfbs@rp@insertround%
    %
    \def\pgfsyssoftpath@movetotoken##1##2{%
      \pgfsyssoftpath@moveto{##1}{##2}}%
    \def\pgfsyssoftpath@linetotoken##1##2{%
      \pgfbs@rp@possibleround\pgfsyssoftpath@lineto{##1}{##2}}%
    \def\pgfsyssoftpath@rectcornertoken##1##2##3##4##5{%
      \pgf@xa=##1\relax%
      \advance\pgf@xa by##4%
      \pgf@ya=##2\relax%
      \advance\pgf@ya by##5%
      \pgfsyssoftpath@moveto{##1}{##2}%
      \pgfbs@rp@possibleround%
      \pgfsyssoftpath@lineto{\the\pgf@xa}{##2}%
      \pgfbs@rp@possibleround%
      \pgfsyssoftpath@lineto{\the\pgf@xa}{\the\pgf@ya}%
      \pgfbs@rp@possibleround%
      \pgfsyssoftpath@lineto{##1}{\the\pgf@ya}%
      \pgfbs@rp@possibleround%
      \pgfsyssoftpath@closepath}%
    \def\pgfsyssoftpath@curvetosupportatoken%
       ##1##2##3##4##5##6##7##8{%
      \pgfbs@rp@possibleround%
      \pgfsyssoftpath@curveto{##1}{##2}{##4}{##5}{##7}{##8}}%
    \def\pgfsyssoftpath@closepathtoken##1##2{%
      \pgfbs@rp@possibleround\pgfsyssoftpath@closepath}%
    \def\pgfsyssoftpath@specialroundtoken##1##2{%
      \pgfmathsetmacro\pgfbs@rp@ra{max(##1,#2)}%
      \pgfmathsetmacro\pgfbs@rp@rb{max(##2,#2)}%
      \pgfsyssoftpath@specialround%
          {\pgfbs@rp@ra pt}{\pgfbs@rp@rb pt}%
      \let\pgfbs@rp@possibleround\pgfbs@rp@skipround%
    }
    #1%
  }
}
%    \end{macrocode}
% \end{macro}
%\begin{macro}{\pgfbs@compute@shadow@bbox}
%\begin{macro}{\pgfbs@minx}
%\begin{macro}{\pgfbs@midx}
%\begin{macro}{\pgfbs@maxx}
%\begin{macro}{\pgfbs@miny}
%\begin{macro}{\pgfbs@midy}
%\begin{macro}{\pgfbs@maxy}
%\begin{macro}{\pgfbs@shadow@bbox}
% This macro figures out the bounding box of the shadow: it's the
% same as the bounding box of the current path, but enlarged by
% twice (for the inverse shadow) the blur radius in each direction.  It also computes the
% coordinates of the center of the bounding box.  These are
% stored in macros |\pgfbs@|\{|min|$\mid$|mid|$\mid$|max|\}\{|x|$\mid$|y|\}.
% It also creates a soft path for the bounding box which is stored in
% |\pgfbs@shadow@bbox|.
%    \begin{macrocode}
\def\pgfbs@compute@shadow@bbox{%
  \edef\pgfbs@minx{\the\pgf@pathminx}%
  \edef\pgfbs@miny{\the\pgf@pathminy}%
  \edef\pgfbs@maxx{\the\pgf@pathmaxx}%
  \edef\pgfbs@maxy{\the\pgf@pathmaxy}%
  \pgfmathsetmacro\pgfbs@midx{0.5*(\pgfbs@minx + \pgfbs@maxx)}%
  \pgfmathsetmacro\pgfbs@midy{0.5*(\pgfbs@miny + \pgfbs@maxy)}%
  \pgfmathsetmacro\pgfbs@minx{\pgfbs@minx - 2*\pgfbs@radius}%
  \pgfmathsetmacro\pgfbs@miny{\pgfbs@miny - 2*\pgfbs@radius}%
  \pgfmathsetmacro\pgfbs@maxx{\pgfbs@maxx + 2*\pgfbs@radius}%
  \pgfmathsetmacro\pgfbs@maxy{\pgfbs@maxy + 2*\pgfbs@radius}%
  \pgfmathsetmacro\pgfbs@wd{\pgfbs@maxx - \pgfbs@minx}%
  \pgfmathsetmacro\pgfbs@ht{\pgfbs@maxy - \pgfbs@miny}%
  \pgfsyssoftpath@setcurrentpath\pgfutil@empty%
  \pgfsyssoftpath@rect{\pgfbs@minx pt}{\pgfbs@miny pt}%
                      {\pgfbs@wd pt}{\pgfbs@ht pt}%
  \pgfsyssoftpath@getcurrentpath{\pgfbs@shadow@bbox}%
  \pgfsyssoftpath@setcurrentpath\pgfutil@empty%
}
%    \end{macrocode}
%\end{macro}
%\end{macro}\end{macro}\end{macro}
%\end{macro}\end{macro}\end{macro}
%\end{macro}
%\begin{macro}{\pgfbs@set@fading@pic@bbox}

% Set the bounding box of the fading picture painted by
% |\pgfbs@paint@fading|.  Normally, the bounding box is updated
% automatically, but this doesn't happen when PGF's soft paths are
% used.  The code that applies a fading needs the dimensions
% of the fading to be correct.  So we explicitly set the picture
% bounding box according to the previously computed values.
% Thanks again to Andrew Stacey for pointing out this subtlety!
%
%    \begin{macrocode}
\def\pgfbs@set@fading@pic@bbox{
  \global\pgf@picminx=\pgfbs@minx pt\relax
  \global\pgf@picminy=\pgfbs@miny pt\relax
  \global\pgf@picmaxx=\pgfbs@maxx pt\relax
  \global\pgf@picmaxy=\pgfbs@maxy pt\relax
}
%    \end{macrocode}
%\end{macro}
%\begin{macro}{\pgfbs@usefadepath}
% The code of the |render blur shadow| option stores the pre-processed
% soft path into the macro |\pgfbs@fadepath|.  This macro `uses'
% this path by executing |\pgfusepath{#1}| on it. 
%
%    \begin{macrocode}
\def\pgfbs@usefadepath#1{%
  \pgfsyssoftpath@setcurrentpath{\pgfbs@fadepath}%
  \pgfsyssoftpath@flushcurrentpath%
  \pgfusepath{#1}%
}
%    \end{macrocode}
%\end{macro}
%\begin{macro}{\pgfbs@usebbox}
% This is similar to the previous macro, but it `uses' the bounding box
% path.
%    \begin{macrocode}
\def\pgfbs@usebbox#1{%
  \pgfsyssoftpath@setcurrentpath{\pgfbs@shadow@bbox}%
  \pgfsyssoftpath@flushcurrentpath%
  \pgfusepath{#1}%
}
%    \end{macrocode}
%\end{macro}
%\begin{macro}{\pgfbs@usefadeandbbox}
% This is similar to the previous macros, but it `uses' both the fading path and the bounding box
% path.
%    \begin{macrocode}
\def\pgfbs@usefadeandbbox#1{%
  \let\pgfbs@temppath\pgfbs@fadepath
  \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfbs@temppath\expandafter\expandafter\expandafter{\expandafter\pgfbs@temppath\pgfbs@shadow@bbox}%
  \pgfsyssoftpath@setcurrentpath{\pgfbs@temppath}%
  \pgfsyssoftpath@flushcurrentpath%
  \pgfusepath{#1}%
}
%    \end{macrocode}
%\end{macro}
%\begin{macro}{\pgfbs@apply@canvas@transform}
% This achieves the scaling and shifting of the shadow.  It is done by a
% canvas transform to avoid iterating through a soft path and transforming
% many coordinates inside \TeX.  Scaling is `around' the bounding box
% mid point computed by |\pgfbs@compute@shadow@bbox|.
%    \begin{macrocode}
\def\pgfbs@apply@canvas@transform{
  \pgflowlevel{
    \pgftransformshift{\pgfpoint{\pgfbs@midx}{\pgfbs@midy}}
    \pgftransformscale{\pgfkeysvalueof{/tikz/shadow scale}}
    \pgftransformshift{\pgfpoint%
      {\pgfkeysvalueof{/tikz/shadow xshift}-\pgfbs@midx}
      {\pgfkeysvalueof{/tikz/shadow yshift}-\pgfbs@midy}
    }
  }
}
%    \end{macrocode}
%\end{macro}
%\begin{macro}{\pgfbs@paint@fading}
% This paints the actual fading picture.  It works by repeatedly
% drawing the |\pgfbs@fadepath| with different line widths and
% different shades of gray, leading to different opacity.  First, the
% outer part of the fading is drawn.  Then, remaining operations
% are clipped to the inside of the path.  Next, the path is filled with
% the shadow opacity.  Finally, the inner part of the fading is drawn.
% As mentioned previously, the bounding box needs to be set explicitly.
%    \begin{macrocode}
\def\pgfbs@paint@fading{
  \pgfpicture
  \pgfsetbaseline{\pgf@picminy}%
    % fix bounding box.
    \pgfbs@set@fading@pic@bbox
    % compute increments for line width and opacity
    \pgfmathsetmacro\pgfbs@op@step{50/\pgfbs@steps}
    \pgfmathsetmacro\pgfbs@wth@step{4*\pgfbs@radius/(2*\pgfbs@steps-1)}
    % draw the outer part of the fading, 
    % starting with lightest, outermost line
    \pgfsetroundjoin
    \pgfmathsetmacro\pgfbs@max@i{\pgfbs@steps-2}
    \pgfmathsetmacro\pgfbs@wth{2*\pgfbs@radius}
    \pgfmathsetmacro\pgfbs@op{100-0.5*\pgfbs@op@step}
    \foreach \pgfbs@i in {0,...,\pgfbs@max@i} {
      \pgfsetlinewidth{\pgfbs@wth pt}
      \pgfsetstrokecolor{black!\pgfbs@op!pstb@shadow@color}
      \pgfbs@usefadepath{stroke}
      \pgfmathsetmacro\pgfbs@wth{\pgfbs@wth-\pgfbs@wth@step}
      \global\let\pgfbs@wth=\pgfbs@wth
      \pgfmathsetmacro\pgfbs@op{\pgfbs@op-\pgfbs@op@step}
      \global\let\pgfbs@op=\pgfbs@op
    }
    % clip to inside of path
    \scope
    \pgfbs@usefadepath{clip}
    % fill inside with final darkest shadow color
    \pgfsetfillcolor{pstb@shadow@color}
    \pgfbs@usebbox{fill}
    % draw the inner part of the fading,
    % starting with the darkest, innermost line
    \pgfmathsetmacro\pgfbs@wth{2*\pgfbs@radius}
    \pgfmathsetmacro\pgfbs@op{0.5*\pgfbs@op@step}
    \foreach \pgfbs@i in {0,...,\pgfbs@max@i} {
      \pgfsetlinewidth{\pgfbs@wth pt}
      \pgfsetstrokecolor{black!\pgfbs@op!pstb@shadow@color}
      \pgfbs@usefadepath{stroke}
      \pgfmathsetmacro\pgfbs@wth{\pgfbs@wth-\pgfbs@wth@step}
      \global\let\pgfbs@wth=\pgfbs@wth
      \pgfmathsetmacro\pgfbs@op{\pgfbs@op+\pgfbs@op@step}
      \global\let\pgfbs@op=\pgfbs@op
    }
    \endscope
    % a final stroke to hide clip/antialiasing artifcats
    \pgfsetstrokecolor{black!50!pstb@shadow@color}
    \pgfsetlinewidth{0.5*\pgfbs@wth@step}
    \pgfbs@usefadepath{stroke}
  \endpgfpicture
}
%    \end{macrocode}
%\end{macro}
%\begin{macro}{\pgfbs@paint@invert@fading}
% This is an inverse fading.
%    \begin{macrocode}
\def\pgfbs@paint@invert@fading{
  \pgfpicture
  \pgfsetbaseline{\pgf@picminy}%
    % fix bounding box.
    \pgfbs@set@fading@pic@bbox
    % compute increments for line width and opacity
    \pgfmathsetmacro\pgfbs@op@step{50/\pgfbs@steps}
    \pgfmathsetmacro\pgfbs@wth@step{4*\pgfbs@radius/(2*\pgfbs@steps-1)}
    % draw the outer part of the fading, 
    % starting with lightest, outermost line
    \pgfsetroundjoin
    \pgfmathsetmacro\pgfbs@max@i{\pgfbs@steps-2}
    \pgfmathsetmacro\pgfbs@wth{2*\pgfbs@radius}
    \pgfmathsetmacro\pgfbs@op{0.5*\pgfbs@op@step}
    \foreach \pgfbs@i in {0,...,\pgfbs@max@i} {
      \pgfsetlinewidth{\pgfbs@wth pt}
      \pgfsetstrokecolor{black!\pgfbs@op!pstb@shadow@color}
      \pgfbs@usefadepath{stroke}
      \pgfmathsetmacro\pgfbs@wth{\pgfbs@wth-\pgfbs@wth@step}
      \global\let\pgfbs@wth=\pgfbs@wth
      \pgfmathsetmacro\pgfbs@op{\pgfbs@op+\pgfbs@op@step}
      \global\let\pgfbs@op=\pgfbs@op
    }
    % clip to inside of path
    \scope
    \pgfseteorule
    \pgfbs@usefadeandbbox{clip}
    % fill inside with final darkest shadow color
    \pgfsetfillcolor{pstb@shadow@color}
    \pgfbs@usebbox{fill}
    \endscope
    \scope
    \pgfbs@usefadepath{clip}
    % draw the inner part of the fading,
    % starting with the darkest, innermost line
    \pgfmathsetmacro\pgfbs@wth{2*\pgfbs@radius}
    \pgfmathsetmacro\pgfbs@op{100-0.5*\pgfbs@op@step}
    \foreach \pgfbs@i in {0,...,\pgfbs@max@i} {
      \pgfsetlinewidth{\pgfbs@wth pt}
      \pgfsetstrokecolor{black!\pgfbs@op!pstb@shadow@color}
      \pgfbs@usefadepath{stroke}
      \pgfmathsetmacro\pgfbs@wth{\pgfbs@wth-\pgfbs@wth@step}
      \global\let\pgfbs@wth=\pgfbs@wth
      \pgfmathsetmacro\pgfbs@op{\pgfbs@op-\pgfbs@op@step}
      \global\let\pgfbs@op=\pgfbs@op
    }
    \endscope
    % a final stroke to hide clip/antialiasing artifcats
    \pgfsetstrokecolor{black!50!pstb@shadow@color}
    \pgfsetlinewidth{0.5*\pgfbs@wth@step}
    \pgfbs@usefadepath{stroke}
  \endpgfpicture
}
%</texfile>
%    \end{macrocode}
%\end{macro}
%
% \Finale
%