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+% \iffalse meta-comment
+%<*internal>
+\iffalse
+%</internal>
+%<*readme>
+----------------------------------------------------------------
+penrose --- TikZ library for producing Penrose tilings
+E-mail: loopspace@mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+This package is for the creation of Penrose tilings using either kite-and-dart or rhombuses, and either by manual placement or automatic generation.
+%</readme>
+%<*internal>
+\fi
+\def\nameofplainTeX{plain}
+\ifx\fmtname\nameofplainTeX\else
+ \expandafter\begingroup
+\fi
+%</internal>
+%<*install>
+\input l3docstrip.tex
+\keepsilent
+\askforoverwritefalse
+\preamble
+----------------------------------------------------------------
+penrose --- TikZ library for producing Penrose tilings
+E-mail: loopspace@mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+\endpreamble
+\postamble
+
+Copyright (C) 2014-2019 by Andrew Stacey <loopspace@mathforge.org>
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License (LPPL), either
+version 1.3c of this license or (at your option) any later
+version. The latest version of this license is in the file:
+
+http://www.latex-project.org/lppl.txt
+
+This work is "maintained" (as per LPPL maintenance status) by
+Andrew Stacey.
+
+This work consists of the files penrose_code.dtx
+ penrose.tex
+and the derived files penrose.ins
+ penrose_code.pdf
+ penrose.pdf
+ tikzlibrarypenrose.code.tex
+ README.txt
+
+\endpostamble
+\usedir{tex/latex/penrose}
+\generate{
+ \file{tikzlibrarypenrose.code.tex}{\from{\jobname.dtx}{package}}
+}
+%</install>
+%<install>\endbatchfile
+%<*internal>
+\usedir{source/latex/penrose}
+\generate{
+ \file{\jobname.ins}{\from{\jobname.dtx}{install}}
+}
+\nopreamble\nopostamble
+\usedir{doc/latex/penrose}
+\generate{
+ \file{README.txt}{\from{\jobname.dtx}{readme}}
+}
+\ifx\fmtname\nameofplainTeX
+ \expandafter\endbatchfile
+\else
+ \expandafter\endgroup
+\fi
+%</internal>
+%<*driver>
+\documentclass{l3doc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+\usepackage{tikz}
+%\usepackage{trace}
+\usetikzlibrary{penrose}
+%\traceoff
+%\usepackage[numbered]{hypdoc}
+\definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9}
+
+\usepackage{listings}
+\lstloadlanguages{[LaTeX]TeX}
+\lstset{breakatwhitespace=true,breaklines=true,language=TeX}
+
+\usepackage{fancyvrb}
+
+\newenvironment{example}
+ {\VerbatimEnvironment
+ \begin{VerbatimOut}[gobble=2]{example.out}}
+ {\end{VerbatimOut}
+ \begin{center}
+% \setlength{\parindent}{0pt}
+ \fbox{\begin{minipage}{.9\linewidth}
+ \lstset{breakatwhitespace=true,breaklines=true,language=TeX,basicstyle=\small}
+ \lstinputlisting[]{example.out}
+ \end{minipage}}
+
+ \fbox{\begin{minipage}{.9\linewidth}
+ \input{example.out}
+ \end{minipage}}
+\end{center}
+}
+\EnableCrossrefs
+\CodelineIndex
+\RecordChanges
+\begin{document}
+ \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{2944}
+%
+% \CharacterTable
+% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+% Digits \0\1\2\3\4\5\6\7\8\9
+% Exclamation \! Double quote \" Hash (number) \#
+% Dollar \$ Percent \% Ampersand \&
+% Acute accent \' Left paren \( Right paren \)
+% Asterisk \* Plus \+ Comma \,
+% Minus \- Point \. Solidus \/
+% Colon \: Semicolon \; Less than \<
+% Equals \= Greater than \> Question mark \?
+% Commercial at \@ Left bracket \[ Backslash \\
+% Right bracket \] Circumflex \^ Underscore \_
+% Grave accent \` Left brace \{ Vertical bar \|
+% Right brace \} Tilde \~}
+%
+%
+% \changes{1.0}{2014/05/07}{Converted to DTX file}
+% \changes{1.2}{2019/02/23}{Added general tile creation code}
+% \changes{1.4}{2021/01/22}{Adapted to latest version of spath3}
+%
+% \DoNotIndex
+% {
+% \begingroup,
+% \catcode,
+% \active,
+% \csname,
+% \endcsname,
+% }%
+%
+%
+% \providecommand*{\url}{\texttt}
+% \GetFileInfo{tikzlibrarypenrose.code.tex}
+% \title{The \textsf{Penrose} package}
+% \author{Andrew Stacey\texorpdfstring{\\ \url{loopspace@mathforge.org}}{}}
+% \date{\fileversion~from \filedate}
+%
+%
+% \maketitle
+%
+% \tableofcontents
+%
+% \begin{documentation}
+%
+% \section{Introduction}
+%
+% This is a TikZ library for drawing Penrose tiles (kite/dart, rhombus, and pentagon versions).
+% It provides two methods of drawing: one in which an automatic pattern is built, and one where the tiles can be placed ``by hand''.
+% The tiles can be shaped and (hopefully!) still fit together.
+% For full user documentation, see the \Verb+penrose.pdf+ file.
+%
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{Implementation}
+%
+% \begin{macrocode}
+%<*package>
+% \end{macrocode}
+% \begin{macrocode}
+%<@@=penrose>
+% \end{macrocode}
+%
+% \subsection{Initialisation}
+%
+%
+% We use the \Verb+spath3+ library for manipulating the paths that will make up the tiles.
+%
+% \begin{macrocode}
+\ProvidesExplFile {tikzlibrarypenrose.code.tex} {2021/01/22} {1.4} {TikZ pics for Penrose and other tiles}
+\RequirePackage{spath3}
+\usetikzlibrary{spath3}
+% \end{macrocode}
+% Now we move in to the realm of \LaTeX3.
+% \begin{macrocode}
+\ExplSyntaxOn
+% \end{macrocode}
+%
+% Start with some basic paths (lines) for the sides of the tiles so that we know that we have well-defined tiles at the outset.
+% These are globally defined as we will frequently want to define them in one tikzpicture and use them in another.
+%
+% \begin{macrocode}
+\tl_new:N \g_@@_side_a_tl
+\tl_new:N \g_@@_side_b_tl
+\tl_new:N \g_@@_side_c_tl
+\tl_new:N \g_@@_side_d_tl
+\tl_new:N \g_@@_side_e_tl
+\tl_new:N \g_@@_side_A_tl
+\tl_new:N \g_@@_side_B_tl
+\tl_new:N \g_@@_side_C_tl
+\tl_new:N \g_@@_side_D_tl
+\tl_new:N \g_@@_side_E_tl
+\tl_gset:Nn \g_@@_side_a_tl
+{
+ \pgfsyssoftpath@movetotoken{0pt}{0pt}
+ \pgfsyssoftpath@linetotoken{1pt}{0pt}
+}
+\tl_gset_eq:NN \g_@@_side_b_tl \g_@@_side_a_tl
+\tl_gset_eq:NN \g_@@_side_c_tl \g_@@_side_a_tl
+\tl_gset_eq:NN \g_@@_side_d_tl \g_@@_side_a_tl
+\tl_gset_eq:NN \g_@@_side_e_tl \g_@@_side_a_tl
+\tl_gset_eq:NN \g_@@_side_A_tl \g_@@_side_a_tl
+\tl_gset_eq:NN \g_@@_side_B_tl \g_@@_side_a_tl
+\tl_gset_eq:NN \g_@@_side_C_tl \g_@@_side_a_tl
+\tl_gset_eq:NN \g_@@_side_D_tl \g_@@_side_a_tl
+\tl_gset_eq:NN \g_@@_side_E_tl \g_@@_side_a_tl
+% \end{macrocode}
+%
+% \begin{variable}{\l_@@_tmpa_fp, \l_@@_tmpb_fp, \l_@@_tmpc_fp, \l_@@_tmpa_tl, \l_@@_tmpb_tl, \l_@@_tmpc_tl, \l_@@_tmpd_tl, \l_@@_tmpa_int, \l_@@_tmpb_int, \l_@@_xa_dim, \l_@@_ya_dim, \l_@@_xb_dim, \l_@@_yb_dim, \l_@@_tmpa_prop}
+% We need a few temporary variables to hold intermediate calculations.
+%
+% \begin{macrocode}
+\fp_new:N \l_@@_tmpa_fp
+\fp_new:N \l_@@_tmpb_fp
+\fp_new:N \l_@@_tmpc_fp
+\str_new:N \l_@@_tmpa_str
+\str_new:N \l_@@_tmpb_str
+\tl_new:N \l_@@_tmpa_tl
+\tl_new:N \l_@@_tmpb_tl
+\tl_new:N \l_@@_tmpc_tl
+\tl_new:N \l_@@_tmpd_tl
+\tl_new:N \l_@@_tmp_tile_path_tl
+\tl_new:N \g_@@_smuggle_tl
+\int_new:N \l_@@_tmpa_int
+\int_new:N \l_@@_tmpb_int
+\dim_new:N \l_@@_xa_dim
+\dim_new:N \l_@@_ya_dim
+\dim_new:N \l_@@_xb_dim
+\dim_new:N \l_@@_yb_dim
+\prop_new:N \l_@@_tmpa_prop
+% \end{macrocode}
+% \end{variable}
+%
+% \subsection{Creating the Tiles}
+%
+% \begin{macro}[internal]{\@@_normalise_path:Nn}
+% When defining the path for a side, we normalise so that it starts at the origin and ends at \Verb+(1pt,0pt)+.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_normalise_path:Nn #1#2
+{
+% \end{macrocode}
+% Get the initial point of the path and convert to floating point.
+% \begin{macrocode}
+ \group_begin:
+ \spath_initialpoint:Nn \l_@@_tmpa_tl {#2}
+ \fp_set:Nn \l_@@_tmpa_fp {\tl_head:N \l_@@_tmpa_tl}
+ \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+ \fp_set:Nn \l_@@_tmpb_fp {\tl_head:N \l_@@_tmpa_tl}
+% \end{macrocode}
+% Get the final point of the path, and compute the difference of the final and initial points.
+%
+% The resulting numbers, say \(a\) and \(b\), will be put into a matrix to rotate and scale the path.
+% The formula for the matrix is:
+%^^A
+% \[
+% \frac{1}{a^2 + b^2}
+% \begin{bmatrix} a & b \\ -b & a \end{bmatrix}
+% \]
+%
+% \begin{macrocode}
+ \spath_finalpoint:Nn \l_@@_tmpa_tl {#2}
+ \fp_set:Nn \l_@@_tmpa_fp
+ {\tl_head:N \l_@@_tmpa_tl - \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+ \fp_set:Nn \l_@@_tmpb_fp
+ {\tl_head:N \l_@@_tmpa_tl - \l_@@_tmpb_fp}
+% \end{macrocode}
+% Now compute the square of the length of the path for scaling.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_tmpc_fp
+ {\l_@@_tmpa_fp^2 + \l_@@_tmpb_fp^2}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_tmpa_fp/\l_@@_tmpc_fp}
+ \fp_set:Nn \l_@@_tmpb_fp {\l_@@_tmpb_fp/\l_@@_tmpc_fp}
+ \fp_set:Nn \l_@@_tmpc_fp {-\l_@@_tmpb_fp}
+% \end{macrocode}
+% Now construct the matrix.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpb_tl
+ {
+ {\fp_use:N \l_@@_tmpa_fp}
+ {\fp_use:N \l_@@_tmpc_fp} % swapped
+ {\fp_use:N \l_@@_tmpb_fp} % swapped
+ {\fp_use:N \l_@@_tmpa_fp}
+ }
+% \end{macrocode}
+% Get the initial point back again for the translation part.
+% \begin{macrocode}
+ \spath_initialpoint:Nn \l_@@_tmpa_tl {#2}
+% \end{macrocode}
+% But we need to premultiply by the matrix because of how the transformations are applied.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_tmpa_fp
+ {
+ (-1) * \l_@@_tmpa_fp * \tl_head:N \l_@@_tmpa_tl
+ + (-1) * \l_@@_tmpb_fp * \tl_tail:N \l_@@_tmpa_tl
+ }
+ \fp_set:Nn \l_@@_tmpb_fp
+ {
+ (-1) * \l_@@_tmpa_fp * \tl_tail:N \l_@@_tmpa_tl
+ + \l_@@_tmpb_fp * \tl_head:N \l_@@_tmpa_tl
+ }
+% \end{macrocode}
+% Finally, we apply the transformation to the path.
+% \begin{macrocode}
+ \tl_put_right:Nx \l_@@_tmpb_tl {
+ {\fp_to_dim:N \l_@@_tmpa_fp}
+ {\fp_to_dim:N \l_@@_tmpb_fp}
+ }
+ \spath_transform:NnV \l_@@_tmpa_tl {#2} \l_@@_tmpb_tl
+ \tl_gset_eq:NN \g_@@_smuggle_tl \l_@@_tmpa_tl
+ \group_end:
+ \tl_set_eq:NN #1 \g_@@_smuggle_tl
+ \tl_gclear:N \g_@@_smuggle_tl
+}
+\cs_generate_variant:Nn \@@_normalise_path:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \@@_normalise_path:N #1
+{
+ \@@_normalise_path:NV #1#1
+}
+\cs_generate_variant:Nn \@@_normalise_path:N {c}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{function}{\SetPenrosePath}
+% This sets the path corresponding to a particular side to the current path, and normalises it.
+% \begin{macrocode}
+\NewDocumentCommand \SetPenrosePath { m }
+{
+ \pgfsyssoftpath@getcurrentpath\l_@@_tmpa_tl
+ \@@_normalise_path:N \l_@@_tmpa_tl
+ \tl_gset_eq:cN {g_@@_side_#1_tl} \l_@@_tmpa_tl
+}
+% \end{macrocode}
+% \end{function}
+%
+% \begin{macro}[internal]{\tikz_scan_point:n}
+% This is a wrapper around \Verb+\tikz@scan@one@point+ to make it easier to use with \LaTeX3 variables.
+% \begin{macrocode}
+\cs_new_nopar:Npn \tikz_scan_point:n #1
+{
+ \tikz@scan@one@point\pgfutil@firstofone#1\relax
+}
+\cs_generate_variant:Nn \tikz_scan_point:n {V}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\@@_make_tile:nnn}
+% This builds the tile path from its pieces.
+% The arguments are the name of the tile, the descriptions of the sides, and a token list of the coordinates.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_make_tile:nnn #1#2#3
+{
+% \end{macrocode}
+% Get the first coordinate and initialise the path with a move to this point.
+% \begin{macrocode}
+ \group_begin:
+ \tl_set:Nn \l_@@_tmpa_tl {#3}
+ \tl_set:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpa_tl}
+ \tl_set:Nn \l_@@_tmpa_tl {\pgfsyssoftpath@movetotoken}
+ \tikz_scan_point:V \l_@@_tmpb_tl
+ \tl_put_right:Nx \l_@@_tmpa_tl
+ {
+ {\dim_use:N \pgf@x}{\dim_use:N \pgf@y}
+ }
+ \tl_set_eq:NN \l_@@_tmp_tile_path_tl \l_@@_tmpa_tl
+% \end{macrocode}
+% Now we have our path initialised, we can start appending the side paths according to the specification in the second argument.
+%
+% We append the initial coordinate to the end of the list to make a closed cycle.
+% \begin{macrocode}
+ \tl_set:Nn \l_@@_tmpa_tl {#3}
+ \tl_put_right:Nx \l_@@_tmpa_tl {{\tl_head:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+% Now we walk through the description of the sides, adding the specified paths to our tile path.
+% \begin{macrocode}
+ \tl_map_inline:nn {#2} {
+% \end{macrocode}
+% Clone the path for this side.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpc_tl {\tl_head:n {##1}}
+ \tl_set_eq:Nc \l_@@_tmpd_tl {g_@@_side_ \tl_use:N \l_@@_tmpc_tl _tl}
+% \end{macrocode}
+% Strip off the next coordinate, and convert it to a point.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpa_tl}
+ \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+ \tikz_scan_point:V \l_@@_tmpb_tl
+% \end{macrocode}
+% Store the resulting coordinate.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_tmpa_fp { \pgf@x }
+ \fp_set:Nn \l_@@_tmpb_fp { \pgf@y }
+% \end{macrocode}
+% Now get the next coordinate.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpa_tl}
+ \tikz_scan_point:V \l_@@_tmpb_tl
+% \end{macrocode}
+% We want the difference between the two coordinates.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_tmpa_fp {\pgf@x - \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpb_fp {\pgf@y - \l_@@_tmpb_fp}
+% \end{macrocode}
+% This is converted into a transformation matrix.
+% \begin{macrocode}
+ \fp_set:Nn \l_@@_tmpc_fp {-\l_@@_tmpb_fp}
+ \tl_set:Nx \l_@@_tmpb_tl
+ {
+ {\fp_use:N \l_@@_tmpa_fp}
+ {\fp_use:N \l_@@_tmpb_fp} % not swapped
+ {\fp_use:N \l_@@_tmpc_fp} % not swapped
+ {\fp_use:N \l_@@_tmpa_fp}
+ {0}
+ {0}
+ }
+% \end{macrocode}
+% The transformation is applied to the cloned path.
+% \begin{macrocode}
+ \spath_transform:NV \l_@@_tmpd_tl \l_@@_tmpb_tl
+% \end{macrocode}
+% And this is welded to the tile path.
+% \begin{macrocode}
+ \spath_weld:NV \l_@@_tmp_tile_path_tl \l_@@_tmpd_tl
+ }
+% \end{macrocode}
+% At the end we close the path.
+% \begin{macrocode}
+ \spath_close:N \l_@@_tmp_tile_path_tl
+ \tl_gset_eq:NN \g_@@_smuggle_tl \l_@@_tmp_tile_path_tl
+ \group_end:
+ \tl_gclear_new:c {g_@@_tile_#1_tl}
+ \tl_gset_eq:cN {g_@@_tile_#1_tl} \g_@@_smuggle_tl
+ \tl_gclear:N \g_@@_smuggle_tl
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\@@_make_tile:nn}
+% A wrapper around the above which allows us to specify the second two arguments as two items in a token list.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_make_tile:nn #1#2
+{
+ \@@_make_tile:nnn {#1} #2
+}
+\cs_generate_variant:Nn \@@_make_tile:nn {nV}
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Specifying the Tiles}
+%
+% The tile specifications are contained in a \Verb+prop+.
+% \begin{macrocode}
+\prop_new:N \g_@@_tiles_prop
+% \end{macrocode}
+%
+% \begin{macro}[internal]{\@@_add_coordinate:Nnn, \@@_add_coordinate:w}
+% Process a coordinate through \Verb+fp+ and adds it to a token list.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_add_coordinate:Nnn #1#2#3 {
+ \fp_set:Nn \l_@@_tmpa_fp{#2}
+ \fp_set:Nn \l_@@_tmpb_fp{#3}
+ \tl_put_right:Nx #1
+ {
+ {(\fp_use:N \l_@@_tmpa_fp, \fp_use:N \l_@@_tmpb_fp)}
+ }
+}
+% \end{macrocode}
+% Wrapper around the add coordinate command to split at a comma.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_add_coordinate:w #1#2,#3 \q_stop
+{
+ \@@_add_coordinate:Nnn \l_@@_tmpa_tl {#2}{#3}
+}
+% \end{macrocode}
+% \end{macro}
+%
+% Now we specify the tiles.
+% The specification is a clockwise list of the vertices together with the labels of the corresponding sides.
+% There are three basic paths, \Verb+a+, \Verb+b+, \Verb+c+, and their complements (which are capitalised).
+%
+% \begin{itemize}
+% \item Thin Rhombus.
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(18)}{sind(18)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {2*cosd(18)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(18)}{-sind(18)}
+
+\prop_gput:Nnx \g_@@_tiles_prop {thin~ rhombus}
+{{a A B b} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Thick Rhombus.
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(36)}{sind(36)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {2*cosd(36)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(36)}{-sind(36)}
+
+\prop_gput:Nnx \g_@@_tiles_prop {thick~ rhombus}
+{{B a A b} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Dart.
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl
+{2*sind(18)*cosd(108)}{2*sind(18)*sind(108)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {2*sind(18)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl
+{2*sind(18)*cosd(108)}{-2*sind(18)*sind(108)}
+
+\prop_gput:Nnx \g_@@_tiles_prop {dart}
+{{c a A C} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Kite.
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(36)}{sind(36)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {1}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(36)}{-sind(36)}
+
+\prop_gput:Nnx \g_@@_tiles_prop {kite}
+{{a c C A} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Golden Triangle.
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(18)}{sind(18)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(18)}{-sind(18)}
+
+\prop_gput:Nnx \g_@@_tiles_prop {golden~ triangle}
+{{a c b} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Reverse Golden Triangle.
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(18)}{sind(18)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(18)}{-sind(18)}
+
+\prop_gput:Nnx \g_@@_tiles_prop {reverse~ golden~ triangle}
+{{B C A} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Golden Gnomon
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(36)}{sind(36)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {2*cosd(36)}{0}
+
+\prop_gput:Nnx \g_@@_tiles_prop {golden~ gnomon}
+{{C b A} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Reverse Golden Gnomon
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {2*cosd(36)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(36)}{-sind(36)}
+\prop_gput:Nnx \g_@@_tiles_prop {reverse~ golden~ gnomon}
+{{a B c} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Primary Pentagon (pentagon 5)
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(108)}{sind(108)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl
+{1+cosd(72)+cosd(144)}{sind(72)+sind(144)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {1+cosd(72)}{sind(72)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {1}{0}
+\prop_gput:Nnx \g_@@_tiles_prop {pentagon~ 5}
+{{a a a a a} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Secondary Pentagon (pentagon 3)
+% \begin{macrocode}
+\prop_gput:Nnx \g_@@_tiles_prop {pentagon~ 3}
+{{A b a a b} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Tertiary Pentagon (pentagon 2)
+% \begin{macrocode}
+\prop_gput:Nnx \g_@@_tiles_prop {pentagon~ 2}
+{{d A e c A} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Pentagram
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {1}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {1-cosd(36)}{-sind(36)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl
+{1-cosd(36)-cosd(108)}{-sind(36)-sind(108)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(108)}{-sind(108)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl
+{-1+3*cosd(108)+cosd(36)}{-sind(36)-sind(108)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl
+{-1+2*cosd(108)+cosd(36)}{-sind(36)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {-1+2*cosd(108)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {2*cosd(108)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(108)}{sind(108)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\prop_gput:Nnx \g_@@_tiles_prop {pentagram}
+{{C E C E C E C E C E} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Boat
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {-1+2*cosd(108)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {2*cosd(108)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(108)}{sind(108)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {1}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {1-cosd(36)}{-sind(36)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl
+{-1+2*cosd(108)+cosd(36)}{-sind(36)}
+\prop_gput:Nnx \g_@@_tiles_prop {boat}
+{{C E C E B D B} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \item Diamond.
+% \begin{macrocode}
+\tl_clear:N \l_@@_tmpa_tl
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {0}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(18)}{sind(18)}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {2*cosd(18)}{0}
+\@@_add_coordinate:Nnn \l_@@_tmpa_tl {cosd(18)}{-sind(18)}
+\prop_gput:Nnx \g_@@_tiles_prop {diamond}
+{{D B B D} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+%
+% \end{itemize}
+%
+% \begin{function}{\BakePenroseTile}
+% This is the user wrapper around the tile creation macros.
+% \begin{macrocode}
+\NewDocumentCommand \BakePenroseTile {m}
+{
+ \prop_get:NnN \g_@@_tiles_prop {#1} \l_@@_tmpa_tl
+ \@@_make_tile:nV {#1} \l_@@_tmpa_tl
+}
+% \end{macrocode}
+% For backwards compatibility.
+% \begin{macrocode}
+\cs_set_eq:NN \MakePenroseTile \BakePenroseTile
+% \end{macrocode}
+% \end{function}
+%
+% \begin{function}{\UsePenroseTile}
+% This is the command that actually places a tile on the page.
+% The first argument is optional and is for styling.
+% \begin{macrocode}
+\NewDocumentCommand \UsePenroseTile {O{} m}
+{
+% \end{macrocode}
+% We need to transform the tile to correspond to the current transformation matrix.
+% To ensure that we only transform the current tile, we clone it first.
+% \begin{macrocode}
+ \tl_set_eq:Nc \l_@@_tmp_tile_path_tl {g_@@_tile_#2_tl}
+% \end{macrocode}
+% The transformation matrix returned by PGF appears to be transposed from what it should be.
+% (This needs a little more investigation, it might be that I've implemented the multiplication incorrectly here.)
+% \begin{macrocode}
+ \pgfgettransform \l_@@_tmpa_tl
+% \tl_clear:N \l_@@_tmpb_tl
+% \tl_set:Nx \l_@@_tmpb_tl {{\tl_head:N \l_@@_tmpa_tl}}
+% \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+% \tl_put_right:Nx \l_@@_tmpb_tl
+% {
+% {\tl_item:Nn \l_@@_tmpa_tl {1}}
+% }
+% \tl_put_right:Nx \l_@@_tmpb_tl
+% {
+% {\tl_item:Nn \l_@@_tmpa_tl {2}}
+% }
+% \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+% \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+% \tl_put_right:NV \l_@@_tmpb_tl \l_@@_tmpa_tl
+% \end{macrocode}
+% Apply the transformation, protocol the path, and render it.
+% \begin{macrocode}
+ \spath_transform:NV \l_@@_tmp_tile_path_tl \l_@@_tmpa_tl
+ \spath_tikz_path:nV {#1} \l_@@_tmp_tile_path_tl
+}
+% \end{macrocode}
+% \end{function}
+%
+% \begin{macro}{save Penrose path}
+% This is a style for a user to take a path and make it into the path for one of the sides.
+% It needs to store both that side and the reverse.
+% \begin{macrocode}
+\tikzset{
+ save~ Penrose~ path/.code={
+ \tikz@addmode{
+% \end{macrocode}
+% Get the current path.
+% \begin{macrocode}
+ \pgfsyssoftpath@getcurrentpath\l_@@_tmpa_tl
+% \end{macrocode}
+% Normalise the path and save.
+% \begin{macrocode}
+ \@@_normalise_path:N \l_@@_tmpa_tl
+ \tl_gclear_new:c {g_@@_side_#1_tl}
+ \tl_gset_eq:cN {g_@@_side_#1_tl} \l_@@_tmpa_tl
+% \end{macrocode}
+% Now create the reverse path.
+% The name is the upper case version.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpb_tl {\str_uppercase:n {#1}}
+% \end{macrocode}
+% Reverse the path, and relocate to the interval \([0,1]\).
+% \begin{macrocode}
+ \spath_reverse:N \l_@@_tmpa_tl
+ \spath_transform:Nnnnnnn \l_@@_tmpa_tl {-1} {0} {0} {-1} {1} {0}
+ \tl_gclear_new:c {g_@@_side_ \tl_use:N \l_@@_tmpb_tl _tl}
+ \tl_gset_eq:cN {g_@@_side_ \tl_use:N \l_@@_tmpb_tl _tl} \l_@@_tmpa_tl
+ }
+ },
+ clone~ Penrose~ side~ path/.style~ 2~ args={
+ spath/set~ name=Penrose~side,
+ spath/clone~ global={#1}{#2}
+ },
+ spath/prefix/Penrose~side/.style={
+ spath/set~ prefix=g_@@_side_,
+ },
+ spath/suffix/Penrose~side/.style={
+ spath/set~ suffix=_tl,
+ },
+ clone~ Penrose~ tile~ path/.style~ 2~ args={
+ spath/set~ name=Penrose~tile,
+ spath/clone~ global={#1}{#2}
+ },
+ spath/prefix/Penrose~tile/.style={
+ spath/set~ prefix=g_@@_tile_,
+ },
+ spath/suffix/Penrose~tile/.style={
+ spath/set~ suffix=_tl,
+ },
+ expand~ key/.code={
+ \exp_args:NV \pgfkeysalso #1
+ }
+}
+% \end{macrocode}
+% \end{macro}
+%
+% Create the basic tile shapes.
+% \begin{macrocode}
+\BakePenroseTile {thin~ rhombus}
+\BakePenroseTile {thick~ rhombus}
+\BakePenroseTile {dart}
+\BakePenroseTile {kite}
+\BakePenroseTile {golden~ triangle}
+\BakePenroseTile {reverse~ golden~ triangle}
+\BakePenroseTile {golden~ gnomon}
+\BakePenroseTile {reverse~ golden~ gnomon}
+\BakePenroseTile {pentagon~ 5}
+\BakePenroseTile {pentagon~ 3}
+\BakePenroseTile {pentagon~ 2}
+\BakePenroseTile {pentagram}
+\BakePenroseTile {boat}
+\BakePenroseTile {diamond}
+% \end{macrocode}
+%
+%
+% \subsection{User-Definable Tiles}
+%
+% The commands in this section are for enabling a user to define their own tile.
+%
+%
+% \begin{macro}[internal]{\@@_transform_side:nn}
+% Apply a transformation to make a given side lie on the x-axis.
+% First argument is the tile, second is the side.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_transform_side:nn #1#2
+{
+% \end{macrocode}
+% Get our tile data.
+% \begin{macrocode}
+ \prop_get:NnN \g_@@_tiles_prop {#1} \l_@@_tmpa_tl
+% \end{macrocode}
+% Start with the edge list.
+%
+% Initialise the counter.
+% \begin{macrocode}
+ \int_zero:N \l_@@_tmpb_int
+ \int_incr:N \l_@@_tmpb_int
+% \end{macrocode}
+% Get the path type list.
+%
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpc_tl {\tl_head:N \l_@@_tmpa_tl}
+% \end{macrocode}
+%
+% Iterate through the path type list, looking for the requested path.
+% \begin{macrocode}
+ \tl_map_inline:Nn \l_@@_tmpc_tl {
+ \str_if_eq:nnT {##1} {#2} {
+ \tl_map_break:
+ }
+ \int_incr:N \l_@@_tmpb_int
+ }
+% \end{macrocode}
+% Get the coordinate list.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpa_tl}
+% \end{macrocode}
+% Strip off the outer braces.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpc_tl {\tl_item:Nn \l_@@_tmpc_tl {1}}
+% \end{macrocode}
+% Add the first coordinate at the end.
+% \begin{macrocode}
+ \tl_put_right:Nx \l_@@_tmpc_tl
+ {{\tl_item:Nn \l_@@_tmpc_tl {1}}}
+% \end{macrocode}
+% Get the coordinates for this edge.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpa_tl
+ {\tl_item:Nn \l_@@_tmpc_tl {\int_use:N \l_@@_tmpb_int}}
+ \tl_set:Nx \l_@@_tmpb_tl
+ {\tl_item:Nn \l_@@_tmpc_tl {\int_use:N \l_@@_tmpb_int + 1}}
+% \end{macrocode}
+% Translate second to origin.
+% \begin{macrocode}
+ \tikz_scan_point:V \l_@@_tmpb_tl
+ \dim_set_eq:Nc \l_@@_xa_dim {pgf@x}
+ \dim_set_eq:Nc \l_@@_ya_dim {pgf@y}
+% \end{macrocode}
+% Rotate and scale first to unit x-vector.
+% \begin{macrocode}
+ \tikz_scan_point:V \l_@@_tmpa_tl
+ \dim_set_eq:Nc \l_@@_xb_dim {pgf@x}
+ \dim_set_eq:Nc \l_@@_yb_dim {pgf@y}
+
+ \dim_sub:Nn \l_@@_xb_dim {\l_@@_xa_dim }
+ \dim_sub:Nn \l_@@_yb_dim {\l_@@_ya_dim }
+% \end{macrocode}
+% And normalise the vector along it.
+% \begin{macrocode}
+ \pgfpointnormalised{\pgfpoint{\l_@@_xb_dim}{\l_@@_yb_dim}}
+ \dim_set_eq:Nc \l_@@_xb_dim {pgf@x}
+ \dim_set_eq:Nc \l_@@_yb_dim {pgf@y}
+% \end{macrocode}
+% Now rotate so that the \(x\)--axis lies along the edge.
+% \begin{macrocode}
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\l_@@_xb_dim}{-\l_@@_yb_dim}}
+ {\pgfpoint{\l_@@_yb_dim}{\l_@@_xb_dim}}
+
+ \pgftransformshift{\pgfpoint{-\l_@@_xa_dim}{-\l_@@_ya_dim}}
+
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macrocode}
+\cs_generate_variant:Nn \tl_if_eq:nnT {nVT}
+\cs_generate_variant:Nn \@@_transform_side:nn {nx,nV}
+% \end{macrocode}
+%
+% \begin{macro}[internal]{\TransformAlongSide}
+% Make this available outside the \LaTeX3 environment.
+% \begin{macrocode}
+\DeclareDocumentCommand \TransformAlongSide {m m}
+{
+ \@@_transform_side:nx {#1}{#2}
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\@@_coordinates_at_vertices:n}
+% This places TikZ coordinates at the vertices of the tile.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_coordinates_at_vertices:n #1
+{
+% \end{macrocode}
+% Get our tile data
+% \begin{macrocode}
+ \prop_get:NnN \g_@@_tiles_prop {#1} \l_@@_tmpa_tl
+% \end{macrocode}
+% Start with the edge list
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpa_tl}
+% \end{macrocode}
+% Get the coordinate list
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpa_tl}
+% \end{macrocode}
+% Strip off the outer braces
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {\tl_item:Nn \l_@@_tmpc_tl {1}}
+% \end{macrocode}
+% Add the first coordinate at the end
+% \begin{macrocode}
+ \tl_put_right:Nx \l_@@_tmpc_tl
+ {{\tl_item:Nn \l_@@_tmpc_tl {1}}}
+% \end{macrocode}
+% Get the first coordinate
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpa_tl {\tl_head:N \l_@@_tmpc_tl}
+ \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+% \end{macrocode}
+% Iterate through the path type list, looking for the requested path
+% \begin{macrocode}
+ \tl_map_inline:Nn \l_@@_tmpb_tl {
+ \tl_set:Nx \l_@@_tmpd_tl {
+ \exp_not:N \coordinate
+ (-edge~ ##1~ start)~ at \tl_use:N \l_@@_tmpa_tl;
+ }
+ \tl_use:N \l_@@_tmpd_tl
+ \tl_set:Nx \l_@@_tmpa_tl {\tl_head:N \l_@@_tmpc_tl}
+ \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+ \tl_set:Nx \l_@@_tmpd_tl {
+ \exp_not:N \coordinate
+ (-edge~ ##1~ end)~ at \tl_use:N \l_@@_tmpa_tl;
+ }
+ \tl_use:N \l_@@_tmpd_tl
+ }
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\CoordinatesAtVertices}
+% User-accessible wrapper around the above.
+% \begin{macrocode}
+\DeclareDocumentCommand \CoordinatesAtVertices {m}
+{
+ \@@_coordinates_at_vertices:n {#1}
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{function}{\DefineTile}
+% This is the user function for defining a tile.
+% \begin{macrocode}
+\DeclareDocumentCommand \DefineTile { m m m }
+{
+% \end{macrocode}
+% Clear the temporary variable.
+% \begin{macrocode}
+ \tl_clear:N \l_@@_tmpa_tl
+% \end{macrocode}
+% The 3rd parameter is a list of coordinates at vertices, iterate through them and add them to the list.
+% \begin{macrocode}
+ \tl_map_inline:nn {#3} {
+ \@@_add_coordinate:w \l_@@_tmpa_tl ##1 \q_stop
+ }
+% \end{macrocode}
+% Now we make a list of the edge types (from the 2nd parameter), using a prop to keep track of whether an edge is repeated.
+% \begin{macrocode}
+ \prop_clear:N \l_@@_tmpa_prop
+ \tl_map_inline:nn {#2} {
+ \prop_if_in:NnTF \l_@@_tmpa_prop {##1}
+ {
+ \prop_put:Nnn \l_@@_tmpa_prop {##1} {1}
+ }
+ {
+ \prop_put:Nnn \l_@@_tmpa_prop {##1} {0}
+ }
+ }
+% \end{macrocode}
+% Having established their multiplicity, we now create the edges with their names, appending numbers to their names if used more than once.
+% \begin{macrocode}
+ \tl_clear:N \l_@@_tmpb_tl
+ \tl_map_inline:nn {#2}
+ {
+ \tl_clear:N \l_@@_tmpc_tl
+ \tl_put_right:Nn \l_@@_tmpc_tl {##1}
+ \int_compare:nF {\prop_item:Nn \l_@@_tmpa_prop {##1} == 0} {
+ \tl_put_right:Nx \l_@@_tmpc_tl
+ {\prop_item:Nn \l_@@_tmpa_prop {##1}}
+ \prop_put:Nnx \l_@@_tmpa_prop {##1}
+ {\int_eval:n {\prop_item:Nn \l_@@_tmpa_prop {##1} + 1}}
+ }
+ \tl_put_right:Nx \l_@@_tmpb_tl {{ \l_@@_tmpc_tl }}
+ }
+% \end{macrocode}
+% Finally, we can create our tile and add it to the global tile prop.
+% \begin{macrocode}
+ \prop_gput:Nnx \g_@@_tiles_prop {#1}
+ {{\tl_use:N \l_@@_tmpb_tl} {\tl_use:N \l_@@_tmpa_tl}}
+% \end{macrocode}
+% Having created the tile, we make a TikZ pic to place it on the page.
+% \begin{macrocode}
+ \tikzset{
+ #1/.pic={
+ \begin{scope}
+% \end{macrocode}
+% Were we given a tile to align ourselves against?
+% \begin{macrocode}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment~ location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+% \end{macrocode}
+% Yes, we were.
+% So we adjust our position accordingly.
+% The first job is to transform so that we're along the edge of the receiving tile.
+% \begin{macrocode}
+ \begingroup
+% \end{macrocode}
+% We get the locations of the start and end of the receiving tile.
+% As \Verb+pic+ sets the node prefix, we have to temporarily suspend that (hence working in a group).
+% \begin{macrocode}
+ \tikzset{name~ prefix~ ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge~ \pgfkeysvalueof{/tikz/Penrose/alignment~ edge}~ start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge~ \pgfkeysvalueof{/tikz/Penrose/alignment~ edge}~ end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+% \end{macrocode}
+% We store the initial points in \Verb+\pgf@xa+ and \Verb+\pgf@ya+ but we want \Verb+\pgf@xb+ and \Verb+\pgf@yb+ to be a vector along the edge.
+% \begin{macrocode}
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+% \end{macrocode}
+% We shift to the start of the edge.
+% \begin{macrocode}
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+% \end{macrocode}
+% And normalise the vector along it.
+% \begin{macrocode}
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+% \end{macrocode}
+% Now rotate so that the \(x\)--axis lies along the edge.
+% \begin{macrocode}
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}
+% \end{macrocode}
+% The next job is to shift and rotate the current tile so that the correct edge ends up against the receiving tile.
+% \begin{macrocode}
+ \str_set:Nx \l_@@_tmpa_str
+ {\pgfkeysvalueof{/tikz/Penrose/alignment~ edge}}
+ \str_set:Nx \l_@@_tmpa_str {\str_head:N \l_@@_tmpa_str}
+ \str_put_right:Nx \l_@@_tmpa_str
+ {\pgfkeysvalueof{/tikz/Penrose/alignment~ new~ edge}}
+ \str_set:Nx \l_@@_tmpb_str {\str_lowercase:f { \l_@@_tmpa_str}}
+ \str_if_eq:NNT \l_@@_tmpa_str \l_@@_tmpb_str
+ {
+ \str_set:Nx \l_@@_tmpb_str
+ {\str_uppercase:f { \l_@@_tmpa_str}}
+ }
+
+ \@@_transform_side:nV {#1} \l_@@_tmpb_str
+ \fi
+% \end{macrocode}
+% Now that the transformation is finalised, we can render the tile.
+% We clip against the tile path so that the tiles don't ``bleed''.
+% If we didn't do this, drawing the tile would result in overlaps which can look a bit ugly.
+% On the other hand, tight clipping can lead to ``gaps'' between the tiles so we make this optional by enclosing it in a style.
+% \begin{macrocode}
+ \UsePenroseTile[
+ every~ Penrose~ tile~ clip/.try,
+ every~ #1~ clip/.try
+ ]{#1}
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ #1/.try,
+ pic~ actions
+ ]{#1}
+% Lastly, we put coordinates at each vertex, labelled by which edge they are.
+% \begin{macrocode}
+ \@@_coordinates_at_vertices:n {#1}
+ \end{scope}
+ },
+% \end{macrocode}
+% This is a shortcut for installing the \Verb+pic+ type.
+% \begin{macrocode}
+ #1/.style={
+ every~ Penrose~ pic/.try,
+ pic~ type=#1,
+ },
+ }
+}
+% \end{macrocode}
+% \end{function}
+%
+%
+% \subsection{Lindenmayer System}
+%
+% This is an implementation of the Lindenmayer System description of Penrose tilings as a way of generating tilings from a specific starting seed.
+%
+% The implementation uses \Verb+prop+s to store \emph{rules} and \emph{actions}.
+% The rules are used to expand the starting seed to a certain level, after which the actions are carried out.
+% The syntax is based on the PGF library, but as we're already using \LaTeX3 it is reimplemented in that.
+%
+% These are the rules for generating rhombus tilings.
+% \begin{macrocode}
+\prop_new:N \g_@@_rhombus_lms_rule_prop
+\prop_gput:Nnn \g_@@_rhombus_lms_rule_prop {T} {[f*sT][f>g]}
+\prop_gput:Nnn \g_@@_rhombus_lms_rule_prop {t} {[f_st][f>G]}
+\prop_gput:Nnn \g_@@_rhombus_lms_rule_prop {G} {[f+sG][sf>g][sf*sT]}
+\prop_gput:Nnn \g_@@_rhombus_lms_rule_prop {g} {[f-sg][sf>G][sf_st]}
+% \end{macrocode}
+%
+% These are the rules for generating kite and dart tilings.
+% \begin{macrocode}
+\prop_new:N \g_@@_kite_lms_rule_prop
+\prop_gput:Nnn \g_@@_kite_lms_rule_prop {T} {[f*sT][f>st][+sg]}
+\prop_gput:Nnn \g_@@_kite_lms_rule_prop {t} {[f_st][f>sT][-sG]}
+\prop_gput:Nnn \g_@@_kite_lms_rule_prop {G} {[f*+sG][sT]}
+\prop_gput:Nnn \g_@@_kite_lms_rule_prop {g} {[f-_sg][st]}
+% \end{macrocode}
+%
+% These are the rules for generating pentagon tilings.
+% \begin{macrocode}
+\prop_new:N \g_@@_pentagon_lms_rule_prop
+\prop_gput:Nnn \g_@@_pentagon_lms_rule_prop {P}
+{[s>P][1sF+Q][1+sF+Q][1*sF+Q][1-sF+Q][1_sF+Q]} % pentagon 5
+\prop_gput:Nnn \g_@@_pentagon_lms_rule_prop {Q}
+{[s>P][1+sFR][1*sF*R][1-sF+Q][1_sF+Q][1sF+Q][->fsD]} % pentagon 3
+\prop_gput:Nnn \g_@@_pentagon_lms_rule_prop {R}
+{[s>P][1-sF+Q][1+sF*R][1*sFR][1_sF*R][1sFR][_>fsD][>fsD]} % pentagon 2
+\prop_gput:Nnn \g_@@_pentagon_lms_rule_prop {G}
+{
+ [s>G]
+ [se[>d+R][e1B]]
+ [+se[>d+R][e1B]]
+ [-se[>d+R][e1B]]
+ [*se[>d+R][e1B]]
+ [_se[>d+R][e1B]]
+} % pentagram
+\prop_gput:Nnn \g_@@_pentagon_lms_rule_prop {B}
+{
+ [s>G]
+ [se[>d+R][e1B]]
+ [+se[>d+R][e1B]]
+ [-se[>d+R][e1B]]
+} % boat
+\prop_gput:Nnn \g_@@_pentagon_lms_rule_prop {D}
+{[s>d+R][s>eG][se1B]} % diamond
+% \end{macrocode}
+%
+% Each of the standard tilings can also be drawn using triangles using the same rules.
+% \begin{macrocode}
+\prop_gset_eq:NN \g_@@_rtriangle_lms_rule_prop
+\g_@@_rhombus_lms_rule_prop
+\prop_gset_eq:NN \g_@@_ktriangle_lms_rule_prop
+\g_@@_kite_lms_rule_prop
+% \end{macrocode}
+%
+% These hold the various actions.
+% \begin{macrocode}
+\prop_new:N \g_@@_default_lms_action_prop
+\prop_new:N \g_@@_rhombus_lms_action_prop
+\prop_new:N \g_@@_kite_lms_action_prop
+\prop_new:N \g_@@_rtriangle_lms_action_prop
+\prop_new:N \g_@@_ktriangle_lms_action_prop
+\prop_new:N \g_@@_pentagon_lms_action_prop
+% \end{macrocode}
+%
+% We need some parameters.
+% \begin{macrocode}
+\dim_new:N \l_@@_step_dim
+\dim_set:Nn \l_@@_step_dim {1cm}
+% \end{macrocode}
+%
+% These are the defaults, which will be used in all the rule sets.
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_default_lms_action_prop {[} {\group_begin:}
+\prop_gput:Nnn \g_@@_default_lms_action_prop {]} {\group_end:}
+\prop_gput:Nnn \g_@@_default_lms_action_prop {f}
+{\pgftransformxshift{\l_@@_step_dim}}
+\prop_gput:Nnn \g_@@_default_lms_action_prop {s} {
+ \fp_set:Nn \l_@@_tmpa_fp { 2 * sind(18) * \l_@@_step_dim }
+ \dim_set:Nn \l_@@_step_dim {\fp_to_dim:N \l_@@_tmpa_fp}
+}
+% \end{macrocode}
+%
+% The rhombus rules need a variety of turns.
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_rhombus_lms_action_prop {+}
+{\pgftransformrotate{144}}
+\prop_gput:Nnn \g_@@_rhombus_lms_action_prop {*}
+{\pgftransformrotate{108}}
+\prop_gput:Nnn \g_@@_rhombus_lms_action_prop {-}
+{\pgftransformrotate{216}}
+\prop_gput:Nnn \g_@@_rhombus_lms_action_prop {_}
+{\pgftransformrotate{252}}
+\prop_gput:Nnn \g_@@_rhombus_lms_action_prop {>}
+{\pgftransformrotate{180}}
+% \end{macrocode}
+%
+% Up to now, the actions for the rhombus and its triangle replacement are the same.
+% \begin{macrocode}
+\prop_gset_eq:NN \g_@@_rtriangle_lms_action_prop
+\g_@@_rhombus_lms_action_prop
+% \end{macrocode}
+%
+% Now we do the actions that actually draw something.
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_rhombus_lms_action_prop {T} {
+ \group_begin:
+% \end{macrocode}
+% As we go through, we keep track of how many tiles we've drawn.
+% \begin{macrocode}
+ \int_gincr:N \g_@@_tile_int
+% \end{macrocode}
+% Set up the position, size, and angle correctly.
+% \begin{macrocode}
+ \pgftransformrotate{198}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*2*cosd(18)}
+ \pgftransformxshift{-\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+% \end{macrocode}
+% Now we draw the thin rhombus, applying every style we can possibly imagine.
+% The \Verb+Penrose tile+ style gets the current tile and total tile numbers passed to it.
+% \begin{macrocode}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ thin~ rhombus/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{thin~rhombus}
+ \group_end:
+}
+% \end{macrocode}
+%
+% Same for the thick rhombus.
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_rhombus_lms_action_prop {G} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)/(2*cosd(36))}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ thick~ rhombus/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{thick~rhombus}
+ \group_end:
+}
+% \end{macrocode}
+%
+% Now we do the same for the kite and dart tiling.
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_kite_lms_action_prop {+} {\pgftransformrotate{36}}
+\prop_gput:Nnn \g_@@_kite_lms_action_prop {*} {\pgftransformrotate{108}}
+\prop_gput:Nnn \g_@@_kite_lms_action_prop {-} {\pgftransformrotate{-36}}
+\prop_gput:Nnn \g_@@_kite_lms_action_prop {_}
+{\pgftransformrotate{-108}}
+\prop_gput:Nnn \g_@@_kite_lms_action_prop {>} {\pgftransformrotate{180}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gset_eq:NN \g_@@_ktriangle_lms_action_prop
+\g_@@_kite_lms_action_prop
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_kite_lms_action_prop {T} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{36}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ kite/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{kite}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_kite_lms_action_prop {g} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{144}
+ \pgftransformxshift{-\l_@@_step_dim * 2 * sin(18)}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ dart/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{dart}
+ \group_end:
+}
+% \end{macrocode}
+%
+% Now we set up the actions for the triangle variations.
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_rtriangle_lms_action_prop {T} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{18}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ reverse~ golden~ triangle/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{reverse~ golden~ triangle}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_rtriangle_lms_action_prop {t} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{-18}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ golden~ triangle/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{golden~ triangle}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_rtriangle_lms_action_prop {G} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{180}
+ \pgftransformxshift{-\l_@@_step_dim}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)/(2*cosd(36))}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ reverse~ golden~ gnomon/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{reverse~ golden~ gnomon}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_rtriangle_lms_action_prop {g} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{180}
+ \pgftransformxshift{-\l_@@_step_dim}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)/(2*cosd(36))}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ golden~ gnomon/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{golden~ gnomon}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_ktriangle_lms_action_prop {T} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{18}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ reverse~ golden~ triangle/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{reverse~ golden~ triangle}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_ktriangle_lms_action_prop {t} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{-18}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ golden~ triangle/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{golden~ triangle}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_ktriangle_lms_action_prop {G} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{180}
+ \pgftransformxshift{-\l_@@_step_dim}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)/(2*cosd(36))}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ reverse~ golden~ gnomon/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{reverse~ golden~ gnomon}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_ktriangle_lms_action_prop {g} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{180}
+ \pgftransformxshift{-\l_@@_step_dim}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)/(2*cosd(36))}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ golden~ gnomon/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{golden~ gnomon}
+ \group_end:
+}
+% \end{macrocode}
+%
+% Now we do the same for the pentagonal tilings.
+%
+% The rules need a variety of turns.
+% \begin{macrocode}
+\int_new:N \l_@@_pentagon_parity_int
+\seq_new:N \l_@@_pentagon_parity_seq
+\seq_set_from_clist:Nn \l_@@_pentagon_parity_seq {odd,even}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {1} {
+ \int_set:Nn \l_@@_pentagon_parity_int
+ {3 - \l_@@_pentagon_parity_int}
+ }
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {+}
+{\pgftransformrotate{72}}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {*}
+{\pgftransformrotate{144}}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {-}
+{\pgftransformrotate{288}}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {_}
+{\pgftransformrotate{216}}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {>}
+{\pgftransformrotate{180}}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {|}
+{\pgftransformxscale{-1}}
+% \end{macrocode}
+% The scale factor is different.
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {s} {
+ \fp_set:Nn \l_@@_tmpa_fp
+ {
+ 1/(2 + 2 * cosd(72) ) * \l_@@_step_dim
+ }
+ \dim_set:Nn \l_@@_step_dim {\fp_to_dim:N \l_@@_tmpa_fp}
+}
+% \end{macrocode}
+% And we tend to work better vertically.
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {f} {
+ \fp_set:Nn \l_@@_tmpa_fp { tand(54)/2 * \l_@@_step_dim }
+ \pgftransformyshift{\fp_to_dim:N \l_@@_tmpa_fp}
+}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {F} {
+ \fp_set:Nn \l_@@_tmpa_fp { tand(54) * \l_@@_step_dim }
+ \pgftransformyshift{\fp_to_dim:N \l_@@_tmpa_fp}
+}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {d} {
+ \fp_set:Nn \l_@@_tmpa_fp
+ {
+ (tand(54)/2 - tand(72)/2 + sind(36) ) * \l_@@_step_dim
+ }
+ \pgftransformyshift{\fp_to_dim:N \l_@@_tmpa_fp}
+}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {e} {
+ \fp_set:Nn \l_@@_tmpa_fp
+ {
+ tand(54) * cosd(36) * \l_@@_step_dim
+ }
+ \pgftransformyshift{\fp_to_dim:N \l_@@_tmpa_fp}
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {P} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/2}
+ \pgftransformxshift{-\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*tand(54)/2}
+ \pgftransformyshift{-\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ pentagon/.try,
+ every~
+ \seq_item:Nn \l_@@_pentagon_parity_seq
+ {\l_@@_pentagon_parity_int}
+ \space pentagon/.try,
+ every~ pentagon~ 5/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{pentagon~5}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {Q} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/2}
+ \pgftransformxshift{-\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*tand(54)/2}
+ \pgftransformyshift{-\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ pentagon/.try,
+ every~
+ \seq_item:Nn \l_@@_pentagon_parity_seq
+ {\l_@@_pentagon_parity_int}
+ \space pentagon/.try,
+ every~ pentagon~ 3/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{pentagon~3}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {R} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/2}
+ \pgftransformxshift{-\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*tand(54)/2}
+ \pgftransformyshift{-\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ pentagon/.try,
+ every~
+ \seq_item:Nn \l_@@_pentagon_parity_seq
+ {\l_@@_pentagon_parity_int}
+ \space pentagon/.try,
+ every~ pentagon~ 2/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{pentagon~2}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {G} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+% \pgftransformrotate{198}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*cosd(72)}
+ \pgftransformxshift{\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*tand(54)*cosd(72)}
+ \pgftransformyshift{\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ pentagram/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{pentagram}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {B} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+% \pgftransformrotate{198}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*cosd(72)}
+ \pgftransformxshift{\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*tand(54)*cosd(72)}
+ \pgftransformyshift{\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ boat/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{boat}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\prop_gput:Nnn \g_@@_pentagon_lms_action_prop {D} {
+ \group_begin:
+ \int_gincr:N \g_@@_tile_int
+ \pgftransformrotate{90}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim*cosd(18)}
+ \pgftransformxshift{-\fp_to_dim:N \l_@@_tmpa_fp}
+ \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)}
+ \pgftransformscale{\fp_use:N \l_@@_tmpa_fp}
+ \tl_set:Nx \l_@@_tmpc_tl
+ {
+ {\int_use:N \g_@@_tile_int}
+ {\int_use:N \g_@@_tiles_int}
+ }
+ \UsePenroseTile[
+ every~ Penrose~ tile/.try,
+ every~ diamond/.try,
+ Penrose~ tile~ \int_use:N \g_@@_tile_int/.try,
+ Penrose~ tile/.try/.expand~ once=\l_@@_tmpc_tl
+ ]{diamond}
+ \group_end:
+}
+% \end{macrocode}
+%
+% \begin{macro}[internal]{\@@_make_lms:Nnnn}
+% This creates the token list of actions, starting with the seed.
+% The arguments are: a token list to store the result in, the name of the system, the number of iterations, and the initial state.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_make_lms:Nnnn #1#2#3#4
+{
+ \group_begin:
+% \end{macrocode}
+% On the first time round, we start with the given seed.
+% \begin{macrocode}
+ \tl_set:Nn \l_@@_tmpb_tl {#4}
+% \end{macrocode}
+% We repeat the specified number of times.
+% \begin{macrocode}
+ \prg_replicate:nn {#3} {
+% \end{macrocode}
+% Duplicate the current state.
+% \begin{macrocode}
+ \tl_set_eq:NN \l_@@_tmpa_tl \l_@@_tmpb_tl
+% \end{macrocode}
+% Clear the receiving token list.
+% \begin{macrocode}
+ \tl_clear:N \l_@@_tmpb_tl
+% \end{macrocode}
+% Walk through the current list, appending to the receiving list according to the rules.
+% \begin{macrocode}
+ \tl_map_inline:Nn \l_@@_tmpa_tl
+ {
+% \end{macrocode}
+% If a rule exists, copy that.
+% \begin{macrocode}
+ \prop_if_in:cnTF {g_@@_#2_lms_rule_prop} {##1}
+ {
+ \tl_put_right:Nx \l_@@_tmpb_tl
+ {\prop_item:cn {g_@@_#2_lms_rule_prop} {##1} }
+ }
+ {
+% \end{macrocode}
+% Otherwise, just copy the token.
+% \begin{macrocode}
+ \tl_put_right:Nn \l_@@_tmpb_tl {##1}
+ }
+ }
+ }
+% \end{macrocode}
+% We've done all this inside a group, now pass the result outside.
+% \begin{macrocode}
+ \tl_set:Nn \l_@@_tmpa_tl {
+ \group_end:
+ \tl_set:Nn #1
+ }
+ \tl_put_right:Nx \l_@@_tmpa_tl {{\tl_use:N \l_@@_tmpb_tl}}
+ \tl_use:N \l_@@_tmpa_tl
+}
+\cs_generate_variant:Nn \@@_make_lms:Nnnn {Nnnx}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\@@_invoke_lms:Nn}
+% This carries out the actions specified by the resulting rules.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_invoke_lms:Nn #1#2
+{
+ \group_begin:
+% \end{macrocode}
+% Walk through the given list, carrying out the corresponding action if it exists.
+% If not, look at the default.
+% Otherwise, just do nothing.
+% \begin{macrocode}
+ \tl_map_inline:Nn #1 {
+ \prop_if_in:cnTF {g_@@_#2_lms_action_prop} {##1}
+ {
+ \prop_item:cn {g_@@_#2_lms_action_prop} {##1}
+ }
+ {
+ \prop_if_in:cnT {g_@@_default_lms_action_prop} {##1}
+ {
+ \prop_item:cn {g_@@_default_lms_action_prop} {##1}
+ }
+ }
+ }
+ \group_end:
+}
+% \end{macrocode}
+% \end{macro}
+%
+% We keep track of the number of tiles.
+% \begin{macrocode}
+\int_new:N \g_@@_tile_int
+\int_new:N \g_@@_tiles_int
+% \end{macrocode}
+%
+% \begin{function}{\PenroseDecomposition}
+% This is the user macro to invoke the decomposition.
+% The arguments are: optional styles, the name, number of iterations, and starting seed.
+% \begin{macrocode}
+\NewDocumentCommand \PenroseDecomposition { O{} m m m }
+{
+ \group_begin:
+ \tikzset{#1}
+ \@@_make_lms:Nnnx \l_@@_tmpa_tl {#2} {#3} {#4}
+ \@@_count_lms:N \l_@@_tmpa_tl
+ \int_gzero:N \g_@@_tile_int
+ \int_set:Nn \l_@@_pentagon_parity_int {2}
+ \@@_invoke_lms:Nn \l_@@_tmpa_tl {#2}
+ \group_end:
+}
+% \end{macrocode}
+% \end{function}
+%
+% \begin{macro}[internal]{\@@_count_lms:N}
+% This counts the number of tiles in the string.
+% \begin{macrocode}
+\cs_new_nopar:Npn \@@_count_lms:N #1
+{
+ \int_gzero:N \g_@@_tiles_int
+ \tl_map_inline:Nn #1
+ {
+ \tl_if_eq:nnT {##1} {T}
+ {
+ \int_gincr:N \g_@@_tiles_int
+ }
+ \tl_if_eq:nnT {##1} {t}
+ {
+ \int_gincr:N \g_@@_tiles_int
+ }
+ \tl_if_eq:nnT {##1} {G}
+ {
+ \int_gincr:N \g_@@_tiles_int
+ }
+ \tl_if_eq:nnT {##1} {g}
+ {
+ \int_gincr:N \g_@@_tiles_int
+ }
+ }
+}
+% \end{macrocode}
+% \end{macro}
+%
+% This is a \Verb+\tikzset+ mechanism for setting the dimensions of the tiling.
+% \begin{macrocode}
+\tikzset{
+ Penrose~ step/.code={
+ \dim_set:Nn \l_@@_step_dim {#1}
+ }
+}
+% \end{macrocode}
+%
+% We're done with \LaTeX3, so turn off the syntax.
+% \begin{macrocode}
+\ExplSyntaxOff
+% \end{macrocode}
+%
+% \subsection{TikZ Pictures}
+%
+% New in TikZ3.0 is the ability to make pictures that can be reused.
+% Penrose tiles seems an obvious use for this.
+% These pictures can be placed alongside other tiles, matching by edge type.
+%
+% There are a variety of constants that are frequently used and reused, so we define them all here.
+% These are the PGF versions.
+%
+% \begin{macrocode}
+\pgfmathsetmacro\pr@chphi{cos(18)}
+\pgfmathsetmacro\pr@shphi{sin(18)}
+\pgfmathsetmacro\pr@cphi{cos(36)}
+\pgfmathsetmacro\pr@sphi{sin(36)}
+\pgfmathsetmacro\pr@invphi{2/(sqrt(5)+1)}
+\pgfmathsetmacro\pr@phi{(sqrt(5)+1)/2}
+\pgfmathsetmacro\pr@invphisq{\pr@invphi*\pr@invphi}
+\pgfmathsetmacro\pr@ominvphisq{\pr@invphi - \pr@invphisq}
+\pgfmathsetmacro\pr@ominvphi{1 - \pr@invphi}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\newif\if@edgealign
+\def\pr@getfirst#1#2\pr@stop{#1}%
+\def\test@edgealign#1{%
+ \pgfkeysgetvalue{/tikz/Penrose/alignment edge}{\@penrose@tmpa}%
+ \edef\@penrose@tmpb{#1}%
+ \edef\@penrose@tmpa{\expandafter\pr@getfirst\@penrose@tmpa.\pr@stop}%
+ \ifx\@penrose@tmpa\@penrose@tmpb
+ \@edgealigntrue
+ \else
+ \@edgealignfalse
+ \fi
+}%
+% \end{macrocode}
+%
+% \begin{macrocode}
+\newif\if@newedge
+\def\test@newedge#1{%
+ \pgfkeysgetvalue{/tikz/Penrose/alignment new edge}{\@penrose@tmpa}%
+ \edef\@penrose@tmpb{#1}%
+ \edef\@penrose@tmpa{\@penrose@tmpa}%
+ \ifx\@penrose@tmpa\@penrose@tmpb
+ \@newedgetrue
+ \else
+ \@newedgefalse
+ \fi
+}%
+% \end{macrocode}
+%
+% The implementation is essentially the same for each, so only the first will be commented.
+% \begin{macrocode}
+\tikzset{
+% \end{macrocode}
+% The key \Verb+align with=<tile> along <edge>+ is used to set the parameters for placing a tile next to an existing one.
+% For most tiles, that's enough to specify how the new tile should be placed.
+% Some, though, need more information.
+% For those, use \Verb+align with=<tile> along <edge> using <number>+.
+% \begin{macrocode}
+ align with/.code args={#1 along #2}{%
+ \pgfutil@in@{ using }{#2}
+ \ifpgfutil@in@%
+ \tikzset{
+ Penrose/alignment location=#1,
+ Penrose/alignment set edges=#2,
+ }%
+ \else
+ \tikzset{
+ Penrose/alignment location=#1,
+ Penrose/alignment edge=#2,
+ }%
+ \fi
+ },
+ Penrose/alignment set edges/.code args={#1 using #2}{%
+ \tikzset{
+ Penrose/alignment edge=#1,
+ Penrose/alignment new edge=#2
+ },
+ },
+ Penrose/alignment location/.initial={},
+ Penrose/alignment edge/.initial=a,
+ Penrose/alignment new edge/.initial={},
+% \end{macrocode}
+% Default clipping style.
+% \begin{macrocode}
+ every Penrose tile clip/.style={clip},
+% \end{macrocode}
+% This is the code for setting up a \Verb+pic+.
+% \begin{macrocode}
+ thin rhombus/.pic={
+ \begin{scope}
+% \end{macrocode}
+% Were we given a tile to align ourselves against?
+% \begin{macrocode}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+% \end{macrocode}
+% Yes, we were.
+% So we adjust our position accordingly.
+% The first job is to transform so that we're along the edge of the receiving tile.
+% \begin{macrocode}
+ \begingroup
+% \end{macrocode}
+% We get the locations of the start and end of the receiving tile.
+% As \Verb+pic+ sets the node prefix, we have to temporarily suspend that (hence working in a group).
+% \begin{macrocode}
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+% \end{macrocode}
+% We store the initial points in \Verb+\pgf@xa+ and \Verb+\pgf@ya+ but we want \Verb+\pgf@xb+ and \Verb+\pgf@yb+ to be a vector along the edge.
+% \begin{macrocode}
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+% \end{macrocode}
+% We shift to the start of the edge.
+% \begin{macrocode}
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+% \end{macrocode}
+% And normalise the vector along it.
+% \begin{macrocode}
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+% \end{macrocode}
+% Now rotate so that the \(x\)--axis lies along the edge.
+% \begin{macrocode}
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}
+% \end{macrocode}
+% The next job is to shift and rotate the current tile so that the correct edge ends up against the receiving tile.
+% \begin{macrocode}
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}b\relax
+ \pgftransformrotate{-18}%
+ \pgftransformshift{\pgfpoint{-\pr@chphi cm}{\pr@shphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}B\relax
+ \pgftransformrotate{18}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+ \pgftransformrotate{198}%
+ \pgftransformshift{\pgfpoint{-2*\pr@chphi cm}{0 cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+ \pgftransformrotate{162}%
+ \pgftransformshift{\pgfpoint{-\pr@chphi cm}{-\pr@shphi cm}}%
+ \fi\fi\fi\fi
+ \fi
+% \end{macrocode}
+% Now that the transformation is finalised, we can render the tile.
+% We clip against the tile path so that the tiles don't ``bleed''.
+% If we didn't do this, drawing the tile would result in overlaps which can look a bit ugly.
+% On the other hand, tight clipping can lead to ``gaps'' between the tiles so we make this optional by enclosing it in a style.
+% \begin{macrocode}
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every thin rhombus clip/.try
+ ]{thin rhombus}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every thin rhombus/.try,
+ pic actions
+ ]{thin rhombus}
+% \end{macrocode}
+% These draw the arcs that designate the joining rules.
+% We draw full circles so that it doesn't matter what shape the tiles are.
+% \begin{macrocode}
+ \UsePenroseTile[
+ every Penrose arc clip/.try,
+ every thin rhombus arc clip/.try
+ ]{thin rhombus}
+ \path[every circle arc/.try] (18:1) circle[radius=1/4];
+ \path[every long arc/.try] (-18:1) circle[radius=1/4];
+% \end{macrocode}
+% Lastly, we put coordinates at each vertex, labelled by which edge they are.
+% \begin{macrocode}
+\coordinate (-edge a start) at (0,0);
+\coordinate (-edge a end) at (18:1);
+\coordinate (-edge A start) at (18:1);
+\coordinate (-edge A end) at (2*\pr@chphi,0);
+\coordinate (-edge B start) at (2*\pr@chphi,0);
+\coordinate (-edge B end) at (-18:1);
+\coordinate (-edge b start) at (-18:1);
+\coordinate (-edge b end) at (0,0);
+ \end{scope}
+ },
+% \end{macrocode}
+% This is a shortcut for installing the \Verb+pic+ type.
+% \begin{macrocode}
+ thin rhombus/.style={
+ every Penrose pic/.try,
+ pic type=thin rhombus,
+ },
+% \end{macrocode}
+% Same again, but for the thick rhombus.
+% \begin{macrocode}
+ thick rhombus/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}b\relax
+ \pgftransformrotate{144}%
+ \pgftransformshift{\pgfpoint{-\pr@cphi cm}{-\pr@sphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}B\relax
+ \pgftransformrotate{36}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+ \pgftransformrotate{-36}%
+ \pgftransformshift{\pgfpoint{-\pr@cphi cm}{\pr@sphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+ \pgftransformrotate{216}%
+ \pgftransformshift{\pgfpoint{-2*\pr@cphi cm}{0 cm}}%
+ \fi\fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every thick rhombus clip/.try
+ ]{thick rhombus}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every thick rhombus/.try,
+ pic actions
+ ]{thick rhombus}
+ \UsePenroseTile[
+ every Penrose arc clip/.try,
+ every thick rhombus arc clip/.try
+ ]{thick rhombus}
+\path[every circle arc/.try] (2*\pr@cphi,0) circle[radius=1/4];
+\path[every long arc/.try] (0,0) circle[radius=3/4];
+\coordinate (-edge B start) at (0,0);
+\coordinate (-edge B end) at (36:1);
+\coordinate (-edge a start) at (36:1);
+\coordinate (-edge a end) at (2*\pr@cphi,0);
+\coordinate (-edge A start) at (2*\pr@cphi,0);
+\coordinate (-edge A end) at (-36:1);
+\coordinate (-edge b start) at (-36:1);
+\coordinate (-edge b end) at (0,0);
+ \end{scope}
+ },
+ thick rhombus/.style={
+ every Penrose pic/.try,
+ pic type=thick rhombus,
+ },
+% \end{macrocode}
+% Now the kite.
+% \begin{macrocode}
+ kite/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}c\relax
+ \pgftransformrotate{-72}%
+ \pgftransformshift{\pgfpoint{-\pr@cphi cm}{\pr@sphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}C\relax
+ \pgftransformrotate{-108}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+ \pgftransformrotate{36}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+ \pgftransformrotate{144}%
+ \pgftransformshift{\pgfpoint{-\pr@cphi cm}{-\pr@sphi cm}}%
+ \fi\fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every kite clip/.try
+ ]{kite}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every kite/.try,
+ pic actions
+ ]{kite}
+ \UsePenroseTile[
+ every Penrose arc clip/.try,
+ every kite arc clip/.try
+ ]{kite}
+\path[every circle arc/.try] (0,0) circle[radius=\pr@invphi];
+\path[every long arc/.try] (1,0) circle[radius=\pr@invphisq];
+\coordinate (-edge a start) at (0,0);
+\coordinate (-edge a end) at (36:1);
+\coordinate (-edge c start) at (36:1);
+\coordinate (-edge c end) at (1,0);
+\coordinate (-edge C start) at (1,0);
+\coordinate (-edge C end) at (-36:1);
+\coordinate (-edge A start) at (-36:1);
+\coordinate (-edge A end) at (0,0);
+ \end{scope}
+ },
+% \end{macrocode}
+% The dart is next.
+% \begin{macrocode}
+ dart/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}c\relax
+ \pgftransformrotate{108}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}C\relax
+ \pgftransformrotate{72}%
+ \pgftransformshift%
+ {\pgfpoint{\pr@invphi*\pr@shphi cm}{-\pr@invphi*\pr@chphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+ \pgftransformrotate{-36}%
+ \pgftransformshift%
+ {\pgfpoint{\pr@invphi*\pr@shphi cm}{\pr@invphi*\pr@chphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+ \pgftransformrotate{216}%
+ \pgftransformshift{\pgfpoint{-\pr@invphi cm}{0 cm}}%
+ \fi\fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every dart clip/.try
+ ]{dart}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every dart/.try,
+ pic actions
+ ]{dart}
+ \UsePenroseTile[
+ every Penrose arc clip/.try,
+ every dart arc clip/.try
+ ]{dart}
+\path[every circle arc/.try] (\pr@invphi,0) circle[radius=\pr@ominvphi];
+\path[every long arc/.try] (0,0) circle[radius=\pr@ominvphisq];
+\coordinate (-edge c start) at (0,0);
+\coordinate (-edge c end) at (108:\pr@invphi);
+\coordinate (-edge a start) at (108:\pr@invphi);
+\coordinate (-edge a end) at (\pr@invphi,0);
+\coordinate (-edge A start) at (\pr@invphi,0);
+\coordinate (-edge A end) at (-108:\pr@invphi);
+\coordinate (-edge C start) at (-108:\pr@invphi);
+\coordinate (-edge C end) at (0,0);
+ \end{scope}
+ },
+ kite/.style={
+ every Penrose pic/.try,
+ pic type=kite,
+ },
+ dart/.style={
+ every Penrose pic/.try,
+ pic type=dart,
+ },
+% \end{macrocode}
+% The golden triangle.
+% \begin{macrocode}
+ golden triangle/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}B\relax
+ \pgftransformrotate{18}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}C\relax
+ \pgftransformrotate{-90}%
+ \pgftransformshift{\pgfpoint{-\pr@chphi cm}{\pr@shphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+ \pgftransformrotate{162}%
+ \pgftransformshift{\pgfpoint{-\pr@chphi cm}{-\pr@shphi cm}}%
+ \fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every golden triangle clip/.try
+ ]{golden triangle}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every golden triangle/.try,
+ pic actions
+ ]{golden triangle}
+\coordinate (-edge a start) at (0,0);
+\coordinate (-edge a end) at (18:1);
+\coordinate (-edge c start) at (18:1);
+\coordinate (-edge c end) at (-18:1);
+\coordinate (-edge b start) at (-18:1);
+\coordinate (-edge b end) at (0,0);
+ \end{scope}
+ },
+ golden triangle/.style={
+ every Penrose pic/.try,
+ pic type=golden triangle,
+ },
+% \end{macrocode}
+% The reverse golden triangle (is there a better name?).
+% \begin{macrocode}
+ reverse golden triangle/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}b\relax
+ \pgftransformrotate{162}%
+ \pgftransformshift{\pgfpoint{-\pr@chphi cm}{-\pr@shphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}c\relax
+ \pgftransformrotate{-90}%
+ \pgftransformshift{\pgfpoint{-\pr@chphi cm}{\pr@shphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+ \pgftransformrotate{18}%
+ \fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every reverse golden triangle clip/.try
+ ]{reverse golden triangle}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every reverse golden triangle/.try,
+ pic actions
+ ]{reverse golden triangle}
+\coordinate (-edge B start) at (0,0);
+\coordinate (-edge B end) at (18:1);
+\coordinate (-edge C start) at (18:1);
+\coordinate (-edge C end) at (-18:1);
+\coordinate (-edge A start) at (-18:1);
+\coordinate (-edge A end) at (0,0);
+ \end{scope}
+ },
+ reverse golden triangle/.style={
+ every Penrose pic/.try,
+ pic type=reverse golden triangle,
+ },
+% \end{macrocode}
+% The golden gnomon.
+% \begin{macrocode}
+ golden gnomon/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}c\relax
+ \pgftransformrotate{144}%
+ \pgftransformshift{\pgfpoint{-\pr@cphi cm}{-\pr@sphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}B\relax
+ \pgftransformrotate{-144}%
+ \pgftransformshift{\pgfpoint{-2*\pr@cphi cm}{0 cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+ \fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every golden gnomon clip/.try
+ ]{golden gnomon}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every golden gnomon/.try,
+ pic actions
+ ]{golden gnomon}
+\coordinate (-edge C start) at (0,0);
+\coordinate (-edge C end) at (36:1);
+\coordinate (-edge b start) at (36:1);
+\coordinate (-edge b end) at (2*\pr@cphi,0);
+\coordinate (-edge A start) at (2*\pr@cphi,0);
+\coordinate (-edge A end) at (0,0);
+ \end{scope}
+ },
+ golden gnomon/.style={
+ every Penrose pic/.try,
+ pic type=golden gnomon,
+ },
+% \end{macrocode}
+% The reverse golden gnomon.
+% \begin{macrocode}
+ reverse golden gnomon/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}C\relax
+ \pgftransformrotate{36}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}b\relax
+ \pgftransformrotate{-36}%
+ \pgftransformshift{\pgfpoint{-\pr@cphi cm}{\pr@sphi cm}}%
+ \else
+ \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+ \pgftransformrotate{180}%
+ \pgftransformshift{\pgfpoint{-2*\pr@cphi cm}{0 cm}}%
+ \fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every reverse golden gnomon clip/.try
+ ]{reverse golden gnomon}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every reverse golden gnomon/.try,
+ pic actions
+ ]{reverse golden gnomon}
+\coordinate (-edge a start) at (0,0);
+\coordinate (-edge a end) at (2*\pr@cphi,0);
+\coordinate (-edge B start) at (2*\pr@cphi,0);
+\coordinate (-edge B end) at (-36:1);
+\coordinate (-edge c start) at (-36:1);
+\coordinate (-edge c end) at (0,0);
+ \end{scope}
+ },
+ reverse golden gnomon/.style={
+ every Penrose pic/.try,
+ pic type=reverse golden gnomon,
+ },
+% \end{macrocode}
+% The primary pentagon.
+% \begin{macrocode}
+ pentagon 5/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \test@newedge{1}%
+ \if@newedge
+ \pgftransformrotate{180}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \test@newedge{2}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+ \pgftransformrotate{108}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \test@newedge{3}%
+ \if@newedge
+ \pgftransformshift%
+ {\pgfpoint{\pr@phi * \pr@shphi cm}{- \pr@phi * \pr@chphi cm}}%
+ \pgftransformrotate{36}%
+ \else
+ \test@newedge{4}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{- \pr@shphi cm}{-\pr@chphi cm}}%
+ \pgftransformrotate{-36}%
+ \else
+ \test@newedge{5}%
+ \if@newedge
+ \pgftransformrotate{-108}%
+ \fi\fi\fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every pentagon clip/.try,
+ every pentagon 5 clip/.try
+ ]{pentagon 5}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every pentagon/.try,
+ every pentagon 5/.try,
+ pic actions
+ ]{pentagon 5}
+\coordinate (-edge a1 start) at (0,0);
+\coordinate (-edge a1 end) at (1,0);
+\coordinate (-edge a2 start) at (1,0);
+\coordinate (-edge a2 end) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge a3 start) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge a3 end) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge a4 start) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge a4 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge a5 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge a5 end) at (0,0);
+ \end{scope}
+ },
+ pentagon 5/.style={
+ every Penrose pic/.try,
+ pic type=pentagon 5,
+ },
+% \end{macrocode}
+% The secondary pentagon.
+% \begin{macrocode}
+ pentagon 3/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \test@edgealign{a}%
+ \if@edgealign
+ \pgftransformrotate{180}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \test@edgealign{B}%
+ \if@edgealign%
+ \test@newedge{1}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+ \pgftransformrotate{108}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \pgftransformrotate{-108}%
+ \fi
+ \else
+ \test@newedge{1}%
+ \if@newedge
+ \pgftransformshift%
+ {\pgfpoint{\pr@phi * \pr@shphi cm}{- \pr@phi * \pr@chphi cm}}%
+ \pgftransformrotate{36}%
+ \else
+ \pgftransformshift{\pgfpoint{- \pr@shphi cm}{-\pr@chphi cm}}%
+ \pgftransformrotate{-36}%
+ \fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every pentagon clip/.try,
+ every pentagon 3 clip/.try
+ ]{pentagon 3}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every pentagon/.try,
+ every pentagon 3/.try,
+ pic actions
+ ]{pentagon 3}
+\coordinate (-edge A start) at (0,0);
+\coordinate (-edge A end) at (1,0);
+\coordinate (-edge b1 start) at (1,0);
+\coordinate (-edge b1 end) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge a1 start) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge a1 end) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge a2 start) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge a2 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge b2 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge b2 end) at (0,0);
+ \end{scope}
+ },
+ pentagon 3/.style={
+ every Penrose pic/.try,
+ pic type=pentagon 3,
+ },
+% \end{macrocode}
+% The tertiary pentagon.
+% \begin{macrocode}
+ pentagon 2/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \test@edgealign{D}%
+ \if@edgealign
+ \pgftransformrotate{180}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \test@edgealign{a}%
+ \if@edgealign%
+ \test@newedge{1}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+ \pgftransformrotate{108}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \pgftransformrotate{-108}%
+ \fi
+ \else
+ \test@newedge{1}%
+ \if@newedge
+ \pgftransformshift%
+ {\pgfpoint{\pr@phi * \pr@shphi cm}{- \pr@phi * \pr@chphi cm}}%
+ \pgftransformrotate{36}%
+ \else
+ \pgftransformshift{\pgfpoint{- \pr@shphi cm}{-\pr@chphi cm}}%
+ \pgftransformrotate{-36}%
+ \fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every pentagon clip/.try,
+ every pentagon 2 clip/.try
+ ]{pentagon 2}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every pentagon/.try,
+ every pentagon 2/.try,
+ pic actions
+ ]{pentagon 2}
+\coordinate (-edge d start) at (0,0);
+\coordinate (-edge d end) at (1,0);
+\coordinate (-edge A1 start) at (1,0);
+\coordinate (-edge A1 end) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge c1 start) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge c1 end) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge c2 start) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge c2 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge A2 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge A2 end) at (0,0);
+ \end{scope}
+ },
+ pentagon 2/.style={
+ every Penrose pic/.try,
+ pic type=pentagon 2,
+ },
+% \end{macrocode}
+% The pentagram.
+% \begin{macrocode}
+ pentagram/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \test@newedge{2}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+ \pgftransformrotate{72}%
+ \else
+ \test@newedge{3}%
+ \if@newedge
+ \pgftransformrotate{-72}%
+ \pgftransformshift{\pgfpoint{2 * \pr@shphi cm}{0 cm}}%
+ \else
+ \test@newedge{4}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1 cm + 2 * \pr@shphi cm}{0 cm}}%
+ \else
+ \test@newedge{5}%
+ \if@newedge
+ \pgftransformrotate{216}%
+ \pgftransformshift{\pgfpoint{\pr@cphi cm}{\pr@sphi cm}}%
+ \else
+ \test@newedge{6}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1cm}{0cm}}%
+ \pgftransformrotate{-72}%
+ \pgftransformshift{\pgfpoint{\pr@cphi cm}{\pr@sphi cm}}%
+ \else
+ \test@newedge{7}%
+ \if@newedge
+ \pgftransformrotate{144}%
+ \pgftransformshift{\pgfpoint{\pr@shphi cm}{\pr@chphi cm}}%
+ \else
+ \test@newedge{8}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1 cm + 2*\pr@shphi cm}{0cm}}%
+ \pgftransformrotate{216}%
+ \pgftransformshift{\pgfpoint{\pr@cphi cm}{\pr@sphi cm}}%
+ \else
+ \test@newedge{9}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{-2*\pr@shphi cm}{0cm}}%
+ \pgftransformrotate{72}%
+ \else
+ \test@newedge{10}%
+ \if@newedge
+ \pgftransformrotate{144}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \fi\fi\fi\fi\fi\fi\fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every pentagram clip/.try
+ ]{pentagram}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every pentagram/.try,
+ pic actions
+ ]{pentagram}
+\coordinate (-edge C1 start) at (1,0);
+\coordinate (-edge C1 end) at (0,0);
+\coordinate (-edge C2 start) at (0,0);
+\coordinate (-edge C2 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge C3 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge C3 end) at (-2*\pr@shphi,0);
+\coordinate (-edge C4 start) at (-2*\pr@shphi,0);
+\coordinate (-edge C4 end) at (-1-2*\pr@shphi,0);
+\coordinate (-edge C5 start) at (-1-2*\pr@shphi,0);
+\coordinate (-edge C5 end) at (-\pr@cphi,-\pr@sphi);
+\coordinate (-edge C6 start) at (-\pr@cphi,-\pr@sphi);
+\coordinate (-edge C6 end) at (-\pr@cphi-\pr@shphi,-\pr@sphi-\pr@chphi);
+\coordinate (-edge C7 start) at (-\pr@cphi-\pr@shphi,-\pr@sphi-\pr@chphi);
+\coordinate (-edge C7 end) at (-\pr@shphi,-\pr@chphi);
+\coordinate (-edge C8 start) at (-\pr@shphi,-\pr@chphi);
+\coordinate (-edge C8 end) at (1-\pr@cphi+\pr@shphi,-\pr@sphi-\pr@chphi);
+\coordinate (-edge C9 start) at (1-\pr@cphi+\pr@shphi,-\pr@sphi-\pr@chphi);
+\coordinate (-edge C9 end) at (1-\pr@cphi,-\pr@sphi);
+\coordinate (-edge C10 start) at (1-\pr@cphi,-\pr@sphi);
+\coordinate (-edge C10 end) at (1,0);
+ \end{scope}
+ },
+ pentagram/.style={
+ every Penrose pic/.try,
+ pic type=pentagram,
+ },
+% \end{macrocode}
+% The boat.
+% \begin{macrocode}
+ boat/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \test@edgealign{d}%
+ \if@edgealign
+ \pgftransformrotate{180}%
+ \pgftransformshift{\pgfpoint{\pr@cphi cm - 1cm}{\pr@sphi cm}}%
+ \else
+ \test@edgealign{b}%
+ \if@edgealign%
+ \test@newedge{2}%
+ \if@newedge
+ \pgftransformrotate{144}%
+ \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+ \else
+ \pgftransformrotate{216}%
+ \pgftransformshift{\pgfpoint{\pr@cphi cm}{\pr@sphi cm}}%
+ \fi
+ \else
+ \test@edgealign{c}%
+ \if@edgealign%
+ \test@newedge{2}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+ \pgftransformrotate{72}%
+ \else
+ \test@newedge{3}%
+ \if@newedge
+ \pgftransformrotate{-72}%
+ \pgftransformshift{\pgfpoint{2 * \pr@shphi cm}{0 cm}}%
+ \else
+ \test@newedge{4}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1 cm + 2 * \pr@shphi cm}{0 cm}}%
+ \else
+ \fi\fi\fi\fi\fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every boat clip/.try
+ ]{boat}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every boat/.try,
+ pic actions
+ ]{boat}
+\coordinate (-edge C1 start) at (1,0);
+\coordinate (-edge C1 end) at (0,0);
+\coordinate (-edge C2 start) at (0,0);
+\coordinate (-edge C2 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge C3 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge C3 end) at (-2*\pr@shphi,0);
+\coordinate (-edge C4 start) at (-2*\pr@shphi,0);
+\coordinate (-edge C4 end) at (-1-2*\pr@shphi,0);
+\coordinate (-edge B1 start) at (-1-2*\pr@shphi,0);
+\coordinate (-edge B1 end) at (-\pr@cphi,-\pr@sphi);
+\coordinate (-edge D start) at (-\pr@cphi,-\pr@sphi);
+\coordinate (-edge D end) at (1-\pr@cphi,-\pr@sphi);
+\coordinate (-edge B2 start) at (1-\pr@cphi,-\pr@sphi);
+\coordinate (-edge B2 end) at (1,0);
+ \end{scope}
+ },
+ boat/.style={
+ every Penrose pic/.try,
+ pic type=boat,
+ },
+% \end{macrocode}
+% The diamond.
+% \begin{macrocode}
+ diamond/.pic={
+ \begin{scope}
+ \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+ \ifx\prloc\pgfutil@empty
+ \else
+ \begingroup
+ \tikzset{name prefix ..}%
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+ \global\pgf@xa=\pgf@x
+ \global\pgf@ya=\pgf@y
+ \tikz@scan@one@point\pgfutil@firstofone%
+ (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+ \global\pgf@xb=\pgf@x
+ \global\pgf@yb=\pgf@y
+ \endgroup
+ \advance\pgf@xb by -\pgf@xa
+ \advance\pgf@yb by -\pgf@ya
+ \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+ \pgf@xb=\pgf@x
+ \pgf@yb=\pgf@y
+ \pgftransformtriangle%
+ {\pgfpoint{0pt}{0pt}}%
+ {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+ {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+ \test@edgealign{d}%
+ \if@edgealign%
+ \test@newedge{2}%
+ \if@newedge
+ \pgftransformshift{\pgfpoint{1cm}{0cm}}%
+ \pgftransformrotate{-162}%
+ \else
+ \pgftransformrotate{-18}%
+ \fi
+ \else
+ \test@newedge{2}%
+ \if@newedge
+ \pgftransformrotate{162}%
+ \pgftransformshift{\pgfpoint{- 2 * \pr@chphi cm}{0cm}}%
+ \else
+ \pgftransformshift{\pgfpoint{- \pr@cphi cm}{-\pr@sphi cm}}%
+ \pgftransformrotate{18}%
+ \fi\fi
+ \fi
+ \UsePenroseTile[
+ every Penrose tile clip/.try,
+ every diamond clip/.try
+ ]{diamond}
+ \UsePenroseTile[
+ every Penrose tile/.try,
+ every diamond/.try,
+ pic actions
+ ]{diamond}
+\coordinate (-edge D1 start) at (0,0);
+\coordinate (-edge D1 end) at (\pr@chphi,\pr@shphi);
+\coordinate (-edge B1 start) at (\pr@chphi,\pr@shphi);
+\coordinate (-edge B1 end) at (2*\pr@chphi,0);
+\coordinate (-edge B2 start) at (2*\pr@chphi,0);
+\coordinate (-edge B2 end) at (\pr@chphi,-\pr@shphi);
+\coordinate (-edge D2 start) at (\pr@chphi,-\pr@shphi);
+\coordinate (-edge D2 end) at (0,0);
+ \end{scope}
+ },
+ diamond/.style={
+ every Penrose pic/.try,
+ pic type=diamond,
+ },
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+%</package>
+% \end{macrocode}
+%
+% \end{implementation}
+%
+%\Finale
+\endinput