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author | Norbert Preining <norbert@preining.info> | 2023-06-06 03:01:00 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2023-06-06 03:01:00 +0000 |
commit | 81c6e34f9b4e2191ee45a1e3236d77914a7af519 (patch) | |
tree | 07469e76956f772db5be93f6b0ff0e5ee2516e9f /graphics/pgf/contrib/tilings | |
parent | efea33d6e2fb0152b0caee865514c497e12a0e8c (diff) |
CTAN sync 202306060300
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-rw-r--r-- | graphics/pgf/contrib/tilings/tilings.tex | 1159 | ||||
-rw-r--r-- | graphics/pgf/contrib/tilings/tilings_code.dtx | 3780 | ||||
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diff --git a/graphics/pgf/contrib/tilings/README b/graphics/pgf/contrib/tilings/README new file mode 100644 index 0000000000..975c66e2f3 --- /dev/null +++ b/graphics/pgf/contrib/tilings/README @@ -0,0 +1,8 @@ +---------------------------------------------------------------- +penrose --- TikZ library for producing tiling patterns +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 and similar tilings. diff --git a/graphics/pgf/contrib/tilings/tilings.pdf b/graphics/pgf/contrib/tilings/tilings.pdf Binary files differnew file mode 100644 index 0000000000..03349e4224 --- /dev/null +++ b/graphics/pgf/contrib/tilings/tilings.pdf diff --git a/graphics/pgf/contrib/tilings/tilings.tex b/graphics/pgf/contrib/tilings/tilings.tex new file mode 100644 index 0000000000..0ca5d2799d --- /dev/null +++ b/graphics/pgf/contrib/tilings/tilings.tex @@ -0,0 +1,1159 @@ +%\immediate\write18{tex tilings_code.dtx} +\documentclass{ltxdoc} +\usepackage[T1]{fontenc} +\usepackage{trace} +\usepackage{lmodern} +\usepackage{morefloats} +\usepackage{multicol} +\usepackage[svgnames]{xcolor} +\usepackage{tikz} +\usetikzlibrary{ + external, + tilings.polykite, + tilings.penrose +} + +\usepackage[numbered]{hypdoc} +\definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9} + +\usepackage{listings} +\lstloadlanguages{[LaTeX]TeX} +\lstset{ + breakatwhitespace=true, + breaklines=true, + language=[LaTeX]TeX, + basicstyle=\small\ttfamily, + keepspaces=true, + columns=fullflexible +} + +\usepackage{fancyvrb} + +\newenvironment{example} + {\VerbatimEnvironment + \begin{VerbatimOut}{example.out}} + {\end{VerbatimOut} + \begin{center} + \setlength{\parindent}{0pt} + \fbox{\begin{minipage}{.9\linewidth} + \lstinputlisting[]{example.out} + \end{minipage}} + + \fbox{\begin{minipage}{.9\linewidth} + \centering + \input{example.out} + \end{minipage}} +\end{center} +} + +\newenvironment{justexample} + {\VerbatimEnvironment + \begin{VerbatimOut}{example.out}} + {\end{VerbatimOut} + \begin{center} + \setlength{\parindent}{0pt} + \fbox{\begin{minipage}{.9\linewidth} + \lstinputlisting[]{example.out} + \end{minipage}} +\end{center} +} + +\colorlet{thinRhombus}{DarkOrchid} +\colorlet{thickRhombus}{DarkSlateGray} +\colorlet{circleArc}{RosyBrown} +\colorlet{longArc}{LawnGreen} + +\colorlet{kite}{HotPink} +\colorlet{dart}{Fuchsia} + +\colorlet{goldenTriangle}{Gold} +\colorlet{reverseGoldenTriangle}{Magenta} +\colorlet{goldenGnomon}{Cyan} +\colorlet{reverseGoldenGnomon}{LimeGreen} + +\makeatletter +\tikzset{ + tint fill colour/.code={% + \edef\@temp{% + \def\noexpand\tikz@fillcolor{\tikz@fillcolor!#1}% + \noexpand\tikz@addoption{\noexpand\pgfsetfillcolor{\tikz@fillcolor!#1}}% + }% + \@temp + } +} +\makeatother + + \tikzexternalize + \tikzsetexternalprefix{tiling-doc-} + +\providecommand*{\url}{\texttt} +\GetFileInfo{tikzlibrarytilings.code.tex} + +\title{The \textsf{Tilings} Package: Documentation} +\author{Andrew Stacey\texorpdfstring{\\ \url{loopspace@mathforge.org}}{}} + \date{\fileversion~from \filedate} + +\begin{document} + +\maketitle + +\tableofcontents + +\section{Introduction} + +The \textsf{Tilings} package is a TikZ library for drawing tiles and tilings, such as Penrose tilings (indeed, it was originally called the \textbf{Penrose} package). +It currently supports natively the various Penrose tile sets -- kite/dart, rhombus, and pentagon -- and the aperiodical polykites, but has provision for defining new tiles. +There are two main methods for their placement: one that automatically generates a tiling, and one that allows for ``by hand'' placement. +Furthermore, the tiles themselves can be deformed and will still (hopefully!) fit together in the correct fashion. + +\section{Initialisation} + +This is actually several libraries. +There is a core library called \Verb+tilings+ which defines the main functionality for working with tiles and tilings but which doesn't define any tiles itself. +For that, there are currently two sublibraries: +% +\begin{itemize} +\item \Verb+tilings.penrose+ for Penrose tiles, +\item \Verb+tilings.polykite+ for the aperiodical polykite tiles. +\end{itemize} +% +The sublibraries automatically load the core library. + +So to use this package, load the \Verb+tikz+ package and load one of the tilings libraries as a TikZ library. +Specifically, your preamble should contain: + +\begin{verbatim} +\usepackage{tikz} +\end{verbatim} + +\noindent and at least one of the following lines: + +\begin{verbatim} +\usetikzlibrary{tilings} +\usetikzlibrary{tilings.penrose} +\usetikzlibrary{tilings.polykite} +\end{verbatim} + +The original version of this package concerned itself only with Penrose tiles so was named \Verb+penrose+. +Since then it has been extended and is more general and so has been renamed \Verb+tilings+. +Some commands have been renamed, but there is a wrapper library which aims to provide backwards compatibility with the original naming scheme. +This is now the \Verb+penrose+ TikZ library, meaning that old documents that use the \Verb+penrose+ TikZ library should still work (please report any that don't on the \href{https://github.com/loopspace/penrose}{issue tracker}). +New documents shouldn't be written using it. + + +\section{Defining the Tiles} + +This package includes the capability to define new tiles. +The command to do this is: +% +\begin{verbatim} +\DefineTile{<name>}{<sides>}{<vertices>} +\end{verbatim} +% +For example, +% +\begin{verbatim} +\DefineTile {square}{a A a A} +{ + {0,0} + {1,0} + {1,1} + {0,1} +} +\end{verbatim} + +The \Verb!<sides>! is a list of letters representing sides for matching rules and positioning. +The first letter in the list corresponds to the edge between the first two vertices, through to the last side which corresponds to the edge between the last and first vertices. + +Each letter used matches against its opposite case (so it is possible to create a side that matches against itself by using a symbol that \TeX\ regards as having the same upper as lower case; not all symbols work, I've used numbers and \Verb+!+ successfully). +These are also used in path replacing, both a letter and its opposite case are replaced by the corresponding path (but in opposite directions) when the tile is ``baked''. + +The vertices can be written in cartesian form: \Verb+{<x>,<y>}+, or in polar: \Verb+{<angle>:<length>}+ (with the angle in degrees). +The vertex can be preceded by upto two \Verb!+! signs which have the same interpretation as in TikZ: the vertex description is taken relative to the previously saved point with a single \Verb!+! additionally not updating the last saved point. +The initial saved point is the origin, so the following defines a hexagonal tile. +% +\begin{verbatim} +\DefineTile {hexagon}{a A a A a A} +{ + +{0:1} + +{60:1} + +{120:1} + +{180:1} + +{240:1} + +{300:1} +} +\end{verbatim} + +The numbers are passed to the \Verb!fp! module of \LaTeX3 so can involve complicated expressions. +Note that the trigonometric functions for angles in degrees are \Verb!cosd!, \Verb!sind!, and \Verb!tand!. + +The tile must be baked via the command \Verb!\BakeTile! before it can be used. + +\begin{example} +\DefineTile {square}{a A a A} +{ + {0,0} + {1,0} + {1,1} + {0,1} +} + +\begin{tikzpicture} +\path[save tiling path=a] (0,0) to[out=45,in=135] (1,0); +\BakeTile{square} +\pic[square,name=A,fill=green]; +\pic[square,align with=A along a1 using 2,name=B,fill=red]; +\pic[square,align with=A along A1 using 2,fill=red]; +\pic[square,align with=A along A2 using 1,fill=red]; +\pic[square,align with=B along a1 using 2,fill=green]; +\pic[square,align with=B along a2 using 1,fill=green]; +\end{tikzpicture} +\end{example} + +\subsection{Predefined Tiles: Penrose} + +The sublibrary \Verb+tilings.penrose+ defines a slew of tiles based on Penrose tilings. + +\tikzset{ + every tile pic/.style={draw,ultra thick}, + every circle arc/.style={draw,thin}, + every long arc/.style={draw,thin}, +} + +\begin{itemize} +\item kite \tikz[baseline=-.5ex] \pic[draw,kite]; +\item dart \tikz[baseline=-.5ex] \pic[draw,dart]; +\item thin rhombus \tikz[baseline=-.5ex] \pic[draw,thin rhombus]; +\item thick rhombus \tikz[baseline=-.5ex] \pic[draw,thick rhombus]; +\item pentagon \(2\), \(3\), and \(5\) \tikz[baseline=-.5ex] \pic[draw, pentagon 5]; +The number signifies how many pentagons it goes next to. +\item pentagram \tikz[baseline=-.5ex] \pic[draw, pentagram]; +\item boat \tikz[baseline=-.5ex] \pic[draw, boat]; +\item diamond \tikz[baseline=-.5ex] \pic[draw, diamond]; +\item golden triangle \tikz[baseline=-.5ex] \pic[draw,golden triangle]; +\item reverse golden triangle \tikz[baseline=-.5ex] \pic[draw,reverse golden triangle]; +\item golden gnomon \tikz[baseline=-.5ex] \pic[draw,golden gnomon]; +\item reverse golden gnomon \tikz[baseline=-.5ex] \pic[draw,reverse golden gnomon]; +\end{itemize} + +The main tiles can have arcs drawn on them to illustrate the matching rules. +The triangles and gnomon are not true Penrose tiles but rather can be used to build tilings so they do not have the arcs. +The two types of each triangle and gnomon are actually different in that they have different matching rules. +This is best illustrated by deforming the paths (see Section~\ref{sec:pathdeform}). + +The edge labelling is as follows. +For the \Verb+pentagon 5+, for example, the edges are all the same and the numbers are used to distinguish between them. + +\begin{multicols}{2} + +\foreach \tile/\edges in { + kite/{a,A,c,C}, + dart/{a,A,c,C}, + thin rhombus/{a,A,b,B}, + thick rhombus/{a,A,b,B}, + pentagon 5/{a1,a2,a3,a4,a5}, + pentagon 3/{A,b1,a1,a2,b2}, + pentagon 2/{d,A1,e,c,A2}, + pentagram/{C1,E1,C2,E2,C3,E3,C4,E4,C5,E5}, + boat/{C1,E1,C2,E2,B1,D,B2}, + diamond/{D1,B1,B2,D2}, + golden triangle/{a,b,c}, + reverse golden triangle/{A,B,C}, + golden gnomon/{A,b,C}, + reverse golden gnomon/{a,B,c}} { + +\begin{tikzpicture} +\pic[draw,\tile,name=tile]; +\foreach \e in \edges { + \path (tile-edge \e\space start) -- node[fill=white,fill opacity=.5,text opacity=1] {\e} (tile-edge \e\space end); +} +\end{tikzpicture} + +} + +\end{multicols} + +\subsection{Predefined Tiles: Polykite} + +The sublibrary \Verb+tilings.polykite+ defines a slew of tiles based on the aperiodical polykite tilings as described in \href{https://arxiv.org/abs/2303.10798}{An Aperiodic Monotile} and \href{https://arxiv.org/abs/2305.17743}{A Chiral Aperiodic Monotile}. +It also defines a wrapper around the \Verb+\DefineTile+ command for creating one of the family of polykite tiles described in that article: + +\begin{verbatim} +\DefinePolykiteTile{<name>}{<a>}{<b>} +\DefinePolykiteTile*{<name>}{<a>}{<b>} +\DefinePolykiteTile{aperiodical hat}{sqrt(3)/2}{1/2} +\end{verbatim} + +The polykite tiles have two types of edge corresponding to the two lengths. +The starred option swaps the labels on these edges so that, for example, the hat and turtle tiles can be used in the same diagram. +Predefined polykite tiles are the \texttt{aperiodical hat}, \texttt{aperiodical turtle}, \texttt{spectral hat}, and \texttt{spectral turtle}. +The aperiodical versions can be swapped in for each other as they have the same edge labelling but the spectral versions have the opposite. +(In actual fact, the aperiodical and spectral hats are the same.) + +The equilateral polykite tile also exists as a \texttt{spectre} with alternating edge matching, as in the second paper \href{https://arxiv.org/abs/2305.17743}{A Chiral Aperiodic Monotile}. + +\begin{itemize} +\item Aperiodical Hat \tikz[baseline=-.5ex] \pic[draw,aperiodical hat]; +\item Aperiodical Turtle \tikz[baseline=-.5ex] \pic[draw,aperiodical turtle]; +\item Spectral Hat \tikz[baseline=-.5ex] \pic[draw,spectral hat]; +\item Spectral Turtle \tikz[baseline=-.5ex] \pic[draw,spectral turtle]; +\item Spectre \tikz[baseline=-.5ex] \pic[draw,spectre]; +\item Meta Cluster H \tikz[baseline=-.5ex] \pic[scale=.5,draw,meta cluster H]; +\item Meta Cluster F \tikz[baseline=-.5ex] \pic[scale=.5,draw,meta cluster F]; +\item Meta Cluster T \tikz[baseline=-.5ex] \pic[scale=.5,draw,meta cluster T]; +\item Meta Cluster P \tikz[baseline=-.5ex] \pic[scale=.5,draw,meta cluster P]; +\item Super Cluster H \tikz[baseline=-.5ex] \pic[scale=.3,draw,super cluster H]; +\item Super Cluster F \tikz[baseline=-.5ex] \pic[scale=.3,draw,super cluster F]; +\item Super Cluster T \tikz[baseline=-.5ex] \pic[scale=.3,draw,super cluster T]; +\item Super Cluster P \tikz[baseline=-.5ex] \pic[scale=.3,draw,super cluster P]; +\item Subcluster H \tikz[baseline=-.5ex] \pic[scale=.5,draw,subcluster H]; +\item Subcluster F \tikz[baseline=-.5ex] \pic[scale=.5,draw,subcluster F]; +\item Subcluster T \tikz[baseline=-.5ex] \pic[scale=.5,draw,subcluster T]; +\item Subcluster P \tikz[baseline=-.5ex] \pic[scale=.5,draw,subcluster P]; +\end{itemize} + +The edges of the meta and super cluster tiles are actually multi-edges for the matching rules. + +The subcluster tiles are a bit different to the others. +The \(H\) and \(T\) tiles are actually equilateral triangles but they have edge deformations applied by default so that they have the appearance of the aperiodical hat tile. +The \(P\) and \(F\) tiles have no area (so are not clipped by default) which means that the edge labels aren't fully clear as to which side they are on. +They match the diagrams given in the \href{https://arxiv.org/abs/2303.10798}{paper}, with the \(L\) sides being the sides labelled \(11\) and \(12\). + +\begin{multicols}{2} + +\tikzset{ + every super cluster scope/.style={ + scale=.3 + }, + every super cluster T scope/.style={every super cluster scope}, + every super cluster P scope/.style={every super cluster scope}, + every super cluster F scope/.style={every super cluster scope}, + every super cluster H scope/.style={every super cluster scope}, + every meta cluster scope/.style={ + scale=.7 + }, + every meta cluster T scope/.style={every meta cluster scope}, + every meta cluster P scope/.style={every meta cluster scope}, + every meta cluster F scope/.style={every meta cluster scope}, + every meta cluster H scope/.style={every meta cluster scope}, +} + +\foreach \tile/\edges in { + aperiodical hat/{11,21,22,23,24,12,13,25,26,14,15,27,28,16}, + aperiodical turtle/{11,21,22,23,24,12,13,25,26,14,15,27,28,16}, + spectral hat/{11,21,22,23,24,12,13,25,26,14,15,27,28,16}, + spectral turtle/{11,21,22,23,24,12,13,25,26,14,15,17,18,16}, + spectre/{a1,a2,a3,a4,a5,a6,a7,A1,A2,A3,A4,A5,A6,A7}, + meta cluster T/{A1,A2,b}, + meta cluster P/{A, 11, D1, d1, b, 12, D2, d2}, + meta cluster F/{11, D1, c, C, d1, b, 12, D2, d2}, + meta cluster H/{a, D1, d1, B1, D2, d2, B2, D3, d3}, + super cluster T/{A1,A2,b}, + super cluster P/{A, 11, D1, d1, b, 12, D2, d2}, + super cluster F/{11, D1, c, C, d1, b, 12, D2, d2}, + super cluster H/{a, D1, d1, B1, D2, d2, B2, D3, d3}, + subcluster T/{A1,A2,b}, + subcluster H/{B1,B2,a}, + subcluster P/{11, A, 12, b}, + subcluster F/{11, 12, F, f, b}% +}{ +\begin{tikzpicture} +\pic[draw,\tile,name=tile]; +\foreach \e in \edges { + \path (tile-edge \e\space start) -- node[fill=white,fill opacity=.5,text opacity=1] {\e} (tile-edge \e\space end); +} +\end{tikzpicture} + +} + +\end{multicols} + + +\section{Using the Tiles} + +\subsection{Positioning} + +The main way to use the tiles is via the \Verb+pic+ syntax that was introduced in TikZ3.0. +These are mini-drawings that are node-like in style, but a little more geared towards repeatable \emph{drawings} than boxes containing text. + +There are two ways in TikZ to specify the \Verb+pic+ type: either as the ``contents'' of the pic or as the argument to the \Verb+pic type+ key. +Each of the tiles comes with a shorthand key which specifies the \Verb+pic type+ and also invokes the keys \Verb+every tile pic+ and \Verb+every <tile type> pic+. +That is, the key \Verb+dart+ calls the \Verb+every tile pic+ and \Verb+every dart pic+ keys and specifies the \Verb+pic type+ as \Verb+dart+. + +The tiles can be placed using standard TikZ methods. +One important thing to note is that by default, \Verb+pic+s are like \Verb+nodes+ in that they only respond to ambient translations, and not to rotations and scaling. +To make them notice this, use the key \Verb+transform shape+ or specify the transformation to the \Verb+pic+ directly. +If the shortcut keys are used to specify the tiles, this can be put in the \Verb+every tile pic+ style. + +TikZ \Verb+pic+s can be named, using the \Verb+name=<name>+ key or using the \Verb+(name)+ syntax (see the TikZ documentation for more details). +When a tile has been named then it can be used for positioning other tiles. +Each edge is assigned a label and a new tile can be aligned with an old one along a matching edge (\Verb+a+ matches with \Verb+A+ and so on). + +To align a tile with an existing one, use the following key: +% +\begin{verbatim} +align with=<tile> along <edge> +\end{verbatim} +% +where \Verb+<tile>+ is the name given to an existing tile, and \Verb+<edge>+ is the label on the existing tile. +If the tile being placed has edges that are identical (for example, \Verb+pentagon 5+), this syntax extends to +% +\begin{verbatim} +align with=<tile> along <edge> using <number> +\end{verbatim} +% +to specify which of the edges on the new tile to use. + +Lastly, it is possible to reflect a tile either in use or in definition in which case the edges might be backwards so the key can be modified with the word \Verb+back+ as in: +% +\begin{verbatim} +align with=<tile> back along <edge> +\end{verbatim} +% +and similarly with \Verb+using ...+. + +A similar key can be used to place the tile so that an edge starts and ends at specified coordinates: +% +\begin{verbatim} +align between=<coordinate> and <coordinate> using <edge> +\end{verbatim} +% +Here, the \Verb+edge+ has to be specified in full since the start and end coordinates don't contain the information about which edge should stretch between them. +To obtain the equivalent of \Verb+back along+ then simply swap the coordinates. + +\begin{example} +\begin{tikzpicture} +\pic[kite,name=tile]; +\pic[dart,align with=tile along c]; +\pic[pentagon 5,name=ptile,at={(3,0)}]; +\pic[pentagon 3,align with=ptile along a1]; +\end{tikzpicture} +\end{example} + +With judicious use of loops, quite complicated pictures can be rendered using simple code. +(Note that the \Verb+transform shape+ is \emph{not} needed to apply the transformations needed to place a tile using this syntax.) + +\begin{example} +\begin{tikzpicture}[ + every rhombus/.style={ + draw=black, + ultra thick, + }, + every thin rhombus/.style={ + every rhombus/.try, + fill=thinRhombus, + }, + every thick rhombus/.style={ + every rhombus/.try, + fill=thickRhombus, + }, + every circle arc/.style={ + draw=circleArc + }, + every long arc/.style={ + draw=longArc + } +] +\pic[rotate=18,thick rhombus,name=a0]; +\foreach[evaluate=\k as \kmo using int(\k-1)] \k in {1,...,4} +{ + \pic[thick rhombus,name=a\k,align with={a\kmo} along A]; +} +\foreach \k in {0,...,4} +{ + \pic[thin rhombus,name=b\k,align with={a\k} along B]; + \pic[thick rhombus,name=c\k,align with={b\k} along A]; + \pic[thick rhombus,name=d\k,align with={b\k} along a]; + \pic[thick rhombus,name=e\k,align with={c\k} along A]; + \foreach \l/\a in {{0/b},{1/B}} + \pic[thin rhombus,name=f\k\l,align with={e\k} along \a]; +} +\pic[thin rhombus,name=g0,align with={f10} along a]; +\pic[thin rhombus,name=g1,align with={f21} along A]; +\foreach \l/\a in {{0/a},{1/A}} + \pic[thick rhombus,name=h\l,align with={g\l} along \a]; +\pic[thick rhombus,name=i,align with=g0 along B]; +\foreach \l/\a in {{0/a},{1/A}} + \pic[thick rhombus,name=j\l,align with=i along \a]; +\end{tikzpicture} +\end{example} + +\subsection{Styling} + +The tiles can be styled, either directly or using various keys. +When a tile is placed then there are various actions that happen with associated keys. +The actions and keys are: +% +\begin{enumerate} +\item A scope is started and the following keys are tried. +% +\begin{enumerate} +\item \Verb+every tile scope+ +\item \Verb+every <name> scope+ where \Verb+name+ is the tile name (not the pic name) +\item \Verb+this tile scope+ +\end{enumerate} + +\item The tile path is used with the intention of it being a clipping path. +The keys for this action are: +% +\begin{enumerate} +\item \Verb+every tile clip+ by default this is set to \Verb+clip+ +\item \Verb+every <name> clip+ +\item \Verb+this tile clip+ +\end{enumerate} + +\item A set of keys are used to allow arbitrary code to be executed before the tile path is rendered. +These are: + +\begin{enumerate} +\item \Verb+every tile before path+ +\item \Verb+every <name> before path+ +\item \Verb+this tile before path+ +\end{enumerate} + +\item The tile path is rendered. +The keys for this action are: +% +\begin{enumerate} +\item \Verb+every tile+ +\item \Verb+every <name>+ +\item \Verb+this tile+ +\item \Verb+pic actions+ +\end{enumerate} + +\item A set of keys are used to allow arbitrary code to be executed after the tile path is rendered. +These are: + +\begin{enumerate} +\item \Verb+every tile after path+ +\item \Verb+every <name> after path+ +\item \Verb+this tile after path+ +\end{enumerate} +\end{enumerate} + + +The \Verb+pic actions+ are any actions given directly to the tile, as in \Verb+\pic[draw,thin rhombus];+. +The kite, dart, and rhombus tiles also have arcs drawn on them which are inserted via the \Verb+every <name> after path+ keys, and these are themselves styled ussing \Verb+every circle arc+ and \Verb+every long arc+. +The names come from the way the arcs look on the rhombus shapes. + +One other point is important to note about the tiles. +They are actually clipped against themselves. +This ensures that the tiles do not overstep their bounds and so when placed alongside each other then they do not go over each other. +In practical terms, this means that if drawn then the line width is half that which might be expected (but when placed next to another tile, the two halves combine to the expected width). + +\subsection{Placing Tiles Automatically} + +There is a way to specify certain tilings using \emph{Lindenmayer systems}. +In brief, this takes a seed pattern and successively applies \emph{substitution rules} which are meant to simulate replacing a tile by smaller versions of it (and others from the same set). +This is implemented for the Penrose tiles and the various clusters related to the aperiodical polykite tile. + +The Penrose rules are \emph{positional} in that when replacing a Penrose tile by smaller versions of it the new tiles can be placed solely based on information about the position and orientation of the original tile. +This is true also for the \emph{super cluster} tiles of the aperiodical polykite, but not for the meta cluster or subclusters. + +The meta and subclusters work on a different system. +The structure that is built up is that of a \emph{tree} with a root tile. +That root tile is positioned, and then the other tiles are placed next to previously placed tiles. +This is a slower process and can mean that the overall shape is different to what might be expected, but from the user's perspective it is the same. + +The user command is one of: +% +\begin{verbatim} +\TilingDecomposition{<type>}{<level>}{<seed>} +\pic{decomposition={<type>}{<level>}{<seed>}}; +\end{verbatim} +% +where \Verb+<type>+ is one of: +% +\begin{itemize} +\item \Verb+kite+ for the kite and dart tiling, +\item \Verb+rhombus+ for the rhombus tiling, +\item \Verb+pentagon+ for the pentagon tiling. +\item \Verb+ktriangle+ for the triangular decomposition used to form the kite and dart tiling but with the individual triangles +\item \Verb+rtriangle+ for the triangular decomposition used to form the rhombus tiling but with the individual triangles. +\item \Verb+supercluster+ for the super cluster substitution system that works on a positional basis. +\item \Verb+cluster+ for the cluster substitution system that uses the neighbour information. +The choice of super, meta, or subcluster is determined by the value of the key \Verb!cluster type!. +\end{itemize} + +The \Verb+<seed>+ is a ``word'' that will be used to initiate the Lindenmayer system. +The key letters in the alphabet for the kite/darts and rhombuses are \Verb+T+, \Verb+t+, \Verb+G+, and \Verb+g+. +These actually correspond to the two triangles and two gnomons. +For the pentagons, the key letters are \Verb+P+, \Verb+Q+, \Verb+R+, \Verb+G+, \Verb+B+, \Verb+D+. +These correspond to the three pentagons, the pentagram, the boat, and the diamond. +For the clusters, the key letters are \Verb+H+, \Verb+T+, \Verb+P+, and \Verb+F+. +Other permitted letters are \Verb+[+, \Verb+]+, \Verb+s+, \Verb+f+, \Verb!+!, \Verb+*+, \Verb+-+, \Verb+_+, \Verb+>+. +These refer to various transformations (for details, see the implementation). + +The \Verb+<level>+ controls how far to take the iteration. +The code is not particularly optimised for speed, and once \Verb+<level>+ gets to about \(5\) or \(6\) then we are at the ``make a cup of tea while compiling'' stage, depending on the processor. + +\begin{example} +\begin{tikzpicture}[ + every tile/.style={draw}, + tiling step=2cm, +] +\TilingDecomposition{kite}{0}{T} +\end{tikzpicture} +\end{example} + +The two types of substitution rules -- positional and neighbourly -- are rendered slightly differently. +The positional tiles are drawn directly but the neighbour ones are drawn via the \Verb!\pic! mechanism. +This is to exploit the existing code for aligning against existing tiles. +This means that the \Verb!\pic! styling options are available for the latter type of decomposition but not for the former. +For the former, only the following keys are used: + +\begin{verbatim} +every tile +every <tile type> +\end{verbatim} + +There are, however, some additional styles which allow styling the tiles by their number: a count is kept of the number of tiles and each tile knows its own number. +Specifically, two keys are tried: +% +\begin{enumerate} +\item \Verb+tile <number>+, and +\item \Verb+tile={<number>}{<total>}+ +\end{enumerate} +% +A word of warning is in order on the second of these. +The \Verb+<total>+ is not guaranteed to be correct. +It is done by a quick count at the start of the process and counts those letters which \emph{might} result in a rendered tile. +Not every letter in the resulting word actually does. +Nevertheless, this can be used to style a tile based on what proportion of tiles have been rendered. + +Lastly, \Verb+tiling step+ is used to control the size of the resulting picture. + +\begin{example} +\begin{tikzpicture}[ + every tile/.style={draw}, + tiling step=4cm, + tile/.code 2 args={ + \pgfmathsetmacro\tint{100*#1/#2} + \pgfkeysalso{fill=black!\tint} + } +] +\TilingDecomposition{rhombus}{3}{T} +\end{tikzpicture} +\end{example} + +Here's the super, meta, and subcluster combinatorial decompositions. +These decompositions also define a style \Verb!first tile! which is applied to the initial tile (that isn't placed next to an existing tile). + +\begin{example} +\begin{tikzpicture}[ + every tile/.style={draw}, + first tile/.style={ + transform shape + }, +] + +\TilingDecomposition[scale=.25,cluster type=super cluster]{cluster}{1}{H} +\TilingDecomposition[xshift=3cm,scale=.5,cluster type=meta cluster]{cluster}{1}{H} +\TilingDecomposition[xshift=5cm,cluster type=subcluster]{cluster}{1}{H} +\end{tikzpicture} +\end{example} + +Here is a subcluster decomposition showing just the \(F_0\) and \(P_0\) tiles. + +\begin{example} +\begin{tikzpicture}[ + every tile/.style={}, + every tile pic/.style={}, + every subcluster F/.style={draw=magenta, ultra thin}, + every subcluster P/.style={draw=magenta, ultra thin}, +] +\pic[ + first tile/.style={transform shape}, + cluster type=subcluster, + scale=3 +] {decomposition={cluster}{3}{H}}; +\end{tikzpicture} +\end{example} + + +\section{Deforming Paths} +\label{sec:pathdeform} + +This package provides the ability to deform the edges of the tiles. +The tiles are built from labelled paths together with their reverses. +By changing these paths, one can get a wide variety of different tiles with the same fundamental matching rules. +Indeed, by using asymmetric paths, the matching rules can be enforced without the need for additional decoration. + +Internally, the \Verb+tiling+ library uses the \Verb+spath3+ package for storing and manipulating the paths. + +To create a new edge path, use the key \Verb+save tiling path=<edge>+ where \Verb+<edge>+ is a symbol used in the edge description of a tile. +There are no constraints on the size of the path as all paths are scaled and transformed to fit the tiles. +Once the edge paths have been specified, they are welded together into the tiles using the following command: +% +\begin{verbatim} +\BakeTile{<name>} +\end{verbatim} +% +Here, \Verb+<name>+ is one of the names of the tiles. +This has global effect, as does the definition of the edge paths. +Paths, both sides and tiles, can be cloned via: +% +\begin{verbatim} +\tikzset{clone tiling side path={target}{source}} +\tikzset{clone tile path={target}{source}} +\end{verbatim} +% +and restored with the same command (but names switched). + +\begin{example} +\begin{tikzpicture} +\pic[draw,dart,name=dart]; +\pic[draw,kite,align with=dart along c]; +\pic[draw,kite,align with=dart along C]; +\tikzset{clone tile path={original kite}{kite}} +\tikzset{clone tile path={original dart}{dart}} +\path[save tiling path=a] (0,0) to[out=-30,in=100] (1,0); +\path[save tiling path=c] (0,0) to[out=-40,in=140] (1,0); +\BakeTile{kite} +\BakeTile{dart} +\pic[xshift=2cm,draw,dart,name=dart]; +\pic[draw,kite,align with=dart along c]; +\pic[draw,kite,align with=dart along C]; +\tikzset{clone tile path={kite}{original kite}} +\tikzset{clone tile path={dart}{original dart}} +\pic[xshift=4cm,draw,dart,name=dart]; +\pic[draw,kite,align with=dart along c]; +\pic[draw,kite,align with=dart along C]; +\end{tikzpicture} +\end{example} + +With deformed tiles there is no guarantee that the inner arcs on the Penrose tiles will match up perfectly. + +Note that the subcluster tiles from the polykite subpackage are actually already deformed tiles. + +\begin{example} +\begin{tikzpicture}[ + every subcluster F/.style={draw, ultra thick}, + every subcluster P/.style={draw, thick}, + every subcluster H/.style={draw, fill, fill opacity=.5} +] +\pic[subcluster F, name=F1, this tile/.style={line width=1mm}]; +\pic[subcluster F, align with=F1 along 12 using 1, name=F2, this tile/.style={line width=1mm}]; +\pic[subcluster F, align with=F1 along 11 using 2, name=F3, this tile/.style={line width=1mm}]; +\pic[subcluster F, align with=F1 along F,name=F1-2]; +\pic[subcluster F, align with=F1 along f,name=F1-3]; +\pic[subcluster F, align with=F2 along F,name=F2-2]; +\pic[subcluster F, align with=F2 along f,name=F2-3]; +\pic[subcluster F, align with=F3 along F,name=F3-2]; +\pic[subcluster F, align with=F3 along f,name=F3-3]; +\pic[subcluster H, align with=F1 along b using 2, fill=red]; +\pic[subcluster H, align with=F2 along b using 2, fill=green]; +\pic[subcluster H, align with=F3 along b using 2, fill=blue]; +\pic[subcluster H, align with=F1-2 along b using 1, fill=yellow]; +\pic[subcluster H, align with=F2-2 along b using 1, fill=cyan]; +\pic[subcluster H, align with=F3-2 along b using 1, fill=magenta]; +\end{tikzpicture} +\end{example} + +\begin{example} +\begin{tikzpicture}[ + every tile pic/.style={}, +% every subcluster F/.style={draw, ultra thick}, +% every subcluster P/.style={draw, thick}, + every subcluster H/.style={draw, fill, fill opacity=.5} +] +\path[save tiling path=a] (0,0) -- (1,0); +\path[save tiling path=b] (0,0) -- (1,0); +\path[save tiling path=f] (0,0) -- (1,0); +\BakeTile{subcluster H} +\BakeTile{subcluster T} +\BakeTile{subcluster P} +\BakeTile{subcluster F} + +\pic[subcluster F, name=F1, this tile/.style={line width=1mm}]; +\pic[subcluster F, align with=F1 along 12 using 1, name=F2, this tile/.style={line width=1mm}]; +\pic[subcluster F, align with=F1 along 11 using 2, name=F3, this tile/.style={line width=1mm}]; +\pic[subcluster F, align with=F1 along F,name=F1-2]; +\pic[subcluster F, align with=F1 along f,name=F1-3]; +\pic[subcluster F, align with=F2 along F,name=F2-2]; +\pic[subcluster F, align with=F2 along f,name=F2-3]; +\pic[subcluster F, align with=F3 along F,name=F3-2]; +\pic[subcluster F, align with=F3 along f,name=F3-3]; +\pic[subcluster H, align with=F1 along b using 2, fill=red]; +\pic[subcluster H, align with=F2 along b using 2, fill=green]; +\pic[subcluster H, align with=F3 along b using 2, fill=blue]; +\pic[subcluster H, align with=F1-2 along b using 1, fill=yellow]; +\pic[subcluster H, align with=F2-2 along b using 1, fill=cyan]; +\pic[subcluster H, align with=F3-2 along b using 1, fill=magenta]; +\end{tikzpicture} +\end{example} + +The spectre tile, from \href{https://arxiv.org/abs/2305.17743}{A Chiral Aperiodic Monotile}, is a natural for deformation as that can be used to force aperiodicity. + +\begin{example} +\begin{tikzpicture}[ + every spectre/.style={ + draw, + thick, + }, + every tile pic/.style={scale=.5,rotate=105}, +] +\pic[spectre]; +\path[save tiling path=a] (0,0) to[out=30,in=150] (1,0); +\BakeTile{spectre} +\pic[spectre,at={(3,0)}]; +\path[save tiling path=a] (0,0) to[out=30,in=210] (1,0); +\BakeTile{spectre} +\pic[spectre,at={(6,0)}]; +\path[save tiling path=a] (0,0) .. controls +(30:1) and +(210:.75) .. (1,0); +\BakeTile{spectre} +\pic[spectre,at={(9,0)}]; +\end{tikzpicture} +\end{example} + +\section{More Examples} + +Let's set some aesthetically pleasing shapes. +Note that I'm using the TikZ \Verb!external! library in creating this document so to deform the paths in the examples I need to add the deformation code to every picture (otherwise the externalisation skips it). +I've saved it into a key \Verb!deform tiles! to avoid overwhelming the example code. +In a document without externalisation then adding the following code will achieve the same effect. + +\begin{justexample} +\begin{tikzpicture} +\path[save tiling path=a] (0,0) to[out=-30,in=100] (1,0); +\path[save tiling path=b] (0,0) to[out=0,in=140] (1,0); +\path[save tiling path=c] (0,0) to[out=-40,in=140] (1,0); +\BakeTile{thin rhombus} +\BakeTile{thick rhombus} +\BakeTile{golden triangle} +\BakeTile{reverse golden triangle} +\BakeTile{golden gnomon} +\BakeTile{reverse golden gnomon} +\BakeTile{kite} +\BakeTile{dart} +\end{tikzpicture} +\end{justexample} + +\tikzset{ + deform tiles/.code={% + \path[save tiling path=a] (0,0) to[out=-30,in=100] (1,0); + \path[save tiling path=b] (0,0) to[out=0,in=140] (1,0); + \path[save tiling path=c] (0,0) to[out=-40,in=140] (1,0); + \BakeTile{thin rhombus} + \BakeTile{thick rhombus} + \BakeTile{golden triangle} + \BakeTile{reverse golden triangle} + \BakeTile{golden gnomon} + \BakeTile{reverse golden gnomon} + \BakeTile{kite} + \BakeTile{dart} + } +} + +Styling the first tile. +Note that as the pattern is formed by repeating two different initial seeds \(5\) times, there are \(10\) ``first tiles'' in each overall pattern. + +\begin{example} +\begin{tikzpicture}[ + deform tiles/.try, + every tile/.style={draw}, + tile 1/.style={fill=yellow}, +] +\foreach \tp/\pos in {rhombus/0cm,rtriangle/2.5cm,kite/5cm,ktriangle/7.5cm} +{ +\begin{scope}[xshift=\pos] +\foreach[evaluate=\k as \mk using {\k+Mod(\k,2)},evaluate=\k as \ax using {Mod(\k,2) == 0 ? "T" : "t"}] \k in {0,...,9} { + \begin{scope}[rotate=\mk*36] + \TilingDecomposition{\tp}{1}{\ax} + \end{scope} +} +\end{scope} +} +\end{tikzpicture} +\end{example} + + + +A more detailed decomposition, with more and more tinting applied to each tile. +Roughly half of the counted tiles are rendered, and the ordering in which they are rendered is not at first an obvious one (though it is in general from ``outside in''). + +Note that the key \Verb+tint fill colour+ is not a TikZ native. +It is defined as: + +\begin{verbatim} +\makeatletter +\tikzset{ + tint fill colour/.code={% + \edef\@temp{% + \def\noexpand\tikz@fillcolor{\tikz@fillcolor!#1}% + \noexpand\tikz@addoption{% + \noexpand\pgfsetfillcolor{\tikz@fillcolor!#1}% + }% + }% + \@temp + } +} +\makeatother +\end{verbatim} + +\begin{example} +\begin{tikzpicture}[ + deform tiles/.try, + every tile/.style={draw}, + every kite/.style={fill=reverseGoldenTriangle}, + every dart/.style={fill=goldenTriangle}, + tile/.code 2 args={ + \pgfmathsetmacro\tint{100*(1 - 1.5*#1/#2))} + \pgfkeysalso{tint fill colour=\tint} + } +] +\foreach[evaluate=\k as \mk using {\k+Mod(\k,2)},evaluate=\k as \ax using {Mod(\k,2) == 0 ? "T" : "t"}] \k in {0,...,9} { + \begin{scope}[rotate=\mk*36] + \TilingDecomposition[tiling step=5cm]{kite}{4}{\ax} + \end{scope} +} +\end{tikzpicture} +\end{example} + +An example with ``manual placement''. + +\begin{example} +\begin{tikzpicture}[ + deform tiles/.try, + every tile/.style={ + draw=black, + ultra thick, + }, + every kite/.style={ + fill=kite, + }, + every dart/.style={ + fill=dart, + }, + every circle arc/.style={ + draw=circleArc + }, + every long arc/.style={ + draw=longArc + } +] +\pic[dart,name=a0]; +\foreach[evaluate=\k as \kmo using int(\k-1)] \k in {1,...,4} { + \pic[dart,name=a\k,align with={a\kmo} along a]; +} +\foreach \k in {0,...,4} { + \foreach \l/\e/\ee in {0/c/a,1/C/A} { + \pic[kite,name=b\l\k,align with={a\k} along \e]; + \pic[dart,name=c\l\k,align with={b\l\k} along \ee]; + \pic[kite,name=d\l\k,align with={c\l\k} along \e]; + } + \pic[kite,name=e\k,align with={c0\k} along C]; + \pic[dart,name=f\k,align with={c0\k} along a]; + \foreach \e in {c,C} { + \pic[kite,name=g\k,align with={f\k} along \e]; + } +} +\end{tikzpicture} +\end{example} + + +The decomposition rules for the Lindenmayer system can be illustrated by drawing each tile together with the result of one decomposition superimposed on top. + +\begin{example} +\foreach \ax in {T,t,G,g} { + +\begin{tikzpicture}[ + deform tiles/.try, +] +\foreach \tp/\pos in {rhombus/0cm,rtriangle/2cm,kite/4cm,ktriangle/6cm} +{ +\begin{scope}[xshift=\pos] + \TilingDecomposition[every path/.style={draw=red,ultra thick}]{\tp}{0}{\ax} + \TilingDecomposition[every path/.style={fill=gray!50,fill opacity=.5,draw=black}]{\tp}{1}{\ax} +\end{scope} +} +\end{tikzpicture} + +} +\end{example} + +The tiles can make interesting forms by themselves. + +\begin{example} +\begin{tikzpicture}[ + deform tiles/.try, + scale=2, + every tile pic/.style={ + transform shape, + }, + every golden triangle/.style={ + draw=black, + ultra thick, + fill=goldenTriangle, + }, + every reverse golden triangle/.style={ + draw=black, + ultra thick, + fill=reverseGoldenTriangle, + }, + every golden gnomon/.style={ + draw=black, + ultra thick, + fill=goldenGnomon, + }, + every reverse golden gnomon/.style={ + draw=black, + ultra thick, + fill=reverseGoldenGnomon, + }, +] +\pic[golden triangle,name=a]; +\pic[reverse golden triangle,align with=a along a]; +\pic[reverse golden triangle,align with=a along b]; +\pic[reverse golden triangle,align with=a along c]; +\begin{scope}[xshift=2cm] +\pic[reverse golden triangle,name=a]; +\pic[golden triangle,align with=a along A]; +\pic[golden triangle,align with=a along B]; +\pic[golden triangle,align with=a along C]; +\end{scope} +\begin{scope}[yshift=-3cm] +\pic[golden gnomon,name=a]; +\pic[reverse golden gnomon,align with=a along C]; +\pic[reverse golden gnomon,align with=a along b]; +\pic[reverse golden gnomon,align with=a along A]; +\begin{scope}[xshift=2cm] +\pic[reverse golden gnomon,name=a]; +\pic[golden gnomon,align with=a along c]; +\pic[golden gnomon,align with=a along B]; +\pic[golden gnomon,align with=a along a]; +\end{scope} +\end{scope} +\end{tikzpicture} +\end{example} + +\begin{example} +\begin{tikzpicture}[ + deform tiles/.try, + every rhombus/.style={ + draw=black, + ultra thick, + }, + every thin rhombus/.style={ + every rhombus/.try, + fill=thinRhombus, + }, + every thick rhombus/.style={ + every rhombus/.try, + fill=thickRhombus, + }, + every circle arc/.style={ + draw=circleArc + }, + every long arc/.style={ + draw=longArc + } +] +\pic[rotate=18,thick rhombus,name=a0]; +\foreach[evaluate=\k as \kmo using int(\k-1)] \k in {1,...,4} +{ + \pic[thick rhombus,name=a\k,align with={a\kmo} along A]; +} +\foreach \k in {0,...,4} +{ + \pic[thin rhombus,name=b\k,align with={a\k} along B]; + \pic[thick rhombus,name=c\k,align with={b\k} along A]; + \pic[thick rhombus,name=d\k,align with={b\k} along a]; + \pic[thick rhombus,name=e\k,align with={c\k} along A]; + \foreach \l/\a in {{0/b},{1/B}} + \pic[thin rhombus,name=f\k\l,align with={e\k} along \a]; +} +\pic[thin rhombus,name=g0,align with={f10} along a]; +\pic[thin rhombus,name=g1,align with={f21} along A]; +\foreach \l/\a in {{0/a},{1/A}} + \pic[thick rhombus,name=h\l,align with={g\l} along \a]; +\pic[thick rhombus,name=i,align with=g0 along B]; +\foreach \l/\a in {{0/a},{1/A}} + \pic[thick rhombus,name=j\l,align with=i along \a]; +\end{tikzpicture} +\end{example} + +Lastly, here's an example that generates full page patterns. + +\begin{justexample} +\foreach \tp/\lvl in {rhombus/5,rhombus/6,kite/5,kite/6} +{ +\tikzset{external/export next=false} +\begin{tikzpicture}[ + every tile/.style={draw}, + remember picture, + overlay, + scale=20 +] +\coordinate (a) at (current page.center); +\begin{scope}[shift={(a)}] +\foreach[evaluate=\k as \mk using {\k+Mod(\k,2)},evaluate=\k as \ax using {Mod(\k,2) == 0 ? "T" : "t"}] \k in {0,...,9} { + \begin{scope}[rotate=\mk*36] + \TilingDecomposition{\tp}{\lvl}{\ax} + \end{scope} +} +\end{scope} +\end{tikzpicture} +\newpage +} +\end{justexample} +\end{document} + +\begin{tikzpicture} +\path[save tiling path=a] (0,0) -- (1,0); +\path[save tiling path=b] (0,0) -- (1,0); +\path[save tiling path=c] (0,0) -- (1,0); +\BakeTile{thin rhombus} +\BakeTile{thick rhombus} +\BakeTile{golden triangle} +\BakeTile{reverse golden triangle} +\BakeTile{golden gnomon} +\BakeTile{reverse golden gnomon} +\BakeTile{kite} +\BakeTile{dart} +\end{tikzpicture} + +\newpage + +\foreach \tp/\lvl in {rhombus/5,rhombus/6,kite/5,kite/6} +{ +\begin{tikzpicture}[ + every tile/.style={draw}, + remember picture, + overlay, + scale=20 +] +\coordinate (a) at (current page.center); +\begin{scope}[shift={(a)}] +\foreach[evaluate=\k as \mk using {\k+Mod(\k,2)},evaluate=\k as \ax using {Mod(\k,2) == 0 ? "T" : "t"}] \k in {0,...,9} { + \begin{scope}[rotate=\mk*36] + \TilingDecomposition{\tp}{\lvl}{\ax} + \end{scope} +} +\end{scope} +\end{tikzpicture} +\newpage +} + + + +%% \foreach \lvl in {5,6} +%% { +%% \begin{tikzpicture}[ +%% every tile/.style={draw}, +%% remember picture, +%% overlay, +%% scale=180 +%% ] +%% \coordinate (a) at (current page.center); +%% \TilingDecomposition{pentagon}{\lvl}{D} +%% \end{tikzpicture} +%% \newpage +%% } + + +\end{document} + +% Local Variables: +% tex-output-type: "pdf18" +% End: diff --git a/graphics/pgf/contrib/tilings/tilings_code.dtx b/graphics/pgf/contrib/tilings/tilings_code.dtx new file mode 100644 index 0000000000..f550e10d4d --- /dev/null +++ b/graphics/pgf/contrib/tilings/tilings_code.dtx @@ -0,0 +1,3780 @@ +% \iffalse meta-comment +%<*internal> +\iffalse +%</internal> +%<*readme> +---------------------------------------------------------------- +penrose --- TikZ library for producing tiling patterns +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 and similar tilings. +%</readme> +%<*internal> +\fi +\def\nameofplainTeX{plain} +\ifx\fmtname\nameofplainTeX\else + \expandafter\begingroup +\fi +%</internal> +%<*install> +\input l3docstrip.tex +\keepsilent +\askforoverwritefalse +\preamble +---------------------------------------------------------------- +tilings --- TikZ library for producing 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) 2014-2023 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 + tikzlibrarytilings.code.tex + tikzlibrarytilings.penrose.code.tex + tikzlibrarytilings.polykite.code.tex + tikzlibrarypenrose.code.tex + README.txt + +\endpostamble +\usedir{tex/latex/penrose} +\generate{ + \file{tikzlibrarytilings.code.tex}{\from{\jobname.dtx}{tilings}} +} +\generate{ + \file{tikzlibrarytilings.penrose.code.tex}{\from{\jobname.dtx}{penrose}} +} +\generate{ + \file{tikzlibrarytilings.polykite.code.tex}{\from{\jobname.dtx}{polykite}} +} +\generate{ + \file{tikzlibrarypenrose.code.tex}{\from{\jobname.dtx}{penrosedep}} +} +%</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[scale=.8]{geometry} +\usepackage[T1]{fontenc} +\usepackage{lmodern} +\usepackage{tikz} +\usepackage{amsmath} +%\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} +% \changes{1.6}{2023/03/22}{Included aperiodical hat} +% \changes{1.8}{2023/05/11}{LMS systems for aperiodical tiles} +% \changes{2.0}{2023/06/01}{Major version change for CTAN} +% +% \DoNotIndex +% { +% \begingroup, +% \catcode, +% \active, +% \csname, +% \endcsname, +% }% +% +% +% \providecommand*{\url}{\texttt} +% \GetFileInfo{tikzlibrarytilings.code.tex} +% \title{The \textsf{Tilings} package: code} +% \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 tiles, such as Penrose tiles (kite/dart, rhombus, and pentagon versions) and the aperiodical polykite tiles. +% 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+tilings.pdf+ file. +% +% +% \end{documentation} +% +% \begin{implementation} +% +% \section{Implementation} +% +% +% \iffalse +%<*tilings> +% \fi +% +% \begin{macrocode} +%<@@=tilings> +% \end{macrocode} +% +% \subsection{Initialisation} +% +% +% We use the \Verb+spath3+ library for manipulating the paths that will make up the tiles. +% +% \begin{macrocode} +\ProvidesExplFile + {tikzlibrarytilings.code.tex} + {2023/06/01} + {2.0} + {TikZ pics for tilings such as Penrose tiles} +\RequirePackage{tikz} +\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_new:c {g_@@_side_1_tl} +\tl_new:c {g_@@_side_2_tl} +\tl_new:c {g_@@_side_3_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 +\tl_gset_eq:cN {g_@@_side_1_tl} \g_@@_side_a_tl +\tl_gset_eq:cN {g_@@_side_2_tl} \g_@@_side_a_tl +\tl_gset_eq:cN {g_@@_side_3_tl} \g_@@_side_a_tl +% \end{macrocode} +% +% \begin{variable}{\l_@@_tmpa_fp, \l_@@_tmpb_fp, \l_@@_tmpc_fp, \l_@@_saved_x_fp, \l_@@_saved_y_fp, \l_@@_tmpa_str, \l_@@_tmpb_str, \l_@@_tmpa_seq, \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, \g_@@_xa_dim, \g_@@_ya_dim, \g_@@_xb_dim, \g_@@_yb_dim, \l_@@_tmpa_prop, \l_@@_cw_bool, \l_@@_update_saved_bool, \l_@@_relative_bool, \g_@@_output_tl} +% 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 +\fp_new:N \l_@@_saved_x_fp +\fp_new:N \l_@@_saved_y_fp +\str_new:N \l_@@_tmpa_str +\str_new:N \l_@@_tmpb_str +\seq_new:N \l_@@_tmpa_seq +\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 \l_@@_action_lms_tl +\tl_new:N \l_@@_parameters_lms_tl +\int_new:N \l_@@_tmpa_int +\int_new:N \l_@@_tmpb_int +\fp_new:N \l_@@_xa_fp +\fp_new:N \l_@@_ya_fp +\fp_new:N \l_@@_xb_fp +\fp_new:N \l_@@_yb_fp +\dim_new:N \l_@@_xa_dim +\dim_new:N \l_@@_ya_dim +\dim_new:N \l_@@_xb_dim +\dim_new:N \l_@@_yb_dim +\dim_new:N \g_@@_xa_dim +\dim_new:N \g_@@_ya_dim +\dim_new:N \g_@@_xb_dim +\dim_new:N \g_@@_yb_dim +\prop_new:N \l_@@_tmpa_prop +\bool_new:N \l_@@_cw_bool +\bool_new:N \l_@@_update_saved_bool +\bool_new:N \l_@@_relative_bool +\bool_new:N \l_@@_edge_bool +\str_const:Nn \c_@@_colon_str {:} +\str_const:Nn \c_@@_comma_str {,} +\fp_const:Nn \c_@@_cm_fp {\dim_to_fp:n {1cm}} +\tl_new:N \g_@@_output_tl +\fp_new:N \g_@@_output_a_fp +\fp_new:N \g_@@_output_b_fp +\prop_new:N \g_@@_tilenames_prop +\regex_const:Nn \c_@@_anchor_regex {\s\w+\Z} +\cs_generate_variant:Nn \seq_set_split:Nnn {NVV} +\cs_generate_variant:Nn \regex_extract_once:NnNTF {NVNTF} +\cs_generate_variant:Nn \tl_if_eq:nnT {nVT} +\cs_generate_variant:Nn \tl_if_in:NnT {NVT} +\cs_generate_variant:Nn \prop_item:Nn {cV} +\cs_generate_variant:Nn \tl_if_head_is_group_p:n {V} +% \end{macrocode} +% \end{variable} +% +% \subsection{Helpful Error Messages} +% +% \begin{macrocode} +\msg_new:nnn { tilings }{ not baked } +{ Tile~ #1~ has~ not~ been~ baked. } +\msg_new:nnn { tilings }{ no tile } +{ Tile~ #1~ has~ not~ been~ defined. } +\msg_new:nnn { tilings }{ no side } +{ Tile~ side~ #1~ has~ not~ been~ defined,~ using~ default. } +\msg_new:nnn { tilings }{ tile no edge } +{ Tile~ #1~ doesn't~ have~ an~ edge~ labelled~ #2; + ~ available~ edges~ are~ #3.} +\msg_new:nnn { tilings }{ no edge } +{ Either~ tile~ #1~ doesn't~ exist + ~ or~ it~ doesn't~ have~ an~ edge~ labelled~ #2.} +% \end{macrocode} +% +% \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_@@_output_tl \l_@@_tmpa_tl + \group_end: + \tl_set_eq:NN #1 \g_@@_output_tl + \tl_gclear:N \g_@@_output_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}{\SetTilingPath} +% This sets the path corresponding to a particular side to the current path, and normalises it. +% \begin{macrocode} +\cs_new_protected_nopar:Npn \@@_set_tiling_path:n #1 +{ + \group_begin: + \pgfsyssoftpath@getcurrentpath\l_@@_tmpa_tl + \@@_normalise_path:N \l_@@_tmpa_tl + \tl_gset_eq:cN {g_@@_side_#1_tl} \l_@@_tmpa_tl + \group_end: +} + +\NewDocumentCommand \SetTilingPath { m } +{ + \@@_set_tiling_path:n {#1} +} +% \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]{\tikz_node_if_defined:TF} +% This extracts the code that tests if a node is defined. +% \begin{macrocode} +\prg_new_conditional:Npnn \tikz_node_if_defined:n #1 {p,T,F,TF} +{ + \tl_if_exist:cTF {pgf@sh@ns@\use:c{tikz@pp@name}{#1}} + { + \prg_return_true: + }{ + \tl_if_exist:cTF + {pgf@sh@ns@not yet positionedPGFINTERNAL\use:c{tikz@pp@name}{#1}} + { + \pgf_return_true: + } + { + \prg_return_false: + } + } +} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}[internal]{\@@_keys_get:Nn,\pgfkeys_get:n} +% This is a wrapper around \Verb+\pgfkeysgetvalue+ to make it easier to use with \LaTeX3 variables. +% \begin{macrocode} +\cs_new_nopar:Npn \@@_keys_get:Nn #1#2 +{ + \pgfkeysgetvalue{/tikz/tiling/#2}{#1} +} +\cs_new_nopar:Npn \@@_keys_get:n #1 +{ + \pgfkeysvalueof{/tikz/tiling/#1} +} +\cs_new_nopar:Npn \@@_tikz_keys_get:Nn #1#2 +{ + \pgfkeysgetvalue{/tikz/#2}{#1} +} +\cs_new_nopar:Npn \@@_tikz_keys_get:n #1 +{ + \pgfkeysvalueof{/tikz/#1} +} +\cs_new_nopar:Npn \@@_pgf_keys_get:Nn #1#2 +{ + \pgfkeysgetvalue{#2}{#1} +} +\cs_new_nopar:Npn \@@_pgf_keys_get:n #1 +{ + \pgfkeysvalueof{#1} +} +% \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} + \tl_put_right:Nx \l_@@_tmpa_tl + { + { + \fp_to_dim:n + {(\tl_item:Nn \l_@@_tmpb_tl {1}) * \c_@@_cm_fp} + } + { + \fp_to_dim:n + {(\tl_item:Nn \l_@@_tmpb_tl {2}) * \c_@@_cm_fp} + } + } + \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_if_exist:cF {g_@@_side_ \tl_use:N \l_@@_tmpc_tl _tl} + { + \msg_error:nnx { tilings }{ no side } { \tl_use:N \l_@@_tmpc_tl } + \tl_gset_eq:cc + {g_@@_side_ \tl_use:N \l_@@_tmpc_tl _tl} + {g_@@_side_a_tl} + } + \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} +% \end{macrocode} +% Store the resulting coordinate. +% \begin{macrocode} + \fp_set:Nn \l_@@_tmpa_fp + { \tl_item:Nn \l_@@_tmpb_tl {1} } + \fp_set:Nn \l_@@_tmpb_fp + { \tl_item:Nn \l_@@_tmpb_tl {2} } +% \end{macrocode} +% Now get the next coordinate. +% \begin{macrocode} + \tl_set:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpa_tl} +% \end{macrocode} +% We want the difference between the two coordinates. +% \begin{macrocode} + \fp_set:Nn \l_@@_tmpa_fp + {\tl_item:Nn \l_@@_tmpb_tl {1} - \l_@@_tmpa_fp} + \fp_set:Nn \l_@@_tmpb_fp + {\tl_item:Nn \l_@@_tmpb_tl {2} - \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_to_dim:n { \l_@@_tmpa_fp * \c_@@_cm_fp }} + {\fp_to_dim:n { \l_@@_tmpb_fp * \c_@@_cm_fp }}% not swapped + {\fp_to_dim:n { \l_@@_tmpc_fp * \c_@@_cm_fp }}% not swapped + {\fp_to_dim:n { \l_@@_tmpa_fp * \c_@@_cm_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_@@_output_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_@@_output_tl + \tl_gclear:N \g_@@_output_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 { + \group_begin: + \fp_set:Nn \l_@@_tmpa_fp {#2} + \fp_set:Nn \l_@@_tmpb_fp {#3} + \bool_if:NT \l_@@_relative_bool + { + \fp_add:Nn \l_@@_tmpa_fp {\l_@@_saved_x_fp} + \fp_add:Nn \l_@@_tmpb_fp {\l_@@_saved_y_fp} + } + \fp_gset_eq:NN \g_@@_output_a_fp \l_@@_tmpa_fp + \fp_gset_eq:NN \g_@@_output_b_fp \l_@@_tmpb_fp + \group_end: + \tl_put_right:Nx #1 + { + {{\fp_use:N \g_@@_output_a_fp}{\fp_use:N \g_@@_output_b_fp}} + } + \bool_if:NT \l_@@_update_saved_bool + { + \fp_set_eq:NN \l_@@_saved_x_fp \g_@@_output_a_fp + \fp_set_eq:NN \l_@@_saved_y_fp \g_@@_output_b_fp + } + \fp_gzero:N \g_@@_output_a_fp + \fp_gzero:N \g_@@_output_b_fp +} +% \end{macrocode} +% Wrapper around the add coordinate command to split at a comma. +% \begin{macrocode} +\cs_new_nopar:Npn \@@_add_xy_coordinate:w #1#2,#3 \q_stop +{ + \@@_add_coordinate:Nnn #1 {#2}{#3} +} +% \end{macrocode} +% +% Wrapper around the add coordinate command to split at a colon. +% \begin{macrocode} +\cs_new_nopar:Npn \@@_add_rth_coordinate:w #1#2:#3 \q_stop +{ + \@@_add_coordinate:Nnn #1 {(#3) * cosd(#2)}{(#3) * sind(#2)} +} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}[internal]{\@@_transform_side_to_axis:Nnn} +% Apply a transformation to make a given side lie on the x-axis. +% Second argument is the tile, third is the side, first is whether to reverse the side. +% \begin{macrocode} +\cs_new_nopar:Npn \@@_transform_side_to_axis:Nnn #1#2#3 +{ +% \end{macrocode} +% Get our tile data, checking if the tile exists. +% \begin{macrocode} + \group_begin: + \prop_get:NnNTF \g_@@_tiles_prop {#2} \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} + \bool_set_false:N \l_@@_edge_bool + \tl_map_inline:Nn \l_@@_tmpc_tl { + \str_if_eq:nnT {##1} {#3} { + \bool_set_true:N \l_@@_edge_bool + \tl_map_break: + } + \int_incr:N \l_@@_tmpb_int + } + \bool_if:NTF \l_@@_edge_bool + { +% \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} +% Possibly swap the ends. +% \begin{macrocode} + \bool_if:NT #1 + { + \tl_set:NV \l_@@_tmpc_tl \l_@@_tmpa_tl + \tl_set:NV \l_@@_tmpa_tl \l_@@_tmpb_tl + \tl_set:NV \l_@@_tmpb_tl \l_@@_tmpc_tl + } +% \end{macrocode} +% Get the coordinates of the first point, which will be the origin of the transformation. +% \begin{macrocode} + \fp_set:Nn \l_@@_xa_fp {\tl_item:Nn \l_@@_tmpb_tl {1}} + \fp_set:Nn \l_@@_ya_fp {\tl_item:Nn \l_@@_tmpb_tl {2}} +% \end{macrocode} +% Get the coordinates of the second point and adjust relative to the first. +% \begin{macrocode} + \fp_set:Nn \l_@@_xb_fp + {\tl_item:Nn \l_@@_tmpa_tl {1} - \l_@@_xa_fp} + \fp_set:Nn \l_@@_yb_fp + {\tl_item:Nn \l_@@_tmpa_tl {2} - \l_@@_ya_fp} +% \end{macrocode} +% And normalise the vector along it. +% \begin{macrocode} +% \fp_set:Nn \l_@@_xb_fp {\l_@@_xb_fp / \c_@@_cm_fp} +% \fp_set:Nn \l_@@_yb_fp {\l_@@_yb_fp / \c_@@_cm_fp} + \fp_set:Nn \l_@@_tmpa_fp + {(\l_@@_xb_fp)^2 + (\l_@@_yb_fp)^2} + \fp_set:Nn \l_@@_xb_fp { \l_@@_xb_fp / \l_@@_tmpa_fp} + \fp_set:Nn \l_@@_yb_fp { \l_@@_yb_fp / \l_@@_tmpa_fp} +% \end{macrocode} +% Now rotate so that the \(x\)--axis lies along the edge. +% \begin{macrocode} + \tl_gset:Nx \g_@@_output_tl + { + \exp_not:N \pgftransformtriangle + { + \exp_not:N \pgfpoint{0pt}{0pt} + } + { + \exp_not:N \pgfpoint + {\fp_to_dim:N \l_@@_xb_fp}{\fp_to_dim:n {-\l_@@_yb_fp}} + } + { + \exp_not:N \pgfpoint + {\fp_to_dim:N \l_@@_yb_fp}{\fp_to_dim:N \l_@@_xb_fp} + } + \exp_not:N \pgftransformshift + { + \exp_not:N \pgfpoint + { + \fp_to_dim:n {-\l_@@_xa_fp * \c_@@_cm_fp} + } + { + \fp_to_dim:n {-\l_@@_ya_fp * \c_@@_cm_fp} + } + } + } + } + { + \msg_error:nnxxx {tilings} {tile no edge} {#2} {#3} + {\tl_use:N \l_@@_tmpc_tl } + \tl_gclear:N \g_@@_output_tl + } + } + { + \msg_error:nnn {tilings} {no tile} {#2} + \tl_gclear:N \g_@@_output_tl + } + \group_end: + \tl_use:N \g_@@_output_tl + \tl_gclear:N \g_@@_output_tl +} +% \end{macrocode} +% \end{macro} +% +% \begin{macrocode} +\cs_generate_variant:Nn +\@@_transform_side_to_axis:Nnn {Nnx,NnV,NVV} +% \end{macrocode} +% +% \begin{macro}[internal]{\@@_translate_vertex_to_origin:Nnn} +% Apply a transformation to make a given vertex sit at the origin. +% Second argument is the tile, third is the side, first is a boolean to determine whether to use the start or end. +% \begin{macrocode} +\cs_new_nopar:Npn \@@_translate_vertex_to_origin:Nnn #1#2#3 +{ +% \end{macrocode} +% Get our tile data, checking if the tile exists. +% \begin{macrocode} + \group_begin: + \prop_get:NnNTF \g_@@_tiles_prop {#2} \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} + \bool_set_false:N \l_@@_edge_bool + \tl_map_inline:Nn \l_@@_tmpc_tl { + \str_if_eq:nnT {##1} {#3} { + \bool_set_true:N \l_@@_edge_bool + \tl_map_break: + } + \int_incr:N \l_@@_tmpb_int + } + \bool_if:NTF \l_@@_edge_bool + { +% \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} +% Possibly swap the ends. +% \begin{macrocode} + \bool_if:NT #1 + { + \tl_set:NV \l_@@_tmpc_tl \l_@@_tmpa_tl + \tl_set:NV \l_@@_tmpa_tl \l_@@_tmpb_tl + \tl_set:NV \l_@@_tmpb_tl \l_@@_tmpc_tl + } +% \end{macrocode} +% Get the coordinates of the first point, which will be the origin of the transformation. +% \begin{macrocode} + \fp_set:Nn \l_@@_xa_fp {\tl_item:Nn \l_@@_tmpb_tl {1}} + \fp_set:Nn \l_@@_ya_fp {\tl_item:Nn \l_@@_tmpb_tl {2}} +% \end{macrocode} +% Shift to place the selected vertex at the origin. +% \begin{macrocode} + \tl_gset:Nx \g_@@_output_tl + { + \exp_not:N \pgftransformshift + { + \exp_not:N \pgfpoint + { + \fp_to_dim:n {-\l_@@_xa_fp * \c_@@_cm_fp} + } + { + \fp_to_dim:n {-\l_@@_ya_fp * \c_@@_cm_fp} + } + } + } + } + { + \msg_error:nnxxx {tilings} {tile no edge} {#2} {#3} + {\tl_use:N \l_@@_tmpc_tl } + \tl_gclear:N \g_@@_output_tl + } + } + { + \msg_error:nnn {tilings} {no tile} {#2} + \tl_gclear:N \g_@@_output_tl + } + \group_end: + \tl_use:N \g_@@_output_tl + \tl_gclear:N \g_@@_output_tl +} +% \end{macrocode} +% \end{macro} +% +% \begin{macrocode} +\cs_generate_variant:Nn +\@@_translate_vertex_to_origin:Nnn {Nnx,NnV,NVV} +% \end{macrocode} +% +% \begin{macro}[internal]{\TransformAlongSide} +% Make this available outside the \LaTeX3 environment. +% The starred version allows for reversing the side. +% \begin{macrocode} +\DeclareDocumentCommand \TransformAlongSide {s m m} +{ +% \end{macrocode} +% Store the star +% \begin{macrocode} + \IfBooleanTF {#1} + { + \bool_set_true:N \l_@@_cw_bool + } + { + \bool_set_false:N \l_@@_cw_bool + } + \@@_transform_side_to_axis:Nnx \l_@@_cw_bool {#2}{#3} +} +% \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 +{ + \group_begin: +% \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 edge list, placing coordinates +% \begin{macrocode} + \tl_map_inline:Nn \l_@@_tmpb_tl { + \tl_set:Nx \l_@@_tmpd_tl { + \exp_not:N \coordinate + (-edge~ ##1~ start)~ + at ( + \tl_item:Nn \l_@@_tmpa_tl {1}, + \tl_item:Nn \l_@@_tmpa_tl {2} + ); + } + \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_item:Nn \l_@@_tmpa_tl {1}, + \tl_item:Nn \l_@@_tmpa_tl {2} + ); + } + \tl_use:N \l_@@_tmpd_tl + } + \group_end: +} +% \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{macrocode} +\tikzset{ + transform~ to~ tile/.code~ args={#1~ along~ #2}{% + \group_begin: + \tl_if_in:nnTF {#1} {back} + { + \tikzset{ + tiling/alignment~ set~ location=#1, + tiling/alignment~ direction={backwards} + } + } + { + \tikzset{ + tiling/alignment~ location=#1, + tiling/alignment~ direction={forewards} + } + } + \tl_if_in:nnTF {#2} {using} + { + \tikzset{ + tiling/alignment~ set~ edges=#2, + } + } + { + \tikzset{ + tiling/alignment~ edge=#2, + } + } + \tikz_scan_point:n { + (\@@_keys_get:n {alignment~ location} + -edge~ \@@_keys_get:n {alignment~ edge}~ start) + } + \dim_set_eq:Nc \l_@@_xa_dim {pgf@x} + \dim_set_eq:Nc \l_@@_ya_dim {pgf@y} + \tikz_scan_point:n { + (\@@_keys_get:n {alignment~ location} + -edge~ \@@_keys_get:n {alignment~ edge}~ end) + } + \dim_set_eq:Nc \l_@@_xb_dim {pgf@x} + \dim_set_eq:Nc \l_@@_yb_dim {pgf@y} + \@@_keys_get:Nn \l_@@_tmpb_tl {alignment~ direction} + \tl_if_eq:NnTF \l_@@_tmpb_tl {forewards} + { + \dim_gset_eq:NN \g_@@_xa_dim \l_@@_xa_dim + \dim_gset_eq:NN \g_@@_ya_dim \l_@@_ya_dim + \dim_gset_eq:NN \g_@@_xb_dim \l_@@_xb_dim + \dim_gset_eq:NN \g_@@_yb_dim \l_@@_yb_dim + } + { + \dim_gset_eq:NN \g_@@_xa_dim \l_@@_xb_dim + \dim_gset_eq:NN \g_@@_ya_dim \l_@@_yb_dim + \dim_gset_eq:NN \g_@@_xb_dim \l_@@_xa_dim + \dim_gset_eq:NN \g_@@_yb_dim \l_@@_ya_dim + } + \dim_gsub:Nn \g_@@_xb_dim {\g_@@_xa_dim} + \dim_gsub:Nn \g_@@_yb_dim {\g_@@_ya_dim} + \dim_gset:Nn \g_@@_xb_dim + {\g_@@_xb_dim * \dim_ratio:nn {1pt}{1cm}} + \dim_gset:Nn \g_@@_yb_dim + {\g_@@_yb_dim * \dim_ratio:nn {1pt}{1cm}} + \group_end: +% \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} +% \end{macrocode} +% We shift to the start of the edge. +% \begin{macrocode} + \pgftransformshift{\pgfpoint{\g_@@_xa_dim}{\g_@@_ya_dim}} +% \end{macrocode} +% Now rotate so that the \(x\)--axis lies along the edge. +% \begin{macrocode} + \pgftransformtriangle + {\pgfpoint{0pt}{0pt}} + {\pgfpoint{\g_@@_xb_dim}{\g_@@_yb_dim}} + {\pgfpoint{-\g_@@_yb_dim}{\g_@@_xb_dim}} + }, + align~ with/.code~ args={#1~ along~ #2}{% + \tl_if_in:nnTF {#1} {back} + { + \tikzset{ + tiling/alignment~ set~ location=#1, + tiling/alignment~ direction={backwards} + } + } + { + \tikzset{ + tiling/alignment~ location=#1, + tiling/alignment~ direction={forewards} + } + } + \tl_if_in:nnTF {#2} {using} + { + \tikzset{ + tiling/alignment~ set~ edges=#2, + } + } + { + \tikzset{ + tiling/alignment~ edge=#2, + } + } + \tikz_node_if_defined:nTF + { + \@@_keys_get:n {alignment~ location} + -edge~ \@@_keys_get:n {alignment~ edge}~ start + } + { + \tikzset{ + tiling/alignment~ start/.expanded={ + (\@@_keys_get:n {alignment~ location} + -edge~ \@@_keys_get:n {alignment~ edge}~ start) + }, + tiling/alignment~ end/.expanded={ + (\@@_keys_get:n {alignment~ location} + -edge~ \@@_keys_get:n {alignment~ edge}~ end) + }, + } + } + { + \@@_keys_get:Nn \l_@@_tmpa_tl {alignment~ location} + \tl_set:Nx \l_@@_tmpa_tl {\tl_use:N \l_@@_tmpa_tl} + \prop_get:NVNTF \g_@@_tilenames_prop + \l_@@_tmpa_tl \l_@@_tmpb_tl + { + \prop_get:NVN \g_@@_tiles_prop + \l_@@_tmpb_tl \l_@@_tmpc_tl + \msg_error:nnxxx { tilings }{ tile no edge } + { + \tl_use:N \l_@@_tmpa_tl \c_space_tl + (type~ \tl_use:N \l_@@_tmpb_tl) + } + {\@@_keys_get:n {alignment~ edge} } + { \tl_item:Nn \l_@@_tmpc_tl {1} } + } + { + \msg_error:nnx { tilings }{ no tile } + {\@@_keys_get:n {alignment~ location} } + } + } + }, + tiling/.is~ family, + tiling/alignment~ set~ location/.code~ args={#1~ back}{ + \tikzset{ + tiling/alignment~ location=#1, + } + }, + tiling/alignment~ set~ edges/.code~ args={#1~ using~ #2}{ + \tikzset{ + tiling/alignment~ edge=#1, + tiling/alignment~ new~ edge=#2 + } + }, + align~ between/.code~ args={#1~ and~ #2~ using~ #3}{ + \tikzset{ + tiling/alignment~ start={#1}, + tiling/alignment~ end={#2}, + } + \str_set:Nn \l_@@_tmpa_str {#3} + \str_set:Nx \l_@@_tmpb_str {\str_tail:N \l_@@_tmpa_str} + \tikzset{ + tiling/alignment~ new~ edge/.expanded={\str_use:N \l_@@_tmpb_str} + } + \str_set:Nx \l_@@_tmpa_str {\str_head:N \l_@@_tmpa_str} + \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}} + } + \tikzset{ + tiling/alignment~ edge/.expanded={\str_use:N \l_@@_tmpb_str}, + } + }, + tiling/alignment~ location/.initial={}, + tiling/alignment~ edge/.initial=a, + tiling/alignment~ new~ edge/.initial={}, + tiling/alignment~ direction/.initial={forewards}, + tiling/alignment~ start/.initial={}, + tiling/alignment~ end/.initial={}, + tiling/anchor/.initial={}, +% \end{macrocode} +% Default clipping style. +% \begin{macrocode} + every~ tile~ clip/.style={clip} +} +% \end{macrocode} +% +% \begin{function}{\DefineTile} +% This is the user function for defining a tile. +% \begin{macrocode} +\DeclareDocumentCommand \DefineTile { s 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} + \int_zero:N \l_@@_tmpa_int + \fp_zero:N \l_@@_saved_x_fp + \fp_zero:N \l_@@_saved_y_fp + \tl_map_inline:nn {#4} { + \str_set:Nn \l_@@_tmpa_str {##1} + \str_if_eq:VnTF \l_@@_tmpa_str {+} + { + \int_incr:N \l_@@_tmpa_int + } + { + \int_case:nn {\l_@@_tmpa_int} + { + {0} { + \bool_set_false:N \l_@@_relative_bool + \bool_set_true:N \l_@@_update_saved_bool + } + {1} { + \bool_set_true:N \l_@@_relative_bool + \bool_set_false:N \l_@@_update_saved_bool + } + {2} { + \bool_set_true:N \l_@@_relative_bool + \bool_set_true:N \l_@@_update_saved_bool + } + + } + \str_if_in:NnTF \l_@@_tmpa_str {:} + { + \seq_set_split:NVV \l_@@_tmpa_seq \c_@@_colon_str \l_@@_tmpa_str + \@@_add_coordinate:Nnn \l_@@_tmpa_tl + { + (\seq_item:Nn \l_@@_tmpa_seq {2}) * cosd (\seq_item:Nn \l_@@_tmpa_seq {1}) + } + { + (\seq_item:Nn \l_@@_tmpa_seq {2}) * sind (\seq_item:Nn \l_@@_tmpa_seq {1}) + } + } + { + \seq_set_split:NVV \l_@@_tmpa_seq \c_@@_comma_str \l_@@_tmpa_str + \@@_add_coordinate:Nnn \l_@@_tmpa_tl + { + (\seq_item:Nn \l_@@_tmpa_seq {1}) + } + { + (\seq_item:Nn \l_@@_tmpa_seq {2}) + } + } + \int_zero:N \l_@@_tmpa_int + } + } +% \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 {#3} { + \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 {#3} + { + \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 {#2} + {{\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{ + #2/.pic={ + \begin{scope}[ + every~ tile~ scope/.try, + every~ #2~ scope/.try, + this~ tile~ scope/.try + ] +% \end{macrocode} +% Save the name and tile type +% \begin{macrocode} + \tikz@fig@mustbenamed + \prop_gput:NVn \g_@@_tilenames_prop \tikz@fig@name {#2} +% \end{macrocode} +% Were we given coordinates to align ourselves against? +% \begin{macrocode} + \@@_keys_get:Nn \l_@@_tmpa_tl {alignment~ start} + \tl_if_empty:NTF \l_@@_tmpa_tl + { +% \end{macrocode} +% No alignment information was given, was an anchor specified? +% \begin{macrocode} + \prop_get:NnN \g_@@_tiles_prop {#2} \l_@@_tmpa_tl + \tl_set:Nx \l_@@_tmpc_tl {\tl_head:N \l_@@_tmpa_tl} + \@@_keys_get:Nn \l_@@_tmpa_tl {anchor} + \tl_if_empty:NTF \l_@@_tmpa_tl + { +% \end{macrocode} +% No positioning information given, but we might have been asked to flip the tile +% \begin{macrocode} + \bool_if:NT \l_@@_cw_bool + { + \pgftransformxscale {-1} + } + } + { + \regex_extract_once:NVNTF + \c_@@_anchor_regex \l_@@_tmpa_tl \l_@@_tmpb_tl + { + \regex_replace_once:NnN \c_@@_anchor_regex {} \l_@@_tmpa_tl + \tl_if_eq:NnTF \l_@@_tmpb_tl {~end} + { + \bool_set_true:N \l_@@_cw_bool + } + { + \bool_set_false:N \l_@@_cw_bool + } + } + { + \bool_set_false:N \l_@@_cw_bool + } + \tl_set:Nx \l_@@_tmpb_tl {{\tl_use:N \l_@@_tmpa_tl}} + \tl_if_in:NVT \l_@@_tmpc_tl \l_@@_tmpb_tl + { + \@@_translate_vertex_to_origin:NnV + \l_@@_cw_bool {#2} \l_@@_tmpa_tl + } + } + } + { +% \end{macrocode} +% Yes, we were. +% So we adjust our position accordingly. +% The first job is to transform so that we're aligned with the specified coordinates. +% \begin{macrocode} + \group_begin: +% \end{macrocode} +% We get the locations of the start and ending coordinates. +% \begin{macrocode} + \tikzset{ + name~ prefix~ .. + } + \tikz_scan_point:n { + \@@_keys_get:n {alignment~ start} + } + \dim_set_eq:Nc \l_@@_xa_dim {pgf@x} + \dim_set_eq:Nc \l_@@_ya_dim {pgf@y} + \tikz_scan_point:n { + \@@_keys_get:n {alignment~ end} + } + \dim_set_eq:Nc \l_@@_xb_dim {pgf@x} + \dim_set_eq:Nc \l_@@_yb_dim {pgf@y} + \@@_keys_get:Nn \l_@@_tmpb_tl {alignment~ direction} + \tl_if_eq:NnTF \l_@@_tmpb_tl {forewards} + { + \dim_gset_eq:NN \g_@@_xa_dim \l_@@_xa_dim + \dim_gset_eq:NN \g_@@_ya_dim \l_@@_ya_dim + \dim_gset_eq:NN \g_@@_xb_dim \l_@@_xb_dim + \dim_gset_eq:NN \g_@@_yb_dim \l_@@_yb_dim + } + { + \dim_gset_eq:NN \g_@@_xa_dim \l_@@_xb_dim + \dim_gset_eq:NN \g_@@_ya_dim \l_@@_yb_dim + \dim_gset_eq:NN \g_@@_xb_dim \l_@@_xa_dim + \dim_gset_eq:NN \g_@@_yb_dim \l_@@_ya_dim + } + \dim_gsub:Nn \g_@@_xb_dim {\g_@@_xa_dim} + \dim_gsub:Nn \g_@@_yb_dim {\g_@@_ya_dim} + \dim_gset:Nn \g_@@_xb_dim {\g_@@_xb_dim * \dim_ratio:nn {1pt}{1cm}} + \dim_gset:Nn \g_@@_yb_dim {\g_@@_yb_dim * \dim_ratio:nn {1pt}{1cm}} + \group_end: +% \end{macrocode} +% We shift to the start of the edge. +% \begin{macrocode} + \pgftransformshift{\pgfpoint{\g_@@_xa_dim}{\g_@@_ya_dim}} +% \end{macrocode} +% And normalise the vector along it. +% \begin{macrocode} +% \pgfpointnormalised{\pgfpoint{\g_@@_xb_dim}{\g_@@_yb_dim}} +% \dim_gset_eq:Nc \g_@@_xb_dim {pgf@x} +% \dim_gset_eq:Nc \g_@@_yb_dim {pgf@y} +% \end{macrocode} +% Now rotate so that the \(x\)--axis lies along the edge. +% \begin{macrocode} + \pgftransformtriangle + {\pgfpoint{0pt}{0pt}} + {\pgfpoint{\g_@@_xb_dim}{\g_@@_yb_dim}} + {\pgfpoint{-\g_@@_yb_dim}{\g_@@_xb_dim}} +% \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 + {\@@_keys_get:n {alignment~ edge}} + \str_set:Nx \l_@@_tmpa_str {\str_head:N \l_@@_tmpa_str} + \str_put_right:Nx \l_@@_tmpa_str + {\@@_keys_get:n {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}} + } + + \IfBooleanT {#1} + { + \bool_set:Nn \l_@@_cw_bool {!\l_@@_cw_bool} + } + \bool_if:NT \l_@@_cw_bool + { + \pgftransformyscale {-1} + } + \@@_transform_side_to_axis:NnV \l_@@_cw_bool {#2} \l_@@_tmpb_str + } +% \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. +% +% We start by putting coordinates at each vertex, labelled by which edge they are. +% \begin{macrocode} + \@@_coordinates_at_vertices:n {#2} +% \end{macrocode} +% And one at the origin of the pic +% \begin{macrocode} + \coordinate[alias=-center] (-centre) at (0,0); +% \end{macrocode} +% +% The first action is to clip against the tile path. +% \begin{macrocode} + \UseTile[ + every~ tile~ clip/.try, + every~ #2~ clip/.try, + this~ tile~ clip/.try + ]{#2} +% \end{macrocode} +% Any pre-actions? +% \begin{macrocode} + \tikzset{ + every~ tile~ before~ path/.try, + every~ #2~ before~ path/.try, + this~ tile~ before~ path/.try + } +% \end{macrocode} +% Now we render the tile path +% \begin{macrocode} + \UseTile[ + every~ tile/.try, + every~ #2/.try, + this~ tile/.try, + pic~ actions + ]{#2} +% \end{macrocode} +% After drawing the tile and placing the coordinates, +% \begin{macrocode} + \tikzset{ + every~ tile~ after~ path/.try, + every~ #2~ after~ path/.try, + this~ tile~ after~ path/.try + } + \end{scope} + }, +% \end{macrocode} +% This is a shortcut for installing the \Verb+pic+ type. +% \begin{macrocode} + #2/.style={ + every~ tile~ pic/.try, + every~ #2~ pic/.try, + pic~ type=#2, + } + } +} +% \end{macrocode} +% \end{function} +% +% \begin{function}{\BakeTile} +% This is the user wrapper around the tile creation macros. +% \begin{macrocode} +\cs_new_protected_nopar:Npn \@@_bake_tile:n #1 +{ + \prop_get:NnN \g_@@_tiles_prop {#1} \l_@@_tmpa_tl + \@@_make_tile:nV {#1} \l_@@_tmpa_tl +} + +\NewDocumentCommand \BakeTile {m} +{ + \@@_bake_tile:n {#1} +} +% \end{macrocode} +% \end{function} +% +% \begin{function}{\UseTile} +% This is the command that actually places a tile on the page. +% The first argument is optional and is for styling. +% \begin{macrocode} +\cs_new_protected_nopar:Npn \@@_use_tile:nn #1#2 +{ +% \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_if_exist:cTF {g_@@_tile_#2_tl} + { + \tl_set_eq:Nc \l_@@_tmp_tile_path_tl {g_@@_tile_#2_tl} +% \end{macrocode} +% We get the current transformation to apply to this path. +% \begin{macrocode} + \pgfgettransform \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 + } + { + \msg_error:nnn { tilings }{ not baked }{#2} + } +} + +\NewDocumentCommand \UseTile {O{} m} +{ + \@@_use_tile:nn {#1}{#2} +} +% \end{macrocode} +% \end{function} +% +% \begin{macro}{save tiling 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~ tiling~ 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~ tiling~ side~ path/.style~ 2~ args={ + spath/set~ name=tiling~ side, + spath/clone~ global={#1}{#2} + }, + flip~ tile/.code={ + \tl_set:Nn \l_@@_tmpa_tl {#1} + \tl_set:Nn \l_@@_tmpb_tl {true} + \bool_set:Nn \l_@@_cw_bool {\tl_if_eq_p:NN \l_@@_tmpa_tl \l_@@_tmpb_tl} + }, + flip~ tile/.default={true}, + spath/prefix/tiling~side/.style={ + spath/set~ prefix=g_@@_side_, + }, + spath/suffix/tiling~side/.style={ + spath/set~ suffix=_tl, + }, + clone~ tile~ path/.style~ 2~ args={ + spath/set~ name=tiling~tile, + spath/clone~ global={#1}{#2} + }, + spath/prefix/tiling~tile/.style={ + spath/set~ prefix=g_@@_tile_, + }, + spath/suffix/tiling~tile/.style={ + spath/set~ suffix=_tl, + }, + expand~ key/.code={ + \exp_args:NV \pgfkeysalso #1 + } +} +% \end{macrocode} +% \end{macro} +% +% \subsection{Lindenmayer System} +% +% This is an implementation of the Lindenmayer System description of Penrose and other 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. +% +% \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} + \tl_set:Nx \l_@@_action_lms_tl {\tl_head:n {##1}} + \tl_set:Nx \l_@@_parameters_lms_tl {\tl_tail:n {##1}} + \prop_if_in:cVTF {g_@@_#2_lms_rule_prop} \l_@@_action_lms_tl + { + \prop_get:cVN {g_@@_#2_lms_rule_prop} \l_@@_action_lms_tl \l_@@_tmpc_tl + \tl_put_right:Nx \l_@@_tmpb_tl {\tl_use:N \l_@@_tmpc_tl} +% {\prop_item:cn {g_@@_#2_lms_rule_prop} {##1} } + } + { +% \end{macrocode} +% Otherwise, just copy the token. +% \begin{macrocode} + \tl_if_single:nTF {##1} + { + \tl_put_right:Nn \l_@@_tmpb_tl {##1} + } + { + \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} { + \tl_set:Nx \l_@@_action_lms_tl {\tl_head:n {##1}} + \tl_set:Nx \l_@@_parameters_lms_tl {\tl_tail:n {##1}} + \prop_if_in:cVTF {g_@@_#2_lms_action_prop} \l_@@_action_lms_tl + { + \prop_item:cV {g_@@_#2_lms_action_prop} \l_@@_action_lms_tl + } + { + \prop_if_in:cVT {g_@@_default_lms_action_prop} \l_@@_action_lms_tl + { + \prop_item:cV {g_@@_default_lms_action_prop} \l_@@_action_lms_tl + } + } + } + \group_end: +} +\cs_generate_variant:Nn \@@_invoke_lms:nn {Vn} +% \end{macrocode} +% \end{macro} +% +% +% 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_new:N \g_@@_default_lms_action_prop +\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 {b} +{\pgftransformxshift{-\l_@@_step_dim}} +% \end{macrocode} +% +% Holds a list of the tiles that actually draw for each tile set +% \begin{macrocode} +\prop_new:N \g_@@_drawables_lms_prop +% \end{macrocode} +% +% 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}{\TilingDecomposition} +% This is the user macro to invoke the decomposition. +% The arguments are: optional styles, the name, number of iterations, and starting seed. +% \begin{macrocode} +\cs_new_protected_nopar:Npn \@@_tiling_decomposition:nnnn #1#2#3#4 +{ + \group_begin: + \tikzset{ + every~ #2~ decomposition/.try, + #1 + } + \@@_make_lms:Nnnx \l_@@_tmpa_tl {#2} {#3} {#4} + \@@_count_lms:Vn \l_@@_tmpa_tl {#2} + \int_gzero:N \g_@@_tile_int + \@@_invoke_lms:Vn \l_@@_tmpa_tl {#2} + \group_end: +} +\cs_new_protected_nopar:Npn \@@_tiling_decomposition:nnn #1#2#3 +{ + \@@_tiling_decomposition:nnnn {}{#1}{#2}{#3} +} +\cs_generate_variant:Nn \@@_tiling_decomposition:nnn {VVV} + +\NewDocumentCommand \TilingDecomposition { O{} m m m } +{ + \@@_tiling_decomposition:nnnn {#1}{#2}{#3}{#4} +} + +\tikzset{ + pics/decomposition/.style~ n~ args={3}{ + code={ + \@@_tiling_decomposition:nnn {#1}{#2}{#3} + } + } +} +% \end{macrocode} +% \end{function} +% +% \begin{macro}[internal]{\@@_count_lms:nn} +% This counts the number of tiles in the string. +% \begin{macrocode} +\cs_new_nopar:Npn \@@_count_lms:nn #1#2 +{ + \group_begin: + \int_gzero:N \g_@@_tiles_int + \prop_get:NnNT \g_@@_drawables_lms_prop {#2} \l_@@_tmpa_tl + { + \tl_map_variable:nNn {#1} \l_@@_tmpb_tl + { + \tl_set:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpb_tl} + \bool_do_while:nn + { + !\tl_if_empty_p:N \l_@@_tmpb_tl + && + \tl_if_head_is_group_p:V \l_@@_tmpb_tl + } + { + \tl_set:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpb_tl} + } + \tl_if_in:NVT \l_@@_tmpa_tl \l_@@_tmpb_tl + { + \int_gincr:N \g_@@_tiles_int + } + } + } + \group_end: +} +\cs_generate_variant:Nn \@@_count_lms:nn {Vn} +% \end{macrocode} +% \end{macro} +% +% This is a \Verb+\tikzset+ mechanism for setting the dimensions of the tiling. +% \begin{macrocode} +\tikzset{ + tiling~ step/.code={ + \dim_set:Nn \l_@@_step_dim {#1} + } +} +% \end{macrocode} +% +% \begin{macrocode} +\ExplSyntaxOff +% \end{macrocode} +% +% \iffalse +%</tilings> +% \fi +% +% +% \iffalse +%<*penrose> +% \fi +% +% \begin{macrocode} +\RequirePackage{tikz} +\usetikzlibrary{tilings} +\ProvidesFile {tikzlibrarytilings.penrose.code.tex} +[2023/06/01 v2.0 TikZ pics for Penrose tiles] +% \end{macrocode} +% +% +% Create the pre-defined tile shapes. +% +% \begin{itemize} +% \item Thin Rhombus. +% \begin{macrocode} +\DefineTile{thin rhombus}{a A B b} +{ + {0 , 0} + {cosd(18) , sind(18)} + {2*cosd(18) , 0} + {cosd(18) , -sind(18)} +} +% \end{macrocode} +% +% \item Thick Rhombus. +% \begin{macrocode} +\DefineTile{thick rhombus}{B a A b} +{ + {0 , 0} + {cosd(36) , sind(36)} + {2*cosd(36) , 0} + {cosd(36) , -sind(36)} +} +% \end{macrocode} +% +% \item Dart. +% \begin{macrocode} +\DefineTile{dart}{c a A C} +{ + {0 , 0} + {2*sind(18)*cosd(108) , 2*sind(18)*sind(108)} + {2*sind(18) , 0} + {2*sind(18)*cosd(108) , -2*sind(18)*sind(108)} +} +% \end{macrocode} +% +% \item Kite. +% \begin{macrocode} +\DefineTile{kite}{a c C A} +{ + {0 , 0} + {cosd(36) , sind(36)} + {1 , 0} + {cosd(36) , -sind(36)} +} +% \end{macrocode} +% +% \item Golden Triangle. +% \begin{macrocode} +\DefineTile{golden triangle}{a c b} +{ + {0 , 0} + {cosd(18) , sind(18)} + {cosd(18) , -sind(18)} +} +% \end{macrocode} +% +% \item Reverse Golden Triangle. +% \begin{macrocode} +\DefineTile {reverse golden triangle}{B C A} +{ + {0 , 0} + {cosd(18) , sind(18)} + {cosd(18) , -sind(18)} +} +% \end{macrocode} +% +% \item Golden Gnomon +% \begin{macrocode} +\DefineTile {golden gnomon}{C b A} +{ + {0 , 0} + {cosd(36) , sind(36)} + {2*cosd(36) , 0} +} +% \end{macrocode} +% +% \item Reverse Golden Gnomon +% \begin{macrocode} +\DefineTile {reverse golden gnomon}{a B c} +{ + {0 , 0} + {2*cosd(36) , 0} + {cosd(36) , -sind(36)} +} +% \end{macrocode} +% +% \item Primary Pentagon (pentagon 5) +% \begin{macrocode} +\DefineTile {pentagon 5}{a a a a a} +{ + {0 , 0} + {cosd(108) , sind(108)} + {1+cosd(72)+cosd(144) , sind(72)+sind(144)} + {1+cosd(72) , sind(72)} + {1 , 0} +} +% \end{macrocode} +% +% \item Secondary Pentagon (pentagon 3) +% \begin{macrocode} +\DefineTile {pentagon 3}{A b a a b} +{ + {0 , 0} + {cosd(108) , sind(108)} + {1+cosd(72)+cosd(144) , sind(72)+sind(144)} + {1+cosd(72) , sind(72)} + {1 , 0} +} +% \end{macrocode} +% +% \item Tertiary Pentagon (pentagon 2) +% \begin{macrocode} +\DefineTile {pentagon 2}{d A e c A} +{ + {0 , 0} + {cosd(108) , sind(108)} + {1+cosd(72)+cosd(144) , sind(72)+sind(144)} + {1+cosd(72) , sind(72)} + {1 , 0} +} +% \end{macrocode} +% +% \item Pentagram +% \begin{macrocode} +\DefineTile {pentagram}{C E C E C E C E C E} +{ + {1 , 0} + {1-cosd(36) , -sind(36)} + {1-cosd(36)-cosd(108) , -sind(36)-sind(108)} + {cosd(108) , -sind(108)} + {-1+3*cosd(108)+cosd(36) , -sind(36)-sind(108)} + {-1+2*cosd(108)+cosd(36) , -sind(36)} + {-1+2*cosd(108) , 0} + {2*cosd(108) , 0} + {cosd(108) , sind(108)} + {0 , 0} +} +% \end{macrocode} +% +% \item Boat +% \begin{macrocode} +\DefineTile {boat}{C E C E B D B} +{ + {-1+2*cosd(108) , 0} + {2*cosd(108) , 0} + {cosd(108) , sind(108)} + {0 , 0} + {1 , 0} + {1-cosd(36) , -sind(36)} + {-1+2*cosd(108)+cosd(36) , -sind(36)} +} +% \end{macrocode} +% +% \item Diamond. +% \begin{macrocode} +\DefineTile {diamond}{D B B D} +{ + {0 , 0} + {cosd(18) , sind(18)} + {2*cosd(18) , 0} + {cosd(18) , -sind(18)} +} +% \end{macrocode} +% \end{itemize} +% +% +% Place the arcs +% \begin{macrocode} +\tikzset{ + every thin rhombus before path/.code={ + \path[every circle arc/.try] (-edge a end) circle[radius=1/4]; + \path[every long arc/.try] (-edge b start) circle[radius=1/4]; + }, + every thick rhombus before path/.code={ + \path[every circle arc/.try] (-edge a end) circle[radius=1/4]; + \path[every long arc/.try] (-edge B start) circle[radius=3/4]; + }, + every kite before path/.code={ + \path[every circle arc/.try] (-edge a start) circle[radius=2/(sqrt(5)+1)]; + \path[every long arc/.try] (-edge c end) circle[radius=2/(3+sqrt(5))]; + }, + every dart before path/.code={ + \path[every circle arc/.try] (-edge a end) circle[radius=1 - 2/(sqrt(5)+1)]; + \path[every long arc/.try] (-edge c start) circle[radius=2/(sqrt(5)+1) - 2/(3+sqrt(5))]; + } +} +% \end{macrocode} +% +% Now bake the tiles. +% +% \begin{macrocode} +\BakeTile {thin rhombus} +\BakeTile {thick rhombus} +\BakeTile {dart} +\BakeTile {kite} +\BakeTile {golden triangle} +\BakeTile {reverse golden triangle} +\BakeTile {golden gnomon} +\BakeTile {reverse golden gnomon} +\BakeTile {pentagon 5} +\BakeTile {pentagon 3} +\BakeTile {pentagon 2} +\BakeTile {pentagram} +\BakeTile {boat} +\BakeTile {diamond} +% \end{macrocode} +% +% +% \subsection{Lindenmayer System} +% +% \begin{macrocode} +\ExplSyntaxOn +% \end{macrocode} +% +% These are the rules for generating rhombus tilings with the Lindenmayer System procedure. +% +% \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 are the lists of tokens that actually draw things +% \begin{macrocode} +\prop_gput:Nnn \g_@@_drawables_lms_prop {rhombus} {TG} +\prop_gput:Nnn \g_@@_drawables_lms_prop {kite} {Tg} +\prop_gput:Nnn \g_@@_drawables_lms_prop {rtriangle} {TtGg} +\prop_gput:Nnn \g_@@_drawables_lms_prop {ktriangle} {TtGg} +\prop_gput:Nnn \g_@@_drawables_lms_prop {pentagon} {PQRGBD} +% \end{macrocode} +% +% +% These hold the various actions. +% \begin{macrocode} +\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} +% +% 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}} +\prop_gput:Nnn \g_@@_rhombus_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} +% +% 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+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} + } + \UseTile[ + every~ tile/.try, + every~ thin~ rhombus/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ thick~ rhombus/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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}} +\prop_gput:Nnn \g_@@_kite_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} +% +% \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} + } + \UseTile[ + every~ tile/.try, + every~ kite/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ dart/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ reverse~ golden~ triangle/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ golden~ triangle/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ reverse~ golden~ gnomon/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ golden~ gnomon/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ reverse~ golden~ triangle/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ golden~ triangle/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ reverse~ golden~ gnomon/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ golden~ gnomon/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} +} +\tikzset{ + every~ pentagon~ decomposition/.code={% + \int_set:Nn \l_@@_pentagon_parity_int {2} + } +} +\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} + } + \UseTile[ + every~ tile/.try, + every~ pentagon/.try, + every~ + \seq_item:Nn \l_@@_pentagon_parity_seq + {\l_@@_pentagon_parity_int} + \space pentagon/.try, + every~ pentagon~ 5/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ pentagon/.try, + every~ + \seq_item:Nn \l_@@_pentagon_parity_seq + {\l_@@_pentagon_parity_int} + \space pentagon/.try, + every~ pentagon~ 3/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ pentagon/.try, + every~ + \seq_item:Nn \l_@@_pentagon_parity_seq + {\l_@@_pentagon_parity_int} + \space pentagon/.try, + every~ pentagon~ 2/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ pentagram/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ boat/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + 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} + } + \UseTile[ + every~ tile/.try, + every~ diamond/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + tile/.try/.expand~ once=\l_@@_tmpc_tl + ]{diamond} + \group_end: +} +% \end{macrocode} +% +% \begin{macrocode} +\ExplSyntaxOff +% \end{macrocode} +% +% \iffalse +%</penrose> +% \fi +% +% \iffalse +%<*polykite> +% \fi +% +% \begin{macrocode} +\RequirePackage{tikz} +\usetikzlibrary{tilings} +\ProvidesFile {tikzlibrarytilings.polykite.code.tex} + [2023/06/01 v2.0 TikZ pics for Aperiodical Polykite tiles] +% \end{macrocode} +% +% \begin{function}{\DefinePolykiteTile} +% Define one of the family of polykite tiles. +% Needs a name and length parameters. +% A star option switches the side labels to enable the hat-turtle pairing of a tile with its ``opposite''. +% \begin{macrocode} +\DeclareDocumentCommand \DefinePolykiteTile {s m m m} +{ + \IfBooleanTF {#1} + { + \DefineTile {#2} {2 2 1 1 2 2 1 1 1 1 2 2 1 1} + } + { + \DefineTile {#2} {1 1 2 2 1 1 2 2 2 2 1 1 2 2} + } + { + {0 : #4} + ++{90 : #3} + ++{150 : #3} + ++{240 : #4} + ++{180 : #4} + ++{-90 : #3} + ++{210 : #3} + ++{-60 : #4} + ++{0 : #4} + ++{0 : #4} + ++{60 : #4} + ++{-30 : #3} + ++{30 : #3} + ++{120 : #4} + } +} +% \end{macrocode} +% \end{function} +% +% Some predefined tiles. +% The aperiodical hat and turtle can be swapped in for each other as they use the same edge definitions. +% The spectral hat and turtle are designed to be used in the same diagram. +% Technically, the spectral and aperiodical hats are the same, but I figured it better to have two names for the two uses. +% The spectre uses the alternating edge scheme. +% +% \begin{itemize} +% \item Aperiodical and Spectral Hat. +% \begin{macrocode} +\DefinePolykiteTile{aperiodical hat}{sqrt(3)/2}{1/2} +\DefinePolykiteTile{spectral hat}{sqrt(3)/2}{1/2} +% \end{macrocode} +% \item Aperiodical and Spectral Turtles. +% \begin{macrocode} +\DefinePolykiteTile{aperiodical turtle}{1/2}{sqrt(3)/2} +\DefinePolykiteTile*{spectral turtle}{1/2}{sqrt(3)/2} +% \end{macrocode} +% \item Aperiodical Spectre. +% \begin{macrocode} +\DefineTile {spectre} {a A a A a A a A a A a A a A} + { + {0 : .75} + ++{90 : .75} + ++{150 : .75} + ++{240 : .75} + ++{180 : .75} + ++{-90 : .75} + ++{210 : .75} + ++{-60 : .75} + ++{0 : .75} + ++{0 : .75} + ++{60 : .75} + ++{-30 : .75} + ++{30 : .75} + ++{120 : .75} + } +% \end{macrocode} +% +% \item Meta Clusters +% +% The mapping between the notation in the \href{preprint}{https://arxiv.org/abs/2303.10798} is: +% +% \begin{align*} +% A^+, A^- &\mapsto a, A \\ +% B^+, B^- &\mapsto b, B\\ +% F^+, F^- &\mapsto c, C\\ +% X^+, X^- &\mapsto d, D\\ +% L &\mapsto 1 +% \end{align*} +% +% \begin{macrocode} +\DefineTile{meta cluster T}{A A b} +{ +{ -1.5 , -sqrt(3)/2 } +{ 1.5 , -sqrt(3)/2 } +{ 0 , sqrt(3) } +} +\DefineTile{meta cluster P}{1 D d A 1 D d b} +{ +{ -2.5, sqrt(3)/2 } +{ -2, 0 } +{ -1.5, -sqrt(3)/2 } +{ -0.5 , -sqrt(3)/2 } +{ 2.5 , -sqrt(3)/2 } +{ 2 , 0 } +{ 1.5 , sqrt(3)/2 } +{ .5 , sqrt(3)/2 } +} +\DefineTile{meta cluster F}{1 D d 1 D c C d b} +{ +{ -2.5, sqrt(3)/2 } +{ -2, 0 } +{ -1.5, -sqrt(3)/2 } +{ -0.5 , -sqrt(3)/2 } +{ .5 , -sqrt(3)/2 } +{ 1.5 , -sqrt(3)/2 } +{ 2 , 0 } +{ 1.5 , sqrt(3)/2 } +{ .5 , sqrt(3)/2 } +} +\DefineTile{meta cluster H}{B D d B D d a D d} +{ +{ -2, -sqrt(3) } +{ 1, -sqrt(3) } +{ 2, -sqrt(3) } +{ 2.5, -sqrt(3)/2 } +{ 1, sqrt(3)} +{ .5 , 3*sqrt(3)/2 } +{ -.5 , 3*sqrt(3)/2 } +{ -2, 0 } +{ -2.5, -sqrt(3)/2 } +} +% \end{macrocode} +% \item Super Clusters +% +% \begin{macrocode} +\DefineTile{super cluster T}{A A b} +{ +{ -30 : 3 * (1 + sqrt(5))/2 / sqrt(3) } +{ 90 : 3 * (1 + sqrt(5))/2 / sqrt(3) } +{ 210 : 3 * (1 + sqrt(5))/2 / sqrt(3) } +} +% 1 + 3phi, 1 + 2phi +\DefineTile{super cluster P}{1 D d A 1 D d b} +{ +{ - 1.75 - sqrt(5), (sqrt(5)/2 + 1) * sqrt(3)/2 } +++{ -60 : 1 + sqrt(5) } +++{ -60 : 1} +++{ 1, 0} +++{ 3*(1 + sqrt(5))/2, 0 } +++{ 120 : 1 + sqrt(5) } +++{ 120 : 1 } +++{ -1, 0 } +} +\DefineTile{super cluster F}{1 D d 1 D c C d b} +{ +{ - 1.75 - sqrt(5), (sqrt(5)/2 + 1) * sqrt(3)/2 } +++{ -60 : 1 + sqrt(5) } +++{ -60 : 1} +++{ 1, 0} +++{ 1 + sqrt(5), 0 } +++{ 1, 0 } ++{ -.75 + (2 + sqrt(5)) * sqrt(3)/4 * sqrt(3)/3, + (2 + sqrt(5)) * sqrt(3)/4 + 3/4 * sqrt(3)/3 } +++{ -1.5, (2 + sqrt(5)) * sqrt(3)/2 } +++{ -1, 0 } +} +\DefineTile{super cluster H}{B D d B D d a D d} +{ +{1.75 + 3*sqrt(5)/4, -(1 + sqrt(5))*sqrt(3)/4} +++{120 : 3*(1+sqrt(5))/2 } +++{120 : 1 } +++{-1,0} +++{240 : 3*(1+sqrt(5))/2} +++{240 : 1} +++{300 : 1} +++{ 3*(1+sqrt(5))/2, 0 } +++{1, 0} +++{60 : 1} +} +% \end{macrocode} +% \item Subclusters +% +% \begin{macrocode} +\DefineTile{subcluster H}{B B a} +{ + { 0, 0 } + { 3, 0 } + { 60 : 3 } +} +\DefineTile{subcluster T}{A A b} +{ + { 0, 0 } + { 3, 0 } + { 60 : 3 } +} +\DefineTile{subcluster P}{ 1 A 1 b } +{ + { 0, 0 } + { 1, 0 } + { 4, 0 } + { 3, 0 } +} +\DefineTile{subcluster F}{ 1 1 f F b } +{ + { 0, 0 } + { 1, 0 } + +{ 60 : 1 } + { 2, 0 } + { 3, 0 } +} +% \end{macrocode} +% \end{itemize} +% +% The P and F subclusters have no area, so clipping against them is not helpful. +% \begin{macrocode} +\tikzset{ + no clip/.code={% + \tikz@addmode{\tikz@mode@clipfalse}% + }, + every subcluster P clip/.style={no clip}, + every subcluster F clip/.style={no clip}, +} +% \end{macrocode} +% +% +% \begin{macrocode} +\BakeTile {aperiodical hat} +\BakeTile {aperiodical turtle} +\BakeTile {spectral hat} +\BakeTile {spectral turtle} +\BakeTile {spectre} +\BakeTile {meta cluster T} +\BakeTile {meta cluster P} +\BakeTile {meta cluster F} +\BakeTile {meta cluster H} +\BakeTile {super cluster T} +\BakeTile {super cluster P} +\BakeTile {super cluster F} +\BakeTile {super cluster H} +% \end{macrocode} +% +% The subclusters are deformed by default. +% +% \begin{macrocode} +\ExplSyntaxOn +\clist_map_inline:nn {a,A,b,B,f,F} +{ + \tl_new:c {g_@@_side_polykite_#1_tl} + \tl_if_exist:cF {g_@@_side_#1_tl} + { + \tl_new:c {g_@@_side_#1_tl} + } +} + +\tl_gset:cn {g_@@_side_polykite_A_tl} +{ + \pgfsyssoftpath@movetotoken {0pt}{-0.3333332942822268pt} + \pgfsyssoftpath@linetotoken {0.0833331478405773pt}{-0.1889954840909892pt} + \pgfsyssoftpath@linetotoken {0.3333332942822268pt}{-0.3333332942822268pt} + \pgfsyssoftpath@linetotoken {0.5833333235705567pt}{-0.1889954840909892pt} + \pgfsyssoftpath@linetotoken {0.6666667057177732pt}{-0.3333332942822268pt} + \pgfsyssoftpath@linetotoken {1pt}{-0.3333332942822268pt} +} +\tl_gset:cn {g_@@_side_polykite_a_tl} +{ + \pgfsyssoftpath@movetotoken {0pt}{0.33333pt} + \pgfsyssoftpath@linetotoken {0.33333pt}{0.33333pt} + \pgfsyssoftpath@linetotoken {0.41667pt}{0.189pt} + \pgfsyssoftpath@linetotoken {0.66667pt}{0.33333pt} + \pgfsyssoftpath@linetotoken {0.91667pt}{0.189pt} + \pgfsyssoftpath@linetotoken {1pt}{0.33333pt} +} +\tl_gset:cn {g_@@_side_polykite_B_tl} +{ + \pgfsyssoftpath@movetotoken {0pt}{0pt} + \pgfsyssoftpath@linetotoken {0.3333332942822268pt}{0pt} + \pgfsyssoftpath@linetotoken {0.4166665592761237pt}{0.1443378101912376pt} + \pgfsyssoftpath@linetotoken {0.6666667057177732pt}{0pt} + \pgfsyssoftpath@linetotoken {0.9166666178527835pt}{0.1443378101912376pt} + \pgfsyssoftpath@linetotoken {1pt}{0pt} +} +\tl_gset:cn {g_@@_side_polykite_b_tl} +{ + \pgfsyssoftpath@movetotoken {0pt}{0pt} + \pgfsyssoftpath@linetotoken {0.08333pt}{-0.14433pt} + \pgfsyssoftpath@linetotoken {0.33333pt}{0pt} + \pgfsyssoftpath@linetotoken {0.58333pt}{-0.14433pt} + \pgfsyssoftpath@linetotoken {0.66667pt}{0pt} + \pgfsyssoftpath@linetotoken {1pt}{0pt} +} +\tl_gset:cn {g_@@_side_polykite_F_tl} +{ + \pgfsyssoftpath@movetotoken {0pt}{-2.00000070292pt} + \pgfsyssoftpath@linetotoken {0.74999982427pt}{-1.566987221617321pt} + \pgfsyssoftpath@linetotoken {1pt}{-2.00000070292pt} +} +\tl_gset:cn {g_@@_side_polykite_f_tl} +{ + \pgfsyssoftpath@movetotoken {0pt}{2pt} + \pgfsyssoftpath@linetotoken {0.25pt}{1.56699pt} + \pgfsyssoftpath@linetotoken {1pt}{2pt} +} + +\clist_map_inline:nn {a,A,b,B,f,F} +{ + \tl_gclear_new:c {g_@@_side_backup_#1_tl} + \tl_gset_eq:cc {g_@@_side_backup_#1_tl} {g_@@_side_#1_tl} + \tl_gclear_new:c {g_@@_side_#1_tl} + \tl_gset_eq:cc {g_@@_side_#1_tl}{g_@@_side_polykite_#1_tl} +} + +\BakeTile{subcluster~ H} +\BakeTile{subcluster~ T} +\BakeTile{subcluster~ P} +\BakeTile{subcluster~ F} + +\clist_map_inline:nn {a,A,b,B,f,F} +{ + \tl_gset_eq:cc {g_@@_side_#1_tl} {g_@@_side_backup_#1_tl} +} +% \end{macrocode} +% +% \subsection{Lindenmayer System} +% +% These are the rules for generating the super cluster tilings with the Lindenmayer System procedure. +% +% \begin{macro}[internal]{\@@_place_cluster_tile:nn} +% Useful auxiliary for placing a cluster tile from a particular set +% \begin{macrocode} +\cs_new_protected_nopar:Npn \@@_place_cluster_tile:nn #1#2 +{ + \group_begin: + \int_gincr:N \g_@@_tile_int + \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} + } + \UseTile[ + every~ tile/.try, + every~ #1~#2/.try, + tile~ \int_use:N \g_@@_tile_int/.try, + tile/.try/.expand~ once=\l_@@_tmpc_tl + ]{#1~ #2} + \group_end: +} +\cs_generate_variant:Nn \@@_place_cluster_tile:nn {Vn} +% \end{macrocode} +% \end{macro} +% +% +% \begin{macrocode} +\prop_new:N \g_@@_supercluster_lms_rule_prop +\prop_gput:Nnn \g_@@_supercluster_lms_rule_prop {T} +{ + [s H] +} +\prop_gput:Nnn \g_@@_supercluster_lms_rule_prop {H} +{ + [s {r{-60}} T] + [s {x{\fp_to_decimal:n{1}}} {y{\fp_to_decimal:n{(1+2*\c_@@_phi_fp)}}} H] + [s + {x{\fp_to_decimal:n{-2-3*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-\c_@@_phi_fp}}} + H] + [s + {x{\fp_to_decimal:n{1+3*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-1-\c_@@_phi_fp}}} + {r{-120}} + H] + [s + {x{\fp_to_decimal:n{-1.5-3.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{2.5*\c_@@_phi_fp+1.5}}} + {r{-120}} + P] + [s + {x{\fp_to_decimal:n{-1.5-2*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-1.5-3*\c_@@_phi_fp}}} + {r{180}} + P] + [s + {x{\fp_to_decimal:n{3+5.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{.5*\c_@@_phi_fp}}} + {r{120}} + P] + [s + {x{\fp_to_decimal:n{-4.5-6.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{.5-.5*\c_@@_phi_fp}}} + {r{-120}} + F] + [s + {x{\fp_to_decimal:n{1.5+4*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-2.5-3*\c_@@_phi_fp}}} + F] + [s + {x{\fp_to_decimal:n{3+2.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{2+3.5*\c_@@_phi_fp}}} + {r{120}} + F] +} +\prop_gput:Nnn \g_@@_supercluster_lms_rule_prop {P} +{ + [s {r{60}} P] + [s + {x{\fp_to_decimal:n{2.5+3.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-.5-.5*\c_@@_phi_fp}}} + {r{-120}} + H] + [s + {x{\fp_to_decimal:n{-2.5-3.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{.5+.5*\c_@@_phi_fp}}} + {r{180}} + H] + [s + {x{\fp_to_decimal:n{4.5+6*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{.5+\c_@@_phi_fp}}} + {r{120}} + F] + [s + {x{\fp_to_decimal:n{-4.5-6*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-.5-\c_@@_phi_fp}}} + {r{-60}} + F] +} +\prop_gput:Nnn \g_@@_supercluster_lms_rule_prop {F} +{ + [s {r{60}} P] + [s + {x{\fp_to_decimal:n{2.5+3.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-.5-.5*\c_@@_phi_fp}}} + {r{-120}} + H] + [s + {x{\fp_to_decimal:n{-2.5-3.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{.5+.5*\c_@@_phi_fp}}} + {r{180}} + H] + [s + {x{\fp_to_decimal:n{4.5+6*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{.5+\c_@@_phi_fp}}} + {r{120}} + F] + [s + {x{\fp_to_decimal:n{-4.5-6*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-.5-\c_@@_phi_fp}}} + {r{-60}} + F] + [s + {x{\fp_to_decimal:n{3+4.5*\c_@@_phi_fp}}} + {y{\fp_to_decimal:n{-2-2.5*\c_@@_phi_fp}}} + F] +} +% \end{macrocode} +% +% \begin{macrocode} +\prop_gput:Nnn \g_@@_drawables_lms_prop {supercluster} {HTPF} +% \end{macrocode} +% +% \begin{macrocode} +\fp_const:Nn \c_@@_phi_fp {(1 + sqrt(5))/2} +\prop_new:N \g_@@_supercluster_lms_action_prop + +\prop_gput:Nnn \g_@@_supercluster_lms_action_prop {r} +{ + \pgftransformrotate{\l_@@_parameters_lms_tl} +} +\prop_gput:Nnn \g_@@_supercluster_lms_action_prop {x} +{ + \pgftransformxshift{ + \fp_to_dim:n + {.5 * (\l_@@_parameters_lms_tl) * \l_@@_step_dim} + } +} +\prop_gput:Nnn \g_@@_supercluster_lms_action_prop {y} +{ + \pgftransformyshift{ + \fp_to_dim:n + {.5 * sqrt(3) * (\l_@@_parameters_lms_tl) * \l_@@_step_dim} + } +} + +\prop_gput:Nnn \g_@@_supercluster_lms_action_prop {s} +{ + \fp_set:Nn \l_@@_tmpa_fp { + \l_@@_step_dim + / + \c_@@_phi_fp + / + \c_@@_phi_fp + } + \dim_set:Nn \l_@@_step_dim {\fp_to_dim:N \l_@@_tmpa_fp} +} +\prop_gput:Nnn \g_@@_supercluster_lms_action_prop {H} +{ + \@@_place_cluster_tile:nn {super~ cluster}{H} +} +\prop_gput:Nnn \g_@@_supercluster_lms_action_prop {T} +{ + \@@_place_cluster_tile:nn {super~ cluster}{T} +} +\prop_gput:Nnn \g_@@_supercluster_lms_action_prop {P} +{ + \@@_place_cluster_tile:nn {super~ cluster}{P} +} +\prop_gput:Nnn \g_@@_supercluster_lms_action_prop {F} +{ + \@@_place_cluster_tile:nn {super~ cluster}{F} +} +% \end{macrocode} +% +% +% Parameters: +% \begin{enumerate} +% \item Cluster type (super cluster, meta cluster, subcluster) +% \item This tile type (H, T, P, F) +% \item This tile's name +% \item Alignment tile's name +% \item Edge to align along +% \item Edge to align with +% \end{enumerate} +% \begin{macrocode} +\cs_new_protected_nopar:Npn \@@_place_cluster_tile_as_pic:nnnnnn #1#2#3#4#5#6 +{ + \group_begin: + \int_gincr:N \g_@@_tile_int + \fp_set:Nn \l_@@_tmpa_fp {\l_@@_step_dim/(1cm)} + \tl_set:Nx \l_@@_tmpc_tl + { + {\int_use:N \g_@@_tile_int} + {\int_use:N \g_@@_tiles_int} + } + \tl_clear:N \l_@@_tmpa_tl + \tl_put_right:Nn \l_@@_tmpa_tl + { + \pic[ + every~ tile/.try, + every~ #1~#2/.try, + } + \tl_put_right:Nx \l_@@_tmpa_tl + { + tile~ \int_use:N \g_@@_tile_int/.try, + tile/.try=\l_@@_tmpc_tl, + scale=\fp_use:N \l_@@_tmpa_fp, + } + \tl_put_right:Nn \l_@@_tmpa_tl + { + name=#3, + } + \tl_if_empty:nTF {#4} + { + \tl_put_right:Nn \l_@@_tmpa_tl + { + first~ tile/.try, + } + } + { + \tl_put_right:Nn \l_@@_tmpa_tl + { + align~ with=#4~along~#5 + } + \tl_if_single:nF {#6} + { + \tl_put_right:Nx \l_@@_tmpa_tl + { + \c_space_tl using~\tl_tail:n {#6} + } + } + \tl_put_right:Nn \l_@@_tmpa_tl {,} + } + \tl_put_right:Nn \l_@@_tmpa_tl + { + #1~ #2 + ]; + } + \tl_use:N \l_@@_tmpa_tl + \group_end: +} +\cs_generate_variant:Nn \@@_place_cluster_tile_as_pic:nnnnnn { + Vnnnnn, VnVnnn, VnVVnn +} +\tikzset{ + cluster~ type/.initial=super~ cluster, + first~ file/.style={transform~ shape} +} +\prop_new:N \g_@@_cluster_lms_rule_prop +% \end{macrocode} +% +% The first set of rules govern when the tile being replaced is a root tile, in which case one of the new tiles becomes the new root and all others are placed with respect to them. +% +% It's convenient for code readability to have aliases for the labels for the parent and adjoining tiles, which are stored in the \Verb!\l_@@_parameters_lms_tl! token list. +% \begin{macrocode} +\cs_new_nopar:Npn \@@_tile_label: +{ + \tl_item:Nn \l_@@_parameters_lms_tl {1} +} +\cs_new_nopar:Npn \@@_adjoint_label: +{ + \tl_item:Nn \l_@@_parameters_lms_tl {2} +} +% \end{macrocode} +% +% A single \(T\) tile is replaced by a single \(H\) tile +% \begin{macrocode} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {T} +{ + [s {H{\@@_tile_label:0}{}}] +} +% \end{macrocode} +% +% An \(H\) tile is replaced by \(10\) tiles, consisting of a \(T\) tile and \(3\) each of \(H\), \(P\), and \(F\). +% \begin{macrocode} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {H} +{ + [s {r{-60}} {T{\@@_tile_label:0}{}}] + [{ {HTa{A1}} {\@@_tile_label:1} {\@@_tile_label:0} }] + [{ {HTa{A2}} {\@@_tile_label:2} {\@@_tile_label:0} }] + [{ {HT{B1}b} {\@@_tile_label:3} {\@@_tile_label:0} }] + [{ {PHb{B2}} {\@@_tile_label:4} {\@@_tile_label:1} }] + [{ {PHb{B2}} {\@@_tile_label:5} {\@@_tile_label:2} }] + [{ {PHAa} {\@@_tile_label:6} {\@@_tile_label:3} }] + [{ {FHb{B1}} {\@@_tile_label:7} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:8} {\@@_tile_label:2} }] + [{ {FHb{B2}} {\@@_tile_label:9} {\@@_tile_label:3} }] +} +% \end{macrocode} +% +% Lastly, the \(P\) and \(F\) tile substitutions. +% \begin{macrocode} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {P} +{ + [s {r{60}} {P{\@@_tile_label:0}{}}] + [{ {HPaA} {\@@_tile_label:1} {\@@_tile_label:0} }] + [{ {HP{B2}b} {\@@_tile_label:2} {\@@_tile_label:0} }] + [{ {FHb{B2}} {\@@_tile_label:3} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:4} {\@@_tile_label:2} }] +} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {F} +{ + [s {r{60}} {P{\@@_tile_label:0}{}}] + [{ {HPaA} {\@@_tile_label:1} {\@@_tile_label:0} }] + [{ {HP{B2}b} {\@@_tile_label:2} {\@@_tile_label:0} }] + [{ {FHb{B2}} {\@@_tile_label:3} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:4} {\@@_tile_label:2} }] + [{ {FHb{B1}} {\@@_tile_label:5} {\@@_tile_label:1} }] +} +% \end{macrocode} +% +% The rest of the rules are for when the tile being replaced was itself positioned by aligning it with another tile. +% For these tiles, one of its edge tiles will be its root and positioned alongside one of the edge tiles of the replacement of the original tile's alignment tile. +% Then all the other tiles are positioned out from that root. +% The labelling has to be the same regardless of the order of drawing the tiles. +% +% Not every edge pairing is necessary to generate a pattern as the edges that can be created are all between \(A^\pm\) edges and between \(B^\pm\) edges. +% However, to avoid errors in case they are part of the seed then for now we create blank substitution rules that will effectively remove any such rogue elements. +% \begin{macrocode} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {TH{A1}a} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {TH{A2}a} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {THb{B1}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {THb{B2}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HTa{A1}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HTa{A2}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HT{B1}b} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HT{B2}b} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HPaA} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HP{B1}b} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HP{B2}b} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HF{B1}b} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {HF{B2}b} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {PHAa} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {PHb{B1}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {PHb{B2}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {PF{11}{11}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {PF{12}{11}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {PF{11}{12}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {PF{12}{12}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FHb{B1}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FHb{B2}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FP{11}{11}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FP{12}{11}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FP{11}{12}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FP{12}{12}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FFfF} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FFFf} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FF{11}{11}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FF{12}{11}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FF{11}{12}} {} +\prop_gput:Nnn \g_@@_cluster_lms_rule_prop {FF{12}{12}} {} +% \end{macrocode} +% +% To help create the rules then we start with some helper macros. +% Each of these creates the substitution rule for a tile given certain information about where the parent tile is positioned. +% Most of the substitution information consists of placing the tiles next to each other, so only the first tile needs to know about a tile from a different set. +% This makes it relatively easy to set up some templates for the substitution rules. +% \begin{macrocode} +\cs_new_nopar:cpn {@@_T{A1}_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {T#1{A1}#2} + { + [{ {H#3{B1}#4} {\@@_tile_label:0} {\@@_adjoint_label:#5} }] + } +} +\cs_new_nopar:cpn {@@_T{A2}_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {T#1{A2}#2} + { + [{ {H#3{B2}#4} {\@@_tile_label:0} {\@@_adjoint_label:#5} }] + } +} +\cs_new_nopar:cpn {@@_Tb_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {T#1b#2} + { + [{ {H#3a#4} {\@@_tile_label:0} {\@@_adjoint_label:#5} }] + } +} + +\cs_new_nopar:cpn {@@_H{B1}_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {H#1{B1}#2} + { + [{ {P#3A#4} {\@@_tile_label:4} {\@@_adjoint_label:#5} }] + + [{ {HP{B2}b} {\@@_tile_label:1} {\@@_tile_label:4} }] + [{ {TH{A1}a} {\@@_tile_label:0} {\@@_tile_label:1} }] + + [{ {HTa{A2}} {\@@_tile_label:2} {\@@_tile_label:0} }] + [{ {PHb{B2}} {\@@_tile_label:5} {\@@_tile_label:2} }] + + [{ {HT{B1}b} {\@@_tile_label:3} {\@@_tile_label:0} }] + [{ {PHAa} {\@@_tile_label:6} {\@@_tile_label:3} }] + + [{ {FHb{B1}} {\@@_tile_label:7} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:8} {\@@_tile_label:2} }] + [{ {FHb{B2}} {\@@_tile_label:9} {\@@_tile_label:3} }] + } +} + +\cs_new_nopar:cpn {@@_H{B2}_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {H#1{B2}#2} + { + [{ {P#3A#4} {\@@_tile_label:5} {\@@_adjoint_label:#5} }] + + [{ {HP{B2}b} {\@@_tile_label:2} {\@@_tile_label:5} }] + [{ {TH{A2}a} {\@@_tile_label:0} {\@@_tile_label:2} }] + + [{ {HTa{A1}} {\@@_tile_label:1} {\@@_tile_label:0} }] + [{ {PHb{B2}} {\@@_tile_label:4} {\@@_tile_label:1} }] + + [{ {HT{B1}b} {\@@_tile_label:3} {\@@_tile_label:0} }] + [{ {PHAa} {\@@_tile_label:6} {\@@_tile_label:3} }] + + [{ {FHb{B1}} {\@@_tile_label:7} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:8} {\@@_tile_label:2} }] + [{ {FHb{B2}} {\@@_tile_label:9} {\@@_tile_label:3} }] + } +} + +\cs_new_nopar:cpn {@@_Ha_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {H#1a#2} + { + [{ {P#3b#4} {\@@_tile_label:6} {\@@_adjoint_label:#5} }] + + [{ {HPaA} {\@@_tile_label:3} {\@@_tile_label:6} }] + [{ {THb{B1}} {\@@_tile_label:0} {\@@_tile_label:3} }] + + [{ {HTa{A1}} {\@@_tile_label:1} {\@@_tile_label:0} }] + [{ {PHb{B2}} {\@@_tile_label:4} {\@@_tile_label:1} }] + + [{ {HTa{A2}} {\@@_tile_label:2} {\@@_tile_label:0} }] + [{ {PHb{B2}} {\@@_tile_label:5} {\@@_tile_label:2} }] + + [{ {FHb{B1}} {\@@_tile_label:7} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:8} {\@@_tile_label:2} }] + [{ {FHb{B2}} {\@@_tile_label:9} {\@@_tile_label:3} }] + } +} + +\cs_new_nopar:cpn {@@_PA_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {P#1A#2} + { + [{ {H#3{B1}#4} {\@@_tile_label:1} {\@@_adjoint_label:#5} }] + [{ {PHAa} {\@@_tile_label:0} {\@@_tile_label:1} }] + [{ {HP{B2}b} {\@@_tile_label:2} {\@@_tile_label:0} }] + + [{ {FHb{B2}} {\@@_tile_label:3} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:4} {\@@_tile_label:2} }] + } +} + +\cs_new_nopar:cpn {@@_Pb_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {P#1b#2} + { + [{ {H#3a#4} {\@@_tile_label:2} {\@@_adjoint_label:#5} }] + [{ {PHb{B2}} {\@@_tile_label:0}{\@@_tile_label:2} }] + [{ {HPaA} {\@@_tile_label:1} {\@@_tile_label:0} }] + + [{ {FHb{B2}} {\@@_tile_label:3} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:4} {\@@_tile_label:2} }] + } +} + +\cs_new_nopar:cpn {@@_Fb_creator:nnnnn} #1#2#3#4#5 +{ + \prop_gput:Nnn \g_@@_cluster_lms_rule_prop {F#1b#2} + { + [{ {H#3a#4} {\@@_tile_label:2} {\@@_adjoint_label:#5} }] + [{ {PHb{B2}} {\@@_tile_label:0}{\@@_tile_label:2} }] + [{ {HPaA} {\@@_tile_label:1} {\@@_tile_label:0} }] + + [{ {FHb{B2}} {\@@_tile_label:3} {\@@_tile_label:1} }] + [{ {FHb{B1}} {\@@_tile_label:4} {\@@_tile_label:2} }] + [{ {FHb{B1}} {\@@_tile_label:5} {\@@_tile_label:1} }] + } +} +% \end{macrocode} +% +% Now that the creators are set up it is time to invoke them. +% \begin{macrocode} +\clist_map_inline:nn +{ + TH{{A1}}a HP{{{B1}}}b06, + TH{{A2}}a HP{{{B2}}}b06, + THb{{B1}} HPaA04, + THb{{B2}} HPaA05, + PHAa HP{{{B1}}}b16, + PHb{{B1}} HPaA24, + PHb{{B2}} HPaA25, + FHb{{B1}} HPaA24, + FHb{{B2}} HPaA25, +} +{ + \tl_clear:N \l_@@_tmpa_tl + \tl_put_right:Nn \l_@@_tmpa_tl { \use:c } + \tl_put_right:Nx \l_@@_tmpa_tl + { + {@@_ \tl_item:nn {#1}{2}\tl_item:nn {#1}{4} _creator:nnnnn} + {\tl_item:nn {#1}{1}}{\tl_item:nn{#1}{3}} + \tl_item:nn {#1}{5}\tl_item:nn{#1}{7} + \tl_item:nn {#1}{9} + } + \tl_use:N \l_@@_tmpa_tl + \tl_clear:N \l_@@_tmpa_tl + \tl_put_right:Nn \l_@@_tmpa_tl { \use:c } + \tl_put_right:Nx \l_@@_tmpa_tl + { + {@@_ \tl_item:nn {#1}{1}\tl_item:nn {#1}{3} _creator:nnnnn} + {\tl_item:nn {#1}{2}}{\tl_item:nn{#1}{4}} + \tl_item:nn {#1}{6}\tl_item:nn{#1}{8} + \tl_item:nn {#1}{10} + } + \tl_use:N \l_@@_tmpa_tl +} + +% \end{macrocode} +% +% \begin{macrocode} +\prop_new:N \g_@@_cluster_lms_action_prop +% \end{macrocode} +% +% \begin{macrocode} +\prop_gput:Nnn \g_@@_drawables_lms_prop {cluster} {HTPF} +% \end{macrocode} +% +% \begin{macrocode} +\prop_gput:Nnn \g_@@_cluster_lms_action_prop {r} +{ + \pgftransformrotate{\l_@@_parameters_lms_tl} +} +\prop_gput:Nnn \g_@@_cluster_lms_action_prop {x} +{ + \pgftransformxshift{ + \fp_to_dim:n + {.5 * (\l_@@_parameters_lms_tl) * \l_@@_step_dim} + } +} +\prop_gput:Nnn \g_@@_cluster_lms_action_prop {y} +{ + \pgftransformyshift{ + \fp_to_dim:n + {.5 * sqrt(3) * (\l_@@_parameters_lms_tl) * \l_@@_step_dim} + } +} + +\prop_gput:Nnn \g_@@_cluster_lms_action_prop {s} +{ + \fp_set:Nn \l_@@_tmpa_fp { + \l_@@_step_dim + / + \c_@@_phi_fp + / + \c_@@_phi_fp + } + \dim_set:Nn \l_@@_step_dim {\fp_to_dim:N \l_@@_tmpa_fp} +} +% \end{macrocode} +% +% The first set of actions are for when this tile is the root so doesn't have a parent +% \begin{macrocode} +\clist_map_inline:nn {H,T,P,F} +{ + + \prop_gput:Nnn \g_@@_cluster_lms_action_prop {#1} + { + \@@_tikz_keys_get:Nn \l_@@_tmpa_tl {cluster~type} + \tl_set:Nx \l_@@_tmpb_tl {\tl_item:Nn \l_@@_parameters_lms_tl {1}} + \@@_place_cluster_tile_as_pic:VnVnnn + \l_@@_tmpa_tl {#1} \l_@@_tmpb_tl {}{}{} + } +} +% \end{macrocode} +% +% The second set is for when there is an adjoining edge +% \begin{macrocode} +\cs_new_protected_nopar:Npn \@@_place_cluster_tile_as_pic_aux:nnnn #1#2#3#4 +{ + \@@_tikz_keys_get:Nn \l_@@_tmpa_tl {cluster~type} + \tl_set:Nx \l_@@_tmpb_tl {\@@_tile_label:} + \tl_set:Nx \l_@@_tmpc_tl {\@@_adjoint_label:} + \@@_place_cluster_tile_as_pic:VnVVnn + \l_@@_tmpa_tl {#1} \l_@@_tmpb_tl \l_@@_tmpc_tl {#4}{#3} +} + +\clist_map_inline:nn { + TH{A1}a, + TH{A2}a, + THb{B1}, + THb{B2}, + HTa{A1}, + HTa{A2}, + HT{B1}b, + HT{B2}b, + HPaA, + HP{B1}b, + HP{B2}b, + HF{B1}b, + HF{B2}b, + PHAa, + PHb{B1}, + PHb{B2}, + PF{11}{11}, + PF{12}{11}, + PF{11}{12}, + PF{12}{12}, + FHb{B1}, + FHb{B2}, + FP{11}{11}, + FP{12}{11}, + FP{11}{12}, + FP{12}{12}, + FFfF, + FFFf, + FF{11}{11}, + FF{12}{11}, + FF{11}{12}, + FF{12}{12} +} +{ + \prop_gput:Nnn \g_@@_cluster_lms_action_prop {#1} + { + \@@_place_cluster_tile_as_pic_aux:nnnn #1 + } +} + +\ExplSyntaxOff +% \end{macrocode} +% +% \iffalse +%</polykite> +% \fi +% +% \iffalse +%<*penrosedep> +% \fi +% +% \begin{macrocode} +\ProvidesFile {tikzlibrarypenrose.code.tex} + [2023/06/01 v2.0 TikZ pics for Penrose tiles] +\usetikzlibrary{tilings.penrose} +% \end{macrocode} +% +% Backwards compatibility mode: +% +% \begin{itemize} +% \item \Verb+\SetPenrosePath+ is \Verb+\SetTilingPath+ +% \item \Verb+\BakePenroseTile+ and \Verb+\MakePenroseTile+ are \Verb+\BakeTile+ +% \item \Verb+\UsePenroseTile+ is \Verb+\UseTile+ +% \item \Verb+\PenroseDecomposition+ is \Verb+\TilingDecomposition+ +% \end{itemize} +% \begin{macrocode} +\ExplSyntaxOn +\NewDocumentCommand \SetPenrosePath { m } +{ + \@@_set_tiling_path:n {#1} +} +\NewDocumentCommand \BakePenroseTile {m} +{ + \@@_bake_tile:n {#1} +} +\NewDocumentCommand \MakePenroseTile {m} +{ + \@@_bake_tile:n {#1} +} +\NewDocumentCommand \UsePenroseTile {O{} m} +{ + \@@_use_tile:nn {#1}{#2} +} +\NewDocumentCommand \PenroseDecomposition { O{} m m m } +{ + \@@_tiling_decomposition:nnnn {#1}{#2}{#3}{#4} +} +\ExplSyntaxOff +% \end{macrocode} +% +% \begin{macrocode} +\tikzset{ + save Penrose path/.forward to=/tikz/save tiling path, + clone Penrose side path/.forward to=/tikz/clone tiling side path, + spath/prefix/Penrose side/.forward to=/tikz/spath/prefix/tiling side, + spath/suffix/Penrose side/.forward to=/tikz/spath/suffix/tiling side, + clone Penrose tile path/.forward to=/tikz/clone tiling tile path, + spath/prefix/Penrose tile/.forward to=/tikz/spath/prefix/tiling tile, + spath/suffix/Penrose tile/.forward to=/tikz/spath/suffix/tiling tile, + Penrose step/.forward to=/tikz/tiling step, + every tile/.append style={ + every Penrose tile/.try + }, + every tile clip/.append style={ + every Penrose tile clip/.try + }, + every tile pic/.append style={ + every Penrose pic/.try + }, + tile/.append style={ + Penrose tile #1/.try, + Penrose tile/.try=#1 + } +} +% \end{macrocode} +% +% \iffalse +%</penrosedep> +% \fi +% +% \end{implementation} +%\Finale +\endinput diff --git a/graphics/pgf/contrib/tilings/tilings_code.pdf b/graphics/pgf/contrib/tilings/tilings_code.pdf Binary files differnew file mode 100644 index 0000000000..d9a672e1df --- /dev/null +++ b/graphics/pgf/contrib/tilings/tilings_code.pdf |