%% polyomino.tex
%% Copyright 2024-2025 Matthias Floré
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% The Current Maintainer of this work is Matthias Floré.
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% This work consists of the files polyomino.pdf, polyomino.sty,
% polyomino.tex and README.md.
\documentclass[a4paper,english,dvipsnames]{ltxdoc}
\usepackage[english]{babel}
\usepackage[a4paper,left=2.25cm,right=2.25cm,top=2.5cm,bottom=2.5cm,nohead]{geometry}
\usepackage{parskip}
\usepackage{mathtools}
\usepackage{amssymb}
\allowdisplaybreaks
\usepackage{pdflscape}
\usepackage{polyomino}
\input{pgfmanual-en-macros.tex}
\usepackage{codehigh}
\usepackage{fancyhdr}
\pagestyle{fancy}
\renewcommand{\headrulewidth}{0pt}
\fancyhead{}
\ExplSyntaxOn
\NewExpandableDocumentCommand \repeatnumber {}
 { \prg_replicate:nn { \thepage } { * } }
\ExplSyntaxOff
\fancyfoot[C]{\IfRefUndefinedExpandable{Thesourcecode}{}{\begin{tikzpicture}[scale=0.9]
\polyomino[
 grid,
 p={*}{style={teal,draw=black}}
]{\repeatnumber}
\end{tikzpicture}}}
\usepackage[nottoc]{tocbibind}
\usepackage{imakeidx}
\makeindex[program=makeindex,columns=2,intoc=true]
\indexsetup{othercode={\thispagestyle{fancy}}}
\AtEndPreamble{\hypersetup{%
linktoc=all,
pdfstartview=FitH,
colorlinks=true,
linkcolor=Mahogany,
citecolor=ForestGreen,
urlcolor=MidnightBlue,
bookmarksnumbered=true,
pdftitle=The polyomino package,
pdfauthor=Matthias Floré,
pdfsubject=Manual,
pdfkeywords={polyomino,puzzle}}}
\setcounter{tocdepth}{2}
\setcounter{secnumdepth}{2}
\title{The \texttt{polyomino} package\\[12pt]\large Polyominoes using \tikzname{} and \LaTeX3}
\author{Matthias Floré\\\href{mailto:[email protected]}{\texttt{[email protected]}}}
\date{Version 2.0 (2025/07/24)}%\\[12pt]
\begin{document}
\maketitle
\thispagestyle{fancy}
\begin{abstract}
\noindent This package is based on the package |tikz| (see \cite{TtTaPGFp}) and can be used to draw polyominoes. It is possible to define custom styles, pics and grids.% This is the manual for version .
\end{abstract}
\tableofcontents
\section{Usage}
The package |polyomino| can be used by putting the following in the preamble.
\begin{codeexample}[code only]
\usepackage{polyomino}
\end{codeexample}
The package |polyomino| loads the package |tikz|.
\section{The command \textbackslash polyomino}
\begin{command}{\polyomino\opt{\oarg{options}}\marg{polyomino specification}}
This command can be placed inside a |tikzpicture| environment. The \meta{polyomino specification} is a token list. Spaces in this list are ignored. With the initial settings, a |,| starts a new row. Otherwise each element in this list corresponds to a cell. An element can consist of multiple characters by surrounding it with braces. The \meta{options} can be given with the keys described in Section \ref{Keys}.
\begin{codeexample}[width=8cm]
\pgfkeys{
 /polyomino,
 p={F}{style={blue,draw=black,ultra thick}},
 p={I}{style={brown,draw=black,ultra thick}},
 p={L}{style={cyan,draw=black,ultra thick}},
 p={N}{style={gray,draw=black,ultra thick}},
 p={P}{style={lime,draw=black,ultra thick}},
 p={T}{style={magenta,draw=black,ultra thick}},
 p={U}{style={olive,draw=black,ultra thick}},
 p={V}{style={orange,draw=black,ultra thick}},
 p={W}{style={pink,draw=black,ultra thick}},
 p={X}{style={purple,draw=black,ultra thick}},
 p={Y}{style={red,draw=black,ultra thick}},
 p={Z}{style={teal,draw=black,ultra thick}}
}
\begin{tikzpicture}
\polyomino[
 grid
]{
 UUUVVV,
 UXUZZV,
 XXXFZV,
 IXFFZZ,
 ILLFFT,
 ILNTTT,
 ILNWWT,
 ILNNWW,
 PPPNYW,
 PPYYYY
}
\end{tikzpicture}
\end{codeexample}
The algorithm constructs the border of each polyomino. It does not consider holes determined by empty cells. Although it does detect a cell inside a polyomino which has a different style. This is illustrated in the example below.
\begin{codeexample}[width=10cm]
\begin{tikzpicture}[scale=0.8]
\polyomino[
 p={a}{style={gray,draw=black,thick}}
]{
 aaaaa,
 a.a.a,
 aaaaa
}
\polyomino[
 at={(0,-4)},
 p={a}{style={gray,draw=black,thick}},
 p={*}{style={white,draw=black,thick}}
]{
 aaaaa,
 a*a*a,
 aaaaa
}
\end{tikzpicture}
\end{codeexample}
\end{command}
\section{Keys}\label{Keys}
The keys in this Section can be given as \meta{options} to the command |\polyomino|.

There are two key families: |/polyomino| and |/polyomino/p_2|. The key family |/polyomino| is intended for usage in documents whereas |/polyomino/p_2| is not. In the key family |/polyomino|, also keys from the key family |/polyomino/p_2| will be looked up. The second argument from the key |p| only accepts keys from the key family |/polyomino/p_2|.
\begin{key}{/polyomino/at=\marg{point} (initially (0,0))}
This key defines the bottom left coordinate of the polyomino.
\end{key}
\begin{key}{/polyomino/p\_2/connected}
This key sets the |pic| type (which is activated by the key |pic|) to false. This is the initial setting.
\end{key}
\begin{key}{/polyomino/p\_2/discrete}
This key sets the |pic| type (which is activated by the key |pic|) to true.
\end{key}
\begin{key}{/polyomino/empty cell=\marg{token list} (initially .)}
A cell corresponding to the \meta{token list} in the \meta{polyomino specification} will be left empty.

A cell corresponding to the empty token list will always be left empty.
\end{key}
\begin{key}{/polyomino/grid=\opt{\meta{boolean}} (default true, initially false)}
If true then a grid is drawn. The grid does not apply to borders of polyominoes. The style of this grid is determined by the key |grid style|. A grid does not apply to a cell with a |pic|.
\end{key}
\begin{stylekey}{/polyomino/grid style=\marg{options} (initially \normalfont empty)}
This key determines the style of the grid.
\begin{codeexample}[width=6.5cm]
\begin{tikzpicture}[rotate=90]
\polyomino[
 grid,
 grid style={gray,dash pattern=on 3mm off 4mm on 3mm off 0mm},
 p={L}{style={darkgray,draw=black}},
 p={P}{style={green,draw=black}},
 p={T}{style={violet,draw=black}},
 p={V}{style={yellow,draw=black}}
]{
 LTVVV,
 LTTTV,
 LTPPV,
 LLPPP
}
\end{tikzpicture}
\end{codeexample}
\end{stylekey}
\begin{stylekey}{/polyomino/p\_2/p=\marg{name}\marg{options} (initially \normalfont empty)}
This key determines the style of the polyomino with \meta{name} in the \meta{polyomino specification}.

The \meta{options} only accept keys from the key family |/polyomino/p_2|.

In the example below, the polyominoes have the same shape but are differentiated by using different names.
\begin{codeexample}[width=10cm]
\begin{tikzpicture}
\pgfkeys{
 /polyomino,
 p={a}{},
 p={b}{},
 style={fill=none,draw}
}
\def\example{
 aa,
 ab,
 ab,
 bb
}
\polyomino{\example}
\polyomino[
 at={(2,0)}
]{\example}
\end{tikzpicture}
\end{codeexample}
\end{stylekey}
\begin{key}{/polyomino/p\_2/pic=\marg{code}}
The \meta{code} defines the |pic| which is used for each cell of the polyomino.

A grid does not apply to a cell with a |pic|.
\begin{codeexample}[width=7cm]
\begin{tikzpicture}
\polyomino[
 empty cell=*,
 grid,
 p={a}{style={red,draw=black}},
 p={b}{style={blue,draw=black}},
 p={c}{style={orange,draw=black}},
 p={circle}{pic={\fill[green] (0,0) circle[radius=0.4];}},
 row sep=;
]{
    {}    * * b    {}    c ;
    a     a b b {circle} c ;
 {circle} a a b    c     c
}
\end{tikzpicture}
\end{codeexample}
\begin{codeexample}[width=5cm]
\begin{tikzpicture}
\polyomino[
 p={circle}{
   pic={\path[pic actions] (0,0) circle[radius=0.45];},
   style={right color=cyan,left color=red,draw,dashed}
 },
 p={L}{
   pic={
     \fill[yellow!80!black] (-0.5,-0.5) rectangle +(1,1);
     \fill[yellow!50,rounded corners] (-0.4,-0.4) rectangle +(0.8,0.8);
   }
 },
 p={square}{
   pic={\path[pic actions] (-0.45,-0.45) rectangle +(0.9,0.9);},
   style={fill=magenta,draw,rounded corners}
 }
]{
 L {circle} {square} {square} ,
 L {circle} {circle} {square} ,
 L    L     {circle} {circle}
}
\end{tikzpicture}
\end{codeexample}
\end{key}
\begin{key}{/polyomino/row sep=\marg{token list} (initially ,)}
The \meta{token list} in the \meta{polyomino specification} will start a new row.
\end{key}
\begin{stylekey}{/polyomino/p\_2/style=\marg{options} (initially \normalfont empty)}
This key determines the style of the polyomino.
\end{stylekey}
\section{Version history}
\begin{itemize}
\item[] \textbf{Version 1.0 (2024/08/01)} First version.
\item[] \textbf{Version 2.0 (2025/07/24)} Updated the documentation.
\end{itemize}
\begin{thebibliography}{9}
\bibitem{TtTaPGFp}
Till Tantau,
\emph{The \tikzname{} and {\upshape\pgfname} Packages},
Manual for version 3.1.10,
\url{https://ctan.org/pkg/pgf},
2023.
\end{thebibliography}
\clearpage
\currentpdfbookmark{\indexname}{\indexname}
\printindex
\newgeometry{left=2.25cm,right=2.25cm,top=2.25cm,bottom=2.25cm}
\pagestyle{plain}
\appendix
\begin{landscape}
\section{The source code}\label{Thesourcecode}
\dochighinput[language=latex/latex3]{polyomino.sty}
\end{landscape}
\end{document}

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