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author | Karl Berry <karl@freefriends.org> | 2017-03-06 21:58:50 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2017-03-06 21:58:50 +0000 |
commit | aba00871ee9f5f5ac8d46fe9d0b8e29cd8ce1e8b (patch) | |
tree | 98276bb92499bc5ceb7c72cda4393f028520fc4a /Master/texmf-dist/source/latex/rubik/rubikcube.dtx | |
parent | 346afec669dbe142884f0794af09981c591e6afd (diff) |
rubik (6mar17)
git-svn-id: svn://tug.org/texlive/trunk@43415 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/source/latex/rubik/rubikcube.dtx')
-rw-r--r-- | Master/texmf-dist/source/latex/rubik/rubikcube.dtx | 6209 |
1 files changed, 4666 insertions, 1543 deletions
diff --git a/Master/texmf-dist/source/latex/rubik/rubikcube.dtx b/Master/texmf-dist/source/latex/rubik/rubikcube.dtx index c2f2411d015..4f57d98a0ee 100644 --- a/Master/texmf-dist/source/latex/rubik/rubikcube.dtx +++ b/Master/texmf-dist/source/latex/rubik/rubikcube.dtx @@ -1,10 +1,9 @@ % \iffalse meta-comment -% % rubikcube.dtx % -% version 3.0 25 September 2015 +% version v4.0 (03 March 2017) % -% Copyright 2015 +% Copyright 2017 % RWD Nickalls (dick@nickalls.org) and % A Syropoulos (asyropoulos@yahoo.com) % @@ -63,7 +62,7 @@ % % % -% \CheckSum{4105} +%%% \CheckSum{5683} % %%% \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 @@ -82,7 +81,9 @@ %% Right brace \} Tilde \~} % % -% \title{The \textsc{rubikcube} package} +% \title{% +% \ifpdf\pdfbookmark[1]{Title}{Title}\else\fi% +% The \textsc{rubikcube} package} % % \author{ % RWD Nickalls (dick@nickalls.org) \\ @@ -96,7 +97,7 @@ % The \rubikcube\ package provides LaTeX commands and macros % for typesetting Rubik cube (3x3x3) notation, configurations, and % rotation sequences using the TikZ graphic language. It is part of the -% rubik `bundle'. +% Rubik `bundle'. % \end{abstract} % % \medskip @@ -104,7 +105,7 @@ % \begin{minipage}{11cm} % \centering % \ifpdf -% \includegraphics[width=10cm]{Rubik-doc-figF.pdf} +% \includegraphics[width=10cm]{rubik-doc-figF.pdf} % \else % \fi % \end{minipage} @@ -118,58 +119,109 @@ % The \rubikcube\ package (part of the \textsc{rubik} `bundle') provides a % collection of \LaTeX\ commands % and macros for typesetting Rubik cube configurations using the -% PGF/TikZ graphic languages. Note that this package relates only to the +% PGF/TikZ graphic languages, and relates only to the % familiar 3x3x3 Rubik cube. -% We have extended the layer-rotation hieroglyphic notation, originally +% We have extended the rotation hieroglyph notation, originally % developed by Garfath-Cox (1981), and improved by Duvoid (2010, 2011). % % The \rubikcube\ package is designed to be used in conjunction -% with the \textsc{rubikrotation} package (see below); the former deals -% primarily with typesetting, while the latter processes rotation sequences -% and keeps track of the cube's configuration. +% with both the \textsc{rubikrotation} package and the \textsc{rubikpatterns} package. +% The \rubikcube\ package deals primarily with typesetting, while the \textsc{rubikrotation} +% package processes rotation sequences and keeps track of the cube's configuration. +% The \textsc{rubikpatterns} package is a small database of Rubik cube rotation sequences +% which generate well-known named cube configurations (patterns). +% For full functionality it is recommended that all three Rubik packages are used +% together; for~example, +%\begin{verbatim} +% \usepackage{tikz,rubikcube,rubikrotation,rubikpatterns} +%\end{verbatim} +% Note that the \verb!TikZ! package must be loaded \textit{before} the \textsc{rubikcube} +% package. % % The \rubikcube\ package has been road-tested on a Microsoft -% platform (with \textsf{MiK}\TeX), a Linux platform (Mandriva and {\TeX}Live), -% and on a Solaris platform (OpenIndiana). +% platform (with \textsf{MiK}\TeX), a GNU-Linux platform (Debian 8.2.0 +% and {\TeX}Live 2016), and on a Solaris platform (OpenIndiana). % % % For the mathematics and group theory associated with the Rubik cube see Chen~(2004), -% Davis (2006), Golomb~(1981, 1982), Joyner~(2008), Hofstadter (1981), Hutchings~(2011), -% Kociemba web site, Rokicki~\textit{et al.} (2013), Tran~(2005). -% Useful web sites for solvers are the Speedsolving website, and those -% maintained by Duvoid, by Fridrich, by Jelinek, by Reid, and by Vandenburgh -% (see References). +% Davis (2006), Golomb~(1981, 1982), Hofstadter (1981), Hutchings~(2011), +% Heise website, Joyner~(2008), Kociemba website, +% Rokicki~\textit{et al.} (2013), Scherphius website, Tran~(2005). +% Other useful websites are the Speedsolving website, and those +% maintained by Duvoid, by Fridrich, by Jelinek, by Reid, and by Vandenburgh. +% A useful online solver utility (based on an algorithm by Kociemba) is +% available at the RuWix website. Websites with good pages on patterns and symmetries are +% those by Fridrich, Kociemba, Longridge, Reid, Randelshofer, Scherphius +% (see References for details). % % % \subsection{Requirements} % -% The \rubikcube\ package requires the TikZ package. -% In particular, we make use the \cmd{\pgfmathsetmacro} command and -% the TikZ picture environment. +% The \rubikcube\ package requires the TikZ package, since it makes +% use of the TikZ picture environment and the \cmd{\pgfmathsetmacro} command. +% Consequently, the \verb!TikZ! package must be loaded \textit{before} +% the \textsc{rubikcube} package. +% +% Both the \textsc{rubikrotation} and \textsc{rubikpatterns} packages (see below) +% require Perl to be installed. % % % \subsection[rubikrotation package]{Supporting tool---the % \textsc{rubikrotation} package} -% \label{sec:addons} +% \label{sec:rubikrotation} % -% The \textsc{rubikrotation} package, is a dynamic extension to -% the \rubikcube\ package, and is part of the `Rubk bundle'. It consists of the +% The \textsc{rubikrotation} package (also part of the \textsc{rubik} `bundle'), +% is a dynamic extension to the \rubikcube\ package. It consists of the % Perl program \texttt{rubikrotation.pl} and the associated style option % \texttt{rubikrotation.sty}. -% The \textsc{rubikrotation} package implements rotation sequences and -% random scrambling of the 3x3x3 Rubik cube on-the-fly using a +% The \textsc{rubikrotation} package implements rotation sequences on-the-fly using a % \cmd{\RubikRotation}\marg{rotation-sequence} command. It returns the -% new state in a form which is then used by the \rubikcube\ package. +% new state in a form which can then be used by the \rubikcube\ package. +% It also returns some useful strings associated with the rotation sequence +% which can be used by the \rubikcube\ +% package---see also Section~\ref{sec:showsequence}. % % Since the \cmd{\RubikRotation} command works by \textsc{call}ing the % \texttt{rubikrotation.pl} program, it follows that the \textsc{rubikrotation} % package requires (a)~Perl to be installed, -% and (b)~\LaTeX\ needs to be run using the \texttt{--shell-escape} commandline option. -% See the \textsc{rubikrotation} documentation for details. +% and (b)~the \LaTeX\ engine needs to be run using the \texttt{--shell-escape} +% command-line option. Those wishing to use Lua\LaTeX\ will also need to have access +% to the recent \texttt{shellesc} package (in {\TeX}Live 2016). +% The \texttt{shellesc} package can always be downloaded from CTAN directly. +% See the \textsc{rubikrotation} documentation for further details. +% +% +% +% \subsection[rubikpatterns]{Supporting database---\textsc{rubikpatterns.sty} } +% \label{sec:patterns} +% +% +% The \textsc{rubikpatterns.sty} file (also part of the \textsc{rubik} `bundle') +% is a small database of some well-known Rubik cube rotation sequences, stored as +% named macros. For~example, the `fourspot' and `sixspot' sequences are encoded in +% this package as follows: +%\begin{verbatim} +% \newcommand{\fourspot}{[fourspot],F2,B2,U,Dp,R2,L2,U,Dp,<(12q*, 8f*)>} +% \newcommand{\sixspot}{[sixspot],U,Dp,R,Lp,F,Bp,U,Dp,<(8q*, 8f*)>} +%\end{verbatim} +% These sequences can be processed by name (using the \cmd{\RubikRotation} command +% which also requires Perl to be installed---see Section~\ref{sec:rubikrotation}), and +% then displayed (using the \cmd{\ShowCube} command in conjunction with various +% \cmd{\DrawRubikCube...} commands). So, for~example, one could typeset the so-called +% `fourspot' configuration using the following code: +%\begin{verbatim} +% \usepackage{tikz,rubikcube,rubikrotation,rubikpatterns} +% ... +% \RubikCubeSolved +% \RubikRotation{\fourspot} +% \ShowCube{2.4cm}{0.6}{\DrawRubikCubeRU} +%\end{verbatim} +% See also the \textsc{rubikrotation} documentation---especially +% Section~5.1.1 \textit{Sequences as macros}. % % % \subsection{Copyright} -% Copyright 2014--2015 RWD Nickalls and A Syropoulos. +% Copyright 2014--2017 RWD Nickalls and A Syropoulos. % % \medskip % {\noindent}This work may be distributed and/or modified under the @@ -181,31 +233,39 @@ % % \section{Installation} % +% The Rubik bundle consists of the three package \rubikcube, \textsc{rubikrotation} +% and \textsc{rubikpatterns}, each of which needs to be installed separately. +% Here we describe the installation of the \rubikcube\ package. % -% \subsection{Generating the files} +% \subsection{Generating the \rubikcube\ files} % % Place the file \texttt{rubikcube.zip} into a temporary directory, and unzip it. % This will generate the following files: %\begin{verbatim} % rubikcube.ins % rubikcube.dtx -% rubikcube.pdf -% Rubik-doc-figA.pdf -% Rubik-doc-figB.pdf -% Rubik-doc-figC.pdf -% Rubik-doc-figD.pdf -% Rubik-doc-figE.pdf -% Rubik-doc-figF.pdf +% rubikcube.pdf --documentation of the rubikcube package +% rubik-doc-figA.pdf +% rubik-doc-figB.pdf +% rubik-doc-figC.pdf +% rubik-doc-figD.pdf +% rubik-doc-figE.pdf +% rubik-doc-figF.pdf +% rubikexamples.tex +% rubikexamples.pdf +% rubikexamples.sh +% rubikexamples.bat %\end{verbatim} +% % The style option \texttt{rubikcube.sty} is generated by running (pdf)\LaTeX\ on % the file \texttt{rubikcube.ins} as follows: %\begin{verbatim} % pdflatex rubikcube.ins %\end{verbatim} % This documentation file (\texttt{rubikcube.pdf}) can then be generated using the following -% steps\,\footnote{Since the documentation includes a complicated indexing -% system as well a \textsc{pdf} index and hyperef links (the package \texttt{hypdoc} -% is used), then several pdflatex runs are required. Prior to the first run it is +% steps\,\footnote{Several pdflatex runs are required, since the documentation includes +% an index as well as hyperef links (the package \texttt{hypdoc} +% is used). Prior to the first run it is % a good idea to delete any relevant \texttt{.toc}, \texttt{.aux}, \texttt{.out} files.}: %\begin{verbatim} % pdflatex rubikcube.dtx @@ -216,6 +276,14 @@ % pdflatex rubikcube.dtx %\end{verbatim} % +% Note that the package includes a `rubikexamples' file (\texttt{rubikexamples.tex}) +% as well as associated \texttt{.sh} (Linux) and \texttt{.bat} (Microsoft) batch +% files which can be used to facilitate processing the file. +% Note that many of the examples in this file use the \cmd{\RubikRotation} command +% (associated with the \textsc{rubikrotation} package), +% and hence this file needs to be run using the \verb!--shell-escape! command-line +% option (see Section~\ref{sec:rubikrotation} for details). + % % \subsection{Placing the files} % @@ -229,7 +297,7 @@ % % \medskip % {\noindent}Finally, (depending on your system) update the \TeX\ file database. -% For example, on a Linux system one uses the \texttt{texhash} command. +% For~example, on a Linux system one uses the \texttt{texhash} command. % % % \subsection{Usage} @@ -240,212 +308,123 @@ % \begin{quote} %\begin{verbatim} % \usepackage{tikz} -% \usepackage{rubikcube,rubikrotation} +% \usepackage{rubikcube,rubikrotation,rubikpatterns} %\end{verbatim} % \end{quote} % However, the \rubikcube\ package does check for the presence of TikZ, and will % load it if TikZ is not already loaded. % While \rubikcube\ is a stand-alone package, it is best to also load the complementary -% \textsc{rubikrotation} package. -% -% -% \section{TikZ picture environment} -% \label{sec:tikz} -% -% For a basic introduction to the use of TikZ see the following manuals -% (from CTAN or from \texttt{http://altermundus.com/}). -% \begin{itemize} -% \item \texttt{pgfmanual.pdf}, version 3.0.1a (August 2015) (1161 pages) -% \item \texttt{pgfplot.pdf}, version 1.12.1 (2015) (504 pages) -% \item tkz-base-screen.pdf -% \end{itemize} -% An example of the TikZ picture environment for use with the \rubikcube\ package -% is as follows: -% \begin{quote} -%\begin{verbatim} -% \begin{tikzpicture}[scale=0.5] -% .... -% \end{tikzpicture}% -%\end{verbatim} -% \end{quote} -% If no scale is used (default scale = 1), then each of the small -% cubie sides will have a length of 1~cm. -% -% A very useful feature of TikZ is that it automatically -% minimises the surrounding white-space, and consequently this is -% mostly quite sufficient. However, it is good practice to place -% a \% symbol after the \verb!\end{tikzpicture}! command *see above) -% to avoid additional white space (see Section~\ref{sec:trailingpercent}). -% -% -% \subsection[ShowCube command]{\cmd{\ShowCube} command} -% \label{sec:showcube} -% -% \DescribeMacro{\ShowCube} -% \DescribeMacro{\ShowCubeF} -% When making side-by-side figures it can be very helpful -% to place each sub-figure inside a minipage. -% In this case, a useful approach is to first adjust -% the tikzpicture `scale' parameter to obtain the appropriate size, and -% then adjust the minipage width as necessary -% (see Section~\ref{sec:sizeofminipage}). -% The \cmd{\ShowCube} macro (See Section~\ref{sec:showcubecode}) places one -% or more commands inside a tikzpicture environment and places all of -% these inside a minipage. It takes three arguments: the first is the -% minipage width (\verb!#1!), second is the tikzpicture scale -% factor (\verb!#2!), and third is a \cmd{\Draw..} command (|#3|). -% -% \noindent\textsc{usage}: -% The following command would display a Rubik cube in a -% minipage of width 2cm using a tikzpicture scale factor of 0.5: -%\begin{verbatim} -% \ShowCube{2cm}{0.5}{\DrawRubikCubeRU} -%\end{verbatim} -% For example, the following two sets of commands are equivalent (see -% Section~\ref{sec:showcubecode} for the code); i.e.,~any commands which are valid in -% a \texttt{tikzpicture} environment may be used as the main argument for the -% \cmd{\ShowCube} command. -% $$ -% \left. -% \begin{array}{l} -% \verb!\RubikCubeSolved!\\ -% \verb!\begin{minipage}{2cm}!\\ -% \ \ \verb!\centering!\\ -% \ \ \verb!\begin{tikzpicture}[scale=0.5]!\\ -% \ \ \ \ \ \verb!\DrawRubikCubeRU!\\ -% \ \ \ \ \ \verb!\draw[->] (0.5,5) -- (0.5,4);!\\ -% \ \ \verb!\end{tikzpicture}!\\ -% \verb!\end{minipage}!\\ -% \end{array} -% \right\} -% \begin{array}{l} -% \verb!\RubikCubeSolved!\\ -% \verb!\ShowCube{2cm}{0.5}{%!\\ -% \ \ \ \ \verb!\DrawRubikCubeRU!\\ -% \ \ \ \ \verb!\draw[->] (0.5,5) -- (0.5,4);!\\ -% \ \verb!}!\\ -% \end{array} -% $$ -% -% The \cmd{\ShowCubeF} command is similar in all respects except that it places -% an fbox around the minipage in order to enable users to see the extent of any -% associated white space. -% -% Unexpected spacing between two adjacent images, or between an -% image and adjacent text, is usually related to -% `hidden' white-space associated with the image itself or excessive width -% of the associated \cmd{\minipage} (see also Section~\ref{sec:trailingpercent}). -% Consequently, a temporary fbox around the minipage can be a -% useful aid when trying to visualise the full extent of the minipage -% (and its associated whitespace). Use the \cmd{\ShowCubeF} command for this, as follows: -% -% \medskip -% -% \RubikCubeSolved -% \ShowCubeF{4cm}{0.3}{\DrawRubikCubeRU} -%\begin{minipage}{5cm} -%\begin{verbatim} -% \ShowCubeF{4cm}{0.3}{\DrawRubikCubeRU} -%\end{verbatim} -%\end{minipage} -% -% \medskip -% {\noindent}Clearly either the minipage is too wide (4cm) or the \texttt{tikzpicture} -% scale factor is too small (0.3). Once the figure/code has been corrected, then the -% \texttt{F} in the \cmd{\ShowCubeF} command can be removed. Note that while -% the \cmd{\ShowCube} command centers the image inside the minipage, \LaTeX\ positions -% the minipage in the \cmd{\textwidth}, and hence it is generally best to minimise -% the white-space as revealed by the \cmd{\ShowCubeF} command. The relationship -% between the required width of the minipage and the TikZ scale factor for the various -% Rubik cube images is detailed in Section~\ref{sec:sizeofminipage}. +% \textsc{rubikrotation} and \textsc{rubikpatterns} packages. % % +% \DescribeMacro{\rubikcube} +% This command generates the logo \rubikcube. % -% \subsection[Draw.. error message]{\cmd{\Draw} error message} -% \label{sec:drawerrormessage} % -% If a \rubikcube\ \cmd{\Draw..} command is used \textit{outside} a -% TikZ picture environment, then \LaTeX\ issues an -% ``Undefined control sequence'' error message, indicating -% that it is trying to draw something using an undefined -% TikZ \cmd{\draw} command. % -% For example, if we use the \rubikcube\ command -% \cmd{\DrawRubikFlat} without a surrounding TikZ picture environment -% then something similar to the following error message will be generated. -%\begin{verbatim} -%! Undefined control sequence. -%\DrawFlatUp ... }{#1}\pgfmathsetmacro {\uy }{#2}\draw -% [line join=round,... -%l.56 \DrawRubikFlat -%\end{verbatim} +% \section{Command conventions} +% \label{sec:conventions} % % +% All \rubikcube\ package commands assume a 3x3x3 cube by default. +% There are three primary command categories: (a)~\cmd{\Draw..} commands +% (which must always be used \textit{inside} a TikZ picture environment), +% (b)~`parameter-allocation' commands---e.g.,~\cmd{\RubikCubeSolved}---which can +% be used either inside or outside a TikZ environment), +% and (c)~commands which can be used in ordinary text +% (e.g.,~|\rr{}| rotation commands). % -% \section{Command conventions} -% \label{sec:conventions} % -% \subsection{Commands and environments} +% \subsection{Environments} % % Although the \rubikcube\ package has been designed with TikZ in mind, -% it is important to appreciate that of all the various \rubikcube\ +% it is important to appreciate that of all the various \rubikcube\ package % commands only the Rubik \cmd{\Draw...} commands and TikZ commands actually % have to be used inside a TikZ picture environment. % -% Indeed, using \rubikcube\ commands which influence the Rubik colour state +% Indeed, using \rubikcube\ package commands which influence the Rubik colour state % (configuration) outside the \texttt{tikzpicture}, \texttt{minipage} or % \texttt{figure} environments can make for useful % flexibility when a document is generating more than one figure % or image. This is because the scope of any colours specified by commands inside % these environments is constrained to % be `local' to that particular environment, and hence any change in the -% Rubik colour state brought about by such commands is not accessable +% Rubik colour state brought about by such commands is not accessible % globally (i.e.,~outside the environment) ---see also Section~5 in the documentation % of the \textsc{rubikrotation} package. % % Consequently users need to be mindful of the environments when -% drawing long sequences of rotations across several figures; for example, keeping -% \cmd{\RubikRotation} commands outside the environments keeps their effects global. +% drawing sequences of rotations across several figures; for~example, keeping commands like +% \cmd{\RubikRotation}, \cmd{\RubikFace..}, \cmd{\RubikSide..}, \cmd{\RubikCubeSolved}, +% outside the environments keeps their effects global. +% % % \subsection{Capital letters} % -% Each `word' in a command (except the word `text') starts with a capital letter. -% For example, \cmd{\DrawRubikCubeRU}, \cmd{\DrawCubieRU}. -% However, as with \LaTeX, `text..' commands start with a lowercase `t'; -% for example \cmd{\textCubieRU}. Letters for colours (R, O, Y, G, B, W, X) are -% always written in uppercase. +% Virtually all Rubik bundle commands start with a capital letter, primarily to +% avoid any confusion with TikZ commands (these generally start with lower-case letters). However, +% each `word' in a Rubik bundle command (except the word `text') also starts +% with a capital letter, primarily to facilitate readability. +% For~example, \cmd{\DrawRubikCubeRU}, \cmd{\DrawCubieRU}. +% However, as with \LaTeX, `text..' commands start with a lower-case `t'; +% for~example \cmd{\textCubieRU}. Letter arguments for colours (R, O, Y, G, B, W, X) are +% always written in upper-case letters. +% % % % \subsection{XYZ argument ordering} +% \label{sec:xyzarguments} +% +% Many commands have an appended two, three, or even six ordered arguments or letters +% which form some feature of the structure of a command; perhaps +% either face or colour code or a viewpoint direction. % -% Many commands have an appended two (XY) or three (XYZ) ordered letter code -% which is used to for specifying some feature of the command; perhaps -% either face or cubie colours or a viewpoint direction. +% We adopt the convention that where ordering of arguments is critical, then the +% arguments are ordered in the XYZ, $+$, $-$ order. An XYZ code implies that +% the first letter in the code relates to an X-related parameter, +% for~example, L (Left) or R (Right); the second letter relates to a Y-related +% parameter, for~example, U (Up) or D (Down); the third (if required) +% relates to a Z-related parameter, for~example, F (Front) or B (Back) +% ---see Figure~\ref{fig:notation}. % -% The convention is that the letter codes are ordered in the XYZ order; -% i.e.,~the first code relates to an X-related parameter; -% for example L (Left) or R (Right); the second relates to a Y-related -% parameter; for example U (Up) or D (Down); the third (if required) -% relates to a Z-related parameter; for example F (Front) or B (Back). +% Some commands have six arguments which adopt an (XYZ;$+$$-$) format. In this case, +% for~example, the \cmd{\SolvedConfig} command, for which the six colour arguments +% are ordered as X$+$, X$-$, Y$+$, Y$-$, Z$+$, Z$-$. Here the colour argument +% associated with a face positioned on the $+$ve axis is ordered before +% its $-$ve complement on the same axis. % +% Another example is the |\DrawCubieRU{G}{Y}{O}| command, which draws a cubie. Here +% the RU letters are XY ordered; i.e.,~RightUp viewpoint. The sequence of colour codes +% for the three visible faces are XYZ ordered, and hence result in the cube having a +% Green Right face, Yellow Up face and Orange Front face. % -% \textsc{example}: |\DrawCubieRU{G}{Y}{O}| draws a cubie from -% the RightUp viewpoint. The sequence of colour codes for the three visible -% faces are XYZ ordered, and hence result in the cube having a Green Right face, -% Yellow Up face and Orange Front face. % % % \subsection{Trailing \% on the end of commands} % \label{sec:trailingpercent} % -% It is important to include a trailing \% on the end of \rubikcube\ -% commands when used \textit{outside} a TikZ picture environment, and -% also on the end of each \cmd{\end\{tikzpicture\}} environment command. -% This is to prevent unwanted `space' characters appearing in -% the graphics. In \TeX\ every newline character is automatically converted +% Since the all the output of this package is drawn using graphic elements +% using TikZ, it is important to include a trailing \% on the end +% of \rubikcube\ package commands when used \textit{outside} a TikZ picture environment, and +% also on the end of the \cmd{\end\{tikzpicture\}} environment command itself. +% In particular it is important to use a trailing \% on +% the end of lines which break before the terminal curly bracket of a \cmd{\newcommand}. +% +% This is to prevent accumulating spurious spaces which may otherwise appear in +% figures and diagrams as a strange or unexpected horizontal shift or white-space. +% That this can occur is because in \TeX\ every newline character is automatically converted % to a white space---unless you have an empty line -% (Feuers\"{a}nger 2015, \S\,3.2.3, page~20). +% (Feuers\"{a}nger 2016). +% +% The \LaTeX\ fbox is a useful aid for visualising unwanted white space +% which may have accumulated, and for identifying the cause. +% See Section~\ref{sec:showcube} on the \cmd{\ShowCubeF} command for +% more regarding this approach. % +% Although this effect is mostly small, and is generally only observed in situations +% when centering a graphic is critical, it is, however, cumulative and can be surprisingly large. +% In these situations, the cure is the addition of terminal \% characters to preceding +% code guided by careful detective use of the fbox technique mentioned above. % % % \subsection{Cubies, cubicles, faces and facelets} @@ -457,38 +436,283 @@ % % We distinguish three types of cubie: % centre-cubies (single colour), edge-cubies (two colours) and corner-cubies -% (three colours). For example, the red/white edge-cubie is called +% (three colours). For~example, the red/white edge-cubie is called % the RW cubie, and the red/white/green corner-cubie is called the % RWG cubie etc. Note that the colour of a particular face of a 3x3x3 Rubik % cube is determined by the colour of its centre-cubie. % % Similarly, the positions (known as `cubicles') occupied by cubies are -% defined using either a two or three letter face code. For example the +% defined using either a two or three letter face code. For~example, the % right edge position in the Up-layer is termed the Up/Right position, % or just the UR position, and the corner joining the \textsc{down} % \textsc{front} and \textsc{right} faces is the DFR position. % % % -% \section{Colours} +% \section{Rubik cube coordinates} +% \label{sec:coordinates} +% +% The coordinate origin of all 2D Rubik cube images is located +% at the bottom-left corner of the \textsc{front} face, as shown in +% Figure~\ref{fig:cubesquaregraph}. Note also that the bottom left +% extent of this particular 2D rendering of the cube is actually at $(-1,-1)$, +% and hence the default height and width of all oblique-view cubes is 4~units +% (i.e.,~equivalent to 4cm if the TikZ scale-factor = 1). +% +% \begin{figure}[hbt] +% \centering +% \ifpdf +% \includegraphics[height=4cm]{rubik-doc-figB.pdf} +% \else +% \includegraphics[height=4cm]{rubik-doc-figB.eps} +% \fi +% +% \parbox{9cm}{\caption{\label{fig:cubesquaregraph}Origin of coordinates +% is at the bottom left corner of the grey \textsc{front} face. +% Since $P$ is at $(-1,-1)$ then the default height and width of the +% 2D~cube image is 4~units.}} +% \end{figure} +% +% Arranging for $P$ to be at $(-1,-1)$, as well as using the bottom-left corner +% of the \textsc{front} face as the origin, are useful design +% features which make it easy to know the coordinates of any point, and hence +% facilitate the use any of the TikZ commands +% (e.g.,~\cmd{\draw} and \cmd{\node} commands) to superimpose lines, +% arrows and text etc.,~onto the Rubik cube (see Section~\ref{sec:arrows}). + +% +% \subsection[Size of cube minipage]{Size of cube \cmd{\minipage}} +% \label{sec:sizeofminipage} +% +% Since the the default height and width of the oblique 2D~cube image is +% 4~units (see Section~\ref{sec:coordinates} above), +% it follows that the width of the \cmd{\minipage} required for a cube in a +% \texttt{tikzpicture} environment can be easily calculated. For~example, +% if the \texttt{tikzpicture} scale factor used is $0.5$, then the minimum +% width of the required minipage for the \cmd{\DrawRubikCubeLD} view (shown above) +% is therefore $0.5 \times 4\mbox{cm} = 2\mbox{cm}$. +% +% Note that the width of the semi-flat (SF) cube representation is therefore +% 10~units ($=3+3+1+3$), and that of the flat (F) cube is 12~units ($=3+3+3+3$) +% --- see Section~\ref{sec:flatcommands} for images of these forms. +% If in doubt check the horizontal extent of an image using the \cmd{\ShowCubeF} command, +% which places an fbox around the image. +% +% +% +% \section{TikZ picture environment} +% \label{sec:tikz} +% +% All the Rubik bundle \cmd{\Draw..} commands are designed to be used +% with the TikZ picture environment, and are compatible with standard TikZ. +% For a basic introduction to the use of TikZ see the following manuals +% (from CTAN or from \texttt{http://altermundus.com/}). +% \begin{itemize} +% \item \texttt{https://en.wikipedia.org/wiki/PGF/TikZ} +% \item \texttt{pgfmanual.pdf}, version 3.0.1a (?\,2013) (1161 pages) +% \item \texttt{pgfplot.pdf}, version 1.13 (2016) (544 pages) +% \item \texttt{tkz-base-screen.pdf}, version 1.16c (2011) (91 pages) +% \end{itemize} +% An example of the TikZ picture environment for use with the Rubik bundle +% is as follows: +% \begin{quote} +%\begin{verbatim} +% \begin{tikzpicture}[scale=0.5] +% ... +% \end{tikzpicture}% +%\end{verbatim} +% \end{quote} +% If no scale-factor is used (default scale-factor = 1), then each of the small +% cubie sides will have a length of 1~cm. +% +% \textsc{useful commands}:\ Probably the most +% useful TikZ commands for use with regard +% to the Rubik bundle are the \cmd{\draw} command (for drawing lines, arrows, circles), +% and the \cmd{\node} command (for writing text at specific coordinate locations). +% The basic structure of these commands is as~follows, where +% (x,y) represent grid coordinates of start or end points of lines or arrows, +% or of a circle centre, or of text position (see Sections~\ref{sec:flatcommands} +% and \ref{sec:arrows} for examples). +% \begin{quote} +% \begin{verbatim} +% \draw[->,thick,color=blue] (4.5, 2.5) -- (3.5,2.5); +% \draw[->,ultra thick,color=red] (4.5, 2.5) -- (3.5,2.5); +% \draw [color=blue, thick] (0.3, 0.3) circle (1.3); +% \node (B) at (7.5, 1.5) [black]{\small\textsf{B}}; +%\end{verbatim} +%\end{quote} +% Remember that all TikZ commands which are valid inside a \texttt{tikzpicture} +% environment require a terminal semicolon (see Section~\ref{sec:arrows} +% for examples). +% +% \textsc{colours}: \ +% The following colors are predefined by TikZ: red, green, blue, cyan, magenta, +% yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, +% purple, teal, violet and white (see \texttt{https://en.wikipedia.org/wiki/PGF/TikZ}). +% +% \textsc{line width}: \ +% TikZ allows line width to be specified directly +% (e.g.,~\texttt{[line width=<dimension>]}), or by using the following abbreviations: +% `ultra thin' for 0.1pt, `very thin' for 0.2pt, `thin' for 0.4pt (the default width), +% `semi thick' for 0.6pt, `thick' for 0.8pt, `very thick' for 1.2pt, +% `ultra thick' for 1.6pt (see \texttt{https://en.wikipedia.org/wiki/PGF/TikZ}). +% +%% \textsc{white space}: \ +% A particularly useful feature of TikZ is that it automatically +% minimises any horizontal white-space. However, it is good practice to place +% a \% symbol after the \verb!\end{tikzpicture}! command *see above) +% to avoid additional white space inadvertently being added by \LaTeX\ +% (see Section~\ref{sec:trailingpercent}). +% +% When making images it can be helpful to place them inside a minipage +% (e.g.,~using the \cmd{\ShowCube} command / environment below). +% A~convenient approach is to first adjust the value of the tikzpicture scale-factor +% (to obtain the appropriate size), and then adjust the minipage-width as necessary, using +% the fbox associated with the \cmd{\ShowCubeF} command +% (see Section~\ref{sec:sizeofminipage} for a useful guide on this). +% +% The main `display' tool for drawing cubes is the \cmd{\ShowCube} command +% (see below), and this incorporates a +% TikZ picture environment inside a minipage. The equivalent tool for +% displaying rotation sequences is the \cmd{\ShowSequence} command. +% +% +% +% +% +% \section[ShowCube command]{\cmd{\ShowCube} command} +% \label{sec:showcube} +% +% +% \DescribeMacro{\ShowCube} +% This command \cmd{\ShowCube}\marg{width}\marg{scale-factor}\marg{commands} +% is a convenient tool which places one or more commands inside a +% tikzpicture environment and places all of these inside a minipage +% (see Section~\ref{sec:showcubecode} for the code). +% This command takes three arguments: the first (\verb!#1!) is the minipage width, +% the second (\verb!#2!) is the tikzpicture scale factor, and the third (\verb!#3!) +% is a series of any \rubikcube\ package \cmd{\Draw..} and other commands, as well as +% any TikZ commands which are valid in a \texttt{tikzpicture} environment +% (e.g.,~\cmd{\draw} or \cmd{\node} etc.). +% +% \medskip +% +% \noindent\textsc{usage}: +% The following \cmd{\ShowCube} command displays a Rubik cube +% (the `SixT's configuration\footnote{The \cmd{\sixts} macro is from the \textsc{rubikpatterns} +% package.}) and a blue arrow in a minipage of width~3cm, using a tikzpicture scale +% factor of~0.5. +% Note that the TikZ \cmd{\draw} command requires a terminal +% semicolon---see Section~\ref{sec:tikz}. +% +% \medskip +% +% {\noindent}% +% \begin{minipage}{6.6cm} +%\begin{verbatim} +% \RubikCubeSolved +% \RubikRotation{\sixts} +% \ShowCube{3cm}{0.5}{% +% \DrawRubikCubeLU +% \draw[->,thick,color=blue] (4.5, 2.5) -- (3.5,2.5); +% } +%\end{verbatim} +% \end{minipage} +% \hspace{2.5cm}% +%\RubikFaceUp{Y}{Y}{W}{W}{W}{W}{Y}{Y}{W}% +%\RubikFaceDown{Y}{W}{W}{Y}{Y}{Y}{Y}{W}{W}% +%\RubikFaceLeft{B}{G}{G}{B}{B}{B}{B}{G}{G}% +%\RubikFaceRight{G}{B}{B}{G}{G}{G}{G}{B}{B}% +%\RubikFaceFront{O}{O}{O}{R}{O}{R}{R}{O}{R}% +%\RubikFaceBack{O}{R}{O}{O}{R}{O}{R}{R}{R}% +% \ShowCube{3cm}{0.5}{% +% \DrawRubikCubeLU +% \draw[->,thick,color=blue] (4.5, 2.5) -- (3.5,2.5); +% } +% +% \medskip +% +% {\noindent}The convenience of the \cmd{\ShowCube} command is illustrated below; the +% \cmd{\ShowCube} command on the left is equivalent to the bunch of commands +% on the right (see Section~\ref{sec:showcubecode} for the complete code). +% $$ +% \left. +% \begin{array}{l} +% {\ }\\ +% {\ }\\ +% \verb!\ShowCube{3cm}{0.5}{...}!\\ +% {\ }\\ +% {\ }\\ +% \end{array} +% \right\{ +% \begin{array}{l} +% \verb!\begin{minipage}{3cm}%!\\ +% \verb!\centering%!\\ +% \verb!\begin{tikzpicture}[scale=0.5]!\\ +% ...\\ +% \verb!\end{tikzpicture}%!\\ +% \verb!\end{minipage}%!\\ +% \end{array} +% $$ +% +% \DescribeMacro{\ShowCubeF} +% The \cmd{\ShowCubeF} command is similar in all respects except that it places +% an fbox around the minipage in order to enable users to see the extent of any +% associated white space. For~example, unexpected spacing between two adjacent images, +% or between an image and adjacent text, is usually related to +% `hidden' white-space associated with the image itself or excessive width +% of the associated \cmd{\minipage} (see also Section~\ref{sec:trailingpercent}). +% Consequently, a temporary fbox around the minipage can be a +% useful aid when trying to visualise the full extent of the minipage +% (and its associated white-space). Use the \cmd{\ShowCubeF} command for this. + +% For~example, the following use of the \cmd{\ShowCubeF} command reveals a significant +% white-space problem: +% +% \medskip +%{\noindent}% +%\begin{minipage}{6.6cm} +%\begin{verbatim} +% \ShowCubeF{4cm}{0.3}{\DrawRubikCubeRU} +%\end{verbatim} +%\end{minipage} +% \RubikCubeSolved +% \ShowCubeF{4cm}{0.3}{\DrawRubikCubeRU} +% +% \medskip +% {\noindent}In this example, clearly either the minipage is too wide (4cm) or the \texttt{tikzpicture} +% scale factor is too small (0.3). Once the figure/code has been corrected, then the +% \texttt{F} in the \cmd{\ShowCubeF} command can be removed. +% +% Note that while the \cmd{\ShowCube} command centres the image +% inside the minipage, \LaTeX\ positions +% the minipage in the \cmd{\textwidth}, and hence it is generally best to minimise +% the white-space as revealed by the \cmd{\ShowCubeF} command. The~relationship +% between the required width of the minipage and the TikZ scale factor for the various +% Rubik cube images is detailed in Section~\ref{sec:sizeofminipage}. +% +% +% +% \section{Colour commands} +% \label{sec:colours} % % The \rubikcube\ package uses seven colours which are defined as follows: -% red~(R), orange~(O), yellow~(Y), green~(G), blue~(B), white~(W), -% and grey~(X). Now according to the following webpage\,\footnote{We thank Peter Bartal -% for bringing this to our attention.} +% R~(red), O~(orange), Y~(yellow), G~(green), B~(blue), W~(white), +% and X~(grey). Now according to the following webpage\,\footnote{We thank Peter Bartal +% for bringing this webpage to our attention.} % % \medskip % \noindent\texttt{http://The-Rubiks-Cube.deviantart.com/journal/Using-Official-Rubik} -% \newline\texttt{-s-Cube-Colors-268760351} +% \newline\texttt{-s-Cube-Colors-268760351} (Nov 2011) % % \medskip % {\noindent}the official Rubik cube colours are defined as % \begin{quote} %\begin{verbatim} -% .... colours which are red (PMS 200C*), green (PMS 347C*), +% ... colours which are red (PMS 200C*), green (PMS 347C*), % blue (PMS 293C*), orange (PMS 021C*), yellow (PMS 012C*) % and white. -% ..... +% ... % Pantone colors can not be accurately converted to RGB colors, % the colors the web runs on. But they can be approximated. % Through some research, I have found some estimations which @@ -512,10 +736,13 @@ %\end{verbatim} % \end{quote} % However, we have optimised these prescribed colours very slightly -% for screen \& print use (for example, the yellow was made very +% for screen \& print use (for~example, the yellow was made very % slightly brighter), and so the actual colours implemented by -% the \rubikcube\ package are as follows -% (see Section~\ref{sec:codecolours}): +% the \rubikcube\ package are as follows:\,\footnote{Although the Pantone +% colours cannot be converted to RGB, there is a subset of of Pantone colours +% which can be be converted using CMYK +% (see \texttt{https://en.wikipedia.org/wiki/Pantone})}. +% (see Section~\ref{sec:codecolours}): % % \begin{quote} %\begin{verbatim} @@ -529,8 +756,8 @@ %\end{verbatim} % \end{quote} % Different colours can be allocated to the ROYGBWX letters (using the -% \cmd{\colorlet} command) as required. For example, the standard `red' -% colour could be allocated to the letter R using the command +% standard \LaTeX\ \cmd{\colorlet} command) as required. For~example, the +% standard `red' colour could be allocated to the letter R using the command % \begin{quote} % \cmd{\colorlet\{R\}\{red\}} % \end{quote} @@ -543,140 +770,495 @@ % \subsection{Colour state of the cube} % \label{sec:colourstate} % +% +% \DescribeMacro{\RubikFace..} +% \DescribeMacro{\RubikSlice..} +% \DescribeMacro{\RubikSide..} +% \DescribeMacro{\RubikCubeSolved} +% \DescribeMacro{\RubikCubeGrey} +% \DescribeMacro{\RubikCubeGreyAll} % Initially, when \LaTeX\ reads the file \texttt{rubikcube.sty} all facelets -% are allocated the code X, which can be regarded as a zero-colour state. -% Until a facelet is allocated one of the six Rubik colours it will be rendered as -% grey by a command which just draws the current colour state of the cube or a face -% (e.g.,~\cmd{\DrawFlatUpSide}). +% are allocated the colour-code X, which can be regarded as a zero-colour state. +% Until a facelet is allocated one of the six Rubik colours (using a suitable command) +% it will be rendered as grey by a Rubik \cmd{\Draw...} command, since these commands +% simply implement the current colour state of the cube (e.g.,~\cmd{\DrawRubikCubeRU}). % % It is important to appreciate that the various commands which typeset faces % or facelets with colours differ in whether they derive the colours % from the current internal colour `state' (configuration) of the Rubik cube, or not. +% +% The colour state of cubies in faces and slices can be allocated using \cmd{\RubikFace...}, +% \cmd{\RubikSlice...} and \cmd{\RubikSide...} commands (see Sections~\ref{sec:facecommands}, +% \ref{sec:slicecommands} and \ref{sec:rubikside}). +% In addition. the command \cmd{\RubikCubeSolved}, allocates a prescribed colour state +% for the whole `solved' cube, and is a very useful starting +% point (configuration) for subsequent rotations. +% The commands \cmd{\RubikCubeGrey} and \cmd{\RubikCubeGreyAll} allocate different colour +% states for the whole cube, and are designed to be useful starting points when illustrating +% aspects of how to solve the cube. These two commands accept both `grey' and `gray' +% (to be consistent with TikZ). +% Cubies retain their colour allocation even if the cubies are moved using +% the \cmd{\RubikRotation} command (\textsc{rubikrotation} package), unless they are +% overwritten by a subsequent colour allocation command. +% +% To visualise the current state of the cube one has to use a Rubik \cmd{\Draw...} command. +% Although some \cmd{\Draw...} commands (e.g.,~\cmd{\DrawRubikLayerFace...}) allow +% you to specify colours as arguments, \cmd{\Draw...} commands really only +% `paint' colours onto cubie positions (on the page, so to speak). +% \cmd{\Draw..} commands never influence the internal Rubik colour state. +% +% The current colour state / configuration of the Rubik cube can be saved and +% written to a named file (using the \cmd{\SaveRubikState} command) in a form +% which can then be easily \cmd{\input} and processed when required. + +% +% \subsection{RubikFace commands} +% \label{sec:facecommands} +% +% \DescribeMacro{\RubikFaceUp} +% \DescribeMacro{\RubikFaceDown} +% \DescribeMacro{\RubikFaceLeft} +% \DescribeMacro{\RubikFaceRight} +% \DescribeMacro{\RubikFaceFront} +% \DescribeMacro{\RubikFaceBack} +% These commands take nine colour arguments and allocate colours to the +% individual cubies of a Rubik cube face. +% The ordering is isomorphic to the sequence 1--9, i.e.,~numbering the small +% squares 1-3~(top row, left to right), 4-6~(middle row, left to right), +% 7-9~(bottom row, left to right), as follows: +% \begin{quote} +% \fbox{ +% \begin{minipage}{1.6cm} +% \#1 \#2 \#3 +% +% \#4 \#5 \#6 +% +% \#7 \#8 \#9 +% \end{minipage} +% } +% \end{quote} +% Conveniently, \LaTeX\ allows the colour arguments to be separated by spaces +% (e.g.,~separated in groups of three), or even spread across several +% lines (e.g.,~in a square block to resemble a 9-face). This is fortunate, as it +% allows the command to be formulated in a visually intuitive way, as in the +% following examples. +% +% \begin{quote} +% \begin{minipage}{8cm} +%\begin{verbatim} +% \RubikFaceUp{G}{B}{G} {G}{W}{O} {G}{O}{G} +% +% \RubikFaceFront{O}{W}{R} +% {W}{W}{W} +% {G}{W}{G} % -% The colour state of cubies in faces and slices can be allocated using \cmd{\RubikFace...} -% and \cmd{\RubikSlice...} (see Sections~\ref{sec:facecommands} and \ref{sec:slicecommands}). -% The commands \cmd{\RubikCubeSolved} and \cmd{RubikCubeGrey} allocate the colour state -% for the whole cube, and are useful starting points for subsequent rotations. -% Note that cubies will retain their colour allocation even if the cubies are are moved by -% rotation commands, unless they are overwritten by a subsequent colour allocation command. -% To then visualise the cube one has to use a \cmd{\Draw...} command. -% -% The \textsc{rubikrotation} package keeps track of the Rubik state following -% rotations and sequences of rotations processed by its \cmd{\RubikRotation} command. -% The current colour state of the Rubik cube can be saved and written to a named file -% using its \cmd{\SaveRubikState} command; this file can then be \cmd{\input} when required. -% -% Note that although some \cmd{\Draw...} commands (e.g.,~\cmd{\DrawRubikLayerFace...}) use -% colours as arguments, these commands really only `paint' colours onto cubie positions -% (on the page, so to speak); i.e.,~these commands do not update the internal Rubik -% colour state, and hence these colours do not exist outside the particular -% \texttt{tikzpicture} environment the \cmd{\Draw..} command was used in. +%\end{verbatim} +% \end{minipage} +% \end{quote} % +% \DescribeMacro{\RubikFaceUpAll} +% \DescribeMacro{\RubikFaceDownAll} +% \DescribeMacro{\RubikFaceLeftAll} +% \DescribeMacro{\RubikFaceRightAll} +% \DescribeMacro{\RubikFaceFrontAll} +% \DescribeMacro{\RubikFaceBackAll} +% Each of the above commands has an associated +% `\texttt{All}' version which allocates the same colour to all the cubies +% on a 9-face (i.e.,~only a single colour argument is required). % -% \section{Rubik cube coordinates} -% \label{sec:coordinates} +% If you want a particular face to be all grey, then +% use the colour-code~X; for~example, \cmd{\RubikFaceUpAll\{X\}}. +% Failure to include a valid colour argument will generate a +% `missing parameter' error, and no colour will be +% allocated (i.e.,~you will see a black-hole). +% Use of these commands is shown in the following figure. % -% The coordinate origin of each view of the Rubik cube is located -% at the bottom-left corner of the \textsc{front} face, as shown in -% Figure~\ref{fig:cubesquaregraph}. Note also that the bottom left -% corner of the cube itself is at $(-1,-1)$, -% and hence the default height and width of the cube is 4cm. +% \bigskip +% +% \begin{minipage}{2.8cm} +% \RubikFaceUpAll{X} +% \RubikFaceRightAll{R} +% \RubikFaceFront{W}{Y}{G} +% {W}{Y}{G} +% {W}{Y}{G} +% \begin{tikzpicture}[scale=0.7] +% \DrawRubikCubeRU +% \end{tikzpicture}% +% \end{minipage} +% \hspace{5mm} +% \begin{minipage}{0.6\textwidth} +%\begin{verbatim} +% \RubikFaceUpAll{X} +% \RubikFaceRightAll{R} +% \RubikFaceFront{W}{Y}{G} +% {W}{Y}{G} +% {W}{Y}{G} +% \ShowCube{3cm}{0.7}{\DrawRubikCubeRU} +% \end{verbatim} +% \end{minipage} +% % -% Using the \textsc{front} bottom-left corner as the origin -% is an important feature since knowing the location of the -% origin enables one to easily use any of the TikZ commands -% (e.g.,~\cmd{\draw} and \cmd{\node} commands) to superimpose lines, -% arrows and text etc.\ onto the Rubik cube (see Section~\ref{sec:arrows}). +% \subsection{Solved Configuration} +% \label{sec:solvedconfig} % -% \begin{figure}[hbt] +% \DescribeMacro{\SolvedConfig} +% This command allocates the six face colours according to the following ordered +% XYZ$+-$ argument rule, namely X$+$, X$-$, Y$+$, Y$-$, Z$+$, Z$-$; i.e.,~the order +% of the six colour arguments follows the face order +% \textsc{right, left, up, down, front, back} (for notation see +% Section~\ref{sec:xyzarguments} and Figure~\ref{fig:notation}). +% {\newline}\textsc{usage}:\ \verb!\SolvedConfig{G}{B}{W}{Y}{O}{R}! +% {\newline}Examples of its use are shown in the next section. +% +% +% \subsection{RubikCubeSolved command} +% \label{sec:rubikcubesolved} +% +% \DescribeMacro{\RubikCubeSolved} +% \DescribeMacro{\RubikCubeSolvedWY} +% The action of both of these commands is identical: +% they both set all the face colours to the following standard `solved' cube +% configuration, namely Up=white, Down=yellow, Right=green, Left=blue, Front=orange, Back=red, +% by invoking the above \cmd{\SolvedConfig} command, as follows: +%\begin{verbatim} +%\newcommand{\RubikCubeSolved}{\SolvedConfig{G}{B}{W}{Y}{O}{R}} +%\end{verbatim} +% Note that this is in fact just a convenient short-hand for the following: +%\begin{verbatim} +%\newcommand{\RubikCubeSolved}{% +% \RubikFaceRightAll{G}% +% \RubikFaceLeftAll{B}% +% \RubikFaceUpAll{W}% +% \RubikFaceDownAll{Y}% +% \RubikFaceFrontAll{O}% +% \RubikFaceBackAll{R}% +%} +%\end{verbatim} +% Note that for convenience, this configuration is also available using the command +% \verb!\RubikCubeSolvedWY! (WY denoting White opposite Yellow). +% This solved configuration is shown in the following +% semi-flat (SF) image. +% +% +% \bigskip +% +% \begin{minipage}{5cm} % \centering -% \ifpdf -% \includegraphics[height=3cm]{Rubik-doc-figB.pdf} -% \else -% \includegraphics[height=3cm]{Rubik-doc-figB.eps} -% \fi +% \begin{tikzpicture}[scale=0.5] +% \RubikCubeSolvedWY +% \DrawRubikCubeSF +% \end{tikzpicture}% +% \end{minipage} +% \begin{minipage}{0.5\textwidth} +%\begin{verbatim} +% \RubikCubeSolvedWY +% \ShowCube{5cm}{0.5}{\DrawRubikCubeSF} +%\end{verbatim} +% \end{minipage} % -% \parbox{9cm}{\caption{\label{fig:cubesquaregraph}Origin of coordinates -% is at the bottom left corner of the grey \textsc{front} face. -% The bottom left corner of the cube itself is at $(-1,-1)$, -% and hence the default height and width of the 3D-cube is 4cm.}} -% \end{figure} +% \bigskip % +% Note that the width of the minipage used in \cmd{\ShowCube} command above +% is set to 5cm. This value is derived from the fact +% that the \textit{unscaled} width of the semi-flat image is 10cm (9 + 1 squares), and hence if +% the TikZ scale factor is set to 0.5 then the minimum minipage width = $10 \times 0.5 = 5$cm +% (see Section~\ref{sec:coordinates} for details). % % -% \subsection[Size of cube minipage]{Size of cube \cmd{\minipage}} -% \label{sec:sizeofminipage} +% \textbf{Other orientations:} If other orientations of the solved cube are required, +% this can be easily achieved using the \cmd{\RubikRotation} command +% (from the \texttt{RubikRotation} package) to rotate the cube as required. +% For~example, we could make a command to show the above solved cube upsidedown +% and rotated slightly, as follows: +%\begin{verbatim} +%\newcommand{\CubeUpSideDown}{\RubikCubeSolved\RubikRotation{x2,y}} +%\end{verbatim} +% ---this uses the rotations \rrx, \rrx, to invert, and then \rry\ to turn +% the cube 90~$\deg$: % -% Since the the default height and width of the 3D-cube is 4cm (see above), -% it follows that the width of the \cmd{\minipage} required for a cube in a -% \texttt{tikzpicture} environment can be easily calculated. For example, -% if the \texttt{tikzpicture} scale factor used is $0.5$, then the minimum -% width of the required minipage for the \cmd{\DrawRubikCubeLD} view (shown above) -% is therefore $0.5 \times 4\mbox{cm} = 2\mbox{cm}$. +% \bigskip +% +% \begin{minipage}{2.6cm} +% \centering +% \begin{tikzpicture}[scale=0.5] +% \DrawNCubeAll{3}{O}{Y}{G} +% \end{tikzpicture}% +% \end{minipage} +% \hspace{5mm} +% \begin{minipage}{0.6\textwidth} +%\begin{verbatim} +% \CubeUpSideDown +% \ShowCube{2cm}{0.5}\DrawRubikCubeRU} +%\end{verbatim} +% \end{minipage} +% +% \bigskip +% +%% \DescribeMacro{\RubikCubeSolvedWB} +% \textbf{Other configurations:} While the `solved' WY colour configuration +% described above (White face opposite Yellow) +% is that of the most commonly occurring Rubik cube, another `solved' colour configuration +% which is also commercially available has the White opposite Blue configuration, which +% is available using the command \verb!\RubikCubeSolvedWB!. +% Its colour configuration is as follows: +% +%\begin{center} +% \RubikCubeSolvedWB +% \ShowCube{4cm}{0.4}{\DrawRubikCubeSF}% +%\end{center} +% +% \bigskip +% +% Note that users can easily create their own alternative `solved' +% face/colour versions. +% For~example, the above mentioned white opposite +% blue~(WB) solved configuration command \verb!\RubikCubeSolvedWB! +% (white opposite blue, red opposite orange, +% and green opposite yellow), was created using \verb!\SolvedConfig{R}{O}{W}{B}{G}{Y}! +% (for the code see \ref{sec:codesolvedconfig}). +% +% +% \subsection{RubikCubeGrey command} +% \label{sec:rubikcubegrey} +% +% \DescribeMacro{\RubikCubeGrey} +% \DescribeMacro{\RubikCubeGreyAll} +% The command \cmd{\RubikCubeGrey} generates a 3x3x3 cube with no colours allocated +% \textit{except} for the central cubie of each face, which takes the same colour +% configuration as defined for the \cmd{\RubikCubeSolved} command. +% The command \cmd{\RubikCubeGreyAll} generates a cube with \textit{all} the faces +% completely grey. +% Both these commands will accept either `grey' or `gray' (to be consistent with TikZ). +% +% These two commands, are designed to be useful starting points when wanting to +% describe the movement of particular cubies. We can see the effect of +% the \cmd{\RubikCubeGrey} command by viewing the cube in a semi-flat (SF) format, +% as follows: +% +% \bigskip +% +% \RubikCubeGrey +% \ShowCube{4.5cm}{0.45}{\DrawRubikCubeSF} +% \hspace{3mm} +% \begin{minipage}{0.6\textwidth} +%\begin{verbatim} +% \RubikCubeGrey +% \ShowCube{4.5cm}{0.45}{\DrawRubikCubeSF} +%\end{verbatim} +% \end{minipage} +% +% \bigskip +% Users can easily set their own alternative face/colour configuration either by `renewing' +% the \cmd{\RubikCubeGrey} command along the lines shown above (the code is +% in Section~\ref{sec:codegrey}), or simply creating a new `variant' command +% altogether. +% +% +% +% \subsection{RubikSlice commands} +% \label{sec:slicecommands} +% +% \DescribeMacro{\RubikSliceTopX} +% \DescribeMacro{\RubikSliceMiddleX} +% \DescribeMacro{\RubikSliceBottomX} +% These three commands allocate the six visible cubie colours associated with a +% \textit{horizontal} slice of a Rubik cube. +% There are three pairs of Slice commands; one pair +% (Left view \& Right view) for each of the horizontal slices Top, Middle, Bottom. +% The six colour arguments associated with a given slice run in sequence +% from left to right irrespective of the viewpoint, e.g.,~\#1 \#2 \#3 \#4 \#5 \#6. % -% The default width of the semi-flat cube representation is 10cm ($=3+3+1+3$), -% and that of the flat cube is 12cm ($=3+3+3+3$). If in doubt check the extent of -% any horizontal white-space using an fbox, or the \cmd{\ShowCubeF} command. +% Since the viewpoint of the Rubik cube (from the Right or from the Left) +% influences which face the colours are associated with, it is necessary +% to have the view (R or L) specified in the command name. % +% The format of the `slice' command is shown in the following example. +% The Rubik cube is shown from the LeftDown (LD) view +% and consequently each of the `slice' commands in this +% particular example ends in L, consistent with +% the final \cmd{\DrawRubikCubeLD} command. +% +% Note that the two legacy `Equator' versions (now replaced by `Middle') +% are retained to allow backward compatibility. +% +% \bigskip +% +% \begin{minipage}{2.8cm} +% \centering +% \RubikFaceDownAll{Y} +% \RubikSliceTopL {G}{G}{G} {R}{R}{R} +% \RubikSliceMiddleL {R}{R}{R} {B}{B}{B} +% \RubikSliceBottomL {O}{O}{O} {G}{G}{G} +% \begin{tikzpicture}[scale=0.7] +% \DrawRubikCubeLD +% \end{tikzpicture}% +% \end{minipage} +% \hspace{5mm} +% \begin{minipage}{0.6\textwidth} +%\begin{verbatim} +% \RubikFaceDownAll{Y} +% \RubikSliceTopL {G}{G}{G} {R}{R}{R} +% \RubikSliceMiddleL {R}{R}{R} {B}{B}{B} +% \RubikSliceBottomL {O}{O}{O} {G}{G}{G} +% \ShowCube{3cm}{0.7}{\DrawRubikCubeLD} +%\end{verbatim} +% \end{minipage} +% +% +% +% \subsection{RubikSide commands} +% \label{sec:rubikside} +% +% \DescribeMacro{\RubikSideLeft} +% \DescribeMacro{\RubikSideRight} +% \DescribeMacro{\RubikSideFront} +% \DescribeMacro{\RubikSideBack} +% These RubikSide commands allocate colours to the side facelets of +% the UP~face, and each takes three ordered colour arguments, running from +% top-left to top-right when looking directly at the side faces---see Section~\ref{sec:rubiksidecode}. +% These facelets are the top three facelets of each side Front, Back, Left, Right. +% +% {\noindent}\textsc{usage}: \verb!\RubikSideBack{B}{G}{G}! +% +% \medskip +% +% \DescribeMacro{\RubikSideLeftAll} +% \DescribeMacro{\RubikSideRightAll} +% \DescribeMacro{\RubikSideFrontAll} +% \DescribeMacro{\RubikSideBackAll} +% These commands allocate the same colour to all three side cubies, and hence +% take only a single colour argument. +% +% {\noindent}\textsc{usage}: \verb!\RubikSideBackAll{R}! +% +% \medskip +% +% The \cmd{\RubikSide..} and \cmd{\RubikFace..} commands are useful for setting up the colours +% for just part of the cube. For~example, the following commands set-up the UP-face and sides, +% and then draws the face and sidebars using \verb!\DrawFlatUpSide!. +% +% \bigskip +% +% \begin{minipage}{4cm} +% \centering +%\RubikFaceUp {R}{Y}{R}% +% {Y}{Y}{Y}% +% {G}{Y}{B}% +%\RubikSideBack{B}{G}{G}% +%\RubikSideFront{Y}{R}{Y}% +%\RubikSideRight{O}{B}{Y}% +%\RubikSideLeft{Y}{O}{O}% +%\ShowCube{2cm}{0.5}{\DrawFlatUpSide} +% \end{minipage} +% \hspace{1cm} +% \begin{minipage}{0.6\textwidth} +%\begin{verbatim} +%%set up the UP face +%\RubikFaceUp {R}{Y}{R}% +% {Y}{Y}{Y}% +% {G}{Y}{B}% +%\RubikSideBack{B}{G}{G}% +%\RubikSideFront{Y}{R}{Y}% +%\RubikSideRight{O}{B}{Y}% +%\RubikSideLeft{Y}{O}{O}% +%%draw the UP face and sides +%\ShowCube{2cm}{0.5}{\DrawFlatUpSide} +%\end{verbatim} +% \end{minipage} +% +% \bigskip +% +% Note that we could instead have drawn the above image using \cmd{\DrawRubikLayer..} +% commands. However, using the \cmd{\RubikSide..} and \cmd{\RubikFace..} commands +% makes for a much more flexible and dynamic system, since the colours allocated using +% these commands (provided they are external to an environment) will be global, +% and hence will follow subsequent \cmd{\RubikRotation} commands. +% +% +% +% \pagebreak % % % \section{Rotation commands} % \label{sec:RubikCommands} % -% We use the standard Rubik cube notation of WCA~(2012)---see article~12---and -% also the `s' (Slice) and `a' (anti-Slice) notation described in the -% `Notation and terminology' section -% in the `Pretty patterns' page on the website of -% Fridrich (see References). -% -% It is recommended that commas are used to separate sequential -% Rubik moves or commands to avoid ambiguity, especially when using just -% lettercodes on their own. -% For example, in the following sequence the commas remove any ambiguity: -% \rr{U},\rr{Lw}2,\rr{Usp},\rr{Da} \ \ (|\rr{U},\rr{Lw}2,\rr{Usp},\rr{Da}|). +% The Rubik bundle implements not only the standard Rubik cube notation of the +% World Cube Association (see WCA website), but also the main variant notations +% used by the Rubik interest groups and websites. +% +% \begin{figure}[hbt] +% \centering +% \ifpdf +% \includegraphics[height=5cm]{rubik-doc-figA.pdf} +% \fi +% \caption{\label{fig:notation}Face rotations} +% \end{figure} +% +% To avoid confusion the Rubik bundle uses a trailing `p' (lower-case) in rotation-codes to denote +% a `prime' (reversed direction); we also recommend that commas are used to separate +% sequential Rubik rotations (moves). +% While these are mainly to avoid ambiguity, they also greatly facilitate computer +% searching and copy-and-pasting of rotation sequences. +% +% Unfortunately, obtaining a good balance between an intuitive notation for defining +% rotations and the need for flexibility is difficult, +% and consequently some notation is more intuitive than others. A good compromise +% seems to be the World Cube Association's FADN structure; i.e.,~Face (L,R,U,D,F,B), +% Action (m,w,s,a,c), Direction (p), +% N (n); for example, codes like \texttt{R, R2, Rc, Rm, Rwp, Rwp2} etc. +% +% +% The \rubikcube\ package includes commands for typesetting a wide range of +% rotation-codes (e.g.,~\rr{R}, \rr{y}, \rr{Bw}) and +% equivalent hieroglyphs (e.g.,~\rrh{R}, \rrh{y}, \rrh{Bw}), as well as commands +% for typesetting 3x3x3 cubes and single cubies. All the rotation-codes and +% hieroglyphs are typeset using one particular font \& size which we call the `rubikfont' +% for convenience (see Section~\ref{sec:rubikfont} for details). +% All of the rotation-codes described +% here are recognised by the \textsc{rubikrotation} package +% (see Section~\ref{sec:rubikrotation}). +% +% Note that there are some rotation codes which are not represented by arrow +% hieroglyphs, since their rotation is not visible from the \textsc{front} face, +% and hence cannot easily be rendered as an arrow hieroglyph. Consequently these +% rotations have a simple `letter' hieroglyph +% in the form of the rotation-code in a square; for~example, \rrhBw, \rrhFm. % -% +% +% \pagebreak % % \subsection{Overview} % \label{sec:overview} % -% The \rubikcube\ notation comprises a range of -% commands for moves or rotations (e.g.,~\rr{R}, \rr{y}, \rr{Bw}) and their equivalent hieroglyphs -% (e.g.,~\rrh{R}, \rrh{y}, \rrh{Bw}), as well as commands for drawing 3x3x3 cubes and single cubies. -% -% Note that there are a few rotation commands which do not have arrow -% hieroglyphs---their their rotation is not visible from the \textsc{front} face -% and hence cannot easily be rendered as an arrow hieroglyph. Consequently these -% rotations have a simple `letter' hieroglyph -% in the form of the rotation-code in a square; for example \rrhBw, \rrhSb. +% We now describe the four commands used for typesetting the various rotation-codes. % % \DescribeMacro{\rr} -% The rotation-code of a rotation is typeset (as in text) using the rubik-rotation -% \cmd{\rr\marg{rotation-code}} command: i.e.,~\rr{R}\ is typeset using the command \cmd{\rr\{R\}}. -% The hieroglyph of a rotation command is generated (in text) by -% \DescribeMacro{\rrh} -% using instead the command \cmd{\rrh\marg{rotation-code}}. Thus the command \cmd{\rrh\{R\}} generates -% \rrh{R}\ which is the hieroglyph associated with \rr{R}. +% The text version of a rotation-code is typeset using the rubik-rotation +% command \cmd{\rr\marg{rotation-code}}, i.e.,~\rr{R}\ is typeset using the command \cmd{\rr\{R\}}. +% The hieroglyph of a rotation is generated (in text) by \DescribeMacro{\rrh} +% using instead the command \cmd{\rrh\marg{rotation-code}}. For~example, the command +% \cmd{\rrh\{R\}} generates \rrh{R}\ which is the hieroglyph associated with +% the rotation \rr{R}. % % \DescribeMacro{\Rubik} % A vertically combined rotation-code and its hieroglyph is generated using the command -% \cmd{\Rubik\marg{rotation-code}}. For example, \Rubik{R}\ is generated by the command \cmd{\Rubik\{R\}}, +% \cmd{\Rubik\marg{rotation-code}}. For~example, \Rubik{R}\ is generated by the command \cmd{\Rubik\{R\}}, % with the square hieroglyph sitting on the baseline. -% For some hieroglyphs (e.g.,~\rrh{x}, \rrh{y}, \rrh{z}\ denoting 90~degree axis rotations) -% the only difference between the \cmd{\rrh\{\}} and \cmd{\Rubik\{\}} forms is that +% For some hieroglyphs (e.g.,~\rrh{x}, \rrh{y}, \rrh{z}\ denoting 90~degree cube-axis rotations) +% the only difference between the \cmd{\rrh\{\}} and \cmd{\Rubik\{\}} form is that % the \cmd{\Rubik\{\}} form is elevated to sit on the baseline just like the other % \cmd{\Rubik\{\}} hieroglyphs. -% For example \cmd{\rrh\{yp\}} generates \rrh{yp}, while +% For~example, \cmd{\rrh\{yp\}} generates \rrh{yp}, while % \cmd{\Rubik\{yp\}} generates \Rubik{yp}. % % \DescribeMacro{\textRubik} % A horizontally combined rotation-code and its hieroglyph (in sequence as in text) -% is generated using the command stem \cmd{\textRubik\marg{rotation-code}}. -% For example, \textRubik{R}\ is typeset using the command \cmd{\textRubik\{R\}}. -% A list of all commands and their associated hieroglyphs is given in +% is generated using the command \cmd{\textRubik\marg{rotation-code}}. +% For~example, \textRubik{R}\ is typeset using the command \cmd{\textRubik\{R\}}. +% A list of all rotation-code commands and their associated hieroglyphs is given in % Section~\ref{sec:listofcommands}. % -% \pagebreak +% % % \subsection{Face rotations} % @@ -688,10 +1270,10 @@ % \DescribeMacro{B} % The six main faces of the cube are denoted as \textsc{front} (towards the observer), % \textsc{back}, \textsc{left}, \textsc{right}, \textsc{up}, \textsc{down}. -% The uppercase initial letter of each face-name (\rr{F}, \rr{B}, \rr{L}, \rr{R}, \rr{U}, \rr{D}) +% The upper-case initial letter of each face-name (\rr{F}, \rr{B}, \rr{L}, \rr{R}, \rr{U}, \rr{D}) % denotes a clockwise 90-degree rotation of the face as shown in % Figure~\ref{fig:notation}. -% For example, \rr{D}\ is generated by the `rubik rotation' command \cmd{\rr\{D\}}. +% For~example, \rr{D}\ is generated by the `rubik rotation' command \cmd{\rr\{D\}}. % % \DescribeMacro{Up} % \DescribeMacro{Dp} @@ -701,57 +1283,69 @@ % \DescribeMacro{Bp} % An appended prime~$^\prime$ indicates an anticlockwise rotation; e.g.,~\rr{Fp}. % This is sometimes written as \rr{F}$\boldmath{^{-1}}$. The `prime' notation is -% achieved by appending a lowercase `p' to the face rotation command. For example, \rr{Rp}\ -% is generated by \cmd{\rr\{Rp\}}. +% achieved by appending a lower-case `p' to the face rotation command. For~example, \rr{Rp}\ +% is generated by \cmd{\rr\{Rp\}}. More formally, \rr{Rp} is the `inverse' of \rr{R}. % -% \vspace{-0.2cm} -% \begin{figure}[hbt] -% \centering -% \ifpdf -% \includegraphics[height=5cm]{Rubik-doc-figA.pdf} -% \fi -% \caption{\label{fig:notation}} -% \end{figure} +% The superscript~$^2$, or sometimes just an ordinary~2, indicates that the rotation +% is applied twice. For~example, \rr{R}\textbf{$^2$} or \rr{R}\textbf{2} +% denote \textit{two} successive 90~degree clockwise rotations of the \textsc{right} face; +% \rr{R}\textbf{$^3$} is equivalent to \rr{Rp} etc. % % -% \subsection{Slice rotations} +% \subsection{Inner-slice rotations} % \label{sec:slicerotations} % -% \DescribeMacro{Su} -% \DescribeMacro{Sd} -% \DescribeMacro{Sl} -% \DescribeMacro{Sr} -% \DescribeMacro{Sf} -% \DescribeMacro{Sb} -% The Rubik cube (3x3x3) has three orthogonal so-called `inner' slices, whose +ve -% rotation direction follows that of a named face. For example the inner slice +% The Rubik cube (3x3x3) has three orthogonal so-called +% `inner' slices (middle layers, middle slices), whose +ve +% rotation direction follows that of a named face. For~example, the inner-slice % rotation between the \textsc{right} and \textsc{left} faces whose rotation -% direction follows the rotation \rr{R}\ (rotation is isomorphic to \rr{R}) is denoted -% as \rr{Sr}, which is typeset using the command \cmd{\rr\{Sr\}}. Note that in these cases -% the trailing \texttt{r} in the command is lowercase. -% -% \bigskip\bigskip\bigskip -% -% \DescribeMacro{Sup} -% \DescribeMacro{Sdp} -% \DescribeMacro{Slp} -% \DescribeMacro{Srp} -% \DescribeMacro{Sfp} -% \DescribeMacro{Sbp} -% Each of these slice rotations (S rotations) has a reversed (primed) p-form, -% the command for which is generated by appending the suffix `p'. -% For example the inner slice rotations \rr{Slp}\ (\cmd{\rr\{Slp\}}) and -% \rr{Sr}\ (\cmd{\rr\{Sr\}}) are identical. -% The equivalence is more obvious when we see their respective hieroglyphs. -% For example, in this case \linebreak \rr{Slp}\ (\cmd{\rr\{Slp\}}) -% $\equiv$ \rrh{Slp}\ (\cmd{\rrh\{Slp\}}), -% and \rr{Sr}\ (\cmd{\rr\{Sr\}}) $\equiv$ \rrh{Sr}\ (\cmd{\rrh\{Sr\}}). -% -% \bigskip -% -% \pagebreak -% -% \subsubsection*{MES slice notation} +% direction follows the rotation \rr{R}\ (i.e.,~its rotation is isomorphic to \rr{R}). +% The inner-slice rotations form a group (the Slice group), originally +% described by John Conway (Frey and Singmaster, 1982, p~105). +% +% +% \subsubsection*{The `m' notation} +% \label{sec:mnotation} +% +% \DescribeMacro{Um} +% \DescribeMacro{Dm} +% \DescribeMacro{Lm} +% \DescribeMacro{Rm} +% \DescribeMacro{Fm} +% \DescribeMacro{Bm} +% Here `m' stands for the `middle' slice, namely that parallel to the designated +% \textsc{face}; its rotation mirrors that of the +% \textsc{face}. The \texttt{m} must be in lower-case. +% Each of these rotation-codes has a complementary `prime' version, formed +% by appending a `p'; for~example, \rr{Rm} (\verb!\rr{Rm}!) is a middle layer rotation +% \rrh{Rm} between the \textsc{right} and \textsc{left} faces, and is in the same +% direction as \rr{R}. The code \rr{Rmp} (\verb!\rr{Rmp}!) refers to the same +% middle slice, but rotated in the opposite direction \rrh{Rmp}. +% +% This notation, which was probably invented by Singmaster, was originally used on the +% Cube Lovers usenet group (1981--1997). It is now much used on the +% Jaap Puzzles website (see Scherphius J) ---see also Section~\ref{sec:codeJaap}. +% +% +% \subsubsection*{The `M' notation} +% \label{sec:Mnotation} +% +% \DescribeMacro{MU} +% \DescribeMacro{MD} +% \DescribeMacro{ML} +% \DescribeMacro{MR} +% \DescribeMacro{MF} +% \DescribeMacro{MB} +% This variant of the above `middle' slice notation (e.g.,~\texttt{MR} $\equiv$ \texttt{Rm}) +% is part of the `superset' notation of Randelshofer. As before, the rotation +% direction follows that of the designated \textsc{face}. +% Each has a complementary `prime' version +% formed by appending a `p'. The \texttt{M} must be in upper-case. +% +% +% \bigskip\bigskip +% +% \subsubsection*{The MES notation} % % \DescribeMacro{M} % \DescribeMacro{E} @@ -759,8 +1353,8 @@ % \DescribeMacro{Mp} % \DescribeMacro{Ep} % \DescribeMacro{Sp} -% An alternative and somewhat confusing (and hence is non-standard) slice notation -% which is sometimes used is the following +% An alternative but very confusing +% inner-slice notation (e.g.,~\texttt{Ep} $\equiv$ \texttt{Um}) which is occasionally used is the % so-called MES notation, as used in the Waterman algorithm % (Treep and Waterman 1987). % \begin{itemize} @@ -771,16 +1365,28 @@ % \item[\rr{S}] \ (\textsc{standing} \rrh{S}, between the \textsc{front} and % \textsc{back} faces; direction follows \rr{F}). % \end{itemize} -% Each of these also has a reversed (prime) version, and a hieroglyph -% (see Section~\ref{sec:listofcommands}). -% The equivalent S notation (see above) is therefore -% as follows: \rr{E}\ $\equiv$ \rr{Sd}, \rr{Ep}\ $\equiv$ \rr{Su}, -% \rr{M}\ $\equiv$ \rr{Sl}, \rr{Mp}\ $\equiv$ \rr{Sr}, \rr{S}\ $\equiv$ \rr{Sf}, -% \rr{Sp}\ $\equiv$ \rr{Sb}. +% Each of these also has an inverse (prime) version. +% +% +% \subsubsection*{The `S' notation} +% +% \DescribeMacro{Su} +% \DescribeMacro{Sd} +% \DescribeMacro{Sl} +% \DescribeMacro{Sr} +% \DescribeMacro{Sf} +% \DescribeMacro{Sb} +% In this equally confusing inner-slice notation, `S' stands for `inner-slice'; +% the face letter must be in lower-case (e.g.,~\texttt{Sr} $\equiv$ \texttt{Rm}). For~example, the inner-slice +% rotation between the \textsc{right} and \textsc{left} faces whose rotation +% direction follows the rotation \rr{R}\ is denoted +% as \rr{Sr}, which is typeset using the command \cmd{\rr\{Sr\}}. +% Each has an inverse (prime) p-form. % -% % -% \subsubsection*{Singmaster slice notation} +% \subsection{Outer-slice rotations} +% +% \subsubsection*{Slice notation} % % \DescribeMacro{Us} % \DescribeMacro{Ds} @@ -788,20 +1394,38 @@ % \DescribeMacro{Rs} % \DescribeMacro{Fs} % \DescribeMacro{Bs} -% These are an alternative (but somewhat less intuitive) form of -% slice notation which can be thought of as complementing the -% inner slice rotations. These were originally described by -% Singmaster (Frey and Singmaster, 1982). -% See the link to `notation' on the `Pretty patterns' page of the -% Fridrich website. +% This is a `paired' form of +% notation (two rotations at once), which can be thought of as complementing the +% inner-slice (middle layer) rotations. +% Each of these `slice' commands denotes a rotation of two opposite faces +% in the \textit{same} direction. +% {\linebreak}For~example, \textRubik{Us}\ $\equiv$ \textRubik{U}\ + \textRubik{Dp}; +% i.e.,~both face-rotations are in the \textit{same} direction +% as \rr{U}. Each of these rotation-codes has a complementary `anti-slice' version (see below). % -% Each of these commands denotes a rotation of two opposite faces -% in the same direction. For example, \textRubik{Us}\ $\equiv$ \textRubik{U}\ + \textRubik{Dp}, -% which is typeset as: -% \newline |\textRubik{Us}\ $\equiv$ \textRubik{U}\ + \textRubik{Dp}|, -% i.e.,~for \rr{Us}\ both face-rotations are in the \textit{same} direction -% as \rr{U}. +% This notation was originally described by +% Singmaster (Frey and Singmaster, 1982), and is much used +% on the `Pretty patterns' page of the Fridrich website (this +% page also has a useful link to `notation'). +% +% +% \bigskip % +% \DescribeMacro{SU} +% \DescribeMacro{SD} +% \DescribeMacro{SL} +% \DescribeMacro{SR} +% \DescribeMacro{SF} +% \DescribeMacro{SB} +% This variant of the above `slice' notation (e.g.,~\texttt{SU} $\equiv$ \texttt{Us}) +% is part of the `superset' notation of Randelshofer. As before, the rotation +% direction follows that of the designated +% \textsc{face}. Each has a complementary `prime' version formed by appending a `p'. +% +% +% \bigskip\bigskip +% + % % \subsubsection*{Anti-slice notation} % @@ -813,11 +1437,9 @@ % \DescribeMacro{Ba} % Each of these commands denotes a rotation of two opposite faces % in \textit{opposite} directions. -% For example, \textRubik{Ua}\ $\equiv$ \textRubik{U}\ + \textRubik{D}, -% which is typeset as: -% \newline |\textRubik{Ua}\ $\equiv$ \textRubik{U}\ + \textRubik{D}|. -% See the link to `notation' on the `Pretty patterns' page of the -% Fridrich website. +% For~example, \textRubik{Ua}\ $\equiv$ \textRubik{U}\ + \textRubik{D}. +% This notation is much used on the `Pretty patterns' page of the +% Fridrich website (see the note above re: `slice notation'). % % \bigskip\bigskip % @@ -829,19 +1451,32 @@ % \DescribeMacro{Rw} % \DescribeMacro{Fw} % \DescribeMacro{Bw} -% The clockwise \textit{combined} rotation of an outer face AND its inner slice -% (officially known as a `double outer slice' rotation) is denoted by appending a -% lowercase \textbf{\textsf{\footnotesize{w}}} (denoting `wide') to a face rotation command. -% For example, a \textsc{right} double outer slice rotation is denoted as \rr{Rw}. -% Similarly, the prime $^\prime$ version \rr{Lwp}\ is generated by \cmd{\rr\{Lwp\}}. +% The clockwise \textit{combined} rotation of an outer face AND its inner-slice +% (officially known as a `double outer slice' rotation, or a `double block' move) +% is denoted by appending a lower-case \textbf{\textsf{\footnotesize{w}}} +% (denoting `wide') to a rotation-code (endorsed by the WCA). +% For~example, a \textsc{right} double outer slice rotation \rrh{Rw} (\verb!\rrh{Rw}!) +% is denoted as \rr{Rw} (\verb!\rr{Rw}!). The `prime' version is formed by +% appending a `p' to the rotation-code. For~example, \rr{Rwp}\ is generated by \verb!\rr{Rwp}!. % -% The superscript~$^2$, or sometimes just an ordinary 2, indicates that the rotation -% is applied twice. For example \rr{R}\textbf{$^2$} or \rr{R}\textbf{2} -% denote \textit{two} successive 90~degree clockwise rotations of the \textsc{right} face. -% Clearly \rr{R}\textbf{$^3$} is equivalent to \rr{Rp} etc. % +% \bigskip % +% \subsubsection*{The `T' notation} +% \label{sec:Tnotation} % +% \DescribeMacro{TU} +% \DescribeMacro{TD} +% \DescribeMacro{TL} +% \DescribeMacro{TR} +% \DescribeMacro{TF} +% \DescribeMacro{TB} +% This confusing variant of the above `w' notation (e.g.,~\texttt{TR} $\equiv$ \texttt{Rw}) is part of +% the `superset' notation of Randelshofer. As before, the rotation direction +% follows that of the designated \textsc{face}. Each has a complementary `prime' version +% formed by appending a `p'. +% +% \bigskip\bigskip % % \subsection{Axis rotations} % @@ -854,17 +1489,17 @@ % with their hieroglyphs (the \cmd{\rrh\{\}} forms) being denoted % as \rrh{x}, \rrh{y}, \rrh{z}\ in order to distinguish them from square layer-rotation % hieroglyphs. -% Note that since \rr{x}, \rr{y}, \rr{z}\ rotations are always expressed in lowercase, -% this practice is extended also to the commands. +% Note that since \rr{x}, \rr{y}, \rr{z}\ rotations are always expressed in lower-case; +% this practice is also extended to the commands. % -% An \rr{x}\textbf{2} rotation (two \rr{x}\ rotations one after +% For example, an \rr{x}\textbf{2} rotation (two \rr{x}\ rotations one after % the other, i.e.,~\rrh{x}\ \rrh{x}) denotes rotating % the cube 180~degrees about its x axis so as to bring the \textsc{down} face % into the \textsc{up} position. % % An appended prime~$^\prime$ indicates an anticlockwise rotation; -% for example, \rr{xp}\ (which is generated by appending a `p' to the end of -% the command, i.e.,~\cmd{\rr\{xp\}}). +% for~example, \rr{xp}\ (which is generated by appending a `p' to the +% rotation-code, i.e.,~\cmd{\rr\{xp\}}). % % The \cmd{\Rubik\{\}} forms (and their prime `p' versions) generate the same % hieroglyphs as their \cmd{\rrh\{\}} versions, except that their spacing is @@ -886,7 +1521,7 @@ % \DescribeMacro{b} % A commonly used alternative for the \rr{x}, \rr{y}, \rr{z}\ notation % (and endorsed by the WCA) uses these -% lowercase face letter to denote a 90~degree whole-cube rotation in the same +% lower-case face letter to denote a 90~degree whole-cube rotation in the same % directional sense as that of the standard face rotations. % % {\noindent}Thus @@ -894,24 +1529,62 @@ % \rr{l}\ $\equiv$ \rr{xp}, \ \rr{r}\ $\equiv$ \rr{x}, \ % \rr{f}\ $\equiv$ \rr{z}, \ \rr{b}\ $\equiv$ \rr{zp}, % -% {\noindent}For example, \rr{d}\ is generated by the command \cmd{\rr\{d\}}. +% {\noindent}For~example, \rr{d}\ is generated by the command \cmd{\rr\{d\}}. % % {\noindent}Note that these rotations do not have prime $^\prime$ versions % since \rr{u}~is the opposite of \rr{d}, \rr{l}~is the opposite of \rr{r}, and % \rr{f}~is the opposite of \rr{b}. % -% As with the \rrh{x}, \rrh{y}, \rrh{z}\ forms (described above) there also -% equivalent \cmd{\rrh\{\}} and \cmd{\Rubik\{\}} forms. For example, +% As with the \rrh{x}, \rrh{y}, \rrh{z}\ forms (described above) there are also +% equivalent \cmd{\rrh\{\}} and \cmd{\Rubik\{\}} forms. For~example, % \rrh{d}\ is generated by the command \cmd{\rrh\{d\}}. % % +% \subsubsection*{The `c' notation} +% \label{sec:cnotation} +% +% \DescribeMacro{Uc} +% \DescribeMacro{Dc} +% \DescribeMacro{Lc} +% \DescribeMacro{Rc} +% \DescribeMacro{Fc} +% \DescribeMacro{Bc} +% This slightly more intuitive notation (the `c' stands for `cube') also associates the rotation +% direction with that of the designated \textsc{face} (e.g.,~\texttt{Rc} $\equiv$ \texttt{x}). +% Each has a complementary `prime' version formed by appending a `p'. +% For~example, \rr{Rc} (\verb!\rr{Rc}!) is equivalent to \rr{x}; +% \rr{Rcp} (\verb!\rr{Rcp}!) is equivalent to \rr{xp}. +% +% This notation, which was probably invented by Singmaster, was originally used on the +% Cube Lovers usenet group (1981--1997). It is now much used on the +% Jaap Puzzles website (see Scherphius J) ---see also Section~\ref{sec:codeJaap}. +% +% \bigskip\bigskip +% +% \subsubsection*{The `C' notation} +% \label{sec:Cnotation} +% +% \DescribeMacro{CU} +% \DescribeMacro{CD} +% \DescribeMacro{CL} +% \DescribeMacro{CR} +% \DescribeMacro{CF} +% \DescribeMacro{CB} +% This variant of the whole cube rotation notation +% (e.g.,~\texttt{CR} $\equiv$ \texttt{Rc} $\equiv$ \texttt{x}) +% is part of the `superset' notation of Randelshofer. As before, the rotation +% direction follows that of the designated \textsc{face}. Each has a complementary +% `prime' version formed by appending a `p'. +% +% +% \bigskip% \bigskip % % \subsection{Examples} % \label{sec:examples} % -% {\noindent}\rr{R}\ is generated by the `rubik rotation' command \cmd{\rr\{R\}} +% {\noindent}\rr{R}\ is generated by the command \cmd{\rr\{R\}} % -% {\noindent}\rr{Fw}\ is generated by the `rubik rotation' command \cmd{\rr\{Fw\}} +% {\noindent}\rr{Fw}\ is generated by the command \cmd{\rr\{Fw\}} % % {\noindent}\rr{L}$^2$ is generated by \cmd{\rr\{L\}}\verb!$^2$! % @@ -924,7 +1597,7 @@ % {\noindent}\rr{x}\ and \rrh{y}\ and \Rubik{zp}\ are generated by % \cmd{\rr\{x\}} and \cmd{\rrh\{y\}} and \cmd{\Rubik\{zp\}} % -% {\noindent}\rr{f}\ and \rrh{b}\ are generated by \cmd{\rr\{f\}} and \cmd{\rrh\{b\}} +% {\noindent}\rr{Fc}\ and \rrh{Bc}\ are generated by \cmd{\rr\{Fc\}} and \cmd{\rrh\{Bc\}} % % {\noindent}\rr{U}\rr{U}\rr{R}\rr{R}\ is generated by % \cmd{\rr\{U\}}\cmd{\rr\{U\}}\cmd{\rr\{R\}}\cmd{\rr\{R\}} @@ -941,7 +1614,7 @@ % % \bigskip % -% {\noindent}Commas can be important in avoiding ambiguity; for example +% {\noindent}Commas can be important in avoiding ambiguity; for~example, % % \bigskip % @@ -956,35 +1629,48 @@ % {\noindent}\rrh{F}\rrh{U}\rrh{y}\rrh{Rp}\rrh{Lwp} \ \ \ \ % \verb!\rrh{F}\rrh{U}\rrh{y}\rrh{Rp}\rrh{Lwp}! % +% \bigskip +% +% Note that if each rotation element uses the \textit{same} font or encoding, then +% typesetting a rotation sequence can be achieved more easily using the +% \verb!\ShowSequence! command (see Section~\ref{sec:showsequence}). For example, we can +% typeset the last sequence much more conveniently, as follows: +% +% \medskip +% +% \verb!\ShowSequence{}{\rrh}{F,U,y,Rp,Lwp}! \ \ $\rightarrow$ \ \ \ShowSequence{}{\rrh}{F,U,y,Rp,Lwp} % % -% \bigskip % % \subsection{Backwards compatibility} % \label{sec:backwardscompat} % % Note that in keeping with `backwards compatibility' all rotation commands (see below) -% can still be written without the usual curley braces \verb!{}!. -% For example, the hieroglyph \rrhD\ (\cmd{\rrh\{D\}}) can also be generated using the command +% can still be written without the usual curly braces \verb!{}!. +% For~example, the hieroglyph \rrhD\ (\cmd{\rrh\{D\}}) can also be generated using the command % \cmd{\rrhD}. % % \bigskip % +% \pagebreak +% % \subsection{Listing of all rotation commands} % \label{sec:listofcommands} % % % Note that all the commands presented here also have a \cmd{\Rubik\{\}} equivalent form which % typesets both the hieroglyph and its lettercode in a vertical format, -% as shown in the `Examples' section above. These have been ommitted here +% as shown in the `Examples' section above. These have been omitted here % owing to the difficulty of including this form easily in the following table. % -% Note also that some \cmd{\rrh\{\}} commands (eg~the \cmd{\rrh\{B\}} command) +% +% Note also that some \cmd{\rrh\{\}} commands (e.g.,~the \cmd{\rrh\{B\}} command) % show only the lettercode in a square box, e.g.,~\rrh{B}. This is because these rotations % do not have a `true' visual representation as seen from the \textsc{front} face, % and hence can be somewhat ambiguous unless typeset with their associated % lettercode. % +% % \newcommand{\dnstrut}{\rule{0pt}{17pt}} % \newcommand{\dns}{\hspace{2mm}} % \newcommand{\dnsp}{\hspace{2mm}} @@ -1016,6 +1702,18 @@ % \dnstrut\rr{Uap}\dns\cmd{\rr\{Uap\}} % & \rrh{Uap}\dns\cmd{\rrh\{Uap\}} % & \textRubik{Uap}\dns\cmd{\textRubik\{Uap\}} \nonumber\\ +% \dnstrut\rr{Um}\dns\cmd{\rr\{Um\}} +% & \rrh{Um}\dns\cmd{\rrh\{Um\}} +% & \textRubik{Um}\dns\cmd{\textRubik\{Um\}} \nonumber\\ +% \dnstrut\rr{Ump}\dns\cmd{\rr\{Ump\}} +% & \rrh{Ump}\dns\cmd{\rrh\{Ump\}} +% & \textRubik{Ump}\dns\cmd{\textRubik\{Ump\}} \nonumber\\ +% \dnstrut\rr{Uc}\dns\cmd{\rr\{Uc\}} +% & \rrh{Uc}\dns\cmd{\rrh\{Uc\}} +% & \Rubik{Uc}\dns\cmd{\Rubik\{Uc\}} \nonumber\\ +% \dnstrut\rr{Ucp}\dns\cmd{\rr\{Ucp\}} +% & \rrh{Ucp}\dns\cmd{\rrh\{Ucp\}} +% & \Rubik{Ucp}\dns\cmd{\Rubik\{Ucp\}} \nonumber\\ % \end{supertabular} % % @@ -1044,6 +1742,18 @@ % \dnstrut\rr{Dap}\dns\cmd{\rr\{Dap\}} % & \rrh{Dap}\dns\cmd{\rrh\{Dap\}} % & \textRubik{Dap}\dns\cmd{\textRubik\{Dap\}} \nonumber\\ +% \dnstrut\rr{Dm}\dns\cmd{\rr\{Dm\}} +% & \rrh{Dm}\dns\cmd{\rrh\{Dm\}} +% & \textRubik{Dm}\dns\cmd{\textRubik\{Dm\}} \nonumber\\ +% \dnstrut\rr{Dmp}\dns\cmd{\rr\{Dmp\}} +% & \rrh{Dmp}\dns\cmd{\rrh\{Dmp\}} +% & \textRubik{Dmp}\dns\cmd{\textRubik\{Dmp\}} \nonumber\\ +% \dnstrut\rr{Dc}\dns\cmd{\rr\{Dc\}} +% & \rrh{Dc}\dns\cmd{\rrh\{Dc\}} +% & \Rubik{Dc}\dns\cmd{\Rubik\{Dc\}} \nonumber\\ +% \dnstrut\rr{Dcp}\dns\cmd{\rr\{Dcp\}} +% & \rrh{Dcp}\dns\cmd{\rrh\{Dcp\}} +% & \Rubik{Dcp}\dns\cmd{\Rubik\{Dcp\}} \nonumber\\ % \end{supertabular} % % @@ -1072,9 +1782,20 @@ % \dnstrut\rr{Lap}\dns\cmd{\rr\{Lap\}} % & \rrh{Lap}\dns\cmd{\rrh\{Lap\}} % & \textRubik{Lap}\dns\cmd{\textRubik\{Lap\}} \nonumber\\ +% \dnstrut\rr{Lm}\dns\cmd{\rr\{Lm\}} +% & \rrh{Lm}\dns\cmd{\rrh\{Lm\}} +% & \textRubik{Lm}\dns\cmd{\textRubik\{Lm\}} \nonumber\\ +% \dnstrut\rr{Lmp}\dns\cmd{\rr\{Lmp\}} +% & \rrh{Lmp}\dns\cmd{\rrh\{Lmp\}} +% & \textRubik{Lmp}\dns\cmd{\textRubik\{Lmp\}} \nonumber\\ +% \dnstrut\rr{Lc}\dns\cmd{\rr\{Lc\}} +% & \rrh{Lc}\dns\cmd{\rrh\{Lc\}} +% & \Rubik{Lc}\dns\cmd{\Rubik\{Lc\}} \nonumber\\ +% \dnstrut\rr{Lcp}\dns\cmd{\rr\{Lcp\}} +% & \rrh{Lcp}\dns\cmd{\rrh\{Lcp\}} +% & \Rubik{Lcp}\dns\cmd{\Rubik\{Lcp\}} \nonumber\\ % \end{supertabular} % -% % \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}} % \dnstrut\rr{R}\dns\cmd{\rr\{R\}} % & \rrh{R}\dns\cmd{\rrh\{R\}} @@ -1100,6 +1821,18 @@ % \dnstrut\rr{Rap}\dns\cmd{\rr\{Rap\}} % & \rrh{Rap}\dns\cmd{\rrh\{Rap\}} % & \textRubik{Rap}\dns\cmd{\textRubik\{Rap\}} \nonumber\\ +% \dnstrut\rr{Rm}\dns\cmd{\rr\{Rm\}} +% & \rrh{Rm}\dns\cmd{\rrh\{Rm\}} +% & \textRubik{Rm}\dns\cmd{\textRubik\{Rm\}} \nonumber\\ +% \dnstrut\rr{Rmp}\dns\cmd{\rr\{Rmp\}} +% & \rrh{Rmp}\dns\cmd{\rrh\{Rmp\}} +% & \textRubik{Rmp}\dns\cmd{\textRubik\{Rmp\}} \nonumber\\ +% \dnstrut\rr{Rc}\dns\cmd{\rr\{Rc\}} +% & \rrh{Rc}\dns\cmd{\rrh\{Rc\}} +% & \Rubik{Rc}\dns\cmd{\Rubik\{Rc\}} \nonumber\\ +% \dnstrut\rr{Rcp}\dns\cmd{\rr\{Rcp\}} +% & \rrh{Rcp}\dns\cmd{\rrh\{Rcp\}} +% & \Rubik{Rcp}\dns\cmd{\Rubik\{Rcp\}} \nonumber\\ % \end{supertabular} % % @@ -1128,6 +1861,18 @@ % \dnstrut\rr{Fap}\dns\cmd{\rr\{Fap\}} % & \rrh{Fap}\dns\cmd{\rrh\{Fap\}} % & \textRubik{Fap}\dns\cmd{\textRubik\{Fap\}} \nonumber\\ +% \dnstrut\rr{Fm}\dns\cmd{\rr\{Fm\}} +% & \rrh{Fm}\dns\cmd{\rrh\{Fm\}} +% & \textRubik{Fm}\dns\cmd{\textRubik\{Fm\}} \nonumber\\ +% \dnstrut\rr{Fmp}\dns\cmd{\rr\{Fmp\}} +% & \rrh{Fmp}\dns\cmd{\rrh\{Fmp\}} +% & \textRubik{Fmp}\dns\cmd{\textRubik\{Fmp\}} \nonumber\\ +% \dnstrut\rr{Fc}\dns\cmd{\rr\{Fc\}} +% & \rrh{Fc}\dns\cmd{\rrh\{Fc\}} +% & \Rubik{Fc}\dns\cmd{\Rubik\{Fc\}} \nonumber\\ +% \dnstrut\rr{Fcp}\dns\cmd{\rr\{Fcp\}} +% & \rrh{Fcp}\dns\cmd{\rrh\{Fcp\}} +% & \Rubik{Fcp}\dns\cmd{\Rubik\{Fcp\}} \nonumber\\ % \end{supertabular} % % @@ -1156,6 +1901,18 @@ % \dnstrut\rr{Bap}\dns\cmd{\rr\{Bap\}} % & \rrh{Bap}\dns\cmd{\rrh\{Bap\}} % & \textRubik{Bap}\dns\cmd{\textRubik\{Bap\}} \nonumber\\ +% \dnstrut\rr{Bm}\dns\cmd{\rr\{Bm\}} +% & \rrh{Bm}\dns\cmd{\rrh\{Bm\}} +% & \textRubik{Bm}\dns\cmd{\textRubik\{Bm\}} \nonumber\\ +% \dnstrut\rr{Bmp}\dns\cmd{\rr\{Bmp\}} +% & \rrh{Bmp}\dns\cmd{\rrh\{Bmp\}} +% & \textRubik{Bmp}\dns\cmd{\textRubik\{Bmp\}} \nonumber\\ +% \dnstrut\rr{Bc}\dns\cmd{\rr\{Bc\}} +% & \rrh{Bc}\dns\cmd{\rrh\{Bc\}} +% & \Rubik{Bc}\dns\cmd{\Rubik\{Bc\}} \nonumber\\ +% \dnstrut\rr{Bcp}\dns\cmd{\rr\{Bcp\}} +% & \rrh{Bcp}\dns\cmd{\rrh\{Bcp\}} +% & \Rubik{Bcp}\dns\cmd{\Rubik\{Bcp\}} \nonumber\\ % \end{supertabular} % % @@ -1265,43 +2022,171 @@ % \end{supertabular} % % -% \pagebreak +% \subsubsection{Randelshofer notation} +% \label{sec:listofRandelshofercommands} % -% \section{Other commands} +% \newcommand{\dnRubik}[1]{% +% \dnstrut\rr{#1}\dns\cmd{\rr\{#1\}}% +% & \rrh{#1}\dns\cmd{\rrh\{#1\}}% +% & \Rubik{#1}\dns\cmd{\Rubik\{#1\}} \nonumber\\% +% }% % +% \newcommand{\dntextRubik}[1]{% +% \dnstrut\rr{#1}\dns\cmd{\rr\{#1\}}% +% & \rrh{#1}\dns\cmd{\rrh\{#1\}}% +% & \textRubik{#1}\dns\cmd{\textRubik\{#1\}} \nonumber\\% +% }% % -% \DescribeMacro{\rubikcube} -% This command generates the logo \rubikcube. % +% \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}} +% \dnRubik{CR} +% \dnRubik{CRp} +% \dnRubik{CL} +% \dnRubik{CLp} +% \dnRubik{CU} +% \dnRubik{CUp} +% \dnRubik{CD} +% \dnRubik{CDp} +% \dnRubik{CF} +% \dnRubik{CFp} +% \dnRubik{CB} +% \dnRubik{CBp} +% \end{supertabular} % -% All \rubikcube\ commands assume a 3x3x3 cube by default. -% There are three primary command categories: (a)~\cmd{\Draw..} commands -% (which must always be used \textit{inside} a TikZ picture environment), -% (b)~parameter-allocation' commands---e.g.,~\cmd{\RubikCubeSolved}---which can -% be used either inside or outside a TikZ environment), -% and (c)~commands which can be used in ordinary text -% (e.g.,~|\rr{}| rotation commands). +% \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}} +% \dntextRubik{MR} +% \dntextRubik{MRp} +% \dntextRubik{ML} +% \dntextRubik{MLp} +% \dntextRubik{MU} +% \dntextRubik{MUp} +% \dntextRubik{MD} +% \dntextRubik{MDp} +% \dntextRubik{MF} +% \dntextRubik{MFp} +% \dntextRubik{MB} +% \dntextRubik{MBp} +% \end{supertabular} % -% Since \LaTeX\ commands have a maximum limit of only 9 parameters, -% it is necessary to use separate `Face' and `Slice' commands (see below) -% in order to accommodate all 27 visible colours of a 3D~Rubik cube. +% \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}} +% \dntextRubik{SR} +% \dntextRubik{SRp} +% \dntextRubik{SL} +% \dntextRubik{SLp} +% \dntextRubik{SU} +% \dntextRubik{SUp} +% \dntextRubik{SD} +% \dntextRubik{SDp} +% \dntextRubik{SF} +% \dntextRubik{SFp} +% \dntextRubik{SB} +% \dntextRubik{SBp} +% \end{supertabular} +% +% \begin{supertabular}[lll]{p{3cm} p{3cm} p{4.5cm}} +% \dntextRubik{TR} +% \dntextRubik{TRp} +% \dntextRubik{TL} +% \dntextRubik{TLp} +% \dntextRubik{TU} +% \dntextRubik{TUp} +% \dntextRubik{TD} +% \dntextRubik{TDp} +% \dntextRubik{TF} +% \dntextRubik{TFp} +% \dntextRubik{TB} +% \dntextRubik{TBp} +% \end{supertabular} % % +% \subsection{The rubikfont} +% \label{sec:rubikfont} +% +% For hieroglyph-related text we use the standard Computer Modern Sans (cmss) +% bold extended (bx) 10pt font for upper-case letters, and the 8pt footnote size for lower-case +% (see Section~\ref{sec:coderubikfont} for details). This font (rubikfont) +% and the `prime' symbol (rubikprime) can be easily changed by `renewing' the three commands there. +% +% For example, to change to the somewhat `lighter' semi-bold extended (sbx) CM Sans (cmss) form +% one can simply include the following in the preamble (the FNS suffix stands for `footnotesize'): +%\begin{verbatim} +% \makeatletter +% \renewcommand{\@rubikfont}{\fontsize{10}{12pt}\usefont{T1}{cmss}{sbx}{n}} +% \renewcommand{\@rubikfontFNS}{\fontsize{8}{12pt}\usefont{T1}{cmss}{sbx}{n}} +% \makeatother +%\end{verbatim} +% +% +% \subsubsection*{The `rubikprime' symbol} +% \label{sec:rubikprime} +% +% We currently use the apostrophe for the prime symbol (see Section~\ref{sec:coderubikfont}), +% since the maths \cmd{\prime} seems to be a bit too faint (especially since we need to use +% the `scriptstyle' size in this setting). However, users can +% easily make the Rubik bundle use the maths prime instead, by loading the following +% in the preamble. +%\begin{verbatim} +% \makeatletter +% \renewcommand{\@rubikprime}{\raisebox{1.2pt}{\ensuremath{\scriptstyle{^\prime}}}} +% \makeatother +%\end{verbatim} +% +% +% +% \section{Draw commands} +% +% A \cmd{\Draw..} command typesets either a Rubik cube, cubie or a face +% or layer using parameters set or defined via +% previous parameter-allocation commands (e.g.,~face colours, dimensions etc). +% Note that those \cmd{\Draw..} commands which do take colours as arguments do not +% update the cube's internal `colour state', but simply `paint' these colours. +% +% It is important to distinguish between the \rubikcube\ package \cmd{\Draw..} commands +% and TikZ \cmd{\draw..} commands. \cmd{\Draw..} commands are implemented by the +% TikZ \cmd{\draw..} commands, and consequently \cmd{\Draw..} commands can only be +% used \textit{inside} a TikZ picture environment---and hence they can also be used safely in +% conjunction with the \cmd{\ShowCube} command, which itself uses a TikZ picture environment. +% See also Section~\ref{sec:drawerrormessage} below.. +% +% +% +% \subsection[Error message]{\cmd{\Draw} error message} +% \label{sec:drawerrormessage} +% +% If a \cmd{\Draw..} command is used \textit{outside} a +% TikZ picture environment, then \LaTeX\ issues an +% ``Undefined control sequence'' error message, indicating +% that it is trying to draw something using an undefined +% TikZ \cmd{\draw} command\,\footnote{Note that the TikZ \cmd{\draw} command +% uses a lower-case `d', while all \rubikcube\ commands start with an upper-case letter.}. +% +% This is because all Rubik \cmd{\Draw..} commands achieve their effects by +% implementing a series of TikZ \cmd{\draw..} and other commands, all of which +% need to be inside a \texttt{tikzpicture} environment. +% +% For~example, if the command \cmd{\DrawRubikCubeF} is used +% without a surrounding TikZ picture environment, +% then something similar to the following error message will be generated. +%\begin{verbatim} +%! Undefined control sequence. +%\DrawFlatUp ... }{#1}\pgfmathsetmacro {\uy }{#2}\draw +% [line join=round,... +%l.56 \DrawRubikCubeF +%\end{verbatim} +% % -% \subsection{Draw commands} % -% A \cmd{\Draw..} command typesets -% either a Rubik cube, cubie or a layer using parameters set or defined via -% previous parameter-allocation commands (eg~face colours, dimensions etc). -% Furthermore, \cmd{\Draw..} commands can only be used \textit{inside} a TikZ -% picture environment (see section~\ref{sec:drawerrormessage}). % +% \subsection{DrawRubikCube commands} % % \DescribeMacro{\DrawRubikCubeXY} -% This command draws Rubik cubes in one of four -% orientations as denoted by the following terminal XY viewing-direction -% codes: RU (RightUp), RD (RightDown), LU (LeftUp), LD (LeftDown). -% For example, the command +% \DescribeMacro{\DrawRubikCubeF} +% \DescribeMacro{\DrawRubikCubeSF} +% This command draws Rubik cubes in one of four oblique +% orientations or configurations as denoted by the following terminal +% XY viewing-direction codes: RU~(RightUp), RD~(RightDown), LU~(LeftUp), +% LD~(LeftDown); two additional terminal codes are F~(Flat) and SF~(Semi-Flat). +% For~example, the command % \begin{quote} % \cmd{\DrawRubikCubeRU} % \end{quote} @@ -1323,7 +2208,7 @@ % \DrawRubikCubeRU % \end{tikzpicture}% %\end{verbatim} -% Note that these commands are equivalent to: +% Note that the above commands are equivalent to: %\begin{verbatim} % \RubikCubeSolved % \ShowCube{3cm}{0.7}{\DrawRubikCubeRU} @@ -1347,42 +2232,32 @@ % the xyz parameters denote the face colours associated with each of % the three axes. % -% For example, the command \cmd{\DrawCubieRU\{O\}\{Y\}\{G\}} draws a +% For~example, the command \cmd{\DrawCubieRU\{O\}\{Y\}\{G\}} draws a % single cubie as viewed from the RightUp direction, % with face colours Orange (x-axis), Yellow (y-axis), Green (z-axis), as follows. % % \medskip % -% \begin{minipage}{1.35cm} -% \begin{tikzpicture}[scale=1] -% \DrawCubieRU{O}{Y}{G} -% \end{tikzpicture}% -% \end{minipage} +% \ShowCube{1.33cm}{1}{\DrawCubieRU{O}{Y}{G}} % \hspace{1cm} % \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \begin{tikzpicture}[scale=1] -% \DrawCubieRU{O}{Y}{G} -% \end{tikzpicture}% +% \ShowCube{1.33cm}{1}{\DrawCubieRU{O}{Y}{G}} %\end{verbatim} % \end{minipage} % % \medskip % -% {\noindent}Since the front face is a unit 1cm and the width of the side approx 1/3cm, -% and the scale factor =1, then the the minimum minipage width required for the cubie -% $=(1.33 \times 1) = 1.33$cm, and hence the above commands are equivalent to -% \begin{verbatim} -% \ShowCube{1.33cm}{1}{\DrawCubieRU{O}{Y}{G}} -% \end{verbatim} -% +% {\noindent}Since the front face is 1~unit wide and the 2D width of the side approx 1/3~unit, +% and the scale-factor =~1, then the minipage width required for the cubie image +% $=(1.33 \times 1) = 1.33$cm. % % \begin{figure}[hbt] % \centering % \ifpdf -% \includegraphics[height=4cm]{Rubik-doc-figC.pdf} +% \includegraphics[height=4cm]{rubik-doc-figC.pdf} % \else -% \includegraphics[height=4cm]{Rubik-doc-figC.eps} +% \includegraphics[height=4cm]{rubik-doc-figC.eps} % \fi % \vspace{-5mm}\caption{\label{fig:cubiedydx}Cubie dy dx parameters} % \end{figure} @@ -1396,25 +2271,23 @@ % \cmd{\Cubiedy\{\}} \\ % \cmd{\Cubiedx\{\}} % \end{quote} -% as shown in the folowing example. +% as shown in the following example. % % \bigskip % -% \begin{minipage}{1.7cm} -% \begin{tikzpicture}[scale=1] -% \Cubiedy{0.4} -% \Cubiedx{0.8} -% \DrawCubieRU{O}{Y}{G} -% \end{tikzpicture}% -% \end{minipage} +% \ShowCube{1.7cm}{1}{% +% \Cubiedy{0.4}% +% \Cubiedx{0.8}% +% \DrawCubieRU{O}{Y}{G}% +% } % \hspace{2cm} % \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \begin{tikzpicture}[scale=1] +% \ShowCube{1.7cm}{1}{% % \Cubiedy{0.4} % \Cubiedx{0.8} % \DrawCubieRU{O}{Y}{G} -% \end{tikzpicture}% +% } %\end{verbatim} % \end{minipage} % @@ -1449,288 +2322,267 @@ % \textCubieLD{O}{Y}{G} \ \ |\textCubieLD{O}{Y}{G}| % \end{quote} % Note that these \cmd{\textCubieXY} commands are not influenced by the -% \cmd{\Cubiedy}, \cmd{\Cubiedx} commands as their size is preset for text use. -% -% -% \subsubsection[Draw.. error message]{\cmd{\draw} error message} -% -% See also section~\ref{sec:drawerrormessage} regarding the error message associated with -% using a \cmd{\Draw...} command \textit{outside} a TikZ picture environment. -% +% \cmd{\Cubiedy}, \cmd{\Cubiedx} commands as their size is pre-set for text use. % -% \subsection{Face commands} -% \label{sec:facecommands} -% -% \DescribeMacro{\RubikFaceUp} -% \DescribeMacro{\RubikFaceDown} -% \DescribeMacro{\RubikFaceLeft} -% \DescribeMacro{\RubikFaceRight} -% \DescribeMacro{\RubikFaceFront} -% \DescribeMacro{\RubikFaceBack} -% These commands take nine colour arguments and allocate colours to the -% individual cubies of a Rubik cube face. -% The ordering is isomorphic to the sequence 1--9, i.e.,~numbering the small -% squares 1-3~(top row, left to right), 4-6~(middle row, left to right), -% 7-9~(bottom row, left to right), as follows: -% \begin{quote} -% \fbox{ -% \begin{minipage}{1.6cm} -% \#1 \#2 \#3 % -% \#4 \#5 \#6 -% -% \#7 \#8 \#9 -% \end{minipage} -% } -% \end{quote} -% Conveniently, \LaTeX\ allows the colour arguments to be separated by spaces -% (e.g.,~separated in groups of three), or even spread across several -% lines (e.g.,~in a square block to resemble a 9-face) in order to -% make the command more visually intuitive, as in the following examples. -% \begin{quote} -%\begin{verbatim} -% \RubikFaceUp{G}{B}{G} {G}{W}{O} {G}{O}{G} -% -% \RubikFaceFront{O}{W}{R} -% {W}{W}{W} -% {G}{W}{G} % -%\end{verbatim} -% \end{quote} -% -% \DescribeMacro{\RubikFaceUpAll} -% \DescribeMacro{\RubikFaceDownAll} -% \DescribeMacro{\RubikFaceLeftAll} -% \DescribeMacro{\RubikFaceRightAll} -% \DescribeMacro{\RubikFaceFrontAll} -% \DescribeMacro{\RubikFaceBackAll} -% For convenience, each of these commands has an associated -% `\texttt{All}' command which allocates the same colour to all the cubies -% on a 9-face (i.e.,~only a single colour argument is required). -% -% If you want a particular face to be all grey, then one can -% either omit the particular `Face' command (since the -% default colour is grey), or use a `Face' command specifying the -% colour-code~X; for example, \cmd{\RubikFaceUpAll\{X\}}. -% However, if you do use a Face command, then all of the command's -% colour arguments must be allocated, as otherwise you will generate a -% `missing parameter' error, and no colour will be -% allocated (i.e.,~you will see a black-hole). -% Use of these commands is shown in the following figure. +% \subsection{Flat commands} +% \label{sec:flatcommands} % -% \bigskip -% -% \begin{minipage}{2.8cm} -% \RubikFaceUpAll{X} -% \RubikFaceRightAll{R} -% \RubikFaceFront{W}{Y}{G} -% {W}{Y}{G} -% {W}{Y}{G} -% \begin{tikzpicture}[scale=0.7] -% \DrawRubikCubeRU -% \end{tikzpicture}% -% \end{minipage} -% \hspace{5mm} -% \begin{minipage}{0.6\textwidth} -%\begin{verbatim} -% \RubikFaceUpAll{X} -% \RubikFaceRightAll{R} -% \RubikFaceFront{W}{Y}{G} -% {W}{Y}{G} -% {W}{Y}{G} -% \ShowCube{3cm}{0.7}{\DrawRubikCubeRU} -% \end{verbatim} -% \end{minipage} -% +% \DescribeMacro{\DrawFlatUp} +% \DescribeMacro{\DrawFlatDown} +% \DescribeMacro{\DrawFlatLeft} +% \DescribeMacro{\DrawFlatRight} +% \DescribeMacro{\DrawFlatFront} +% \DescribeMacro{\DrawFlatBack} +% These commands \cmd{\DrawFlat..}\marg{x}\marg{y} draw a `flat' (square) +% representation of the current state of a specified face such that its +% bottom left corner is positioned at ($x$, $y$). +% They are designed to supplement the \cmd{\DrawRubikCube...} commands and +% allow hidden faces to be represented. +% Each command (except \cmd{\DrawFlatFront}) takes two arguments, +% namely the X-coordinate and Y-coordinate of the bottom left +% corner of the face. This ($x$,$y$) pair allows the user to position +% the face. % -% \subsection{RubikCubeSolved command} -% \label{sec:rubikcubesolved} +% Note that the Y-argument set for the \cmd{\DrawFlatLeft} +% and \cmd{\DrawFlatRight} commands is not currently actioned +% (see Section~\ref{sec:drawflatxcommands}). +% This is because both the \textsc{left} and \textsc{right} faces, as used by the +% \cmd{\DrawRubikCubeSF} (Semi-Flat) command which incorporates the RU +% view, require only Y=0. It is anticipated that this (x,y) facility +% will be fully extended to the left and right forms in a later version. +% +% Note also that the \cmd{\DrawFlatFront} command currently takes \textit{no} +% arguments, since by definition the bottom left corner of this face is +% always at (0,0), and there seems to be no reason (just now) for +% this face to have the (x,y) facility. +% +% \textsc{usage}:\ In the following example we use the command \verb!\DrawFlatBack{4}{1}! to +% append the \textsc{back} face to the side of a 3D cube. Note that since +% the coordinates of the bottom/back/right corner of the cube rendered by the +% command \cmd{\DrawRubikCubeRU} is (4,1) +% (see Section~\ref{sec:coordinates}), we can position the +% lower/left corner of the \textsc{back} face at this point using the command +% \verb!\DrawFlatBack{4}{1}! as follows: % -% \DescribeMacro{\RubikCubeSolved} -% This command sets all the face colours to that of a standard `solved' cube -% and is equivalent to the following set of face commands +% \bigskip +% +% \begin{minipage}{0.4\textwidth} +% \centering +% \RubikCubeSolved +% \begin{tikzpicture}[scale=0.4] +% \DrawRubikCubeRU +% \DrawFlatBack{4}{1} +% \end{tikzpicture}% +% \end{minipage} +% \begin{minipage}{5cm} %\begin{verbatim} -% \RubikFaceUpAll{W}% -% \RubikFaceDownAll{Y}% -% \RubikFaceLeftAll{B}% -% \RubikFaceRightAll{G}% -% \RubikFaceFrontAll{O}% -% \RubikFaceBackAll{R}% +% \RubikCubeSolved +% \ShowCube{3cm}{0.4}{% +% \DrawRubikCubeRU +% \DrawFlatBack{4}{1} +% } %\end{verbatim} -% as shown in the following semi-flat image. -% -% \bigskip +% \end{minipage} +% +% \bigskip % -% \begin{minipage}{5cm} -% \centering -% \begin{tikzpicture}[scale=0.5] -% \RubikCubeSolved -% \DrawRubikCubeFlat -% \end{tikzpicture}% -% \end{minipage} -% \begin{minipage}{0.5\textwidth} +% \DescribeMacro{\DrawRubikCubeF} +% This command draws the completely flat (F) format of the cube, as shown in the following example. +% +% \bigskip +% +% \begin{minipage}{0.4\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \RubikCubeSolved +% \DrawRubikCubeF +% \node (U) at (1.5, 4.5) [black]{\small\textsf{U}}; +% \node (D) at (1.5, -1.5) [black]{\small\textsf{D}}; +% \node (L) at (-1.5, 1.5) [black]{\small\textsf{L}}; +% \node (R) at (4.5, 1.5) [black]{\small\textsf{R}}; +% \node (F) at (1.5, 1.5) [black]{\small\textsf{F}}; +% \node (B) at (7.5, 1.5) [black]{\small\textsf{B}}; +% \end{tikzpicture}% +% \end{minipage} +% \begin{minipage}{5cm} %\begin{verbatim} % \RubikCubeSolved -% \showcube{5cm}{0.5}{\DrawRubikCubeFlat} +% \ShowCube{5cm}{0.4}{\DrawRubikCubeF} %\end{verbatim} -% \end{minipage} -% -% \bigskip -% -% Note that the width of the minipage above is set to 5cm. This is derived from the fact -% that the unscaled width of the semi-flat image is 10cm, and hence if -% the TikZ scale factor is to be 0.5 then the minimum minipage width = $10 \times 0.5 = 5$cm -% (see Section~\ref{sec:coordinates} for details). -% -% If other orientations of the solved cube are required, this can be easily achieved -% using the \cmd{\RubikRotation} command (from the \texttt{RubikRotation} package). -% For example, if one wants to show the solved cube upsidedown, then this format -% could be defined as follows (here we have used the rotations \rrx, \rrx, \rry, to -% invert the cube): +% \end{minipage} +% +% \bigskip +% +% The addition of text (numbers or letters) in the faces is +% straightforward---the origin of the 1-unit grid is located at the +% bottom left corner of the \textsc{front} face (orange here). +% The letters were placed using the following TikZ code inside the +% TikZ picture environment. +% %\begin{verbatim} -%\newcommand{\CubeUpSideDown}{\RubikCubeSolved\RubikRotation{x2,y}} +% \RubikCubeSolved +% \ShowCube{5cm}{0.4}{% +% \DrawRubikCubeF +% \node (U) at (1.5, 4.5) [black]{\small\textsf{U}}; +% \node (D) at (1.5, -1.5) [black]{\small\textsf{D}}; +% \node (L) at (-1.5, 1.5) [black]{\small\textsf{L}}; +% \node (R) at (4.5, 1.5) [black]{\small\textsf{R}}; +% \node (F) at (1.5, 1.5) [black]{\small\textsf{F}}; +% \node (B) at (7.5, 1.5) [black]{\small\textsf{B}}; +% } %\end{verbatim} -% This command would then generate the following: -% -% \bigskip +% +% \DescribeMacro{\DrawRubikCubeSF} +% {\noindent}A useful `semi-flat' (SF) alternative format, which uses +% the standard RU view of the cube and appends the three hidden +% sides (cf.,~Rokicki \textit{et~al.}, 2013), is generated by the +% command \cmd{\DrawRubikCubeSF} as follows. +% +% \bigskip % -% \begin{minipage}{2.8cm} -% \centering -% \begin{tikzpicture}[scale=0.6] -% \DrawNCubeAll{3}{O}{Y}{G} -% \end{tikzpicture}% -% \end{minipage} -% \hspace{5mm} -% \begin{minipage}{0.6\textwidth} +% \begin{minipage}{5cm} +% \begin{tikzpicture}[scale=0.5] +% \RubikCubeSolved +% \DrawRubikCubeSF +% \node (B) at (5.5, 2.5) [white]{\small\textsf{B}}; +% \end{tikzpicture}% +% \end{minipage} +% \begin{minipage}{5cm} %\begin{verbatim} -% \CubeUpSideDown -% \ShowCube{2.4cm}{0.6}\DrawRubikCubeRU} +% \RubikCubeSolved +% \ShowCube{5cm}{0.5}{% +% \DrawRubikCubeSF +% \node (B) at (5.5, 2.5) +% [white]{\small\textsf{B}}; +% } %\end{verbatim} -% \end{minipage} -% +% \end{minipage} +% % \bigskip % -% Users can easily set their own alternative `solved' face/colour configuration by `renewing' -% the \cmd{\RubikCubeSolved} command as follows---remember to include the trailing \% (note also -% that the colours ROYGBWX are currently hardwired so do not use a different set -% of uppercase letters). -%\begin{verbatim} -% \renewcommand{\RubikCubeSolved}{% -% \RubikFaceUpAll{..}% -% \RubikFaceDownAll{..}% -% \RubikFaceLeftAll{..}% -% \RubikFaceRightAll{..}% -% \RubikFaceFrontAll{..}% -% \RubikFaceBackAll{..}% -% } -%\end{verbatim} -% -% -% -% \subsection{RubikCubeGrey command} -% \label{sec:rubikcubegrey} +% Note that even in this configuration it is straight-forward to +% write text on the graphic, since the 2D width (on the page) of +% the green \textsc{right} face is exactly 1-unit, and the +% bottom right-hand corner of the green face is raised exactly 1-unit +% (see Figure~\ref{fig:cubesquaregraph}). +% Consequently, since the origin of the coordinate-grid is at the bottom left +% corner of the \textsc{front} face (the orange face here), the coordinates +% of the centre of the red \textsc{back} face are easily determined to be (5.5, 2.5). +% % -% \DescribeMacro{\RubikCubeGrey} -% This command generates a 3x3x3 cube with no colours allocated except for the central -% cubie of each face, which takes the same colour configuration as defined for the -% \cmd{\RubikCubeSolved} command. -% This command, which is useful starting point when wanting to describe the movement of -% particular cubies, generates the following cube: +% \subsection{Face commands} +% \label{sec:facecommands} +% +% +% \DescribeMacro{\DrawFaceUp} +% \DescribeMacro{\DrawFaceDown} +% \DescribeMacro{\DrawFaceLeft} +% \DescribeMacro{\DrawFaceRight} +% \DescribeMacro{\DrawFaceFront} +% \DescribeMacro{\DrawFaceBack} +% \DescribeMacro{\DrawFaceUpSide} +% \DescribeMacro{\DrawFaceDownSide} +% \DescribeMacro{\DrawFaceLeftSide} +% \DescribeMacro{\DrawFaceRightSide} +% \DescribeMacro{\DrawFaceFrontSide} +% \DescribeMacro{\DrawFaceBackSide} +% These commands draw the current state of a specified face +% (e.g.,~\cmd{\DrawFaceUp}), or the face and all the associated side-bars +% (e.g.,~\cmd{\DrawFaceUpSide}). +% \textsc{Note}: these commands do \textsc{not} take any +% arguments---for code see Section~\ref{sec:drawfacecode}. % -% \bigskip +% In the following example we use the \cmd{\DrawFlatUpSide} command to +% draw the \textsc{up} face and all its side-bars of a cube having +% a `solved' configuration. % -% \RubikCubeGrey -% \ShowCube{3cm}{0.5}{\DrawRubikCubeRU} -% \hspace{5mm} -% \begin{minipage}{0.6\textwidth} +% \bigskip +% +% \begin{minipage}{0.4\textwidth} +% \centering +% \RubikCubeSolved +% \begin{tikzpicture}[scale=0.4] +% \DrawFaceUpSide +% \end{tikzpicture}% +% \end{minipage} +% \begin{minipage}{5cm} %\begin{verbatim} -% \RubikCubeGrey -% \ShowCube{3cm}{0.5}{\DrawRubikCubeRU} +% \RubikCubeSolved +% \ShowCube{1.6cm}{0.4}{% +% \DrawFaceUpSide +% } %\end{verbatim} -% \end{minipage} -% -% \bigskip -% Users can easily set their own alternative face/colour configuration by `renewing' -% the \cmd{\RubikCubeGrey} command along the lines shown above (the code is in Section~\ref{sec:codegrey}). +% \end{minipage} % +% \vspace{1cm} % % -% \subsection{Slice commands} -% \label{sec:slicecommands} -% -% \DescribeMacro{\RubikSliceTopX} -% \DescribeMacro{\RubikSliceMiddleX} -% \DescribeMacro{\RubikSliceBottomX} -% These three commands allocate the six visible cubie colours associated with a -% \textit{horizontal} slice of a Rubik cube. -% There are three pairs of Slice commands; one pair -% (Left view \& Right view) for each of the horizontal slices Top, Middle, Bottom. -% The six colour arguments associated with a given slice run in sequence -% from left to right irrespective of the viewpoint, e.g.,~\#1 \#2 \#3 \#4 \#5 \#6. -% -% Since the viewpoint of the Rubik cube (from the Right or from the Left) -% influences which face the colours are associated with, it is necessary -% to have the view (R or L) specified in the command name. +% \subsection[NCube]{NCube (NxNxN)} +% \label{sec:NCube} +% +% \DescribeMacro{\DrawNCubeAll} +% An `NCube' is a solved NxNxN cube drawn from the RU direction; +% (i.e.,~only shows faces \textsc{up}, \textsc{front}, \textsc{right}). +% The cubie colours of each face are All the same. +% \begin{quote} +% \cmd{\DrawNCubeAll\{N\}\{Xcolour\}\{Ycolour\}\{Zcolour\}}. +% \end{quote} +% This command takes four ordered parameters (N, X, Y, Z)---the number +% (integer; $N>0$) of cubies along an edge, followed by three face +% colours in XYZ order. +% Since the viewpoint is only from the RU direction, the three colour +% parameters are: X(Right), Y(Up), Z(Front). +% +% \bigskip +% +% \begin{minipage}{0.3\textwidth} +% \begin{tikzpicture}[scale=0.5] +% \DrawNCubeAll{5}{O}{Y}{G} +% \end{tikzpicture}% +% \end{minipage} +% \begin{minipage}{0.5\textwidth} +%\begin{verbatim} +% \ShowCube{3.5cm}{0.5}{\DrawNCubeAll{5}{O}{Y}{G}} +%\end{verbatim} +% \end{minipage} % -% The format of the `slice' command is shown in the following example. -% The Rubik cube is shown from the LeftDown (LD) view -% and consequently each of the `slice' commands in this -% particular example ends in L, consistent with -% the final \cmd{\DrawRubikCubeLD} command. % -% Note that the two legacy `Equator' versions (now replaced by `Middle') -% are retained to allow backward compatibility. % -% \bigskip % -% \begin{minipage}{2.8cm} -% \centering -% \RubikFaceDownAll{Y} -% \RubikSliceTopL {G}{G}{G} {R}{R}{R} -% \RubikSliceMiddleL {R}{R}{R} {B}{B}{B} -% \RubikSliceBottomL {O}{O}{O} {G}{G}{G} -% \begin{tikzpicture}[scale=0.7] -% \DrawRubikCubeLD -% \end{tikzpicture}% -% \end{minipage} -% \hspace{5mm} -% \begin{minipage}{0.6\textwidth} -%\begin{verbatim} -% \RubikFaceDownAll{Y} -% \RubikSliceTopL {G}{G}{G} {R}{R}{R} -% \RubikSliceMiddleL {R}{R}{R} {B}{B}{B} -% \RubikSliceBottomL {O}{O}{O} {G}{G}{G} -% \ShowCube{3cm}{0.7}{\DrawRubikCubeLD} -%\end{verbatim} -% \end{minipage} % +% \subsection{LayerFace} +% \label{sec:layerface} % -% \subsection{LayerFace \& LayerSide commands} -% \label{sec:layerface} +% While a cube has faces and layers, a layer has a face (the face you are looking +% at or drawing) and four sides (consisting of the nine side facelets of the +% associated cubies). +% The two `Layer' commands described here are intended for drawing final layer +% configurations from `scratch' without any prior configuration information. % -% These commands are intended for drawing final layer -% configurations (i.e.,~typically using the yellow face in the \textsc{up} position) -% with or without the associated side faces of the cubies of the top layer -% (see also the \cmd{\DrawFlatUpSide} command in Section~\ref{sec:flatcommands}) +% Typically, we might wish to show the yellow face in +% the \textsc{up} position, with or without the associated side faces of the +% cubies of this layer. +% Of course, if we already know the rotation history from some initial configuration, +% it would be much simpler just to invoke the \cmd{\RubikRotation} command and then use the +% \cmd{\DrawFlatUpSide} command (see Section~\ref{sec:flatcommands}). % -% \subsubsection{LayerFace} % % \DescribeMacro{\DrawRubikLayerFace} -% This LayerFace command draws a simple Rubik cube 3x3 face and allocates colours -% to the 9~cubies. -% The command takes nine ordered colour arguments. -% Their use is illustrated in the following example, which shows a yellow cross configuration. +% \DescribeMacro{\DrawRubikLayerFaceAll} +% These two LayerFace commands draw a simple 3x3 face and allocate colours +% to the 9~facelets. +% The \cmd{\DrawRubikLayerFace} command takes nine ordered colour arguments. +% The command is illustrated in the following example, which shows a yellow cross configuration. % % \bigskip % -% \begin{minipage}{2.5cm} -% \centering -% \begin{tikzpicture}[scale=0.7] -% \DrawRubikLayerFace{X}{Y}{X} -% {Y}{Y}{Y} -% {X}{Y}{X} -% \end{tikzpicture}% -% \end{minipage} +% \ShowCube{2.1cm}{0.7}{% +% \DrawRubikLayerFace{X}{Y}{X} +% {Y}{Y}{Y} +% {X}{Y}{X} +% }% % \hspace{1cm} % \begin{minipage}{0.6\textwidth} %\begin{verbatim} @@ -1738,35 +2590,34 @@ % \DrawRubikLayerFace{X}{Y}{X} % {Y}{Y}{Y} % {X}{Y}{X} -% } +% } %\end{verbatim} % \end{minipage} % -% \medskip -% -% \subsubsection[Draw.. error message]{\cmd{\draw} error message} +% \bigskip % -% See also section~\ref{sec:drawerrormessage} regarding the error message associated with -% using a \cmd{\Draw...} command \textit{outside} a TikZ picture environment. +% {\noindent}The \cmd{\DrawRubikLayerFaceAll} command takes a single colour argument, and paints +% the whole face the same colour. % % \medskip % -% \subsubsection{LayerSide} -% \label{sec:layerside} +% \subsection{LayerSide (sidebars)} +% \label{sec:layerside} \label{sec:sidebars} % % \DescribeMacro{\DrawRubikLayerSideXYp} % LayerSide commands draw the associated side colours of -% the top layer as small rectangular sidebars. -% The LayerSide commands adopt a three-letter XYp \textbf{position} notation +% the layer as small rectangular sidebars. +% The LayerSide command adopts a three-letter XYp \textbf{position} notation % where the XY pair define the location (X:[Left \verb!|! Middle \verb!|! Right]; -% Y:[Top \verb!|! Middle \verb!|! Bottom]) of a particular cubie in the layer face. +% Y:[Top \verb!|! Middle \verb!|! Bottom]) of a particular cubie in the layer face, +% as depicted in Figure~\ref{fig:facenotation}. % % \begin{figure}[hbt] % \centering % \ifpdf -% \includegraphics[height=3cm]{Rubik-doc-figD.pdf} +% \includegraphics[height=3cm]{rubik-doc-figD.pdf} % \else -% \includegraphics[height=3cm]{Rubik-doc-figD.eps} +% \includegraphics[height=3cm]{rubik-doc-figD.eps} % \fi % \vspace{-5mm}\caption{\label{fig:facenotation}LayerSide rotation-codes } % \end{figure} @@ -1782,7 +2633,7 @@ % Various different LayerSide commands are available: those for % drawing a single colour side bar, and others for facilitating % drawing all 12 side bars. -% For example, \textit{either} of the following commands +% For~example, \textit{either} of the following commands % % \begin{quote} %\begin{verbatim} @@ -1805,9 +2656,9 @@ %\end{verbatim} % \end{quote} % where the T and B forms require the colour parameters to be in left-right -% horizontal order (eg, left, middle, right), +% horizontal order (e.g.,~left, middle, right), % while the L and R forms require the colour parameters to be in top-down -% vertical order (eg, top, middle, bottom). +% vertical order (e.g.,~top, middle, bottom). % Note that this means that the colour parameters of the L and R commands % can (if required) then be positioned intuitively (vertically) as follows: % \begin{quote} @@ -1864,11 +2715,9 @@ % \DrawRubikLayerSideR{O}{B}{R} % \DrawRubikLayerSideB{R}{G}{O} % -% \node (LT) at (0.5, 2.5) -% [red]{\small\textsf{LT}}; -% \node (LM) at (0.5, 1.5) -% [red]{\small\textsf{LM}}; -% } +% \node (LT) at (0.5, 2.5) [red]{\small\textsf{LT}}; +% \node (LM) at (0.5, 1.5) [red]{\small\textsf{LM}}; +% } %\end{verbatim} % \end{minipage} % @@ -1903,21 +2752,19 @@ % {R} {O} % {Y} {O} % \DrawRubikLayerSideB {O}{G}{G} -% } +% } %\end{verbatim} % \end{minipage} % % \bigskip % -% \DescribeMacro{\DrawFlatUpSide} -% \textsc{important note}: If the colour configuration of the \textit{whole} -% cube is already known to the system (i.e.,~it has been specified before, -% and (possibly) been manipulated using the \cmd{\RubikRotation..} command +% \DescribeMacro{\DrawFaceUpSide} +% \textsc{important note}: If the colour configuration of the layer shown above +% is already known to the system (i.e.,~it has been specified before, +% and (possibly) been manipulated using the \cmd{\RubikRotation} command % from \textsc{rubikrotation} package), then the above figure could be -% drawn much more simply using just the single \cmd{\DrawFlatUpSide} command, -% as described in Section~\ref{sec:flatcommands}. In short, using the -% \texttt{rubikrotation} package to keep track of the Rubik cube configuration makes -% drawing these images considerably simpler. +% drawn much more simply using just the single \cmd{\DrawFaceUpSide} command, +% as described in Section~\ref{sec:facecommands}. % % \bigskip % @@ -1930,14 +2777,15 @@ % These sidebar values (decimal values $\geq 0$; no units) can be % changed from their default values using the three commands. % \begin{quote} -% \cmd{\RubikSideBarWidth\{\}}\\ -% \cmd{\RubikSideBarLength\{\}}\\ -% \cmd{\RubikSideBarSep\{\}} +% \cmd{\RubikSideBarWidth\{\}}\hspace{35.751pt}(default = 0.3)\\ +% \cmd{\RubikSideBarLength\{\}}\hspace{30pt}(default = 1.0)\\ +% \cmd{\RubikSideBarSep\{\}}\hspace{46.251pt}(default = 0.3) % \end{quote} % Values set in the document preamble will apply globally, while values % set within a TikZ picture environment will apply only locally to that % particular environment, as shown in the following example where we have -% set both the sidebar width and length to 0.7. +% set both the sidebar width and length to 0.7 in position MTy using the command +% \verb!\DrawRubikLayerSideMTy{G}! (for the MTy code see Figure~\ref{fig:facenotation}). % % \bigskip % @@ -1965,7 +2813,7 @@ % \RubikSideBarWidth{0.7} % \RubikSideBarLength{0.7} % \DrawRubikLayerSideMTy{G} -% } +% } %\end{verbatim} % \end{minipage} % @@ -1979,12 +2827,11 @@ % Since the \textsc{front} face drawn using the \cmd{\DrawRubikCube} command is % identical with that drawn using the \cmd{\DrawLayerFace} command it % follows that LayerSide commands can also be used in conjunction with -% the \textsc{front} face drawn using \cmd{\DrawRubikCube} command, as -% shown in the following example. Note that in this example we have used the -% \cmd{\ShowCubeF} command as an exercise to implement the fbox and reveal -% the extent of the surrounding white space associated with a minipage width of -% 3.5cm ($=5 \times 0.7$) ---showing that a sidebar increases the image width by about -% 0.5 the width of a cubie. +% the \textsc{front} face drawn using \cmd{\DrawRubikCube} command. This +% shown in the following example, where we have used the +% \cmd{\ShowCubeF} command as an exercise (to implement the fbox) and reveal +% the extent of the surrounding white space associated with the minipage width of +% 3.5cm ($=5 \times 0.7$). % % \bigskip % @@ -2025,233 +2872,219 @@ % \DrawRubikCubeRU % \DrawRubikLayerSideL{G}{B}{R} % \DrawRubikLayerSideB{R}{G}{O} -% } +% } %\end{verbatim} % \end{minipage} % % \bigskip % -% {\noindent}Note that since using a left or a right \cmd{\DrawRubikLayerSide} -% command in conjunction with a \cmd{\DrawRubikCube} command will necessarily -% increase the width of the image, one may also have to adjust the width of -% the associated minipage. -% -% \pagebreak +% Since using left and/or right sidebars (e.g.,~\cmd{\DrawRubikLayerSide}) +% in conjunction with a \cmd{\DrawRubikCube} command, will increase +% the width of the image, one may also have to adjust the width of +% the associated minipage. Note that the width of a 2D oblique view of the cube +% is 4~units (= width of 4~cubies). With the default sidebar width and sep settings +% (see above) one sidebar increases the 2D cube image width by 0.6\,units (= 0.3 + 0.3). +% Sidebars on both sides increase the width by 1.2\,units. Note also that setting +% both the sidebar width and separation to 0.25\,units has the convenience that +% the 2D width of a cube face $+$ left and right sidebars (e.g.,~using \cmd{\DrawFaceUpSide}) +% is then exactly 5\,units. +% +% +% +% +% \section[ShowSequence command]{\cmd{\ShowSequence} command} +% \label{sec:showsequence} +% +% \DescribeMacro{\ShowSequence} +% \DescribeMacro{\ShowSequenceF} +% \DescribeMacro{\ShowSequencef} +% The \cmd{\ShowSequence}\marg{separator}\marg{font-code}\marg{sequence} command +% typesets a comma-separated sequence of rotation +% codes---for code see Section~\ref{sec:codeshowsequence}. +% Appending an `F' to the command-name (\cmd{\ShowSequenceF}) results in an fbox about +% the whole output (cf.~the \cmd{\ShowCubeF} command). +% Appending an `f' to the command-name (\cmd{\ShowSequencef}) results in an fbox about +% each element in the output (these two forms can be helpful when checking white space). +% +% The \cmd{\ShowSequence} command takes three mandatory arguments: +% the first is the separator (\verb!#1!), +% the second is the font or style code (\verb!#2!), +% and third is a comma-separated sequence of Rubik rotation codes (|#3|). +% +% The separator (e.g.,~comma) used for typesetting the sequence can be specified +% (or just omitted---i.e.,~an empty bracket); +% the sequence can be either a named sequence (i.e.,~encoded as a macro) or just a +% comma separated sequence of rotation codes. % -% \subsection{Flat commands} -% \label{sec:flatcommands} +% \noindent\textsc{usage}: +% The following command displays the rotation sequence F, R, U, Rp, Up, using +% the \verb!\rr! encoding and comma \& space separated. % -% \DescribeMacro{\DrawFlatUp} -% \DescribeMacro{\DrawFlatDown} -% \DescribeMacro{\DrawFlatLeft} -% \DescribeMacro{\DrawFlatRight} -% \DescribeMacro{\DrawFlatFront} -% \DescribeMacro{\DrawFlatBack} -% These commands \cmd{\DrawFlat..}\marg{x}\marg{y} draw a `flat' (square) -% representation of a specified face such that its bottom left corner -% is positioned at ($x$, $y$). -% They are designed to supplement the \cmd{\DrawRubikCube...} commands and -% allow hidden faces to be represented. -% Each command (except \cmd{\DrawFlatFront}) takes two arguments, -% namely the X-coordinate and Y-coordinate of the bottom left -% corner of the face. This ($x$,$y$) pair allows the user to position -% the face. +% \medskip % -% Note that the Y-argument set for the \cmd{\DrawFlatLeft} -% and \cmd{\DrawFlatRight} commands is not currently actioned -% (see Section~\ref{sec:drawflatxcommands}), -% since both the \textsc{left} and \textsc{right} faces as used by the -% \cmd{\DrawRubikCubeFlat} command---since this shows the RU view---requires only Y=0 -% (this (x,y) facility will be fully extended to the left and right forms in a -% later version). -% Note also that the \cmd{\DrawFlatFront} command currently takes no arguments, -% since by definition the bottom left corner of this face is always at (0,0), -% and there seems to be no reason (just now) for this face to have the -% (x,y) facility. +% \verb!\ShowSequence{,\ }{\rr}{F,R,U,Rp,Up}! \ \ $\rightarrow$ \ \ \ShowSequence{,\ }{\rr}{F,R,U,Rp,Up} % -% In the following example we use the command \verb!\DrawFlatBack{4}{1}! to -% append the \textsc{back} face to the side of a 3D cube. Note that since -% the coordinates of the bottom/back/right corner of the cube rendered by the -% command \cmd{\DrawRubikCubeRU} is (4,1) -% (see Section~\ref{sec:coordinates}), we can position the -% lower/left corner of the \textsc{back} face at this point using the command -% \verb!\DrawFlatBack{4}{1}! as follows: +% \medskip % -% \bigskip -% -% \begin{minipage}{0.4\textwidth} -% \centering -% \RubikCubeSolved -% \begin{tikzpicture}[scale=0.4] -% \DrawRubikCubeRU -% \DrawFlatBack{4}{1} -% \end{tikzpicture}% -% \end{minipage} -% \begin{minipage}{5cm} -%\begin{verbatim} -% \RubikCubeSolved -% \ShowCube{3cm}{0.4}{% -% \DrawRubikCubeRU -% \DrawFlatBack{4}{1} -% } -%\end{verbatim} -% \end{minipage} -% -% \bigskip +% Remember that if you want a very long sequence to break automatically +% at the line-ends, then you need to include at least one space between +% the sequence elements, either with or without a comma; for this the +% separator argument needs to include a space, i.e.,~something like +% \verb!{,\ }! or \verb!{\ }! or just \verb!{ }! perhaps. % % -% \DescribeMacro{\DrawFlatUpSide} -% \DescribeMacro{\DrawFlatDownSide} -% \DescribeMacro{\DrawFlatLeftSide} -% \DescribeMacro{\DrawFlatRightSide} -% \DescribeMacro{\DrawFlatFrontSide} -% \DescribeMacro{\DrawFlatBackSide} -% These commands draw a face and all the associated side facelets. -% In the following example we use the \cmd{\DrawFlatUpSide} command to -% draw the \textsc{up} face and all its side-bars of a cube having -% a `solved' configuration. +% For~example, the following commands typeset the comma-separated +% rotation sequence U,D,Lp,R using different separators and fonts. +% For convenience, we start by encoding the sequence as the macro \verb!\myseq!. % % -% \bigskip -% -% \begin{minipage}{0.4\textwidth} -% \centering -% \RubikCubeSolved -% \begin{tikzpicture}[scale=0.4] -% \DrawFlatUpSide -% \end{tikzpicture}% -% \end{minipage} -% \begin{minipage}{5cm} -%\begin{verbatim} -% \RubikCubeSolved -% \ShowCube{1.6cm}{0.4}{% -% \DrawFlatUpSide -% } -%\end{verbatim} -% \end{minipage} -% -% \bigskip +% \newcommand{\myseq}{U,D,Lp,R} % -% \DescribeMacro{\DrawRubikFlat} -% This command draws the completely flat format of the cube, as shown in the following example. -% -% \bigskip -% -% \begin{minipage}{0.4\textwidth} -% \centering -% \begin{tikzpicture}[scale=0.4] -% \RubikCubeSolved -% \DrawRubikFlat -% \node (U) at (1.5, 4.5) [black]{\small\textsf{U}}; -% \node (D) at (1.5, -1.5) [black]{\small\textsf{D}}; -% \node (L) at (-1.5, 1.5) [black]{\small\textsf{L}}; -% \node (R) at (4.5, 1.5) [black]{\small\textsf{R}}; -% \node (F) at (1.5, 1.5) [black]{\small\textsf{F}}; -% \node (B) at (7.5, 1.5) [black]{\small\textsf{B}}; -% \end{tikzpicture}% -% \noindent\strut\hspace{5mm}\texttt{$\backslash$DrawRubikFlat} -% \end{minipage} -% \begin{minipage}{5cm} -%\begin{verbatim} -% \RubikCubeSolved -% \ShowCube{5cm}{0.4}{\DrawRubikFlat} -%\end{verbatim} -% \end{minipage} -% -% \bigskip -% -% The addition of text (numbers or letters) in the faces is -% straightforward---the origin of the 1-unit grid is located at the -% bottom left corner of the front face (orange here). -% The letters were placed using the following TikZ code inside the -% TikZ picture environment. -% -%\begin{verbatim} -% \RubikCubeSolved -% \ShowCube{5cm}{0.4}{% -% \DrawRubikFlat -% \node (U) at (1.5, 4.5) [black]{\small\textsf{U}}; -% \node (D) at (1.5, -1.5) [black]{\small\textsf{D}}; -% \node (L) at (-1.5, 1.5) [black]{\small\textsf{L}}; -% \node (R) at (4.5, 1.5) [black]{\small\textsf{R}}; -% \node (F) at (1.5, 1.5) [black]{\small\textsf{F}}; -% \node (B) at (7.5, 1.5) [black]{\small\textsf{B}}; -% } -%\end{verbatim} -% -% \DescribeMacro{\DrawRubikCubeFlat} -% {\noindent}A useful `semi-flat' alternative format, which uses -% the standard RU view of the cube and appends the three hidden -% sides (see Rokicki \textit{etal.}, 2013), is generated by the -% command \cmd{\DrawRubikCubeFlat} as follows. -% -% \bigskip +% \medskip\noindent\verb!\newcommand{\myseq}{U,D,Lp,R}! % -% \begin{minipage}{5cm} -% \begin{tikzpicture}[scale=0.5] -% \RubikCubeSolved -% \DrawRubikCubeFlat -% \node (B) at (5.5, 2.5) [white]{\small\textsf{B}}; -% \end{tikzpicture}% -% \end{minipage} -% \begin{minipage}{5cm} -%\begin{verbatim} -% \RubikCubeSolved -% \ShowCube{5cm}{0.5}{% -% \DrawRubikCubeFlat -% \node (B) at (5.5, 2.5) -% [white]{\small\textsf{B}}; -% } -%\end{verbatim} -% \end{minipage} -% -% \bigskip +% \medskip\noindent\verb!\ShowSequence{,}{\texttt}{\myseq}! \ $\longrightarrow$ \ \ShowSequence{,}{\texttt}{\myseq} % -% Note that even in this configuration it is straight-forward to -% write text on the graphic, since the width (on the page) of -% the green \textsc{right} face is exactly 1-unit, and the -% bottom right-hand corner of the green face is raised exactly 1-unit -% (see Figure~\ref{fig:cubesquaregraph}). -% Consequently, since the origin of the grid is at the bottom left -% corner of the front face, the coordinates of the center of the -% red \textsc{back} face is (5.5, 2.5). -% -% \section[NCube]{NCube (NxNxN)} -% \label{sec:NCube} +% \medskip\noindent\verb!\ShowSequence{,}{\rr}{\myseq}! \ $\longrightarrow$ \ \rr{U},\rr{D},\rr{Lp},\rr{R} +% +% \medskip\noindent\verb!\ShowSequence{}{\rrh}{\myseq}! \ $\longrightarrow$ \ \rrh{U}\rrh{D}\rrh{Lp}\rrh{R} +% +% \medskip\noindent\verb!\ShowSequence{\ }{\rrh}{\myseq}! \ $\longrightarrow$ \ \rrh{U}\ \rrh{D}\ \rrh{Lp}\ \rrh{R} % -% \DescribeMacro{\DrawNCubeAll} -% An `NCube' is a solved NxNxN cube drawn from the RU direction; -% (i.e.,~only shows faces \textsc{up}, \textsc{front}, \textsc{right}). -% The cubie colours of each face are All the same. -% \begin{quote} -% \cmd{\DrawNCubeAll\{N\}\{Xcolour\}\{Ycolour\}\{Zcolour\}}. -% \end{quote} -% This command takes four ordered parameters (N, X, Y, Z)---the number -% (integer; $N>0$) of cubies along an edge, followed by three face -% colours in XYZ order. -% Since the viewpoint is only from the RU direction, the three colour -% parameters are: X(Right), Y(Up), Z(Front). -% -% \bigskip -% -% \begin{minipage}{0.3\textwidth} -% \begin{tikzpicture}[scale=0.5] -% \DrawNCubeAll{5}{O}{Y}{G} -% \end{tikzpicture}% -% \end{minipage} -% \begin{minipage}{0.5\textwidth} +% \medskip\noindent\verb!\ShowSequence{,\ }{\textRubik}{\myseq}! \ $\longrightarrow$ \ \textRubik{U},\ \textRubik{D},\ +% \textRubik{Lp},\ \textRubik{R} +% +% +% \subsection*{Trailing digits} +% +% Note that the fonts denoted by \verb!\rr!, \verb!\rrh!, \verb!\Rubik! +% and \verb!\textRubik! will fail for rotation codes which +% have a trailing digit, e.g.,~R2, Dp3 (so-called `short' codes), since the +% \verb!\ShowSequence! macro currently only reads the whole string between pairs of +% commas (i.e.,~it does not interpret each string). However, the typewriter font \verb!\texttt! +% does work correctly in this case, as you would expect. +% +% An effective `work-around' for this limitation is provided by the \verb!\RubikRotation{}! +% command\,\footnote{Using the \texttt{--shell-escape} command-line option +% with the \LaTeX\ engine---see Section~\ref{sec:rubikrotation}.} +% (part of the \textsc{rubikrotation} package), since this returns (via the Perl program +% \texttt{rubikrotation.pl}) an extended (`long') form of a given sequence in which +% any `short' rotation codes are converted into their separate (atomic) long-form rotation codes; +% the associated string is \verb!\SequenceLong!. +% In fact three different forms of the sequence are returned, as shown below. +% +% For~example, consider the following short-form sequence L,R,D2,L3, and denote +% it as `seqA' as follows: \verb!\newcommand{\seqA}{[seqA],L,R,D2,L3,<test>}!. +% In this case D2,L3, and the name `seqA' fail to be typeset when using +% the \verb!\rr! font with the \verb!\ShowSequence! command as follows: +% +% \newcommand{\seqA}{[seqA],L,R,D2,L3,<test>} +% +% \medskip\noindent\verb!\newcommand{\seqA}{[seqA],L,R,D2,L3,<test>}! +% +% \medskip\noindent\verb!\ShowSequence{,}{\texttt}{\seqA}! \ $\longrightarrow$ \ \ShowSequence{,}{\texttt}{\seqA} +% +% \medskip\noindent\verb!\ShowSequence{,}{\rr}{\seqA}! \ $\longrightarrow$ \ \ShowSequence{,}{\rr}{\seqA} +% +% \medskip +% +% However, if we now run the command \verb!\RubikRotation{\seqA}! we shall then have +% at our disposal the following four strings: +% +% \medskip +% +% \verb!\SequenceInfo = ! test +% +% \verb!\SequenceName = ! seqA +% +% \verb!\SequenceShort = ! L,R,D2,L3 +% +% \verb!\SequenceLong = ! L,R,D,D,L,L,L +% +% \medskip +% +% {\noindent}and therefore have full control over typesetting rotation sequences. +% This approach therefore offers sufficient flexibility for most purposes. +% For~example, if we now write the command \verb!\ShowSequence{,}{\rr}{\SequenceLong}! +% we obtain +% +% \medskip\noindent\verb!\ShowSequence{,}{\rr}{\SequenceLong}! \ $\longrightarrow$ \ +% \ShowSequence{,}{\rr}{L,R,D,D,L,L,L} +% +% \medskip +% +% In practice, any trailing digit is converted (modulo~4) and expanded accordingly, the details being +% copied to the log-file. For~example, if one writes the command +% \cmd{\RubikRotation\{[test],R,D28978\}}, then since $28978 \equiv 2$\,(modulo~4) then \cmd{\SequenceLong} +% will be returned containing the string |R,D,D|. The associated entries in the log-file are +% as follows: %\begin{verbatim} -% \ShowCube{3.5cm}{0.5}{\DrawNCubeAll{5}{O}{Y}{G}} +%...rotation R OK +%...Expanding D28978 (28978 = 2 mod 4) ... +%...rotation D OK (= Dp3) +%...rotation D OK (= Dp3) +%...writing new Rubik state to file rubikstateNEW.dat +%...SequenceName = test +%...SequenceShort = R,D28978 +%...SequenceLong = R,D,D %\end{verbatim} -% \end{minipage} % -% \medskip % -% \subsubsection[Draw.. error message]{\cmd{\draw} error message} % -% See also section~\ref{sec:drawerrormessage} regarding the error message associated with -% using a \cmd{\Draw...} command \textit{outside} a TikZ picture environment. -% +% \section{SequenceBrace commands} +% \label{sec:sequencebrace} +% +% \DescribeMacro{\SequenceBraceA} +% \DescribeMacro{\SequenceBraceB} +% \DescribeMacro{\SequenceBraceAF} +% \DescribeMacro{\SequenceBraceBF} +% The \cmd{\SequenceBraceX}\marg{name}\marg{sequence} command +% is a tool for displaying a named sequence using a brace. The trailing~A +% denotes that the brace is placed Above the sequence; the trailing~B denotes +% the brace is Below the sequence. +% Appending an `F' to the command-name (e.g.,~\cmd{\SequenceBraceAF}) results +% in a surrounding fbox (cf.~the \cmd{\ShowCubeF} command). +% For the code see Section~\ref{sec:sequencebracecode}. +% +% {\noindent}Thus \verb!\SequenceBraceB{myseq}{U,D,L,R}! generates +% \ \SequenceBraceB{myseq}{U,D,L,R}. +% +% {\noindent}A typical example of its use might be: +% +% \bigskip +% +%\noindent% +%\RubikCubeSolved% +%\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% +%\quad\SequenceBraceA{fourspot}{\ShowSequence{}{\Rubik}{F,F,B,B,U,Dp,R,R,L,L,U,Dp}}% +%\quad$\longrightarrow$\quad% +%\RubikFaceFront{R}{R}{R}% +% {R}{O}{R}% +% {R}{R}{R}% +%\RubikFaceRight{B}{B}{B}% +% {B}{G}{B}% +% {B}{B}{B}% +%\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% +% +% +% \bigskip +% +% {\noindent}which was generated by the following code, showing that the \cmd{\ShowSequence} +% command can be used as an argument for the \cmd{\SequenceBraceA} command: +%\begin{verbatim} +%\newcommand{\fourspot}{[fourspot],F2,B2,U,Dp,R2,L2,U,Dp}% +%\noindent% +%\RubikCubeSolved% +%\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% +%\RubikRotation{\fourspot}% +%\quad\SequenceBraceA{\SequenceName}{% +% \ShowSequence{}{\Rubik}{\SequenceLong}}% +%\quad$\longrightarrow$\quad% +%\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% +%\end{verbatim} +% Note (1)~that the `fourspot' listing is included in the \textsc{rubikpatterns} package, and +% (2)~the \cmd{\RubikRotation} command requires using the \texttt{--shell-escape} command-line +% option with the \LaTeX\ engine---see Section~\ref{sec:rubikrotation} for details. +% % % % \section{Arrows} @@ -2259,31 +3092,40 @@ % % The \rubikcube\ package does not offer any special commands for drawing % arrows since it is straightforward just to include the appropriate TikZ -% `draw' commands in the \texttt{tikzpicture} environment. +% `draw' commands in the \texttt{tikzpicture} environment (i.e.,~in our +% own \cmd{\ShowCube} environment). % -% In order to facilitate using the standard TikZ `draw' commands both -% the RubikCubeFaceFront and LayerFace commands have the coordinate origin -% at the bottom left corner, and draw `faces' consisting of 9~unit-squares -% in a 3x3 grid, as shown in Figure~\ref{fig:facegraph}. +% In order to facilitate using the standard TikZ `draw' commands +% the graphic grid origin of Rubik cube images is located at the bottom left corner +% of the \textsc{front} face (see also Section~\ref{sec:coordinates} for details of the +% cube's coordinate system). Similarly, single face images (e.g.,~drawn using the +% \cmd{\DrawFlatUp} or \cmd{\DrawFlatUpSide} and LayerFace commands etc.) have +% their grid origin at the bottom left corner of the face. % Consequently the start and finish coordinates for any arrow or line are -% easy to determine. +% easy to determine. % % \begin{figure}[hbt] % \centering % \ifpdf -% \includegraphics[height=3cm]{Rubik-doc-figE.pdf} +% \includegraphics[height=3cm]{rubik-doc-figE.pdf} % \else -% \includegraphics[height=3cm]{Rubik-doc-figE.eps} +% \includegraphics[height=3cm]{rubik-doc-figE.eps} % \fi -% \vspace{-5mm}\caption{\label{fig:facegraph}RubikCubeFaceFront and RubikLayerFace coordinates} +% +% \parbox{9cm}{% +% \caption{\label{fig:facegraph}Grid showing the positive coordinates +% associated with \textsc{front} face of a cube image, or of a face-only image.} +% }% % \end{figure} % -% For example, in Figure~\ref{fig:facegraph} we have drawn a green -% arrow from the centre of cubie LB $(0.5, 0.5)$ to the centre of +% \medskip +% +% For~example, Figure~\ref{fig:facegraph} shows a green +% arrow drawn from the centre of cubie LB $(0.5, 0.5)$ to the centre of % cubie MM\,\footnote{The code MM stands for x=Middle, y=Middle; % see also Figure~\ref{fig:facenotation} on Rubik face-notation} $(1.5, 1.5)$. -% To do this we just include the following TikZ command in the -% \texttt{tikzpicture} environment. +% To do this we just include the following TikZ command, remembering that TikZ +% commands require a terminal semicolon. % \begin{quote} %\begin{verbatim} % \draw[->,color=green] (0.5,0.5) -- (1.5, 1.5); @@ -2316,7 +3158,7 @@ % \draw[->,thick,color=magenta] (1.3, 2.3) -- (1.3, 0.5); % \draw[<->,thick,color=magenta] (0.5,2.6) -- (2.5, 2.6); % \draw[<->,thick,color=magenta] (0.5,0.3) -- (2.5, 0.3); -% } +% } %\end{verbatim} % \end{minipage} % @@ -2357,7 +3199,7 @@ % {Y} {O} % \DrawRubikLayerSideB {O}{G}{G} % \draw[->,ultra thick,color=green] (0.5,5) -- (0.5, 4); -% } +% } %\end{verbatim} % \end{minipage} % @@ -2408,39 +3250,77 @@ % \DrawRubikCubeRD % \draw[ultra thick,->,color=blue] % (1.5,0.5) -- (2.5, 1.5); -% } +% } %\end{verbatim} % \end{minipage} -% +% +% \bigskip +% +% In the following example we use a blue circle to highlight the cubie +% to be rotated into the top layer. +% +% \bigskip +% +% \noindent% +% \RubikCubeGrey +% \RubikFaceUp{X}{W}{X}% +% {W}{W}{W}% +% {W}{W}{X}% +% \RubikSliceBottomR{X}{X}{W}{G}{X}{X}% +% \ShowCube{2.5cm}{0.5}{% +% \DrawRubikCubeRU +% \DrawRubikLayerSideRBy{O} +% \draw[ultra thick,->,color=blue] (2.5,0.5) -- (2.5, 2.5); +% \draw [color=blue, thick] (2.7, 0.3) circle (1.3); +% }% +% \hspace{3mm} +% \begin{minipage}{0.6\textwidth} +%\begin{verbatim} +% \noindent% +% \RubikCubeGrey +% \RubikFaceUp{X}{W}{X} +% {W}{W}{W} +% {W}{W}{X} +% \RubikSliceBottomR{X}{X}{W}{G}{X}{X} +% \ShowCube{2.5cm}{0.5}{% +% \DrawRubikCubeRU +% \DrawRubikLayerSideRBy{O} +% \draw[ultra thick,->,color=blue] +% (2.5,0.5) -- (2.5, 2.5); +% \draw [color=blue, thick] (2.7, 0.3) circle (1.3); +% }% +%\end{verbatim} +% \end{minipage} % % % \section{Final example} % % We now present, as a final example, the code used to draw the front page -% figure\,\footnote{This is a sequence of order 6 used to generate the `cross' -% configuration when solving the cube. Doing it on a `solved' cube allows you -% to see how the three edge cubies move, and either flip (magenta arrows) or do -% not flip (black arrow).}. -% This code uses both the \rubikcube\ and \textsc{rubikrotation} packages, -% and therefore needs to be run using the \LaTeX\ \verb!--shell-escape! command-line switch, -% as described in the \textsc{rubikrotation} package. -% +% figure\,\footnote{This is a well-known sequence of order 6 used to cycle three +% edge cubies; it is used to generate the `cross' configuration in the final layer +% when solving the cube. Here we are performing the sequence on a `solved' cube, +% since this allows you to see how the three edge cubies move, and either +% flip (magenta arrows) or do not flip (black arrow).}. +% This code uses the \cmd{\RubikRotation} command (from the \textsc{rubikrotation} +% package), and therefore the \LaTeX\ engine needs to be run using the +% \verb!--shell-escape! command-line switch (see Section~\ref{sec:rubikrotation} for details). % % \bigskip -% \hfil -% \RubikCubeSolved -% \ShowCube{2cm}{0.4}{\DrawRubikCubeRU} -% \ShowCube{2cm}{0.4}{% +% +% \noindent\hfil% +% \RubikCubeSolved% +% \ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% +% \quad\ShowCube{1.6cm}{0.4}{% % \DrawFlatUpSide % \draw[thick,->,color=magenta] (1.5,0.5) -- (2.4, 1.4); % \draw[thick,->] (2.5,1.5) -- (1.6, 2.4); % \draw[thick,->,color=magenta] (1.3, 2.3) -- (1.3, 0.5); % \draw[thick,<->, color=blue] (0.5,2.6) -- (2.5, 2.6); % \draw[thick,<->, color=blue] (0.5,0.3) -- (2.5, 0.3); -% } -% \Rubik{F}\Rubik{R}\Rubik{U}\Rubik{Rp}\Rubik{Up}\Rubik{Fp}% -% \ \ \ $\longrightarrow$ -% \ShowCube{2cm}{0.4}{% +% }% +% \quad\Rubik{F}\Rubik{R}\Rubik{U}\Rubik{Rp}\Rubik{Up}\Rubik{Fp}% +% \quad$\longrightarrow$% +% \quad\ShowCube{1.6cm}{0.4}{% % \DrawRubikLayerFace{W}{W}{B} % {W}{W}{O} % {W}{R}{B} @@ -2451,31 +3331,30 @@ % \DrawRubikLayerSideB {G}{W}{O} % } % \hfil -% \bigskip % +% \bigskip % %\begin{verbatim} -% \hfil -% \RubikCubeSolved -% \ShowCube{2cm}{0.4}{\DrawRubikCubeRU} -% \ShowCube{2cm}{0.4}{% -% \DrawFlatUpSide +% \noindent\hfil% +% \RubikCubeSolved% +% \ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% +% \quad\ShowCube{1.6cm}{0.4}{% +% \DrawFlatUpSide% % \draw[thick,->,color=magenta] (1.5,0.5) -- (2.4, 1.4); % \draw[thick,->] (2.5,1.5) -- (1.6, 2.4); % \draw[thick,->,color=magenta] (1.3, 2.3) -- (1.3, 0.5); % \draw[thick,<->, color=blue] (0.5,2.6) -- (2.5, 2.6); % \draw[thick,<->, color=blue] (0.5,0.3) -- (2.5, 0.3); -% } -% \Rubik{F}\Rubik{R}\Rubik{U}\Rubik{Rp}\Rubik{Up}\Rubik{Fp}% -% \ \ \ $\longrightarrow$ -% \RubikRotation{F,R,U,Rp,Up,Fp} -% \ShowCubeF{2cm}{0.4}{\DrawFlatUpSide} +% }% +% \RubikRotation{F,R,U,Rp,Up,Fp}% +% \quad\ShowSequence{}{\Rubik}{\SequenceLong}\quad$\longrightarrow$% +% \ShowCube{1.6cm}{0.4}{\DrawFlatUpSide}% % \hfil %\end{verbatim} % % % -% \subsection[Without using {\textbackslash}RubikRotation]{Without using \cmd{\RubikRotation..}} +% \subsection[Without using {\textbackslash}RubikRotation]{Without using \cmd{\RubikRotation}} % % If you really need to draw the above figure \textit{without} using % the \textsc{rubikrotation} package (as we had to in order to write @@ -2483,11 +3362,14 @@ % commands %\begin{verbatim} % \RubikRotation{F,R,U,Rp,Up,Fp} -% \ShowCubeF{2cm}{0.4}{\DrawFlatUpSide} +% \ShowSequence{,}{\Rubik}{\SequenceLong} \ \ \ $\longrightarrow$ +% \ShowCube{2cm}{0.4}{\DrawFlatUpSide} %\end{verbatim} -% with the following set of \cmd{\DrawRubikLayer...} commands. +% with the following commands: % %\begin{verbatim} +% \Rubik{F}\Rubik{R}\Rubik{U}\Rubik{Rp}\Rubik{Up}\Rubik{Fp} +% \ \ \ $\longrightarrow$ % \ShowCube{2cm}{0.4}{% % \DrawRubikLayerFace{W}{W}{B} % {W}{W}{O} @@ -2497,71 +3379,129 @@ % {B} {W} % {O} {W} % \DrawRubikLayerSideB {G}{W}{O} -% } +% } %\end{verbatim} % % % % % -% \section{Known issues \& shortcomings} +% \section{Known limitations} % -% Please contact the authors regarding any ideas, errors or shortcomings etc. +% Please contact the authors regarding any ideas for improvement, errors, +% problems or shortcomings etc. % % \begin{itemize} % -% \item The rotation hieroglyphs are optimised for a 10pt font, and do -% not scale with document font size. However, they do -% seem to work reasonably well with both 11pt and 12pt fonts. -% Any suggestions are welcome. -% -% \item The sidebars cannot be arbitrarily positioned. +% \item Note that the rotation hieroglyphs are optimised for a 10pt font +% and do not scale with document font size. However, they do work well in +% conjunction with the standard 11pt and 12pt document fonts sizes. Nevertheless, +% the font size can of course be changed by renewing the font command +% (see Section~\ref{sec:rubikfont} for details). +% +% \item The sidebars cannot be arbitrarily positioned (note: hidden +% faces can be arbitrarily positioned). % % \end{itemize} % % -% \section{Acknowledgements} -% -% We would like to thank Peter Bartal and Peter Grill for useful ideas and -% suggestions. We have built on some of their ideas and have acknowledged -% these instances in the documentation. -% We would also like to thank Christian Tellechea for the \cmd{\@join\{\}\{\}} command. -% -% -% -% \section{Future supporting packages} +% \section{Future packages} % % Since Rubik-type cubes currently exist in a variety of sizes (from 2x2x2 to 11x11x11) -% it is possible that similar packages dealing with cubes of other sizes may be made in -% the future. Supporting tools may also be made +% other authors may well create similar packages dealing with +% cubes of other sizes the future. Supporting tools may also be made % using various programming languages, e.g.,~Lua etc. Consequently the naming of such % packages and tools, and even the associated CTAN directories, needs to be given % some thought in order to prevent possible confusion. % -% In the event of new packages being made, we suggest that a CTAN directory structure +% In the event of new packages being made, may we suggest that a CTAN directory structure % along the following lines might be appropriate. % % $$ -% \textsc{rubik} \left\{ -% \begin{array}{l} -% \mbox{rubiktools}\\ -% \mbox{rubik2x}\\ -% \mbox{rubik3x}\\ -% \ldots\\ -% \mbox{rubik11x}\\ -% \end{array} -% \right.\\ +% \textsc{rubik} +% \left\{ +% \begin{array}{l} +% \mbox{rubiktools}\\ +% \mbox{rubik2x}\\ +% \mbox{rubik3x}\\ +% \ldots\\ +% \mbox{rubik11x}\\ +% \end{array} +% \right.\\ % $$ % % % -% \section{History} +% \section{Change history} % % \begin{itemize} - +% +% \item Version 4.0 (March 2017) +% +% ---Improved documentation. +% +% ---Improved inter-hieroglyph spacing and vertical position. The Computer Moderm sans bold font +% (10/12pt) is used for the hieroglyphs and rotation codes (see Section~\ref{sec:coderubikfont} +% for details). +% +% ---Improved the \cmd{\ShowCube} and \cmd{\ShowCubeF} macros (see Sections~\ref{sec:showcube} +% and \ref{sec:showcubecode}). +% +% ---Additional notation for middle slice rotations (`m' notation), e.g.,~\rr{Rm}, \rr{Rmp} etc +% (see Sections~\ref{sec:mnotation} and \ref{sec:codeJaap}). +% +% ---Additional notation for whole cube rotations (`c' notation), e.g.,~\rr{Rc}, \rr{Rcp} etc +% (see Sections~\ref{sec:cnotation} and \ref{sec:codeJaap}). +% +% ---Added Randelshofer notation (the `CMST' rotations), e.g.,~\rr{CR}, \rr{MR} etc +% (see Sections~\ref{sec:listofRandelshofercommands} and \ref{sec:codeRandelshofer}). +% +% +% ---Two new (more-intuitive) \cmd{\Draw..} commands replace earlier (now deprecated) +% ambiguous versions; these new versions are now consistent with +% the other \cmd{\DrawRubikCubeXX} commands (see Section~\ref{sec:flatcommands}). +% \begin{quote} +% \cmd{\DrawRubikCubeF} (F = flat) ---replaces \cmd{\DrawRubikFlat}. +% \newline\cmd{\DrawRubikCubeSF} (SF = semi-flat) ---replaces \cmd{\DrawRubikCubeFlat}. +% \end{quote} +% +% +% ---Six new commands for showing and annotating rotation sequences; the versions with a +% terminal `F' also surround the object with an fbox to allow users to see the extent +% of any associated white space +% (see Sections~\ref{sec:showsequence} \& \ref{sec:sequencebrace}): +% \begin{quote} +% \cmd{\ShowSequence} +% \newline\cmd{\ShowSequenceF} +% \newline\cmd{\ShowSequencef} +% \newline\cmd{\SequenceBraceA} +% \newline\cmd{\SequenceBraceAF} +% \newline\cmd{\SequenceBraceB} +% \newline\cmd{\SequenceBraceBF} +% +% \end{quote} +% +% ---A new command for setting up or allocating a `solved' colour configuration. +% (see Section~\ref{sec:solvedconfig}): +% \begin{quote} +% \cmd{\SolvedConfig} +% \end{quote} +% +% ---A new command for setting up a `starter cube' for which the \textit{whole} cube +% is allocated the default `grey' colour (see Section~\ref{sec:rubikcubegrey}): +% \begin{quote} +% \cmd{\RubikCubeGreyAll} +% \end{quote} +% +% ---A new supporting \textsc{rubikpatterns} package has been added to +% the Rubik bundle. It is a small macro database of well-known named Rubik patterns +% and associated sequences (see Section~\ref{sec:patterns}). +% +% +% % \item Version 3.0 (September 2015) % -% ---All rotation commands can now use the rotation-code as an argument; for example, +% ---All rotation commands can now use the rotation-code as an argument; for~example, % the rotation \rr{D} can now be typeset using the command \cmd{\rr\{D\}} etc % (see Section~\ref{sec:RubikCommands}). % The new rotation commands are: @@ -2605,13 +3545,13 @@ % % ---Changed `Equator' $\rightarrow$ `Middle' in all \cmd{\DrawLayer..} % commands (for consistency). Hence `E' $\rightarrow$ `M' in all Flat -% commands and Slice commands. Note although former use of `Equator' is +% commands and Slice commands. Note that although the former use of `Equator' is % retained for backward compatibility (for the moment) it is now deprecated. % % ---Fixed a conflict with the \TeX\ \cmd{\sb} command as used by the \textbf{url} % package which resulted in reference chaos when the \textbf{url} package was used with -% the \Rubikcube\ package (internalised \cmd{\sb} to \cmd{\@sb}). Also internalised for -% convenience \cmd{\sd} to \cmd{\@sd}; \cmd{\sh} to \cmd{\@sh}; \cmd{\sc} to \cmd{\@sc}; +% the \Rubikcube\ package (internalised \cmd{\sb} to \cmd{\@sb}). Also internalised, for +% convenience, \cmd{\sd} to \cmd{\@sd}; \cmd{\sh} to \cmd{\@sh}; \cmd{\sc} to \cmd{\@sc}; % \cmd{\sq} to \cmd{\@sq}. % % @@ -2623,13 +3563,25 @@ % % % +% \section{Acknowledgements} +% +% We would like to thank Peter Bartal and Peter Grill for useful ideas and +% suggestions. We have built on some of their ideas and have acknowledged +% these instances in the documentation. +% Finally, we would like to thank Christian Tellechea for the \cmd{\@join\{\}\{\}} +% command (see Section~\ref{sec:usefulinternalcommands}), +% Christian Schr\"{o}ppel for help regarding the \textsf{forarray} package +% (see Section~\ref{sec:codeshowsequence}), and Herbert Kociemba for helpful comments. +% +% +% +% % \section{References} % % \begin{itemize} % % -% \item Bartal P (2011) -% +% \item Bartal P (2011). \ % \url{http://tex.stackexchange.com/questions/34482/} % % \item Chen JJ (2004). Group theory and the Rubik's cube. @@ -2638,7 +3590,7 @@ % % \item Davis T (2006). Group theory via Rubik's cube. % \url{http://www.geometer.org/rubik/group.pdf} - +% % \item Demaine ED, Demaine ML, Eisenstat S, Lubiw A and Winslow A (2011). % Algorithms for solving Rubik's cubes. % \url{http://www.arxiv.org/abs/1106.5736/} @@ -2658,14 +3610,16 @@ % \newline\url{http://duvoid.fr/rubik/rubik-friddrich-couleurs.pdf} % \newline\url{http://duvoid.fr/rubik/sources/rubik-friddrich-couleurs.tex} % -% \item Feuers\"{a}nger (2015). Manual for package \textsc{pgfplots} -% (\texttt{pgfplots.pdf}). v\,1.12.1 (2015/05/02), \S\,3.2.3, page~20. -% \url{http://www.ctan.org/pkg/pgfplots}. +% \item Feuers\"{a}nger (2016). Manual for package \textsc{pgfplots}. +% v\,1.13 (2016/01/06), \S\,3.2.3, page~21. (\texttt{pgfplots.pdf}) +% \url{http://www.ctan.org/pkg/pgfplots}. [re: preventing extra white space] % -% \item Fridrich J. \ \ \url{http://www.ws.binghamton.edu/fridrich/}. +% \item Fridrich website (Fridrich J.) \ \ \url{http://www.ws.binghamton.edu/fridrich/}. % See the useful `notation' section on the `Pretty patterns' webpage at % \url{http://www.ws.binghamton.edu/fridrich/ptrns.html}. % +% \item Frey AH and Singmaster D (1982). \textit{Handbook of cubik math}, +% (Enslow Publishers, Inc.) (republished: 2010, Lutterworth Press, UK) % % \item Golomb SW (1981). Rubik's cube and a model of quark confinement. % \textit{Am.\ J.\ Phys.}; vol~49, pp~1030--1031. @@ -2678,12 +3632,13 @@ % \item Gymrek M (2009). The mathematics of the Rubik's cube. % \newline\url{http://web.mit.edu/sp.268/www/rubik.pdf} % +% \item Heise website (Heise R). Rubik's cube theory. \url{http://www.ryanheise.com/cube/theory.html} +% % \item Hofstadter D (1981). Rubik cube. \textit{Scientific American}; March issue. % % \item Hutchings M (2011). The mathematics of Rubik's cube (slide presentation). % \url{http://math.berkeley.edu/~hutching/rubik.pdf} % -% % \item Jelinek website (Jelinek J). Rubik's cube solution methods. % \url{http://www.rubikscube.info/} % @@ -2691,18 +3646,29 @@ % Rubik's cube, Merlin's machine and other mathematical toys}; pp~322. % \url{http://www.mike.verdone.ca/media/rubiks.pdf} % -% \item Kociemba website (Kociemba H). \url{http://www.kociemba.org/cube.htm} -% +% +% \item Kociemba website (Kociemba H). \url{http://www.kociemba.org/cube.htm} +% {\newline}---for superflip see: \url{http://www.kociemba.org/math/oh.htm} +% +% % \item Kriz I and Siegel P (2008). Rubik's cube-inspired puzzles demonstrate math's % simple groups. \textit{Scientific American}; July 2008 % +% \item Longridge website (Longridge M). The cube pattern archive. \url{http://www.cubeman.org} % % \item Randelshofer website (Randelshofer W). Pretty patterns. % \url{http://www.randelshofer.ch/rubik/patterns/} % -% \item Reid website (Reid M) \ \ \url{http://www.cflmath.com/Rubik/}, +% \item Reid website (Reid M) \ \ \url{http://www.cflmath.com/Rubik}, % for patterns see \url{http://www.cflmath.com/Rubik/patterns.html} % +% \item Reid M. (1995). Superflip requires 20 face turns. (January 1995) +% \url{http://www.math.ucf.edu/~reid/Rubik/CubeLovers/} +% {\newline}[cited from Rokicki \textit{et~al.}, 2013]. +% {\newline}(Note: easier to use is the following html indexed version of the +% archive of the Cube-Lovers usenet group (1982--1997) +% \url{http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/}) +% % % \item Rokicki T, Kociemba H, Davidson M and Dethridge J (2013). The diameter of the % Rubik's cube is twenty. \textit{SIAM.\ J.\ Discrete Math.}, \underline{27}, 1082--1105. @@ -2711,7 +3677,15 @@ % \item Rubik's cube. See Section on notation. % \newline\url{http://en.wikipedia.org/wiki/Rubik's_Cube} % -% \item Speedsolving website. \url{www.speedsolving.com/} +% \item RuWix website (Ferenec D) \ \ \url{http://www.ruwix.com}. +% See the online Rubik's cube solver \url{http://www.ruwix.com/online-rubiks-cube-solver-program}. +% +% \item Scherphius website (Scherphius J). Jaap Puzzles website +% \url{http://www.jaapsch.net/puzzles/symmetr1.htm} +% +% \item Singmaster D (1981). \textit{Notes on Rubik's magic cube} (Harmondsworth, Eng., Penguin Books) +% +% \item Speedsolving website. \url{http://www.speedsolving.com/} % % \item Tran R (2005). A mathematical approach to solving Rubik's cube. % \url{http://www.math.ubc.ca/~cass/courses/m308/projects/rtran/rtran.pdf} @@ -2722,9 +3696,9 @@ % [cited from \textit{Wikipedia} (Rubik's cube)] % % -% \item Vandenbergh L. \ \ \textsc{cubezone} \url{http://www.cubezone.be} +% \item Vandenbergh website (Vandenbergh L.) \ \ \textsc{cubezone} \url{http://www.cubezone.be} % -% \item WCA (2015). World Cube Association Regulations. See Section~12 for notation. +% \item WCA (2016). World Cube Association Regulations. See \S\,12 for notation. % \url{http://www.worldcubeassociation.org/regulations.htm} % % @@ -2742,17 +3716,17 @@ % The conventions we adopt regarding capital letters and the % XYZ argument ordering are detailed in Section~\ref{sec:conventions}. % -% Note that it is important in a graphics package to use a trailing \% on -% the end of lines which break before the terminal curley bracket of a newcommand. +% Note that it is important when using a graphics package to use a trailing \% on +% the end of lines which break before the terminal curly bracket of a \cmd{\newcommand}. % This is to prevent accumulating spurious spaces which may otherwise appear in -% figures and diagrams as a strange or unexpected horizontal shift or whitespace. +% figures and diagrams as a strange or unexpected horizontal shift or white-space. % % \subsection{\hspace{3mm}Package heading} % % \begin{macrocode} %<*rubikcube> -\def\RCfileversion{3.0}% -\def\RCfiledate{2015/09/25}% +\def\RCfileversion{4.0}% +\def\RCfiledate{2017/03/03}% \NeedsTeXFormat{LaTeX2e} \ProvidesPackage{rubikcube}[\RCfiledate\space (v\RCfileversion)] % \end{macrocode} @@ -2763,100 +3737,38 @@ \RequirePackage{tikz}}% % \end{macrocode} % -% \begin{macro}{\rubikcube} -% First we create a suitable logo +% The package requires the Forarray package (see Section~\ref{sec:codeshowsequence})---so +% we load it if not already loaded. % \begin{macrocode} -\newcommand{\rubikcube}{\textsc{rubikcube}}% -\newcommand{\Rubikcube}{\textsc{Rubikcube}}% +\@ifpackageloaded{forarray}{}{% + \typeout{---rubikcube requires the Forarray package.}% + \RequirePackage{forarray}}% % \end{macrocode} -% \end{macro} -% -% -% \subsection{\hspace{3mm}Some useful internal commands} -% \label{sec:usefulinternalcommands} -% -% \begin{macro}{\@rr} -% \begin{macro}{\@rrp} -% \begin{macro}{\@rrw} -% \begin{macro}{\@rrwp} -% \begin{macro}{\@rrs} -% \begin{macro}{\@rrsp} -% \begin{macro}{\@rra} -% \begin{macro}{\@rrap} -% \begin{macro}{\@xyzh} -% \begin{macro}{\@xyzhp} -% \begin{macro}{\@xyzRubik} -% \begin{macro}{\@xyzRubikp} -% \begin{macro}{\@SquareLetter} -% \begin{macro}{\@hRubik} -% Internal commands. These are used to generate the -% prime, w, w-prime, s, s-prime, a, a-prime -% rotation commands. The \cmd{\@xyz..} commands are used to generate the -% x,y,z,u,d,l,r,f,b, and their prime rotation commands. -% The \cmd{\@SquareLetter} command is used to form the separate square hieroglyph form -% used for rotations with no visible representation from the front -% (eg~B.., Fs, Fsp, Fa, Fap, S, Sp, Sf, Sfp, Sb, Sbp). -% The \cmd{\@hRubik} is the vertical shift used to raise the box carying the rotation -% rotation-code in \cmd{\Rubik..} commands not visible from the front. % -% The idea is that by using these internal -% tools we will be able to more easily standardise the size and position -% of all the various glyphs. However, these internal tools are currently -% only partially implemented (= work in progress). -% \begin{macrocode} -\newcommand{\@rr}[1]{\textbf{\textsf{#1}}} -\newcommand{\@rrp}[1]{\textbf{\textsf{#1}$^\prime$}} -\newcommand{\@rrw}[1]{\textbf{\textsf{#1\footnotesize{w}}}} -\newcommand{\@rrwp}[1]{\textbf{\textsf{#1\footnotesize{w}}$^\prime$}} -\newcommand{\@rrs}[1]{\textbf{\textsf{#1\footnotesize{s}}}} -\newcommand{\@rrsp}[1]{\textbf{\textsf{#1\footnotesize{s}}$^\prime$}} -\newcommand{\@rra}[1]{\textbf{\textsf{#1\footnotesize{a}}}} -\newcommand{\@rrap}[1]{\textbf{\textsf{#1\footnotesize{a}}$^\prime$}} -\newcommand{\@xyzh}[1]{\textbf{[\textsf{#1}]}\,} -\newcommand{\@xyzhp}[1]{\textbf{[\textsf{#1}$^\prime$]}\,} -\newcommand{\@xyzRubik}[1]{\raisebox{3.45pt}{\textbf{[\textsf{#1}]}}} -\newcommand{\@xyzRubikp}[1]{\raisebox{3.45pt}{\textbf{[\textsf{#1}$^\prime$]}}} -\newcommand{\@SquareLetter}[1]{\setlength\fboxsep{2.5pt}\fboxrule=0.8pt% - \fbox{\rule[-1pt]{0pt}{8.5pt}\raisebox{-0.5pt}{#1}}} -\newlength\@hRubik% -\setlength{\@hRubik}{0.185cm}% +% The package requires the IfThen package (see Section~\ref{sec:codeshowsequence})---so +% we load it if not already loaded. +% \begin{macrocode} +\@ifpackageloaded{ifthen}{}{% + \typeout{---rubikcube requires the IfThen package.}% + \RequirePackage{ifthen}}% % \end{macrocode} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} % % -% \begin{macro}{\@join} -% We also require a macro for joining two strings so we can convert -% a rotation-code, say U, into a macro which typesets it in some form, say \cmd{\rrhU}. -% The following \cmd{\@join\{\}\{\}} command is by Christian Tellechea. -% {\newline}Usage: \cmd{\@join\marg{command-stem}\marg{rotation-code}}. For example, -% to create the command \cmd{\rrhU} we would write |\@join{\rrh}{U}|, and hence -% the command |\rrh{U}| is equivalent to \cmd{\rrhU} (see Section~\ref{sec:cmdsusingjoin}). -% {\newline}Since this macro is also useful for processing rotation-codes in a list, -% which may also include macros, it is important that |#2| is not detokenized. -% \begin{macrocode} -\newcommand*\@join[2]{% - \csname\expandafter\@gobble\string#1#2\endcsname} +% +% \begin{macro}{\rubikcube} +% First we create a suitable logo +% \begin{macrocode} +\newcommand{\rubikcube}{\textsc{rubikcube}}% +\newcommand{\Rubikcube}{\textsc{Rubikcube}}% % \end{macrocode} -% \end{macro} +% \end{macro} % % % \subsection{\hspace{3mm}Colours} % \label{sec:codecolours} % -% These colour allocations were initially defined by Peter Bartal (2011). +% We have adopted the following colour allocations; these were initially +% defined by Peter Bartal (2011) ---see Section~\ref{sec:colours}. % We have modified only the colour grey, which is now defined as {black!30}. % % \begin{macrocode} @@ -2871,6 +3783,37 @@ % % % +% \subsection{\hspace{3mm}The rubikfont} +% \label{sec:coderubikfont} +% +% \begin{macro}{\@rubikfont} +% \begin{macro}{\@rubikfontFNS} +% \begin{macro}{\@rubikprime} +% We define two fonts for text associated with the Rubik glyphs +% (both the `arrow' glyphs and the `letter' glyphs), +% namely, (1)~Computer Modern Sans (cmss), bold extended (bx), normal shape (n) +% at 10/12pt, and (2)~a footnotesize (FNS) version (8pt) for the lower-case letters +% [for cmss see Latex Companion (2004), p.\,417 \& p.\,354\,\footnote{Note the typo in Table~7.5 (p.\,354): +% the font-series code for the Sans semi-bold condensed form is `sbx' (not sbc).}]. +% This has the effect of keeping the size +% of Rubik glyphs constant in the face of any changes in the document fonts. +% We make the baseline-skip values the same, since the `arrow' glyphs generated by +% the \cmd{\Rubik} commands involve a single baseline-skip (for example, as with +% \verb!\Rubik{D}!; see Section~\ref{sec:coderotationD}). +% We use the cmss font apostrophe as the `prime' symbol (the user has +% the opportunity to use the maths \cmd{\prime} +% instead---see Section~\ref{sec:rubikprime}). +%\begin{macrocode} +\newcommand{\@rubikfont}{\fontsize{10}{12pt}\usefont{T1}{cmss}{bx}{n}} +\newcommand{\@rubikfontFNS}{\fontsize{8}{12pt}\usefont{T1}{cmss}{bx}{n}} +\newcommand{\@rubikprime}{'} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% % \subsection{\hspace{3mm}ShowCube command} % \label{sec:showcubecode} % @@ -2880,42 +3823,181 @@ % displays the cube inside a minipage, so that we can easily tailor the minipage % width (|#1|) and also the TikZ scale factor (|#2|). The \cmd{\ShowCubeF} command % places an fbox around the minipage so users can see the extent of any white space. -% {\newline}\textsc{usage}: |\ShowCube{2cm}{0.5}{\DrawRubikCubeRU}| +% {\newline}\textsc{usage}: |\ShowCube{2cm}{0.5}{\DrawRubikCubeRU}| +% +% February 2017 (RWDN): \ We first require a new length variable (which will become the minipage-width), +% so we can add the length 1.6pt to it (this is the width of the TikZ ultra-thick line +% which is used to draw the Rubik cubes). +% In order for a width of an image made up of $x$~units to be equal +% to $x \times (\mbox{scale-factor})$ we need to add an extra line-width +% (i.e.,~to include the right-hand edge). +% \begin{macrocode} +\newlength{\@showcubewidth}% +% \end{macrocode} +% We can now build the two macros. We set the \cmd{\fboxsep} value to zero. % \begin{macrocode} \newcommand{\ShowCube}[3]{% - \begin{minipage}{#1}% + \setlength{\fboxsep}{0cm}% + \setlength{\@showcubewidth}{#1}% + \advance\@showcubewidth by 1.6pt\relax% + \begin{minipage}{\the\@showcubewidth}% \centering% \begin{tikzpicture}[scale=#2]% #3% \end{tikzpicture}% \end{minipage}% -} +}% \newcommand{\ShowCubeF}[3]{% - \fbox{% - \begin{minipage}{#1}% + \setlength{\fboxsep}{0cm}% + \setlength{\fboxrule}{0.4pt}% + \setlength{\@showcubewidth}{#1}% + \advance\@showcubewidth by 1.6pt\relax% + \framebox{% + \begin{minipage}{\the\@showcubewidth}% \centering% \begin{tikzpicture}[scale=#2]% #3% \end{tikzpicture}% \end{minipage}% -}} +}}% +% \end{macrocode} +% \end{macro} +% \end{macro} +% +% +% +% +% \subsection{\hspace{3mm}ShowSequence command} +% \label{sec:codeshowsequence} +% +% \begin{macro}{\ShowSequence} +% \begin{macro}{\ShowSequenceF} +% \begin{macro}{\ShowSequencef} +% The \cmd{\ShowSequence}\marg{separator}\marg{font-code}\marg{sequence} command +% typesets a comma separated sequence of rotation commands. +% (See Section~\ref{sec:showsequence}). +% This command takes three mandatory arguments: the first is the separator (\verb!#1!), +% the second is the font or style code (\verb!#2!), and third is a comma-separated +% sequence of Rubik rotation commands (|#3|). +% +% This command requires the \texttt{forarray} +% package---by Christian Schr\"{o}ppel---(for the \cmd{\ForEachX} command) +% and the \texttt{ifthen} package---by David Carlisle---(for the \cmd{\ifthenelse} command). +% These two packages are loaded at startup if not already loaded. +% We first need to define two variables for use by the command; these are +% derived from the \texttt{forarray} package. +% +% \begin{macrocode} +\newcommand{\x}{\thislevelitem} +\newcommand{\xcount}{\thislevelcount} +% \end{macrocode} +% +% The \cmd{\ShowSequence} command typesets a sequence of elements, and places +% an optional separator (|#1|) between them. +% For each element of |#3| this command forms the construction |#2{element of #3}|. +% For~example, if |#2 = \rr|, and an element of |#3| is D, then it forms |\rr{D}| etc. +% +% Note that in order to avoid placing a trailing comma after the final element, +% we identify the first element (using |\xcount|) and then place a comma in front +% all the remaining elements. This is because it is easy to identify the first element +% of a sequence, but very difficult to identify the final element. +% +% We also create two fbox forms: the `F' form places an fbox about the whole output; +% the `f' form places an fbox about each element in the output (these forms can be +% helpful when checking white space. +% +% \noindent\textsc{usage}: |\ShowSequence{,}{\rr}{R,L,Up,Dp.....}| +% +% \begin{macrocode} +\newcommand{\ShowSequence}[3]{% + \ForEachX{,}{% + \ifthenelse{\xcount=1}{#2{\x}}{#1#2{\x}}% + }{#3}% +}% +\newcommand{\ShowSequenceF}[3]{% +\fbox{% + \ForEachX{,}{% + \ifthenelse{\xcount=1}{#2{\x}}{#1#2{\x}}% + }{#3}% +}}% +\newcommand{\ShowSequencef}[3]{% + \ForEachX{,}{% + \ifthenelse{\xcount=1}{\fbox{#2{\x}}}{#1{\fbox{#2{\x}}}}% + }{#3}% +}% % \end{macrocode} +% \begin{macro}{\SequenceInfo} +% \begin{macro}{\SequenceName} +% \begin{macro}{\SequenceShort} +% \begin{macro}{\SequenceLong} +% \noindent\textsc{Sequence holders}: providing none of the Rubik rotation-codes has a trailing +% integer (e.g.,~R3) then the Rubik macros (|\rr|, |\rrh|, |\Rubik|, |\textRubik|) will work +% as expected when used as the second argument in the \cmd{\ShowSequence} command +% (described above). However, a problem arises when trying to process in this way any Rubik +% rotation-codes having a terminal integer (for example, short-codes e.g.,~R2, D3,...), since the +% \cmd{\ShowSequence} macro cannot expand short-codes into their long-code +% elements (e.g.,~~R,R,D,D,D,...). +% +% Accommodating such codes when using the \cmd{\ShowSequence} command is currently +% solved by using separate `holders' for four derived strings, namely: \cmd{\SequenceInfo}, +% \cmd{\SequenceName},\cmd{\SequenceShort} and \cmd{\SequenceLong} +% (for details see Section~\ref{sec:showsequence}). +% These are generated automatically by the Perl \textsc{rubikrotation} program, which returns +% a so-called `long' version of the `short' string (the argument of the \cmd{\RubikRotation} +% command). For~example, the Perl program converts +% any short codes (e.g.,~R2, D3,... ) $\rightarrow$ long form, e.g.,~R,R,D,D,D,... +% (see the \textsc{rubikrotation} documentation for details). +% In order for the four `holders' of these derived strings generated by the Perl program +% (written to the file \texttt{rubikstateNEW.dat}) to be accessible to the user they need to +% defined here so that they can then be `redefined' (by the Perl program) in the file +% \texttt{rubikstateNEW.dat}: +% \begin{macrocode} +\newcommand{\SequenceInfo}{{}}% %% INFO only +\newcommand{\SequenceName}{{}}% %% NAME only +\newcommand{\SequenceShort}{{}}% %% original SHORT seq but with NO NAME +\newcommand{\SequenceLong}{{}}% %% just the LONG string \& no name +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} % \end{macro} % \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \subsection{\hspace{3mm}SequenceBrace commands} +% \label{sec:sequencebracecode} % +% \begin{macro}{\SequenceBraceA} +% \begin{macro}{\SequenceBraceB} +% The \cmd{\SequenceBraceX}\marg{name}\marg{sequence} command +% is a tool for displaying a named sequence using a brace. The trailing~A +% denotes that the brace is placed Above the sequence; B~denotes the brace is Below the sequence. +% For usage see Section~\ref{sec:sequencebrace}. +% +% \begin{macrocode} +\newcommand{\SequenceBraceA}[2]{$\overbrace{\mbox{#2}}^{\mbox{#1}}$}% +\newcommand{\SequenceBraceB}[2]{$\underbrace{\mbox{#2}}_{\mbox{#1}}$}% +\newcommand{\SequenceBraceAF}[2]{\fbox{$\overbrace{\mbox{#2}}^{\mbox{#1}}$}}% +\newcommand{\SequenceBraceBF}[2]{\fbox{$\underbrace{\mbox{#2}}_{\mbox{#1}}$}}% +% \end{macrocode} +% \end{macro} +% \end{macro} % % % \subsection{\hspace{3mm}Face commands} % -% Cube face notation = U, D, L, R, F, B (Singmaster) -% {\newline}Cubie-square notation = t, m, b, l, m, r = top, middle, +% Cube face notation: U, D, L, R, F, B (Singmaster) +% {\newline}Cubie-square notation: t, m, b, l, m, r = top, middle, % bottom, left, middle, right. -% We use t,b for cubie-squares (facelets) to avoid confusion with cube Face notation. +% We use the t, b notation for cubie-squares (facelets) to avoid confusion with cube Face notation. % We number the cubie-squares on a face 1--9 reading from left-to-right, % starting top-left, ending bottom-right, as follows % (see also Figure~\ref{fig:facenotation}): % {\newline}\strut\hspace{1cm}top row \ \ \ \ \ (1,2,3) = tl, tm, tr -% {\newline}\strut\hspace{1cm}middle row (4,5,6) = ml, mm, mr +% {\newline}\strut\hspace{1cm}middle row\, (4,5,6) = ml, mm, mr % {\newline}\strut\hspace{1cm}bottom row (7,8,9) = bl, bm, br % % \begin{macro}{\RubikFaceUp} @@ -2936,12 +4018,12 @@ % Each letter is an initial letter of the words Up, Down, Left, Right, Front, Back, % left, middle, right, top, middle, bottom. % -% For example, in the command \cmd{\Urt\{\#1\}} +% For~example, in the command \cmd{\Urt\{\#1\}} % the U stands for the Up face of the cube, while the \texttt{rt} stands % for the ``right-top'' facelet on this face. Note that the order -% of the two lowercase letters (in this case \texttt{rt}) are always written -% in the $x,y$ order; i.e.,~the first of the two lowercase letters relates to the $x$ -% direction (either left, middle, or right), while the second lowercase letter +% of the two lower-case letters (in this case \texttt{rt}) are always written +% in the $x,y$ order; i.e.,~the first of the two lower-case letters relates to the $x$ +% direction (either left, middle, or right), while the second lower-case letter % relates to the $y$ direction (either top, middle, or bottom)---this rule makes it % easy to remember the order. % \end{macro} @@ -2989,9 +4071,11 @@ % \begin{macro}{\RubikFaceRightAll} % \begin{macro}{\RubikFaceFrontAll} % \begin{macro}{\RubikFaceBackAll} -% These 5 commands allocate the same colour to all 9 cubiesquares in the specified face (Up, Down, Left, Right, Front). Each command therefore takes only 1 argument (one of the colour codes). +% These 5 commands allocate the same colour to all 9 cubie-squares +% in the specified face (Up, Down, Left, Right, Front). +% Each command therefore takes only 1~argument (one of the colour codes). % -% {\noindent}For example, \cmd{\RubikFaceUpAll\{R\}} +% {\noindent}For~example, \cmd{\RubikFaceUpAll\{R\}} % \end{macro} % \end{macro} % \end{macro} @@ -3031,7 +4115,8 @@ } % \end{macrocode} % -% {\noindent}We now use these commands to initialise all visible faces to default colour grey (X) +% {\noindent}Finally, we now use these commands to initialise all +% visible faces to the default colour grey~(X) % % \begin{macrocode} \RubikFaceUpAll{X}% @@ -3051,7 +4136,9 @@ % \begin{macro}{\RubikCubeGrey} % This command sets the face/colour configuration (state) of a 3x3x3 % Rubik cube with no colours allocated except for the central cubie of each face. -% These central colours match those defined for the RubikCubeSolved command. +% The colour configuration of the central cubies matches those defined for +% the RubikCubeSolved command (i.e.,~white opposite yellow etc). +% We also implement an equivalent `gray' version (to be consistent with TikZ). % \begin{macrocode} \newcommand{\RubikCubeGrey}{% \RubikFaceUp {X}{X}{X}{X}{W}{X}{X}{X}{X}% @@ -3061,29 +4148,73 @@ \RubikFaceFront{X}{X}{X}{X}{O}{X}{X}{X}{X}% \RubikFaceBack {X}{X}{X}{X}{R}{X}{X}{X}{X}% } +\newcommand{\RubikCubeGray}{\RubikCubeGrey} % \end{macrocode} % \end{macro} % % -% \subsection{\hspace{3mm}RubikCubeSolved command} % -% \begin{macro}{\RubikCubeSolved} +% +% \subsection{\hspace{3mm}SolvedConfig command} +% +% \begin{macro}{\SolvedConfig} % This command sets the face/colour configuration (state) of a typical -% solved Rubik cube. +% solved Rubik cube. Note that the order is Right, Left, Up, Down, Front, Back +% (i.e.,~X$+$, X$-$, Y$+$, Y$-$, Z$+$, Z$-$, order). +% We shall use this command to define solved cube configurations. % \begin{macrocode} -\newcommand{\RubikCubeSolved}{% - \RubikFaceUpAll{W}% - \RubikFaceDownAll{Y}% - \RubikFaceLeftAll{B}% - \RubikFaceRightAll{G}% - \RubikFaceFrontAll{O}% - \RubikFaceBackAll{R}% +\newcommand{\SolvedConfig}[6]{% + \RubikFaceRightAll{#1}% + \RubikFaceLeftAll{#2}% + \RubikFaceUpAll{#3}% + \RubikFaceDownAll{#4}% + \RubikFaceFrontAll{#5}% + \RubikFaceBackAll{#6}% } % \end{macrocode} % \end{macro} % % % +% +% \subsection{\hspace{3mm}RubikCubeGreyAll command} +% \label{sec:codegreyall} +% +% \begin{macro}{\RubikCubeGreyAll} +% This command sets the face/colour configuration (state) of a 3x3x3 +% Rubik cube with no colours allocated. +% This colour configuration is the same as the startup default state---all cubies will +% appear grey. We implement it using the \cmd{\SolvedConfig} command (above). +% We also implement an equivalent `gray' version (to be consistent with TikZ). +% \begin{macrocode} +\newcommand{\RubikCubeGreyAll}{\SolvedConfig{X}{X}{X}{X}{X}{X}}% +\newcommand{\RubikCubeGrayAll}{\RubikCubeGreyAll} +% \end{macrocode} +% \end{macro} +% +% +% \subsection{\hspace{3mm}RubikCubeSolved command} +% \label{sec:codesolvedconfig} +% +% \begin{macro}{\RubikCubeSolved} +% \begin{macro}{\RubikCubeSolvedWY} +% \begin{macro}{\RubikCubeSolvedWB} +% The first (default) command sets the face/colour configuration (state) one of the standard +% commercially available solved Rubik cube (white opposite yellow). The argument order +% follows the XYZ notation. For convenience we make a copy named \cmd{\RubikCubeSolvedWY} +% (denoting the White opposite Yellow configuration), and also a different version named +% \cmd{\RubikCubeSolvedWB} (denoting the White opposite Blue configuration). +% These represent the two standard versions of the Rubik Cube. +% \begin{macrocode} +\newcommand{\RubikCubeSolved}{\SolvedConfig{G}{B}{W}{Y}{O}{R}}% +\newcommand{\RubikCubeSolvedWY}{\RubikCubeSolved}% +\newcommand{\RubikCubeSolvedWB}{\SolvedConfig{R}{O}{W}{B}{G}{Y}}% +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% % \subsection{\hspace{3mm}Slice commands} % % \begin{macro}{\RubikSliceTopR} @@ -3148,7 +4279,7 @@ % and \TeX\ has only 9 macro parameters available, we are forced to draw % Rubik cubes by first specifying the colours on each of the three faces, % and then using a `DrawRubikCubeXY' command, where the trailing XY code -% defines the view direction (X = either R, L; Y = either U, D). +% defines the viewing direction (X = either R or L; Y = either U or D). % The order of the XY code is important: X~first, Y~second (so it is easy to remember). % % On each face the facelets are drawn in the following order: Top row @@ -3158,7 +4289,7 @@ % through the four corners of the facelet in the following order: % lb $\rightarrow$ lt $\rightarrow$ rt $\rightarrow$ rb; the code being % lb (LeftBottom), lt (LeftTop), rt (RightTop), rb (RightBottom) -% (only need four coords); the grid origin is at the bottom-left corner of the +% (only need four coords); the (x,y) grid origin is at the bottom-left corner of the % \textsc{front} face. % % \begin{macro}{\DrawRubikCubeFrontFace} @@ -3197,7 +4328,7 @@ % \subsubsection{\hspace{3mm}Viewing direction} % % The command `DrawRubikCubeXY' command uses the trailing XY code -% to specify the view direction (X = either R, L; Y = either U, D). +% to specify the view direction (X = either R or L; Y = either U or D). % The order of the XY code is important: X~first, Y~second (so it is easy % to remember). % @@ -3209,7 +4340,8 @@ % The colours are allocated to particular facelets using the \cmd{\RubikFaceUp}, % \cmd{\RubikFaceRight} and \cmd{\RubikFaceFront} commands. % -% The (x,y) grid origin is at the bottom-left corner of the \textsc{front} face. +% The (x,y) grid origin is at the bottom-left corner of the \textsc{front} face +% (see Section~\ref{sec:coordinates}). % The perspective is designed so that the 2D~graphic image of the side face % (\textsc{right} in this particular case) has its `horizontal' lines running % at 45~degrees. This has the useful advantage that the 2D~width of the side is @@ -3450,9 +4582,10 @@ % These two LayerFace commands each draw and paint a single % face of 9~facelets. The first command takes 9 ordered colour parameters, % (ordered in layers from top left to bottom right, so \texttt{\#1} -% is the placeholder for the colour of the TopLeft facelet etc.) -% The second takes only one colour parameter (since \texttt{All} the +% is the place-holder for the colour of the TopLeft facelet etc.) +% The second command takes only one colour parameter (since \texttt{All} the % colours are the same). +% % The drawing origin (0,0) = bottom left corner. The facelets are drawn % from left to right. % NOTE: this macro is SAME as the internal command @@ -3517,8 +4650,12 @@ % % [\textsc{note}: These new commands (version 3.0) were modified from the % earlier \cmd{\FlatUp}, \cmd{\FlatDown} etc., commands; i.e.,~they were -% reformulated as a set of \cmd{\Draw...} commands to make them consistent -% with all the other \cmd{\Draw..} commands]. +% reformulated as a set of \cmd{\Draw...} commands so as to make this +% notation consistent with the other \cmd{\Draw..} commands. +% Note also that, for user convenience, all of these commands have +% been copied (in version~4.0) to equivalent \cmd{\DrawFace..} +% versions associated with their two coordinate arguments +% set to $x=0$, $y=0$---see Section~\ref{sec:drawfacecode}] % % \begin{macro}{\DrawFlatUp} % \begin{macro}{\DrawFlatDown} @@ -3526,11 +4663,13 @@ % \begin{macro}{\DrawFlatRight} % \begin{macro}{\DrawFlatFront} % \begin{macro}{\DrawFlatBack} -% Each of these commands draws a separate (flat) face (9~facelets). +% Each of these commands draws a separate (flat) face (9~facelets) +% (see Section~\ref{sec:flatcommands}). % Each command (except \cmd{\DrawFlatFront}) takes two arguments, % namely the X-coordinate and Y-coordinate of the bottom-left % corner of the face. This (X,Y) pair of coordinates therefore allows -% the user to position the face. These commands were motivated by a need to +% the user to position the face in relation to the cube itself. +% These commands were motivated by a need to % be able to show hidden faces under certain circumstances. % % Note that the Y-argument currently only works fully @@ -3553,9 +4692,9 @@ % of a Rubik cube. % % The (x,y) variables are here encoded as (\cmd{\ux}, \cmd{\uy}) where the -% `u' stands for Up etc. However, since we are unable to use `dx, dy' with the -% \cmd{\DrawFlatDown} command (since dx and dy are already used in the -% \cmd{\cube@dxdydz...} command) we encode these instead as (\cmd{\ddx}, \cmd{\ddy}). +% `u' stands for Up etc. However, since we are unable to use a `dx, dy' notation +% with the \cmd{\DrawFlatDown} command (since dx and dy are already used by the +% \cmd{\cube@dxdydz...} command), we encode these instead as (\cmd{\ddx}, \cmd{\ddy}). % % \end{macro} % \end{macro} @@ -3689,7 +4828,7 @@ } %%----------------------- \newcommand{\DrawFlatFront}{% -%% This command is used /only/ by the \cmd{\DrawRubikFlat} command. +%% This command is used /only/ by the \cmd{\DrawRubikCubeF} command. %% NOTE: x, y variables not implemented as not required here %%---top row \draw[line join=round,line cap=round,ultra thick,fill=\Flt]% @@ -3756,12 +4895,12 @@ } % \end{macrocode} % -% \begin{macro}{\DrawRubikFlat} -% Draws a standard flat representation of the Rubik -% cube (colours only). Note that \cmd{\DrawFlatFront} does not -% take any arguments (x,y) arguments. +% \begin{macro}{\DrawRubikCubeF} +% Draws a standard flat (F) representation of the Rubik +% cube (colours only). Note that \cmd{\DrawFlatFront} (below) +% does not take any arguments (x,y). % \begin{macrocode} -\newcommand{\DrawRubikFlat}{% +\newcommand{\DrawRubikCubeF}{% \DrawFlatUp{0}{3}% \DrawFlatDown{0}{-3}% \DrawFlatLeft{-3}{0}% @@ -3772,12 +4911,13 @@ % \end{macrocode} % \end{macro} % -% \begin{macro}{\DrawRubikCubeFlat} +% +% \begin{macro}{\DrawRubikCubeSF} % Draws a Rubik cube together with the three hidden faces -% (colours only) in a semi-flat representation. The (x,y) -% arguments are for the bottom-left corner of the face. +% (colours only) in a semi-flat (SF) representation. The (x,y) +% arguments (below) are for the bottom-left corner of the face. % \begin{macrocode} -\newcommand{\DrawRubikCubeFlat}{% +\newcommand{\DrawRubikCubeSF}{% \DrawRubikCube% \DrawFlatDown{0}{-3}% \DrawFlatLeft{-3}{0}% @@ -3789,6 +4929,7 @@ % % % \subsubsection{DrawFlatXSide commands} +% \label{sec:drawflatxsidecode} % % These six commands draw a face together with all four sidebars % (colours only). We use the \cmd{\DrawFlatX} commands to draw the face. @@ -3798,7 +4939,10 @@ % Top (T) and Bottom (B) = left to right; % Left (L) and Right (R) = top to bottom; % (see the \cmd{\DrawRubikLayerSideX} command for details of the arguments). -% +% +% Note that for user convenience, we we have copied many of these commands +% to a \cmd{\DrawFace..} version (see Section~\ref{sec:drawfacecode}). +% % % \begin{macro}{\DrawFlatUpSide} % Draws the \textsc{up} face together with all four sidebars @@ -3891,6 +5035,31 @@ % % % +% \subsection{\hspace{3mm}DrawFace commands} +% \label{sec:drawfacecode} +% +% We now copy the above \cmd{\DrawFlat..} commands +% as \cmd{\DrawFace..} commands for the purpose of user +% convenience, since most of the time the user wants just to +% draw a particular face with or without the associated side bars. +% In a future version we may well, therefore, deprecate some of the above +% `Flat' command names. +% \begin{macrocode} +\newcommand{\DrawFaceUp}{\DrawFlatUp{0}{0}} +\newcommand{\DrawFaceDown}{\DrawFlatDown{0}{0}} +\newcommand{\DrawFaceLeft}{\DrawFlatLeft{0}{0}} +\newcommand{\DrawFaceRight}{\DrawFlatRight{0}{0}} +\newcommand{\DrawFaceFront}{\DrawFlatFront{0}{0}} +\newcommand{\DrawFaceBack}{\DrawFlatBack{0}{0}} +\newcommand{\DrawFaceUpSide}{\DrawFlatUpSide} +\newcommand{\DrawFaceDownSide}{\DrawFlatDownSide} +\newcommand{\DrawFaceLeftSide}{\DrawFlatLeftSide} +\newcommand{\DrawFaceRightSide}{\DrawFlatRightSide} +\newcommand{\DrawFaceFrontSide}{\DrawFlatFrontSide} +\newcommand{\DrawFaceBackSide}{\DrawFlatBackSide} +% \end{macrocode} +% +% % \subsection{\hspace{3mm}SideBar commands} % % SideBar commands draw narrow bars of colour indicating the @@ -3949,7 +5118,7 @@ % Note that the TikZ \cmd{\pgfmathsetmacro} commands (which do the maths) % must be inside the TeX sidebar command in order to work. % The start point of the TikZ \cmd{\draw} command for each bar rectangle -% is botton Left corner of the bar =(\cmd{\dx},\cmd{\dy}) +% is bottom Left corner of the bar =(\cmd{\dx},\cmd{\dy}) % \end{macro} % \end{macro} % \end{macro} @@ -3999,15 +5168,15 @@ % Right, Top, Middle, Bottom, x, y, as follows: % \begin{quote} % X$_1$ is an $x$ parameter: either $\langle L\mid M \mid R\rangle$ -% {\newline}X$_2$ is an $y$ parameter: either $\langle T\mid M \mid B\rangle$ +% {\newline}X$_2$ is a \, $y$ parameter: either $\langle T\mid M \mid B\rangle$ % {\newline}X$_3$ is an extra parameter: either $\langle x\mid y \rangle$, % required by corner sidebars to indicate whether the sidebar was either % above or below $\langle y \rangle$, or to the left or % right $\langle x \rangle$ of the associated cubie. % An $X_3$ parameter is not required for the sidebar of an edge cubie, since -% only one location is posible in these cases. +% only one location is possible in these cases. % \end{quote} -% For example, the following command +% For~example, the following command % \begin{quote} % \cmd{\DrawRubikLayerSideLTy\{G\}} % \end{quote} @@ -4038,7 +5207,7 @@ % \end{macrocode} % % -% \subsubsection{\hspace{3mm}Drawing multiple cubie sidebars} +% \subsubsection{\hspace{3mm}Drawing multiple cubie sidebars} % % \begin{macro}{\DrawRubikLayerSideT} % \begin{macro}{\DrawRubikLayerSideB} @@ -4107,6 +5276,65 @@ % \end{macro} % % +% \subsection{\hspace{3mm}RubikSide commands} +% \label{sec:rubiksidecode} +% +% \begin{macro}{\RubikSideLeft} +% \begin{macro}{\RubikSideRight} +% \begin{macro}{\RubikSideFront} +% \begin{macro}{\RubikSideBack} +% RubikSide commands allocate colours to the side facelets of the +% UP~face---see Section~\ref{sec:rubikside}. +% These facelets are the top three facelets of each side Front, Back, Left, Right. +% \begin{macrocode} +\newcommand{\RubikSideFront}[3]{% +\def\Flt{#1}\def\Fmt{#2}\def\Frt{#3}% +} +\newcommand{\RubikSideRight}[3]{% +\def\Rlt{#1}\def\Rmt{#2}\def\Rrt{#3}% +} +\newcommand{\RubikSideLeft}[3]{% +\def\Llt{#1}\def\Lmt{#2}\def\Lrt{#3}% +} +\newcommand{\RubikSideBack}[3]{% +\def\Blt{#1}\def\Bmt{#2}\def\Brt{#3}% +} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\RubikSideLeftAll} +% \begin{macro}{\RubikSideRightAll} +% \begin{macro}{\RubikSideFrontAll} +% \begin{macro}{\RubikSideBackAll} +% These 4 commands allocate the same colour to all 3 cubiesquares in the specified face +% (Left, Right, Front, Back). Each command therefore takes only 1 argument +% (one of the colour codes). +% +% {\noindent}For~example, \cmd{\RubikSideUpAll\{R\}} +% \begin{macrocode} +\newcommand{\RubikSideFrontAll}[1]{% +\def\Flt{#1}\def\Fmt{#1}\def\Frt{#1}% +} +\newcommand{\RubikSideRightAll}[1]{% +\def\Rlt{#1}\def\Rmt{#1}\def\Rrt{#1}% +} +\newcommand{\RubikSideLeftAll}[1]{% +\def\Llt{#1}\def\Lmt{#1}\def\Lrt{#1}% +} +\newcommand{\RubikSideBackAll}[1]{% +\def\Blt{#1}\def\Bmt{#1}\def\Brt{#1}% +} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% % % \subsection{\hspace{3mm}NCube command} % @@ -4123,7 +5351,7 @@ % The command takes four ordered arguments, as follows: % \begin{quote} % \#1 = number of cubies ($n>0$) along each side, -% {\newline}\#2, \#3, \#4 = colors of the visible faces (in X,Y,Z order); +% {\newline}\#2, \#3, \#4 = colours of the visible faces (in X,Y,Z order); % X=Right face colour, Y=Up face colour, Z=Front face colour. % \end{quote} % We use the \cmd{\pgfmathsetmacro}\marg{variable-name}\marg{numeric value or maths} @@ -4144,10 +5372,11 @@ % \end{macro} % % \begin{macro}{\cube@dxdydz} -% This internal command is used only by the \cmd{\DrawNCubeAll} command. -% The original version of this command was developed by Peter Bartal (see Bartal, 2011). -% It was modified (2012) by RWD Nickalls (to implement a more -% intuitive X, Y, Z ordering of parameters). +% This internal command is used only by the \cmd{\DrawNCubeAll} command +% (see above). The original version of this command was developed +% by Peter Bartal (see Bartal, 2011). +% It was later modified (2012) by RWD Nickalls (to implement a more +% intuitive X, Y, Z ordering of the face colour parameters). % % The cube need not be in the origin, the distances of % the \textsc{down}-behind [L] corner from @@ -4175,7 +5404,7 @@ % options to each of the TikZ \cmd{\draw} commands, in order to improve % the line joining (first two options); (2) adjusted the \cmd{\cube@dxdydz} macro % to adopt the ordered XYZ face colour notation -% (by reassigning \#2, \#3, \#4). +% (by reassigning \#2, \#3, \#4 to the X, Y, Z face colours, as shown above). % % \begin{macrocode} \newcommand{\cube@dxdydz}[7]{% @@ -4192,7 +5421,7 @@ \draw[line join=round,line cap=round,ultra thick,fill=#4]% (#5,#6,\dz) -- (\dx,#6,\dz) -- (\dx,\dy,\dz) -- (#5,\dy,\dz) -- cycle; %% The 'rectangle' command does not work with 3D coordinates, -%% so this is the way to draw the squres with space coordinates +%% so this is the way to draw the squares with space coordinates %% Draw UP face (using the Y colour = #3) \draw[line join=round,line cap=round,ultra thick,fill=#3]% (#5,\dy,\dz) -- (\dx,\dy,\dz) -- (\dx,\dy,#7) -- (#5,\dy,#7) -- cycle; @@ -4214,10 +5443,10 @@ % (adjust \texttt{cy}) and horizontal viewpoint (adjust \texttt{cx}) % of a single cubie (described in more detail in the \rubikcube\ % package documentation). -% Note that we cannot use the names \texttt{dx}, \texttt{dy} for variables since -% these have been allocated already (see above). However, we do use -% \texttt{dx}, \texttt{dy} in the command names as these will be more -% readily understood by the user. +% Note that we cannot use the names \texttt{dx}, \texttt{dy} for the +% variables here since these names have been allocated already +% (see above). However, we can use \texttt{dx}, \texttt{dy} in the +% command names as these will be more readily understood by the user. % \begin{macrocode} \newcommand{\Cubiedx}[1]{\pgfmathsetmacro{\cx}{#1}} \newcommand{\Cubiedy}[1]{\pgfmathsetmacro{\cy}{#1}} @@ -4307,8 +5536,8 @@ % % As before, the viewpoint is specified using an appended % two-letter XY ordered viewpoint code: either RU, RD, LU, LD. -% These commands take three arguments, namely three different XYZ -% ordered colour codes (R,O,Y,G,B,W,X). +% These commands take three arguments (since just three faces are visible with this +% cube format), namely three different XYZ ordered colour codes (R,O,Y,G,B,W,X). % \newline\textsc{format}: \cmd{\textCubieRU}\marg{Xcolour}\marg{Ycolour}\marg{Zcolour} % \newline\textsc{usage}: |\textCubieRU{G}{B}{W}| % \end{macro} @@ -4361,27 +5590,50 @@ % % \subsubsection{\hspace{3mm}Introduction} % -% We use a special prefix notation to denote each of four different repreresentations -% of the various Rubik cube rotations as follows: the name of the rotation (rr), its +% We use a special prefix notation to denote each of four different representations +% of the various Rubik cube rotations as follows: the name of the Rubik rotation (rr), its % associated hieroglyph (rrh), and combinations of name and hieroglyph both vertical (Rubik) % and horizontal (textRubik). A rotation command is a combination of a rotation-code appended % to one of the four prefixes. % -% For example, the command \cmd{\rrhD} generates the hieroglyph (rrh) associated with +% For~example, the command \cmd{\rrhD} generates the hieroglyph (rrh) associated with % the rotation-code D. In this form it is used internally, but it is also available for the user. -% However, it is also made available to the user in the more intuitive form -% |\rrh{D}| by the use of the internal macro |\@join| (see Sections~\ref{sec:cmdsusingjoin} -% and \ref{sec:usefulinternalcommands}). +% +% In version~3.0, however, all the rotation commands were also made available to the user +% in the much more intuitive form stem\{argument\} form, for~example, +% |\rrh{D}|. In practice, this `argument' form actually generates the original non-argument +% form by the use of the internal macro |\@join|. +% For example, \verb!\rrh{D}! $\rightarrow$ join(\verb!\rrh! + \verb!D!) $\rightarrow$ \verb!\rrhD! +% (see Sections~\ref{sec:cmdsusingjoin} for details). % -% The square hieroglyphs are built up in stages. We first create an internal -% command for drawing the square (\cmd{\DrawNotationBox}), and then draw the -% contents (lines, arrows, arcs of circles, and sometimes just text). -% (for the TikZ ARC command see TikZ pgfmanual (2012) page~146 (\S 14.8)). +% The hieroglyphs are of two types: `arrow' glyphs (all exactly square), +% and `letter' glyphs (mostly square, but many are rectangular); however both +% types are made to have the same height so they sit nicely when arranged side-by-side. +% A lot of special macros for handling and generating these glyphs are described below +% in Section~\ref{sec:usefulinternalcommands} (and also in Section~\ref{sec:codedrawnotationbox}). +% +% The `arrow' hieroglyphs are built up in stages using TikZ. We first create a +% command for drawing the square (\cmd{\DrawNotationBox}; +% see Section~\ref{sec:codedrawnotationbox}) and then draw the +% contents (lines, arrows, arcs of circles). For an example, +% see the D~form \rrh{D}\ constructed in Section~\ref{sec:coderotationD}. +% +% The `letter' hieroglyphs (glyphs for which the rotations cannot be seen from the front, +% and hence cannot have arrows) just give a letter representation of the rotation +% (say, Bw for `back wide'). These glyphs are therefore made using an fbox (for convenience), +% and therefore these are sometimes not square. Some vertical fine-tuning using +% the \verb!\raisebox! command is often required to force these `letter' glyphs to +% have the same vertical position as their `arrow' cousins. For an example, +% see the form \rrh{Bw}\ constructed Section~\ref{sec:coderotationBw}). % % The presence of small overfilled \cmd{\hbox}es associated with these squares % were originally checked using the \texttt{ltugboat.cls}, and all fixed mainly % by setting the associated minipages $\rightarrow$ width = 0.6cm, % and using TikZ scale=0.5. +% +% +% \subsubsection{\hspace{3mm}DrawNotationBox} +% \label{sec:codedrawnotationbox} % % % \begin{macro}{\DrawNotationBox} @@ -4389,7 +5641,7 @@ % Note that we start at (0,0) and draw to the final point % in order to make a nice corner join. % -% TODO: ? make this a proper internal command +% todo: ? make this a proper internal command % using \verb!@! sometime. % % \begin{macrocode} @@ -4403,10 +5655,11 @@ % (e.g.,~\cmd{\@sd}, \cmd{\@sh} \ldots\ etc.) which will be required % for use in drawing the various lines and arrows. % Some hieroglyphs contain either one circular arc, or two concentric arcs, -% and these arcs require both a center and a start point. +% and these arcs require both a centre and a start point. % Note that the final argument does not use any units. +% For the TikZ ARC command see TikZ pgfmanual (2012) page~146 (\S 14.8). % -% TODO: make a small diagram to illustrate the position of these +% todo: make a small diagram to illustrate the position of these % parameters and make things a bit clearer sometime. % %\begin{macrocode} @@ -4422,23 +5675,148 @@ \pgfmathsetmacro{\@sqcy}{\@scy+0.25} %% SQuare CenterY cpprd % \end{macrocode} % -% All the \verb!@! internal commands used in the following commands -% and macros are described in Section~\ref{sec:usefulinternalcommands}. % % % -% \subsubsection{\hspace{3mm}Using {\textbackslash}\texttt{join}} +% \subsubsection{\hspace{3mm}Some useful internal commands} +% \label{sec:usefulinternalcommands} +% +% \begin{macro}{\@rr} +% \begin{macro}{\@rrp} +% \begin{macro}{\@rrw} +% \begin{macro}{\@rrwp} +% \begin{macro}{\@rrs} +% \begin{macro}{\@rrsp} +% \begin{macro}{\@rra} +% \begin{macro}{\@rrap} +% \begin{macro}{\@xyzh} +% \begin{macro}{\@xyzhp} +% \begin{macro}{\@xyzRubik} +% \begin{macro}{\@xyzRubikp} +% \begin{macro}{\@SquareLetter} +% \begin{macro}{\@hRubik} +% These internal commands are used to generate the +% prime, w, w-prime, s, s-prime, a, a-prime +% rotation commands. The \cmd{\@xyz..} commands are used to generate the +% x, y, z, u, d, l, r, f, b commands and their associated prime rotation commands. +% The \cmd{\@SquareLetter} command is used to form the separate square hieroglyph form +% used for rotations with no visible representation from the front +% (e.g.,~B.., Fs, Fsp, Fa, Fap, S, Sp, Sf, Sfp, Sb, Sbp). +% The \cmd{\@hRubik} is the vertical shift used to raise the box carrying the rotation +% rotation-code in \cmd{\Rubik..} commands not visible from the front. +% +% The commands \verb!\@xyzhbdfl! and \verb!\@xyzbdflRubik! relate to the +% axis rotations denoted as b, d, f, l; since these four letters have long upstrokes +% they require special fine-tuning for vertical position. +% +% The idea is that by using these internal +% tools taking parameters we are able to more easily standardise the size +% and position of all the various glyphs. For details of the +% rubikfont and rubikprime see Section~\ref{sec:coderubikfont}). +% +% Note that the TikZ `thick' line code = 0.8pt (used in \cmd{\@SquareLetter}). +% +% \begin{macrocode} +\newcommand{\@rr}[1]{{\@rubikfont #1}} +\newcommand{\@rrp}[1]{{\@rubikfont #1\@rubikprime}} +\newcommand{\@rrw}[1]{{\@rubikfont #1{\@rubikfontFNS w}}} +\newcommand{\@rrwp}[1]{{\@rubikfont #1{\@rubikfontFNS w}\@rubikprime}} +\newcommand{\@rrs}[1]{{\@rubikfont #1{\@rubikfontFNS s}}} +\newcommand{\@rrsp}[1]{{\@rubikfont #1{\@rubikfontFNS s}\@rubikprime}} +\newcommand{\@rra}[1]{{\@rubikfont #1{\@rubikfontFNS a}}} +\newcommand{\@rrap}[1]{{\@rubikfont #1{\@rubikfontFNS a}\@rubikprime}} +\newcommand{\@rru}[1]{{\@rubikfont #1{\@rubikfontFNS u}}} +\newcommand{\@rrup}[1]{{\@rubikfont #1{\@rubikfontFNS u}\@rubikprime}} +\newcommand{\@rrd}[1]{{\@rubikfont #1{\@rubikfontFNS d}}} +\newcommand{\@rrdp}[1]{{\@rubikfont #1{\@rubikfontFNS d}\@rubikprime}} +\newcommand{\@rrl}[1]{{\@rubikfont #1{\@rubikfontFNS l}}} +\newcommand{\@rrlp}[1]{{\@rubikfont #1{\@rubikfontFNS l}\@rubikprime}} +\newcommand{\@rrr}[1]{{\@rubikfont #1{\@rubikfontFNS r}}} +\newcommand{\@rrrp}[1]{{\@rubikfont #1{\@rubikfontFNS r}\@rubikprime}} +\newcommand{\@rrf}[1]{{\@rubikfont #1{\@rubikfontFNS f}}} +\newcommand{\@rrfp}[1]{{\@rubikfont #1{\@rubikfontFNS f}\@rubikprime}} +\newcommand{\@rrb}[1]{{\@rubikfont #1{\@rubikfontFNS b}}} +\newcommand{\@rrbp}[1]{{\@rubikfont #1{\@rubikfontFNS b}\@rubikprime}} +\newcommand{\@rrc}[1]{{\@rubikfont #1{\@rubikfontFNS c}}} +\newcommand{\@rrcp}[1]{{\@rubikfont #1{\@rubikfontFNS c}\@rubikprime}} +\newcommand{\@rrm}[1]{{\@rubikfont #1{\@rubikfontFNS m}}} +\newcommand{\@rrmp}[1]{{\@rubikfont #1{\@rubikfontFNS m}\@rubikprime}} +\newcommand{\@xyzh}[1]{[{\@rubikfont #1}]} +\newcommand{\@xyzhp}[1]{[{\@rubikfont #1\@rubikprime}]} +\newcommand{\@xyzRubik}[1]{\raisebox{3.45pt}{[{\@rubikfont #1}]}} +\newcommand{\@xyzRubikp}[1]{\raisebox{3.45pt}{[{\@rubikfont #1\@rubikprime}]}} +\newcommand{\@xyzhbdfl}[1]{[\raisebox{-0.6pt}{{\@rubikfont #1}}]} +\newcommand{\@xyzbdflRubik}[1]{\raisebox{3.45pt}{[\raisebox{-0.6pt}{{\@rubikfont #1}}]}} +\newcommand{\@SquareLetter}[1]{\setlength{\fboxsep}{2.5pt}% + \setlength{\fboxrule}{0.8pt}% + \fbox{\rule[-1pt]{0pt}{8.5pt}\raisebox{-0.5pt}{#1}}} +\newlength\@hRubik% +\setlength{\@hRubik}{0.185cm}% +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \begin{macro}{\@tlen} +% Feb 2017 (RWDN): \ We also need to define a small length for fine-tuning the default +% horizontal space between a pair of `letter' hieroglyphs, eg~B (i.e.,~when no +% additional space has been added by the user), so that this matches that between a pair of +% `arrow' hieroglyphs. This length is inserted on both sides of the square frame. +% This length is used in two settings: (a)~in `letter' hieroglyphs (for an example, +% see the definition of the macro \cmd{\SquareB} in Section~\ref{sec:coderotationB}), +% and in (b)~in `arrow' hieroglyphs (for an example, +% see the definition of the macro \cmd{\rrhD} in Section~\ref{sec:coderotationD}). +% +%\begin{macrocode} +\newcommand{\@tlen}{\hspace{1pt}}% +% \end{macrocode} +% \end{macro} +% +% +% +% \begin{macro}{\@join} +% We also require a macro for joining two strings so we can convert +% a rotation-code, say U, into a macro which typesets it in some form, say \cmd{\rrhU}. +% The following \cmd{\@join\{\}\{\}} command is by Christian Tellechea (many thanks\,!). +% {\newline}\textsc{usage}: \cmd{\@join\marg{command-stem}\marg{rotation-code}}. For~example, +% to create the command \cmd{\rrhU} we would write |\@join{\rrh}{U}|, and hence +% the command |\rrh{U}| is equivalent to \cmd{\rrhU} (see Section~\ref{sec:cmdsusingjoin}). +% {\newline}Since this macro is also useful for processing rotation-codes in a list, +% which may also include macros, it is important that |#2| is not detokenized. +% \begin{macrocode} +\newcommand*\@join[2]{% + \csname\expandafter\@gobble\string#1#2\endcsname} +% \end{macrocode} +% \end{macro} +% +% +% +% +% \subsubsection{\hspace{3mm}Using {\textbackslash}\texttt{@join}} % \label{sec:cmdsusingjoin} % % \begin{macro}{\textRubik} % \begin{macro}{\Rubik} % \begin{macro}{\rr} % \begin{macro}{\rrh} -% The following four commands typeset a single rotation, where the rotation-code (eg~U) is +% The following four commands typeset a single rotation, where the rotation-code (e.g.,~U) is % the argument (see Section~\ref{sec:overview}). As an example, the format for % the \cmd{\rrh\{\}} command is % \cmd{\rrh}\marg{rotation-code}. In practice, these four commands are really a -% sort of front-end for all the commands which follow this section. For example, the +% sort of front-end for all the commands which follow this section. For~example, the % command \cmd{\rrh\{U\}} generates the command \cmd{\rrhU} which itself typesets the % rotation hieroglyph for the rotation~U, etc. % @@ -4461,6 +5839,7 @@ % % % \subsubsection{\hspace{3mm}Rotation B} +% \label{sec:coderotationB} % % \begin{macro}{\rrB} % \begin{macro}{\SquareB} @@ -4469,12 +5848,20 @@ % \begin{macro}{\textRubikB} % These commands all draw forms which denote the B (\textsc{back}-face) rotation. % Not visible from the front. +% +% Feb 2017 (RWDN): added the \cmd{\@tlen} length (= 1pt; defined above) to the +% \cmd{\SquareB} command, and removed the terminal \cmd{\,} space +% from the rrhB, RubikB, textRubikB commands, and copied +% this action with all the subsequent Letter hieroglyphs (e.g.,~B, Bw,..). +% These minor changes were to improve the spacing between two Letter hieroglyphs, +% and make it match that between two square `arrow' hieroglyphs. +% The same changes were made to all the `letter' hieroglyphs. % \begin{macrocode} \newcommand{\rrB}{\@rr{B}} -\newcommand{\SquareB}{\@SquareLetter{\rrB}} -\newcommand{\rrhB}{\raisebox{-0.25mm}{\SquareB}\,} -\newcommand{\RubikB}{\raisebox{\@hRubik}{\SquareB}\,} -\newcommand{\textRubikB}{\rrhB\,} +\newcommand{\SquareB}{\@tlen\@SquareLetter{\rrB}\@tlen} +\newcommand{\rrhB}{\raisebox{-0.25mm}{\SquareB}} +\newcommand{\RubikB}{\raisebox{\@hRubik}{\SquareB}} +\newcommand{\textRubikB}{\rrhB} % \end{macrocode} % \end{macro} % \end{macro} @@ -4494,10 +5881,10 @@ % Not visible from the front. % \begin{macrocode} \newcommand{\rrBp}{\@rrp{B}} -\newcommand{\SquareBp}{\@SquareLetter{\rrBp}} -\newcommand{\rrhBp}{\raisebox{-0.25mm}{\SquareBp}\,} -\newcommand{\RubikBp}{\raisebox{\@hRubik}{\SquareBp}\,} -\newcommand{\textRubikBp}{\rrhBp\,} +\newcommand{\SquareBp}{\@tlen\@SquareLetter{\rrBp}\@tlen} +\newcommand{\rrhBp}{\raisebox{-0.25mm}{\SquareBp}} +\newcommand{\RubikBp}{\raisebox{\@hRubik}{\SquareBp}} +\newcommand{\textRubikBp}{\rrhBp} % \end{macrocode} % \end{macro} % \end{macro} @@ -4507,6 +5894,7 @@ % % % \subsubsection{\hspace{3mm}Rotation Bw} +% \label{sec:coderotationBw} % % \begin{macro}{\rrBw} % \begin{macro}{\SquareBw} @@ -4516,12 +5904,11 @@ % These commands all draw forms which denote the Bw rotation. % Not visible from the front. % \begin{macrocode} -%\newcommand{\rrBw}{\textbf{\textsf{Bw}}} \newcommand{\rrBw}{\@rrw{B}} -\newcommand{\SquareBw}{\@SquareLetter{\rrBw}} -\newcommand{\rrhBw}{\raisebox{-0.25mm}{\SquareBw}\,} -\newcommand{\RubikBw}{\raisebox{\@hRubik}{\SquareBw}\,} -\newcommand{\textRubikBw}{\rrhBw\,} +\newcommand{\SquareBw}{\@tlen\@SquareLetter{\rrBw}\@tlen} +\newcommand{\rrhBw}{\raisebox{-0.25mm}{\SquareBw}} +\newcommand{\RubikBw}{\raisebox{\@hRubik}{\SquareBw}} +\newcommand{\textRubikBw}{\rrhBw} % \end{macrocode} % \end{macro} % \end{macro} @@ -4540,12 +5927,11 @@ % These commands all draw forms which denote the Bwp rotation. % Not visible from the front. % \begin{macrocode} -%\newcommand{\rrBwp}{\textbf{\textsf{Bwp}}} \newcommand{\rrBwp}{\@rrwp{B}} -\newcommand{\SquareBwp}{\@SquareLetter{\rrBwp}} -\newcommand{\rrhBwp}{\raisebox{-0.25mm}{\SquareBwp}\,} -\newcommand{\RubikBwp}{\raisebox{\@hRubik}{\SquareBwp}\,} -\newcommand{\textRubikBwp}{\rrhBwp\,} +\newcommand{\SquareBwp}{\@tlen\@SquareLetter{\rrBwp}\@tlen} +\newcommand{\rrhBwp}{\raisebox{-0.25mm}{\SquareBwp}} +\newcommand{\RubikBwp}{\raisebox{\@hRubik}{\SquareBwp}} +\newcommand{\textRubikBwp}{\rrhBwp} % \end{macrocode} % \end{macro} % \end{macro} @@ -4564,12 +5950,11 @@ % These commands all draw forms which denote the Bs rotation. % Not visible from the front. % \begin{macrocode} -%\newcommand{\rrBs}{\textbf{\textsf{Bs}}} \newcommand{\rrBs}{\@rrs{B}} -\newcommand{\SquareBs}{\@SquareLetter{\rrBs}} -\newcommand{\rrhBs}{\raisebox{-0.25mm}{\SquareBs}\,} -\newcommand{\RubikBs}{\raisebox{\@hRubik}{\SquareBs}\,} -\newcommand{\textRubikBs}{\rrhBs\,} +\newcommand{\SquareBs}{\@tlen\@SquareLetter{\rrBs}\@tlen} +\newcommand{\rrhBs}{\raisebox{-0.25mm}{\SquareBs}} +\newcommand{\RubikBs}{\raisebox{\@hRubik}{\SquareBs}} +\newcommand{\textRubikBs}{\rrhBs} % \end{macrocode} % \end{macro} % \end{macro} @@ -4588,12 +5973,11 @@ % These commands all draw forms which denote the Bsp rotation. % Not visible from the front. % \begin{macrocode} -%\newcommand{\rrBsp}{\textbf{\textsf{Bsp}}} \newcommand{\rrBsp}{\@rrsp{B}} -\newcommand{\SquareBsp}{\@SquareLetter{\rrBsp}} -\newcommand{\rrhBsp}{\raisebox{-0.25mm}{\SquareBsp}\,} -\newcommand{\RubikBsp}{\raisebox{\@hRubik}{\SquareBsp}\,} -\newcommand{\textRubikBsp}{\rrhBsp\,} +\newcommand{\SquareBsp}{\@tlen\@SquareLetter{\rrBsp}\@tlen} +\newcommand{\rrhBsp}{\raisebox{-0.25mm}{\SquareBsp}} +\newcommand{\RubikBsp}{\raisebox{\@hRubik}{\SquareBsp}} +\newcommand{\textRubikBsp}{\rrhBsp} % \end{macrocode} % \end{macro} % \end{macro} @@ -4612,12 +5996,11 @@ % These commands all draw forms which denote the Ba rotation. % Not visible from the front. % \begin{macrocode} -%\newcommand{\rrBa}{\textbf{\textsf{Ba}}} \newcommand{\rrBa}{\@rra{B}} -\newcommand{\SquareBa}{\@SquareLetter{\rrBa}} -\newcommand{\rrhBa}{\raisebox{-0.25mm}{\SquareBa}\,} -\newcommand{\RubikBa}{\raisebox{\@hRubik}{\SquareBa}\,} -\newcommand{\textRubikBa}{\rrhBa\,} +\newcommand{\SquareBa}{\@tlen\@SquareLetter{\rrBa}\@tlen} +\newcommand{\rrhBa}{\raisebox{-0.25mm}{\SquareBa}} +\newcommand{\RubikBa}{\raisebox{\@hRubik}{\SquareBa}} +\newcommand{\textRubikBa}{\rrhBa} % \end{macrocode} % \end{macro} % \end{macro} @@ -4636,12 +6019,11 @@ % These commands all draw forms which denote the Bap rotation. % Not visible from the front. % \begin{macrocode} -%\newcommand{\rrBap}{\textbf{\textsf{Bap}}} \newcommand{\rrBap}{\@rrap{B}} -\newcommand{\SquareBap}{\@SquareLetter{\rrBap}} -\newcommand{\rrhBap}{\raisebox{-0.25mm}{\SquareBap}\,} -\newcommand{\RubikBap}{\raisebox{\@hRubik}{\SquareBap}\,} -\newcommand{\textRubikBap}{\rrhBap\,} +\newcommand{\SquareBap}{\@tlen\@SquareLetter{\rrBap}\@tlen} +\newcommand{\rrhBap}{\raisebox{-0.25mm}{\SquareBap}} +\newcommand{\RubikBap}{\raisebox{\@hRubik}{\SquareBap}} +\newcommand{\textRubikBap}{\rrhBap} % \end{macrocode} % \end{macro} % \end{macro} @@ -4651,6 +6033,7 @@ % % % \subsubsection{\hspace{3mm}Rotation D} +% \label{sec:coderotationD} % % \begin{macro}{\rrD} % \begin{macro}{\SquareD} @@ -4658,8 +6041,12 @@ % \begin{macro}{\RubikD} % \begin{macro}{\textRubikD} % These commands all draw forms which denote the D rotation. +% +% Feb 2017 (RWDN): \ added the \cmd{\@tlen} length to the \cmd{\rrhD} command to improve the +% spacing between two `arrow' square hieroglyphs; and also removed the terminal \cmd{\,} +% space. The same changes were made to all the `arrow' hieroglyphs. % \begin{macrocode} -\newcommand{\rrD}{\textbf{\textsf{D}}} +\newcommand{\rrD}{\@rr{D}} %% \newcommand{\SquareD}{% \begin{tikzpicture}[scale=0.5] @@ -4669,15 +6056,16 @@ \draw [thick, ->] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhD}{\raisebox{-0.333\height}{\SquareD}\,} +\newcommand{\rrhD}{\raisebox{-0.333\height}{\@tlen\SquareD\@tlen}} %% \newcommand{\RubikD}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareD\\ -\rrD +\rrD% \end{minipage}% -} +}} \newcommand{\textRubikD}{\rrD\,\rrhD} % \end{macrocode} % \end{macro} @@ -4696,7 +6084,7 @@ % \begin{macro}{\textRubikDp} % These commands all draw forms which denote the Dp rotation. % \begin{macrocode} -\newcommand{\rrDp}{\textbf{\textsf{D}$^\prime$}} +\newcommand{\rrDp}{\@rrp{D}} %% \newcommand{\SquareDp}{% \begin{tikzpicture}[scale=0.5] @@ -4706,15 +6094,16 @@ \draw [thick, <-] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhDp}{\raisebox{-0.333\height}{\SquareDp}\,} +\newcommand{\rrhDp}{\raisebox{-0.333\height}{\@tlen\SquareDp\@tlen}} %% \newcommand{\RubikDp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareDp\\ -\rrDp +\rrDp% \end{minipage}% -} +}} \newcommand{\textRubikDp}{\rrDp\,\rrhDp} % \end{macrocode} % \end{macro} @@ -4733,7 +6122,7 @@ % \begin{macro}{\textRubikDw} % These commands all draw forms which denote the Dw rotation. % \begin{macrocode} -\newcommand{\rrDw}{\textbf{\textsf{D\footnotesize{w}}}} +\newcommand{\rrDw}{\@rrw{D}} %% \newcommand{\SquareDw}{% \begin{tikzpicture}[scale=0.5] @@ -4743,15 +6132,16 @@ \draw [thick, ->] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhDw}{\raisebox{-0.333\height}{\SquareDw}\,} +\newcommand{\rrhDw}{\raisebox{-0.333\height}{\@tlen\SquareDw\@tlen}} %% \newcommand{\RubikDw}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareDw\\ -\rrDw +\rrDw% \end{minipage}% -} +}} \newcommand{\textRubikDw}{\rrDw\,\rrhDw} % \end{macrocode} % \end{macro} @@ -4770,7 +6160,7 @@ % \begin{macro}{\textRubikDwp} % These commands all draw forms which denote the Dwp rotation. % \begin{macrocode} -\newcommand{\rrDwp}{\textbf{\textsf{D\footnotesize{w}}$^\prime$}} +\newcommand{\rrDwp}{\@rrwp{D}} %% \newcommand{\SquareDwp}{% \begin{tikzpicture}[scale=0.5] @@ -4780,15 +6170,16 @@ \draw [thick, <-] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhDwp}{\raisebox{-0.333\height}{\SquareDwp}\,} +\newcommand{\rrhDwp}{\raisebox{-0.333\height}{\@tlen\SquareDwp\@tlen}} %% \newcommand{\RubikDwp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareDwp\\ -\rrDwp +\rrDwp% \end{minipage}% -} +}} \newcommand{\textRubikDwp}{\rrDwp\,\rrhDwp} % \end{macrocode} % \end{macro} @@ -4817,15 +6208,16 @@ \draw [thick, ->] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhDs}{\raisebox{-0.333\height}{\SquareDs}\,} +\newcommand{\rrhDs}{\raisebox{-0.333\height}{\@tlen\SquareDs\@tlen}} %% \newcommand{\RubikDs}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareDs\\ -\rrDs +\rrDs% \end{minipage}% -} +}} \newcommand{\textRubikDs}{\rrDs\,\rrhDs} % \end{macrocode} % \end{macro} @@ -4854,15 +6246,16 @@ \draw [thick, <-] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhDsp}{\raisebox{-0.333\height}{\SquareDsp}\,} +\newcommand{\rrhDsp}{\raisebox{-0.333\height}{\@tlen\SquareDsp\@tlen}} %% \newcommand{\RubikDsp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareDsp\\ -\rrDsp +\rrDsp% \end{minipage}% -} +}} \newcommand{\textRubikDsp}{\rrDsp\,\rrhDsp} % \end{macrocode} % \end{macro} @@ -4891,15 +6284,16 @@ \draw [thick, ->] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhDa}{\raisebox{-0.333\height}{\SquareDa}\,} +\newcommand{\rrhDa}{\raisebox{-0.333\height}{\@tlen\SquareDa\@tlen}} %% \newcommand{\RubikDa}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareDa\\ -\rrDa +\rrDa% \end{minipage}% -} +}} \newcommand{\textRubikDa}{\rrDa\,\rrhDa} % \end{macrocode} % \end{macro} @@ -4928,15 +6322,16 @@ \draw [thick, <-] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhDap}{\raisebox{-0.333\height}{\SquareDap}\,} +\newcommand{\rrhDap}{\raisebox{-0.333\height}{\@tlen\SquareDap\@tlen}} %% \newcommand{\RubikDap}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareDap\\ -\rrDap +\rrDap% \end{minipage}% -} +}} \newcommand{\textRubikDap}{\rrDap\,\rrhDap} % \end{macrocode} % \end{macro} @@ -4955,7 +6350,7 @@ % \begin{macro}{\textRubikE} % These commands all draw forms which denote the E rotation. % \begin{macrocode} -\newcommand{\rrE}{\textbf{\textsf{E}}} +\newcommand{\rrE}{\@rr{E}} %% \newcommand{\SquareE}{% \begin{tikzpicture}[scale=0.5] @@ -4965,15 +6360,16 @@ \draw [thick] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhE}{\raisebox{-0.333\height}{\SquareE}\,} +\newcommand{\rrhE}{\raisebox{-0.333\height}{\@tlen\SquareE\@tlen}} %% \newcommand{\RubikE}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareE\\ -\rrE +\rrE% \end{minipage}% -} +}} \newcommand{\textRubikE}{\rrE\,\rrhE} % \end{macrocode} % \end{macro} @@ -4992,7 +6388,7 @@ % \begin{macro}{\textRubikEp} % These commands all draw forms which denote the Ep rotation. % \begin{macrocode} -\newcommand{\rrEp}{\textbf{\textsf{E}$^\prime$}} +\newcommand{\rrEp}{\@rrp{E}} %% \newcommand{\SquareEp}{% \begin{tikzpicture}[scale=0.5] @@ -5002,15 +6398,16 @@ \draw [thick] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhEp}{\raisebox{-0.333\height}{\SquareEp}\,} +\newcommand{\rrhEp}{\raisebox{-0.333\height}{\@tlen\SquareEp\@tlen}} %% \newcommand{\RubikEp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareEp\\ -\rrEp +\rrEp% \end{minipage}% -} +}} \newcommand{\textRubikEp}{\rrEp\,\rrhEp} % \end{macrocode} % \end{macro} @@ -5029,7 +6426,7 @@ % \begin{macro}{\textRubikF} % These commands all draw forms which denote the F rotation. % \begin{macrocode} -\newcommand{\rrF}{\textbf{\textsf{F}}} +\newcommand{\rrF}{\@rr{F}} %% \newcommand{\SquareF}{% \begin{tikzpicture}[scale=0.5] @@ -5037,15 +6434,16 @@ \draw [thick, <-] (\@scx, \@scy) arc[radius=0.35, start angle=-60, delta angle=290]; \end{tikzpicture}% } -\newcommand{\rrhF}{\raisebox{-0.333\height}{\SquareF}\,} +\newcommand{\rrhF}{\raisebox{-0.333\height}{\@tlen\SquareF\@tlen}} %% \newcommand{\RubikF}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareF\\ -\rrF +\rrF% \end{minipage}% -} +}} \newcommand{\textRubikF}{\rrF\,\rrhF} % \end{macrocode} % \end{macro} @@ -5064,7 +6462,7 @@ % \begin{macro}{\textRubikFp} % These commands all draw forms which denote the Fp rotation. % \begin{macrocode} -\newcommand{\rrFp}{\textbf{\textsf{F}$^\prime$}} +\newcommand{\rrFp}{\@rrp{F}} %% \newcommand{\SquareFp}{% \begin{tikzpicture}[scale=0.5] @@ -5072,15 +6470,16 @@ \draw [thick, ->] (\@scx, \@scy) arc[radius=0.35, start angle=-60, delta angle=290]; \end{tikzpicture}% } -\newcommand{\rrhFp}{\raisebox{-0.333\height}{\SquareFp}\,} +\newcommand{\rrhFp}{\raisebox{-0.333\height}{\@tlen\SquareFp\@tlen}} %% \newcommand{\RubikFp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareFp\\ -\rrFp +\rrFp% \end{minipage}% -} +}} \newcommand{\textRubikFp}{\rrFp\,\rrhFp} % \end{macrocode} % \end{macro} @@ -5099,7 +6498,7 @@ % \begin{macro}{\textRubikFw} % These commands all draw forms which denote the Fw rotation. % \begin{macrocode} -\newcommand{\rrFw}{\textbf{\textsf{F\footnotesize{w}}}} +\newcommand{\rrFw}{\@rrw{F}} %% \newcommand{\SquareFw}{% \begin{tikzpicture}[scale=0.5] @@ -5109,15 +6508,16 @@ %\node (squareLab) at (0.5,0.5) {$o$}; \end{tikzpicture}% } -\newcommand{\rrhFw}{\raisebox{-0.333\height}{\SquareFw}\,} +\newcommand{\rrhFw}{\raisebox{-0.333\height}{\@tlen\SquareFw\@tlen}} %% \newcommand{\RubikFw}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareFw\\ -\rrFw +\rrFw% \end{minipage}% -} +}} \newcommand{\textRubikFw}{\rrFw\,\rrhFw} % \end{macrocode} % \end{macro} @@ -5136,7 +6536,7 @@ % \begin{macro}{\textRubikFwp} % These commands all draw forms which denote the Fwp rotation. % \begin{macrocode} -\newcommand{\rrFwp}{\textbf{\textsf{F\footnotesize{w}}$^\prime$}} +\newcommand{\rrFwp}{\@rrwp{F}} %% \newcommand{\SquareFwp}{% \begin{tikzpicture}[scale=0.5] @@ -5145,15 +6545,16 @@ \draw [thick] (\@sqcx,\@sqcy) arc[radius=0.1, start angle=-60, delta angle=360]; \end{tikzpicture}% } -\newcommand{\rrhFwp}{\raisebox{-0.333\height}{\SquareFwp}\,} +\newcommand{\rrhFwp}{\raisebox{-0.333\height}{\@tlen\SquareFwp\@tlen}} %% \newcommand{\RubikFwp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareFwp\\ -\rrFwp +\rrFwp% \end{minipage}% -} +}} \newcommand{\textRubikFwp}{\rrFwp\,\rrhFwp} %% % \end{macrocode} @@ -5179,10 +6580,10 @@ % Not visible from the front. % \begin{macrocode} \newcommand{\rrFs}{\@rrs{F}} -\newcommand{\SquareFs}{\@SquareLetter{\rrFs}} -\newcommand{\rrhFs}{\raisebox{-0.25mm}{\SquareFs}\,} -\newcommand{\RubikFs}{\raisebox{\@hRubik}{\SquareFs}\,} -\newcommand{\textRubikFs}{\rrhFs\,} +\newcommand{\SquareFs}{\@tlen\@SquareLetter{\rrFs}\@tlen} +\newcommand{\rrhFs}{\raisebox{-0.25mm}{\SquareFs}} +\newcommand{\RubikFs}{\raisebox{\@hRubik}{\SquareFs}} +\newcommand{\textRubikFs}{\rrhFs} % \end{macrocode} % \end{macro} % \end{macro} @@ -5205,10 +6606,10 @@ % Not visible from the front. % \begin{macrocode} \newcommand{\rrFsp}{\@rrsp{F}} -\newcommand{\SquareFsp}{\@SquareLetter{\rrFsp}} -\newcommand{\rrhFsp}{\raisebox{-0.25mm}{\SquareFsp}\,} -\newcommand{\RubikFsp}{\raisebox{\@hRubik}{\SquareFsp}\,} -\newcommand{\textRubikFsp}{\rrhFsp\,} +\newcommand{\SquareFsp}{\@tlen\@SquareLetter{\rrFsp}\@tlen} +\newcommand{\rrhFsp}{\raisebox{-0.25mm}{\SquareFsp}} +\newcommand{\RubikFsp}{\raisebox{\@hRubik}{\SquareFsp}} +\newcommand{\textRubikFsp}{\rrhFsp} % \end{macrocode} % \end{macro} % \end{macro} @@ -5231,10 +6632,10 @@ % Not visible from the front. % \begin{macrocode} \newcommand{\rrFa}{\@rra{F}} -\newcommand{\SquareFa}{\@SquareLetter{\rrFa}} -\newcommand{\rrhFa}{\raisebox{-0.25mm}{\SquareFa}\,} -\newcommand{\RubikFa}{\raisebox{\@hRubik}{\SquareFa}\,} -\newcommand{\textRubikFa}{\rrhFa\,} +\newcommand{\SquareFa}{\@tlen\@SquareLetter{\rrFa}\@tlen} +\newcommand{\rrhFa}{\raisebox{-0.25mm}{\SquareFa}} +\newcommand{\RubikFa}{\raisebox{\@hRubik}{\SquareFa}} +\newcommand{\textRubikFa}{\rrhFa} % \end{macrocode} % \end{macro} % \end{macro} @@ -5257,10 +6658,10 @@ % Not visible from the front. % \begin{macrocode} \newcommand{\rrFap}{\@rrap{F}} -\newcommand{\SquareFap}{\@SquareLetter{\rrFap}} -\newcommand{\rrhFap}{\raisebox{-0.25mm}{\SquareFap}\,} -\newcommand{\RubikFap}{\raisebox{\@hRubik}{\SquareFap}\,} -\newcommand{\textRubikFap}{\rrhFap\,} +\newcommand{\SquareFap}{\@tlen\@SquareLetter{\rrFap}\@tlen} +\newcommand{\rrhFap}{\raisebox{-0.25mm}{\SquareFap}} +\newcommand{\RubikFap}{\raisebox{\@hRubik}{\SquareFap}} +\newcommand{\textRubikFap}{\rrhFap} % \end{macrocode} % \end{macro} % \end{macro} @@ -5277,7 +6678,7 @@ % \begin{macro}{\textRubikL} % These commands all draw forms which denote the L rotation. % \begin{macrocode} -\newcommand{\rrL}{\textbf{\textsf{L}}} +\newcommand{\rrL}{\@rr{L}} %% \newcommand{\SquareL}{% \begin{tikzpicture}[scale=0.5] @@ -5287,15 +6688,16 @@ \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhL}{\raisebox{-0.333\height}{\SquareL}\,} +\newcommand{\rrhL}{\raisebox{-0.333\height}{\@tlen\SquareL\@tlen}} %% \newcommand{\RubikL}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareL\\ -\rrL +\rrL% \end{minipage}% -} +}} \newcommand{\textRubikL}{\rrL\,\rrhL} % \end{macrocode} % \end{macro} @@ -5314,7 +6716,7 @@ % \begin{macro}{\textRubikLp} % These commands all draw forms which denote the Lp rotation. % \begin{macrocode} -\newcommand{\rrLp}{\textbf{\textsf{L}$^\prime$}} +\newcommand{\rrLp}{\@rrp{L}} %% \newcommand{\SquareLp}{% \begin{tikzpicture}[scale=0.5] @@ -5324,15 +6726,16 @@ \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhLp}{\raisebox{-0.333\height}{\SquareLp}\,} +\newcommand{\rrhLp}{\raisebox{-0.333\height}{\@tlen\SquareLp\@tlen}} %% \newcommand{\RubikLp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareLp\\ -\rrLp +\rrLp% \end{minipage}% -} +}} \newcommand{\textRubikLp}{\rrLp\,\rrhLp} % \end{macrocode} % \end{macro} @@ -5351,7 +6754,7 @@ % \begin{macro}{\textRubikLw} % These commands all draw forms which denote the Lw rotation. % \begin{macrocode} -\newcommand{\rrLw}{\textbf{\textsf{L\footnotesize{w}}}} +\newcommand{\rrLw}{\@rrw{L}} %% \newcommand{\SquareLw}{% \begin{tikzpicture}[scale=0.5] @@ -5361,15 +6764,16 @@ \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhLw}{\raisebox{-0.333\height}{\SquareLw}\,} +\newcommand{\rrhLw}{\raisebox{-0.333\height}{\@tlen\SquareLw\@tlen}} %% \newcommand{\RubikLw}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareLw\\ -\rrLw +\rrLw% \end{minipage}% -} +}} \newcommand{\textRubikLw}{\rrLw\,\rrhLw} % \end{macrocode} % \end{macro} @@ -5388,7 +6792,7 @@ % \begin{macro}{\textRubikLwp} % These commands all draw forms which denote the Lwp rotation. % \begin{macrocode} -\newcommand{\rrLwp}{\textbf{\textsf{L\footnotesize{w}}$^\prime$}} +\newcommand{\rrLwp}{\@rrwp{L}} %% \newcommand{\SquareLwp}{% \begin{tikzpicture}[scale=0.5] @@ -5398,15 +6802,16 @@ \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhLwp}{\raisebox{-0.333\height}{\SquareLwp}\,} +\newcommand{\rrhLwp}{\raisebox{-0.333\height}{\@tlen\SquareLwp\@tlen}} %% \newcommand{\RubikLwp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareLwp\\ -\rrLwp +\rrLwp% \end{minipage}% -} +}} \newcommand{\textRubikLwp}{\rrLwp\,\rrhLwp} % \end{macrocode} % \end{macro} @@ -5435,15 +6840,16 @@ \draw [thick, <-] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhLs}{\raisebox{-0.333\height}{\SquareLs}\,} +\newcommand{\rrhLs}{\raisebox{-0.333\height}{\@tlen\SquareLs\@tlen}} %% \newcommand{\RubikLs}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareLs\\ -\rrLs +\rrLs% \end{minipage}% -} +}} \newcommand{\textRubikLs}{\rrLs\,\rrhLs} % \end{macrocode} % \end{macro} @@ -5472,15 +6878,16 @@ \draw [thick, ->] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhLsp}{\raisebox{-0.333\height}{\SquareLsp}\,} +\newcommand{\rrhLsp}{\raisebox{-0.333\height}{\@tlen\SquareLsp\@tlen}} %% \newcommand{\RubikLsp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareLsp\\ -\rrLsp +\rrLsp% \end{minipage}% -} +}} \newcommand{\textRubikLsp}{\rrLsp\,\rrhLsp} % \end{macrocode} % \end{macro} @@ -5509,15 +6916,16 @@ \draw [thick, ->] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhLa}{\raisebox{-0.333\height}{\SquareLa}\,} +\newcommand{\rrhLa}{\raisebox{-0.333\height}{\@tlen\SquareLa\@tlen}} %% \newcommand{\RubikLa}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareLa\\ -\rrLa +\rrLa% \end{minipage}% -} +}} \newcommand{\textRubikLa}{\rrLa\,\rrhLa} % \end{macrocode} % \end{macro} @@ -5546,15 +6954,16 @@ \draw [thick, <-] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhLap}{\raisebox{-0.333\height}{\SquareLap}\,} +\newcommand{\rrhLap}{\raisebox{-0.333\height}{\@tlen\SquareLap\@tlen}} %% \newcommand{\RubikLap}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareLap\\ -\rrLap +\rrLap% \end{minipage}% -} +}} \newcommand{\textRubikLap}{\rrLap\,\rrhLap} % \end{macrocode} % \end{macro} @@ -5573,7 +6982,7 @@ % \begin{macro}{\textRubikM} % These commands all draw forms which denote the M rotation. % \begin{macrocode} -\newcommand{\rrM}{\textbf{\textsf{M}}} +\newcommand{\rrM}{\@rr{M}} %% \newcommand{\SquareM}{% \begin{tikzpicture}[scale=0.5] @@ -5583,15 +6992,16 @@ \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhM}{\raisebox{-0.333\height}{\SquareM}\,} +\newcommand{\rrhM}{\raisebox{-0.333\height}{\@tlen\SquareM\@tlen}} %% \newcommand{\RubikM}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareM\\ -\rrM +\rrM% \end{minipage}% -} +}} \newcommand{\textRubikM}{\rrM\,\rrhM} % \end{macrocode} % \end{macro} @@ -5610,7 +7020,7 @@ % \begin{macro}{\textRubikMp} % These commands all draw forms which denote the Mp rotation. % \begin{macrocode} -\newcommand{\rrMp}{\textbf{\textsf{M}$^\prime$}} +\newcommand{\rrMp}{\@rrp{M}} %% \newcommand{\SquareMp}{% \begin{tikzpicture}[scale=0.5] @@ -5620,15 +7030,16 @@ \draw [thick] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhMp}{\raisebox{-0.333\height}{\SquareMp}\,} +\newcommand{\rrhMp}{\raisebox{-0.333\height}{\@tlen\SquareMp\@tlen}} %% \newcommand{\RubikMp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareMp\\ -\rrMp +\rrMp% \end{minipage}% -} +}} \newcommand{\textRubikMp}{\rrMp\,\rrhMp} % \end{macrocode} % \end{macro} @@ -5647,7 +7058,7 @@ % \begin{macro}{\textRubikR} % These commands all draw forms which denote the R rotation. % \begin{macrocode} -\newcommand{\rrR}{\textbf{\textsf{R}}} +\newcommand{\rrR}{\@rr{R}} %% \newcommand{\SquareR}{% \begin{tikzpicture}[scale=0.5] @@ -5658,15 +7069,16 @@ \draw [thick, ->] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhR}{\raisebox{-0.333\height}{\SquareR}\,} +\newcommand{\rrhR}{\raisebox{-0.333\height}{\@tlen\SquareR\@tlen}} %% \newcommand{\RubikR}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareR\\ -\rrR +\rrR% \end{minipage}% -} +}} \newcommand{\textRubikR}{\rrR\,\rrhR} % \end{macrocode} % \end{macro} @@ -5685,7 +7097,7 @@ % \begin{macro}{\textRubikRp} % These commands all draw forms which denote the Rp rotation. % \begin{macrocode} -\newcommand{\rrRp}{\textbf{\textsf{R}$^\prime$}} +\newcommand{\rrRp}{\@rrp{R}} %% \newcommand{\SquareRp}{% \begin{tikzpicture}[scale=0.5] @@ -5695,15 +7107,16 @@ \draw [thick, <-] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhRp}{\raisebox{-0.333\height}{\SquareRp}\,} +\newcommand{\rrhRp}{\raisebox{-0.333\height}{\@tlen\SquareRp\@tlen}} %% \newcommand{\RubikRp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareRp\\ -\rrRp +\rrRp% \end{minipage}% -} +}} \newcommand{\textRubikRp}{\rrRp\,\rrhRp} % \end{macrocode} % \end{macro} @@ -5722,7 +7135,7 @@ % \begin{macro}{\textRubikRw} % These commands all draw forms which denote the Rw rotation. % \begin{macrocode} -\newcommand{\rrRw}{\textbf{\textsf{R\footnotesize{w}}}} +\newcommand{\rrRw}{\@rrw{R}} %% \newcommand{\SquareRw}{% \begin{tikzpicture}[scale=0.5] @@ -5732,15 +7145,16 @@ \draw [thick, ->] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhRw}{\raisebox{-0.333\height}{\SquareRw}\,} +\newcommand{\rrhRw}{\raisebox{-0.333\height}{\@tlen\SquareRw\@tlen}} %% \newcommand{\RubikRw}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareRw\\ -\rrRw +\rrRw% \end{minipage}% -} +}} \newcommand{\textRubikRw}{\rrRw\,\rrhRw} % \end{macrocode} % \end{macro} @@ -5759,7 +7173,7 @@ % \begin{macro}{\textRubikRwp} % These commands all draw forms which denote the Rwp rotation. % \begin{macrocode} -\newcommand{\rrRwp}{\textbf{\textsf{R\footnotesize{w}}$^\prime$}} +\newcommand{\rrRwp}{\@rrwp{R}} %% \newcommand{\SquareRwp}{% \begin{tikzpicture}[scale=0.5] @@ -5769,15 +7183,16 @@ \draw [thick, <-] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhRwp}{\raisebox{-0.333\height}{\SquareRwp}\,} +\newcommand{\rrhRwp}{\raisebox{-0.333\height}{\@tlen\SquareRwp\@tlen}} %% \newcommand{\RubikRwp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareRwp\\ -\rrRwp +\rrRwp% \end{minipage}% -} +}} \newcommand{\textRubikRwp}{\rrRwp\,\rrhRwp} % \end{macrocode} % \end{macro} @@ -5806,15 +7221,16 @@ \draw [thick,->] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhRs}{\raisebox{-0.333\height}{\SquareRs}\,} +\newcommand{\rrhRs}{\raisebox{-0.333\height}{\@tlen\SquareRs\@tlen}} %% \newcommand{\RubikRs}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareRs\\ -\rrRs +\rrRs% \end{minipage}% -} +}} \newcommand{\textRubikRs}{\rrRs\,\rrhRs} % \end{macrocode} % \end{macro} @@ -5843,15 +7259,16 @@ \draw [thick,<-] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhRsp}{\raisebox{-0.333\height}{\SquareRsp}\,} +\newcommand{\rrhRsp}{\raisebox{-0.333\height}{\@tlen\SquareRsp\@tlen}} %% \newcommand{\RubikRsp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareRsp\\ -\rrRsp +\rrRsp% \end{minipage}% -} +}} \newcommand{\textRubikRsp}{\rrRsp\,\rrhRsp} % \end{macrocode} % \end{macro} @@ -5880,15 +7297,16 @@ \draw [thick,->] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhRa}{\raisebox{-0.333\height}{\SquareRa}\,} +\newcommand{\rrhRa}{\raisebox{-0.333\height}{\@tlen\SquareRa\@tlen}} %% \newcommand{\RubikRa}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareRa\\ -\rrRa +\rrRa% \end{minipage}% -} +}} \newcommand{\textRubikRa}{\rrRa\,\rrhRa} % \end{macrocode} % \end{macro} @@ -5917,15 +7335,16 @@ \draw [thick,<-] (\@sddd, \@sb) -- (\@sddd, \@sbh); \end{tikzpicture}% } -\newcommand{\rrhRap}{\raisebox{-0.333\height}{\SquareRap}\,} +\newcommand{\rrhRap}{\raisebox{-0.333\height}{\@tlen\SquareRap\@tlen}} %% \newcommand{\RubikRap}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareRap\\ -\rrRap +\rrRap% \end{minipage}% -} +}} \newcommand{\textRubikRap}{\rrRap\,\rrhRap} % \end{macrocode} % \end{macro} @@ -5946,10 +7365,10 @@ % Not visible from the front. % \begin{macrocode} \newcommand{\rrS}{\@rr{S}} -\newcommand{\SquareS}{\@SquareLetter{\rrS}} -\newcommand{\rrhS}{\raisebox{-0.25mm}{\SquareS}\,} -\newcommand{\RubikS}{\raisebox{\@hRubik}{\SquareS}\,} -\newcommand{\textRubikS}{\rrhS\,} +\newcommand{\SquareS}{\@tlen\@SquareLetter{\rrS}\@tlen} +\newcommand{\rrhS}{\raisebox{-0.25mm}{\SquareS}} +\newcommand{\RubikS}{\raisebox{\@hRubik}{\SquareS}} +\newcommand{\textRubikS}{\rrhS} % \end{macrocode} % \end{macro} % \end{macro} @@ -5969,10 +7388,10 @@ % Not visible from the front. % \begin{macrocode} \newcommand{\rrSp}{\@rrp{S}} -\newcommand{\SquareSp}{\@SquareLetter{\rrSp}} -\newcommand{\rrhSp}{\raisebox{-0.25mm}{\SquareSp}\,} -\newcommand{\RubikSp}{\raisebox{\@hRubik}{\SquareSp}\,} -\newcommand{\textRubikSp}{\rrhSp\,} +\newcommand{\SquareSp}{\@tlen\@SquareLetter{\rrSp}\@tlen} +\newcommand{\rrhSp}{\raisebox{-0.25mm}{\SquareSp}} +\newcommand{\RubikSp}{\raisebox{\@hRubik}{\SquareSp}} +\newcommand{\textRubikSp}{\rrhSp} % \end{macrocode} % \end{macro} % \end{macro} @@ -5988,18 +7407,19 @@ % \begin{macro}{\RubikSu} % \begin{macro}{\textRubikSu} % These commands draw forms of the Singmaster Su slice rotation. -% We also need to finetune the spacing +% We also need to fine-tune the spacing % between these `slice' hieroglyphs (especially Fs and Bs). % \begin{macrocode} -\newcommand{\rrSu}{\textbf{\textsf{S\footnotesize{u}}}} +\newcommand{\rrSu}{\@rru{S}} \newcommand{\rrhSu}{\rrhEp}% \newcommand{\RubikSu}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareEp\\ -\rrSu +\rrSu% \end{minipage}% -} +}} \newcommand{\textRubikSu}{\rrSu\,\rrhEp} % \end{macrocode} % \end{macro} @@ -6015,18 +7435,19 @@ % \begin{macro}{\RubikSup} % \begin{macro}{\textRubikSup} % These commands draw forms of the Singmaster Sup slice rotation. -% We also need to finetune the spacing +% We also need to fine-tune the spacing % between these `slice' hieroglyphs (especially Fs and Bs). % \begin{macrocode} -\newcommand{\rrSup}{\textbf{\textsf{S\footnotesize{u}}$^\prime$}} +\newcommand{\rrSup}{\@rrup{S}} \newcommand{\rrhSup}{\rrhE}% \newcommand{\RubikSup}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareE\\ -\rrSup +\rrSup% \end{minipage}% -} +}} \newcommand{\textRubikSup}{\rrSup\,\rrhE} % \end{macrocode} % \end{macro} @@ -6043,15 +7464,16 @@ % \begin{macro}{\textRubikSd} % These commands draw forms of the Singmaster Sd slice rotation. % \begin{macrocode} -\newcommand{\rrSd}{\textbf{\textsf{S\footnotesize{d}}}} +\newcommand{\rrSd}{\@rrd{S}} \newcommand{\rrhSd}{\rrhE}% \newcommand{\RubikSd}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareE\\ -\rrSd +\rrSd% \end{minipage}% -} +}} \newcommand{\textRubikSd}{\rrSd\,\rrhE} % \end{macrocode} % \end{macro} @@ -6068,15 +7490,16 @@ % \begin{macro}{\textRubikSdp} % These commands draw forms of the Singmaster Sdp slice rotation. % \begin{macrocode} -\newcommand{\rrSdp}{\textbf{\textsf{S\footnotesize{d}}$^\prime$}} +\newcommand{\rrSdp}{\@rrdp{S}} \newcommand{\rrhSdp}{\rrhEp}% \newcommand{\RubikSdp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareEp\\ -\rrSdp +\rrSdp% \end{minipage}% -} +}} \newcommand{\textRubikSdp}{\rrSdp\,\rrhEp} % \end{macrocode} % \end{macro} @@ -6093,15 +7516,16 @@ % \begin{macro}{\textRubikSl} % These commands draw forms of the Singmaster Sl slice rotation. % \begin{macrocode} -\newcommand{\rrSl}{\textbf{\textsf{S\footnotesize{l}}}} +\newcommand{\rrSl}{\@rrl{S}} \newcommand{\rrhSl}{\rrhM}% \newcommand{\RubikSl}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareM\\ -\rrSl +\rrSl% \end{minipage}% -} +}} \newcommand{\textRubikSl}{\rrSl\,\rrhM} % \end{macrocode} % \end{macro} @@ -6118,15 +7542,16 @@ % \begin{macro}{\textRubikSlp} % These commands draw forms of the Singmaster Slp slice rotation. % \begin{macrocode} -\newcommand{\rrSlp}{\textbf{\textsf{S\footnotesize{l}}$^\prime$}} +\newcommand{\rrSlp}{\@rrlp{S}} \newcommand{\rrhSlp}{\rrhMp}% \newcommand{\RubikSlp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareMp\\ -\rrSlp +\rrSlp% \end{minipage}% -} +}} \newcommand{\textRubikSlp}{\rrSlp\,\rrhMp} % \end{macrocode} % \end{macro} @@ -6143,15 +7568,16 @@ % \begin{macro}{\textRubikSr} % These commands draw forms of the Singmaster Sr slice rotation. % \begin{macrocode} -\newcommand{\rrSr}{\textbf{\textsf{S\footnotesize{r}}}} +\newcommand{\rrSr}{\@rrr{S}} \newcommand{\rrhSr}{\rrhMp}% \newcommand{\RubikSr}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareMp\\ -\rrSr +\rrSr% \end{minipage}% -} +}} \newcommand{\textRubikSr}{\rrSr\,\rrhMp} % \end{macrocode} % \end{macro} @@ -6168,15 +7594,16 @@ % \begin{macro}{\textRubikSrp} % These commands draw forms of the Singmaster Srp slice rotation. % \begin{macrocode} -\newcommand{\rrSrp}{\textbf{\textsf{S\footnotesize{r}}$^\prime$}} +\newcommand{\rrSrp}{\@rrrp{S}} \newcommand{\rrhSrp}{\rrhM}% \newcommand{\RubikSrp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareM\\ -\rrSrp +\rrSrp% \end{minipage}% -} +}} \newcommand{\textRubikSrp}{\rrSrp\,\rrhM} % \end{macrocode} % \end{macro} @@ -6199,11 +7626,11 @@ % bounded by \{\} so no need to reset to defaults. % Not visible from the front. % \begin{macrocode} -\newcommand{\rrSf}{\textbf{\textsf{S\footnotesize{f}}}} -\newcommand{\SquareSf}{\@SquareLetter{\rrSf}} -\newcommand{\rrhSf}{\raisebox{-0.25mm}{\SquareSf}\,} -\newcommand{\RubikSf}{\raisebox{\@hRubik}{\SquareSf}\,} -\newcommand{\textRubikSf}{\rrhSf\,} +\newcommand{\rrSf}{\@rrf{S}} +\newcommand{\SquareSf}{\@tlen\@SquareLetter{\rrSf}\@tlen} +\newcommand{\rrhSf}{\raisebox{-0.25mm}{\SquareSf}} +\newcommand{\RubikSf}{\raisebox{\@hRubik}{\SquareSf}} +\newcommand{\textRubikSf}{\rrhSf} % \end{macrocode} % \end{macro} % \end{macro} @@ -6225,11 +7652,11 @@ % bounded by \{\} so no need to reset to defaults. % Not visible from the front. % \begin{macrocode} -\newcommand{\rrSfp}{\textbf{\textsf{S\footnotesize{f}}$^\prime$}} -\newcommand{\SquareSfp}{\@SquareLetter{\rrSfp}} -\newcommand{\rrhSfp}{\raisebox{-0.25mm}{\SquareSfp}\,} -\newcommand{\RubikSfp}{\raisebox{\@hRubik}{\SquareSfp}\,} -\newcommand{\textRubikSfp}{\rrhSfp\,} +\newcommand{\rrSfp}{\@rrfp{S}} +\newcommand{\SquareSfp}{\@tlen\@SquareLetter{\rrSfp}\@tlen} +\newcommand{\rrhSfp}{\raisebox{-0.25mm}{\SquareSfp}} +\newcommand{\RubikSfp}{\raisebox{\@hRubik}{\SquareSfp}} +\newcommand{\textRubikSfp}{\rrhSfp} % \end{macrocode} % \end{macro} % \end{macro} @@ -6251,11 +7678,11 @@ % bounded by \{\} so no need to reset to defaults. % Not visible from the front. % \begin{macrocode} -\newcommand{\rrSb}{\textbf{\textsf{S\footnotesize{b}}}} -\newcommand{\SquareSb}{\@SquareLetter{\rrSb}} -\newcommand{\rrhSb}{\raisebox{-0.25mm}{\SquareSb}\,} -\newcommand{\RubikSb}{\raisebox{\@hRubik}{\SquareSb}\,} -\newcommand{\textRubikSb}{\rrhSb\,} +\newcommand{\rrSb}{\@rrb{S}} +\newcommand{\SquareSb}{\@tlen\@SquareLetter{\rrSb}\@tlen} +\newcommand{\rrhSb}{\raisebox{-0.25mm}{\SquareSb}} +\newcommand{\RubikSb}{\raisebox{\@hRubik}{\SquareSb}} +\newcommand{\textRubikSb}{\rrhSb} % \end{macrocode} % \end{macro} % \end{macro} @@ -6277,11 +7704,11 @@ % bounded by \{\} so no need to reset to defaults. % Not visible from th front. % \begin{macrocode} -\newcommand{\rrSbp}{\textbf{\textsf{S\footnotesize{b}}$^\prime$}} -\newcommand{\SquareSbp}{\@SquareLetter{\rrSbp}} -\newcommand{\rrhSbp}{\raisebox{-0.25mm}{\SquareSbp}\,} -\newcommand{\RubikSbp}{\raisebox{\@hRubik}{\SquareSbp}\,} -\newcommand{\textRubikSbp}{\rrhSbp\,} +\newcommand{\rrSbp}{\@rrbp{S}} +\newcommand{\SquareSbp}{\@tlen\@SquareLetter{\rrSbp}\@tlen} +\newcommand{\rrhSbp}{\raisebox{-0.25mm}{\SquareSbp}} +\newcommand{\RubikSbp}{\raisebox{\@hRubik}{\SquareSbp}} +\newcommand{\textRubikSbp}{\rrhSbp} % \end{macrocode} % \end{macro} % \end{macro} @@ -6298,7 +7725,7 @@ % \begin{macro}{\textRubikU} % These commands all draw forms which denote the U rotation. % \begin{macrocode} -\newcommand{\rrU}{\textbf{\textsf{U}}} +\newcommand{\rrU}{\@rr{U}} %% \newcommand{\SquareU}{% \begin{tikzpicture}[scale=0.5] @@ -6308,15 +7735,16 @@ \draw [thick] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhU}{\raisebox{-0.333\height}{\SquareU}\,} +\newcommand{\rrhU}{\raisebox{-0.333\height}{\@tlen\SquareU\@tlen}} %% \newcommand{\RubikU}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareU\\ -\rrU +\rrU% \end{minipage}%% -} +}} \newcommand{\textRubikU}{\rrU\,\rrhU} % \end{macrocode} % \end{macro} @@ -6335,7 +7763,7 @@ % \begin{macro}{\textRubikUw} % These commands all draw forms which denote the Uw rotation. % \begin{macrocode} -\newcommand{\rrUw}{\textbf{\textsf{U\footnotesize{w}}}} +\newcommand{\rrUw}{\@rrw{U}} %% \newcommand{\SquareUw}{% \begin{tikzpicture}[scale=0.5] @@ -6346,15 +7774,16 @@ \end{tikzpicture}% } % -\newcommand{\rrhUw}{\raisebox{-0.333\height}{\SquareUw}\,} +\newcommand{\rrhUw}{\raisebox{-0.333\height}{\@tlen\SquareUw\@tlen}} %% \newcommand{\RubikUw}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareUw\\ -\rrUw +\rrUw% \end{minipage}%% -} +}} %% \newcommand{\textRubikUw}{\rrUw\,\rrhUw} % \end{macrocode} @@ -6374,7 +7803,7 @@ % \begin{macro}{\textRubikUp} % These commands all draw forms which denote the Up rotation. % \begin{macrocode} -\newcommand{\rrUp}{\textbf{\textsf{U}$^\prime$}} +\newcommand{\rrUp}{\@rrp{U}} %% \newcommand{\SquareUp}{% \begin{tikzpicture}[scale=0.5] @@ -6384,15 +7813,16 @@ \draw [thick] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhUp}{\raisebox{-0.333\height}{\SquareUp}\,} +\newcommand{\rrhUp}{\raisebox{-0.333\height}{\@tlen\SquareUp\@tlen}} %% \newcommand{\RubikUp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareUp\\ -\rrUp +\rrUp% \end{minipage}%% -} +}} \newcommand{\textRubikUp}{\rrUp\,\rrhUp} % \end{macrocode} % \end{macro} @@ -6411,7 +7841,7 @@ % \begin{macro}{\textRubikUwp} % These commands all draw forms which denote the Uwp rotation. % \begin{macrocode} -\newcommand{\rrUwp}{\textbf{\textsf{U\footnotesize{w}}$^\prime$}} +\newcommand{\rrUwp}{\@rrwp{U}} %% \newcommand{\SquareUwp}{% \begin{tikzpicture}[scale=0.5] @@ -6421,15 +7851,16 @@ \draw [thick] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhUwp}{\raisebox{-0.333\height}{\SquareUwp}\,} +\newcommand{\rrhUwp}{\raisebox{-0.333\height}{\@tlen\SquareUwp\@tlen}} %% \newcommand{\RubikUwp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareUwp\\ -\rrUwp +\rrUwp% \end{minipage}%% -} +}} \newcommand{\textRubikUwp}{\rrUwp\,\rrhUwp} % \end{macrocode} % \end{macro} @@ -6458,15 +7889,16 @@ \draw [thick, <-] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhUs}{\raisebox{-0.333\height}{\SquareUs}\,} +\newcommand{\rrhUs}{\raisebox{-0.333\height}{\@tlen\SquareUs\@tlen}} %% \newcommand{\RubikUs}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareUs\\ -\rrUs +\rrUs% \end{minipage}% -} +}} \newcommand{\textRubikUs}{\rrUs\,\rrhUs} % \end{macrocode} % \end{macro} @@ -6495,15 +7927,16 @@ \draw [thick, ->] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhUsp}{\raisebox{-0.333\height}{\SquareUsp}\,} +\newcommand{\rrhUsp}{\raisebox{-0.333\height}{\@tlen\SquareUsp\@tlen}} %% \newcommand{\RubikUsp}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareUsp\\ -\rrUsp +\rrUsp% \end{minipage}% -} +}} \newcommand{\textRubikUsp}{\rrUsp\,\rrhUsp} % \end{macrocode} % \end{macro} @@ -6532,15 +7965,16 @@ \draw [thick, ->] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhUa}{\raisebox{-0.333\height}{\SquareUa}\,} +\newcommand{\rrhUa}{\raisebox{-0.333\height}{\@tlen\SquareUa\@tlen}} %% \newcommand{\RubikUa}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareUa\\ -\rrUa +\rrUa% \end{minipage}% -} +}} \newcommand{\textRubikUa}{\rrUa\,\rrhUa} % \end{macrocode} % \end{macro} @@ -6569,15 +8003,16 @@ \draw [thick, <-] (\@sb,\@sd) -- (\@sbh, \@sd); \end{tikzpicture}% } -\newcommand{\rrhUap}{\raisebox{-0.333\height}{\SquareUap}\,} +\newcommand{\rrhUap}{\raisebox{-0.333\height}{\@tlen\SquareUap\@tlen}} %% \newcommand{\RubikUap}{% +{\@rubikfont% \begin{minipage}{0.6cm} -\centering +\centering% \SquareUap\\ -\rrUap +\rrUap% \end{minipage}% -} +}} \newcommand{\textRubikUap}{\rrUap\,\rrhUap} % \end{macrocode} % \end{macro} @@ -6595,7 +8030,7 @@ % \begin{macro}{\Rubikx} % These commands all draw forms which denote the x rotation. % \begin{macrocode} -\newcommand{\rrx}{\textbf{\textsf{x}}} +\newcommand{\rrx}{\@rr{x}} \newcommand{\Rubikx}{\@xyzRubik{x}} \newcommand{\rrhx}{\@xyzh{x}} % \end{macrocode} @@ -6607,7 +8042,7 @@ % \begin{macro}{\Rubikxp} % These commands all draw forms which denote the xp rotation. % \begin{macrocode} -\newcommand{\rrxp}{\textbf{\textsf{x}$^\prime$}} +\newcommand{\rrxp}{\@rrp{x}} \newcommand{\Rubikxp}{\@xyzRubikp{x}} \newcommand{\rrhxp}{\@xyzhp{x}} % \end{macrocode} @@ -6623,7 +8058,7 @@ % \begin{macro}{\Rubiky} % These commands all draw forms which denote the y rotation. % \begin{macrocode} -\newcommand{\rry}{\textbf{\textsf{y}}} +\newcommand{\rry}{\@rr{y}} \newcommand{\Rubiky}{\@xyzRubik{y}} \newcommand{\rrhy}{\@xyzh{y}} % \end{macrocode} @@ -6635,7 +8070,7 @@ % \begin{macro}{\Rubikyp} % These commands all draw forms which denote the yp rotation. % \begin{macrocode} -\newcommand{\rryp}{\textbf{\textsf{y}$^\prime$}} +\newcommand{\rryp}{\@rrp{y}} \newcommand{\Rubikyp}{\@xyzRubikp{y}} \newcommand{\rrhyp}{\@xyzhp{y}} % \end{macrocode} @@ -6651,7 +8086,7 @@ % \begin{macro}{\Rubikz} % These commands all draw forms which denote the z rotation. % \begin{macrocode} -\newcommand{\rrz}{\textbf{\textsf{z}}} +\newcommand{\rrz}{\@rr{z}} \newcommand{\Rubikz}{\@xyzRubik{z}} \newcommand{\rrhz}{\@xyzh{z}} % \end{macrocode} @@ -6663,7 +8098,7 @@ % \begin{macro}{\Rubikzp} % These commands all draw forms which denote the zp rotation. % \begin{macrocode} -\newcommand{\rrzp}{\textbf{\textsf{z}$^\prime$}} +\newcommand{\rrzp}{\@rrp{z}} \newcommand{\Rubikzp}{\@xyzRubikp{z}} \newcommand{\rrhzp}{\@xyzhp{z}} % \end{macrocode} @@ -6679,7 +8114,7 @@ % \begin{macro}{\Rubiku} % These commands all draw forms which denote the u rotation. % \begin{macrocode} -\newcommand{\rru}{\textbf{\textsf{u}}} +\newcommand{\rru}{\@rr{u}} \newcommand{\Rubiku}{\@xyzRubik{u}} \newcommand{\rrhu}{\@xyzh{u}} % \end{macrocode} @@ -6691,9 +8126,9 @@ % \begin{macro}{\Rubikd} % These commands all draw forms which denote the d rotation. % \begin{macrocode} -\newcommand{\rrd}{\textbf{\textsf{d}}} -\newcommand{\Rubikd}{\@xyzRubik{d}} -\newcommand{\rrhd}{\@xyzh{d}} +\newcommand{\rrd}{\@rr{d}} +\newcommand{\rrhd}{\@xyzhbdfl{d}} +\newcommand{\Rubikd}{\@xyzbdflRubik{d}} % \end{macrocode} % \end{macro} % \end{macro} @@ -6707,9 +8142,9 @@ % \begin{macro}{\Rubikl} % These commands all draw forms which denote the l rotation. % \begin{macrocode} -\newcommand{\rrl}{\textbf{\textsf{l}}} -\newcommand{\Rubikl}{\@xyzRubik{l}} -\newcommand{\rrhl}{\@xyzh{l}} +\newcommand{\rrl}{\@rr{l}} +\newcommand{\rrhl}{\@xyzhbdfl{l}} +\newcommand{\Rubikl}{\@xyzbdflRubik{l}} % \end{macrocode} % \end{macro} % \end{macro} @@ -6719,7 +8154,7 @@ % \begin{macro}{\Rubikr} % These commands all draw forms which denote the r rotation. % \begin{macrocode} -\newcommand{\rrr}{\textbf{\textsf{r}}} +\newcommand{\rrr}{\@rr{r}} \newcommand{\Rubikr}{\@xyzRubik{r}} \newcommand{\rrhr}{\@xyzh{r}} % \end{macrocode} @@ -6735,9 +8170,9 @@ % \begin{macro}{\Rubikf} % These commands all draw forms which denote the f rotation. % \begin{macrocode} -\newcommand{\rrf}{\textbf{\textsf{f}}} -\newcommand{\Rubikf}{\@xyzRubik{f}} -\newcommand{\rrhf}{\@xyzh{f}} +\newcommand{\rrf}{\@rr{f}} +\newcommand{\rrhf}{\@xyzhbdfl{f}} +\newcommand{\Rubikf}{\@xyzbdflRubik{f}} % \end{macrocode} % \end{macro} % \end{macro} @@ -6747,15 +8182,1703 @@ % \begin{macro}{\Rubikb} % These commands all draw forms which denote the b rotation. % \begin{macrocode} -\newcommand{\rrb}{\textbf{\textsf{b}}} -\newcommand{\Rubikb}{\@xyzRubik{b}} -\newcommand{\rrhb}{\@xyzh{b}} +\newcommand{\rrb}{\@rr{b}} +\newcommand{\rrhb}{\@xyzhbdfl{b}} +\newcommand{\Rubikb}{\@xyzbdflRubik{b}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsection{\hspace{3mm}Face(c) and Face(m) rotations} +% \label{sec:codeJaap} +% +% This subsection (added Nov 2016) is to accommodate some additional notation, +% much used on the Jaap Puzzles website (Scherphius J), which, although quite +% convenient, is technically `non-standard'. This additional notation +% makes available the (middle slice) rotations of the form Rm, Rmp, Lm, Lmp, ... and +% also the (whole cube) rotations Rc, Lc, ... (referenced to a face) as used on the +% Cube Lovers usenet group (1981--1997). This notation was probably invented by Singmaster +% (see Scherphius J). +% +% \begin{macro}{\@xyzhc} +% \begin{macro}{\@xyzhcp} +% \begin{macro}{\@xyzRubikc} +% \begin{macro}{\@xyzRubikcp} +% First we have some useful facilitating commands we shall make use of in +% conjunction with the Face(c) and Face(cp) notation. +% \begin{macrocode} +\newcommand{\@xyzhc}[1]{[\raisebox{-1.2pt}% + {{\@rubikfont #1\@rubikfontFNS c}}]} +\newcommand{\@xyzhcp}[1]{[\raisebox{-1.2pt}% + {{\@rubikfont #1{\@rubikfontFNS c}\@rubikprime}}]} +\newcommand{\@xyzRubikc}[1]{\raisebox{3.45pt}% + {[\raisebox{-1.2pt}{{\@rubikfont #1\@rubikfontFNS c}}]}} +\newcommand{\@xyzRubikcp}[1]{\raisebox{3.45pt}% + {[\raisebox{-1.2pt}{{\@rubikfont #1{\@rubikfontFNS c}\@rubikprime}}]}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Rc and Rcp} +% +% Whole cube rotations Rc = x, Rcp = xp. +% +% \begin{macro}{\rrRc} +% \begin{macro}{\rrhRc} +% \begin{macro}{\RubikRc} +% These commands all draw forms which denote the Rc rotation. +% \begin{macrocode} +\newcommand{\rrRc}{\@rrc{R}} +\newcommand{\RubikRc}{\@xyzRubikc{R}} +\newcommand{\rrhRc}{\@xyzhc{R}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrRcp} +% \begin{macro}{\rrhRcp} +% \begin{macro}{\RubikRcp} +% These commands all draw forms which denote the Rcp rotation. +% \begin{macrocode} +\newcommand{\rrRcp}{\@rrcp{R}} +\newcommand{\RubikRcp}{\@xyzRubikcp{R}} +\newcommand{\rrhRcp}{\@xyzhcp{R}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Lc and Lcp} +% +% Whole cube rotations Lc = xp, Lcp = x. +% +% \begin{macro}{\rrLc} +% \begin{macro}{\rrhLc} +% \begin{macro}{\RubikLc} +% These commands all draw forms which denote the Lc rotation. +% \begin{macrocode} +\newcommand{\rrLc}{\@rrc{L}} +\newcommand{\RubikLc}{\@xyzRubikc{L}} +\newcommand{\rrhLc}{\@xyzhc{L}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrLcp} +% \begin{macro}{\rrhLcp} +% \begin{macro}{\RubikLcp} +% These commands all draw forms which denote the Lcp rotation. +% \begin{macrocode} +\newcommand{\rrLcp}{\@rrcp{L}} +\newcommand{\RubikLcp}{\@xyzRubikcp{L}} +\newcommand{\rrhLcp}{\@xyzhcp{L}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Uc and Ucp} +% +% Whole cube rotation Uc = y, Ucp=yp. +% +% \begin{macro}{\rrUc} +% \begin{macro}{\rrhUc} +% \begin{macro}{\RubikUc} +% These commands all draw forms which denote the Uc rotation. +% \begin{macrocode} +\newcommand{\rrUc}{\@rrc{U}} +\newcommand{\RubikUc}{\@xyzRubikc{U}} +\newcommand{\rrhUc}{\@xyzhc{U}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrUcp} +% \begin{macro}{\rrhUcp} +% \begin{macro}{\RubikUcp} +% These commands all draw forms which denote the Ucp rotation. +% \begin{macrocode} +\newcommand{\rrUcp}{\@rrcp{U}} +\newcommand{\RubikUcp}{\@xyzRubikcp{U}} +\newcommand{\rrhUcp}{\@xyzhcp{U}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Dc and Dcp} +% +% Whole cube rotations Dc = yp, Dcp = y. +% +% \begin{macro}{\rrDc} +% \begin{macro}{\rrhDc} +% \begin{macro}{\RubikDc} +% These commands all draw forms which denote the Dc rotation. +% \begin{macrocode} +\newcommand{\rrDc}{\@rrc{D}} +\newcommand{\RubikDc}{\@xyzRubikc{D}} +\newcommand{\rrhDc}{\@xyzhc{D}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrDcp} +% \begin{macro}{\rrhDcp} +% \begin{macro}{\RubikDcp} +% These commands all draw forms which denote the Dcp rotation. +% \begin{macrocode} +\newcommand{\rrDcp}{\@rrcp{D}} +\newcommand{\RubikDcp}{\@xyzRubikcp{D}} +\newcommand{\rrhDcp}{\@xyzhcp{D}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Fc and Fcp} +% +% Whole cube rotations Fc = z, Fcp = zp. +% +% \begin{macro}{\rrFc} +% \begin{macro}{\rrhFc} +% \begin{macro}{\RubikFc} +% These commands all draw forms which denote the Fc rotation. +% \begin{macrocode} +\newcommand{\rrFc}{\@rrc{F}} +\newcommand{\RubikFc}{\@xyzRubikc{F}} +\newcommand{\rrhFc}{\@xyzhc{F}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrFcp} +% \begin{macro}{\rrhFcp} +% \begin{macro}{\RubikFcp} +% These commands all draw forms which denote the Fcp rotation. +% \begin{macrocode} +\newcommand{\rrFcp}{\@rrcp{F}} +\newcommand{\RubikFcp}{\@xyzRubikcp{F}} +\newcommand{\rrhFcp}{\@xyzhcp{F}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Bc and Bcp} +% +% Whole cube rotation Bc = zp, Bcp = z. +% +% \begin{macro}{\rrBc} +% \begin{macro}{\rrhBc} +% \begin{macro}{\RubikBc} +% These commands all draw forms which denote the Bc rotation. +% \begin{macrocode} +\newcommand{\rrBc}{\@rrc{B}} +\newcommand{\RubikBc}{\@xyzRubikc{B}} +\newcommand{\rrhBc}{\@xyzhc{B}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrBcp} +% \begin{macro}{\rrhBcp} +% \begin{macro}{\RubikBcp} +% These commands all draw forms which denote the Bcp rotation. +% \begin{macrocode} +\newcommand{\rrBcp}{\@rrcp{B}} +\newcommand{\RubikBcp}{\@xyzRubikcp{B}} +\newcommand{\rrhBcp}{\@xyzhcp{B}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Rm and Rmp} +% +% Rm = Mp= Sr (M follows Left). We use Sr and Srp as the templates. +% +% \begin{macro}{\rrRm} +% \begin{macro}{\rrhRm} +% \begin{macro}{\RubikRm} +% \begin{macro}{\textRubikRm} +% These commands draw forms of the Rm slice rotation. +% \begin{macrocode} +\newcommand{\rrRm}{\@rrm{R}} +\newcommand{\rrhRm}{\rrhMp}% +\newcommand{\RubikRm}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareMp\\ +\rrRm% +\end{minipage}% +}} +\newcommand{\textRubikRm}{\rrRm\,\rrhMp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrRmp} +% \begin{macro}{\rrhRmp} +% \begin{macro}{\RubikRmp} +% \begin{macro}{\textRubikRmp} +% These commands draw forms of the Rmp slice rotation. +% \begin{macrocode} +\newcommand{\rrRmp}{\@rrmp{R}} +\newcommand{\rrhRmp}{\rrhM}% +\newcommand{\RubikRmp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareM\\ +\rrRmp% +\end{minipage}% +}} +\newcommand{\textRubikRmp}{\rrRmp\,\rrhM} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Lm and Lmp} +% +% Lm = M = Sl (M follows Left). We use Sl and Slp as the templates. +% +% \begin{macro}{\rrLm} +% \begin{macro}{\rrhLm} +% \begin{macro}{\RubikLm} +% \begin{macro}{\textRubikLm} +% These commands draw forms of the Lm slice rotation. +% \begin{macrocode} +\newcommand{\rrLm}{\@rrm{L}} +\newcommand{\rrhLm}{\rrhM}% +\newcommand{\RubikLm}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareM\\ +\rrLm% +\end{minipage}% +}} +\newcommand{\textRubikLm}{\rrLm\,\rrhM} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrLmp} +% \begin{macro}{\rrhLmp} +% \begin{macro}{\RubikLmp} +% \begin{macro}{\textRubikLmp} +% These commands draw forms of the Lmp slice rotation. +% \begin{macrocode} +\newcommand{\rrLmp}{\@rrmp{L}} +\newcommand{\rrhLmp}{\rrhMp}% +\newcommand{\RubikLmp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareMp\\ +\rrLmp% +\end{minipage}% +}} +\newcommand{\textRubikLmp}{\rrLmp\,\rrhMp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Um and Ump} +% +% Um = Ep = Su (E follows Down). We use Su and Sup as the templates. +% +% \begin{macro}{\rrUm} +% \begin{macro}{\rrhUm} +% \begin{macro}{\RubikUm} +% \begin{macro}{\textRubikUm} +% These commands draw forms of the Um slice rotation. +% We also need to fine-tune the spacing +% between these `slice' hieroglyphs (especially Fs and Bs). +% \begin{macrocode} +\newcommand{\rrUm}{\@rrm{U}} +\newcommand{\rrhUm}{\rrhEp}% +\newcommand{\RubikUm}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareEp\\ +\rrUm% +\end{minipage}% +}} +\newcommand{\textRubikUm}{\rrUm\,\rrhEp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrUmp} +% \begin{macro}{\rrhUmp} +% \begin{macro}{\RubikUmp} +% \begin{macro}{\textRubikUmp} +% These commands draw forms of the Ump slice rotation. +% We also need to fine-tune the spacing +% between these `slice' hieroglyphs (especially Fs and Bs). +% \begin{macrocode} +\newcommand{\rrUmp}{\@rrmp{U}} +\newcommand{\rrhUmp}{\rrhE}% +\newcommand{\RubikUmp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareE\\ +\rrUmp% +\end{minipage}% +}} +\newcommand{\textRubikUmp}{\rrUmp\,\rrhE} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Dm and Dmp} +% +% Dm = E = Sd (E follows Down). We use Sd and Sdp as the templates. +% +% \begin{macro}{\rrDm} +% \begin{macro}{\rrhDm} +% \begin{macro}{\RubikDm} +% \begin{macro}{\textRubikDm} +% These commands draw forms of the Singmaster Dm slice rotation. +% \begin{macrocode} +\newcommand{\rrDm}{\@rrm{D}} +\newcommand{\rrhDm}{\rrhE}% +\newcommand{\RubikDm}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareE\\ +\rrDm% +\end{minipage}% +}} +\newcommand{\textRubikDm}{\rrDm\,\rrhE} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrDmp} +% \begin{macro}{\rrhDmp} +% \begin{macro}{\RubikDmp} +% \begin{macro}{\textRubikDmp} +% These commands draw forms of the Singmaster Dmp slice rotation. +% \begin{macrocode} +\newcommand{\rrDmp}{\@rrmp{D}} +\newcommand{\rrhDmp}{\rrhEp}% +\newcommand{\RubikDmp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareEp\\ +\rrDmp% +\end{minipage}% +}} +\newcommand{\textRubikDmp}{\rrDmp\,\rrhEp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Fm and Fmp} +% +% Fm = S = Sf (S follows Front). +% S is not visible from the front, so is represented in a square box. +% We use Sf and Sfp as the templates. +% +% \begin{macro}{\rrFm} +% \begin{macro}{\rrhFm} +% \begin{macro}{\RubikFm} +% \begin{macro}{\textRubikFm} +% These commands draw forms of the Fm slice rotation. +% We need to just make square with Fm in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrFm}{\@rrm{F}} +\newcommand{\SquareFm}{\@tlen\@SquareLetter{\rrFm}\@tlen} +\newcommand{\rrhFm}{\raisebox{-0.25mm}{\SquareFm}} +\newcommand{\RubikFm}{\raisebox{\@hRubik}{\SquareFm}} +\newcommand{\textRubikFm}{\rrhFm} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrFmp} +% \begin{macro}{\rrhFmp} +% \begin{macro}{\RubikFmp} +% \begin{macro}{\textRubikFmp} +% These commands draw forms of the Fmp slice rotation. +% We need to just make square with Fmp in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrFmp}{\@rrmp{F}} +\newcommand{\SquareFmp}{\@tlen\@SquareLetter{\rrFmp}\@tlen} +\newcommand{\rrhFmp}{\raisebox{-0.25mm}{\SquareFmp}} +\newcommand{\RubikFmp}{\raisebox{\@hRubik}{\SquareFmp}} +\newcommand{\textRubikFmp}{\rrhFmp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations Bm and Bmp} +% +% Bm = Sp = Sb. We use Sb and Sbp as the templates. +% +% \begin{macro}{\rrBm} +% \begin{macro}{\rrhBm} +% \begin{macro}{\RubikBm} +% \begin{macro}{\textRubikBm} +% These commands draw forms of the Bm slice rotation. +% We need to just make square with Bm in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrBm}{\@rrm{B}} +\newcommand{\SquareBm}{\@tlen\@SquareLetter{\rrBm}\@tlen} +\newcommand{\rrhBm}{\raisebox{-0.25mm}{\SquareBm}} +\newcommand{\RubikBm}{\raisebox{\@hRubik}{\SquareBm}} +\newcommand{\textRubikBm}{\rrhBm} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrBmp} +% \begin{macro}{\rrhBmp} +% \begin{macro}{\RubikBmp} +% \begin{macro}{\textRubikBmp} +% These commands draw forms of the Bmp slice rotation. +% We need to just make square with Bmp in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrBmp}{\@rrmp{B}} +\newcommand{\SquareBmp}{\@tlen\@SquareLetter{\rrBmp}\@tlen} +\newcommand{\rrhBmp}{\raisebox{-0.25mm}{\SquareBmp}} +\newcommand{\RubikBmp}{\raisebox{\@hRubik}{\SquareBmp}} +\newcommand{\textRubikBmp}{\rrhBmp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% +% \subsection{\hspace{3mm}Randelshofer superset ENG rotations (CMST)} +% \label{sec:codeRandelshofer} +% +% (see webpage: \verb!Randelshofer.ch/rubik/patterns/doc/supersetENG_3x3.html!) +% +% This section relates to the recent Rubik notation developed +% by Randelshofer (see URL above), known as the ``superset ENG rotations'' +% (see Sections~\ref{sec:RubikCommands} and \ref{sec:listofRandelshofercommands} +% for details). +% +% I denote this notation as ``CMST'' (i.e.,~his C, M, S and T notation). +% Although this notation replicates previously existing World Cube Association notation, +% we include it here for completeness. Fortunately the Randelshofer notation does +% not conflict with existing notation. +% +% Briefly, the CMST letters denote whole Cube, Middle, outer-Slice and wide (T) +% rotations associated with named faces. For example, the rotation-code MR +% indicates a rotation of the middle slice parallel to the \textsc{right} face, +% and in the same sense (direction) as \rr{R}\ (see Section~\ref{sec:RubikCommands} for details). +% +% +% First we make some useful facilitating commands for the CX1 and CX1p forms +% as these are handled with raised square brackets. +% We model these four macros on the equivalent +% \verb!\@xyzh!, \verb!\@xyzhp!,\verb!\@xyzRubik!,\verb!\@xyzRubikp! macros defined above. +% \begin{macrocode} +\newcommand{\@randhc}[1]{[\raisebox{-1.2pt}{{\@rubikfont C#1}}]} +\newcommand{\@randhcp}[1]{[\raisebox{-1.2pt}{{\@rubikfont C#1\@rubikprime}}]} +\newcommand{\@randRubikc}[1]% + {\raisebox{3.45pt}{[\raisebox{-1.2pt}{{\@rubikfont C#1}}]}} +\newcommand{\@randRubikcp}[1]% + {\raisebox{3.45pt}{[\raisebox{-1.2pt}{{\@rubikfont C#1\@rubikprime}}]}} +% \end{macrocode} +% +% +% In the following we create the base form of a rotation code, eg \rrhCR\ and then +% the user typesets this rotation using CR as the argument for \verb!\rrh{}!. +% This works because the macro \verb!\@join{}{}! is used to join \cmd{\rrh} +% and CR $\rightarrow$ \cmd{\rrhCR} etc. +% +% The = signs at the beginning of each new section indicate the equivalence +% between the Randelshofer notation and the current (World Cube Association) +% notation. +% +% +% \subsubsection{\hspace{3mm}Rotations CR and CRp} +% +% Whole cube rotations CR = Rc = x, CRp = Rcp = xp. +% +% \begin{macro}{\rrCR} +% \begin{macro}{\rrhCR} +% \begin{macro}{\RubikCR} +% These commands all draw forms which denote the CR = Rc rotation. +% \begin{macrocode} +\newcommand{\rrCR}{\@rr{CR}} +\newcommand{\RubikCR}{\@randRubikc{R}} +\newcommand{\rrhCR}{\@randhc{R}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrCRp} +% \begin{macro}{\rrhCRp} +% \begin{macro}{\RubikCRp} +% These commands all draw forms which denote the CRp = Rcp rotation. +% \begin{macrocode} +\newcommand{\rrCRp}{\@rrp{CR}} +\newcommand{\RubikCRp}{\@randRubikcp{R}} +\newcommand{\rrhCRp}{\@randhcp{R}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations CL and CLp} +% +% Whole cube rotations CL = Lc = xp, CLp = Lcp = x. +% +% \begin{macro}{\rrCL} +% \begin{macro}{\rrhCL} +% \begin{macro}{\RubikCL} +% These commands all draw forms which denote the CL rotation. +% \begin{macrocode} +\newcommand{\rrCL}{\@rr{CL}} +\newcommand{\RubikCL}{\@randRubikc{L}} +\newcommand{\rrhCL}{\@randhc{L}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrCLp} +% \begin{macro}{\rrhCLp} +% \begin{macro}{\RubikCLp} +% These commands all draw forms which denote the CLp rotation. +% \begin{macrocode} +\newcommand{\rrCLp}{\@rrp{CL}} +\newcommand{\RubikCLp}{\@randRubikcp{L}} +\newcommand{\rrhCLp}{\@randhcp{L}} % \end{macrocode} % \end{macro} % \end{macro} % \end{macro} % % +% \subsubsection{\hspace{3mm}Rotations CU and CUp} +% +% Whole cube rotation CU = Uc = y, CUp = Ucp=yp. +% +% \begin{macro}{\rrCU} +% \begin{macro}{\rrhCU} +% \begin{macro}{\RubikCU} +% These commands all draw forms which denote the CU rotation. +% \begin{macrocode} +\newcommand{\rrCU}{\@rr{CU}} +\newcommand{\RubikCU}{\@randRubikc{U}} +\newcommand{\rrhCU}{\@randhc{U}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrCUp} +% \begin{macro}{\rrhCUp} +% \begin{macro}{\RubikCUp} +% These commands all draw forms which denote the CUp rotation. +% \begin{macrocode} +\newcommand{\rrCUp}{\@rrp{CU}} +\newcommand{\RubikCUp}{\@randRubikcp{U}} +\newcommand{\rrhCUp}{\@randhcp{U}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations CD and CDp} +% +% Whole cube rotations CD = Dc = yp, CDp = Dcp = y. +% +% \begin{macro}{\rrCD} +% \begin{macro}{\rrhCD} +% \begin{macro}{\RubikCD} +% These commands all draw forms which denote the CD rotation. +% \begin{macrocode} +\newcommand{\rrCD}{\@rr{CD}} +\newcommand{\RubikCD}{\@randRubikc{D}} +\newcommand{\rrhCD}{\@randhc{D}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrCDp} +% \begin{macro}{\rrhCDp} +% \begin{macro}{\RubikCDp} +% These commands all draw forms which denote the CDp rotation. +% \begin{macrocode} +\newcommand{\rrCDp}{\@rrp{CD}} +\newcommand{\RubikCDp}{\@randRubikcp{D}} +\newcommand{\rrhCDp}{\@randhcp{D}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations CF and CFp} +% +% Whole cube rotations CF = Fc = z, CFp = Fcp = zp. +% +% \begin{macro}{\rrCF} +% \begin{macro}{\rrhCF} +% \begin{macro}{\RubikCF} +% These commands all draw forms which denote the CF rotation. +% \begin{macrocode} +\newcommand{\rrCF}{\@rr{CF}} +\newcommand{\RubikCF}{\@randRubikc{F}} +\newcommand{\rrhCF}{\@randhc{F}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrCFp} +% \begin{macro}{\rrhCFp} +% \begin{macro}{\RubikCFp} +% These commands all draw forms which denote the CFp rotation. +% \begin{macrocode} +\newcommand{\rrCFp}{\@rrp{CF}} +\newcommand{\RubikCFp}{\@randRubikcp{F}} +\newcommand{\rrhCFp}{\@randhcp{F}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations CB and CBp} +% +% Whole cube rotation CB = Bc = zp, CBp = Bcp = z. +% +% \begin{macro}{\rrCB} +% \begin{macro}{\rrhCB} +% \begin{macro}{\RubikCB} +% These commands all draw forms which denote the CB rotation. +% \begin{macrocode} +\newcommand{\rrCB}{\@rr{CB}} +\newcommand{\RubikCB}{\@randRubikc{B}} +\newcommand{\rrhCB}{\@randhc{B}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \begin{macro}{\rrCBp} +% \begin{macro}{\rrhCBp} +% \begin{macro}{\RubikCBp} +% These commands all draw forms which denote the CBp rotation. +% \begin{macrocode} +\newcommand{\rrCBp}{\@rrp{CB}} +\newcommand{\RubikCBp}{\@randRubikcp{B}} +\newcommand{\rrhCBp}{\@randhcp{B}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \subsubsection{\hspace{3mm}Rotations MR and MRp} +% +% MR = Rm = Mp= Sr (M follows Left). We use Sr and Srp as the templates. +% +% \begin{macro}{\rrMR} +% \begin{macro}{\rrhMR} +% \begin{macro}{\RubikMR} +% \begin{macro}{\textRubikMR} +% These commands draw forms of the MR middle slice rotation. +% \begin{macrocode} +\newcommand{\rrMR}{\@rr{MR}} +\newcommand{\rrhMR}{\rrhMp}% +\newcommand{\RubikMR}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareMp\\ +\rrMR% +\end{minipage}% +}} +\newcommand{\textRubikMR}{\rrMR\,\rrhMp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrMRp} +% \begin{macro}{\rrhMRp} +% \begin{macro}{\RubikMRp} +% \begin{macro}{\textRubikMRp} +% These commands draw forms of the MRp slice rotation. +% \begin{macrocode} +\newcommand{\rrMRp}{\@rrp{MR}} +\newcommand{\rrhMRp}{\rrhM}% +\newcommand{\RubikMRp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareM\\ +\rrMRp% +\end{minipage}% +}} +\newcommand{\textRubikMRp}{\rrMRp\,\rrhM} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations ML and MLp} +% +% ML = Lm = M = Sl (M follows Left). We use Sl and Slp as the templates. +% +% \begin{macro}{\rrML} +% \begin{macro}{\rrhML} +% \begin{macro}{\RubikML} +% \begin{macro}{\textRubikML} +% These commands draw forms of the ML slice rotation. +% \begin{macrocode} +\newcommand{\rrML}{\@rr{ML}} +\newcommand{\rrhML}{\rrhM}% +\newcommand{\RubikML}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareM\\ +\rrML% +\end{minipage}% +}} +\newcommand{\textRubikML}{\rrML\,\rrhM} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrMLp} +% \begin{macro}{\rrhMLp} +% \begin{macro}{\RubikMLp} +% \begin{macro}{\textRubikMLp} +% These commands draw forms of the MLp slice rotation. +% \begin{macrocode} +\newcommand{\rrMLp}{\@rrp{ML}} +\newcommand{\rrhMLp}{\rrhMp}% +\newcommand{\RubikMLp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareMp\\ +\rrMLp% +\end{minipage}% +}} +\newcommand{\textRubikMLp}{\rrMLp\,\rrhMp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations MU and MUp} +% +% MU = Um = Ep = Su (E follows Down). We use Su and Sup as the templates. +% +% \begin{macro}{\rrMU} +% \begin{macro}{\rrhMU} +% \begin{macro}{\RubikMU} +% \begin{macro}{\textRubikMU} +% These commands draw forms of the MU slice rotation. +% \begin{macrocode} +\newcommand{\rrMU}{\@rr{MU}} +\newcommand{\rrhMU}{\rrhEp}% +\newcommand{\RubikMU}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareEp\\ +\rrMU% +\end{minipage}% +}} +\newcommand{\textRubikMU}{\rrMU\,\rrhEp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrMUp} +% \begin{macro}{\rrhMUp} +% \begin{macro}{\RubikMUp} +% \begin{macro}{\textRubikMUp} +% These commands draw forms of the MUp slice rotation. +% \begin{macrocode} +\newcommand{\rrMUp}{\@rrp{MU}} +\newcommand{\rrhMUp}{\rrhE}% +\newcommand{\RubikMUp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareE\\ +\rrMUp% +\end{minipage}% +}} +\newcommand{\textRubikMUp}{\rrMUp\,\rrhE} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations MD and MDp} +% +% MD = Dm = E = Sd (E follows Down). We use Sd and Sdp as the templates. +% +% \begin{macro}{\rrMD} +% \begin{macro}{\rrhMD} +% \begin{macro}{\RubikMD} +% \begin{macro}{\textRubikMD} +% These commands draw forms of the Randelshofer MD slice rotation. +% \begin{macrocode} +\newcommand{\rrMD}{\@rr{MD}} +\newcommand{\rrhMD}{\rrhE}% +\newcommand{\RubikMD}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareE\\ +\rrMD% +\end{minipage}% +}} +\newcommand{\textRubikMD}{\rrMD\,\rrhE} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrMDp} +% \begin{macro}{\rrhMDp} +% \begin{macro}{\RubikMDp} +% \begin{macro}{\textRubikMDp} +% These commands draw forms of the Randelshofer MDp slice rotation. +% \begin{macrocode} +\newcommand{\rrMDp}{\@rrp{MD}} +\newcommand{\rrhMDp}{\rrhEp}% +\newcommand{\RubikMDp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareEp\\ +\rrMDp% +\end{minipage}% +}} +\newcommand{\textRubikMDp}{\rrMDp\,\rrhEp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations MF and MFp} +% +% MF = Fm = S = Sf (S follows Front). +% MF = S is not visible from the front, so is represented in a square box. +% We use Sf and Sfp as the templates. +% +% \begin{macro}{\rrMF} +% \begin{macro}{\rrhMF} +% \begin{macro}{\RubikMF} +% \begin{macro}{\textRubikMF} +% These commands draw forms of the MF slice rotation. +% We need to just make square with MF in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrMF}{\@rr{MF}} +\newcommand{\SquareMF}{\@tlen\@SquareLetter{\rrMF}\@tlen} +\newcommand{\rrhMF}{\raisebox{-0.25mm}{\SquareMF}} +\newcommand{\RubikMF}{\raisebox{\@hRubik}{\SquareMF}} +\newcommand{\textRubikMF}{\rrhMF} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrMFp} +% \begin{macro}{\rrhMFp} +% \begin{macro}{\RubikMFp} +% \begin{macro}{\textRubikMFp} +% These commands draw forms of the MFp slice rotation. +% We need to just make square with MFp in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrMFp}{\@rrp{MF}} +\newcommand{\SquareMFp}{\@tlen\@SquareLetter{\rrMFp}\@tlen} +\newcommand{\rrhMFp}{\raisebox{-0.25mm}{\SquareMFp}} +\newcommand{\RubikMFp}{\raisebox{\@hRubik}{\SquareMFp}} +\newcommand{\textRubikMFp}{\rrhMFp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations MB and MBp} +% +% MB = Bm = Sp = Sb. We use Sb and Sbp as the templates. +% +% \begin{macro}{\rrMB} +% \begin{macro}{\rrhMB} +% \begin{macro}{\RubikMB} +% \begin{macro}{\textRubikMB} +% These commands draw forms of the MB slice rotation. +% We need to just make square with MB in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrMB}{\@rr{MB}} +\newcommand{\SquareMB}{\@tlen\@SquareLetter{\rrMB}\@tlen} +\newcommand{\rrhMB}{\raisebox{-0.25mm}{\SquareMB}} +\newcommand{\RubikMB}{\raisebox{\@hRubik}{\SquareMB}} +\newcommand{\textRubikMB}{\rrhMB} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrMBp} +% \begin{macro}{\rrhMBp} +% \begin{macro}{\RubikMBp} +% \begin{macro}{\textRubikMBp} +% These commands draw forms of the MBp slice rotation. +% We need to just make square with MBp in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrMBp}{\@rrp{MB}} +\newcommand{\SquareMBp}{\@tlen\@SquareLetter{\rrMBp}\@tlen} +\newcommand{\rrhMBp}{\raisebox{-0.25mm}{\SquareMBp}} +\newcommand{\RubikMBp}{\raisebox{\@hRubik}{\SquareMBp}} +\newcommand{\textRubikMBp}{\rrhMBp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \subsubsection{\hspace{3mm}Rotations T (wide)} +% +% TR = Rw \ \ (We use Rw and Rwp as the templates). +% +% {\noindent}We first set up some useful T and Tp macros for use with (L,R,U,D,F,B) +% slightly more general than before. As before the rubikfont command needs to be +% delimited using two curly brackets to contain the font expression. +% \begin{macrocode} +\newcommand{\@rrT}[1]{{\@rubikfont T#1}} +\newcommand{\@rrhT}[1]{\@join{\rrh#1}{w}}% +\newcommand{\@textRubikT}[1]{\@rrT{#1}\,\@join{\rrh#1}{w}} +% +\newcommand{\@RubikT}[1]{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering%% +\@join{\Square#1}{w}\\% +\@rrT{#1}%% +\end{minipage}% +}} +%% +\newcommand{\@rrTp}[1]{{\@rubikfont T#1\@rubikprime}} +\newcommand{\@rrhTp}[1]{\@join{\rrh#1}{wp}}% +\newcommand{\@textRubikTp}[1]{\@rrTp{#1}\,\@join{\rrh#1}{wp}} +%% +\newcommand{\@RubikTp}[1]{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering%% +\@join{\Square#1}{wp}\\% +\@rrTp{#1}%% +\end{minipage}% +}} +% \end{macrocode} +% +% +% +% \begin{macro}{\rrTL} +% \begin{macro}{\rrhTL} +% \begin{macro}{\RubikTL} +% \begin{macro}{\textRubikTL} +% These commands draw forms of the TL = Lw wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTL}{\@rrT{L}}% = rrLw +\newcommand{\rrhTL}{\@rrhT{L}} +\newcommand{\textRubikTL}{\@textRubikT{L}} +\newcommand{\RubikTL}{\@RubikT{L}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% \begin{macro}{\rrTLp} +% \begin{macro}{\rrhTLp} +% \begin{macro}{\RubikTLp} +% \begin{macro}{\textRubikTLp} +% These commands draw forms of the TLp = Lwp wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTLp}{\@rrTp{L}} +\newcommand{\rrhTLp}{\@rrhTp{L}} +\newcommand{\textRubikTLp}{\@textRubikTp{L}} +\newcommand{\RubikTLp}{\@RubikTp{L}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \begin{macro}{\rrTR} +% \begin{macro}{\rrhTR} +% \begin{macro}{\RubikTR} +% \begin{macro}{\textRubikTR} +% These commands draw forms of the TR = Rw wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTR}{\@rrT{R}} +\newcommand{\rrhTR}{\@rrhT{R}} +\newcommand{\textRubikTR}{\@textRubikT{R}} +\newcommand{\RubikTR}{\@RubikT{R}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% \begin{macro}{\rrTRp} +% \begin{macro}{\rrhTRp} +% \begin{macro}{\RubikTRp} +% \begin{macro}{\textRubikTRp} +% These commands draw forms of the TRp = Rmp wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTRp}{\@rrTp{R}} +\newcommand{\rrhTRp}{\@rrhTp{R}} +\newcommand{\textRubikTRp}{\@textRubikTp{R}} +\newcommand{\RubikTRp}{\@RubikTp{R}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \begin{macro}{\rrTU} +% \begin{macro}{\rrhTU} +% \begin{macro}{\RubikTU} +% \begin{macro}{\textRubikTU} +% These commands draw forms of the TU = Uw wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTU}{\@rrT{U}} +\newcommand{\rrhTU}{\@rrhT{U}} +\newcommand{\textRubikTU}{\@textRubikT{U}} +\newcommand{\RubikTU}{\@RubikT{U}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% \begin{macro}{\rrTUp} +% \begin{macro}{\rrhTUp} +% \begin{macro}{\RubikTUp} +% \begin{macro}{\textRubikTUp} +% These commands draw forms of the TUp = Uwp wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTUp}{\@rrTp{U}} +\newcommand{\rrhTUp}{\@rrhTp{U}} +\newcommand{\textRubikTUp}{\@textRubikTp{U}} +\newcommand{\RubikTUp}{\@RubikTp{U}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \begin{macro}{\rrTD} +% \begin{macro}{\rrhTD} +% \begin{macro}{\RubikTD} +% \begin{macro}{\textRubikTD} +% These commands draw forms of the TD = Dw wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTD}{\@rrT{D}} +\newcommand{\rrhTD}{\@rrhT{D}} +\newcommand{\textRubikTD}{\@textRubikT{D}} +\newcommand{\RubikTD}{\@RubikT{D}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% \begin{macro}{\rrTDp} +% \begin{macro}{\rrhTDp} +% \begin{macro}{\RubikTDp} +% \begin{macro}{\textRubikTDp} +% These commands draw forms of the TDp = Dwp wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTDp}{\@rrTp{D}} +\newcommand{\rrhTDp}{\@rrhTp{D}} +\newcommand{\textRubikTDp}{\@textRubikTp{D}} +\newcommand{\RubikTDp}{\@RubikTp{D}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrTF} +% \begin{macro}{\rrhTF} +% \begin{macro}{\RubikTF} +% \begin{macro}{\textRubikTF} +% These commands draw forms of the TF = Fw wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTF}{\@rrT{F}} +\newcommand{\rrhTF}{\@rrhT{F}} +\newcommand{\textRubikTF}{\@textRubikT{F}} +\newcommand{\RubikTF}{\@RubikT{F}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% \begin{macro}{\rrTFp} +% \begin{macro}{\rrhTFp} +% \begin{macro}{\RubikTFp} +% \begin{macro}{\textRubikTFp} +% These commands draw forms of the TFp = Fwp wide slice rotation. +% \begin{macrocode} +\newcommand{\rrTFp}{\@rrTp{F}} +\newcommand{\rrhTFp}{\@rrhTp{F}} +\newcommand{\textRubikTFp}{\@textRubikTp{F}} +\newcommand{\RubikTFp}{\@RubikTp{F}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \begin{macro}{\rrTB} +% \begin{macro}{\rrhTB} +% \begin{macro}{\RubikTB} +% \begin{macro}{\textRubikTB} +% These commands draw forms of the TB = Bw wide slice rotation. +% NOTE we just use the letters TB in a square +% \begin{macrocode} +\newcommand{\rrTB}{\@rrT{B}} +\newcommand{\SquareTB}{\@tlen\@SquareLetter{\rrTB}\@tlen} +\newcommand{\rrhTB}{\raisebox{-0.25mm}{\SquareTB}} +\newcommand{\textRubikTB}{\rrhTB} +\newcommand{\RubikTB}{\raisebox{\@hRubik}{\SquareTB}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% \begin{macro}{\rrTBp} +% \begin{macro}{\rrhTBp} +% \begin{macro}{\RubikTBp} +% \begin{macro}{\textRubikTBp} +% These commands draw forms of the TBp = Bwp wide slice rotation. +% NOTE we just use the letters TB' in a square +% \begin{macrocode} +\newcommand{\rrTBp}{\@rrTp{B}} +\newcommand{\SquareTBp}{\@tlen\@SquareLetter{\rrTBp}\@tlen} +\newcommand{\rrhTBp}{\raisebox{-0.25mm}{\SquareTBp}} +\newcommand{\textRubikTBp}{\rrhTBp} +\newcommand{\RubikTBp}{\raisebox{\@hRubik}{\SquareTBp}} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \subsubsection{\hspace{3mm}Rotations SR and SRp (opposite slices)} +% +% opposite slices in same direction +% SR = Rs (both rotating in R direction) +% +% \begin{macro}{\rrSR} +% \begin{macro}{\rrhSR} +% \begin{macro}{\RubikSR} +% \begin{macro}{\textRubikSR} +% These commands draw forms of the SR opposite slice rotation. +% \begin{macrocode} +\newcommand{\rrSR}{\@rr{SR}} +\newcommand{\rrhSR}{\rrhRs}% +\newcommand{\RubikSR}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareRs\\ +\rrSR% +\end{minipage}% +}} +\newcommand{\textRubikSR}{\rrSR\,\rrhRs} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrSRp} +% \begin{macro}{\rrhSRp} +% \begin{macro}{\RubikSRp} +% \begin{macro}{\textRubikSRp} +% These commands draw forms of the SRp opposite slice rotation. +% \begin{macrocode} +\newcommand{\rrSRp}{\@rrp{SR}} +\newcommand{\rrhSRp}{\rrhRsp}% +\newcommand{\RubikSRp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareRsp\\ +\rrSRp% +\end{minipage}% +}} +\newcommand{\textRubikSRp}{\rrSRp\,\rrhRsp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations SL and SLp} +% +% SL = Ls (both rotating in L direction) +% +% \begin{macro}{\rrSL} +% \begin{macro}{\rrhSL} +% \begin{macro}{\RubikSL} +% \begin{macro}{\textRubikSL} +% These commands draw forms of the SL opposite slice rotation. +% \begin{macrocode} +\newcommand{\rrSL}{\@rr{SL}} +\newcommand{\rrhSL}{\rrhLs}% +\newcommand{\RubikSL}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareLs\\ +\rrSL% +\end{minipage}% +}} +\newcommand{\textRubikSL}{\rrSL\,\rrhLs} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrSLp} +% \begin{macro}{\rrhSLp} +% \begin{macro}{\RubikSLp} +% \begin{macro}{\textRubikSLp} +% These commands draw forms of the SLp opposite slice rotation. +% \begin{macrocode} +\newcommand{\rrSLp}{\@rrp{SL}} +\newcommand{\rrhSLp}{\rrhLsp}% +\newcommand{\RubikSLp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareLsp\\ +\rrSLp% +\end{minipage}% +}} +\newcommand{\textRubikSLp}{\rrSLp\,\rrhLsp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations SU and SUp} +% +% SU = Us (both rotating in U direction) +% +% \begin{macro}{\rrSU} +% \begin{macro}{\rrhSU} +% \begin{macro}{\RubikSU} +% \begin{macro}{\textRubikSU} +% These commands draw forms of the SU opposite slice rotation. +% \begin{macrocode} +\newcommand{\rrSU}{\@rr{SU}} +\newcommand{\rrhSU}{\rrhUs}% +\newcommand{\RubikSU}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareUs\\ +\rrSU% +\end{minipage}% +}} +\newcommand{\textRubikSU}{\rrSU\,\rrhUs} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrSUp} +% \begin{macro}{\rrhSUp} +% \begin{macro}{\RubikSUp} +% \begin{macro}{\textRubikSUp} +% These commands draw forms of the SUp opposite slice rotation. +% \begin{macrocode} +\newcommand{\rrSUp}{\@rrp{SU}} +\newcommand{\rrhSUp}{\rrhUsp}% +\newcommand{\RubikSUp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareUsp\\ +\rrSUp% +\end{minipage}% +}} +\newcommand{\textRubikSUp}{\rrSUp\,\rrhUsp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations SD and SDp} +% +% SD = Ds (both rotating in D direction) +% +% \begin{macro}{\rrSD} +% \begin{macro}{\rrhSD} +% \begin{macro}{\RubikSD} +% \begin{macro}{\textRubikSD} +% These commands draw forms of the SD opposite slice rotation. +% \begin{macrocode} +\newcommand{\rrSD}{\@rr{SD}} +\newcommand{\rrhSD}{\rrhDs}% +\newcommand{\RubikSD}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareDs\\ +\rrSD% +\end{minipage}% +}} +\newcommand{\textRubikSD}{\rrSD\,\rrhDs} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrSDp} +% \begin{macro}{\rrhSDp} +% \begin{macro}{\RubikSDp} +% \begin{macro}{\textRubikSDp} +% These commands draw forms of the SDp opposite slice rotation. +% \begin{macrocode} +\newcommand{\rrSDp}{\@rrp{SD}} +\newcommand{\rrhSDp}{\rrhDsp}% +\newcommand{\RubikSDp}{% +{\@rubikfont% +\begin{minipage}{0.6cm} +\centering% +\SquareDsp\\ +\rrSDp% +\end{minipage}% +}} +\newcommand{\textRubikSDp}{\rrSDp\,\rrhDsp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \subsubsection{\hspace{3mm}Rotations SF and SFp} +% +% SF = Fs is not visible from the front, so is represented in a square box. +% Both rotating in the F direction +% We use Fs and Fsp as the templates. +% +% \begin{macro}{\rrSF} +% \begin{macro}{\rrhSF} +% \begin{macro}{\RubikSF} +% \begin{macro}{\textRubikSF} +% These commands draw forms of the SF opposite slice rotation. +% We need to just make square with SF in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrSF}{\@rr{SF}} +\newcommand{\SquareSF}{\@tlen\@SquareLetter{\rrSF}\@tlen} +\newcommand{\rrhSF}{\raisebox{-0.25mm}{\SquareSF}} +\newcommand{\RubikSF}{\raisebox{\@hRubik}{\SquareSF}} +\newcommand{\textRubikSF}{\rrhSF} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrSFp} +% \begin{macro}{\rrhSFp} +% \begin{macro}{\RubikSFp} +% \begin{macro}{\textRubikSFp} +% These commands draw forms of the SFp opposite slice rotation. +% We need to just make square with SFp in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrSFp}{\@rrp{SF}} +\newcommand{\SquareSFp}{\@tlen\@SquareLetter{\rrSFp}\@tlen} +\newcommand{\rrhSFp}{\raisebox{-0.25mm}{\SquareSFp}} +\newcommand{\RubikSFp}{\raisebox{\@hRubik}{\SquareSFp}} +\newcommand{\textRubikSFp}{\rrhSFp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% +% \subsubsection{\hspace{3mm}Rotations SB and SBp} +% +% SB = Bs is not visible from the front, so is represented in a square box. +% Both rotating in the B direction +% We use Bs and Bsp as the templates. +% +% \begin{macro}{\rrSB} +% \begin{macro}{\rrhSB} +% \begin{macro}{\RubikSB} +% \begin{macro}{\textRubikSB} +% These commands draw forms of the SB opposite slice rotation. +% We need to just make square with SB in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrSB}{\@rr{SB}} +\newcommand{\SquareSB}{\@tlen\@SquareLetter{\rrSB}\@tlen} +\newcommand{\rrhSB}{\raisebox{-0.25mm}{\SquareSB}} +\newcommand{\RubikSB}{\raisebox{\@hRubik}{\SquareSB}} +\newcommand{\textRubikSB}{\rrhSB} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% \begin{macro}{\rrSBp} +% \begin{macro}{\rrhSBp} +% \begin{macro}{\RubikSBp} +% \begin{macro}{\textRubikSBp} +% These commands draw forms of the SBp opposite slice rotation. +% We need to just make square with SBp in square; +% adjust box height using a \cmd{\rule}; +% adjust \cmd{\fboxsep} (default=3pt); +% adjust \cmd{\fboxrule} (default=0.4pt); +% bounded by \{\} so no need to reset to defaults. +% Not visible from the front. +% \begin{macrocode} +\newcommand{\rrSBp}{\@rrp{SB}} +\newcommand{\SquareSBp}{\@tlen\@SquareLetter{\rrSBp}\@tlen} +\newcommand{\rrhSBp}{\raisebox{-0.25mm}{\SquareSBp}} +\newcommand{\RubikSBp}{\raisebox{\@hRubik}{\SquareSBp}} +\newcommand{\textRubikSBp}{\rrhSBp} +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% +% +% +% \subsection{\hspace{3mm}Axis rotations (textRubik versions)} +% \label{sec:codetextrubikaxisversions} +% +% For completeness we include a \cmd{\textRubik} version of all the +% axis rotation codes (making them equal to their hieroglyphic \cmd{\rrh} version). +% Obviously this list must go at the end of this file. While these commands are perhaps +% strictly unnecessary, the motivation is to allow users to include them in +% a \cmd{\ShowSequence} command when using the \cmd{\textRubik} font argument. +% +% \begin{macrocode} +\newcommand{\textRubikx}{\rrhx} +\newcommand{\textRubikxp}{\rrhxp} +\newcommand{\textRubiky}{\rrhy} +\newcommand{\textRubikyp}{\rrhyp} +\newcommand{\textRubikz}{\rrhz} +\newcommand{\textRubikzp}{\rrhzp} +\newcommand{\textRubikl}{\rrhl} +\newcommand{\textRubikr}{\rrhr} +\newcommand{\textRubiku}{\rrhu} +\newcommand{\textRubikd}{\rrhd} +\newcommand{\textRubikf}{\rrhf} +\newcommand{\textRubikb}{\rrhb} +\newcommand{\textRubikLc}{\rrhLc} +\newcommand{\textRubikLcp}{\rrhLcp} +\newcommand{\textRubikRc}{\rrhRc} +\newcommand{\textRubikRcp}{\rrhRcp} +\newcommand{\textRubikUc}{\rrhUc} +\newcommand{\textRubikUcp}{\rrhUcp} +\newcommand{\textRubikDc}{\rrhDc} +\newcommand{\textRubikDcp}{\rrhDcp} +\newcommand{\textRubikFc}{\rrhFc} +\newcommand{\textRubikFcp}{\rrhFcp} +\newcommand{\textRubikBc}{\rrhBc} +\newcommand{\textRubikBcp}{\rrhBcp} +\newcommand{\textRubikCL}{\rrhCL} +\newcommand{\textRubikCLp}{\rrhCLp} +\newcommand{\textRubikCR}{\rrhCR} +\newcommand{\textRubikCRp}{\rrhCRp} +\newcommand{\textRubikCU}{\rrhCU} +\newcommand{\textRubikCUp}{\rrhCUp} +\newcommand{\textRubikCD}{\rrhCD} +\newcommand{\textRubikCDp}{\rrhCDp} +\newcommand{\textRubikCF}{\rrhCF} +\newcommand{\textRubikCFp}{\rrhCFp} +\newcommand{\textRubikCB}{\rrhCB} +\newcommand{\textRubikCBp}{\rrhCBp} +% \end{macrocode} +% +% +% % -------------------------- % End of this package % -------------------------- |