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diff --git a/Master/texmf-dist/source/latex/rubik/rubikcube.dtx b/Master/texmf-dist/source/latex/rubik/rubikcube.dtx index 4f57d98a0ee..c9812ed4bad 100644 --- a/Master/texmf-dist/source/latex/rubik/rubikcube.dtx +++ b/Master/texmf-dist/source/latex/rubik/rubikcube.dtx @@ -1,9 +1,9 @@ % \iffalse meta-comment % rubikcube.dtx % -% version v4.0 (03 March 2017) +% version v5.0 (February 25, 2018) % -% Copyright 2017 +% Copyright 2018 % RWD Nickalls (dick@nickalls.org) and % A Syropoulos (asyropoulos@yahoo.com) % @@ -19,7 +19,7 @@ % This work consists of the files rubikcube.dtx and rubikcube.ins % and the derived file rubikcube.sty. % -%<*readme> +%<*readme> % % The rubikcube package provides a collection of LaTeX commands and macros % for the typesetting of Rubik cube configurations and rotation @@ -41,6 +41,8 @@ (Generate rubikcube.sty by (La)TeXing rubikcube.ins, and then^^J process rubikcube.dtx again)^^J}\stop }% +\pagestyle{myheadings} +\markright{\texttt{rubikcube} \ \ (Rubik bundle v5.0, 2018) \ \ \texttt{www.ctan.org/pkg/rubik}} \usepackage{ifpdf} \usepackage{url,path} %% for references \usepackage{supertabular} %% for Notation table @@ -62,7 +64,7 @@ % % % -%%% \CheckSum{5683} +%%% \CheckSum{6231} % %%% \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 @@ -118,33 +120,39 @@ % % 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, and relates only to the -% familiar 3x3x3 Rubik cube. +% and macros for typesetting Rubik cube (3x3x3) configurations using the +% PGF/TikZ graphic languages. % 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 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, +% The \rubikcube\ package is the `base' package of the bundle, and is required by all of +% the Rubik packages; it deals primarily with typesetting 3x3x3 cube (Rubik cube) +% configurations. +% The \textsc{rubikrotation} package processes rotation sequences and keeps track of +% the cube's configuration during rotations. +% The \textsc{rubikpatterns} package is a small database of 3x3x3 (Rubik) cube rotation +% sequences which generate well-known named cube configurations (patterns). +% The \textsc{rubiktwocube} package allows the typesetting of 2x2x2 cube (Two cube) +% configurations. +% +% Full 3x3x3 functionality requires the following packages to be loaded +% (TikZ first; \textsc{rubikcube} second), as follows: %\begin{verbatim} -% \usepackage{tikz,rubikcube,rubikrotation,rubikpatterns} +% \usepackage{tikz} +% \usepackage{rubikcube,rubikrotation,rubikpatterns} %\end{verbatim} +% Full 2x2x2 functionality requires the \textsc{rubiktwocube} package \textit{in addition} to the +% packages listed above. % 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 GNU-Linux platform (Debian 8.2.0 -% and {\TeX}Live 2016), and on a Solaris platform (OpenIndiana). +% and {\TeX}Live 2017), 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), Hofstadter (1981), Hutchings~(2011), +% Davis (2006), Fung website, 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 @@ -152,7 +160,10 @@ % 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). +% (see References for details). +% +% For historical and technical details regarding Rubik's cube see Sher (2014), +% and also the Wikipedia article \textit{Rubik's Cube}. % % % \subsection{Requirements} @@ -161,9 +172,8 @@ % 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. +% The \textsc{rubikrotation} package (see below) +% requires Perl to be installed. % % % \subsection[rubikrotation package]{Supporting tool---the @@ -186,19 +196,19 @@ % package requires (a)~Perl to be installed, % 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. +% to the \texttt{shellesc} package (this can always be downloaded from CTAN directly). % See the \textsc{rubikrotation} documentation for further details. +% See also the examples in the file \texttt{RubikExamples.pdf}. % % % -% \subsection[rubikpatterns]{Supporting database---\textsc{rubikpatterns.sty} } +% \subsection[rubikpatterns]{Supporting database---\textsc{rubikpatterns} package } % \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 +% is a small database of some well-known 3x3x3 cube (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*)>} @@ -213,15 +223,30 @@ % \usepackage{tikz,rubikcube,rubikrotation,rubikpatterns} % ... % \RubikCubeSolved -% \RubikRotation{\fourspot} +% \RubikRotation{\fourspot} % this runs the Perl program \texttt{rubikrotation.pl} % \ShowCube{2.4cm}{0.6}{\DrawRubikCubeRU} %\end{verbatim} +% The sequence itself can be readily typeset using the \cmd{\ShowSequence} command +% (see Section~\ref{sec:showsequence}). % See also the \textsc{rubikrotation} documentation---especially -% Section~5.1.1 \textit{Sequences as macros}. +% Section~5.1.1 \textit{Sequences as macros}. +% See also the examples in the file \texttt{RubikExamples.pdf}. +% % % +% \subsection[rubiktwocube]{Supporting 2x2x2 package---\textsc{rubiktwocube} package } +% \label{sec:patterns} +% +% The \textsc{rubiktwocube} package carries the macros and commands necessary +% for processing and displaying 2x2x2 cubes (TwoCubes). The 2x2x2 commands are isomorphic +% with the 3x3x3 commands---i.e.,~the word `\texttt{Two}' has replaced the +% word `\texttt{Rubik}' in commands. +% Consequently, users of this package will need to be familiar with the \textsc{rubikcube} package. +% There are lots of 2x2x2 examples in the file \texttt{RubikExamples.pdf}. +% +% % \subsection{Copyright} -% Copyright 2014--2017 RWD Nickalls and A Syropoulos. +% Copyright 2014--2018 RWD Nickalls and A Syropoulos. % % \medskip % {\noindent}This work may be distributed and/or modified under the @@ -233,9 +258,11 @@ % % \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. +% The Rubik bundle consists of the four packages \rubikcube, \textsc{rubikrotation}, +% \textsc{rubikpatterns} and \textsc{rubiktwocube}. Although installing the Rubik bundle +% will typically install everything automatically (eg.,~from the {\TeX}Live DVD), +% each package can be installed separately if necessary. +% Here we detail only the \rubikcube\ package. % % \subsection{Generating the \rubikcube\ files} % @@ -276,14 +303,23 @@ % 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{RubikExamples file} +% +% Note that the package includes a `rubikexamples' file (\texttt{rubikexamples.pdf}), +% as well as the source file (\texttt{rubikexamples.tex}), and +% associated \texttt{.sh} (Linux) and \texttt{.bat} (Microsoft) batch +% files, which can be used to facilitate processing the source \texttt{.tex} file. +% The file \texttt{rubikexamples.pdf} showcases both 3x3x3 (Rubik cube) +% and 2x2x2 (Two cube) examples. +% +% Note that should you need to generate the file \texttt{rubikexamples.pdf} +% from the source file (\texttt{rubikexamples.tex}) you will require +% the \textsc{rubikrotation}, \textsc{rubikpatterns} and +% \textsc{rubiktwocube} packages to be installed, +% and will also need to use the \verb!--shell-escape! command-line +% option (see Section~\ref{sec:rubikrotation} for details). +% % % \subsection{Placing the files} % @@ -308,32 +344,92 @@ % \begin{quote} %\begin{verbatim} % \usepackage{tikz} -% \usepackage{rubikcube,rubikrotation,rubikpatterns} +% \usepackage{rubikcube,rubikrotation,rubikpatterns,rubiktwocube} %\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} and \textsc{rubikpatterns} packages. -% % -% \DescribeMacro{\rubikcube} -% This command generates the logo \rubikcube. +% While \rubikcube\ is a stand-alone package, for full 3x3x3 functionality it is necessary +% to load the complementary packages \textsc{rubikrotation}, \textsc{rubikpatterns}. +% For full 2x2x2 functionality you need to load all four packages. % % +% \pagebreak % % \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). +% Since all cubes are displayed or `drawn' using the TikZ picture environment, +% it is useful (initially at least) to categorise commands with regard to this environment +% (and also with regard to the \cmd{\ShowCube..} command since this +% is simply a convenient wrapper for the TikZ picture environment). +% On~this basis, we can distingush three conceptually useful categories, as follows: +% +% \begin{enumerate} +% +% \item \cmd{\Draw..} commands +% (which must \textit{always} be used \textit{inside} a TikZ picture environment), +% +% \item `parameter-allocation' commands (which can be used either inside +% or outside a TikZ environment); for example, \cmd{\RubikFace..} (for allocating +% facelet colours), and +% +% \item commands which can be used in ordinary text; for example, |\rr{}| (for typesetting +% certain rotation codes). +% +% \end{enumerate} +% From a functional point of view, however, we can view the Rubik bundle commands as +% splitting into the following groups: +% \begin{enumerate} % +% \item those that allocate colour +% to faces, facelets etc., ---these commands all start with \cmd{\Rubik} (for 3x3x3 cubes) or \cmd{\Two} +% (for 2x2x2 cubes \footnote{Requires the \textsc{rubiktwocube} package}), +% +% \item those that % draw ---these commands all start with \cmd{\Draw}, +% +% \item those that typeset rotation codes or hieroglyphs; +% ---there are just four of these for 3x3x3 cubes (these commands +% start with \cmd{\rr}, \cmd{\rrh}, \cmd{\Rubik}, +% and \cmd{\textRubik}), and an equivalent four commands for 2x2x2 cubes +% (these start with \cmd{\tr}, \cmd{\trh}, \cmd{\Two}, and \cmd{\textTwo}). +% +% \end{enumerate} + +% \medskip +% +% \DescribeMacro{\rubikcube} +% {\noindent}This command generates the logo \rubikcube. +% +% +% +% \subsection[Keywords Rubik and Two]{The keywords Rubik and Two in commands} +% \label{sec:rubikandtwo} +% +% In order to try and keep commands intuitive\,\footnote{This is a tricky problem +% given the large number of commands, so any feedback or ideas on how to avoid ambiguity, +% including pruning or revising `bad' commands, is always welcome.} +% we adopt the convention that +% the word `Rubik' in a command reflects the fact that the command +% relates to a 3x3x3 cube (i.e.,~a `Rubik' cube). Similarly, commands which relate +% to a 2x2x2 cube (a `Two' cube) ---see the \textsc{rubiktwocube} package--- +% use instead the word `Two'. +% For~example, the commands for drawing a 3x3x3 cube and a 2x2x2 cube from a RU viewpoint +% are respectively \cmd{\DrawRubikCubeRU} and \cmd{\DrawTwoCubeRU}. +% +% Having packages now for both 3x3x3 and 2x2x2 cubes (v5) means we need to be more careful regarding +% command names, and try to make commands (a)~as intuitive as possible, and (b)~use the +% same command name format for equivalent 3x3x3 and 2x2x2 commands (as shown in the example above). +% +% In keeping with this approach, some commands have had to be renamed. +% For~example, in this new version we have therefore renamed the +% earlier \cmd{\DrawFace..} commands $\rightarrow$ \cmd{\DrawRubikFace..} +% (see Section~\ref{sec:deprecated}). +% % % \subsection{Environments} % @@ -355,8 +451,9 @@ % % Consequently users need to be mindful of the environments when % 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. +% \cmd{\RubikRotation}, \cmd{\RubikFace..}, \cmd{\RubikCubeSolved}, +% outside the environments keeps their effects global +% (an example of this problem is presented in the file \texttt{RubikExamples.pdf}). % % % \subsection{Capital letters} @@ -388,7 +485,7 @@ % ---see Figure~\ref{fig:notation}. % % 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 +% for~example, the \cmd{\RubikSolvedConfig} 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. @@ -419,7 +516,7 @@ % 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. +% more details 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. @@ -452,12 +549,12 @@ % \section{Rubik cube coordinates} % \label{sec:coordinates} % -% The coordinate origin of all 2D Rubik cube images is located +% The coordinate origin of all 2D 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). +% extent of this particular 2D rendering of the 3x3x3 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 @@ -474,12 +571,13 @@ % \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 +% of the \textsc{front} face as the origin, is a useful design +% feature which make it easy to figure-out the coordinates of any point on +% the image plane (either on the cube or outside the cube), and hence +% facilitates the use of 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} @@ -509,8 +607,8 @@ % (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{pgfmanual.pdf}, version 3.0.1a (2015) (1161 pages) +% \item \texttt{pgfplot.pdf}, version 1.14 (2016) (561 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 @@ -531,8 +629,8 @@ % 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). +% or of a circle centre, or of text position +% (see Sections~\ref{sec:drawrubikcubecommands} and \ref{sec:arrows} for examples). % \begin{quote} % \begin{verbatim} % \draw[->,thick,color=blue] (4.5, 2.5) -- (3.5,2.5); @@ -560,7 +658,7 @@ %% \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) +% a \% symbol after the \verb!\end{tikzpicture}! command % to avoid additional white space inadvertently being added by \LaTeX\ % (see Section~\ref{sec:trailingpercent}). % @@ -586,8 +684,8 @@ % % \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 +% is a convenient tool for placing one or more commands inside a +% tikzpicture environment which is also 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!) @@ -603,7 +701,7 @@ % 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}. +% semicolon (see Section~\ref{sec:tikz}). % % \medskip % @@ -632,7 +730,7 @@ % % \medskip % -% {\noindent}The convenience of the \cmd{\ShowCube} command is illustrated below; the +% {\noindent}The action 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). % $$ @@ -657,12 +755,12 @@ % % \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 +% an \texttt{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 +% Consequently, a temporary \texttt{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. @@ -680,23 +778,67 @@ % \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 +% {\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 +% the horizontal 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{Optimum strategy} +% \label{sec:optimumstrategy} +% +% +% We suggest that the most convenient (and intuitive) approach for drawing +% cubes or particular faces is to do it in stages, as follows +% (all these steps are well illustrated in the examples file +% \texttt{RubikExamples.pdf}): +%\begin{itemize} +% \item first, start by setting the colour state of the cube. This can be done using +% either (a)~a \cmd{\RubikCubeSolved..} or \cmd{\RubikCubeGrey..} command +% (for defining the whole cube), or (b)~using one or more \cmd{\RubikFace..} +% commands (for defining parts of faces), or (c)~by imputting a file containing +% a previously saved colour state\footnote{See the \textsc{rubikrotation} package documentation +% for details of the \cmd{\SaveRubikState} command; see also the `SaveRubikState' example in the +% file \texttt{RubikExamples.pdf}.}. +% +% \item second, use the \cmd{\RubikRotation}\ command to process a sequence of rotations +% (remembering that this requires use of the \verb!--shell-escape! command-line option). +% The \textsc{rubikpatterns} package is a small library of named rotation sequences. +% +% \item third, draw the image(s) using \cmd{\DrawRubikCube..} or +% \cmd{\DrawRubikFace..} commands, plus any TikZ commands +% (e.g.,~\cmd{\draw} and/or \cmd{\node}) in conjunction with the \cmd{\ShowCube} command. +% Use the \cmd{\ShowCube} scale factor to adjust the size, and use the \cmd{\ShowCubeF} +% command to reveal the extent of any \texttt{minipage} whitespace. +% +% \item fourth, spacing between graphic elements can be influenced by adjusting either +% (a)~horizontal whitespace as set by the \cmd{\ShowCube} command, or (b)~using standard +% \TeX\ spacing commands, e.g.,~\cmd{\quad}, \cmd{\qquad}, \cmd{\hspace..} etc. +% +% \item finally, give some thought to using a trailing \verb!%! in commands which are +% broken across multiple lines (see Section~\ref{sec:trailingpercent}). +% +%\end{itemize} +% With this approach the internal colour state +% will be updated and processed correctly by all subsequent +% \cmd{\Draw..} or \cmd{\RubikRotation}\ commands. +% Note that exchanging the word `\texttt{Rubik}' for the word `\texttt{Two}' in a command will +% generate the equivalent TwoCube version of the command (see Section~\ref{sec:rubikandtwo}). +% +% +% % \section{Colour commands} % \label{sec:colours} % -% The \rubikcube\ package uses seven colours which are defined as follows: +% The Rubik bundle of packages uses seven colours which are defined as follows: % 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.} @@ -735,13 +877,26 @@ % White {HTML}{FFFFFF} %\end{verbatim} % \end{quote} -% However, we have optimised these prescribed colours very slightly +% +% {\noindent}The following RGB specifications are given by Sher (2014): +% \begin{quote} +%\begin{verbatim} +% White {RGB}{255,255,255} +% Red {RGB}{137,18,20} +% Blue {RGB}{13,72,172} +% Orange {RGB}{255,85,37} +% Green {RGB}{25,155,76} +% Yellow {RGB}{254,213,47} +%\end{verbatim} +% \end{quote} +% +% {\noindent}However, we have tried to optimise these prescribed colours very slightly % 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:\,\footnote{Although the Pantone +% 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 \texttt{https://en.wikipedia.org/wiki/Pantone}).} % (see Section~\ref{sec:codecolours}): % % \begin{quote} @@ -770,50 +925,62 @@ % \subsection{Colour state of the cube} % \label{sec:colourstate} % +% A given cubie facelet on a given face is denoted using an ordered sequence +% of three letters, as follows: first the face code (U,D,L,R,F,B), +% second the X-position of the column (l,m,r), +% and third the Y-position of the row (t,m,b). +% For example, the `right-bottom' facelet of the \textsc{front} face is denoted as +% \texttt{Frb}, and consequently the curent colour-code (R,O,Y,G,B,W,X) of this facelet +% is held as the variable \cmd{\Frb} etc.\ +% (see Section~\ref{sec:rubikfacecode} for details and code). +% % -% \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 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 +% Until a facelet is allocated one of the six cube colours (using a suitable command) +% it will be rendered as grey by a \cmd{\Draw...} command, since these commands % simply implement the current colour state of the cube (e.g.,~\cmd{\DrawRubikCubeRU}). +% Facelets retain their colour allocation even if they are moved using +% the \cmd{\RubikRotation} command (see \textsc{rubikrotation} package), unless they are +% overwritten by a subsequent colour allocation command. % -% 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 +% \DescribeMacro{\RubikFace..} +% \DescribeMacro{\RubikSlice..} +% \DescribeMacro{\RubikCubeSolved..} +% \DescribeMacro{\RubikCubeGrey..} +% \DescribeMacro{\RubikCubeGreyAll} +% Colours are allocated to facelets using using \cmd{\Rubik..} commands. +% For example, the commands \cmd{\RubikCubeSolvedWY} and \cmd{\RubikCubeSolvedWB} +% allocate prescribed colour states for the whole `solved' cube, and are +% a very useful starting point (configuration) for subsequent rotations. +% The commands \cmd{\RubikCubeGreyWY} 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. +% Colours can also be allocated to subsets of facelets (eg faces, slices etc); +% for example, using the +% commands \cmd{\RubikFace...} and \cmd{\RubikSlice...} +% commands (see Sections~\ref{sec:rubikfacecommands} and \ref{sec:slicecommands}). +% +% To visualise the current state of the cube one has to use a \cmd{\Draw...} command. +% \cmd{\Draw..} commands never influence the internal colour state of the +% cube.\footnote{That said, the now deprecated \cmd{\DrawRubikLayerFace...} +% and \cmd{\DrawRubikLayerSice...} commands +% (see Section~\ref{sec:deprecated}) did, confusingly, allow you to specify colours +% as arguments, but they only `painted' colours onto facelet positions +% (on the page, so to speak), and for this reason they are now deprecated, +% and will be phased out in due course.} +% +% The current colour state / configuration of a cube can also be saved and +% written to a named file, which can then be \cmd{\input} and processed later when required, +% using the \cmd{\SaveRubikState} command (3x3x3 cube) +% or \cmd{\SaveTwoState} command (2x2x2 cube). +% % -% 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} +% \label{sec:rubikfacecommands} % % \DescribeMacro{\RubikFaceUp} % \DescribeMacro{\RubikFaceDown} @@ -821,8 +988,9 @@ % \DescribeMacro{\RubikFaceRight} % \DescribeMacro{\RubikFaceFront} % \DescribeMacro{\RubikFaceBack} -% These commands take nine colour arguments and allocate colours to the -% individual cubies of a Rubik cube face. +% These commands allocate colours to the +% individual cubies of a 3x3x3 cube face; they take nine colour arguments +% (see Section~\ref{sec:rubikfacecode} for the code). % 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: @@ -838,10 +1006,9 @@ % } % \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 +% (e.g.,~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. +% allows the command to be written in several visually intuitive ways, as follows: % % \begin{quote} % \begin{minipage}{8cm} @@ -855,6 +1022,9 @@ %\end{verbatim} % \end{minipage} % \end{quote} +% 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) when it is rendered. % % \DescribeMacro{\RubikFaceUpAll} % \DescribeMacro{\RubikFaceDownAll} @@ -865,19 +1035,16 @@ % 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). +% For example, if you want the \textsc{right} face to be all orange, then +% use the command \cmd{\RubikFaceRightAll\{O\}}. +% Use of these commands is shown in the following example. % -% 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. % % \bigskip % % \begin{minipage}{2.8cm} -% \RubikFaceUpAll{X} -% \RubikFaceRightAll{R} +% \RubikCubeGreyAll +% \RubikFaceRightAll{O} % \RubikFaceFront{W}{Y}{G} % {W}{Y}{G} % {W}{Y}{G} @@ -888,30 +1055,50 @@ % \hspace{5mm} % \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \RubikFaceUpAll{X} -% \RubikFaceRightAll{R} +% \RubikCubeGreyAll +% \RubikFaceRightAll{O} % \RubikFaceFront{W}{Y}{G} % {W}{Y}{G} % {W}{Y}{G} % \ShowCube{3cm}{0.7}{\DrawRubikCubeRU} % \end{verbatim} % \end{minipage} -% % -% \subsection{Solved Configuration} -% \label{sec:solvedconfig} +% \bigskip +% +% +% Note that instead of using \cmd{\RubikCubeGreyAll} we could have used the +% command \verb!\RubikFaceUpAll{X}! to allocate grey to the whole of the +% \textsc{up} face. However, the \cmd{\RubikCubeGreyAll} command can be a useful +% starting point when dealing with a new cube, +% since it resets all the faces to their initial default colour. % -% \DescribeMacro{\SolvedConfig} +% Finally, it is important to bear in mind that when allocating colours using +% the \cmd{\RubikFace..} commands it is very +% easy to inadvertently create a non-valid cube (ie a cube with either the wrong number +% of facelets with particular colours, or one which has a non-sovable configuration). +% However, some basic error checking of this sort is done whenever the +% \cmd{\RubikRotation} command is used +% (see the \textsc{rubikrotation} package documentation). + +% +% +% \subsection{RubikSolvedConfig command} +% \label{sec:rubiksolvedconfig} +% +% \DescribeMacro{\RubikSolvedConfig} % 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}\textsc{usage}:\ \verb!\RubikSolvedConfig{G}{B}{W}{Y}{O}{R}! % {\newline}Examples of its use are shown in the next section. % % -% \subsection{RubikCubeSolved command} +% +% +% \subsection{RubikCubeSolved commands} % \label{sec:rubikcubesolved} % % \DescribeMacro{\RubikCubeSolved} @@ -919,9 +1106,9 @@ % 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: +% by invoking the above \cmd{\RubikSolvedConfig} command, as follows: %\begin{verbatim} -%\newcommand{\RubikCubeSolved}{\SolvedConfig{G}{B}{W}{Y}{O}{R}} +%\newcommand{\RubikCubeSolved}{\RubikSolvedConfig{G}{B}{W}{Y}{O}{R}} %\end{verbatim} % Note that this is in fact just a convenient short-hand for the following: %\begin{verbatim} @@ -958,17 +1145,17 @@ % % \bigskip % -% Note that the width of the minipage used in \cmd{\ShowCube} command above +% Note that the width of the minipage used in the \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). +% the TikZ scale factor is set to 0.5 (as in the above example) then the minimum minipage +% width = $10 \times 0.5 = 5$cm (see Section~\ref{sec:coordinates} for details). % % % \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 +% For~example, we could make a command to show the above solved cube upside-down % and rotated slightly, as follows: %\begin{verbatim} %\newcommand{\CubeUpSideDown}{\RubikCubeSolved\RubikRotation{x2,y}} @@ -1014,44 +1201,46 @@ % 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}! +% and green opposite yellow), was created using \verb!\RubikSolvedConfig{R}{O}{W}{B}{G}{Y}! % (for the code see \ref{sec:codesolvedconfig}). % % -% \subsection{RubikCubeGrey command} +% +% +% \subsection{RubikCubeGrey.. commands} % \label{sec:rubikcubegrey} % -% \DescribeMacro{\RubikCubeGrey} +% \DescribeMacro{\RubikCubeGreyWY} +% \DescribeMacro{\RubikCubeGreyWB} % \DescribeMacro{\RubikCubeGreyAll} -% The command \cmd{\RubikCubeGrey} generates a 3x3x3 cube with no colours allocated +% The command \cmd{\RubikCubeGreyWY} 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. +% configuration as defined for the \cmd{\RubikCubeSolvedWY} 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). +% completely grey; this is useful as it can be used to reset all the facelets to +% the initial default state. +% 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 +% These 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, +% the \cmd{\RubikCubeGreyWY} command by viewing the cube in a semi-flat (SF) format, % as follows: % % \bigskip % -% \RubikCubeGrey +% \RubikCubeGreyWY % \ShowCube{4.5cm}{0.45}{\DrawRubikCubeSF} % \hspace{3mm} % \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \RubikCubeGrey +% \RubikCubeGreyWY % \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. +% Users can of course set up their own alternative face/colour configuration +% by creating a new `variant' command altogether. % % % @@ -1106,77 +1295,6 @@ % % % -% \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} @@ -1194,7 +1312,7 @@ % \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 +% 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 @@ -1205,13 +1323,14 @@ % 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. +% 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 +% for typesetting 3x3x3 cubes\,\footnote{See the \textsc{rubiktwocube} package documentation +% for 2x2x2 cube commands.} 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 @@ -1225,10 +1344,9 @@ % in the form of the rotation-code in a square; for~example, \rrhBw, \rrhFm. % % -% \pagebreak % -% \subsection{Overview} -% \label{sec:overview} +% \subsection{Typesetting} +% \label{sec:typesetting} % % We now describe the four commands used for typesetting the various rotation-codes. % @@ -1315,7 +1433,7 @@ % \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. +% \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 @@ -1340,7 +1458,7 @@ % 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. +% formed by appending a `p'. The \texttt{M} must be in upper case. % % % \bigskip\bigskip @@ -1354,9 +1472,9 @@ % \DescribeMacro{Ep} % \DescribeMacro{Sp} % 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). +% 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), and the Roux method (Giles Roux). % \begin{itemize} % \item[\rr{M}] \ (\textsc{middle} \rrh{M}, between the \textsc{left} % and \textsc{right} faces; direction follows \rr{L}), @@ -1377,7 +1495,8 @@ % \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 +% 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\}}. @@ -1386,7 +1505,7 @@ % % \subsection{Outer-slice rotations} % -% \subsubsection*{Slice notation} +% \subsubsection*{The `s' (slice) notation} % % \DescribeMacro{Us} % \DescribeMacro{Ds} @@ -1427,7 +1546,7 @@ % % -% \subsubsection*{Anti-slice notation} +% \subsubsection*{The `a' (anti-slice) notation} % % \DescribeMacro{Ua} % \DescribeMacro{Da} @@ -1443,16 +1562,20 @@ % % \bigskip\bigskip % +% % \subsection{Wide rotations} % +% \subsubsection*{The `w' notation} +% \label{sec:wnotation} +% % \DescribeMacro{Uw} % \DescribeMacro{Dw} % \DescribeMacro{Lw} % \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, or a `double block' move) +% The clockwise \textit{combined} rotation of an outer face AND its adjacent inner-slice +% (officially known as a `double block', or `double outer slice' 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}!) @@ -1478,8 +1601,12 @@ % % \bigskip\bigskip % +% % \subsection{Axis rotations} % +% \subsubsection*{The x, y, z notation} +% \label{sec:xyznotation} +% % \DescribeMacro{x} % \DescribeMacro{y} % \DescribeMacro{z} @@ -1489,10 +1616,10 @@ % 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 lower-case; +% Note that since \rr{x}, \rr{y}, \rr{z}\ rotations are always expressed in lower case; % this practice is also extended to the commands. % -% For example, 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. @@ -1513,33 +1640,31 @@ % % \subsubsection*{The u, d, l, r, f, b notation} % +% % \DescribeMacro{u} % \DescribeMacro{d} % \DescribeMacro{l} % \DescribeMacro{r} % \DescribeMacro{f} % \DescribeMacro{b} -% A commonly used alternative for the \rr{x}, \rr{y}, \rr{z}\ notation -% (and endorsed by the WCA) uses these -% lower-case face letter to denote a 90~degree whole-cube rotation in the same -% directional sense as that of the standard face rotations. +% These are a commonly used alternative for the \rr{x}, \rr{y}, \rr{z}\ notation +% (and also endorsed by the WCA), and denote a 90~degree whole-cube rotation in the same +% directional sense as that of the associated face rotation. % % {\noindent}Thus -% \rr{u}\ $\equiv$ \rr{y}, \ \rr{d}\ $\equiv$ \rr{yp}, \ -% \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}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}. +% \rr{d}\ $\equiv$ \rr{up} $\equiv$ \rr{yp} etc. +% For~example, \rr{d}\ and \rr{dp}\ are generated by the commands \cmd{\rr\{d\}} +% and \cmd{\rr\{dp\}} respectively. +% Note that \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}, etc. % % 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\}}. % % +% \pagebreak +% % \subsubsection*{The `c' notation} % \label{sec:cnotation} % @@ -1602,7 +1727,7 @@ % {\noindent}\rr{U}\rr{U}\rr{R}\rr{R}\ is generated by % \cmd{\rr\{U\}}\cmd{\rr\{U\}}\cmd{\rr\{R\}}\cmd{\rr\{R\}} % -% \bigskip +% \medskip % % {\noindent}\Rubik{F}\Rubik{U}\Rubik{y}\Rubik{Rp}\Rubik{Lwp}\ % \ \ \verb!\Rubik{F}\Rubik{U}\Rubik{y}\Rubik{Rp}\Rubik{Lwp}! @@ -1612,28 +1737,31 @@ % {\noindent}\textRubik{F}\ \textRubik{U}\ \ \ \ % \verb!\textRubik{F}\ \textRubik{U}! % -% \bigskip +% \medskip % % {\noindent}Commas can be important in avoiding ambiguity; for~example, % -% \bigskip +% \medskip % % {\noindent}\rr{D},\rr{U}2,\rr{F}2,\rr{Ds}2,\rr{B}, \ \ \ \ \verb!\rr{U}2,\rr{F}2,\rr{Ds}2,\rr{B},! % -% \bigskip +% \medskip % -% {\noindent}\rrh{U}2,\,\rrh{F}2,\,\rrh{Ds}2,\, \ \ \ \ \verb!\rrh{U}2,\,\rrh{F}2,\,\rrh{Ds}2,! +% {\noindent}\rrh{U}2,\,\rrh{F}2,\,\rrh{Ds}2,\, \ \ \ \ \verb!\rrh{U}2,\,\rrh{F}2,\,\rrh{Ds}2! % -% \bigskip +% \medskip +% +% {\noindent}Finally, if each rotation element uses the \textit{same} font or encoding, for~example +% +% \medskip % % {\noindent}\rrh{F}\rrh{U}\rrh{y}\rrh{Rp}\rrh{Lwp} \ \ \ \ % \verb!\rrh{F}\rrh{U}\rrh{y}\rrh{Rp}\rrh{Lwp}! % -% \bigskip +% \medskip % -% 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 +% {\noindent}then typesetting such 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 @@ -1650,9 +1778,7 @@ % 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} @@ -2004,21 +2130,44 @@ % \dnstrut\rr{u}\dns\cmd{\rr\{u\}} % & \rrh{u}\dns\cmd{\rrh\{u\}} % & \Rubik{u}\dns\cmd{\Rubik\{u\}} \nonumber\\ +% \dnstrut\rr{up}\dns\cmd{\rr\{up\}} +% & \rrh{up}\dns\cmd{\rrh\{up\}} +% & \Rubik{up}\dns\cmd{\Rubik\{up\}} \nonumber\\ +% % \dnstrut\rr{d}\dns\cmd{\rr\{d\}} % & \rrh{d}\dns\cmd{\rrh\{d\}} % & \Rubik{d}\dns\cmd{\Rubik\{d\}} \nonumber\\ +% \dnstrut\rr{dp}\dns\cmd{\rr\{dp\}} +% & \rrh{dp}\dns\cmd{\rrh\{dp\}} +% & \Rubik{dp}\dns\cmd{\Rubik\{dp\}} \nonumber\\ +% % \dnstrut\rr{l}\dns\cmd{\rr\{l\}} % & \rrh{l}\dns\cmd{\rrh\{l\}} % & \Rubik{l}\dns\cmd{\Rubik\{l\}} \nonumber\\ +% \dnstrut\rr{lp}\dns\cmd{\rr\{lp\}} +% & \rrh{lp}\dns\cmd{\rrh\{lp\}} +% & \Rubik{lp}\dns\cmd{\Rubik\{lp\}} \nonumber\\ +% % \dnstrut\rr{r}\dns\cmd{\rr\{r\}} % & \rrh{r}\dns\cmd{\rrh\{r\}} -% & \Rubik{r}\dns\cmd{\Rubik\{r\}} \nonumber\\ +% & \Rubik{r}\dns\cmd{\Rubik\{r\}} \nonumber\\ +% \dnstrut\rr{rp}\dns\cmd{\rr\{rp\}} +% & \rrh{rp}\dns\cmd{\rrh\{rp\}} +% & \Rubik{rp}\dns\cmd{\Rubik\{rp\}} \nonumber\\ +% % \dnstrut\rr{f}\dns\cmd{\rr\{f\}} % & \rrh{f}\dns\cmd{\rrh\{f\}} -% & \Rubik{f}\dns\cmd{\Rubik\{f\}} \nonumber\\ +% & \Rubik{f}\dns\cmd{\Rubik\{f\}} \nonumber\\ +% \dnstrut\rr{fp}\dns\cmd{\rr\{fp\}} +% & \rrh{fp}\dns\cmd{\rrh\{fp\}} +% & \Rubik{fp}\dns\cmd{\Rubik\{fp\}} \nonumber\\ +% % \dnstrut\rr{b}\dns\cmd{\rr\{b\}} % & \rrh{b}\dns\cmd{\rrh\{b\}} % & \Rubik{b}\dns\cmd{\Rubik\{b\}} \nonumber\\ +% \dnstrut\rr{bp}\dns\cmd{\rr\{bp\}} +% & \rrh{bp}\dns\cmd{\rrh\{bp\}} +% & \Rubik{bp}\dns\cmd{\Rubik\{bp\}} \nonumber\\ % \end{supertabular} % % @@ -2104,10 +2253,10 @@ % % 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) +% letters (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 +% 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 @@ -2135,19 +2284,30 @@ % % \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. +% A \cmd{\Draw..} command typesets either a cubie, cube or face +% using parameters set or defined via +% previous parameter-allocation commands (e.g.,~colours, dimensions etc). % % It is important to distinguish between the \rubikcube\ package \cmd{\Draw..} commands -% and TikZ \cmd{\draw..} commands. \cmd{\Draw..} commands are implemented by the +% (with an upper-case~D) and TikZ \cmd{\draw..} commands (with a lowercase~d). +% Rubik \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.. +% See also Section~\ref{sec:drawerrormessage} below. % +% There are six types of \cmd{\Draw..} commands, as follows: +% \begin{quote} +% \noindent\cmd{\DrawCubie..} +% \newline\noindent\cmd{\DrawRubikCube..} +% \newline\noindent\cmd{\DrawRubikCubeSidebar..} +% \newline\noindent\cmd{\DrawRubikFace..} +% \newline\noindent\cmd{\DrawRubikFlat..} +% \newline\noindent\cmd{\DrawNCube..} +% \end{quote} +% Note that the former \cmd{\DrawRubikLayer..}, \cmd{\DrawCube..}, \cmd{\DrawFace..} +% commands are now deprecated, since they have +% been superseded by more versatile and intuitive commands (see Section~\ref{sec:deprecated}). % % % \subsection[Error message]{\cmd{\Draw} error message} @@ -2169,62 +2329,23 @@ % then something similar to the following error message will be generated. %\begin{verbatim} %! Undefined control sequence. -%\DrawFlatUp ... }{#1}\pgfmathsetmacro {\uy }{#2}\draw +%\DrawRubikFlatUp ... }{#1}\pgfmathsetmacro {\uy }{#2}\draw % [line join=round,... %l.56 \DrawRubikCubeF %\end{verbatim} % % % +% \subsection{DrawCubie commands} +% \label{sec:drawcubie} % -% \subsection{DrawRubikCube commands} -% -% \DescribeMacro{\DrawRubikCubeXY} -% \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} -% will draw a Rubik cube as viewed from the RightUp direction (RU), as -% shown in the following figure. -% -% \bigskip -% -% \begin{minipage}{2.8cm} -% \begin{tikzpicture}[scale=0.7] -% \DrawRubikCubeRU -% \end{tikzpicture}% -% \end{minipage} -% \hspace{5mm} -% \begin{minipage}{0.6\textwidth} -%\begin{verbatim} -% \RubikCubeSolved -% \begin{tikzpicture}[scale=0.7] -% \DrawRubikCubeRU -% \end{tikzpicture}% -%\end{verbatim} -% Note that the above commands are equivalent to: -%\begin{verbatim} -% \RubikCubeSolved -% \ShowCube{3cm}{0.7}{\DrawRubikCubeRU} -%\end{verbatim} -% \end{minipage} -% -% \bigskip -% -% -% \DescribeMacro{\DrawCubieXYxyz} +% \DescribeMacro{\DrawCubieXY} % This command draws a single cubie in one of four % orientations as denoted by the terminal XY viewing-direction % codes. -% Since a single cubie has only three visible faces we can include -% colour parameters in \cmd{\DrawCubie} commands. Consequently \cmd{\DrawCubie} -% commands have the format +% Since a single cubie has only three visible faces this command takes three +% xyz-ordered colour parameter arguments. Consequently the \cmd{\DrawCubie} +% command has the format % \begin{quote} % \cmd{\DrawCubieXY\{x\}\{y\}\{z\}} % \end{quote} @@ -2259,13 +2380,13 @@ % \else % \includegraphics[height=4cm]{rubik-doc-figC.eps} % \fi -% \vspace{-5mm}\caption{\label{fig:cubiedydx}Cubie dy dx parameters} +% \vspace{-5mm}\caption{\label{fig:cubiedydx}Cubiedy and Cubiedx parameters} % \end{figure} % % \DescribeMacro{\Cubiedy} % \DescribeMacro{\Cubiedx} % Minor cubie configuration changes can be effected -% by adjusting the dy and dx values ($> 0$; no units) +% by adjusting the Cubiedy and Cubiedx values ($> 0$; no units) % shown in Figure~\ref{fig:cubiedydx} via the two commands % \begin{quote} % \cmd{\Cubiedy\{\}} \\ @@ -2296,9 +2417,11 @@ % {\noindent}Note that the \textsc{front} face of the cubie is a unit square, % and the graphic origin of the cubie image is at the bottom left corner of the % \textsc{front} face (see also the section on Arrows: Section~\ref{sec:arrows}). -% The default values of dy and dx are 0.4. +% The default values of \cmd{\Cubiedy} and \cmd{\Cubiedx} are 0.4. +% % -% \medskip +% +% \subsection{textCubie commands} % % \DescribeMacro{\textCubieRU} % \DescribeMacro{\textCubieRD} @@ -2325,67 +2448,40 @@ % \cmd{\Cubiedy}, \cmd{\Cubiedx} commands as their size is pre-set for text use. % % -% -% \subsection{Flat commands} -% \label{sec:flatcommands} -% -% \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. -% -% 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: +% \subsection{DrawRubikCube commands} +% \label{sec:drawrubikcubecommands} % -% \bigskip -% -% \begin{minipage}{0.4\textwidth} -% \centering -% \RubikCubeSolved -% \begin{tikzpicture}[scale=0.4] -% \DrawRubikCubeRU -% \DrawFlatBack{4}{1} -% \end{tikzpicture}% -% \end{minipage} -% \begin{minipage}{5cm} +% \DescribeMacro{\DrawRubikCubeXY} +% \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} +% will draw a Rubik cube as viewed from the RightUp direction (RU), as +% shown in the following figure. +% +% \bigskip +% +% \begin{minipage}{2.8cm} +% \begin{tikzpicture}[scale=0.7] +% \RubikCubeSolvedWY +% \DrawRubikCubeRU +% \end{tikzpicture}% +% \end{minipage} +% \hspace{5mm} +% \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \RubikCubeSolved -% \ShowCube{3cm}{0.4}{% -% \DrawRubikCubeRU -% \DrawFlatBack{4}{1} -% } +% \RubikCubeSolvedWY +% \ShowCube{3cm}{0.7}{\DrawRubikCubeRU} %\end{verbatim} -% \end{minipage} -% +% \end{minipage} +% % \bigskip % % \DescribeMacro{\DrawRubikCubeF} @@ -2396,7 +2492,7 @@ % \begin{minipage}{0.4\textwidth} % \centering % \begin{tikzpicture}[scale=0.4] -% \RubikCubeSolved +% \RubikCubeSolvedWY % \DrawRubikCubeF % \node (U) at (1.5, 4.5) [black]{\small\textsf{U}}; % \node (D) at (1.5, -1.5) [black]{\small\textsf{D}}; @@ -2408,7 +2504,7 @@ % \end{minipage} % \begin{minipage}{5cm} %\begin{verbatim} -% \RubikCubeSolved +% \RubikCubeSolvedWY % \ShowCube{5cm}{0.4}{\DrawRubikCubeF} %\end{verbatim} % \end{minipage} @@ -2419,7 +2515,8 @@ % 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. +% TikZ picture environment +% (remember TikZ commands require a terminal semi-colon~;). % %\begin{verbatim} % \RubikCubeSolved @@ -2431,7 +2528,7 @@ % \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{\DrawRubikCubeSF} @@ -2444,19 +2541,19 @@ % % \begin{minipage}{5cm} % \begin{tikzpicture}[scale=0.5] -% \RubikCubeSolved +% \RubikCubeSolvedWY % \DrawRubikCubeSF % \node (B) at (5.5, 2.5) [white]{\small\textsf{B}}; % \end{tikzpicture}% % \end{minipage} % \begin{minipage}{5cm} %\begin{verbatim} -% \RubikCubeSolved +% \RubikCubeSolvedWY % \ShowCube{5cm}{0.5}{% % \DrawRubikCubeSF % \node (B) at (5.5, 2.5) % [white]{\small\textsf{B}}; -% } +% } %\end{verbatim} % \end{minipage} % @@ -2468,352 +2565,139 @@ % 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 +% corner of the \textsc{front} face (the orange face here), the ($x,y$) coordinates % of the centre of the red \textsc{back} face are easily determined to be (5.5, 2.5). % % -% \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}. % -% 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. +% \subsection{DrawRubikFace.. commands} +% \label{sec:drawrubikfacecommands} % -% \bigskip -% -% \begin{minipage}{0.4\textwidth} -% \centering -% \RubikCubeSolved -% \begin{tikzpicture}[scale=0.4] -% \DrawFaceUpSide -% \end{tikzpicture}% -% \end{minipage} -% \begin{minipage}{5cm} -%\begin{verbatim} -% \RubikCubeSolved -% \ShowCube{1.6cm}{0.4}{% -% \DrawFaceUpSide -% } -%\end{verbatim} -% \end{minipage} % -% \vspace{1cm} +% \DescribeMacro{\DrawRubikFaceUp} +% \DescribeMacro{\DrawRubikFaceDown} +% \DescribeMacro{\DrawRubikFaceLeft} +% \DescribeMacro{\DrawRubikFaceRight} +% \DescribeMacro{\DrawRubikFaceFront} +% \DescribeMacro{\DrawRubikFaceBack} +% \DescribeMacro{\DrawRubikFaceUpSide} +% \DescribeMacro{\DrawRubikFaceDownSide} +% \DescribeMacro{\DrawRubikFaceLeftSide} +% \DescribeMacro{\DrawRubikFaceRightSide} +% \DescribeMacro{\DrawRubikFaceFrontSide} +% \DescribeMacro{\DrawRubikFaceBackSide} +% These commands draw the current state of a specified face +% (e.g.,~\cmd{\DrawRubikFaceUp}), or the face and all the associated sidebars +% (e.g.,~\cmd{\DrawRubikFaceUpSide}). These commands do \textsc{not} take any +% arguments---for code see Section~\ref{sec:drawrubikfacecode}. % +% \textsc{Note}: These commands replace the earlier +% \cmd{\DrawFace...} commands (see Section~\ref{sec:deprecated}). % -% \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). +% For example, a simple way to show the yellow-cross configuration in +% the \textsc{up}~face would be to first define the colours using +% the \cmd{\RubikFaceUp} command, and then draw the \textsc{up} face +% using the \cmd{\DrawRubikFaceUp} command, as follows: % % \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} +% \RubikFaceUp{X}{Y}{X} +% {Y}{Y}{Y} +% {X}{Y}{X} +% \ShowCube{2.1cm}{0.7}{\DrawRubikFaceUp} +% \hspace{1cm} +% \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \ShowCube{3.5cm}{0.5}{\DrawNCubeAll{5}{O}{Y}{G}} +% \RubikFaceUp{X}{Y}{X} +% {Y}{Y}{Y} +% {X}{Y}{X} +% \ShowCube{2.1cm}{0.7}{\DrawRubikFaceUp} %\end{verbatim} % \end{minipage} % % % +% \subsection[Drawing Sidebars (Face)]{Sidebars \& DrawRubikFaceXSide commands} +% \label{sec:sidebars} % % -% \subsection{LayerFace} -% \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. -% -% 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}). -% +% In the next example we use the \cmd{\DrawRubikFaceUpSide} command to +% draw the \textsc{up}~face and all its sidebars in a cube having +% a `solved' WY (White opposite Yellow) configuration. % -% \DescribeMacro{\DrawRubikLayerFace} -% \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 -% -% \ShowCube{2.1cm}{0.7}{% -% \DrawRubikLayerFace{X}{Y}{X} -% {Y}{Y}{Y} -% {X}{Y}{X} -% }% -% \hspace{1cm} +% +% \RubikCubeSolvedWY +% \ShowCube{1.6cm}{0.5}{\DrawRubikFaceUpSide} +% \hspace{1cm} % \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \ShowCube{2.1cm}{0.7}{% -% \DrawRubikLayerFace{X}{Y}{X} -% {Y}{Y}{Y} -% {X}{Y}{X} -% } +% \RubikCubeSolvedWY +% \ShowCube{1.6cm}{0.5}{\DrawRubikFaceUpSide} %\end{verbatim} % \end{minipage} % % \bigskip +% +% \noindent\textbf{Short-hand versions}: For convenience each of these commands +% has an equivalent short-hand version generated by using just the first letter of the +% face name and (where appropriate) the first letter of the word Side. For~example, +% \newline\cmd{\DrawRubikFaceR} $\equiv$ \cmd{\DrawRubikFaceRight}, +% \newline \cmd{\DrawRubikFaceRS} $\equiv$ \cmd{\DrawRubikFaceRightSide}, etc. % -% {\noindent}The \cmd{\DrawRubikLayerFaceAll} command takes a single colour argument, and paints -% the whole face the same colour. % -% \medskip % -% \subsection{LayerSide (sidebars)} -% \label{sec:layerside} \label{sec:sidebars} -% -% \DescribeMacro{\DrawRubikLayerSideXYp} -% LayerSide commands draw the associated side colours of -% 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, -% as depicted in Figure~\ref{fig:facenotation}. % -% \begin{figure}[hbt] -% \centering -% \ifpdf -% \includegraphics[height=3cm]{rubik-doc-figD.pdf} -% \else -% \includegraphics[height=3cm]{rubik-doc-figD.eps} -% \fi -% \vspace{-5mm}\caption{\label{fig:facenotation}LayerSide rotation-codes } -% \end{figure} -% -% Since corner cubies have two side faces, the `p' parameter -% (p:[x\verb!|!y]) is required to denote the directional `position' of -% the cubie side-face relative to the cubicle XY position -% (x indicates adjacent along the x-axis, and y indicates adjacent along the y-axis). -% Since edge cubies have only one side face, the `p' parameter is optional -% (for consistency), since it is not strictly necessary. -% -% \medskip\noindent\textbf{Commands}: \ -% 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 % -% \begin{quote} -%\begin{verbatim} -% \DrawRubikLayerSideLM{G} -% \DrawRubikLayerSideLMx{G} -%\end{verbatim} -% \end{quote} -% draws a single small vertical green rectangle -% \begin{tikzpicture}[scale=0.5] -% \DrawRubikLayerSideLMx{G} -% \end{tikzpicture}% -% just to the left of the Left Middle (LM) square of the 9-face. -% The following commands draw all three side bars of a given side (Top, Bottom, Left, Right) -% \begin{quote} -%\begin{verbatim} -% \DrawRubikLayerSideT{}{}{} -% \DrawRubikLayerSideB{}{}{} -% \DrawRubikLayerSideL{}{}{} -% \DrawRubikLayerSideR{}{}{} -%\end{verbatim} -% \end{quote} -% where the T and B forms require the colour parameters to be in left-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 (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} -%\begin{verbatim} -% \DrawRubikLayerSideL{} -% {} -% {} -%\end{verbatim} -% \end{quote} -% Extending this idea, the L and R forms are combined in the LR command, -% which takes six colour arguments ordered in left-right pairs, -% \begin{quote} -%\begin{verbatim} -% \DrawRubikLayerSideLR{}{} {}{} {}{} -%\end{verbatim} -% \end{quote} -% so that they can also be written vertically as left-right pairs. -% Use of these commands is shown in the following two examples. -% -% \bigskip -% -% \begin{minipage}{2.5cm} -% \centering -% \begin{tikzpicture}[scale=0.7] -% -% -% \DrawRubikLayerFace{X}{Y}{X} -% {Y}{Y}{Y} -% {X}{Y}{X} -% -% \DrawRubikLayerSideLTy{B} -% \DrawRubikLayerSideLTx{O} -% \DrawRubikLayerSideLM{G} -% \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}}; -% \end{tikzpicture}% -% \end{minipage} -% \hspace{1cm} -% \begin{minipage}{0.6\textwidth} -%\begin{verbatim} -% \ShowCube{3cm}{0.7}{% -% \DrawRubikLayerFace{X}{Y}{X} -% {Y}{Y}{Y} -% {X}{Y}{X} -% -% \DrawRubikLayerSideLTy{B} -% \DrawRubikLayerSideLTx{O} -% \DrawRubikLayerSideLM{G} -% -% \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}}; -% } -%\end{verbatim} -% \end{minipage} -% -% \bigskip -% -% \begin{minipage}{2.5cm} -% \centering -% \begin{tikzpicture}[scale=0.7] -% -% \DrawRubikLayerFace{G}{Y}{R} -% {Y}{Y}{Y} -% {B}{Y}{Y} -% -% \DrawRubikLayerSideT {Y}{B}{B} -% \DrawRubikLayerSideLR{R} {Y} -% {R} {O} -% {Y} {O} -% \DrawRubikLayerSideB {O}{G}{G} -% -% \end{tikzpicture}% -% \end{minipage} -% \hspace{1cm} -% \begin{minipage}{0.6\textwidth} -%\begin{verbatim} -% \ShowCube{3cm}{0.7}{% -% \DrawRubikLayerFace{G}{Y}{R} -% {Y}{Y}{Y} -% {B}{Y}{Y} -% -% \DrawRubikLayerSideT {Y}{B}{B} -% \DrawRubikLayerSideLR{R} {Y} -% {R} {O} -% {Y} {O} -% \DrawRubikLayerSideB {O}{G}{G} -% } -%\end{verbatim} -% \end{minipage} -% -% \bigskip -% -% \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{\DrawFaceUpSide} command, -% as described in Section~\ref{sec:facecommands}. -% -% \bigskip +% \subsection{Sidebar parameters} +% \label{sec:sidebarparameters} % -% \DescribeMacro{\RubikSideBarWidth} -% \DescribeMacro{\RubikSideBarLength} -% \DescribeMacro{\RubikSideBarSep} +% \DescribeMacro{\RubikSidebarWidth} +% \DescribeMacro{\RubikSidebarLength} +% \DescribeMacro{\RubikSidebarSep} % The default values (size) of the sidebars are as follows: -% width (0.3), length(1) and separation from the square face (0.3). +% width (0.3), length(1) and separation from the square face (0.3) +% ---see Section~\ref{sec:sidebarcode} for the code. % Note that the default value of the length of a cubie side is 1. % These sidebar values (decimal values $\geq 0$; no units) can be % changed from their default values using the three commands. % \begin{quote} -% \cmd{\RubikSideBarWidth\{\}}\hspace{35.751pt}(default = 0.3)\\ -% \cmd{\RubikSideBarLength\{\}}\hspace{30pt}(default = 1.0)\\ -% \cmd{\RubikSideBarSep\{\}}\hspace{46.251pt}(default = 0.3) +% \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 in position MTy using the command -% \verb!\DrawRubikLayerSideMTy{G}! (for the MTy code see Figure~\ref{fig:facenotation}). +% particular environment. Alternatively, one can keep the effect local +% using braces (see below). +% +% In the following example, we show the effect +% on the \textsc{up} face and sidebars of a normally solved (WY) cube +% after dramatically changing the sidebar width, length and separation +% from the default values---compare with the previous image. +% For~convenience, we have used a pair of braces +% to keep the effect local to this example. % % \bigskip % -% \begin{minipage}{2.5cm} -% \centering -% \begin{tikzpicture}[scale=0.7] -% -% -% \DrawRubikLayerFace{X}{Y}{X} -% {Y}{Y}{Y} -% {X}{Y}{X} -% -% \RubikSideBarWidth{0.7} -% \RubikSideBarLength{0.7} -% \DrawRubikLayerSideMTy{G} -% \end{tikzpicture}% -% \end{minipage} -% \hspace{1cm} +% { +% \RubikCubeSolvedWY +% \RubikSidebarWidth{0.8} +% \RubikSidebarLength{0.5} +% \RubikSidebarSep{0.7} +% \ShowCube{2cm}{0.5}{\DrawRubikFaceUpSide} +% } +% \hspace{2cm} % \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \ShowCube{3cm}{0.7}{% -% \DrawRubikLayerFace{X}{Y}{X} -% {Y}{Y}{Y} -% {X}{Y}{X} -% \RubikSideBarWidth{0.7} -% \RubikSideBarLength{0.7} -% \DrawRubikLayerSideMTy{G} -% } +% { +% \RubikCubeSolvedWY +% \RubikSidebarWidth{0.8} +% \RubikSidebarLength{0.5} +% \RubikSidebarSep{0.7} +% \ShowCube{2cm}{0.5}{\DrawRubikFaceUpSide} +% } %\end{verbatim} % \end{minipage} % @@ -2824,70 +2708,248 @@ % to visualise this) and may therefore require some fine-tuning of the % minipage width setting in order to optimise appearance. % -% 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. 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 ($=5 \times 0.7$). -% +% +% +% +% \subsection[NoSidebar command]{\cmd{\NoSidebar} command} +% \label{sec:nosidebar} +% +% \DescribeMacro{\NoSidebar} +% The \cmd{\NoSidebar}\marg{colour-code} command +% (which takes a single colour code argument) +% allows the user to disable the drawing of sidebars having a particular colour +% (for code see Section~\ref{sec:nosidebarcode}). +% Its action can be localised by placing the command inside an environment +% (e.g.,~inside the \verb!\ShowCube! environment). +% Alternatively, the action of this command can be disabled simply by writing it with an empty +% argument, e.g.,~\verb!\NoSidebar{}!. +% +% This command is designed to facilitate the drawing of so-called +% OLL (Orientate Last Layer) configurations, +% which are typically rendered using the yellow face. +% +% For~example, the following figure uses the \verb!\DrawRubikFaceUpSide! command to +% draw the commonly encountered OLL configuration known as the `yellow cross' +% (the remaining four yellow facelets associated with this layer are shown as sidebars). +% In this example, we first define the colours for the whole cube (grey), and then +% redefine the colours for the \textsc{up}~face and its four adjacent faces. +% Finally we draw the \textsc{up}~face and sidebars; we also show an alternative +% way of writing the facelet colour codes (ie without using the curly brackets). +% +% \bigskip +% +% \begin{minipage}{3cm} +% \RubikCubeGreyAll +% \RubikFaceUp XYX +% YYY +% XYX +% \RubikFaceFront YXY XXXXXX +% \RubikFaceRight XXY XXXXXX +% \RubikFaceBack XXX XXXXXX +% \RubikFaceLeft YXX XXXXXX +% \ShowCube{2.6cm}{0.6}{\DrawRubikFaceUpSide} +% \end{minipage} +% \hspace{4mm} +% \begin{minipage}{5cm} +% \begin{verbatim} +% \RubikCubeGreyAll +% \RubikFaceUp XYX +% YYY +% XYX +% \RubikFaceFront YXY XXXXXX +% \RubikFaceRight XXY XXXXXX +% \RubikFaceBack XXX XXXXXX +% \RubikFaceLeft YXX XXXXXX +% \ShowCube{2.6cm}{0.6}{\DrawRubikFaceUpSide} +% \end{verbatim} +% \end{minipage} +% \bigskip +% +% {\noindent}However, we can greatly improve the OLL image by +% disabling the drawing of all the grey (X) sidebars by using the +% \verb!\NoSidebar{X}! command as follows (here we have placed the +% \verb!\NoSidebar{X}! command inside the \verb!\ShowCube! environment +% in order to limit its action locally). Note also that this time we +% have used the short-hand US (UpSide) version of the +% \cmd{\DrawRubikFaceUpSide} command. +% +% \bigskip +% +% \begin{minipage}{3cm} +% \RubikCubeGreyAll +% \RubikFaceUp XYX +% YYY +% XYX +% \RubikFaceFront YXY XXXXXX +% \RubikFaceRight XXY XXXXXX +% \RubikFaceBack XXX XXXXXX +% \RubikFaceLeft YXX XXXXXX +% \ShowCube{2.6cm}{0.6}{\NoSidebar{X}\DrawRubikFaceUS} +% \end{minipage} +% \hspace{4mm} +% \begin{minipage}{5cm} +% \begin{verbatim} +% \RubikCubeGreyAll +% ... +% ... +% \ShowCube{2.6cm}{0.6}{\NoSidebar{X}% +% \DrawRubikFaceUS% +% } +% \end{verbatim} +% \end{minipage} +% +% \bigskip +% +% +% +% \subsection[Drawing Sidebars (Cube)]{Cube sidebars \& DrawRubikCubeSidebar commands} +% \label{sec:sidebarscube} +% +% +% +% +% Cube sidebars are drawn adjacent to cube edges which are +% defined by the two faces forming the edge. +% Thus the BR (Back-Right) sidebar is placed adjacent to the +% edge formed by the \textsc{back} and \textsc{right} faces. +% +% Since the cube orientation (view direction; RU, RD, LU, LD) +% determines which sidebars are visible, the command for drawing +% the sidebar (\texttt{DrawRubikCubeSidebar..}) also needs to +% incorporate the view direction. The command takes +% two mandatory arguments: the first is the pair of face codes defining the edge (XX); +% the second is the view direction, as follows: +% \begin{quote} +% \cmd{\DrawRubikCubeSidebarXX}\marg{view direction} +% +% \textsc{example:} \verb!\DrawRubikCubeSidebarRB{LD}! +% \end{quote} +% Note that the pair of face codes are order \textit{independent}, +% and hence can be written in any order, which makes remembering the commands very easy. +% +% Note also that at present commands are only available for the +% eight sidebars which are parallel to X,Y axes, as these seem +% to be the most useful. +% +% In the following example, we input a previously saved cube state +% (in the file \texttt{cubestate-A.tex}) and draw the cube and the +% four main sidebars (BR, BD, FL, FU) visible from the RD view direction. +% +% \bigskip +% +% \RubikFaceUp{O}{G}{Y}{B}{B}{O}{R}{B}{G}% +% \RubikFaceDown{Y}{R}{B}{R}{W}{O}{W}{Y}{R}% +% \RubikFaceLeft{Y}{G}{W}{W}{Y}{R}{O}{W}{B}% +% \RubikFaceRight{B}{B}{B}{W}{G}{O}{R}{G}{W}% +% \RubikFaceFront{G}{R}{O}{Y}{R}{O}{R}{G}{G}% +% \RubikFaceBack{O}{W}{W}{Y}{O}{Y}{Y}{B}{G}% +% \ShowCube{4cm}{0.6}{ +% \DrawRubikCubeRD +% \DrawRubikCubeSidebarBR{RD} +% \DrawRubikCubeSidebarBD{RD} +% \DrawRubikCubeSidebarFL{RD} +% \DrawRubikCubeSidebarFU{RD} +% } +% \begin{minipage}{5cm} +%\begin{verbatim} +% \input{cubestate-A.tex} +% \ShowCube{3cm}{0.6}{ +% \DrawRubikCubeRD +% \DrawRubikCubeSidebarBR{RD} +% \DrawRubikCubeSidebarBD{RD} +% \DrawRubikCubeSidebarFL{RD} +% \DrawRubikCubeSidebarFU{RD} +% } +%\end{verbatim} +% \end{minipage} +% +%\bigskip +% +% +% +% +% \subsection{DrawRubikFlat commands} +% \label{sec:drawrubikflatcommands} +% +% \DescribeMacro{\DrawRubikFlatUp} +% \DescribeMacro{\DrawRubikFlatDown} +% \DescribeMacro{\DrawRubikFlatLeft} +% \DescribeMacro{\DrawRubikFlatRight} +% \DescribeMacro{\DrawRubikFlatFront} +% \DescribeMacro{\DrawRubikFlatBack} +% The \cmd{\DrawRubikFlat..}\marg{x}\marg{y} commands draw a `flat' square +% representation of a specified face, located such that its +% bottom left corner is positioned at ($x,y$). +% Each command (except \cmd{\DrawRubikFlatFront}) 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 (see Section~\ref{sec:codedrawrubikflatcommands} for the code). +% +% These commands are designed to supplement the \cmd{\DrawRubikCube...} commands and +% allow hidden faces to be represented. +% +% Note also that the \cmd{\DrawRubikFlatFront} 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}:\ The following example uses the command \verb!\DrawRubikFlatBack{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!\DrawRubikFlatBack{4}{1}! as follows: +% % \bigskip % -% \begin{minipage}{4cm} +% \begin{minipage}{0.4\textwidth} % \centering -% \RubikFaceUp {X}{W}{X}% -% {W}{W}{W}% -% {X}{W}{X}% -% -% \RubikFaceFront{O}{O}{X}% -% {O}{O}{X}% -% {X}{X}{W}% -% -% \RubikFaceRight{X}{G}{G}% -% {X}{G}{G}% -% {G}{X}{X}% -% \ShowCubeF{3.5cm}{0.7}{% -% \DrawRubikCubeRU -% \DrawRubikLayerSideL{G}{B}{R} -% \DrawRubikLayerSideB{R}{G}{O} -% } +% \RubikCubeSolvedWY +% \begin{tikzpicture}[scale=0.5] +% \DrawRubikCubeRU +% \DrawRubikFlatBack{4}{1} +% \end{tikzpicture}% % \end{minipage} -% \hspace{1cm} -% \begin{minipage}{0.6\textwidth} +% \begin{minipage}{5cm} %\begin{verbatim} -% \RubikFaceUp {X}{W}{X}% -% {W}{W}{W}% -% {X}{W}{X}% -% -% \RubikFaceFront{O}{O}{X}% -% {O}{O}{X}% -% {X}{X}{W}% -% -% \RubikFaceRight{X}{G}{G}% -% {X}{G}{G}% -% {G}{X}{X}% -% \ShowCubeF{3.5cm}{0.7}{% -% \DrawRubikCubeRU -% \DrawRubikLayerSideL{G}{B}{R} -% \DrawRubikLayerSideB{R}{G}{O} -% } +% \RubikCubeSolvedWY +% \ShowCube{3cm}{0.5}{% +% \DrawRubikCubeRU +% \DrawRubikFlatBack{4}{1} +% } %\end{verbatim} % \end{minipage} +% +% +% \subsection[DrawNCube]{DrawNCube (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 % -% 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. +% \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} % % % @@ -2901,10 +2963,10 @@ % 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 +% Appending an `F' to the command-name (\cmd{\ShowSequenceF}) results in an fbox around % 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). +% Appending a lower-case `f' to the command-name (\cmd{\ShowSequencef}) generates fboxs around +% \textit{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!), @@ -2953,17 +3015,21 @@ % \medskip\noindent\verb!\ShowSequence{,\ }{\textRubik}{\myseq}! \ $\longrightarrow$ \ \textRubik{U},\ \textRubik{D},\ % \textRubik{Lp},\ \textRubik{R} % +% +% % -% \subsection*{Trailing digits} +% \subsection{Trailing digits} % -% Note that the fonts denoted by \verb!\rr!, \verb!\rrh!, \verb!\Rubik! +% Note that the commands \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. +% commas (i.e.,~it does not \textit{interpret} strings like R2 $\rightarrow$ R,R etc.). +% However, if you just want to `see' the text, then the standard \LaTeX\ typewriter command +% \verb!\texttt! will typeset the text correctly, as you would expect +% (but using the \texttt{tt} font of course). % -% An effective `work-around' for this limitation is provided by the \verb!\RubikRotation{}! +% A useful `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 @@ -2974,17 +3040,19 @@ % % 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: +% In~this case D2,L3, and the name `seqA' fail to be typeset when using +% the \verb!\rr! font with the \verb!\ShowSequence! command +% (notice there are lots of commas with nothing between them), +% while \cmd{\texttt} does work, 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{,}{\rr}{\seqA}! \ $\longrightarrow$ \ \ShowSequence{,}{\rr}{\seqA} +% % \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 @@ -3053,7 +3121,7 @@ % \bigskip % %\noindent% -%\RubikCubeSolved% +%\RubikCubeSolvedWY% %\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% @@ -3073,7 +3141,7 @@ %\begin{verbatim} %\newcommand{\fourspot}{[fourspot],F2,B2,U,Dp,R2,L2,U,Dp}% %\noindent% -%\RubikCubeSolved% +%\RubikCubeSolvedWY% %\ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% %\RubikRotation{\fourspot}% %\quad\SequenceBraceA{\SequenceName}{% @@ -3099,7 +3167,7 @@ % 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 +% \cmd{\DrawRubikFace..} or \cmd{\DrawRubikFlat..} commands etc.) and also Sidebars, 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. @@ -3108,8 +3176,6 @@ % \centering % \ifpdf % \includegraphics[height=3cm]{rubik-doc-figE.pdf} -% \else -% \includegraphics[height=3cm]{rubik-doc-figE.eps} % \fi % % \parbox{9cm}{% @@ -3121,18 +3187,17 @@ % \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, remembering that TikZ -% commands require a terminal semicolon. +% arrow drawn from the centre of the lower-left cubie $(0.5, 0.5)$ to the centre of +% middle cubie $(1.5, 1.5)$. +% To do this we just include the following TikZ command (remember that TikZ +% commands require a terminal semicolon): % \begin{quote} %\begin{verbatim} % \draw[->,color=green] (0.5,0.5) -- (1.5, 1.5); %\end{verbatim} % \end{quote} % -% The following example shows the cubie changes in the \textsc{up} face +% The following example shows the cubie movement in the \textsc{up} face % generated by the rotation sequence \rrF\rrR\rrU\rrRp\rrUp\rrFp. % The magenta arrows indicate movement \textit{with} cubie rotations, % while the black arrow indicates movement \textit{without} rotation. @@ -3141,8 +3206,9 @@ % % \bigskip % \noindent +% \RubikCubeSolvedWY % \ShowCube{2.5cm}{0.7}{% -% \DrawRubikLayerFaceAll{W} +% \DrawRubikFaceUp % \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); @@ -3151,8 +3217,9 @@ % } % \begin{minipage}{0.6\textwidth} %\begin{verbatim} +% \RubikCubeSolvedWY % \ShowCube{2.5cm}{0.7}{% -% \DrawRubikLayerFaceAll{W} +% \DrawRubikFaceUp % \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); @@ -3165,41 +3232,32 @@ % \bigskip % Since the coordinates shown in Figure~\ref{fig:facegraph} extend % outwards in all directions, they can also be used as a guide for drawing -% arrows (or other structures) outside this 3x3 `face' square. This approach -% is shown in the following example, where we have changed the \texttt{tikzpicture} scale -% factor to~0.4 in order to generate a small figure in order to facilitate placing the -% figure and the code side-by-side. -% -% \bigskip +% arrows (or other structures) outside this 3x3 `face' square. +% The origin is at lower left corner of the face. +% +% In the following example, we input a Rubik cube configuration +% (previously saved as the file \texttt{CubeFour.tex} +% (see the \textsc{rubikrotation} package documentation for details)\footnote{See also +% the `SaveRubikState' example in the file \texttt{RubikExamples.pdf}.}, and +% draw an arrow to highlight a yellow side facelet. % +% \bigskip % \noindent -% \ShowCube{1.8cm}{0.4}{% -% \DrawRubikLayerFace{G}{Y}{R}% -% {Y}{Y}{Y}% -% {B}{Y}{Y}% -% % -% \DrawRubikLayerSideT {Y}{B}{B} -% \DrawRubikLayerSideLR{R} {Y} -% {R} {O} -% {Y} {O} -% \DrawRubikLayerSideB {O}{G}{G} -% \draw[->,ultra thick,color=green] (0.5,5) -- (0.5, 4); -% } +% \RubikCubeGreyAll +% \RubikFaceUp OYG YYY BYY +% \RubikFaceFront YRR XXXXXX +% \RubikFaceRight GOO XXXXXX +% \RubikFaceBack YBB XXXXXX +% \RubikFaceLeft YGR XXXXXX +% \ShowCube{2.2cm}{0.5}{\DrawRubikFaceUpSide% +% \draw[->,ultra thick,color=green] (2.5,5) -- (2.5, 4); +% } % \begin{minipage}{0.6\textwidth} %\begin{verbatim} -% \noindent -% \ShowCube{1.8cm}{0.4}{% -% \DrawRubikLayerFace{G}{Y}{R}% -% {Y}{Y}{Y}% -% {B}{Y}{Y}% -% % -% \DrawRubikLayerSideT {Y}{B}{B} -% \DrawRubikLayerSideLR{R} {Y} -% {R} {O} -% {Y} {O} -% \DrawRubikLayerSideB {O}{G}{G} -% \draw[->,ultra thick,color=green] (0.5,5) -- (0.5, 4); -% } +% \input{CubeFour.tex} +% \ShowCube{2.2cm}{0.5}{\DrawRubikFaceUpSide% +% \draw[->,ultra thick,color=green] (2.5,5) -- (2.5, 4); +% } %\end{verbatim} % \end{minipage} % @@ -3256,35 +3314,39 @@ % % \bigskip % -% In the following example we use a blue circle to highlight the cubie -% to be rotated into the top layer. +% In the following example we use a blue circle to highlight a corner cubie +% to be rotated into the top layer. Note we also use the command +% \verb!\DrawRubikCubeSidebarFD{RU}! to draw the sidebar along +% the FD (Front-Down) edge, and show the colour of the hidden facelet +% of the corner-cubie. % % \bigskip % % \noindent% -% \RubikCubeGrey +% \RubikCubeGreyWY % \RubikFaceUp{X}{W}{X}% % {W}{W}{W}% % {W}{W}{X}% +% \RubikFaceDown{X}{X}{O}{X}{X}{X}{X}{X}{X}% % \RubikSliceBottomR{X}{X}{W}{G}{X}{X}% % \ShowCube{2.5cm}{0.5}{% % \DrawRubikCubeRU -% \DrawRubikLayerSideRBy{O} +% \DrawRubikCubeSidebarFD{RU} % \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 +% \RubikCubeGreyWY % \RubikFaceUp{X}{W}{X} % {W}{W}{W} % {W}{W}{X} +% \RubikFaceDown{X}{X}{O}{X}{Y}{X}{X}{X}{X}% % \RubikSliceBottomR{X}{X}{W}{G}{X}{X} % \ShowCube{2.5cm}{0.5}{% % \DrawRubikCubeRU -% \DrawRubikLayerSideRBy{O} +% \DrawRubikCubeSidebarFD{RU} % \draw[ultra thick,->,color=blue] % (2.5,0.5) -- (2.5, 2.5); % \draw [color=blue, thick] (2.7, 0.3) circle (1.3); @@ -3293,6 +3355,9 @@ % \end{minipage} % % +% +% +% % \section{Final example} % % We now present, as a final example, the code used to draw the front page @@ -3308,10 +3373,10 @@ % \bigskip % % \noindent\hfil% -% \RubikCubeSolved% +% \RubikCubeSolvedWY% % \ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% % \quad\ShowCube{1.6cm}{0.4}{% -% \DrawFlatUpSide +% \DrawRubikFaceUpSide % \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); @@ -3320,26 +3385,23 @@ % }% % \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} -% \DrawRubikLayerSideT {G}{G}{R} -% \DrawRubikLayerSideLR{R} {W} -% {B} {W} -% {O} {W} -% \DrawRubikLayerSideB {G}{W}{O} -% } -% \hfil +% \RubikFaceUp WWB WWOWRB% +% \RubikFaceBack RGG XXXXXX% +% \RubikFaceLeft RBO XXXXXX% +% \RubikFaceFront GWO XXXXXX% +% \RubikFaceRight WWW XXXXXX% +% \quad\ShowCube{1.6cm}{0.4}{\DrawRubikFaceUpSide} +% \hfil% % -% \bigskip +% +% \bigskip % %\begin{verbatim} % \noindent\hfil% -% \RubikCubeSolved% +% \RubikCubeSolvedWY% % \ShowCube{1.6cm}{0.4}{\DrawRubikCubeRU}% % \quad\ShowCube{1.6cm}{0.4}{% -% \DrawFlatUpSide% +% \DrawRubikFaceUpSide% % \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); @@ -3348,7 +3410,7 @@ % }% % \RubikRotation{F,R,U,Rp,Up,Fp}% % \quad\ShowSequence{}{\Rubik}{\SequenceLong}\quad$\longrightarrow$% -% \ShowCube{1.6cm}{0.4}{\DrawFlatUpSide}% +% \ShowCube{1.6cm}{0.4}{\DrawRubikFaceUpSide}% % \hfil %\end{verbatim} % @@ -3363,29 +3425,65 @@ %\begin{verbatim} % \RubikRotation{F,R,U,Rp,Up,Fp} % \ShowSequence{,}{\Rubik}{\SequenceLong} \ \ \ $\longrightarrow$ -% \ShowCube{2cm}{0.4}{\DrawFlatUpSide} +% \ShowCube{2cm}{0.4}{\DrawRubikFaceUpSide} %\end{verbatim} % 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} -% {W}{R}{B} -% \DrawRubikLayerSideT {G}{G}{R} -% \DrawRubikLayerSideLR{R} {W} -% {B} {W} -% {O} {W} -% \DrawRubikLayerSideB {G}{W}{O} -% } +% \RubikFaceUp WWB WWOWRB +% \RubikFaceBack RGG XXXXXX +% \RubikFaceLeft RBO XXXXXX +% \RubikFaceFront GWO XXXXXX +% \RubikFaceRight WWW XXXXXX +% \quad\ShowCube{1.6cm}{0.4}{\DrawRubikFaceUpSide} +% \hfil %\end{verbatim} % % % % % +% \section{Deprecated commands} +% \label{sec:deprecated} +% +% +% The \cmd{\DrawRubikLayerFace..} and \cmd{\DrawRubikLayerSide..} +% are now deprecated; they were found to be +% confusing since (a)~they both drew faces \textit{and} took colour arguments +% for facelets, and (b)~they did not update the internal colour state of a +% cube or face---i.e.,~their colouring was simply a local `painting' action +% without memory. +% They have both been superseded by the more versatile +% \cmd{\DrawRubikFace..}\ commands (see Section~\ref{sec:drawrubikfacecommands}). +% +% The \cmd{\RubikSide..} commands are also deprecated, since they duplicated +% some of the function of the \cmd{\RubikFace..}\ commands. +% +% The earlier \cmd{\DrawFace..}\ (v4) and \cmd{\DrawFlat..}\ (v3) commands +% are also deprecated since they lacked the Rubik or Two keyword +% (see Sections~\ref{sec:rubikandtwo} and \ref{sec:drawrubikfacecommands}). +% +% \medskip +% +% {\noindent}Summary of all deprecated commands (and their current versions) since v3. +% +% \smallskip +% +% \begin{supertabular}[ll]{p{4cm} p{6cm}} +% \verb!\DrawRubikCubeFlat! & $\rightarrow$ \hspace{0.5cm} \verb!\DrawRubikCubeSF! \ (Semi-Flat) \\ +% \verb!\DrawRubikFlat! & $\rightarrow$ \hspace{0.5cm} \verb!\DrawRubikCubeF! \ \ (Flat) \\ +% \verb!\DrawFace..! & $\rightarrow$ \hspace{0.5cm} \verb!\DrawRubikFace..! \\ +% \verb!\DrawFlat..! & $\rightarrow$ \hspace{0.5cm} \verb!\DrawRubikFlat..! \\ +% \verb!\DrawFlat..Side! & $\rightarrow$ \hspace{0.5cm} \verb!\DrawRubikFace..Side! \\ +% \verb!\DrawRubikLayerFace..! & $\rightarrow$ \hspace{0.5cm} \verb!\DrawRubikFace..! \\ +% \verb!\DrawRubikLayerSide..! & $\rightarrow$ \hspace{0.5cm} \verb!\DrawRubikFace..! \\ +% \end{supertabular} +% +% +% +% % \section{Known limitations} % % Please contact the authors regarding any ideas for improvement, errors, @@ -3405,42 +3503,45 @@ % \end{itemize} % % -% \section{Future packages} -% -% Since Rubik-type cubes currently exist in a variety of sizes (from 2x2x2 to 11x11x11) -% 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, may we suggest that a CTAN directory structure -% along the following lines might be appropriate. -% -% $$ -% \textsc{rubik} -% \left\{ -% \begin{array}{l} -% \mbox{rubiktools}\\ -% \mbox{rubik2x}\\ -% \mbox{rubik3x}\\ -% \ldots\\ -% \mbox{rubik11x}\\ -% \end{array} -% \right.\\ -% $$ -% % % % \section{Change history} % % \begin{itemize} % +% \item Version 5 (February 2018) +% +% -- Removed some now unnecessary commands (see Section~\ref{sec:deprecated}) +% and made some of the internal code a bit more efficient. +% +% ---Added two new `grey' commands: \cmd{\RubikCubeGreyWY} and \cmd{\RubikCubeGreyWB} +% (so as to complement the related \cmd{\RubikCubeSolvedXX} commands). +% +% ---Bugfix: added a pair of containing braces around the \cmd{\ifthenelse..} command +% used by the \cmd{\ShowSequence} command (for code see Section~\ref{sec:codeshowsequence}). +% This fixed an occasional problem of a font not being contained. +% +% +% ---Added missing lowercase cube `prime' versions of whole cube rotation notation +% (\rr{up}, \rr{dp}, \rr{lp}, \rr{rp}, \rr{fp}, \rr{bp}); see Section~\ref{sec:xyznotation}. +% +% +% ---New \cmd{\NoSidebar} command for disabling the drawing of sidebars of a particular colour +% (see Section~\ref{sec:nosidebar}). +% +% +% ---Implemented the terminal $x,y$ position parameters for +% the \cmd{\DrawRubikFlatLeft} and \cmd{\DrawRubikFlatRight} +% commands; all the \cmd{\DrawRubikFlat..} commands work correctly now +% (see Section~\ref{sec:codedrawrubikflatcommands}) +% +% +% % \item Version 4.0 (March 2017) % % ---Improved documentation. % -% ---Improved inter-hieroglyph spacing and vertical position. The Computer Moderm sans bold font +% ---Improved inter-hieroglyph spacing and vertical position. The Computer Modern sans bold font % (10/12pt) is used for the hieroglyphs and rotation codes (see Section~\ref{sec:coderubikfont} % for details). % @@ -3457,14 +3558,6 @@ % (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 @@ -3482,9 +3575,9 @@ % \end{quote} % % ---A new command for setting up or allocating a `solved' colour configuration. -% (see Section~\ref{sec:solvedconfig}): +% (see Section~\ref{sec:rubiksolvedconfig}): % \begin{quote} -% \cmd{\SolvedConfig} +% \cmd{\RubikSolvedConfig} % \end{quote} % % ---A new command for setting up a `starter cube' for which the \textit{whole} cube @@ -3524,8 +3617,8 @@ % % ---Fixed typos and minor errors in the documentation. % -% ---Added the following commands to facilitate typesetting a face, -% as described in Section~\ref{sec:flatcommands}. +% ---Added the following commands to facilitate typesetting a face +% (but see Section~\ref{sec:deprecated}). %\begin{quote} %\begin{verbatim} %\DrawFlatUp @@ -3565,15 +3658,15 @@ % % \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 +% We 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\{\}\{\}} +% We also 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. -% -% +% (see Section~\ref{sec:codeshowsequence}), Herbert Kociemba for helpful comments, +% and Robert Ma\v{r}\'{\i}k for suggesting the \cmd{\NoSidebar\{\}} command +% (see Section~\ref{sec:nosidebar}). % % % \section{References} @@ -3594,11 +3687,7 @@ % \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/} -% -% \item Garfath-Cox, A (1981). \textit{The cube}, (Bolden Publishing Co., -% East Molesey, Surrey) pp.32. [copy in British Library] -% -% +% % \item Duvoid T (2010). % M\'{e}thode simple pour remonter le Rubik's cube. % \newline\url{http://duvoid.fr/rubik/rubik-debutant-couleurs.pdf} @@ -3614,23 +3703,35 @@ % 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 website (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 Fung website (Fung A). Solving the Rubik's cube systematically. +% \url{http://alexfung.info/favorite/cube/cube.htm} +% +% \item Garfath-Cox, A (1981). \textit{The cube}, (Bolden Publishing Co., +% East Molesey, Surrey) pp.32. [copy in British Library] +% % \item Golomb SW (1981). Rubik's cube and a model of quark confinement. % \textit{Am.\ J.\ Phys.}; vol~49, pp~1030--1031. % % \item Golomb SW (1982). Rubik's cube and quarks: twists on the eight corner cells % of Rubik's cube provide a model for many aspects of quark behaviour. -% \textit{American Scientist}; -% \underline{70}, pp.~257--259. \url{http://www.jstor.org/stable/27851433} +% \textit{American Scientist}; \underline{70}, No~3 (May--June 1982), +% pp.~257--259. \url{http://www.jstor.org/stable/27851433} % % \item Gymrek M (2009). The mathematics of the Rubik's cube. % \newline\url{http://web.mit.edu/sp.268/www/rubik.pdf} +% +% \item Harris D (2008). Speedsolving the cube. +% (Sterling Publishing Co.\ Inc., New York, USA.) pp.~166. +% [covers 2x2x2, 3x3x3, 4x4x4, 5x5x5 cubes] +% +% \item Harris website (Harris D). \url{http://www.cubestation.co.uk} % % \item Heise website (Heise R). Rubik's cube theory. \url{http://www.ryanheise.com/cube/theory.html} % @@ -3659,7 +3760,7 @@ % \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) @@ -3674,19 +3775,31 @@ % Rubik's cube is twenty. \textit{SIAM.\ J.\ Discrete Math.}, \underline{27}, 1082--1105. % (\url{http://tomas.rokicki.com/rubik20.pdf}) % +% \item Roux website (Roux G). \ \ \url{http://www.grroux.free.fr} +% % \item Rubik's cube. See Section on notation. % \newline\url{http://en.wikipedia.org/wiki/Rubik's_Cube} % -% \item RuWix website (Ferenec D) \ \ \url{http://www.ruwix.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 Sher S.\ T-H.\ (2014). The new durable Rubik's cube (technical description). +% \url{http://www.scf.usc.edu/~tsher/files/Rubiks_Cube.pdf} [includes RGB colour specification] +% +% % \item Singmaster D (1981). \textit{Notes on Rubik's magic cube} (Harmondsworth, Eng., Penguin Books) % % \item Speedsolving website. \url{http://www.speedsolving.com/} +% +% +% \item Storer website (Storer JA). \url{http://www.cs.brandeis.edu/~storer/JimPuzzles/} +% {\newline} For Rubik cube, see: \url{http://www.cs.brandeis.edu/~storer/JimPuzzles/RUBIK/Rubik3x3x3.pdf} +% {\newline} For puzzle book, see: \url{http://www.cs.brandeis.edu/~storer/zzzJimPuzzles/JimPuzzlesBook.pdf} % +% % \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} % @@ -3696,7 +3809,7 @@ % [cited from \textit{Wikipedia} (Rubik's cube)] % % -% \item Vandenbergh website (Vandenbergh L.) \ \ \textsc{cubezone} \url{http://www.cubezone.be} +% \item Vandenbergh website (Vandenbergh L). \ \ \textsc{cubezone} \url{http://www.cubezone.be} % % \item WCA (2016). World Cube Association Regulations. See \S\,12 for notation. % \url{http://www.worldcubeassociation.org/regulations.htm} @@ -3725,8 +3838,8 @@ % % \begin{macrocode} %<*rubikcube> -\def\RCfileversion{4.0}% -\def\RCfiledate{2017/03/03}% +\def\RCfileversion{5.0}% +\def\RCfiledate{2018/02/25}% February 25, 2018 \NeedsTeXFormat{LaTeX2e} \ProvidesPackage{rubikcube}[\RCfiledate\space (v\RCfileversion)] % \end{macrocode} @@ -3767,9 +3880,8 @@ % \subsection{\hspace{3mm}Colours} % \label{sec:codecolours} % -% 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}. +% We have adopted the following colour allocations---see Section~\ref{sec:colours} +% for details. % % \begin{macrocode} \definecolor{R}{HTML}{C41E33}% @@ -3798,7 +3910,7 @@ % 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 +% 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} @@ -3892,37 +4004,61 @@ \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. +% \noindent\textsc{example usage:} |\ForEachX{;}{\texttt{\x}}{L;R;U;D}| % -% 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. +% An important feature of the |\ForEachX| command is that it expands its third argument +% (the list of elements), since this allows the list of elements to be presented as +% a macro, which is extremely convenient for the user. % -% 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. +% The \cmd{\ShowSequence} command typesets a sequence of elements (|#3|), and places +% an optional separator (|#1|) between them. +% For each element (|\x|, see above) of the sequence |#3| this command forms the +% construction |#2{element of #3}|. +% For~example, if |#2 = \rr|, and D is an element of |#3|, then it will form the +% command |\rr{D}| etc. +% +% Note that it is not straightforward to place the separator (|#1|) \textit{only between} +% the derived elements (i.e.,~without the separator being either before the first element, +% or following the last element) using only the |ForEachX| command. This is because +% the |ForEachX| command processes each element in exactly the +% same way---i.e.,~a comma after the first element (good) means there will be a comma after +% the final element (bad). +% +% We solve this problem by using the |\ifthenelse| command to allow the first element +% to be processed differently from all the remaining elements. This is because it is easy +% for \TeX\ to identify the first element of a sequence, but very difficult for it to +% identify the final element since we generally don't know the number of elements beforehand. +% Consequently we identify the first element (using the |\xcount|) variable (see above), +% and then process this first element \textit{without} any comma; +% we then place a comma in front of each of the remaining elements. +% +% We also create two fbox versions of the command: the `F' version places an fbox about the +% whole output; the `f' version places an fbox about each element in the output +% (these two versions can be helpful when checking white space). +% +% Note: bugfix 22 October 2017 (RWDN): if the user implemented tt output using \cmd{\tt} +% instead of the standard \cmd{\texttt} as the \verb!#2! argument, then the action would +% not of course remain local, and consequently we have added a leading brace and +% complementary trailing brace around the the \cmd{\ifthenelse...} command in each of +% the following three macros to limit the action. % % \noindent\textsc{usage}: |\ShowSequence{,}{\rr}{R,L,Up,Dp.....}| % % \begin{macrocode} \newcommand{\ShowSequence}[3]{% \ForEachX{,}{% - \ifthenelse{\xcount=1}{#2{\x}}{#1#2{\x}}% + {\ifthenelse{\xcount=1}{#2{\x}}{#1#2{\x}}}% }{#3}% }% \newcommand{\ShowSequenceF}[3]{% \fbox{% \ForEachX{,}{% - \ifthenelse{\xcount=1}{#2{\x}}{#1#2{\x}}% + {\ifthenelse{\xcount=1}{#2{\x}}{#1#2{\x}}}% }{#3}% }}% \newcommand{\ShowSequencef}[3]{% \ForEachX{,}{% - \ifthenelse{\xcount=1}{\fbox{#2{\x}}}{#1{\fbox{#2{\x}}}}% + {\ifthenelse{\xcount=1}{\fbox{#2{\x}}}{#1{\fbox{#2{\x}}}}}% }{#3}% }% % \end{macrocode} @@ -3934,7 +4070,7 @@ % 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 +% 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,...). % @@ -3987,18 +4123,26 @@ % \end{macro} % % -% \subsection{\hspace{3mm}Face commands} +% \subsection{\hspace{3mm}RubikFace commands} +% \label{sec:rubikfacecode} % % Cube face notation: U, D, L, R, F, B (Singmaster) -% {\newline}Cubie-square notation: t, m, b, l, m, r = top, middle, +% {\newline}Cubie-facelet notation: t, m, b, l, m, r = top, middle, % bottom, left, middle, right. -% 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}bottom row (7,8,9) = bl, bm, br +% We use this lower case notation in XY-pairs to denote individual cubie facelets +% on a given face (to avoid confusion with cube Face notation), as follows: +% {\newline}\strut\hspace{1cm}top row \ \ \ \ \ (1,2,3) = lt, \ \, mt, \ rt +% {\newline}\strut\hspace{1cm}middle row\, (4,5,6) = lm, mm, rm +% {\newline}\strut\hspace{1cm}bottom row (7,8,9) = lb, \ mb, \ rb +% {\newline}For example, the current colour of the \textbf{r}ight \textbf{b}ottom facelet +% on the \textsc{front} face is held as the variable \cmd{\Frb} etc. +% +% The cubie-facelets (squares) on a face are also parameterized numerically +% \verb!#1!--\verb!#9! reading from left-to-right, starting top-left \& +% ending bottom-right, when used as arguments for specifying particular colours +% (as in the \cmd{\RubikFace..} commands---see below). + +% % % \begin{macro}{\RubikFaceUp} % \begin{macro}{\RubikFaceDown} @@ -4018,10 +4162,10 @@ % 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\}} -% 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 lower-case letters (in this case \texttt{rt}) are always written +% For~example, in the command \verb!\def\Urt{#1}! +% the U denotes the Up face of the cube, while the \texttt{rt} denotes +% the ``right-top'' facelet on this face. Note that the order +% of the two lower-case letters (\texttt{rt}) is % 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 @@ -4128,42 +4272,59 @@ % \end{macrocode} % % - +% % % \subsection{\hspace{3mm}RubikCubeGrey command} % \label{sec:codegrey} % % \begin{macro}{\RubikCubeGrey} +% \begin{macro}{\RubikCubeGreyWY} +% \begin{macro}{\RubikCubeGreyWB} % 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. % 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). +% We also make WY and WB versions, and implement equivalent `gray' versions +% (to be consistent with TikZ). % \begin{macrocode} \newcommand{\RubikCubeGrey}{% -\RubikFaceUp {X}{X}{X}{X}{W}{X}{X}{X}{X}% -\RubikFaceDown {X}{X}{X}{X}{Y}{X}{X}{X}{X}% -\RubikFaceLeft {X}{X}{X}{X}{B}{X}{X}{X}{X}% -\RubikFaceRight{X}{X}{X}{X}{G}{X}{X}{X}{X}% -\RubikFaceFront{X}{X}{X}{X}{O}{X}{X}{X}{X}% -\RubikFaceBack {X}{X}{X}{X}{R}{X}{X}{X}{X}% + \RubikFaceRight{X}{X}{X}{X}{G}{X}{X}{X}{X}% + \RubikFaceLeft {X}{X}{X}{X}{B}{X}{X}{X}{X}% + \RubikFaceUp {X}{X}{X}{X}{W}{X}{X}{X}{X}% + \RubikFaceDown {X}{X}{X}{X}{Y}{X}{X}{X}{X}% + \RubikFaceFront{X}{X}{X}{X}{O}{X}{X}{X}{X}% + \RubikFaceBack {X}{X}{X}{X}{R}{X}{X}{X}{X}% } \newcommand{\RubikCubeGray}{\RubikCubeGrey} +\newcommand{\RubikCubeGreyWY}{\RubikCubeGrey} +\newcommand{\RubikCubeGrayWY}{\RubikCubeGreyWY} +%% +\newcommand{\RubikCubeGreyWB}{% + \RubikFaceRight{X}{X}{X}{X}{R}{X}{X}{X}{X}% + \RubikFaceLeft {X}{X}{X}{X}{O}{X}{X}{X}{X}% + \RubikFaceUp {X}{X}{X}{X}{W}{X}{X}{X}{X}% + \RubikFaceDown {X}{X}{X}{X}{B}{X}{X}{X}{X}% + \RubikFaceFront{X}{X}{X}{X}{G}{X}{X}{X}{X}% + \RubikFaceBack {X}{X}{X}{X}{Y}{X}{X}{X}{X}% +} +\newcommand{\RubikCubeGrayWB}{\RubikCubeGreyWB} % \end{macrocode} % \end{macro} +% \end{macro} +% \end{macro} % % % % % \subsection{\hspace{3mm}SolvedConfig command} % -% \begin{macro}{\SolvedConfig} +% \begin{macro}{\RubikSolvedConfig} % This command sets the face/colour configuration (state) of a typical % 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{\SolvedConfig}[6]{% +\newcommand{\RubikSolvedConfig}[6]{% \RubikFaceRightAll{#1}% \RubikFaceLeftAll{#2}% \RubikFaceUpAll{#3}% @@ -4184,10 +4345,10 @@ % 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). +% appear grey. We implement it using the \cmd{\RubikSolvedConfig} 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{\RubikCubeGreyAll}{\RubikSolvedConfig{X}{X}{X}{X}{X}{X}}% \newcommand{\RubikCubeGrayAll}{\RubikCubeGreyAll} % \end{macrocode} % \end{macro} @@ -4206,9 +4367,9 @@ % \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{\RubikCubeSolved}{\RubikSolvedConfig{G}{B}{W}{Y}{O}{R}}% \newcommand{\RubikCubeSolvedWY}{\RubikCubeSolved}% -\newcommand{\RubikCubeSolvedWB}{\SolvedConfig{R}{O}{W}{B}{G}{Y}}% +\newcommand{\RubikCubeSolvedWB}{\RubikSolvedConfig{R}{O}{W}{B}{G}{Y}}% % \end{macrocode} % \end{macro} % \end{macro} @@ -4348,7 +4509,6 @@ % exactly 1-unit, and so makes it easy to determine the 2D~(x,y) coordinates % of any position, and hence facilitates typesetting text onto the image of % the cube using TikZ commands. - % \end{macro} % \begin{macrocode} \newcommand{\DrawRubikCubeRU}{% @@ -4574,110 +4734,36 @@ } % \end{macrocode} % +% RWDN19D removed DrawRubikLayerFace commands Feb 19 2018 % -% \subsection{\hspace{3mm}LayerFace commands} -% -% \begin{macro}{\DrawRubikLayerFace} -% \begin{macro}{\DrawRubikLayerFaceAll} -% 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 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 -% \cmd{\DrawRubikCubeFrontFace} -% which is used for drawing the front face of a Rubik cube. -% \end{macro} -% \end{macro} -% \begin{macrocode} -\newcommand{\DrawRubikLayerFace}[9]{% -%%-----------FRONT face--------- -%%---top row -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(0,2) -- (0, 3) -- (1,3) -- (1,2) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#2]% -(1,2) -- (1, 3) -- (2,3) -- (2,2) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#3]% -(2,2) -- (2, 3) -- (3,3) -- (3,2) -- cycle; -%%-----middle row -\draw[line join=round,line cap=round,ultra thick,fill=#4]% -(0,1) -- (0, 2) -- (1,2) -- (1,1) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#5]% -(1,1) -- (1, 2) -- (2,2) -- (2,1) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#6]% -(2,1) -- (2, 2) -- (3,2) -- (3,1) -- cycle; -%%----bottom row -\draw[line join=round,line cap=round,ultra thick,fill=#7]% -(0,0) -- (0, 1) -- (1,1) -- (1,0) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#8]% -(1,0) -- (1, 1) -- (2,1) -- (2,0) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#9]% -(2,0) -- (2, 1) -- (3,1) -- (3,0) -- cycle; -} -\newcommand{\DrawRubikLayerFaceAll}[1]{% -%%----------FRONT face----------- -%%---top row -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(0,2) -- (0, 3) -- (1,3) -- (1,2) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(1,2) -- (1, 3) -- (2,3) -- (2,2) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(2,2) -- (2, 3) -- (3,3) -- (3,2) -- cycle; -%%-----middle row -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(0,1) -- (0, 2) -- (1,2) -- (1,1) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(1,1) -- (1, 2) -- (2,2) -- (2,1) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(2,1) -- (2, 2) -- (3,2) -- (3,1) -- cycle; -%%----bottom row -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(0,0) -- (0, 1) -- (1,1) -- (1,0) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(1,0) -- (1, 1) -- (2,1) -- (2,0) -- cycle; -\draw[line join=round,line cap=round,ultra thick,fill=#1]% -(2,0) -- (2, 1) -- (3,1) -- (3,0) -- cycle; -} -% \end{macrocode} % % -% \subsection{\hspace{3mm}DrawFlatX commands} -% \label{sec:drawflatxcommands} +% \subsection{\hspace{3mm}DrawRubikFlatX commands} +% \label{sec:codedrawrubikflatcommands} % -% [\textsc{note}: These new commands (version 3.0) were modified from the +% [\textsc{Background}: These commands (new in 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 so as to make this +% renamed 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} -% \begin{macro}{\DrawFlatLeft} -% \begin{macro}{\DrawFlatRight} -% \begin{macro}{\DrawFlatFront} -% \begin{macro}{\DrawFlatBack} -% Each of these commands draws a separate (flat) face (9~facelets) -% (see Section~\ref{sec:flatcommands}). -% Each command (except \cmd{\DrawFlatFront}) takes two arguments, +% Note also that the \cmd{\DrawRubikFace..} commands are essentially +% these same commands but with their two coordinate arguments X,Y +% set to $x=0$, $y=0$---see Section~\ref{sec:drawrubikfacecode}] +% +% \begin{macro}{\DrawRubikFlatUp} +% \begin{macro}{\DrawRubikFlatDown} +% \begin{macro}{\DrawRubikFlatLeft} +% \begin{macro}{\DrawRubikFlatRight} +% \begin{macro}{\DrawRubikFlatFront} +% \begin{macro}{\DrawRubikFlatBack} +% Each of these commands draws a separate (flat) face (9~facelets). +% Each command (except \cmd{\DrawRubikFlatFront}) 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 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 -% with the \cmd{\DrawFlatUp}, \cmd{\DrawFlatDown} and \cmd{\DrawFlatBack} -% commands, since all the other faces currently only require Y=0 -% (this will be made more flexible in a later version). -% -% Note also that the \cmd{\DrawFlatFront} command takes no arguments, +% Note also that the \cmd{\DrawRubikFlatFront} command takes no arguments, % since by definition the bottom left corner of this face is at (0,0), % and there seems to be no reason (just now) for this face to have the % facility to be positioned otherwise. @@ -4685,15 +4771,15 @@ % \textsc{example}: The following command positions the Up face so % that its bottom left corner is located at (0,3): % \begin{quote} -% \cmd{\DrawFlatUp\{0\}\{3\}} +% \cmd{\DrawRubikFlatUp\{0\}\{3\}} % \end{quote} -% These new commands are also used by the commands \cmd{\DrawRubikFlat} and -% \cmd{\DrawRubikCubeFlat} to draw various `flat' representations +% These new commands are also used by the commands \cmd{\DrawRubikCubeF} and +% \cmd{\DrawRubikCubeSF} to draw various `flat' representations % 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 a `dx, dy' notation -% with the \cmd{\DrawFlatDown} command (since dx and dy are already used by the +% with the \cmd{\DrawRubikFlatDown} 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} @@ -4703,7 +4789,7 @@ % \end{macro} % \end{macro} % \begin{macrocode} -\newcommand{\DrawFlatUp}[2]{% +\newcommand{\DrawRubikFlatUp}[2]{% \pgfmathsetmacro{\ux}{#1}% \pgfmathsetmacro{\uy}{#2}% %%---top row @@ -4738,7 +4824,7 @@ -- (\ux + 3,\uy + 0) -- cycle; } %%------------------------- -\newcommand{\DrawFlatDown}[2]{% +\newcommand{\DrawRubikFlatDown}[2]{% \pgfmathsetmacro{\ddx}{#1}% \pgfmathsetmacro{\ddy}{#2}% %%---top row @@ -4773,61 +4859,77 @@ -- (\ddx + 3,\ddy + 0) -- cycle; } %%------------------------- -\newcommand{\DrawFlatLeft}[2]{% +\newcommand{\DrawRubikFlatLeft}[2]{% \pgfmathsetmacro{\lx}{#1}% \pgfmathsetmacro{\ly}{#2}% -%% NOTE: y variable coord not yet implemented %%---top row \draw[line join=round,line cap=round,ultra thick,fill=\Llt]% -(\lx + 0,2) -- (\lx + 0, 3) -- (\lx + 1,3) -- (\lx + 1,2) -- cycle; +(\lx + 0, \ly + 2) -- (\lx + 0, \ly + 3) -- (\lx + 1, \ly + 3)% + -- (\lx + 1, \ly + 2) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Lmt]% -(\lx + 1,2) -- (\lx + 1, 3) -- (\lx + 2,3) -- (\lx + 2,2) -- cycle; +(\lx + 1, \ly + 2) -- (\lx + 1, \ly + 3) -- (\lx + 2, \ly + 3)% + -- (\lx + 2, \ly + 2) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Lrt]% -(\lx + 2,2) -- (\lx + 2, 3) -- (\lx + 3,3) -- (\lx + 3,2) -- cycle; +(\lx + 2, \ly + 2) -- (\lx + 2, \ly + 3) -- (\lx + 3, \ly + 3)% + -- (\lx + 3, \ly + 2) -- cycle; %%-----middle row \draw[line join=round,line cap=round,ultra thick,fill=\Llm]% -(\lx + 0,1) -- (\lx + 0, 2) -- (\lx + 1,2) -- (\lx + 1,1) -- cycle; +(\lx + 0, \ly + 1) -- (\lx + 0, \ly + 2) -- (\lx + 1, \ly + 2)% + -- (\lx + 1, \ly + 1) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Lmm]% -(\lx + 1,1) -- (\lx + 1, 2) -- (\lx + 2,2) -- (\lx + 2,1) -- cycle; +(\lx + 1, \ly + 1) -- (\lx + 1, \ly + 2) -- (\lx + 2, \ly + 2)% + -- (\lx + 2, \ly + 1) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Lrm]% -(\lx + 2,1) -- (\lx + 2, 2) -- (\lx + 3,2) -- (\lx + 3,1) -- cycle; +(\lx + 2, \ly + 1) -- (\lx + 2, \ly + 2) -- (\lx + 3, \ly + 2)% + -- (\lx + 3, \ly + 1) -- cycle; %%----bottom row \draw[line join=round,line cap=round,ultra thick,fill=\Llb]% -(\lx + 0,0) -- (\lx + 0, 1) -- (\lx + 1,1) -- (\lx + 1,0) -- cycle; +(\lx + 0, \ly + 0) -- (\lx + 0, \ly + 1) -- (\lx + 1, \ly + 1)% + -- (\lx + 1, \ly + 0) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Lmb]% -(\lx + 1,0) -- (\lx + 1, 1) -- (\lx + 2,1) -- (\lx + 2,0) -- cycle; +(\lx + 1, \ly + 0) -- (\lx + 1, \ly + 1) -- (\lx + 2, \ly + 1)% + -- (\lx + 2, \ly + 0) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Lrb]% -(\lx + 2,0) -- (\lx + 2, 1) -- (\lx + 3,1) -- (\lx + 3,0) -- cycle; +(\lx + 2, \ly + 0) -- (\lx + 2, \ly + 1) -- (\lx + 3, \ly + 1)% + -- (\lx + 3, \ly + 0) -- cycle; } %%-------------------------- -\newcommand{\DrawFlatRight}[2]{% -\pgfmathsetmacro{\rx}{#1}% %3 -\pgfmathsetmacro{\ry}{#2}% %0 -%% NOTE: y variable coord not yet implemented +\newcommand{\DrawRubikFlatRight}[2]{% +\pgfmathsetmacro{\rx}{#1}% +\pgfmathsetmacro{\ry}{#2}% %%---top row \draw[line join=round,line cap=round,ultra thick,fill=\Rlt]% -(\rx + 0,2) -- (\rx + 0, 3) -- (\rx + 1,3) -- (\rx + 1,2) -- cycle; +(\rx + 0, \ry + 2) -- (\rx + 0, \ry + 3) -- (\rx + 1, \ry + 3)% + -- (\rx + 1, \ry + 2) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Rmt]% -(\rx + 1,2) -- (\rx + 1, 3) -- (\rx + 2,3) -- (\rx + 2,2) -- cycle; +(\rx + 1, \ry + 2) -- (\rx + 1, \ry + 3) -- (\rx + 2, \ry + 3)% + -- (\rx + 2, \ry + 2) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Rrt]% -(\rx + 2,2) -- (\rx + 2, 3) -- (\rx + 3,3) -- (\rx + 3,2) -- cycle; +(\rx + 2, \ry + 2) -- (\rx + 2, \ry + 3) -- (\rx + 3, \ry + 3)% + -- (\rx + 3, \ry + 2) -- cycle; %%-----middle row \draw[line join=round,line cap=round,ultra thick,fill=\Rlm]% -(\rx + 0,1) -- (\rx + 0, 2) -- (\rx + 1,2) -- (\rx + 1,1) -- cycle; +(\rx + 0, \ry + 1) -- (\rx + 0, \ry + 2) -- (\rx + 1, \ry + 2)% + -- (\rx + 1, \ry + 1) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Rmm]% -(\rx + 1,1) -- (\rx + 1, 2) -- (\rx + 2,2) -- (\rx + 2,1) -- cycle; +(\rx + 1, \ry + 1) -- (\rx + 1, \ry + 2) -- (\rx + 2, \ry + 2)% + -- (\rx + 2, \ry + 1) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Rrm]% -(\rx + 2,1) -- (\rx + 2, 2) -- (\rx + 3,2) -- (\rx + 3,1) -- cycle; +(\rx + 2, \ry + 1) -- (\rx + 2, \ry + 2) -- (\rx + 3, \ry + 2)% + -- (\rx + 3, \ry + 1) -- cycle; %%----bottom row \draw[line join=round,line cap=round,ultra thick,fill=\Rlb]% -(\rx + 0,0) -- (\rx + 0, 1) -- (\rx + 1,1) -- (\rx + 1,0) -- cycle; +(\rx + 0, \ry + 0) -- (\rx + 0, \ry + 1) -- (\rx + 1, \ry + 1)% + -- (\rx + 1, \ry + 0) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Rmb]% -(\rx + 1,0) -- (\rx + 1, 1) -- (\rx + 2,1) -- (\rx + 2,0) -- cycle; +(\rx + 1, \ry + 0) -- (\rx + 1, \ry + 1) -- (\rx + 2, \ry + 1)% + -- (\rx + 2, \ry + 0) -- cycle; \draw[line join=round,line cap=round,ultra thick,fill=\Rrb]% -(\rx + 2,0) -- (\rx + 2, 1) -- (\rx + 3,1) -- (\rx + 3,0) -- cycle; +(\rx + 2, \ry + 0) -- (\rx + 2, \ry + 1) -- (\rx + 3, \ry + 1)% + -- (\rx + 3, \ry + 0) -- cycle; } %%----------------------- -\newcommand{\DrawFlatFront}{% +\newcommand{\DrawRubikFlatFront}{% %% This command is used /only/ by the \cmd{\DrawRubikCubeF} command. %% NOTE: x, y variables not implemented as not required here %%---top row @@ -4859,7 +4961,7 @@ (2,0) -- (2, 1) -- (3,1) -- (3,0) -- cycle; } %%------------------------- -\newcommand{\DrawFlatBack}[2]{% +\newcommand{\DrawRubikFlatBack}[2]{% \pgfmathsetmacro{\bx}{#1}% \pgfmathsetmacro{\by}{#2}% %%---top row @@ -4897,16 +4999,16 @@ % % \begin{macro}{\DrawRubikCubeF} % Draws a standard flat (F) representation of the Rubik -% cube (colours only). Note that \cmd{\DrawFlatFront} (below) +% cube (colours only). Note that \cmd{\DrawRubikFlatFront} (below) % does not take any arguments (x,y). % \begin{macrocode} \newcommand{\DrawRubikCubeF}{% - \DrawFlatUp{0}{3}% - \DrawFlatDown{0}{-3}% - \DrawFlatLeft{-3}{0}% - \DrawFlatFront% - \DrawFlatRight{3}{0}% - \DrawFlatBack{6}{0}% + \DrawRubikFlatUp{0}{3}% + \DrawRubikFlatDown{0}{-3}% + \DrawRubikFlatLeft{-3}{0}% + \DrawRubikFlatFront% + \DrawRubikFlatRight{3}{0}% + \DrawRubikFlatBack{6}{0}% } % \end{macrocode} % \end{macro} @@ -4918,157 +5020,246 @@ % arguments (below) are for the bottom-left corner of the face. % \begin{macrocode} \newcommand{\DrawRubikCubeSF}{% - \DrawRubikCube% - \DrawFlatDown{0}{-3}% - \DrawFlatLeft{-3}{0}% - \DrawFlatBack{4}{1}% + \DrawRubikCubeRU% + \DrawRubikFlatDown{0}{-3}% + \DrawRubikFlatLeft{-3}{0}% + \DrawRubikFlatBack{4}{1}% } % \end{macrocode} % \end{macro} % % % -% \subsubsection{DrawFlatXSide commands} -% \label{sec:drawflatxsidecode} +% \subsubsection{DrawRubikFaceXSide commands} +% \label{sec:drawrubikflatxsidecode} % % These six commands draw a face together with all four sidebars -% (colours only). We use the \cmd{\DrawFlatX} commands to draw the face. -% We use the \cmd{\DrawRubikLayerSideX} commands to draw the sidebars. -% The parameter orders for the \cmd{\DrawRubikLayerSideX} -% commands are as follows: -% Top (T) and Bottom (B) = left to right; +% (colours only). They use the \cmd{\DrawRubikFlatX} commands to draw the face, +% and the \cmd{\side@bar..} commands to draw the sidebars. Since each +% of the four sides of a face has three small (side) bars, we use a total +% of 12 side@bar commands for each command. +% +% The parameter codes for the \cmd{\side@bar..} +% commands are as follows (see Section~\ref{sec:side@barcode} for full details). +% 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}). % +% Note that since these commands are quite long, thay all have a +% slightly more convenient short-hand version whereby the terminal two words +% are contracted to their two initial letters (see Section~\ref{sec:drawrubikfacecode}). +% RWDN19B % -% \begin{macro}{\DrawFlatUpSide} -% Draws the \textsc{up} face together with all four sidebars -% (colours only). +% \begin{macro}{\DrawRubikFaceUpSide} +% Draws the \textsc{up} face together with all four sidebars. % \begin{macrocode} -\newcommand{\DrawFlatUpSide}{% -\DrawFlatUp{0}{0}% -\DrawRubikLayerSideT{\Brt}{\Bmt}{\Blt}% -\DrawRubikLayerSideL{\Llt}{\Lmt}{\Lrt}% -\DrawRubikLayerSideR{\Rrt}{\Rmt}{\Rlt}% -\DrawRubikLayerSideB{\Flt}{\Fmt}{\Frt}% +\newcommand{\DrawRubikFaceUpSide}{% +\DrawRubikFlatUp{0}{0}% +%Top is a horizontal sidebar, so 1 = r, 3=l +\side@barT{1}{\Brt} +\side@barT{2}{\Bmt} +\side@barT{3}{\Blt} +%Left is a vertical sidebar, so 1 = r, 3=l +\side@barL{1}{\Lrt} +\side@barL{2}{\Lmt} +\side@barL{3}{\Llt} +%Right is a vertical sidebar, so 1 = l, 3=r +\side@barR{1}{\Rlt} +\side@barR{2}{\Rmt} +\side@barR{3}{\Rrt} +%Bottom is a horizontal sidebar, so 1 = l, 3=r +\side@barB{1}{\Flt} +\side@barB{2}{\Fmt} +\side@barB{3}{\Frt} } % \end{macrocode} % \end{macro} % % -% \begin{macro}{\DrawFlatFrontSide} -% Draws the \textsc{front} face together with all four sidebars -% (colours only). +% \begin{macro}{\DrawRubikFaceFrontSide} +% Draws the \textsc{front} face together with all four sidebars. % \begin{macrocode} -\newcommand{\DrawFlatFrontSide}{% -\DrawFlatFront{0}{0}% -\DrawRubikLayerSideT{\Ulb}{\Umb}{\Urb}% -\DrawRubikLayerSideL{\Lrt}{\Lrm}{\Lrb}% -\DrawRubikLayerSideR{\Rlt}{\Rlm}{\Rlb}% -\DrawRubikLayerSideB{\Dlt}{\Dmt}{\Drt}% +\newcommand{\DrawRubikFaceFrontSide}{% +\DrawRubikFlatFront{0}{0}% +%Top +\side@barT{1}{\Ulb} +\side@barT{2}{\Umb} +\side@barT{3}{\Urb} +%Left +\side@barL{1}{\Lrb} +\side@barL{2}{\Lrm} +\side@barL{3}{\Lrt} +%Right +\side@barR{1}{\Rlb} +\side@barR{2}{\Rlm} +\side@barR{3}{\Rlt} +%Bottom +\side@barB{1}{\Dlt} +\side@barB{2}{\Dmt} +\side@barB{3}{\Drt} } % \end{macrocode} % \end{macro} % % -% \begin{macro}{\DrawFlatRightSide} -% Draws the \textsc{right} face together with all four sidebars -% (colours only). +% \begin{macro}{\DrawRubikFaceRightSide} +% Draws the \textsc{right} face together with all four sidebars. % \begin{macrocode} -\newcommand{\DrawFlatRightSide}{% -\DrawFlatRight{0}{0}% -\DrawRubikLayerSideT{\Urb}{\Urm}{\Urt}% -\DrawRubikLayerSideL{\Frt}{\Frm}{\Frb}% -\DrawRubikLayerSideR{\Blt}{\Blm}{\Blb}% -\DrawRubikLayerSideB{\Drt}{\Drm}{\Drb}% +\newcommand{\DrawRubikFaceRightSide}{% +\DrawRubikFlatRight{0}{0}% +%Top +\side@barT{1}{\Urb} +\side@barT{2}{\Urm} +\side@barT{3}{\Urt} +%Left +\side@barL{1}{\Frb} +\side@barL{2}{\Frm} +\side@barL{3}{\Frt} +%Right +\side@barR{1}{\Blb} +\side@barR{2}{\Blm} +\side@barR{3}{\Blt} +%Bottom +\side@barB{1}{\Drt} +\side@barB{2}{\Drm} +\side@barB{3}{\Drb} } % \end{macrocode} % \end{macro} % % -% \begin{macro}{\DrawFlatLeftSide} -% Draws the \textsc{left} face together with all four sidebars -% (colours only). +% \begin{macro}{\DrawRubikFaceLeftSide} +% Draws the \textsc{left} face together with all four sidebars. % \begin{macrocode} -\newcommand{\DrawFlatLeftSide}{% -\DrawFlatLeft{0}{0}% -\DrawRubikLayerSideT{\Ult}{\Ulm}{\Ulb}% -\DrawRubikLayerSideL{\Brt}{\Brm}{\Brb}% -\DrawRubikLayerSideR{\Flt}{\Flm}{\Flb}% -\DrawRubikLayerSideB{\Dlb}{\Dlm}{\Dlt}% +\newcommand{\DrawRubikFaceLeftSide}{% +\DrawRubikFlatLeft{0}{0}% +%Top +\side@barT{1}{\Ult} +\side@barT{2}{\Ulm} +\side@barT{3}{\Ulb} +%Left +\side@barL{1}{\Brb} +\side@barL{2}{\Brm} +\side@barL{3}{\Brt} +%Right +\side@barR{1}{\Flb} +\side@barR{2}{\Flm} +\side@barR{3}{\Flt} +%Bottom +\side@barB{1}{\Dlb} +\side@barB{2}{\Dlm} +\side@barB{3}{\Dlt} } % \end{macrocode} % \end{macro} % % -% \begin{macro}{\DrawFlatBackSide} -% Draws the \textsc{back} face together with all four sidebars -% (colours only). +% \begin{macro}{\DrawRubikFaceBackSide} +% Draws the \textsc{back} face together with all four sidebars. % \begin{macrocode} -\newcommand{\DrawFlatBackSide}{% -\DrawFlatBack{0}{0}% -\DrawRubikLayerSideT{\Urt}{\Umt}{\Ult}% -\DrawRubikLayerSideL{\Rrt}{\Rrm}{\Rrb}% -\DrawRubikLayerSideR{\Llt}{\Llm}{\Llb}% -\DrawRubikLayerSideB{\Drb}{\Dmb}{\Dlb}% +\newcommand{\DrawRubikFaceBackSide}{% +\DrawRubikFlatBack{0}{0}% +%Top +\side@barT{1}{\Urt} +\side@barT{2}{\Umt} +\side@barT{3}{\Ult} +%Left +\side@barL{1}{\Rrb} +\side@barL{2}{\Rrm} +\side@barL{3}{\Rrt} +%Right +\side@barR{1}{\Llb} +\side@barR{2}{\Llm} +\side@barR{3}{\Llt} +%Bottom +\side@barB{1}{\Drb} +\side@barB{2}{\Dmb} +\side@barB{3}{\Dlb} } % \end{macrocode} % \end{macro} % % -% \begin{macro}{\DrawFlatDownSide} -% Draws the \textsc{down} face together with all four sidebars -% (colours only). +% \begin{macro}{\DrawRubikFaceDownSide} +% Draws the \textsc{down} face together with all four sidebars. % \begin{macrocode} -\newcommand{\DrawFlatDownSide}{% -\DrawFlatDown{0}{0}% -\DrawRubikLayerSideT{\Flb}{\Fmb}{\Frb}% -\DrawRubikLayerSideL{\Lrb}{\Lmb}{\Llb}% -\DrawRubikLayerSideR{\Rlb}{\Rmb}{\Rrb}% -\DrawRubikLayerSideB{\Brb}{\Bmb}{\Blb}% +\newcommand{\DrawRubikFaceDownSide}{% +\DrawRubikFlatDown{0}{0}% +%Top +\side@barT{1}{\Flb} +\side@barT{2}{\Fmb} +\side@barT{3}{\Frb} +%Left +\side@barL{1}{\Llb} +\side@barL{2}{\Lmb} +\side@barL{3}{\Lrb} +%Right +\side@barR{1}{\Rrb} +\side@barR{2}{\Rmb} +\side@barR{3}{\Rlb} +%Bottom +\side@barB{1}{\Brb} +\side@barB{2}{\Bmb} +\side@barB{3}{\Blb} } % \end{macrocode} % \end{macro} % % % -% \subsection{\hspace{3mm}DrawFace commands} -% \label{sec:drawfacecode} +% \subsection{\hspace{3mm}DrawRubikFace commands} +% \label{sec:drawrubikfacecode} +% +% \textsc{Background}: \ The above \cmd{\DrawRubikFlat..} commands were originally just +% \cmd{\DrawFlat..} commands. They were subsequently copied \& renamed +% (here) as the more intuitive \cmd{\DrawFace..} commands, since most of +% the time the user wants just to draw a particular face with or +% without sidebars. % -% 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. +% In v5 it was necessary to rename them as \cmd{\DrawRubikFace...} commands +% since they relate to a 3x3x3 cube. At the same time we also included +% their more convenient short-hand versions +% (eg \cmd{\DrawRubikFaceUpSide} $\rightarrow$ \cmd{\DrawRubikFaceUS} etc), +% as the commands were getting a bit too long. +% +% We therefore now deprecate the use of the earlier +% \cmd{\DrawFace...} commands, although they will be maintained for the +% moment at least. +% \begin{macrocode} +\newcommand{\DrawRubikFaceUp}{\DrawRubikFlatUp{0}{0}} +\newcommand{\DrawRubikFaceDown}{\DrawRubikFlatDown{0}{0}} +\newcommand{\DrawRubikFaceLeft}{\DrawRubikFlatLeft{0}{0}} +\newcommand{\DrawRubikFaceRight}{\DrawRubikFlatRight{0}{0}} +\newcommand{\DrawRubikFaceFront}{\DrawRubikFlatFront{0}{0}} +\newcommand{\DrawRubikFaceBack}{\DrawRubikFlatBack{0}{0}} +% \end{macrocode} +%% RWDN19A Finally, we create the short-hand versions. % \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} +\newcommand{\DrawRubikFaceU}{\DrawRubikFaceUp} +\newcommand{\DrawRubikFaceD}{\DrawRubikFaceDown} +\newcommand{\DrawRubikFaceL}{\DrawRubikFaceLeft} +\newcommand{\DrawRubikFaceR}{\DrawRubikFaceRight} +\newcommand{\DrawRubikFaceF}{\DrawRubikFaceFront} +\newcommand{\DrawRubikFaceB}{\DrawRubikFaceBack} +\newcommand{\DrawRubikFaceUS}{\DrawRubikFaceUpSide} +\newcommand{\DrawRubikFaceDS}{\DrawRubikFaceDownSide} +\newcommand{\DrawRubikFaceLS}{\DrawRubikFaceLeftSide} +\newcommand{\DrawRubikFaceRS}{\DrawRubikFaceRightSide} +\newcommand{\DrawRubikFaceFS}{\DrawRubikFaceFrontSide} +\newcommand{\DrawRubikFaceBS}{\DrawRubikFaceBackSide} % \end{macrocode} % % -% \subsection{\hspace{3mm}SideBar commands} +% \subsection{Sidebars (Face)} +% \label{sec:sidebarcode} % -% SideBar commands draw narrow bars of colour indicating the +% Sidebar commands draw narrow bars of colour indicating the % side colours of each of the facelets forming the side of -% a given layer (face). Each SideBar is the length of a single facelet. +% a given layer (face). Each Sidebar is the length of a +% single facelet (see Section~\ref{sec:sidebars}). % -% \begin{macro}{\RubikSideBarWidth} -% \begin{macro}{\RubikSideBarLength} -% \begin{macro}{\RubikSideBarSep} +% \begin{macro}{\RubikSidebarWidth} +% \begin{macro}{\RubikSidebarLength} +% \begin{macro}{\RubikSidebarSep} % These three commands allow the user to set the Width, Length % and Separation parameters for the sidebar (in decimal values, % where 1~is equivalent to the length of the side of a facelet). @@ -5076,267 +5267,670 @@ % \end{macro} % \end{macro} % \begin{macrocode} -\newcommand{\RubikSideBarWidth}[1]{\pgfmathsetmacro{\bw}{#1}} -\newcommand{\RubikSideBarLength}[1]{\pgfmathsetmacro{\bl}{#1}} -\newcommand{\RubikSideBarSep}[1]{\pgfmathsetmacro{\bs}{#1}} +\newcommand{\RubikSidebarWidth}[1]{\pgfmathsetmacro{\bw}{#1}} +\newcommand{\RubikSidebarLength}[1]{\pgfmathsetmacro{\bl}{#1}} +\newcommand{\RubikSidebarSep}[1]{\pgfmathsetmacro{\bs}{#1}} % \end{macrocode} % We first set some default values % \begin{macrocode} -\RubikSideBarWidth{0.3}% -\RubikSideBarLength{1}% -\RubikSideBarSep{0.3}% +\RubikSidebarWidth{0.3}% +\RubikSidebarLength{1}% +\RubikSidebarSep{0.3}% +% \end{macrocode} +% In order to avoid conflicting nomenclature (between bar and Bar) we recommend +% using the lowercase `bar' and deprecate the use of `Bar' in commands. +% For backwards compatibility, however, we will retain the three original `Bar' +% commands (for the moment at least), as follows: +% \begin{macrocode} +\newcommand{\RubikSideBarWidth}[1]{\pgfmathsetmacro{\bw}{#1}} +\newcommand{\RubikSideBarLength}[1]{\pgfmathsetmacro{\bl}{#1}} +\newcommand{\RubikSideBarSep}[1]{\pgfmathsetmacro{\bs}{#1}} % \end{macrocode} % % -% \subsubsection{\hspace{3mm}Allocating a colour to a single facelet sidebar} +% +% +% \subsubsection{\hspace{3mm}Drawing and allocating a colour to a single facelet sidebar} +% \label{sec:side@barcode} +% +% +% Full length face sidebars are really multiple instances of +% small single facelet bars, each of which is drawn using one of the internal sidebar +% commands. +% +% +% \begin{figure}[hbt] +% \centering +% \ifpdf +% \includegraphics[height=3cm]{rubik-doc-figD.pdf} +% \fi +% \vspace{-5mm} +% \caption{\label{fig:facenotation}Face-edge and facelet-position codes +% (see text) } +% \end{figure} % +% % \begin{macro}{\side@barT} % \begin{macro}{\side@barB} % \begin{macro}{\side@barL} % \begin{macro}{\side@barR} -% Internal commands. -% Full length face SideBars are really multiple instances of -% single facelet bars, -% each of which is drawn using one of four internal SideBar -% commands---one for each of the sides which we shall -% call Top, Bottom, Left, Right. -% Each SideBar command takes two arguments: one for facelet position -% \marg{$ 1 \mid 2 \mid 3$} and one for -% the colour-code \marg{$ R \mid O \mid Y \mid G \mid B \mid W \mid X $}. -% -% \textsc{example}: the following command allocates a colour to a single -% facelet sidebar on the Left of a Rubik face: +% There are four \cmd{\side@barX} commands, each with a trailing letter code X, which indicates the +% position of the sidebar relative to the square face displayed, +% namely either T (Top), B (Bottom), L (Left) or R (Right) +% ---see Figure~\ref{fig:facenotation}. + +% \cmd{\side@barL}\marg{position-number}\marg{facelet location-code}. +% Each \cmd{\side@barX} command takes two arguments: +% The first argument is a number (distance) \marg{$ 1 \mid 2 \mid 3$} +% from the relevant axis depending on whether it is a vertical or horizontal sidebar +% (e.g.,~1 = first bar (nearest the origin); 2 = second bar, +% 3 = third bar). +% +% The second argument is the facelet location-code expressed as a command +% (e.g.,~\cmd{\Lrt}, \cmd{\Dlb} etc. Note that the facelet location +% uses a three letter code: the first (capital) letter (U, D, L, R, F, B) denotes the \textsc{face}; +% the second (lower-case) letter (l,m,r) is the `x' position in the 3x3 matrix; +% the third (lower-case) letter (t,m,b) is the `y' position ---see Figure~\ref{fig:facenotation}. +% +% \textsc{example}: the following command draws a small single Right sidebar, +% in the middle position (no.~2), with the colour +% allocated to the Rlt facelet (left top facelet in the \textsc{right} face. % \begin{quote} -% \cmd{\side@barL}\marg{facelet-position}\marg{colour-code} +% \verb!\side@barR{2}{\Rlt}! % \end{quote} -% There are three facelet positions on each of the four sides -% of a face, and these -% are numbered 1 to 3 starting from the bottom left corner (1,1). -% The SideBar command also implements the set (or default) -% Length (\cmd{\bl}), Width (\cmd{\bw}) and Separation (\cmd{\bs}) +% Notice that we use the command \cmd{\Rlt} as the argument; this is because +% the command is defined as: \verb!\def{\Rlt}{#1}!, and hence the command gets replaced by the +% colour-code currently allocated to this particular facelet. +% +% There are three small rectangular sidebars on each of the four sides +% of a 3x3 square face, and these are embedded in a coordinate system with origin +% at the bottom left corner (0,0) of the square face (see Figure~\ref{fig:facenotation}). +% +% The \cmd{\side@bar..} command also implements the set (or default) +% RubikSidebarLength \cmd{\bl}, RubikSidebarWidth \cmd{\bw} +% and RubikSidebarSep \cmd{\bs} (separation) % values mentioned above. \cmd{\blh} = Half \cmd{\bl} = \cmd{\bl}/2. % 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 bottom Left corner of the bar =(\cmd{\dx},\cmd{\dy}) +% must be inside the \cmd{\side@bar..} command in order to work. +% The start point of the TikZ \cmd{\draw} command for each rectangular sidebar +% is the bottom Left corner of the sidebar = (\cmd{\dx},\cmd{\dy}). % \end{macro} % \end{macro} % \end{macro} % \end{macro} % +% +% \label{sec:nosidebarcode} +% \begin{macro}{\no@sidebar} +% The \cmd{\NoSidebar}\marg{colour code} command defines a (single) colour for which +% sidebars should \textit{not} be drawn (particularly useful when drawing OLL configurations). +% This idea was suggested by Robert Ma\v{r}\'{\i}k (May 2017) ---see Section~\ref{sec:nosidebar}. +% {\newline}The principle is that we let the command \cmd{\NoSidebar} define a face colour, +% and then we use the \verb!\ifthenelse{\equal{#2}{\no@sidebar}}{}{...}! structure +% inside the \cmd{\side@bar..} commands (see below) +% to either (a)~draw all sidebars as usual (if \cmd{\NoSidebar} is undefined), +% or (b)~draw all sidebars \textit{except} +% those having the \cmd{\NoSidebar} colour (if \cmd{\NoSidebar} colour = \verb!#2!). +% \newline\textsc{usage}: \verb!\NoSidebar{X}! \ If this command in \textit{not} +% inside an environment, then its action will continue until it is disabled +% (undefined) as follows: \verb!\NoSidebar{}!. +% \begin{macrocode} +\def\no@sidebar{}% +\newcommand{\NoSidebar}[1]{\def\no@sidebar{#1}} +% \end{macrocode} +% \end{macro} +% +% % \begin{macrocode} \newcommand{\side@barL}[2]{% -%% #1 = cubie possn no, #2 = colour -\pgfmathsetmacro{\blh}{\bl*(0.5)}% -\pgfmathsetmacro{\dx}{0 - \bs - \bw}% -\pgfmathsetmacro{\dy}{#1-1+0.5-\blh}% -\draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) + %% #1 = cubie possn no, #2 = colour + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{0 - \bs - \bw}% + \pgfmathsetmacro{\dy}{#1-1+0.5-\blh}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) -- (\dx+\bw,\dy+\bl) -- (\dx+\bw,\dy) -- cycle; -} +}} \newcommand{\side@barR}[2]{% -%% #1 = cubie possn no, #2 = colour -\pgfmathsetmacro{\blh}{\bl*(0.5)}% -\pgfmathsetmacro{\dx}{3 + \bs}% -\pgfmathsetmacro{\dy}{#1 -1+0.5-\blh}% -\draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) + %% #1 = cubie possn no, #2 = colour + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{3 + \bs}% + \pgfmathsetmacro{\dy}{#1 -1+0.5-\blh}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) -- (\dx+\bw,\dy+\bl) -- (\dx+\bw,\dy) -- cycle; -} +}} \newcommand{\side@barT}[2]{% -%% #1 = cubie possn no, #2 = colour -\pgfmathsetmacro{\blh}{\bl*(0.5)}% -\pgfmathsetmacro{\dx}{#1 -1+0.5-\blh}% -\pgfmathsetmacro{\dy}{3 +\bs}% -\draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw) + %% #1 = cubie possn no, #2 = colour + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{#1 -1+0.5-\blh}% + \pgfmathsetmacro{\dy}{3 +\bs}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw) -- (\dx+\bl,\dy+\bw) -- (\dx+\bl,\dy) -- cycle; -} +}} \newcommand{\side@barB}[2]{% -%% #1 = cubie possn no, #2 = colour -\pgfmathsetmacro{\blh}{\bl*(0.5)}% -\pgfmathsetmacro{\dx}{#1 -1+0.5-\blh}% -\pgfmathsetmacro{\dy}{0 -\bs-\bw}% -\draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw) + %% #1 = cubie possn no, #2 = colour + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{#1 -1+0.5-\blh}% + \pgfmathsetmacro{\dy}{0 -\bs-\bw}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw) -- (\dx+\bl,\dy+\bw) -- (\dx+\bl,\dy) -- cycle; -} +}} % \end{macrocode} % +% RWDN19C removed 20:17:2 and 20:17:3 19 Feb 2018 % -% \subsubsection{\hspace{3mm}Drawing a single facelet sidebar} -% -% \begin{macro}{\DrawRubikLayerSideX$_1$X$_2$X$_3$} -% This command draws a single facelet sidebar using the above \cmd{\sidebar} command. -% The X$_1$X$_2$X$_3$ parameters refer to the options Left, Middle, -% 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 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 possible in these cases. -% \end{quote} -% For~example, the following command -% \begin{quote} -% \cmd{\DrawRubikLayerSideLTy\{G\}} -% \end{quote} -% draws a Green sidebar above the Top Left cubie. -% \end{macro} -% -% \begin{macrocode} -%%---Left side -\newcommand{\DrawRubikLayerSideLTx}[1]{\side@barL{3}{#1}} -\newcommand{\DrawRubikLayerSideLMx}[1]{\side@barL{2}{#1}} -\newcommand{\DrawRubikLayerSideLM}[1]{\side@barL{2}{#1}} -\newcommand{\DrawRubikLayerSideLBx}[1]{\side@barL{1}{#1}} -%---Right side -\newcommand{\DrawRubikLayerSideRTx}[1]{\side@barR{3}{#1}} -\newcommand{\DrawRubikLayerSideRMx}[1]{\side@barR{2}{#1}} -\newcommand{\DrawRubikLayerSideRM}[1]{\side@barR{2}{#1}} -\newcommand{\DrawRubikLayerSideRBx}[1]{\side@barR{1}{#1}} -%---Top side -\newcommand{\DrawRubikLayerSideLTy}[1]{\side@barT{1}{#1}} -\newcommand{\DrawRubikLayerSideMTy}[1]{\side@barT{2}{#1}} -\newcommand{\DrawRubikLayerSideMT}[1]{\side@barT{2}{#1}} -\newcommand{\DrawRubikLayerSideRTy}[1]{\side@barT{3}{#1}} -%---Bottom side -\newcommand{\DrawRubikLayerSideLBy}[1]{\side@barB{1}{#1}} -\newcommand{\DrawRubikLayerSideMBy}[1]{\side@barB{2}{#1}} -\newcommand{\DrawRubikLayerSideMB}[1]{\side@barB{2}{#1}} -\newcommand{\DrawRubikLayerSideRBy}[1]{\side@barB{3}{#1}} -% \end{macrocode} -% -% -% \subsubsection{\hspace{3mm}Drawing multiple cubie sidebars} -% -% \begin{macro}{\DrawRubikLayerSideT} -% \begin{macro}{\DrawRubikLayerSideB} -% \begin{macro}{\DrawRubikLayerSideL} -% \begin{macro}{\DrawRubikLayerSideR} -% These commands allow the drawing of 3 small sidebars along -% one particular side (Top, Bottom, Left, Right), as indicated -% by the appended T, B, L, R letter code. -% Each command takes three ordered colour arguments, which are ordered -% either from left to right (the T and B forms), or from top to bottom -% (the L and R forms) -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} -% \begin{macrocode} -%%--Top side--- -\newcommand{\DrawRubikLayerSideT}[3]{% - \DrawRubikLayerSideLTy{#1}% - \DrawRubikLayerSideMTy{#2}% - \DrawRubikLayerSideRTy{#3}% -} -%%--Bottom side--- -\newcommand{\DrawRubikLayerSideB}[3]{% - \DrawRubikLayerSideLBy{#1}% - \DrawRubikLayerSideMBy{#2}% - \DrawRubikLayerSideRBy{#3}% +% +% +% +% +% +% \subsection{Sidebars (Cube)} +% \label{sec:sidebarscubecode} +% +% +% In order to position sidebars adjacent to a Rubik Cube (ie in 3D) +% requires that we first make some new \cmd{\side@bar..} +% commands for drawing sidebars adjacent to the \textsc{back} face of the cube +% (we have already made the macros for the front +% face sidebars---see Section~\ref{sec:sidebarcode}). +% Furthermore, these new macros need to be tailored to each of the +% four standard cube viewing directions RU, LU, RD, LD. +% +% Finally, the USER commands for drawing these sidebars need +% to accommodate (a)~some code for identifying each set of sidebars, +% and (b)~the viewing direction. So, for example, a USER command for +% drawing the sidebars associated with the cube edge formed +% by the \textsc{right} face and the \textsc{back} face +% (lets define this as the RB sidebar) as viewed from the RU direction, +% might be something like \cmd{\DrawRubikCubeSidebarRBRU}. +% Since this is not particularly user-friendly, +% we can improve on this slightly for the USER by +% (a)~defining the sidebar as \texttt{SidebarRB}, and +% (b)~appending the view direction in a curly bracket, say as \verb!{RU}!. +% This allows a more intuitive command structure for the USER, +% as follows: \verb!\DrawRubikCubeSidebarRB{RU}!. +% We then use the \cmd{\@join} command to append the string \verb!RU! to the string +% \verb!DrawRubicCubeSidebarRB! forming the (internal) +% command \cmd{\DrawRubicCubeSidebarRBRU}. +% +% In the following we will group the code according to to the view +% direction (RU, LU, RD, LD). +% +% +% +% \subsubsection{Sidebars: RU view} +% +% \subsubsection*{Right-Back vert sidebar (RU view)} +% +% +% Need to write a new command for this position +% modified from \cmd{\side@barR} (in Section 20.16.1) +% draws only a single small bar +% each of the three small bars has a numbered position (1,2,3); +% (dx,dy) = bottom Left corner of single facelet bar +% \begin{macrocode} +\newcommand{\side@barRubikRbackRU}[2]{% + %% #1 = cubie possn no, #2 = colour + %% dx --> dx+1 + %% dy --> dy+1 + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{3 + \bs +1}% + \pgfmathsetmacro{\dy}{#1 -1+0.5-\blh +1}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) + -- (\dx+\bw,\dy+\bl) -- (\dx+\bw,\dy) -- cycle; +}} +% \end{macrocode} +% Make the RB (RightBack) version; +% bar 1 is at the bottom +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarRBRU}{% +\side@barRubikRbackRU{3}{\Blt}% +\side@barRubikRbackRU{2}{\Blm}% +\side@barRubikRbackRU{1}{\Blb}% } -%%--Left side-------- -%% colours run vertically DOWN -\newcommand{\DrawRubikLayerSideL}[3]{% - \DrawRubikLayerSideLTx{#1}% - \DrawRubikLayerSideLMx{#2}% - \DrawRubikLayerSideLBx{#3}% +% \end{macrocode} +% Now do the reverse (BR) = RB +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarBRRU}{\DrawRubikCubeSidebarRBRU} +% \end{macrocode} +% Make the join commands +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarRB}[1]{\@join{\DrawRubikCubeSidebarRB}{#1}} +\newcommand{\DrawRubikCubeSidebarBR}[1]{\@join{\DrawRubikCubeSidebarBR}{#1}} +% \end{macrocode} +% +% +% \medskip +% +% \subsubsection*{Up-Back horiz sidebar (RU view)} +% +% +% Need to write a new command for this position +% modified from \cmd{\side@barT} (in Section 20.16.1) +% draws only a single small bar +% each of the three small bars has a numbered position (1,2,3); +% (dx,dy) = bottom Left corner of single facelet bar +% \begin{macrocode} +\newcommand{\side@barRubikTbackRU}[2]{% + %% #1 = cubie possn no; #2 = colour + %% dx --> dx+1 + %% dy --> dy+1 + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{#1 -1+0.5-\blh +1}% + \pgfmathsetmacro{\dy}{3 +\bs +1}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw) + -- (\dx+\bl,\dy+\bw) -- (\dx+\bl,\dy) -- cycle; +}} +% \end{macrocode} +% Make the UB (Up-Back) version; +% bar 1 is at the left, 3 on the rhs (as we look at the image) +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarUBRU}{% +\side@barRubikTbackRU{1}{\Brt}% +\side@barRubikTbackRU{2}{\Bmt}% +\side@barRubikTbackRU{3}{\Blt}% } -%%--Right side-------- -%% colours run vertically DOWN -\newcommand{\DrawRubikLayerSideR}[3]{% - \DrawRubikLayerSideRTx{#1}% - \DrawRubikLayerSideRMx{#2}% - \DrawRubikLayerSideRBx{#3}% +% \end{macrocode} +% Now do the reverse (BU) = UB +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarBURU}{\DrawRubikCubeSidebarUBRU} +% \end{macrocode} +% Make the join commands +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarUB}[1]{\@join{\DrawRubikCubeSidebarUB}{#1}} +\newcommand{\DrawRubikCubeSidebarBU}[1]{\@join{\DrawRubikCubeSidebarBU}{#1}} +% \end{macrocode} +% +% +% \medskip +% +% \subsubsection*{Front-Left vert sidebar (RU view)} +% +% For the front face we can use the regular \cmd{side@barL} commands +% since it is the same as for an ordinary face sidebar +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFLRU}{% +\side@barL{3}{\Lrt}% +\side@barL{2}{\Lrm}% +\side@barL{1}{\Lrb}% } % \end{macrocode} +% Now do the reverse (LF) +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarLFRU}{\DrawRubikCubeSidebarFLRU} +% \end{macrocode} +% Now do the two join commands +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFL}[1]{\@join{\DrawRubikCubeSidebarFL}{#1}} +\newcommand{\DrawRubikCubeSidebarLF}[1]{\@join{\DrawRubikCubeSidebarLF}{#1}} +% \end{macrocode} % -% \begin{macro}{\DrawRubikLayerSideLR} -% This command draws six cubie sidebars, three on each side, drawn in (L, R) -% pairs. The command takes six colour arguments, ordered in pairs, -% as shown in the following example. -% \begin{quote} -%\begin{verbatim} -% \DrawRubikLayerSideLR{G} {G} -% {R} {B} -% {Y} {B} -%\end{verbatim} -% \end{quote} -% \begin{macrocode} -\newcommand{\DrawRubikLayerSideLR}[6]{% - \DrawRubikLayerSideLTx{#1}% - \DrawRubikLayerSideRTx{#2}% - \DrawRubikLayerSideLMx{#3}% - \DrawRubikLayerSideRMx{#4}% - \DrawRubikLayerSideLBx{#5}% - \DrawRubikLayerSideRBx{#6}% +% +% \medskip +% +% \subsubsection*{Front-Down horizontal sidebar (RU view)} +% +% Horiz sidebar, so 1 at the left, 2=middle, 3= rhs) +% here we have to use the B for bottom (of front face) and the +% facelets of the top row of the Down face +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFDRU}{% +\side@barB{1}{\Dlt}% +\side@barB{2}{\Dmt}% +\side@barB{3}{\Drt}% } % \end{macrocode} -% \end{macro} +% Now do the reverse (DF) = FD +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarDFRU}{\DrawRubikCubeSidebarFDRU} +% \end{macrocode} +% Now do the two join commands +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFD}[1]{\@join{\DrawRubikCubeSidebarFD}{#1}} +\newcommand{\DrawRubikCubeSidebarDF}[1]{\@join{\DrawRubikCubeSidebarDF}{#1}} +% \end{macrocode} +% But FD-LU is the same as FD-RU, so need to make copies of each +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarDFLU}{\DrawRubikCubeSidebarDFRU} +\newcommand{\DrawRubikCubeSidebarFDLU}{\DrawRubikCubeSidebarFDRU} +% \end{macrocode} +% +% +% \medskip +% +% \subsubsection{Sidebars: LU view} % % -% \subsection{\hspace{3mm}RubikSide commands} -% \label{sec:rubiksidecode} +% \subsubsection*{Left-Back vert sidebar (LU view)} % -% \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. +% Need to write a new command for this position +% modified from \cmd{\side@barL} (in Section 20.16.1) +% draws only a single small bar +% each of the three small bars has a numbered position (1,2,3); +% (dx,dy) = bottom Left corner of single facelet bar % \begin{macrocode} -\newcommand{\RubikSideFront}[3]{% -\def\Flt{#1}\def\Fmt{#2}\def\Frt{#3}% +\newcommand{\side@barRubikLbackLU}[2]{% + %% #1 = cubie possn no, #2 = colour + %% dx --> dx-1 + %% dy --> dy+1 + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{0 - \bs -\bw -1}% + \pgfmathsetmacro{\dy}{#1 -1+0.5-\blh +1}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) + -- (\dx+\bw,\dy+\bl) -- (\dx+\bw,\dy) -- cycle; +}} +% \end{macrocode} +% Make the LB (LeftBack) version; +% bar 1 is at the bottom +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarLBLU}{% +\side@barRubikLbackLU{3}{\Brt}% +\side@barRubikLbackLU{2}{\Brm}% +\side@barRubikLbackLU{1}{\Brb}% } -\newcommand{\RubikSideRight}[3]{% -\def\Rlt{#1}\def\Rmt{#2}\def\Rrt{#3}% +% \end{macrocode} +% Now do the reverse (BL) = LB +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarBLLU}{\DrawRubikCubeSidebarLBLU} +% \end{macrocode} +% Make the join commands +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarLB}[1]{\@join{\DrawRubikCubeSidebarLB}{#1}} +\newcommand{\DrawRubikCubeSidebarBL}[1]{\@join{\DrawRubikCubeSidebarBL}{#1}} +% \end{macrocode} +% +% +% \medskip +% +% \subsubsection*{Up-Back horizontal sidebar (LU view)} +% +% Modified from \cmd{\side@barT} (in Section 20.16.1) +% draws only a single small bar +% each of the three small bars has a numbered position (1,2,3); +% (dx,dy) = bottom Left corner of single facelet bar +% \begin{macrocode} +\newcommand{\side@barRubikTbackLU}[2]{% + %% #1 = cubie possn no; #2 = colour + %% dx --> dx-1 + %% dy --> dy+1 + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{#1 -1+0.5-\blh -1}% + \pgfmathsetmacro{\dy}{3 +\bs +1}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw) + -- (\dx+\bl,\dy+\bw) -- (\dx+\bl,\dy) -- cycle; +}} +% \end{macrocode} +% Make the UB (Up-Back) version; +% bar 1 is at the left, 3 on the rhs (as we look at the image) +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarUBLU}{% +\side@barRubikTbackLU{1}{\Brt}% +\side@barRubikTbackLU{2}{\Bmt}% +\side@barRubikTbackLU{3}{\Blt}% } -\newcommand{\RubikSideLeft}[3]{% -\def\Llt{#1}\def\Lmt{#2}\def\Lrt{#3}% +% \end{macrocode} +% Now do the reverse (BU) = UB +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarBULU}{\DrawRubikCubeSidebarUBLU} +% \end{macrocode} +% Do not need to make the join commands +% as the USER commands for BU and UB are the same as for the RU. +% +% +% \medskip +% +% \subsubsection*{Front-Right vertical sidebar (LU view)} +% +% Only needed for the LU view and LD. +% for the front face we can use the regular side@barR commands +% since it is the same as for an ordinary face sidebar RHS +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFRLU}{% +\side@barR{3}{\Rlt}% +\side@barR{2}{\Rlm}% +\side@barR{1}{\Rlb}% } -\newcommand{\RubikSideBack}[3]{% -\def\Blt{#1}\def\Bmt{#2}\def\Brt{#3}% +% \end{macrocode} +% Now do the reverse (RF) +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarRFLU}{\DrawRubikCubeSidebarFRLU} +% \end{macrocode} +% Now do the two join commands +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFR}[1]{\@join{\DrawRubikCubeSidebarFR}{#1}} +\newcommand{\DrawRubikCubeSidebarRF}[1]{\@join{\DrawRubikCubeSidebarRF}{#1}} +% \end{macrocode} +% +% +% +% +% \subsubsection{Sidebars: RD view} +% +% \medskip +% +% \subsubsection*{Front-Up horizontal sidebar (RD view)} +% +% Horiz sidebar, so 1 at the left, 2=middle, 3= rhs +% here we have to use the T for bottom (of front face) and the +% facelets of the top row of the Down face +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFURD}{% +\side@barT{1}{\Ulb}% +\side@barT{2}{\Umb}% +\side@barT{3}{\Urb}% } % \end{macrocode} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} +% Now do the reverse (UF) = FU +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarUFRD}{\DrawRubikCubeSidebarFURD} +% \end{macrocode} +% Now do the two join commands +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFU}[1]{\@join{\DrawRubikCubeSidebarFU}{#1}} +\newcommand{\DrawRubikCubeSidebarUF}[1]{\@join{\DrawRubikCubeSidebarUF}{#1}} +% \end{macrocode} +% +% \medskip % +% \subsubsection*{Front-Left vertical sidebar (RD view)} % -% \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\}} +% +% Front LEFT (RD view = same as for RU) % \begin{macrocode} -\newcommand{\RubikSideFrontAll}[1]{% -\def\Flt{#1}\def\Fmt{#1}\def\Frt{#1}% +\newcommand{\DrawRubikCubeSidebarFLRD}{\DrawRubikCubeSidebarFLRU} +\newcommand{\DrawRubikCubeSidebarLFRD}{\DrawRubikCubeSidebarLFRU} +% \end{macrocode} +% +% +% \medskip +% +% \subsubsection*{Right-Back vertical sidebar (RD view)} +% +% Modified from \cmd{\side@barR} (in Section 20.16.1) +% draws only a single small bar +% each of the three small bars has a numbered position (1,2,3); +% (dx,dy) = bottom Left corner of single facelet bar +% \begin{macrocode} +\newcommand{\side@barRubikRbackRD}[2]{% + %% #1 = cubie possn no, #2 = colour + %% dx --> dx+1 + %% dy --> dy-1 + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{3 + \bs +1}% + \pgfmathsetmacro{\dy}{#1 -1+0.5-\blh -1}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) + -- (\dx+\bw,\dy+\bl) -- (\dx+\bw,\dy) -- cycle; +}} +% \end{macrocode} +% Make the RB (RightBack) version; +% bar 1 is at the bottom +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarRBRD}{% +\side@barRubikRbackRD{3}{\Blt}% +\side@barRubikRbackRD{2}{\Blm}% +\side@barRubikRbackRD{1}{\Blb}% } -\newcommand{\RubikSideRightAll}[1]{% -\def\Rlt{#1}\def\Rmt{#1}\def\Rrt{#1}% +% \end{macrocode} +% Now do the reverse (BR) = RB +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarBRRD}{\DrawRubikCubeSidebarRBRD} +% \end{macrocode} +% Do NOT need to make the join commands (same as for the RU view) +% +% +% \medskip +% +% \subsubsection*{Down-Back horizotal sidebar (RD view)} +% +% Modified from \cmd{\side@barB} (in Section 20.16.1) +% draws only a single small bar +% each of the three small bars has a numbered position (1,2,3); +% (dx,dy) = bottom Left corner of single facelet bar +% \begin{macrocode} +\newcommand{\side@barRubikBbackRD}[2]{% + %% #1 = cubie possn no; #2 = colour + %% dx --> dx+1 + %% dy --> dy-1 + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{#1 -1+0.5-\blh +1}% + \pgfmathsetmacro{\dy}{0 -\bs - \bw -1}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw) + -- (\dx+\bl,\dy+\bw) -- (\dx+\bl,\dy) -- cycle; +}} +% \end{macrocode} +% Make the DB (Down-Back) version; +% bar 1 is at the left, 3 on the rhs (as we look at the image) +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarDBRD}{% +\side@barRubikBbackRD{1}{\Brb}% +\side@barRubikBbackRD{2}{\Bmb}% +\side@barRubikBbackRD{3}{\Blb}% } -\newcommand{\RubikSideLeftAll}[1]{% -\def\Llt{#1}\def\Lmt{#1}\def\Lrt{#1}% +% \end{macrocode} +% Now do the reverse (BD) = DB +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarBDRD}{\DrawRubikCubeSidebarDBRD} +% \end{macrocode} +% Make the join commands +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarDB}[1]{\@join{\DrawRubikCubeSidebarDB}{#1}} +\newcommand{\DrawRubikCubeSidebarBD}[1]{\@join{\DrawRubikCubeSidebarBD}{#1}} +% \end{macrocode} +% +% +% +% \subsubsection{Sidebars: LD view} +% +% +% \medskip +% +% \subsubsection*{Front-Up horizontal sidebar (LD view)} +% +% But FR (LD view) is the same as for (RU view), (see above) +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFULD}{\DrawRubikCubeSidebarFURD} +\newcommand{\DrawRubikCubeSidebarUFLD}{\DrawRubikCubeSidebarUFRD} +% \end{macrocode} +% +% \medskip +% +% \subsubsection*{Front-Right vertical sidebar (LD view)} +% +% Front Right (LDview) = same as for (LU view), (see above) +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarFRLD}{\DrawRubikCubeSidebarFRLU} +\newcommand{\DrawRubikCubeSidebarRFLD}{\DrawRubikCubeSidebarRFLU} +% \end{macrocode} +% +% +% \medskip +% +% \subsubsection*{Left-Back vertical sidebar (LD view)} +% +% Modified from \cmd{\side@barL} (in Section 20.16.1) +% draws only a single small bar +% each of the three small bars has a numbered position (1,2,3); +% (dx,dy) = bottom Left corner of single facelet bar +% \begin{macrocode} +\newcommand{\side@barRubikLbackLD}[2]{% + %% #1 = cubie possn no, #2 = colour + %% dx --> dx-1 + %% dy --> dy-1 + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{0 - \bs -\bw -1}% + \pgfmathsetmacro{\dy}{#1 -1+0.5-\blh -1}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bl) + -- (\dx+\bw,\dy+\bl) -- (\dx+\bw,\dy) -- cycle; +}} +% \end{macrocode} +% Make the LB (LeftBack) version; +% bar 1 is at the bottom +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarLBLD}{% +\side@barRubikLbackLD{3}{\Brt}% +\side@barRubikLbackLD{2}{\Brm}% +\side@barRubikLbackLD{1}{\Brb}% } -\newcommand{\RubikSideBackAll}[1]{% -\def\Blt{#1}\def\Bmt{#1}\def\Brt{#1}% +% \end{macrocode} +% Now do the reverse (BL) = LB +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarBLLD}{\DrawRubikCubeSidebarLBLD} +% \end{macrocode} +% Do NOT need to make the join commands (same as for the LU view) +% +% +% \medskip +% +% \subsubsection*{Down-Back horizontal sidebar (LD view)} +% +% +% Modified from \cmd{\side@barB} (in Section 20.16.1) +% draws only a single small bar +% each of the three small bars has a numbered position (1,2,3); +% (dx,dy) = bottom Left corner of single facelet bar +% \begin{macrocode} +\newcommand{\side@barRubikBbackLD}[2]{% + %% #1 = cubie possn no; #2 = colour + %% dx --> dx-1 + %% dy --> dy-1 + \ifthenelse{\equal{#2}{\no@sidebar}}{}{% + \pgfmathsetmacro{\blh}{\bl*(0.5)}% + \pgfmathsetmacro{\dx}{#1 -1+0.5-\blh -1}% + \pgfmathsetmacro{\dy}{0 -\bs - \bw -1}% + \draw[fill=#2] (\dx,\dy) -- (\dx,\dy + \bw) + -- (\dx+\bl,\dy+\bw) -- (\dx+\bl,\dy) -- cycle; +}} +% \end{macrocode} +% Make the DB (Down-Back) version; +% bar 1 is at the left, 3 on the rhs (as we look at the image) +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarDBLD}{% +\side@barRubikBbackLD{1}{\Brb}% +\side@barRubikBbackLD{2}{\Bmb}% +\side@barRubikBbackLD{3}{\Blb}% } % \end{macrocode} -% \end{macro} -% \end{macro} -% \end{macro} -% \end{macro} +% Now do the reverse (BD) = DB +% \begin{macrocode} +\newcommand{\DrawRubikCubeSidebarBDLD}{\DrawRubikCubeSidebarDBLD} +% \end{macrocode} +% Do NOT need to make the join commands (same as for the RD view +% % % % -% \subsection{\hspace{3mm}NCube command} +% \subsection{\hspace{3mm}DrawNCube command} % % \textsc{history}: The essence of this command was originally developed by Peter Bartal % as his command \cmd{\rubikcube} (see Bartal, @@ -5585,7 +6179,7 @@ % % % \subsection{\hspace{3mm}Rotation commands} -% \label{sec:rotationcommands} +% \label{sec:rotationcommandscode} % % % \subsubsection{\hspace{3mm}Introduction} @@ -5603,13 +6197,13 @@ % 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). +% For~example, \verb!\rrh{D}! $\rightarrow$ join(\verb!\rrh! + \verb!D!) $\rightarrow$ \verb!\rrhD! +% (see Section~\ref{sec:cmdsusingjoin} for details). % % 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 +% types are designed to have the same height so they sit nicely when arranged side-by-side. +% A lot of special macros for 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 @@ -5623,12 +6217,12 @@ % (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}). +% have the same vertical position as their `arrow' cousins. A typical example +% is the form \rrh{Bw}\ which is detailed in 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, +% were originally checked for using the \texttt{ltugboat.cls}, and all fixed mainly +% by setting their associated small minipages $\rightarrow$ width = 0.6cm, % and using TikZ scale=0.5. % % @@ -5641,7 +6235,7 @@ % 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 +% \textsc{todo}: ? make this a proper internal command % using \verb!@! sometime. % % \begin{macrocode} @@ -5652,14 +6246,14 @@ % \end{macro} % % We now define a number of points and line-segments inside the square -% (e.g.,~\cmd{\@sd}, \cmd{\@sh} \ldots\ etc.) which will be required +% `notationbox' (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 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 +% \textsc{todo}: make a small diagram to illustrate the position of these % parameters and make things a bit clearer sometime. % %\begin{macrocode} @@ -5697,25 +6291,31 @@ % \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 +% rotation commands. They attach a letter or a prime to the associated argument; +% for~example, the command \verb!\@rrwp{B}! appends a `w' and a prime (p) to the +% argument `B', i.e.~$\rightarrow$ \rr{Bwp} (see Section~\ref{sec:coderotationBwp}). +% Users are then able to access this glyph by typing the command \verb!\rrBwp!, or, +% more intuitively, \verb!\rr{Bwp}! +% (see also \verb!\@join! detailed in Section~\ref{sec:cmdsusingjoin}). +% +% 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 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 \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). +% Note that the TikZ `thick' line code = 0.8pt (used in \cmd{\@SquareLetter}). % 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}} @@ -5742,14 +6342,22 @@ \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{\@xyzhp}[1]{[{\@rubikfont #1\raisebox{-0.6pt}{\@rubikprime}}]} +\newcommand{\@xyzRubik}[1]% + {\raisebox{3.45pt}{[{\@rubikfont #1}]}} +\newcommand{\@xyzRubikp}[1]% + {\raisebox{3.45pt}{[{\@rubikfont #1\raisebox{-0.6pt}{\@rubikprime}}]}} +\newcommand{\@xyzhbdfl}[1]% + {[\raisebox{-0.6pt}{{\@rubikfont #1}}]} +\newcommand{\@xyzhbdflp}[1]% + {[\raisebox{-0.6pt}{{\@rubikfont #1\@rubikprime}}]} +\newcommand{\@xyzbdflRubik}[1]% + {\raisebox{3.45pt}{[\raisebox{-0.6pt}{{\@rubikfont #1}}]}} +\newcommand{\@xyzbdflRubikp}[1]% + {\raisebox{3.45pt}{[\raisebox{-0.6pt}{{\@rubikfont #1\@rubikprime}}]}} \newcommand{\@SquareLetter}[1]{\setlength{\fboxsep}{2.5pt}% - \setlength{\fboxrule}{0.8pt}% - \fbox{\rule[-1pt]{0pt}{8.5pt}\raisebox{-0.5pt}{#1}}} + \setlength{\fboxrule}{0.8pt}% + \fbox{\rule[-1pt]{0pt}{8.5pt}\raisebox{-0.5pt}{#1}}} \newlength\@hRubik% \setlength{\@hRubik}{0.185cm}% % \end{macrocode} @@ -5787,33 +6395,35 @@ % % % +% +% \subsubsection{\hspace{3mm}Using {\textbackslash}\texttt{@join}} +% \label{sec:cmdsusingjoin} +% +% % \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}. +% a rotation-code, say U, into a macro (say, \cmd{\rrhU}) which typesets it in some form. % 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}). +% the intuitive command |\rrh{U}| is equivalent to \cmd{\rrhU}. % {\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} +% The following section shows how this command is used in practice. % \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 (e.g.,~U) is -% the argument (see Section~\ref{sec:overview}). As an example, the format for +% The following four commands typeset a single rotation, where a rotation-code (e.g.,~U) is +% the argument (see Section~\ref{sec:typesetting}). 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 @@ -5821,9 +6431,9 @@ % rotation hieroglyph for the rotation~U, etc. % % These four commands, which use the -% internal \cmd{\@join} command (see Section~\ref{sec:usefulinternalcommands}), are +% internal \cmd{\@join} command (see above), are % especially useful when typesetting a list of rotation-codes. -% Furthermore, it seems more intuitive to specify a rotation command +% Furthermore, it is more intuitive for the user to specify a rotation command % using the rotation-code as an argument. % \begin{macrocode} \newcommand*{\Rubik}[1]{\@join{\Rubik}{#1}} @@ -5918,6 +6528,7 @@ % % % \subsubsection{\hspace{3mm}Rotation Bwp} +% \label{sec:coderotationBwp} % % \begin{macro}{\rrBwp} % \begin{macro}{\SquareBwp} @@ -8112,11 +8723,14 @@ % \begin{macro}{\rru} % \begin{macro}{\rrhu} % \begin{macro}{\Rubiku} -% These commands all draw forms which denote the u rotation. +% These commands all draw forms which denote the u and up cube rotation. % \begin{macrocode} \newcommand{\rru}{\@rr{u}} -\newcommand{\Rubiku}{\@xyzRubik{u}} +\newcommand{\rrup}{\@rrp{u}} \newcommand{\rrhu}{\@xyzh{u}} +\newcommand{\rrhup}{\@xyzhp{u}} +\newcommand{\Rubiku}{\@xyzRubik{u}} +\newcommand{\Rubikup}{\@xyzRubikp{u}} % \end{macrocode} % \end{macro} % \end{macro} @@ -8124,11 +8738,14 @@ % \begin{macro}{\rrd} % \begin{macro}{\rrhd} % \begin{macro}{\Rubikd} -% These commands all draw forms which denote the d rotation. +% These commands all draw forms which denote the d and dp cube rotation. % \begin{macrocode} \newcommand{\rrd}{\@rr{d}} +\newcommand{\rrdp}{\@rrp{d}} \newcommand{\rrhd}{\@xyzhbdfl{d}} +\newcommand{\rrhdp}{\@xyzhbdflp{d}} \newcommand{\Rubikd}{\@xyzbdflRubik{d}} +\newcommand{\Rubikdp}{\@xyzbdflRubikp{d}} % \end{macrocode} % \end{macro} % \end{macro} @@ -8140,11 +8757,14 @@ % \begin{macro}{\rrl} % \begin{macro}{\rrhl} % \begin{macro}{\Rubikl} -% These commands all draw forms which denote the l rotation. +% These commands all draw forms which denote the l and lp cube rotation. % \begin{macrocode} \newcommand{\rrl}{\@rr{l}} +\newcommand{\rrlp}{\@rrp{l}} \newcommand{\rrhl}{\@xyzhbdfl{l}} +\newcommand{\rrhlp}{\@xyzhbdflp{l}} \newcommand{\Rubikl}{\@xyzbdflRubik{l}} +\newcommand{\Rubiklp}{\@xyzbdflRubikp{l}} % \end{macrocode} % \end{macro} % \end{macro} @@ -8152,11 +8772,14 @@ % \begin{macro}{\rrr} % \begin{macro}{\rrhr} % \begin{macro}{\Rubikr} -% These commands all draw forms which denote the r rotation. +% These commands all draw forms which denote the r and rp cube rotation. % \begin{macrocode} \newcommand{\rrr}{\@rr{r}} -\newcommand{\Rubikr}{\@xyzRubik{r}} +\newcommand{\rrrp}{\@rrp{r}} \newcommand{\rrhr}{\@xyzh{r}} +\newcommand{\rrhrp}{\@xyzhp{r}} +\newcommand{\Rubikr}{\@xyzRubik{r}} +\newcommand{\Rubikrp}{\@xyzRubikp{r}} % \end{macrocode} % \end{macro} % \end{macro} @@ -8168,11 +8791,14 @@ % \begin{macro}{\rrf} % \begin{macro}{\rrhf} % \begin{macro}{\Rubikf} -% These commands all draw forms which denote the f rotation. +% These commands all draw forms which denote the f and fp cube rotation. % \begin{macrocode} \newcommand{\rrf}{\@rr{f}} +\newcommand{\rrfp}{\@rrp{f}} \newcommand{\rrhf}{\@xyzhbdfl{f}} +\newcommand{\rrhfp}{\@xyzhbdflp{f}} \newcommand{\Rubikf}{\@xyzbdflRubik{f}} +\newcommand{\Rubikfp}{\@xyzbdflRubikp{f}} % \end{macrocode} % \end{macro} % \end{macro} @@ -8180,11 +8806,14 @@ % \begin{macro}{\rrb} % \begin{macro}{\rrhb} % \begin{macro}{\Rubikb} -% These commands all draw forms which denote the b rotation. +% These commands all draw forms which denote the b and bp cube rotation. % \begin{macrocode} \newcommand{\rrb}{\@rr{b}} +\newcommand{\rrbp}{\@rrp{b}} \newcommand{\rrhb}{\@xyzhbdfl{b}} +\newcommand{\rrhbp}{\@xyzhbdflp{b}} \newcommand{\Rubikb}{\@xyzbdflRubik{b}} +\newcommand{\Rubikbp}{\@xyzbdflRubikp{b}} % \end{macrocode} % \end{macro} % \end{macro} @@ -8740,7 +9369,7 @@ % 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 +% 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). % @@ -9846,11 +10475,17 @@ \newcommand{\textRubikz}{\rrhz} \newcommand{\textRubikzp}{\rrhzp} \newcommand{\textRubikl}{\rrhl} +\newcommand{\textRubiklp}{\rrhlp} \newcommand{\textRubikr}{\rrhr} +\newcommand{\textRubikrp}{\rrhrp} \newcommand{\textRubiku}{\rrhu} +\newcommand{\textRubikup}{\rrhup} \newcommand{\textRubikd}{\rrhd} +\newcommand{\textRubikdp}{\rrhdp} \newcommand{\textRubikf}{\rrhf} +\newcommand{\textRubikfp}{\rrhfp} \newcommand{\textRubikb}{\rrhb} +\newcommand{\textRubikbp}{\rrhbp} \newcommand{\textRubikLc}{\rrhLc} \newcommand{\textRubikLcp}{\rrhLcp} \newcommand{\textRubikRc}{\rrhRc} |