20

Taking inspiration from Playing around with a Rubik's Cube in TikZ, I want to generate diagrams of Rubik's cubes that look like this

enter image description hereenter image description hereenter image description hereenter image description here

Using a solution from Playing around with a Rubik's Cube in TikZ, I was able to generate this diagram

enter image description here

My question is what is the best way to modify the code so I can quickly generate the diagrams in the above graphic? Something like a command \cube{....}? But even I am not sure how you can specify the colour info in this manner. Use a symbol for each colour? G - green, B - blue etc. So there are 27 square faces in this diagram, so does that mean you need 27 arguments? And if you leave it blank then it will display a gray tile? I would appreciate any advice the best way to code this in LaTeX. My ultimate goal is to make over 100 diagrams like the ones above. So if it was possible to make a really efficient code to generate the diagrams that would be amazing.

MWE

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\begin{document}
\pgfmathsetmacro\radius{0.1}
\newcommand{\frontcolor}{red}
\newcommand{\sidecolor}{blue}
            \tdplotsetmaincoords{55}{135}
            \begin{tikzpicture}
                \clip (-3,-2.5) rectangle (3,2.5);
                \begin{scope}[tdplot_main_coords]
                    \filldraw [canvas is yz plane at x=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \filldraw [canvas is xz plane at y=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \filldraw [canvas is yx plane at z=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \foreach \X in {-1.5,-0.5,0.5}{
                        \foreach \Y in {-1.5,-0.5,0.5}{
                            \draw [thick,canvas is yz plane at x=1.5,shift={(\X,\Y)},fill=\sidecolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                            \draw [thick,canvas is xz plane at y=1.5,shift={(\X,\Y)},fill=\frontcolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                            \draw [thick,canvas is yx plane at z=1.5,shift={(\X,\Y)},fill=yellow] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                        }
                    }
                \end{scope}
            \end{tikzpicture}
\end{document} 
0
28

That's a neat question, and here is a proposal for an answer. The colors are stored in an array called \myarray, which determines the colors of the cells. The relation between entry (the index starts at 0) and cell is illustrated by this example

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\newif\ifshowcellnumber
\showcellnumbertrue
\begin{document}
\definecolor{R}{RGB}{202,65,55}
\definecolor{G}{RGB}{151,216,56}
\definecolor{B}{RGB}{51,72,237}
\definecolor{W}{RGB}{255,255,255}
\definecolor{X}{RGB}{65,65,65}

\newcommand{\TikZRubikFaceLeft}[9]{\def\myarrayL{#1,#2,#3,#4,#5,#6,#7,#8,#9}}
\newcommand{\TikZRubikFaceRight}[9]{\def\myarrayR{#1,#2,#3,#4,#5,#6,#7,#8,#9}}
\newcommand{\TikZRubikFaceTop}[9]{\def\myarrayT{#1,#2,#3,#4,#5,#6,#7,#8,#9}}
\newcommand{\BuildArray}{\foreach \X [count=\Y] in \myarrayL%
{\ifnum\Y=1%
\xdef\myarray{"\X"}%
\else%
\xdef\myarray{\myarray,"\X"}%
\fi}%
\foreach \X in \myarrayR%
{\xdef\myarray{\myarray,"\X"}}%
\foreach \X in \myarrayT%
{\xdef\myarray{\myarray,"\X"}}%
\xdef\myarray{{\myarray}}%
}
\TikZRubikFaceLeft
        {X}{X}{X}
        {X}{X}{X}
        {X}{X}{G}
\TikZRubikFaceRight
        {W}{X}{X}
        {R}{G}{G}
        {X}{G}{G}
\TikZRubikFaceTop
        {X}{X}{R}
        {R}{R}{G}
        {R}{R}{X}
\BuildArray
%\def\myarray{{"X","X","B","X","G","X","R","R","X","X","X","X","G","X","B","B","X","X","G","B","R","X","R","B","X","X","X"}}
\pgfmathsetmacro\radius{0.1}
\tdplotsetmaincoords{55}{135}
\begin{tikzpicture}
 \clip (-3,-2.5) rectangle (3,2.5);
 \begin{scope}[tdplot_main_coords]
  \filldraw [canvas is yz plane at x=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
  \filldraw [canvas is xz plane at y=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
  \filldraw [canvas is yx plane at z=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
  \foreach \X [count=\XX starting from 0] in {-1.5,-0.5,0.5}{
   \foreach \Y [count=\YY starting from 0] in {-1.5,-0.5,0.5}{
   \pgfmathtruncatemacro{\Z}{\XX+3*(2-\YY)}
   \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
    \draw [thick,canvas is yz plane at x=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
    \ifshowcellnumber
     \node[canvas is yz plane at x=1.5,shift={(\X+0.5,\Y+0.5)}] {\Z};
    \fi 
    \pgfmathtruncatemacro{\Z}{2-\XX+3*(2-\YY)+9}
    \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
    \draw [thick,canvas is xz plane at y=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
    \ifshowcellnumber
     \node[canvas is xz plane at y=1.5,shift={(\X+0.5,\Y+0.5)},xscale=-1] {\Z};
    \fi 
    \pgfmathtruncatemacro{\Z}{2-\YY+3*\XX+18}
    \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
    \draw [thick,canvas is yx plane at z=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
    \ifshowcellnumber
     \node[canvas is yx plane at z=1.5,shift={(\X+0.5,\Y+0.5)},xscale=-1,rotate=-90] {\Z};
    \fi 
    }
   }
 \end{scope}
\end{tikzpicture}

\TikZRubikFaceLeft
    {X}{X}{X}
    {X}{X}{X}
    {X}{G}{X}
\TikZRubikFaceRight
    {X}{X}{X}
    {X}{B}{X}
    {W}{B}{X}
\TikZRubikFaceTop
    {X}{R}{X}
    {X}{W}{X}
    {X}{W}{G}
\BuildArray
\showcellnumberfalse
\begin{tikzpicture}
 \clip (-3,-2.5) rectangle (3,2.5);
 \begin{scope}[tdplot_main_coords]
  \filldraw [canvas is yz plane at x=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
  \filldraw [canvas is xz plane at y=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
  \filldraw [canvas is yx plane at z=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
  \foreach \X [count=\XX starting from 0] in {-1.5,-0.5,0.5}{
   \foreach \Y [count=\YY starting from 0] in {-1.5,-0.5,0.5}{
   \pgfmathtruncatemacro{\Z}{\XX+3*(2-\YY)}
   \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
    \draw [thick,canvas is yz plane at x=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
    \ifshowcellnumber
     \node[canvas is yz plane at x=1.5,shift={(\X+0.5,\Y+0.5)}] {\Z};
    \fi 
    \pgfmathtruncatemacro{\Z}{2-\XX+3*(2-\YY)+9}
    \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
    \draw [thick,canvas is xz plane at y=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
    \ifshowcellnumber
     \node[canvas is xz plane at y=1.5,shift={(\X+0.5,\Y+0.5)},xscale=-1] {\Z};
    \fi 
    \pgfmathtruncatemacro{\Z}{2-\YY+3*\XX+18}
    \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
    \draw [thick,canvas is yx plane at z=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
    \ifshowcellnumber
     \node[canvas is yx plane at z=1.5,shift={(\X+0.5,\Y+0.5)},xscale=-1,rotate=-90] {\Z};
    \fi 
    }
   }
 \end{scope}
\end{tikzpicture}   
\end{document} 

enter image description here

As you can see, if you replace \showcellnumbertrue by \showcellnumberfalse, the numbers are suppressed.

EDITs: Illustrated the relation between array index and cell (which is almost redundant now) and adjusted the color (big thanks to @manooooh!). I also used now the conventions of the rubik package, which I did not really know before seeing Peter Grill's nice answer. The conventions are still slightly different since I refer to the faces as left, right and top. This is because this thingy can be rotated in some range, but left will always be left in that range. I also added some %, which were added in first in this answer.

ADDENDUM: Encouraged by @LoopSpace's comment:

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\newif\ifshowcellnumber
\showcellnumberfalse
\begin{document}
\definecolor{R}{RGB}{202,65,55}
\definecolor{G}{RGB}{151,216,56}
\definecolor{B}{RGB}{51,72,237}
%\definecolor{W}{RGB}{255,255,255}
\definecolor{W}{RGB}{65,65,65}

\def\myarray{{"W","W","B","W","G","W","R","R","W","W","W","W","G","W","B","B","W","W","G","B","R","W","R","B","W","W","W"}}
\pgfmathsetmacro\radius{0.1}
\newcommand{\frontcolor}{red}
\newcommand{\sidecolor}{blue}
\foreach \X in {95,100,...,175}
{            \tdplotsetmaincoords{55}{\X}
            \begin{tikzpicture}
                \clip (-3,-2.5) rectangle (3,2.5);
                \begin{scope}[tdplot_main_coords]
                    \filldraw [canvas is yz plane at x=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \filldraw [canvas is xz plane at y=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \filldraw [canvas is yx plane at z=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \foreach \X [count=\XX starting from 0] in {-1.5,-0.5,0.5}{
                        \foreach \Y [count=\YY starting from 0] in {-1.5,-0.5,0.5}{
                        \pgfmathtruncatemacro{\Z}{\XX+3*(2-\YY)}
                        \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
                            \draw [thick,canvas is yz plane at
x=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc
(-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc
(90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
        \ifshowcellnumber
            \node[canvas is yz plane at x=1.5,shift={(\X+0.5,\Y+0.5)}] {\Z};
        \fi 
                        \pgfmathtruncatemacro{\Z}{2-\XX+3*(2-\YY)+9}
                        \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
                            \draw [thick,canvas is xz plane at
y=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc
(-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc
(90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
        \ifshowcellnumber
            \node[canvas is xz plane at y=1.5,shift={(\X+0.5,\Y+0.5)},xscale=-1] {\Z};
        \fi 
                        \pgfmathtruncatemacro{\Z}{2-\YY+3*\XX+18}
                        \pgfmathsetmacro{\mycolor}{\myarray[\Z]}
                            \draw [thick,canvas is yx plane at
z=1.5,shift={(\X,\Y)},fill=\mycolor] (0.5,0) -- ({1-\radius},0) arc
(-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc
(90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
        \ifshowcellnumber
            \node[canvas is yx plane at z=1.5,shift={(\X+0.5,\Y+0.5)},xscale=-1,rotate=-90] {\Z};
        \fi 
                        }
                    }
                \end{scope}
\end{tikzpicture}}
\end{document} 

enter image description here

9
  • According to the first image of OP the white cubes should be black. – manooooh Nov 10 '18 at 4:18
  • Lovely, as always. Can we tweak the cube to add perspective? There's a question here somewhere about it. – Andrew Stacey Nov 10 '18 at 6:56
  • 1
    @LoopSpace Yes. That is what \tdplotsetmaincoords{55}{135} does. And the question is most likely where the answer that the OP and I build on is from. – user121799 Nov 10 '18 at 14:33
  • Thank you @marmot this is really excellent. The package rubik has a really nice format for specifying the colours of the faces and generating the diagram of the cube. I was wondering if it is possible to get that sort of functionality with your TikZ method? The reason why your TikZ method is superior to the package rubik is because here we have full control over the viewing angle (I really need an isometric viewing angle). There seems to be no way to adjust the angle using rubik so your code is much better. – Sam Nov 10 '18 at 18:08
  • So my question is can we take \myarray{...} and make it into \RubikFaceUp {X}{X}{X} {X}{X}{X} {X}{G}{X} etc... Followed by a single command like \ShowCube{7cm}{0.7}{\DrawRubikCube}. I guess you would save the tikzpicture code to generate the cube in the preamble. – Sam Nov 10 '18 at 18:10
24

There is also a rubik package designed specifically for this. The MWE below generates the four cube positions shown in the question.

enter image description here

Code:

\documentclass{article}
\usepackage{tikz}%% load tikz BEFORE rubikcube
\usepackage{rubikcube}
%\usepackage{rubikrotation,rubikpatterns,rubiktwocube}% Related packages

\begin{document}
\noindent
\begin{minipage}{0.4\linewidth}
    \RubikFaceUp
        {X}{X}{X}
        {X}{X}{X}
        {X}{X}{G}
    \RubikFaceRight
        {W}{X}{X}
        {R}{G}{G}
        {X}{G}{G}
    \RubikFaceFront
        {X}{X}{R}
        {R}{R}{G}
        {R}{R}{X}
   \ShowCube{7cm}{0.7}{\DrawRubikCube}
\end{minipage}
\begin{minipage}{0.4\linewidth}
    \RubikFaceUp
        {X}{X}{X}
        {X}{X}{X}
        {X}{G}{X}
    \RubikFaceRight
        {X}{X}{X}
        {X}{B}{X}
        {W}{B}{X}
    \RubikFaceFront
        {X}{R}{X}
        {X}{O}{X}
        {X}{O}{G}
   \ShowCube{7cm}{0.7}{\DrawRubikCube}
\end{minipage}

\par\medskip
\noindent
\begin{minipage}{0.4\linewidth}
    \RubikFaceRight
        {X}{X}{X}
        {G}{B}{X}
        {G}{B}{X}
    \RubikFaceFront
        {X}{X}{X}
        {X}{O}{R}
        {X}{O}{R}
   \ShowCube{7cm}{0.7}{\DrawRubikCube}
\end{minipage}
\begin{minipage}{0.4\linewidth}
    \RubikFaceUp
        {X}{X}{X}
        {G}{X}{X}
        {X}{X}{G}
    \RubikFaceRight
        {W}{X}{X}
        {X}{G}{G}
        {X}{G}{G}
    \RubikFaceFront
        {X}{X}{X}
        {R}{R}{X}
        {R}{R}{X}
   \ShowCube{7cm}{0.7}{\DrawRubikCubeRU}
\end{minipage}   
\end{document}
2
  • Thank you this is really interesting, I did not know of this package. I've had a look at the documentation and it seems there is no way to adjust the viewing angle so that it is 'isometric' like in my example? This is quite crucial to my use as the focus is on the edge between the front and right faces. This is for doing F2L diagrams. Don't know if anyone knows a way to adapt this package to making the viewing angle isometric? – Sam Nov 10 '18 at 18:04
  • @Sam: Try emailing the package authors. Might make sense to add that feature directly to the package. – Peter Grill Nov 10 '18 at 18:30

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