Wie zeichnet man einen Würfel wie folgt?

Question

\documentclass[pstricks,border=10pt]{standalone}
\usepackage{pst-solides3d}
\begin{document}
\psset{viewpoint=120 50 30 rtp2xyz,Decran=50}
\pstVerb{/Colors [(red)(yellow)(orange)(green)(blue)] def }
\def\figure#1#2{%
\begin{pspicture}(-3,-3)(3,3)
\psframe[linestyle=none,fillstyle=solid,fillcolor=blue!50](-3,-3)(3,3)
    \psSolid[action=draw**,a=8,object=cube,fillcolor=green!30,ngrid=3,%
    rm=4 40 13 31 53 22,hollow,incolor=pink!50,Rot#2=-#1\space]%
    \end{pspicture}
}
    \multido{\iA=0+5}{72}{\figure{\iA}{X}}
\end{document}

Es ist im Inneren des Würfels ausgehöhlt.

Wie erhält man also eine ähnliche Ausgabe wie das folgende Bild?

%% Aus Herberts Kommentar

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}
\begin{document}

\begin{pspicture}(-4.5,-3.5)(6,6)
\psset{Decran=60,viewpoint=80 35 15 rtp2xyz,a=1,lightsrc=80 30 20,}
%   \psSolid[object=grille,base=0 7 0 7,fillcolor=gray!40]%%
%   \psSolid[object=grille,base=0 7 0 7,RotY=90,fillcolor=gray!30](0,0,7)%
%   \psSolid[object=grille,base=0 7 0 7,RotX=-90,fillcolor=gray!20](0,0,7)%
\def\figure#1#2#3{\psSolid[object=cube,fcol=1 (green) 2 (blue) 3 (red) 4 (pink) 5 (orange) 6 (cyan)](#1,#2,#3)}
    \foreach \i in {0.5,1.5,2.5}{\figure{0.5}{\i}{0.5}}
    \foreach \i in {1.5,2.5}{\figure{\i}{.5}{0.5}}
    \figure{1.5}{2.5}{0.5}
    \foreach \i in {1.5,2.5}{\figure{2.5}{\i}{0.5}}
    \foreach \i in {1.5,2.5}{\figure{.5}{.5}{\i}}
    \figure{2.5}{.5}{1.5}
    \figure{.5}{1.5}{2.5}
    \foreach \i in {1.5,2.5}{\figure{\i}{.5}{2.5}}
    \figure{2.5}{1.5}{2.5}
    \foreach \i in {1.5,2.5}{\figure{.5}{2.5}{\i}}
    \figure{1.5}{2.5}{2.5}
    \foreach \i in {1.5,2.5}{\figure{2.5}{2.5}{\i}}
\end{pspicture}
\end{document}

Aber mit viewpoint=80 135 15 rtp2xyz erhalte ich Folgendes:

Answer 1

Wenn Sie das Innere nicht auch noch mit Würfeln befüllen möchten, geht es ganz einfach:

\documentclass[pstricks,border=10pt]{standalone}
\usepackage{pst-solides3d}
\begin{document}
\psset{viewpoint=120 60 30 rtp2xyz,Decran=50}
\pstVerb{/Colors [(red)(yellow)(orange)(green)(blue)] def }
\begin{pspicture}(-3,-3)(3,3)
\psSolid[action=draw**,a=8,object=cube,fillcolor=green!30,ngrid=7,%
    rm=  8  12  24  36  40 
        57  61  73  85  89
       106 110 122 134 138
       155 159 171 183 187
       208 212 220 228 232
       269 273 281 289 293,
        hollow,incolor=blue!30]%
\end{pspicture}
\end{document}

Und als Einzelwürfel:

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}
\def\Figure#1#2#3#4{%
    \psSolid[object=cube,name=c#4,ngrid=1,a=1,
             action=none,fcol=1 (green) 2 (blue) 3 (red) 4 (pink) 5 (orange) 6 (cyan)](#1,#2,#3)}

\begin{document}

    \begin{pspicture}(-4.5,-3.5)(6,6)
    \psset{Decran=60,viewpoint=80 10 15 rtp2xyz,lightsrc=viewpoint,solidmemory}
    \foreach \i/\j in {0.5/1,1.5/2,2.5/3}{\Figure{0.5}{\i}{0.5}{\j}}
    \foreach \i/\j in {1.5/4,2.5/5}{\Figure{\i}{.5}{0.5}{\j}}
    \Figure{1.5}{2.5}{0.5}{6}
    \foreach \i/\j in {1.5/7,2.5/8}{\Figure{2.5}{\i}{0.5}{\j}}
    \foreach \i/\j in {1.5/9,2.5/10}{\Figure{.5}{.5}{\i}{\j}}
    \Figure{2.5}{.5}{1.5}{11}
    \Figure{.5}{1.5}{2.5}{12}
    \foreach \i/\j in {1.5/13,2.5/14}{\Figure{\i}{.5}{2.5}{\j}}
    \Figure{2.5}{1.5}{2.5}{15}
    \foreach \i/\j in {1.5/16,2.5/17}{\Figure{.5}{2.5}{\i}{\j}}
    \Figure{1.5}{2.5}{2.5}{18}
    \foreach \i/\j in {1.5/19,2.5/20}{\Figure{2.5}{2.5}{\i}{\j}}
    \psSolid[object=fusion,
             base=c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 c16 c17 c18 c19 c20]
    \composeSolid
    \end{pspicture}
\end{document}

Für viele Würfel kann man das Fusionsobjekt vereinfachen:

\def\cubes{}
\multido{\iA=1+1}{20}{\xdef\cubes{\cubes\space c\iA}}
\begin{pspicture} ....
    ....    
    \psSolid[object=fusion, base=\cubes]
    ....

und hier ist eine Möglichkeit, wie Sie den kompletten Würfel bauen können:

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}
\newcounter{fig}
\def\Figure#1#2#3{%
    \stepcounter{fig}%
    \psSolid[object=cube,name=c\thefig,ngrid=1,a=1,
             action=none,fcol=1 (green) 2 (blue) 3 (red) 4 (pink) 5 (orange) 6 (cyan)](#1,#2,#3)}

\begin{document}

    \begin{pspicture}(-5,-3.5)(4,6)
    \psset{Decran=60,viewpoint=80 60 15 rtp2xyz,lightsrc=viewpoint,solidmemory}
    \multido{\iA=0+1}{7}{%
      \multido{\iB=0+1}{7}{%
         \multido{\iC=0+1}{7}{%
           \Figure{\iB}{\iA}{\iC}%
    }}}%
    \psSolid[object=fusion, base=
    % 1
       c1   c2   c3   c4   c5   c6   c7
       c8        c10  c11  c12       c14
       c15  c16  c17  c18  c19  c20  c21
       c22  c23  c24       c26  c27  c28
       c29  c30  c31  c32  c33  c34  c35
       c36       c38  c39  c40       c42
       c43  c44  c45  c46  c47  c48  c49
    % 2
       c50       c52  c53  c54       c56
    %      
       c64       c66  c67  c68       c70
       c71       c73       c75       c77
       c78       c80  c81  c82       c84
    %      
       c92       c94  c95  c96       c98
     % 3 ...
      ]
    \composeSolid
    \end{pspicture}
\end{document}

und das komplette Bild:

Answer 2

Etwas wie das?

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{calc}
\tikzset{plane/.style n args={3}{insert path={%
#1 -- ++ #2 -- ++ #3 -- ++ ($-1*#2$) -- cycle}},
unit xy plane/.style={plane={#1}{(1,0,0)}{(0,1,0)}},
unit xz plane/.style={plane={#1}{(1,0,0)}{(0,0,1)}},
unit yz plane/.style={plane={#1}{(0,1,0)}{(0,0,1)}},
get projections/.style={insert path={%
let \p1=(1,0,0),\p2=(0,1,0)  in 
[/utils/exec={\pgfmathtruncatemacro{\xproj}{sign(\x1)}\xdef\xproj{\xproj}
\pgfmathtruncatemacro{\yproj}{sign(\x2)}\xdef\yproj{\yproj}
\pgfmathtruncatemacro{\zproj}{sign(cos(\tdplotmaintheta))}\xdef\zproj{\zproj}}]}},
pics/unit cube/.style={code={
\path[get projections];
\draw (0,0,0) -- (1,1,1);
\ifnum\zproj=-1
 \path[3d cube/every face,3d cube/xy face,unit xy plane={(0,0,0)}]; 
\fi
\ifnum\yproj=1
 \path[3d cube/every face,3d cube/yz face,unit yz plane={(1,0,0)}]; 
\else
 \path[3d cube/every face,3d cube/yz face,unit yz plane={(0,0,0)}]; 
\fi
\ifnum\xproj=1
 \path[3d cube/every face,3d cube/xz face,unit xz plane={(0,0,0)}]; 
\else
 \path[3d cube/every face,3d cube/xz face,unit xz plane={(0,1,0)}]; 
\fi
\ifnum\zproj>-1
 \path[3d cube/every face,3d cube/xy face,unit xy plane={(0,0,1)}]; 
\fi
}},
3d cube/.cd,
xy face/.style={fill=orange},
xz face/.style={fill=blue},
yz face/.style={fill=red},
every face/.style={draw,very thick}
}
\begin{document}
\foreach \Angle in {5,15,...,355} 
{\tdplotsetmaincoords{60}{\Angle} % the first argument cannot be larger than 90
\begin{tikzpicture}[line join=round]
 \pgfmathtruncatemacro{\NumCubes}{7}
 \path[use as bounding box] (-\NumCubes/2-3,-\NumCubes/2-2) 
 rectangle (\NumCubes/2+3,\NumCubes/2+4);
 \begin{scope}[tdplot_main_coords]
  \pgfmathtruncatemacro{\NextToLast}{\NumCubes-1}
  \path[get projections];
  \ifnum\yproj=1
   \def\LstX{1,...,\NumCubes}
  \else 
   \def\LstX{\NumCubes,\NextToLast,...,1}
  \fi
  \ifnum\xproj=-1
   \def\LstY{1,...,\NumCubes}
  \else 
   \def\LstY{\NumCubes,\NextToLast,...,1}
  \fi
  \ifnum\zproj=1
   \def\LstZ{1,...,\NumCubes}
  \else 
   \def\LstZ{\NumCubes,\NextToLast,...,1}
  \fi
  \foreach \X in \LstX
  {\foreach \Y in \LstY
   {\foreach \Z in \LstZ
    {\xdef\itest{1}
     \ifodd\X
     \else
       \pgfmathtruncatemacro{\jtest}{mod(\X+\Y,4)}
       \ifnum\jtest=0
        \xdef\itest{0}
       \fi
       \pgfmathtruncatemacro{\jtest}{mod(\X+\Z,4)}
       \ifnum\jtest=0
        \xdef\itest{0}
       \fi
     \fi
     \ifodd\Y
     \else
       \pgfmathtruncatemacro{\jtest}{mod(\Y+\Z,4)}
       \ifnum\jtest=0
        \xdef\itest{0}
       \fi
     \fi
     \ifnum\itest=1
     \path (\X-\NumCubes/2-1/2,\Y-\NumCubes/2-1/2,\Z-\NumCubes/2-1/2) pic{unit cube};
     \fi}}
  }
 \end{scope}
\end{tikzpicture}}
\end{document}