Need help creating a 3D cube from a 2D set of nodes in TikZ

Question

I'm working on a figure where I need a 3D cube. My plan was to create a 2D set of nodes, then draw the top and right side of the cube, and lastly draw the missing lines. I got this far until I ran into trouble:

I can't get the side to align properly with the face of the cube. Also, I have a vague idea on how to draw the lines but I bet I will have problems with that, too.

Here's the code:

\documentclass[a4paper, 11pt]{article}

\usepackage[rgb]{xcolor}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows}
\usetikzlibrary{positioning}
\usetikzlibrary{calc}

\definecolor{shade0}{named}{white}
\definecolor{shade1}{rgb}{0.9, 0.9, 0.9}
\definecolor{shade2}{rgb}{0.8, 0.8, 0.8}
\definecolor{shade3}{rgb}{0.65, 0.65, 0.65}
\definecolor{shade4}{rgb}{0.45, 0.45, 0.45}

\newlength{\gpgpuElemSize}
\setlength{\gpgpuElemSize}{8mm}
\newlength{\gpgpuElemSep}
\setlength{\gpgpuElemSep}{1mm}

\begin{document}
\begin{tikzpicture}[%
    auto,
    box/.style={%
      draw,
      rectangle,
      semithick,
    },
    thread-s/.style={
      draw,
      semithick,
      fill=shade1,
    },
    thread/.style={%
      box,
      thread-s,
      minimum size=0.5\gpgpuElemSize,
      inner sep=0,
      node distance=0pt,
    },
  ]

  % Draw boxes
  \foreach \i in {1, ..., 4} {%
    \foreach \j in {1, ..., 4} {%
      \ifnum \j=1
        \ifnum \i=1
          \node [thread] (thread\i-\j) {};
        \else
          \pgfmathtruncatemacro\prevI{\i-1}
          \node [thread, below=of thread\prevI-1, yshift=\pgflinewidth]
            (thread\i-\j) {};
        \fi
      \else
        \pgfmathtruncatemacro\prevJ{\j-1}
        \node [thread, right=of thread\i-\prevJ, xshift=-\pgflinewidth]
          (thread\i-\j) {};
      \fi
    }
  }

  % Create 3D perspective
  \path let \p1 = (thread4-4.south east),
            \p2 = (thread1-4.north east)
         in
           [thread-s]
           (thread1-4.north east) -- ++(30:0.5\gpgpuElemSize)
           -- ++(0, \y1-\y2-\pgflinewidth) -- (thread4-4.south east) --   
           cycle;
\end{tikzpicture}
\end{document}

Answer 1

Using a single \foreach loop with different uses in the coordinates is much easier:

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
\foreach \x in{0,...,4}
{   \draw (0,\x ,4) -- (4,\x ,4);
    \draw (\x ,0,4) -- (\x ,4,4);
    \draw (4,\x ,4) -- (4,\x ,0);
    \draw (\x ,4,4) -- (\x ,4,0);
    \draw (4,0,\x ) -- (4,4,\x );
    \draw (0,4,\x ) -- (4,4,\x );
}
\end{tikzpicture}

\end{document}

---

Edit 1: I generalized it a little, now you can draw cuboids by simply specifying the diemnsions and the scale (and also cubes of size n):

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{tikz}

\newcommand{\tikzcuboid}[4]{% width, height, depth, scale
\begin{tikzpicture}[scale=#4]
\foreach \x in {0,...,#1}
{   \draw (\x ,0  ,#3 ) -- (\x ,#2 ,#3 );
    \draw (\x ,#2 ,#3 ) -- (\x ,#2 ,0  );
}
\foreach \x in {0,...,#2}
{   \draw (#1 ,\x ,#3 ) -- (#1 ,\x ,0  );
    \draw (0  ,\x ,#3 ) -- (#1 ,\x ,#3 );
}
\foreach \x in {0,...,#3}
{   \draw (#1 ,0  ,\x ) -- (#1 ,#2 ,\x );
    \draw (0  ,#2 ,\x ) -- (#1 ,#2 ,\x );
}
\end{tikzpicture}
}

\newcommand{\tikzcube}[2]{% length, scale
\tikzcuboid{#1}{#1}{#1}{#2}
}

\begin{document}

\tikzcuboid{11}{7}{5}{0.5}

\tikzcube{13}{0.25}

\end{document}

Furthermore one could improve upon this e.g. by:

• specifying the density of lines for each dimension
• rotating the cuboid
• defining the coordinate axes (e.g. specify an angle for each)
• use colored/thick/dashed lines
• use it in a scope rather than a tikzpicture environment so it can be used together with other things
• parameters for X- and Y-fhift (again for use along with other things in a tikzpicture)

Also one could probably:

• use quadrilaterals instead of lines, so one can use fillings, shadings etc.
• specify a shading pattern (either for whole faces or each individual quadrilateral)

Probably I will get to this, but don't bet on it ;)

---

Edit 2: Turns out I had some spare time today ;)

Done:

• shiftx
• shifty
• dimx
• dimy
• dimz
• scale
• densityx
• densityy
• densityz
• rotation

Remains:

• anglex
• angley
• anglez
• scalex
• scaley
• scalez
• linefront
• linetop
• lineright
• fillfront
• filltop
• fillright
• newcoords
• shaded

newcoords and shaded are switches (which are unused so far). Note that the densitys must fullfill K/densityA = dimensionA for natural numbers K, otherwise strange effects occur (basically this means that each face must be divided in a whole number of segments; for dimension=3 and density=0.5 one would draw a line every 2 centimeters, so it would be 1.5 segments, which is not good)

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm,landscape]{geometry}
\usepackage{tikz}
\usepackage{keyval}
\usepackage{ifthen}

\makeatletter
% Standard Values for Parameters
\newcommand{\tikzcuboid@shiftx}{0}
\newcommand{\tikzcuboid@shifty}{0}
\newcommand{\tikzcuboid@dimx}{4}
\newcommand{\tikzcuboid@dimy}{4}
\newcommand{\tikzcuboid@dimz}{4}
\newcommand{\tikzcuboid@scale}{1}
\newcommand{\tikzcuboid@densityx}{1}
\newcommand{\tikzcuboid@densityy}{1}
\newcommand{\tikzcuboid@densityz}{1}
\newcommand{\tikzcuboid@rotation}{0}
\newcommand{\tikzcuboid@anglex}{0}
\newcommand{\tikzcuboid@angley}{90}
\newcommand{\tikzcuboid@anglez}{225}
\newcommand{\tikzcuboid@scalex}{1}
\newcommand{\tikzcuboid@scaley}{1}
\newcommand{\tikzcuboid@scalez}{1}
\newcommand{\tikzcuboid@linefront}{}
\newcommand{\tikzcuboid@linetop}{}
\newcommand{\tikzcuboid@lineright}{}
\newcommand{\tikzcuboid@fillfront}{}
\newcommand{\tikzcuboid@filltop}{}
\newcommand{\tikzcuboid@fillright}{}
\newcommand{\tikzcuboid@newcoords}{N}
\newcommand{\tikzcuboid@filled}{N}
\newcommand{\tikzcuboid@shaded}{N}
% Definition of Keys
\define@key{tikzcuboid}{shiftx}[\tikzcuboid@shiftx]{\renewcommand{\tikzcuboid@shiftx}{#1}}
\define@key{tikzcuboid}{shifty}[\tikzcuboid@shifty]{\renewcommand{\tikzcuboid@shifty}{#1}}
\define@key{tikzcuboid}{dimx}[\tikzcuboid@dimx]{\renewcommand{\tikzcuboid@dimx}{#1}}
\define@key{tikzcuboid}{dimy}[\tikzcuboid@dimy]{\renewcommand{\tikzcuboid@dimy}{#1}}
\define@key{tikzcuboid}{dimz}[\tikzcuboid@dimz]{\renewcommand{\tikzcuboid@dimz}{#1}}
\define@key{tikzcuboid}{scale}[\tikzcuboid@scale]{\renewcommand{\tikzcuboid@scale}{#1}}
\define@key{tikzcuboid}{densityx}[\tikzcuboid@densityx]{\renewcommand{\tikzcuboid@densityx}{#1}}
\define@key{tikzcuboid}{densityy}[\tikzcuboid@densityy]{\renewcommand{\tikzcuboid@densityy}{#1}}
\define@key{tikzcuboid}{densityz}[\tikzcuboid@densityz]{\renewcommand{\tikzcuboid@densityz}{#1}}
\define@key{tikzcuboid}{rotation}[\tikzcuboid@rotation]{\renewcommand{\tikzcuboid@rotation}{#1}}
\define@key{tikzcuboid}{anglex}[\tikzcuboid@anglex]{\renewcommand{\tikzcuboid@anglex}{#1}}
\define@key{tikzcuboid}{angley}[\tikzcuboid@angley]{\renewcommand{\tikzcuboid@angley}{#1}}
\define@key{tikzcuboid}{anglez}[\tikzcuboid@anglez]{\renewcommand{\tikzcuboid@anglez}{#1}}
\define@key{tikzcuboid}{scalex}[\tikzcuboid@scalex]{\renewcommand{\tikzcuboid@scalex}{#1}}
\define@key{tikzcuboid}{scaley}[\tikzcuboid@scaley]{\renewcommand{\tikzcuboid@scaley}{#1}}
\define@key{tikzcuboid}{scalez}[\tikzcuboid@scalez]{\renewcommand{\tikzcuboid@scalez}{#1}}
\define@key{tikzcuboid}{linefront}[\tikzcuboid@linefront]{\renewcommand{\tikzcuboid@linefront}{#1}}
\define@key{tikzcuboid}{linetop}[\tikzcuboid@linetop]{\renewcommand{\tikzcuboid@linetop}{#1}}
\define@key{tikzcuboid}{lineright}[\tikzcuboid@lineright]{\renewcommand{\tikzcuboid@lineright}{#1}}
\define@key{tikzcuboid}{fillfront}[\tikzcuboid@fillfront]{\renewcommand{\tikzcuboid@fillfront}{#1}}
\define@key{tikzcuboid}{filltop}[\tikzcuboid@filltop]{\renewcommand{\tikzcuboid@filltop}{#1}}
\define@key{tikzcuboid}{fillright}[\tikzcuboid@fillright]{\renewcommand{\tikzcuboid@fillright}{#1}}
\define@key{tikzcuboid}{newcoords}[\tikzcuboid@newcoords]{\renewcommand{\tikzcuboid@newcoords}{#1}}
\define@key{tikzcuboid}{filled}[\tikzcuboid@filled]{\renewcommand{\tikzcuboid@filled}{#1}}
\define@key{tikzcuboid}{shaded}[\tikzcuboid@shaded]{\renewcommand{\tikzcuboid@shaded}{#1}}
% Commands
\newcommand{\tikzcuboid}[1]{
    \setkeys{tikzcuboid}{#1} % Process Keys passed to command
    \begin{scope}[xshift=\tikzcuboid@shiftx,yshift=\tikzcuboid@shifty,scale=\tikzcuboid@scale,rotate=\tikzcuboid@rotation]
    \pgfmathsetmacro{\steppingx}{1/\tikzcuboid@densityx}
    \pgfmathsetmacro{\steppingy}{1/\tikzcuboid@densityy}
    \pgfmathsetmacro{\steppingz}{1/\tikzcuboid@densityz}
    \newcommand{\dimx}{\tikzcuboid@dimx}
    \newcommand{\dimy}{\tikzcuboid@dimy}
    \newcommand{\dimz}{\tikzcuboid@dimz}
    \pgfmathsetmacro{\secondx}{2*\steppingx}
    \pgfmathsetmacro{\secondy}{2*\steppingy}
    \pgfmathsetmacro{\secondz}{2*\steppingz}
    \foreach \x in {\steppingx,\secondx,...,\dimx}
    {   \foreach \y in {\steppingy,\secondy,...,\dimy}
        {   \pgfmathsetmacro{\lowx}{(\x-\steppingx)}
            \pgfmathsetmacro{\lowy}{(\y-\steppingy)}
            \filldraw[fill=orange,draw=blue] (\lowx,\lowy,\dimz) -- (\lowx,\y,\dimz) -- (\x,\y,\dimz) -- (\x,\lowy,\dimz) -- cycle;

        }
    }
    \foreach \x in {\steppingx,\secondx,...,\dimx}
    {   \foreach \z in {\steppingz,\secondz,...,\dimz}
        {   \pgfmathsetmacro{\lowx}{(\x-\steppingx)}
            \pgfmathsetmacro{\lowz}{(\z-\steppingz)}
            \filldraw[fill=green,draw=red] (\lowx,\dimy,\lowz) -- (\lowx,\dimy,\z) -- (\x,\dimy,\z) -- (\x,\dimy,\lowz) -- cycle;
        }
    }
    \foreach \y in {\steppingy,\secondy,...,\dimy}
    {   \foreach \z in {\steppingz,\secondz,...,\dimz}
        {   \pgfmathsetmacro{\lowy}{(\y-\steppingy)}
            \pgfmathsetmacro{\lowz}{(\z-\steppingz)}
            \filldraw[fill=red!50!blue,draw=yellow] (\dimx,\lowy,\lowz) -- (\dimx,\lowy,\z) -- (\dimx,\y,\z) -- (\dimx,\y,\lowz) -- cycle;
        }
    }
    \end{scope}

    % Write parameters to log file, just for checking       
%   \typeout{=============================}
%   \typeout{*****************************}
%   \typeout{tikzcuboid shiftx = \tikzcuboid@shiftx}
%   \typeout{tikzcuboid shifty = \tikzcuboid@shifty}
%   \typeout{tikzcuboid dimx = \tikzcuboid@dimx}
%   \typeout{tikzcuboid dimy = \tikzcuboid@dimy}
%   \typeout{tikzcuboid dimz = \tikzcuboid@dimz}
%   \typeout{tikzcuboid scale = \tikzcuboid@scale}
%   \typeout{tikzcuboid densityx = \tikzcuboid@densityx}
%   \typeout{tikzcuboid densityy = \tikzcuboid@densityy}
%   \typeout{tikzcuboid densityz = \tikzcuboid@densityz}
%   \typeout{tikzcuboid rotation = \tikzcuboid@rotation}
%   \typeout{tikzcuboid anglex = \tikzcuboid@anglex}
%   \typeout{tikzcuboid angley = \tikzcuboid@angley}
%   \typeout{tikzcuboid anglez = \tikzcuboid@anglez}
%   \typeout{tikzcuboid scalex = \tikzcuboid@scalex}
%   \typeout{tikzcuboid scaley = \tikzcuboid@scaley}
%   \typeout{tikzcuboid scalez = \tikzcuboid@scalez}
%   \typeout{tikzcuboid linefront = \tikzcuboid@linefront}
%   \typeout{tikzcuboid linetop = \tikzcuboid@linetop}
%   \typeout{tikzcuboid lineright = \tikzcuboid@lineright}
%   \typeout{tikzcuboid fillfront = \tikzcuboid@fillfront}
%   \typeout{tikzcuboid filltop = \tikzcuboid@filltop}
%   \typeout{tikzcuboid fillright = \tikzcuboid@fillright}
%   \typeout{tikzcuboid newcoords = \tikzcuboid@newcoords}
%   \typeout{tikzcuboid filled = \tikzcuboid@filled}
%   \typeout{tikzcuboid shaded = \tikzcuboid@shaded}
%   \typeout{*****************************}
%   \typeout{=============================}
}

\makeatother

\begin{document}

\begin{tikzpicture}
    \tikzcuboid{shiftx=0cm,%
        shifty=0cm,%
        scale=1.00,%
        rotation=30,%
        densityx=1,%
        densityy=2,%
        densityz=3%
    }
    \tikzcuboid{%
        shiftx=0cm,%
        shifty=8cm,%
        scale=1.00,%
        rotation=60,%
        densityx=3,%
        densityy=2,%
        densityz=5%
    }
    \tikzcuboid{%
        shiftx=8cm,%
        shifty=8cm,%
        scale=1.00,%
        rotation=45,%
        densityx=0.5,%
        densityy=1,%
        densityz=2%
    }
    \tikzcuboid{%
        shiftx=8cm,%
        shifty=0cm,%
        scale=1.00,%
        rotation=75,%
        densityx=2,%
        densityy=7,%
        densityz=2%
    }
\end{tikzpicture}

\end{document}

And finally, some output (colors are just for showing off):

---

Edit 3: Now I have everythinh except for shading:

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm,landscape]{geometry}
\usepackage{tikz}
\usepackage{keyval}
\usepackage{ifthen}
%====================================
%emphasize vertices --> switch and emph style (e.g. thick,black)
%====================================
\makeatletter
% Standard Values for Parameters
\newcommand{\tikzcuboid@shiftx}{0}
\newcommand{\tikzcuboid@shifty}{0}
\newcommand{\tikzcuboid@dimx}{3}
\newcommand{\tikzcuboid@dimy}{3}
\newcommand{\tikzcuboid@dimz}{3}
\newcommand{\tikzcuboid@scale}{1}
\newcommand{\tikzcuboid@densityx}{1}
\newcommand{\tikzcuboid@densityy}{1}
\newcommand{\tikzcuboid@densityz}{1}
\newcommand{\tikzcuboid@rotation}{0}
\newcommand{\tikzcuboid@anglex}{0}
\newcommand{\tikzcuboid@angley}{90}
\newcommand{\tikzcuboid@anglez}{225}
\newcommand{\tikzcuboid@scalex}{1}
\newcommand{\tikzcuboid@scaley}{1}
\newcommand{\tikzcuboid@scalez}{sqrt(0.5)}
\newcommand{\tikzcuboid@linefront}{black}
\newcommand{\tikzcuboid@linetop}{black}
\newcommand{\tikzcuboid@lineright}{black}
\newcommand{\tikzcuboid@fillfront}{white}
\newcommand{\tikzcuboid@filltop}{white}
\newcommand{\tikzcuboid@fillright}{white}
\newcommand{\tikzcuboid@shaded}{N}
\newcommand{\tikzcuboid@shadecolor}{black}
\newcommand{\tikzcuboid@shadeperc}{25}
\newcommand{\tikzcuboid@emphedge}{N}
\newcommand{\tikzcuboid@emphstyle}{thick}

% Definition of Keys
\define@key{tikzcuboid}{shiftx}[\tikzcuboid@shiftx]{\renewcommand{\tikzcuboid@shiftx}{#1}}
\define@key{tikzcuboid}{shifty}[\tikzcuboid@shifty]{\renewcommand{\tikzcuboid@shifty}{#1}}
\define@key{tikzcuboid}{dimx}[\tikzcuboid@dimx]{\renewcommand{\tikzcuboid@dimx}{#1}}
\define@key{tikzcuboid}{dimy}[\tikzcuboid@dimy]{\renewcommand{\tikzcuboid@dimy}{#1}}
\define@key{tikzcuboid}{dimz}[\tikzcuboid@dimz]{\renewcommand{\tikzcuboid@dimz}{#1}}
\define@key{tikzcuboid}{scale}[\tikzcuboid@scale]{\renewcommand{\tikzcuboid@scale}{#1}}
\define@key{tikzcuboid}{densityx}[\tikzcuboid@densityx]{\renewcommand{\tikzcuboid@densityx}{#1}}
\define@key{tikzcuboid}{densityy}[\tikzcuboid@densityy]{\renewcommand{\tikzcuboid@densityy}{#1}}
\define@key{tikzcuboid}{densityz}[\tikzcuboid@densityz]{\renewcommand{\tikzcuboid@densityz}{#1}}
\define@key{tikzcuboid}{rotation}[\tikzcuboid@rotation]{\renewcommand{\tikzcuboid@rotation}{#1}}
\define@key{tikzcuboid}{anglex}[\tikzcuboid@anglex]{\renewcommand{\tikzcuboid@anglex}{#1}}
\define@key{tikzcuboid}{angley}[\tikzcuboid@angley]{\renewcommand{\tikzcuboid@angley}{#1}}
\define@key{tikzcuboid}{anglez}[\tikzcuboid@anglez]{\renewcommand{\tikzcuboid@anglez}{#1}}
\define@key{tikzcuboid}{scalex}[\tikzcuboid@scalex]{\renewcommand{\tikzcuboid@scalex}{#1}}
\define@key{tikzcuboid}{scaley}[\tikzcuboid@scaley]{\renewcommand{\tikzcuboid@scaley}{#1}}
\define@key{tikzcuboid}{scalez}[\tikzcuboid@scalez]{\renewcommand{\tikzcuboid@scalez}{#1}}
\define@key{tikzcuboid}{linefront}[\tikzcuboid@linefront]{\renewcommand{\tikzcuboid@linefront}{#1}}
\define@key{tikzcuboid}{linetop}[\tikzcuboid@linetop]{\renewcommand{\tikzcuboid@linetop}{#1}}
\define@key{tikzcuboid}{lineright}[\tikzcuboid@lineright]{\renewcommand{\tikzcuboid@lineright}{#1}}
\define@key{tikzcuboid}{fillfront}[\tikzcuboid@fillfront]{\renewcommand{\tikzcuboid@fillfront}{#1}}
\define@key{tikzcuboid}{filltop}[\tikzcuboid@filltop]{\renewcommand{\tikzcuboid@filltop}{#1}}
\define@key{tikzcuboid}{fillright}[\tikzcuboid@fillright]{\renewcommand{\tikzcuboid@fillright}{#1}}
\define@key{tikzcuboid}{shaded}[\tikzcuboid@shaded]{\renewcommand{\tikzcuboid@shaded}{#1}}
\define@key{tikzcuboid}{shadecolor}[\tikzcuboid@shadecolor]{\renewcommand{\tikzcuboid@shadecolor}{#1}}
\define@key{tikzcuboid}{shadeperc}[\tikzcuboid@shadeperc]{\renewcommand{\tikzcuboid@shadeperc}{#1}}
\define@key{tikzcuboid}{emphedge}[\tikzcuboid@emphedge]{\renewcommand{\tikzcuboid@emphedge}{#1}}
\define@key{tikzcuboid}{emphstyle}[\tikzcuboid@emphstyle]{\renewcommand{\tikzcuboid@emphstyle}{#1}}
% Commands
\newcommand{\tikzcuboid}[1]{
    \setkeys{tikzcuboid}{#1} % Process Keys passed to command
    \pgfmathsetmacro{\vectorxx}{\tikzcuboid@scalex*cos(\tikzcuboid@anglex)}
    \pgfmathsetmacro{\vectorxy}{\tikzcuboid@scalex*sin(\tikzcuboid@anglex)}
    \pgfmathsetmacro{\vectoryx}{\tikzcuboid@scaley*cos(\tikzcuboid@angley)}
    \pgfmathsetmacro{\vectoryy}{\tikzcuboid@scaley*sin(\tikzcuboid@angley)}
    \pgfmathsetmacro{\vectorzx}{\tikzcuboid@scalez*cos(\tikzcuboid@anglez)}
    \pgfmathsetmacro{\vectorzy}{\tikzcuboid@scalez*sin(\tikzcuboid@anglez)}
    \begin{scope}[xshift=\tikzcuboid@shiftx, yshift=\tikzcuboid@shifty, scale=\tikzcuboid@scale, rotate=\tikzcuboid@rotation, x={(\vectorxx,\vectorxy)}, y={(\vectoryx,\vectoryy)}, z={(\vectorzx,\vectorzy)}]
    \pgfmathsetmacro{\steppingx}{1/\tikzcuboid@densityx}
    \pgfmathsetmacro{\steppingy}{1/\tikzcuboid@densityy}
    \pgfmathsetmacro{\steppingz}{1/\tikzcuboid@densityz}
    \newcommand{\dimx}{\tikzcuboid@dimx}
    \newcommand{\dimy}{\tikzcuboid@dimy}
    \newcommand{\dimz}{\tikzcuboid@dimz}
    \pgfmathsetmacro{\secondx}{2*\steppingx}
    \pgfmathsetmacro{\secondy}{2*\steppingy}
    \pgfmathsetmacro{\secondz}{2*\steppingz}
    \foreach \x in {\steppingx,\secondx,...,\dimx}
    {   \foreach \y in {\steppingy,\secondy,...,\dimy}
        {   \pgfmathsetmacro{\lowx}{(\x-\steppingx)}
            \pgfmathsetmacro{\lowy}{(\y-\steppingy)}
            \filldraw[fill=\tikzcuboid@fillfront,draw=\tikzcuboid@linefront] (\lowx,\lowy,\dimz) -- (\lowx,\y,\dimz) -- (\x,\y,\dimz) -- (\x,\lowy,\dimz) -- cycle;

        }
    }
    \foreach \x in {\steppingx,\secondx,...,\dimx}
    {   \foreach \z in {\steppingz,\secondz,...,\dimz}
        {   \pgfmathsetmacro{\lowx}{(\x-\steppingx)}
            \pgfmathsetmacro{\lowz}{(\z-\steppingz)}
            \filldraw[fill=\tikzcuboid@filltop,draw=\tikzcuboid@linetop] (\lowx,\dimy,\lowz) -- (\lowx,\dimy,\z) -- (\x,\dimy,\z) -- (\x,\dimy,\lowz) -- cycle;
        }
    }
    \foreach \y in {\steppingy,\secondy,...,\dimy}
    {   \foreach \z in {\steppingz,\secondz,...,\dimz}
        {   \pgfmathsetmacro{\lowy}{(\y-\steppingy)}
            \pgfmathsetmacro{\lowz}{(\z-\steppingz)}
            \filldraw[fill=\tikzcuboid@fillright,draw=\tikzcuboid@lineright] (\dimx,\lowy,\lowz) -- (\dimx,\lowy,\z) -- (\dimx,\y,\z) -- (\dimx,\y,\lowz) -- cycle;
        }
    }
    \ifthenelse{\equal{\tikzcuboid@emphedge}{Y}}%
        {\draw[\tikzcuboid@emphstyle](0,\dimy,0) -- (\dimx,\dimy,0) -- (\dimx,\dimy,\dimz) -- (0,\dimy,\dimz) -- cycle;%
        \draw[\tikzcuboid@emphstyle] (0,0,\dimz) -- (0,\dimy,\dimz) -- (\dimx,\dimy,\dimz) -- (\dimx,0,\dimz) -- cycle;%
        \draw[\tikzcuboid@emphstyle](\dimx,0,0) -- (\dimx,\dimy,0) -- (\dimx,\dimy,\dimz) -- (\dimx,0,\dimz) -- cycle;%
        }%
        {}
    \end{scope}
}

\makeatother

\begin{document}

\begin{tikzpicture}
    \tikzcuboid{shiftx=0cm,%
        shifty=0cm,%
        scale=1.00,%
        rotation=30,%
        densityx=1,%
        densityy=2,%
        densityz=3,%
        dimx=4,%
        dimy=5,%
        dimy=2,%
        linefront=yellow!30!black,%
        linetop=red!30!black,%
        lineright=blue!30!black,%
        fillfront=yellow!30!white,%
        filltop=red!30!white,%
        fillright=blue!30!white%
    }
    \tikzcuboid{%
        shiftx=0cm,%
        shifty=8cm,%
        scale=1.00,%
        rotation=60,%
        densityx=3,%
        densityy=2,%
        densityz=5,%
        dimx=4,%
        dimy=4,%
        dimy=4,%
        linefront=orange!75!black,%
        linetop=green!75!black,%
        lineright=violet!75!black,%
        fillfront=orange!75!white,%
        filltop=green!75!white,%
        fillright=violet!75!white%
    }
    \tikzcuboid{%
        shiftx=8cm,%
        shifty=8cm,%
        scale=1.00,%
        rotation=45,%
        densityx=1,%
        densityy=(2/3),%
        densityz=2,%
        dimx=3,%
        dimy=3,%
        dimy=3,%
        linefront=white!15!black,%
        linetop=white!30!black,%
        lineright=white!45!black,%
        fillfront=black!15!white,%
        filltop=black!30!white,%
        fillright=black!45!white%
    }
    \tikzcuboid{%
        shiftx=8cm,%
        shifty=0cm,%
        scale=1.00,%
        rotation=75,%
        densityx=2,%
        densityy=3,%
        densityz=2,%
        dimx=6,%
        dimy=8,%
        dimy=1,%
        linefront=red!75!black,%
        linetop=red!50!black,%
        lineright=red!25!black,%
        fillfront=red!25!white,%
        filltop=red!50!white,%
        fillright=red!75!white%
    }
    \tikzcuboid{%
        shiftx=16cm,%
        shifty=8cm,%
        scale=1.00,%
        rotation=0,%
        densityx=2,%
        densityy=2,%
        densityz=2,%
        dimx=4,%
        dimy=4,%
        dimy=4,%
        linefront=green!75!black,%
        linetop=green!50!black,%
        lineright=green!25!black,%
        fillfront=green!25!white,%
        filltop=green!50!white,%
        fillright=green!75!white,%
        emphedge=Y,%
        emphstyle=very thick,
    }
    \tikzcuboid{%
        shiftx=16cm,%
        shifty=0cm,%
        scale=1.00,%
        rotation=0,%
        densityx=1,%
        densityy=1,%
        densityz=1,%
        dimx=4,%
        dimy=4,%
        dimy=4,%
        linefront=blue!75!black,%
        linetop=blue!50!black,%
        lineright=blue!25!black,%
        fillfront=blue!25!white,%
        filltop=blue!50!white,%
        fillright=blue!75!white,%
        anglex=15,%
        angley=135,%
        anglez=225,%
        scalex=1,%
        scaley=1,%
        scalez=1,%
        emphedge=N,%
    }
\end{tikzpicture}

\end{document}

And some samples:

Also, you can play around a little:

There are still some issues (certain axis transformations don't work, the emphstyle can only be passed one option...), and I'm not yet certain about how to do the shading, I'll experiment some more.

---

Edit 4: Finally I got everything, special thanks to Altermundus and Andrew Stacey for helping me with some issues. I finally incorporated all options and switched to pgfkeys, now I'm writing on a manual, CTAN package coming soon!

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm,landscape]{geometry}
\usepackage{tikz}

\newif\ifcuboidshade
\newif\ifcuboidemphedge

\tikzset{
  cuboid/.is family,
  cuboid,
  shiftx/.initial=0,
  shifty/.initial=0,
  dimx/.initial=3,
  dimy/.initial=3,
  dimz/.initial=3,
  scale/.initial=1,
  densityx/.initial=1,
  densityy/.initial=1,
  densityz/.initial=1,
  rotation/.initial=0,
  anglex/.initial=0,
  angley/.initial=90,
  anglez/.initial=225,
  scalex/.initial=1,
  scaley/.initial=1,
  scalez/.initial=0.5,
  front/.style={draw=black,fill=white},
  top/.style={draw=black,fill=white},
  right/.style={draw=black,fill=white},
  shade/.is if=cuboidshade,
  shadecolordark/.initial=black,
  shadecolorlight/.initial=white,
  shadeopacity/.initial=0.15,
  shadesamples/.initial=16,
  emphedge/.is if=cuboidemphedge,
  emphstyle/.style={thick},
}

\newcommand{\tikzcuboidkey}[1]{\pgfkeysvalueof{/tikz/cuboid/#1}}

% Commands
\newcommand{\tikzcuboid}[1]{
    \tikzset{cuboid,#1} % Process Keys passed to command
  \pgfmathsetlengthmacro{\vectorxx}{\tikzcuboidkey{scalex}*cos(\tikzcuboidkey{anglex})*28.452756}
  \pgfmathsetlengthmacro{\vectorxy}{\tikzcuboidkey{scalex}*sin(\tikzcuboidkey{anglex})*28.452756}
  \pgfmathsetlengthmacro{\vectoryx}{\tikzcuboidkey{scaley}*cos(\tikzcuboidkey{angley})*28.452756}
  \pgfmathsetlengthmacro{\vectoryy}{\tikzcuboidkey{scaley}*sin(\tikzcuboidkey{angley})*28.452756}
  \pgfmathsetlengthmacro{\vectorzx}{\tikzcuboidkey{scalez}*cos(\tikzcuboidkey{anglez})*28.452756}
  \pgfmathsetlengthmacro{\vectorzy}{\tikzcuboidkey{scalez}*sin(\tikzcuboidkey{anglez})*28.452756}
  \begin{scope}[xshift=\tikzcuboidkey{shiftx}, yshift=\tikzcuboidkey{shifty}, scale=\tikzcuboidkey{scale}, rotate=\tikzcuboidkey{rotation}, x={(\vectorxx,\vectorxy)}, y={(\vectoryx,\vectoryy)}, z={(\vectorzx,\vectorzy)}]
    \pgfmathsetmacro{\steppingx}{1/\tikzcuboidkey{densityx}}
  \pgfmathsetmacro{\steppingy}{1/\tikzcuboidkey{densityy}}
  \pgfmathsetmacro{\steppingz}{1/\tikzcuboidkey{densityz}}
  \newcommand{\dimx}{\tikzcuboidkey{dimx}}
  \newcommand{\dimy}{\tikzcuboidkey{dimy}}
  \newcommand{\dimz}{\tikzcuboidkey{dimz}}
  \pgfmathsetmacro{\secondx}{2*\steppingx}
  \pgfmathsetmacro{\secondy}{2*\steppingy}
  \pgfmathsetmacro{\secondz}{2*\steppingz}
  \foreach \x in {\steppingx,\secondx,...,\dimx}
  { \foreach \y in {\steppingy,\secondy,...,\dimy}
    {   \pgfmathsetmacro{\lowx}{(\x-\steppingx)}
      \pgfmathsetmacro{\lowy}{(\y-\steppingy)}
      \filldraw[cuboid/front] (\lowx,\lowy,\dimz) -- (\lowx,\y,\dimz) -- (\x,\y,\dimz) -- (\x,\lowy,\dimz) -- cycle;
    }
    }
  \foreach \x in {\steppingx,\secondx,...,\dimx}
  { \foreach \z in {\steppingz,\secondz,...,\dimz}
    {   \pgfmathsetmacro{\lowx}{(\x-\steppingx)}
      \pgfmathsetmacro{\lowz}{(\z-\steppingz)}
      \filldraw[cuboid/top] (\lowx,\dimy,\lowz) -- (\lowx,\dimy,\z) -- (\x,\dimy,\z) -- (\x,\dimy,\lowz) -- cycle;
        }
    }
    \foreach \y in {\steppingy,\secondy,...,\dimy}
  { \foreach \z in {\steppingz,\secondz,...,\dimz}
    {   \pgfmathsetmacro{\lowy}{(\y-\steppingy)}
      \pgfmathsetmacro{\lowz}{(\z-\steppingz)}
      \filldraw[cuboid/right] (\dimx,\lowy,\lowz) -- (\dimx,\lowy,\z) -- (\dimx,\y,\z) -- (\dimx,\y,\lowz) -- cycle;
    }
  }
  \ifcuboidemphedge
    \draw[cuboid/emphstyle] (0,\dimy,0) -- (\dimx,\dimy,0) -- (\dimx,\dimy,\dimz) -- (0,\dimy,\dimz) -- cycle;%
    \draw[cuboid/emphstyle] (0,\dimy,\dimz) -- (0,0,\dimz) -- (\dimx,0,\dimz) -- (\dimx,\dimy,\dimz);%
    \draw[cuboid/emphstyle] (\dimx,\dimy,0) -- (\dimx,0,0) -- (\dimx,0,\dimz);%
    \fi

    \ifcuboidshade
    \pgfmathsetmacro{\cstepx}{\dimx/\tikzcuboidkey{shadesamples}}
    \pgfmathsetmacro{\cstepy}{\dimy/\tikzcuboidkey{shadesamples}}
    \pgfmathsetmacro{\cstepz}{\dimz/\tikzcuboidkey{shadesamples}}
    \foreach \s in {1,...,\tikzcuboidkey{shadesamples}}
    {   \pgfmathsetmacro{\lows}{\s-1}
        \pgfmathsetmacro{\cpercent}{(\lows)/(\tikzcuboidkey{shadesamples}-1)*100}
        \fill[opacity=\tikzcuboidkey{shadeopacity},color=\tikzcuboidkey{shadecolorlight}!\cpercent!\tikzcuboidkey{shadecolordark}] (0,\s*\cstepy,\dimz) -- (\s*\cstepx,\s*\cstepy,\dimz) -- (\s*\cstepx,0,\dimz) -- (\lows*\cstepx,0,\dimz) -- (\lows*\cstepx,\lows*\cstepy,\dimz) -- (0,\lows*\cstepy,\dimz) -- cycle;
        \fill[opacity=\tikzcuboidkey{shadeopacity},color=\tikzcuboidkey{shadecolorlight}!\cpercent!\tikzcuboidkey{shadecolordark}] (0,\dimy,\s*\cstepz) -- (\s*\cstepx,\dimy,\s*\cstepz) -- (\s*\cstepx,\dimy,0) -- (\lows*\cstepx,\dimy,0) -- (\lows*\cstepx,\dimy,\lows*\cstepz) -- (0,\dimy,\lows*\cstepz) -- cycle;
        \fill[opacity=\tikzcuboidkey{shadeopacity},color=\tikzcuboidkey{shadecolorlight}!\cpercent!\tikzcuboidkey{shadecolordark}] (\dimx,0,\s*\cstepz) -- (\dimx,\s*\cstepy,\s*\cstepz) -- (\dimx,\s*\cstepy,0) -- (\dimx,\lows*\cstepy,0) -- (\dimx,\lows*\cstepy,\lows*\cstepz) -- (\dimx,0,\lows*\cstepz) -- cycle;
    }
    \fi 

  \end{scope}
}

\makeatother

\begin{document}

\begin{tikzpicture}
    \tikzcuboid{%
    shiftx=0cm,%
    shifty=8cm,%
    scale=1.00,%
    rotation=0,%
    densityx=2,%
    densityy=2,%
    densityz=2,%
    dimx=3,%
    dimy=3,%
    dimz=3,%
    scalex=1,%
    scaley=1,%
    scalez=1,%
    anglex=-30,%
    angley=90,%
    anglez=210,%
    front/.style={draw=green!50!black,fill=green!50!white},%
    top/.style={draw=green!50!black,fill=green!50!white},%
    right/.style={draw=green!50!black,fill=green!50!white},%
    emphedge,%
    emphstyle/.style={line width=1pt, green!12!black,densely dashed},
    shade,%
    shadesamples=64,%
    shadeopacity=0.15,%
    }
    \tikzcuboid{%
    shiftx=8cm,%
    shifty=8cm,%
    shadeopacity=0.30,%
    }   
    \tikzcuboid{%
    shiftx=16cm,%
    shifty=8cm,%
    shadeopacity=0.60,%
    }   
    \tikzcuboid{%
    shiftx=0cm,%
    shifty=0cm,%
    scale=1.00,%
    rotation=0,%
    densityx=1,%
    densityy=1,%
    densityz=1,%
    dimx=4,%
    dimy=4,%
    dimz=4,%
    front/.style={draw=blue!75!black,fill=blue!25!white},%
    right/.style={draw=blue!25!black,fill=blue!75!white},%
    top/.style={draw=blue!50!black,fill=blue!50!white},%
    anglex=-7,%
    angley=90,%
    anglez=221.5,%
    scalex=1,%
    scaley=1,%
    scalez=0.5,%
    emphedge=false,%
    shade,%
    shadeopacity=0.15,%
    }
    \tikzcuboid{%
    shiftx=8cm,%
    shifty=0cm,%
    shadeopacity=0.30,%
    }
    \tikzcuboid{%
    shiftx=16cm,%
    shifty=0cm,%
    shadeopacity=0.60,%
    }
\end{tikzpicture}

\end{document}

And some examples: first line is isometric, the second is simetric projection, from left to right the shading opacity is 0.15, 0.30 and 0.60

Answer 2

Here is a fixed version of Bombadil's code for dimensions equal to 1.

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm,landscape]{geometry}
\usepackage{tikz}
\usepackage{ifthen}
%-------------------
\newif\ifcuboidshade
\newif\ifcuboidemphedge

\tikzset{
  cuboid/.is family,
  cuboid,
  shiftx/.initial=0,
  shifty/.initial=0,
  dimx/.initial=3,
  dimy/.initial=3,
  dimz/.initial=3,
  scale/.initial=1,
  densityx/.initial=1,
  densityy/.initial=1,
  densityz/.initial=1,
  rotation/.initial=0,
  anglex/.initial=0,
  angley/.initial=90,
  anglez/.initial=225,
  scalex/.initial=1,
  scaley/.initial=1,
  scalez/.initial=0.5,
  front/.style={draw=black,fill=white},
  top/.style={draw=black,fill=white},
  right/.style={draw=black,fill=white},
  shade/.is if=cuboidshade,
  shadecolordark/.initial=black,
  shadecolorlight/.initial=white,
  shadeopacity/.initial=0.15,
  shadesamples/.initial=16,
  emphedge/.is if=cuboidemphedge,
  emphstyle/.style={thick},
}

\newcommand{\tikzcuboidkey}[1]{\pgfkeysvalueof{/tikz/cuboid/#1}}

% Commands
\newcommand{\tikzcuboid}[1]{
    \tikzset{cuboid,#1} % Process Keys passed to command
  \pgfmathsetlengthmacro{\vectorxx}{\tikzcuboidkey{scalex}*cos(\tikzcuboidkey{anglex})*28.452756}
  \pgfmathsetlengthmacro{\vectorxy}{\tikzcuboidkey{scalex}*sin(\tikzcuboidkey{anglex})*28.452756}
  \pgfmathsetlengthmacro{\vectoryx}{\tikzcuboidkey{scaley}*cos(\tikzcuboidkey{angley})*28.452756}
  \pgfmathsetlengthmacro{\vectoryy}{\tikzcuboidkey{scaley}*sin(\tikzcuboidkey{angley})*28.452756}
  \pgfmathsetlengthmacro{\vectorzx}{\tikzcuboidkey{scalez}*cos(\tikzcuboidkey{anglez})*28.452756}
  \pgfmathsetlengthmacro{\vectorzy}{\tikzcuboidkey{scalez}*sin(\tikzcuboidkey{anglez})*28.452756}
  \begin{scope}[xshift=\tikzcuboidkey{shiftx}, yshift=\tikzcuboidkey{shifty}, scale=\tikzcuboidkey{scale}, rotate=\tikzcuboidkey{rotation}, x={(\vectorxx,\vectorxy)}, y={(\vectoryx,\vectoryy)}, z={(\vectorzx,\vectorzy)}]
    \pgfmathsetmacro{\steppingx}{1/\tikzcuboidkey{densityx}}
  \pgfmathsetmacro{\steppingy}{1/\tikzcuboidkey{densityy}}
  \pgfmathsetmacro{\steppingz}{1/\tikzcuboidkey{densityz}}
  \newcommand{\dimx}{\tikzcuboidkey{dimx}}
  \newcommand{\dimy}{\tikzcuboidkey{dimy}}
  \newcommand{\dimz}{\tikzcuboidkey{dimz}}
  \pgfmathsetmacro{\secondx}{2*\steppingx}
  \pgfmathsetmacro{\secondy}{2*\steppingy}
  \pgfmathsetmacro{\secondz}{2*\steppingz}
  \ifthenelse{\equal{\dimx}{1}}
    {\foreach \x in {\steppingx,...,\dimx}}
    {\foreach \x in {\steppingx,\secondx,...,\dimx}}
  {     \ifthenelse{\equal{\dimy}{1}}
    {\foreach \y in {\steppingy,...,\dimy}}
    {\foreach \y in {\steppingy,\secondy,...,\dimy}}
    {   \pgfmathsetmacro{\lowx}{(\x-\steppingx)}
      \pgfmathsetmacro{\lowy}{(\y-\steppingy)}
      \filldraw[cuboid/front] (\lowx,\lowy,\dimz) -- (\lowx,\y,\dimz) -- (\x,\y,\dimz) -- (\x,\lowy,\dimz) -- cycle;
    }
    }
    \ifthenelse{\equal{\dimx}{1}}
    {\foreach \x in {\steppingx,...,\dimx}}
    {\foreach \x in {\steppingx,\secondx,...,\dimx}}
  { \ifthenelse{\equal{\dimz}{1}}
    {\foreach \z in {\steppingz,...,\dimz}}
    {\foreach \z in {\steppingz,\secondz,...,\dimz}}
    {   \pgfmathsetmacro{\lowx}{(\x-\steppingx)}
      \pgfmathsetmacro{\lowz}{(\z-\steppingz)}
      \filldraw[cuboid/top] (\lowx,\dimy,\lowz) -- (\lowx,\dimy,\z) -- (\x,\dimy,\z) -- (\x,\dimy,\lowz) -- cycle;
        }
    }
    \ifthenelse{\equal{\dimy}{1}}
    {\foreach \y in {\steppingy,...,\dimy}}
    {\foreach \y in {\steppingy,\secondy,...,\dimy}}
  { \ifthenelse{\equal{\dimz}{1}}
    {\foreach \z in {\steppingz,...,\dimz}}
    {\foreach \z in {\steppingz,\secondz,...,\dimz}}
    {   \pgfmathsetmacro{\lowy}{(\y-\steppingy)}
      \pgfmathsetmacro{\lowz}{(\z-\steppingz)}
      \filldraw[cuboid/right] (\dimx,\lowy,\lowz) -- (\dimx,\lowy,\z) -- (\dimx,\y,\z) -- (\dimx,\y,\lowz) -- cycle;
    }
  }
  \ifcuboidemphedge
    \draw[cuboid/emphstyle] (0,\dimy,0) -- (\dimx,\dimy,0) -- (\dimx,\dimy,\dimz) -- (0,\dimy,\dimz) -- cycle;%
    \draw[cuboid/emphstyle] (0,\dimy,\dimz) -- (0,0,\dimz) -- (\dimx,0,\dimz) -- (\dimx,\dimy,\dimz);%
    \draw[cuboid/emphstyle] (\dimx,\dimy,0) -- (\dimx,0,0) -- (\dimx,0,\dimz);%
    \fi

    \ifcuboidshade
    \pgfmathsetmacro{\cstepx}{\dimx/\tikzcuboidkey{shadesamples}}
    \pgfmathsetmacro{\cstepy}{\dimy/\tikzcuboidkey{shadesamples}}
    \pgfmathsetmacro{\cstepz}{\dimz/\tikzcuboidkey{shadesamples}}
    \foreach \s in {1,...,\tikzcuboidkey{shadesamples}}
    {   \pgfmathsetmacro{\lows}{\s-1}
        \pgfmathsetmacro{\cpercent}{(\lows)/(\tikzcuboidkey{shadesamples}-1)*100}
        \fill[opacity=\tikzcuboidkey{shadeopacity},color=\tikzcuboidkey{shadecolorlight}!\cpercent!\tikzcuboidkey{shadecolordark}] (0,\s*\cstepy,\dimz) -- (\s*\cstepx,\s*\cstepy,\dimz) -- (\s*\cstepx,0,\dimz) -- (\lows*\cstepx,0,\dimz) -- (\lows*\cstepx,\lows*\cstepy,\dimz) -- (0,\lows*\cstepy,\dimz) -- cycle;
        \fill[opacity=\tikzcuboidkey{shadeopacity},color=\tikzcuboidkey{shadecolorlight}!\cpercent!\tikzcuboidkey{shadecolordark}] (0,\dimy,\s*\cstepz) -- (\s*\cstepx,\dimy,\s*\cstepz) -- (\s*\cstepx,\dimy,0) -- (\lows*\cstepx,\dimy,0) -- (\lows*\cstepx,\dimy,\lows*\cstepz) -- (0,\dimy,\lows*\cstepz) -- cycle;
        \fill[opacity=\tikzcuboidkey{shadeopacity},color=\tikzcuboidkey{shadecolorlight}!\cpercent!\tikzcuboidkey{shadecolordark}] (\dimx,0,\s*\cstepz) -- (\dimx,\s*\cstepy,\s*\cstepz) -- (\dimx,\s*\cstepy,0) -- (\dimx,\lows*\cstepy,0) -- (\dimx,\lows*\cstepy,\lows*\cstepz) -- (\dimx,0,\lows*\cstepz) -- cycle;
    }
    \fi 

  \end{scope}
}

\makeatother
%-------------------
\begin{document}   
\begin{tikzpicture}   

\tikzcuboid{dimx=1,dimy=1,dimz=1};
\tikzcuboid{dimx=1,dimy=2,dimz=3,shiftx=100};
\tikzcuboid{dimx=3,dimy=1,dimz=2,shiftx=0,shifty=80};
\tikzcuboid{dimx=2,dimy=3,dimz=1,shiftx=100,shifty=80};

\end{tikzpicture}
\end{document}

Here is the output

The main changes are ifthenelse hacks that check if dim{x,y,z} is equal to 1 and in that case cancel foreach stepping.

  \ifthenelse{\equal{\dimx}{1}}
    {\foreach \x in {\steppingx,...,\dimx}}
    {\foreach \x in {\steppingx,\secondx,...,\dimx}}

Answer 3

Starting from Stefan Kottwitz's "Sudoku 3D cube" example (http://www.texample.net/tikz/examples/sudoku-3d-cube/ the idea of using yslant and xslant to achieve a 3D like appearance), I have developed an alternative visualization for Pasigraphy Rhapsody, https://gitlab.com/nbatfai/pasigraphy-rhapsody/blob/master/para/docs/prelpara.lua I think it can be used easily for the purpose in question by the following:

\begin{tikzpicture}[thick, scale=2, every node/.style={scale=2}]
\prelparaIIID{1}{"1:3:3:0:1:2:2:3:4:10:2:0:9:9:0:1:0"}
\end{tikzpicture}

 \begin{tikzpicture}[thick, scale=2, every node/.style={scale=2}]
 \prelparaIIID{1}{"1:3:3:0:1:2:2:3:4:10:2:0:9:9:0:8:2:1:6:6:1"}
 \end{tikzpicture}

 \begin{tikzpicture}[thick, scale=2, every node/.style={scale=2}]
 \prelparaIIID{1}{"3:4:3:0:1:2:2:3:4:10:2:0:9:9:0:8:2:1:6:6:1:6:2:1:5:5:1:8:2:1:7:7:1:4:2:1:3:3:1:4:2:1:3:3:1:10:2:1:7:7:1:6:2:1:5:5:1"}
 \prelparaIIID{2} {"4:4:3:1:2:2:2:3:4:10:2:0:9:9:0:8:2:1:6:6:1:6:2:1:5:5:1:8:2:1:7:7:1:4:2:1:3:3:1:4:2:1:3:3:1:2:1:1:1:6:2:1:5:5:1:4:1:1:1:8:2:2:2:4:4:2:1:1:1"}
 \prelparaIIID{1}{"3:4:3:0:1:2:2:3:4:10:2:0:9:9:0:8:2:1:6:6:1:6:2:1:5:5:1:8:2:1:7:7:1:4:2:1:3:3:1:4:2:1:3:3:1:10:2:1:7:7:1:6:2:1:5:5:1"}
 \end{tikzpicture}

At @siracusa suggestion, I have attached a full example

demo.tex

\documentclass[a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{t1enc}
\usepackage{luacode}
\directlua{require('prelpara')}
\usepackage{tikz}

\newcommand\N[1]{\directlua{N(#1) }} 
\newcommand\D[3]{\directlua{D(#1,#2,#3) }} 
\newcommand\prelparaIID[1]{\directlua{para2D(#1)}}
\newcommand\prelparaIIID[2]{\directlua{para3D(#1,#2)}}

\begin{document}

\begin{tikzpicture}[thick, scale=2, every node/.style={scale=2}]
\prelparaIIID{1}{"3:4:3:0:1:2:2:3:4:10:2:0:9:9:0:8:2:1:6:6:1:6:2:1:5:5:1:8:2:1:7:7:1:4:2:1:3:3:1:4:2:1:3:3:1:10:2:1:7:7:1:6:2:1:5:5:1"}
\prelparaIIID{2} {"4:4:3:1:2:2:2:3:4:10:2:0:9:9:0:8:2:1:6:6:1:6:2:1:5:5:1:8:2:1:7:7:1:4:2:1:3:3:1:4:2:1:3:3:1:2:1:1:1:6:2:1:5:5:1:4:1:1:1:8:2:2:2:4:4:2:1:1:1"}
\prelparaIIID{1}{"3:4:3:0:1:2:2:3:4:10:2:0:9:9:0:8:2:1:6:6:1:6:2:1:5:5:1:8:2:1:7:7:1:4:2:1:3:3:1:4:2:1:3:3:1:10:2:1:7:7:1:6:2:1:5:5:1"}
\end{tikzpicture}

\end{document}

prelpara.lua

--[[

% Esport Language (PaRa) , first experiments 
% This is a rapid prototype for planning Pasigraphy Rhapsody (Paszigráfia Rapszódia, PaRa)
%
% prelpara.lua
%
% Copyright (C) 2019 Norbert Bátfai, [email protected], [email protected]
%
%  This program is free software: you can redistribute it and/or modify
%  it under the terms of the GNU General Public License as published by
%  the Free Software Foundation, either version 3 of the License, or
%  (at your option) any later version.
%
%  This program is distributed in the hope that it will be useful,
%  but WITHOUT ANY WARRANTY; without even the implied warranty of
%  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%  GNU General Public License for more details.
%
%  You should have received a copy of the GNU General Public License
%  along with this program.  If not, see <https://www.gnu.org/licenses/>.
%
% Version history
%
% Initial hack
%
% for vis_prel_para.tex
% Working title: Visualization of the Language of the Esports Culture: A Preliminary Study
% 
% A LuaLaTeX based visualization experiment for Pasigraphy Rhapsody
%
% The idea of using yslant and xslant to achieve a 3D effect like appearance 
% comes from Stefan Kottwitz's example http://www.texample.net/tikz/examples/sudoku-3d-cube/
% 
%
--]]
function para2D(fmts)
        local sntnc = fmts:split(":")
        r=sntnc[1]
        fmts_shift = 1
        for i = 0, r-1 do
            fmts_shift = fmts_shift +1
            n=sntnc[fmts_shift]
            fmts_shift = fmts_shift +1
            nod=sntnc[fmts_shift]
            tex.sprint(
                    "\\tikzstyle{shifting}=[xshift=", i,"cm]"                   
                    ,"\\shade[shifting, left color=gray!10, right color=black!80] (0,0) rectangle +(1,1);"
                    ,"\\draw[shifting, step=\\N{",n,"}cm, cyan] (0,0) grid (1,1);")     
            for j = 1, nod do
                fmts_shift = fmts_shift +1
                x=sntnc[fmts_shift]
                fmts_shift = fmts_shift +1
                y=sntnc[fmts_shift]+1
                tex.sprint(
                    "\\node[shifting, fill=orange, anchor=north west,  inner sep=0pt,minimum size=\\N{",n,"}cm-\\pgflinewidth] at \\D{",n,"}{",x,"}{",y,"} {};")
            end
        end
    end

function para3D(direct, fmts)
        dir=tonumber(direct)
        d={{2,1,2,-1,1,-1}, {1,0,1,-1,0,-1}}
        local sntnc = fmts:split(":")
        r=sntnc[1]
        fmts_shift = 1
        for i = 0, r-1 do
            fmts_shift = fmts_shift +1
            n=sntnc[fmts_shift]
            fmts_shift = fmts_shift +1
            nod=sntnc[fmts_shift]
            tex.sprint(
            "\\tikzstyle{leftslant}=[yslant=-.5, xshift=",-1+i*d[dir][1],"cm, yshift=",-1+i*d[dir][2],"cm]"
            ,"\\tikzstyle{rightslant}=[yslant=0.5, xshift=",i*d[dir][3],"cm, yshift=",-1+i*d[dir][4],"cm]"
            ,"\\tikzstyle{topslant}=[yslant=0.5, xslant=-1, xshift=", i*d[dir][5],"cm, yshift=", i*d[dir][6],"cm]"
            ,"\\shade[leftslant, right color=gray!10,left color=black!80] (0,0) rectangle +(1,1);"
            ,"\\draw[leftslant, step=\\N{",n,"}cm, cyan] (0,0) grid (1,1);")
            for j = 1, nod do
                fmts_shift = fmts_shift +1
                x=sntnc[fmts_shift]
                fmts_shift = fmts_shift +1
                y=sntnc[fmts_shift]+1
                tex.sprint(
                "\\node[leftslant, fill=orange, anchor=north west,  inner sep=0pt,minimum size=\\N{",n,"}cm-\\pgflinewidth] at \\D{",n,"}{",x,"}{",y,"-.5*",x,"} {};")
            end    
            fmts_shift = fmts_shift +1    
            n=sntnc[fmts_shift]
            fmts_shift = fmts_shift +1
            nod=sntnc[fmts_shift]
            tex.sprint(
                "\\shade[rightslant, right color=black!70,left color=gray!20] (0,0) rectangle +(1,1);",
                "\\draw[rightslant, step=\\N{",n,"}cm, pink](0,0) grid (1,1);")
            for j = 1, nod do
                fmts_shift = fmts_shift +1
                x=sntnc[fmts_shift]
                fmts_shift = fmts_shift +1
                y=sntnc[fmts_shift]
                tex.sprint(
                    "\\node[rightslant, fill=cyan, anchor=south west,  inner sep=0pt,minimum size=\\N{",n,"}cm-\\pgflinewidth] at \\D{",n,"}{",x,"}{",y,"+.5*",x,"} {};")
            end    
            fmts_shift = fmts_shift +1
            n=sntnc[fmts_shift]
            fmts_shift = fmts_shift +1
            nod=sntnc[fmts_shift]       
            tex.sprint(
                "\\shade[topslant, bottom color=gray!10,top color=black!80] (0,0) rectangle +(1,1);",
                "\\draw[topslant, step=\\N{",n,"}cm, orange] (0,0) grid (1,1);")
            for j = 1, nod do
                fmts_shift = fmts_shift +1
                x=sntnc[fmts_shift]
                fmts_shift = fmts_shift +1
                y=sntnc[fmts_shift]     
                tex.sprint(
                    "\\node[topslant, fill=yellow, anchor=south west,  inner sep=0pt,minimum size=\\N{",n,"}cm-\\pgflinewidth] at \\D{",n,"}{",y,"-",x,"}{",tonumber(y)/2,"+.5*",x,"} {};")
           end    
    end
end

function N(n) 
            tex.sprint(1/n)
end 

function D(n, x, y) 
            tex.sprint("(",       (1/n)*x,     ", ",   (1/n)*y,       ")")
end