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使用 TikZ 复制此视觉证明

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使用 TikZ 复制此视觉证明

我对 TikZ 还不太熟悉，想复制不显示文字的证明这里。

平方和的视觉证明

有没有什么办法可以以 3D 形式构建这些干净的立方体，而不用逐行绘制它们？

感谢您的帮助:)

答案1

这是一个使用正交投影的版本。也就是说，你可以调整视角，至少在一定程度上，而且视图是真实的（在远距离观察者的极限内）。一切都存储在 pgf 键中，因此高度可调。样式和键基本上取自这个答案和这个答案，您可以找到动画说明了视图可调的含义。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\tikzset{plane/.style n args={3}{insert path={%
#1 -- ++ #2 -- ++ #3 -- ++ ($-1*#2$) -- cycle}},
unit xy plane/.style={plane={#1}{(\CubeX,0,0)}{(0,\CubeY,0)}},
unit xz plane/.style={plane={#1}{(\CubeX,0,0)}{(0,0,\CubeZ)}},
unit yz plane/.style={plane={#1}{(0,\CubeY,0)}{(0,0,\CubeZ)}},
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];
\ifnum\zproj=-1
 \path[3d cube/every face,3d cube/xy face,unit xy plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\fi
\ifnum\yproj=1
 \path[3d cube/every face,3d cube/yz face,unit yz plane={(\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\else
 \path[3d cube/every face,3d cube/yz face,unit yz plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\fi
\ifnum\xproj=1
 \path[3d cube/every face,3d cube/xz face,unit xz plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\else
 \path[3d cube/every face,3d cube/xz face,unit xz plane={(-\CubeX/2,\CubeY/2,-\CubeZ/2)}]; 
\fi
\ifnum\zproj>-1
 \path[3d cube/every face,3d cube/xy face,unit xy plane={(-\CubeX/2,-\CubeY/2,\CubeZ/2)}]; 
\fi
}},
3d cube/.cd,
xy face/.style={fill=red!20},
xz face/.style={fill=blue!20},
yz face/.style={fill=orange!30},
num cubes x/.estore in=\NumCubesX,
num cubes y/.estore in=\NumCubesY,
num cubes z/.estore in=\NumCubesZ,
num cubes x/.initial=1,num cubes y/.initial=1,num cubes z/.initial=1,
cube x/.estore in=\CubeX,
cube y/.estore in=\CubeY,
cube z/.estore in=\CubeZ,
cube x=1,cube y=1,cube z=1,
cube scale/.initial=1,
every face/.style={draw,very thick},
/tikz/pics/.cd,
cube array/.style={code={%
 \tikzset{3d cube/.cd,#1}
 %\typeout{\NumCubesX,\NumCubesY,\NumCubesZ}
  \path[get projections];
  \ifnum\yproj=1
   \def\LstX{1,...,\NumCubesX}
  \else 
   \ifnum\NumCubesX>1
    \pgfmathtruncatemacro{\NextToLast}{\NumCubesX-1}
    \def\LstX{\NumCubesX,\NextToLast,...,1}
   \else
    \def\LstX{1}   
   \fi 
  \fi
  \ifnum\xproj=-1
   \def\LstY{1,...,\NumCubesY}
  \else 
   \ifnum\NumCubesY>1
    \pgfmathtruncatemacro{\NextToLast}{\NumCubesY-1}
    \def\LstY{\NumCubesY,\NextToLast,...,1}
   \else
    \def\LstY{1}   
   \fi 
  \fi
  \ifnum\zproj=1
   \def\LstZ{1,...,\NumCubesZ}
  \else 
   \ifnum\NumCubesZ>1
    \pgfmathtruncatemacro{\NextToLast}{\NumCubesZ-1}
    \def\LstZ{\NumCubesZ,\NextToLast,...,1}
   \else
    \def\LstZ{1}   
   \fi 
  \fi
  \foreach \X in \LstX
  {\foreach \Y in \LstY
   {\foreach \Z in \LstZ
    {\path (\X-\NumCubesX/2-1/2,\Y-\NumCubesY/2-1/2,\Z-\NumCubesY/2-1/2)
      pic[scale=\pgfkeysvalueof{/tikz/3d cube/cube scale}]{unit cube};}}
  } 
}}
}

\begin{document}
\tdplotsetmaincoords{70}{50} % the first argument cannot be larger than 90
\begin{tikzpicture}[line join=round,tdplot_main_coords,font=\sffamily,3d cube/.cd,
 num cubes x=1,num cubes y=1,num cubes z=1]
\begin{scope} 
% top left
 \path (-3,0,0) pic{cube array={num cubes y=3,num cubes z=3}}
 ++(1,-1/2,1/2) pic{cube array={num cubes y=2,num cubes z=2}}
 ++(1,-1/2,1/2) pic{cube array={num cubes y=1,num cubes z=1}};
% top right
 \path (3,3,0) pic{cube array={num cubes x=3,num cubes z=3}}
  ++ (1/2,-1,1) pic{cube array={num cubes x=2,num cubes z=2}}
  ++ (1/2,-1,1) pic{cube array={num cubes y=1,num cubes z=1}};
% bottom
 \path (0,2,-3) pic{cube array={num cubes x=3,num cubes y=3}}
   ++ (1/2,-1/2,1/2) pic{cube array={num cubes x=2,num cubes y=2}}
   ++ (1/2,-1/2,1/2) pic{cube array={num cubes x=1,num cubes y=1}};
\end{scope}
\begin{scope}[xshift=11cm] 
% top left
 \path (0,0,-1) pic{cube array={num cubes x=4,num cubes y=3,num cubes z=3}}
 (1/2,1,1) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
 \draw[line width=2pt] (-1,-1.5,-5/2) -- ++ (0,0,1)
 -- ++ (1,0,0) -- ++ (0,0,1)  -- ++ (1,0,0) -- ++ (0,0,1)
 -- ++ (1,0,0) -- ++ (0,1,0) -- ++ (0,0,-1) -- ++ (0,1,0) -- ++ (0,0,-1)
 -- ++ (0,1,0) -- ++ (0,0,-1);
\end{scope}
\tikzset{darker/.style={3d cube/.cd,cube z=1/2,xy face/.style={fill=red!40},
    xz face/.style={fill=blue!40},yz face/.style={fill=orange!60}}}
\begin{scope}[yshift=-8cm] 
% top left
 \path (0,0,-1) pic{cube array={num cubes x=4,num cubes y=3,num cubes z=3}};
 \path[3d cube/cube z=1/2]
 (1/2,1,3/4) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
 \path[3d cube/.cd,cube z=1/2]
 (1/2,1,3/4) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
 \path[darker]
 (1/2,1,5/4) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
\end{scope}
\begin{scope}[yshift=-8cm,xshift=11cm] 
% top left
 \path (0,0,-1) pic{cube array={num cubes x=4,num cubes y=3,num cubes z=3}};
 \path[3d cube/.cd,cube z=1/2]
 (-3/2,1,3/4) pic[darker]{cube array={num cubes x=1,num cubes y=1,num cubes z=1}}
 (1/2,1,3/4) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 (-1,0,3/4) pic[darker]{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 (1,0,3/4) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 (-1/2,-1,3/4) pic[darker]{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 (3/2,-1,3/4) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
\end{scope}
\end{tikzpicture}
\end{document}

在此处输入图片描述

为了允许非平凡的不透明度，还需要绘制隐藏的面，因为如果覆盖它们的面变得透明，它们就会取消隐藏。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\tikzset{plane/.style n args={3}{insert path={%
#1 -- ++ #2 -- ++ #3 -- ++ ($-1*#2$) -- cycle}},
unit xy plane/.style={plane={#1}{(\CubeX,0,0)}{(0,\CubeY,0)}},
unit xz plane/.style={plane={#1}{(\CubeX,0,0)}{(0,0,\CubeZ)}},
unit yz plane/.style={plane={#1}{(0,\CubeY,0)}{(0,0,\CubeZ)}},
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];
\ifnum\zproj=-1
 \path[3d cube/every face,3d cube/xy face,unit xy plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\else 
 \path[3d cube/every face,3d cube/xy face,unit xy plane={(-\CubeX/2,-\CubeY/2,\CubeZ/2)}]; 
\fi
\ifnum\yproj=1
 \path[3d cube/every face,3d cube/yz face,unit yz plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\else
 \path[3d cube/every face,3d cube/yz face,unit yz plane={(\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\fi
\ifnum\xproj=1
 \path[3d cube/every face,3d cube/xz face,unit xz plane={(-\CubeX/2,\CubeY/2,-\CubeZ/2)}]; 
\else
 \path[3d cube/every face,3d cube/xz face,unit xz plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\fi
\ifnum\yproj=1
 \path[3d cube/every face,3d cube/yz face,unit yz plane={(\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\else
 \path[3d cube/every face,3d cube/yz face,unit yz plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\fi
\ifnum\xproj=1
 \path[3d cube/every face,3d cube/xz face,unit xz plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\else
 \path[3d cube/every face,3d cube/xz face,unit xz plane={(-\CubeX/2,\CubeY/2,-\CubeZ/2)}]; 
\fi
\ifnum\zproj>-1
 \path[3d cube/every face,3d cube/xy face,unit xy plane={(-\CubeX/2,-\CubeY/2,\CubeZ/2)}]; 
\else 
 \path[3d cube/every face,3d cube/xy face,unit xy plane={(-\CubeX/2,-\CubeY/2,-\CubeZ/2)}]; 
\fi
}},
3d cube/.cd,
xy face/.style={fill=red!20},
xz face/.style={fill=blue!20},
yz face/.style={fill=orange!30},
num cubes x/.estore in=\NumCubesX,
num cubes y/.estore in=\NumCubesY,
num cubes z/.estore in=\NumCubesZ,
num cubes x/.initial=1,num cubes y/.initial=1,num cubes z/.initial=1,
cube x/.estore in=\CubeX,
cube y/.estore in=\CubeY,
cube z/.estore in=\CubeZ,
cube x=1,cube y=1,cube z=1,
cube scale/.initial=1,
every face/.style={draw,very thick},
/tikz/pics/.cd,
cube array/.style={code={%
 \tikzset{3d cube/.cd,#1}
 %\typeout{\NumCubesX,\NumCubesY,\NumCubesZ}
  \path[get projections];
  \ifnum\yproj=1
   \def\LstX{1,...,\NumCubesX}
  \else 
   \ifnum\NumCubesX>1
    \pgfmathtruncatemacro{\NextToLast}{\NumCubesX-1}
    \def\LstX{\NumCubesX,\NextToLast,...,1}
   \else
    \def\LstX{1}   
   \fi 
  \fi
  \ifnum\xproj=-1
   \def\LstY{1,...,\NumCubesY}
  \else 
   \ifnum\NumCubesY>1
    \pgfmathtruncatemacro{\NextToLast}{\NumCubesY-1}
    \def\LstY{\NumCubesY,\NextToLast,...,1}
   \else
    \def\LstY{1}   
   \fi 
  \fi
  \ifnum\zproj=1
   \def\LstZ{1,...,\NumCubesZ}
  \else 
   \ifnum\NumCubesZ>1
    \pgfmathtruncatemacro{\NextToLast}{\NumCubesZ-1}
    \def\LstZ{\NumCubesZ,\NextToLast,...,1}
   \else
    \def\LstZ{1}   
   \fi 
  \fi
  \foreach \X in \LstX
  {\foreach \Y in \LstY
   {\foreach \Z in \LstZ
    {\path (\X-\NumCubesX/2-1/2,\Y-\NumCubesY/2-1/2,\Z-\NumCubesY/2-1/2)
      pic[scale=\pgfkeysvalueof{/tikz/3d cube/cube scale}]{unit cube};}}
  } 
}}
}

\begin{document}
\tdplotsetmaincoords{70}{50} % the first argument cannot be larger than 90
\begin{tikzpicture}[line join=round,tdplot_main_coords,font=\sffamily,3d cube/.cd,
 num cubes x=1,num cubes y=1,num cubes z=1]
\begin{scope} 
% top left
 \path (-3,0,0) pic{cube array={num cubes y=3,num cubes z=3}}
 ++(1,-1/2,1/2) pic{cube array={num cubes y=2,num cubes z=2}}
 ++(1,-1/2,1/2) pic{cube array={num cubes y=1,num cubes z=1}};
% top right
 \path (3,3,0) pic{cube array={num cubes x=3,num cubes z=3}}
  ++ (1/2,-1,1) pic{cube array={num cubes x=2,num cubes z=2}}
  ++ (1/2,-1,1) pic{cube array={num cubes y=1,num cubes z=1}};
% bottom
 \path (0,2,-3) pic{cube array={num cubes x=3,num cubes y=3}}
   ++ (1/2,-1/2,1/2) pic{cube array={num cubes x=2,num cubes y=2}}
   ++ (1/2,-1/2,1/2) pic{cube array={num cubes x=1,num cubes y=1}};
\end{scope}
\begin{scope}[xshift=11cm] 
% top left
 \path (0,0,-1) pic{cube array={num cubes x=4,num cubes y=3,num cubes z=3}}
 (1/2,1,1) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
 \draw[line width=2pt] (-1,-1.5,-5/2) -- ++ (0,0,1)
 -- ++ (1,0,0) -- ++ (0,0,1)  -- ++ (1,0,0) -- ++ (0,0,1)
 -- ++ (1,0,0) -- ++ (0,1,0) -- ++ (0,0,-1) -- ++ (0,1,0) -- ++ (0,0,-1)
 -- ++ (0,1,0) -- ++ (0,0,-1);
\end{scope}
\tikzset{darker/.style={3d cube/.cd,cube z=1/2,xy face/.style={fill=red!40},
    xz face/.style={fill=blue!40},yz face/.style={fill=orange!60}}}
\begin{scope}[yshift=-8cm] 
% top left
 \path (0,0,-1) pic{cube array={num cubes x=4,num cubes y=3,num cubes z=3}};
 \path[3d cube/cube z=1/2]
 (1/2,1,3/4) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
 \path[3d cube/.cd,cube z=1/2]
 (1/2,1,3/4) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
 \path[darker,/tikz/opacity=0.6]
 (1/2,1,5/4) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 ++(1/2,-1,0) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
\end{scope}
\begin{scope}[yshift=-8cm,xshift=11cm] 
% top left
 \path (0,0,-1) pic{cube array={num cubes x=4,num cubes y=3,num cubes z=3}};
 \path[3d cube/.cd,cube z=1/2,/tikz/opacity=0.6]
 (-3/2,1,3/4) pic[darker]{cube array={num cubes x=1,num cubes y=1,num cubes z=1}}
 (1/2,1,3/4) pic{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 (-1,0,3/4) pic[darker]{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 (1,0,3/4) pic{cube array={num cubes x=2,num cubes y=1,num cubes z=1}}
 (-1/2,-1,3/4) pic[darker]{cube array={num cubes x=3,num cubes y=1,num cubes z=1}}
 (3/2,-1,3/4) pic{cube array={num cubes x=1,num cubes y=1,num cubes z=1}};
\end{scope}
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

这里给出一个答案：我们可以很好地使用 Jang Soo Kim 的代码例程来复制这个无需言语的证明。

这是结果，复制并不准确，因为这个透视的角度破坏了透视效果。

截屏

因此，在不改变常规的情况下，我修改了一些面的角度和长度，以获得更好的 3D 渲染。

结果如下：

截屏

以下是本回答中我自己修改的Jang Soo Kim代码生成的图的代码：https://tex.stackexchange.com/a/470985/138900 （图片位于本页顶部）

\documentclass[tikz,border=5mm]{standalone}
% Three counters
\newcounter{x}
\newcounter{y}
\newcounter{z}
% The angles of x,y,z-axes
\newcommand\xaxis{210}
\newcommand\yaxis{-30}
\newcommand\zaxis{90}
% The top side of a cube
\newcommand\topside[3]{
  \fill[fill=yellow!30,fill opacity=1, draw=black,shift={(\xaxis:#1)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (30:1) -- (0,1) --(150:1)--(0,0);
}
% The left side of a cube
\newcommand\leftside[3]{
  \fill[fill=cyan!50,fill opacity=1, draw=black,shift={(\xaxis:#1)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (0,-1) -- (210:1) --(150:1)--(0,0);
}
% The right side of a cube
\newcommand\rightside[3]{
  \fill[fill=yellow!40!green!80!white,fill opacity=1, draw=black,shift={(\xaxis:#1)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (30:1) -- (-30:1) --(0,-1)--(0,0);
}
% The cube 
\newcommand\cube[3]{
  \topside{#1}{#2}{#3} \leftside{#1}{#2}{#3} \rightside{#1}{#2}{#3}
}
% Definition of \planepartition
% To draw the following plane partition, just write \planepartition{ {a, b, c}, {d,e} }.
%  a b c
%  d e
\newcommand\planepartition[2][0]{
 \setcounter{x}{-1}
  \foreach \a in {#2} {
        \addtocounter{x}{1}
        \setcounter{y}{-1}
            \foreach \b in \a {
            \addtocounter{y}{1}
            \setcounter{z}{-1}
            \addtocounter{z}{#1} %partition of the desired floor (layer)
            \ifnum \b>0
            \foreach \c in {1,...,\b} {
                \addtocounter{z}{1}
                \cube{\value{x}}{\value{y}}{\value{z}}
      }\fi
    }
  }
}
\begin{document} 


\begin{tikzpicture}
\planepartition{{3},{3},{3}}% Old syntax is functional
\planepartition[1]{{0,0},{0,2},{0,2}}
\planepartition[2]{{0},{0},{0,0,1}}

\begin{scope}[xshift=5cm]
\planepartition{{3,3,3}}% Old syntax is functional
\planepartition[1]{{0},{0,2,2}}
\planepartition[2]{{0},{0},{0,0,1}}
\end{scope}

\begin{scope}[shift={(3,-4)}]
\planepartition{{1},{1},{1}}
\planepartition{{0,1},{0,2},{0,2}}
\planepartition{{0,0,1},{0,0,2},{0,0,3}}
\end{scope}
\end{tikzpicture}
\end{document}

该算法（marmot称之为例程），即命令的代码\planepartition尚未被修改。

\newcommand\planepartition[2][0]{
 \setcounter{x}{-1}
  \foreach \a in {#2} {
        \addtocounter{x}{1}
        \setcounter{y}{-1}
            \foreach \b in \a {
            \addtocounter{y}{1}
            \setcounter{z}{-1}
            \addtocounter{z}{#1} %partition of the desired floor (layer)
            \ifnum \b>0
            \foreach \c in {1,...,\b} {
                \addtocounter{z}{1}
                \cube{\value{x}}{\value{y}}{\value{z}}
      }\fi
    }
  }
}

仅修改了初始条件（角度和面长）。\planepartition两个版本中对例程 ( ) 的调用相同：

\begin{tikzpicture}
\planepartition{{3},{3},{3}}% Old syntax is functional
\planepartition[1]{{0,0},{0,2},{0,2}}
\planepartition[2]{{0},{0},{0,0,1}}

\begin{scope}[xshift=5cm]
\planepartition{{3,3,3}}% Old syntax is functional
\planepartition[1]{{0},{0,2,2}}
\planepartition[2]{{0},{0},{0,0,1}}
\end{scope}

\begin{scope}[shift={(3,-4)}]
\planepartition{{1},{1},{1}}
\planepartition{{0,1},{0,2},{0,2}}
\planepartition{{0,0,1},{0,0,2},{0,0,3}}
\end{scope}
\end{tikzpicture}

完整代码：

\documentclass[tikz,border=5mm]{standalone}

\newcounter{x}
\newlength{\x}
\setlength{\x}{.8cm}
\newcounter{y}
\newcounter{z}
% The angles of x,y,z-axes
\def\xangle{30}
\def\yangle{10}
\newcommand\xaxis{180+\xangle}
\newcommand\yaxis{-\yangle}
\newcommand\zaxis{90}
% The top side of a cube
\newcommand\topside[3]{
  \fill[fill=yellow!60,fill opacity=1, draw=black,shift={(\xaxis:#1\x)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (\xangle:\x) --++ (180-\yangle:1) --++(180+\xangle:\x)--cycle;
}
% The left side of a cube
\newcommand\leftside[3]{
  \fill[fill=orange!60,fill opacity=1, draw=black,shift={(\xaxis:#1\x)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (0,-1) --++ (180-\yangle:1) --(180-\yangle:1)--(0,0);
}
% The right side of a cube
\newcommand\rightside[3]{
  \fill[fill=blue!60,fill opacity=1, draw=black,shift={(\xaxis:#1\x)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (\xangle:\x) --++ (0,-1)--(0,-1)--(0,0);
}
% The cube 
\newcommand\cube[3]{
  \topside{#1}{#2}{#3} \leftside{#1}{#2}{#3} \rightside{#1}{#2}{#3}
}
% Definition of \planepartition
% To draw the following plane partition, just write \planepartition{ {a, b, c}, {d,e} }.
%  a b c
%  d e
\newcommand\planepartition[2][0]{
 \setcounter{x}{-1}
  \foreach \a in {#2} {
        \addtocounter{x}{1}
        \setcounter{y}{-1}
            \foreach \b in \a {
            \addtocounter{y}{1}
            \setcounter{z}{-1}
            \addtocounter{z}{#1} %partition of the desired floor (layer)
            \ifnum \b>0
            \foreach \c in {1,...,\b} {
                \addtocounter{z}{1}
                \cube{\value{x}}{\value{y}}{\value{z}}
      }\fi
    }
  }
}
\begin{document} 



\begin{tikzpicture}
\planepartition{{3},{3},{3}}% Old syntax is functional
\planepartition[1]{{0,0},{0,2},{0,2}}
\planepartition[2]{{0},{0},{0,0,1}}

\begin{scope}[xshift=5cm]
\planepartition{{3,3,3}}% Old syntax is functional
\planepartition[1]{{0},{0,2,2}}
\planepartition[2]{{0},{0},{0,0,1}}
\end{scope}

\begin{scope}[shift={(3,-4)}]
\planepartition{{1},{1},{1}}
\planepartition{{0,1},{0,2},{0,2}}
\planepartition{{0,0,1},{0,0,2},{0,0,3}}
\end{scope}
\end{tikzpicture}
\end{document}

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