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TikZ：如何用长方体填充立方体？

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TikZ：如何用长方体填充立方体？

我想用长方体（a、b、c，它们是 L 的分母）以棋盘样式填充立方体（边长为 L）。

出了点问题。我该怎么办？
（我暂时没有填屋顶。）

在此处输入图片描述

\documentclass[margin=5pt, tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}
\pgfmathsetmacro{\L}{10}
\pgfmathsetmacro{\a}{2}
\pgfmathsetmacro{\b}{2}
\pgfmathsetmacro{\c}{1}

\begin{tikzpicture}[scale=1.5,
z ={(0,0,-cos(45))},  % z ={(0,0,-1)},
>=latex, 
font=\footnotesize,
]

% Big Cube
\coordinate[] (A) at (0,0,0);
\coordinate[] (B) at (\L,0,0);
\coordinate[] (C) at (\L,0,\L);
\coordinate[] (D) at (0,0,\L);
\coordinate[] (A-s) at (0,\L,0);
\coordinate[] (B-s) at (\L,\L,0);
\coordinate[] (C-s) at (\L,\L,\L);
\coordinate[] (D-s) at (0,\L,\L);
\draw[] (A)  --  (B)  -- (C)  -- (D) --cycle;
\draw[] (A-s)  --  (B-s)  -- (C-s)  -- (D-s) --cycle;
\foreach \Punkt in {A,B,C,D} \draw[gray] (\Punkt) -- (\Punkt-s); 

% Front Filling
\pgfmathsetmacro{\A}{int(\L-1)}
\foreach \x in {0,...,\A}   \foreach \y in {0,...,\A}{%
\pgfmathparse{mod(\x+\y,2)==0 ? "lightgray" : "red!50"}
\colorlet{Color}{\pgfmathresult}
\pgfmathsetmacro\M{mod(\x,2)==0 && mod(\y,2)==0  ? 1 : 0}
\ifnum\M=1
\draw[shift={(\x,\y)}, very thick, fill=Color] (0,0) rectangle (\a,\b);
\else\fi
}%% %

% Side Filling
\foreach \y in {0,...,\A} \foreach \z in {0,...,\A}  {%
\pgfmathparse{mod(\y+\z,2)==0 ? "lightgray" : "red!50"}
\colorlet{Color}{\pgfmathresult}
\pgfmathsetmacro\M{mod(\y,2)==0  ? 1 : 0}
\ifnum\M=1
\draw[shift={(0,\y,\z)}, very thick, fill=Color] (10,0,0) -- (10,0,\c) -- (10,\b,\c)  -- (10,\b,0) --cycle;
\else\fi
}

% Roof Filling
% ......


% CoSy
\draw[->] (-0.5,0,0) -- (3,0,0) node[right]{$x$};
\draw[->] (0,-0.5,0) -- (0,3,0) node[above]{$y$};
\draw[->] (0,0,-1) -- (0,0,3) node[pos=1.05]{$z$};
\end{tikzpicture}

\end{document}

答案1

在此处输入图片描述

\documentclass[margin=5pt, tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}

\pgfmathsetmacro{\L}{10}
\pgfmathsetmacro{\a}{2}
\pgfmathsetmacro{\b}{2}
\pgfmathsetmacro{\c}{1}

\def\ColorA{yellow!33} % lightgray
\def\ColorB{red!50}  % red!50

\begin{tikzpicture}[scale=1.0,
z={({0.5cm*cos(45)},{0.5cm*sin(45)})},
>=latex, 
font=\footnotesize,
]
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

% Big Cube ================
\coordinate[] (A) at (0,0,0);
\coordinate[] (B) at (\L,0,0);
\coordinate[] (C) at (\L,\L,0);
\coordinate[] (D) at (0,\L,0);
\coordinate[] (A-s) at (0,0,\L);
\coordinate[] (B-s) at (\L,0,\L);
\coordinate[] (C-s) at (\L,\L,\L);
\coordinate[] (D-s) at (0,\L,\L);
\begin{pgfonlayer}{foreground}
\draw[gray] (A)  --  (B)  -- (C)  -- (D) --cycle;
\foreach \Punkt in {B,C,D} \draw[gray] (\Punkt) -- (\Punkt-s); 
\end{pgfonlayer}
\draw[gray] (A)  --  (A-s); 
\draw[gray] (A-s)  --  (B-s)  -- (C-s)  -- (D-s) --cycle;
% =======================

%% Cuboids ==============
\pgfmathsetmacro{\A}{floor(\L/\a-1)}
\pgfmathsetmacro{\B}{floor(\L/\b-1)}
\pgfmathsetmacro{\C}{floor(\L/\c-1)}
\pgfmathsetmacro{\Xmax}{floor(\L/\a)*\a}
\pgfmathsetmacro{\Ymax}{floor(\L/\b)*\b}
% Front Filling
\foreach \x in {0,...,\A}   \foreach \y in {0,...,\B}{%
\pgfmathparse{mod(\x+\y,2)==0 ? "\ColorA" : "\ColorB"}
\colorlet{Color}{\pgfmathresult}
\draw[shift={(\x*\a,\y*\b)}, very thick, fill=Color] (0,0) rectangle (\a,\b);
}%

% Side Filling
\foreach \y in {0,...,\B} \foreach \z in {0,...,\C}  {%
\pgfmathparse{mod(\y+\z,2)==0 ? "\ColorA" : "\ColorB"}
\colorlet{Color}{\pgfmathresult}
\pgfmathsetmacro\M{mod(\y,2)==0  ? 1 : 0}
\draw[shift={(0,\y*\b,\z*\c)}, very thick, fill=Color] (\Xmax,0,0) -- (\Xmax,0,\c) -- (\Xmax,\b,\c)  -- (\Xmax,\b,0) --cycle;
}

% Roof Filling
\foreach \x in {0,...,\A} \foreach \z in {0,...,\C}  {%
\pgfmathparse{mod(\x+\z,2)==0 ? "\ColorA" : "\ColorB"}
\colorlet{Color}{\pgfmathresult}
\draw[shift={(\x*\a,0,\z*\c)}, very thick, fill=Color] (0,\Ymax,0) -- (\a,\Ymax,0) -- (\a,\Ymax,\c)  -- (0,\Ymax,\c) --cycle;
}
%% ================

% Annotation
\draw[] (\Xmax-\a,0) --+ (0,0,-0.2*\L) coordinate[pos=0.5] (X1);
\draw[] (\Xmax,0) --+ (0,0,-0.2*\L) coordinate[pos=0.5] (X2);
\draw[<->] (X1) -- (X2) node[midway, above]{$a$}; 
\draw[] (\Xmax,0) --+ (0.2*\L,0) coordinate[pos=0.5] (Y1);
\draw[] (\Xmax,\b) --+ (0.2*\L,0) coordinate[pos=0.5] (Y2);
\draw[<->] (Y1) -- (Y2) node[near start, right]{$b$}; 
\draw[] (\Xmax,0,0) --+ (0.2*\L,0) coordinate[pos=0.7] (Z1);
\draw[] (\Xmax,0,\c) --+ (0.2*\L,0) coordinate[pos=0.7] (Z2);
\draw[<->] (Z1) -- (Z2) node[midway, right]{$c$}; 
\end{tikzpicture}

\end{document}

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