绘制 3D 网格（立方体）

Question

阅读了一些例子，虽然不是最优的，也不是有条理的，但我还是能够画出下面这张 3D 网格

\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}[scale=2,every node/.style={minimum size=1cm},on grid]

    \begin{scope}[
            yshift=0,every node/.append style={
            yslant=0.5,xslant=-1},yslant=0.5,xslant=-1
        ]
        \fill[white,fill opacity=0.9] (0,0) rectangle (3,3);
        \draw[step=1mm, black!20,thin] (0,0) grid (3,3);
        \draw[step=10mm, black] (0,0) grid (3,3);
    \end{scope}

    \foreach \y in {1,2,...,19} {
        \begin{scope}[
                yshift=\y mm,every node/.append style={
                yslant=0.5,xslant=-1},yslant=0.5,xslant=-1
            ]
            \fill[white,fill opacity=0.9] (0,0) rectangle (3,3);
            \draw[step=1mm, black!20,thin] (0,0) grid (3,3); 
        \end{scope}
    }

    \begin{scope}[
            yshift=20mm,every node/.append style={
            yslant=0.5,xslant=-1},yslant=0.5,xslant=-1
        ]
        \fill[white,fill opacity=0.9] (0,0) rectangle (3,3);
        \draw[step=1mm, black!20,thin] (0,0) grid (3,3);
        \draw[step=10mm, black] (0,0) grid (3,3);
    \end{scope}

    \begin{scope}[
            yshift=10mm,every node/.append style={
            yslant=0.5,xslant=-1},yslant=0.5,xslant=-1
        ]
        \draw[step=10mm, black] (0,0) rectangle (3,3);
    \end{scope}


    \draw [black] (0    ,0)        to (0,2);

    \draw [black] (1    ,0+.5)   to (1,2.5);
    \draw [black] (2    ,0+1)        to (2,3.0);
    \draw [black] (3    ,0+1.5)  to (3,3.5);

    \draw [black] (-1   ,0+.5)   to  (-1,2.5);
    \draw [black] (-2   ,0+1)        to (-2,3.0);
    \draw [black] (-3   ,+1.5)   to (-3,3.5);

    \foreach \s in {0.05, 0.1, ..., 1.5} {
        \draw [black!20, thin] (\s * 2, \s ) to (\s * 2,2 + \s);
        \draw [black!20, thin] (\s * -2, \s ) to (\s * -2,2 + \s);
    }

\end{tikzpicture}

\end{document} 

显示为：

但是我会在论文中画很多立方体，以至于这种方法变得太复杂了，我希望能够轻松做到这一点：

1. 改变较大立方体的数量（在本例中为 3x3x2），我可以使用 2x2x2 或者有时使用 3x3x3 或 5x5x5。

2. 网格间距大小，在本例中为 1mm 和 10mm，可以是 2mm 和 4mm，或者 1mm 和 5mm

关于如何改进此代码，您有什么想法吗？此外，也非常欢迎提出有关如何更好地显示 3D 网格的想法。

Answer 1

以下是基于的提议Jake 的回答在这里。

\documentclass[tikz,border=3.14mm]{standalone}

\usepackage{xparse}
\usepackage{tikz}

\usetikzlibrary{3d}
\makeatletter % from https://tex.stackexchange.com/a/48776/121799
\tikzoption{canvas is xy plane at z}[]{%
  \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}%
  \def\tikz@plane@x{\pgfpointxyz{1}{0}{#1}}%
  \def\tikz@plane@y{\pgfpointxyz{0}{1}{#1}}%
  \tikz@canvas@is@plane
}
\makeatother


\NewDocumentCommand{\DrawCubes}{O{} m m m m m m}{%
    \def\XGridMin{#2}
    \def\XGridMax{#3}
    \def\YGridMin{#4}
    \def\YGridMax{#5}
    \def\ZGridMin{#6}
    \def\ZGridMax{#7}
    %
    \begin{scope}[canvas is xy plane at z=\ZGridMax]
      \draw [#1] (\XGridMin,\YGridMin) grid (\XGridMax,\YGridMax);
    \end{scope}
    \begin{scope}[canvas is yz plane at x=\XGridMax]
      \draw [#1] (\YGridMin,\ZGridMin) grid (\YGridMax,\ZGridMax);
    \end{scope}
    \begin{scope}[canvas is xz plane at y=\YGridMax]
      \draw [#1] (\XGridMin,\ZGridMin) grid (\XGridMax,\ZGridMax);
    \end{scope}
}%



\begin{document}
\begin{tikzpicture}[scale=2,
    x={(1.0cm,0.0cm)}, y={(0.0cm,1.0cm), z={(-0.5cm,-0.1cm)}}% All grids are ok
    ]
    \DrawCubes[step=1mm]{0}{3}{0}{2}{0}{2}
    \DrawCubes[step=1cm,thick]{0}{3}{0}{2}{0}{2}
\end{tikzpicture}
%
\end{document}

为了获得与您的图片相似的东西，您只需要调整坐标（以及一个平面的一个位置）。

\documentclass[tikz,border=3.14mm]{standalone}

\usepackage{xparse}
\usepackage{tikz}

\usetikzlibrary{3d}
\makeatletter % from https://tex.stackexchange.com/a/48776/121799
\tikzoption{canvas is xy plane at z}[]{%
  \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}%
  \def\tikz@plane@x{\pgfpointxyz{1}{0}{#1}}%
  \def\tikz@plane@y{\pgfpointxyz{0}{1}{#1}}%
  \tikz@canvas@is@plane
}
\makeatother


\NewDocumentCommand{\DrawCubes}{O{} m m m m m m}{%
    \def\XGridMin{#2}
    \def\XGridMax{#3}
    \def\YGridMin{#4}
    \def\YGridMax{#5}
    \def\ZGridMin{#6}
    \def\ZGridMax{#7}
    %
    \begin{scope}[canvas is xy plane at z=\ZGridMax]
      \draw [#1] (\XGridMin,\YGridMin) grid (\XGridMax,\YGridMax);
    \end{scope}
    \begin{scope}[canvas is yz plane at x=\XGridMax]
      \draw [#1] (\YGridMin,\ZGridMin) grid (\YGridMax,\ZGridMax);
    \end{scope}
    \begin{scope}[canvas is xz plane at y=0]
      \draw [#1] (\XGridMin,\ZGridMin) grid (\XGridMax,\ZGridMax);
    \end{scope}
}%



\begin{document}
\begin{tikzpicture}[scale=3,
   y={(0.5cm,0.25cm)},x={(0.5cm,-0.25cm)},z={(0cm,{veclen(0.5,0.25)*1cm})}
    ]
    \DrawCubes[step=1mm,thin]{0}{3}{0}{3}{0}{2}
    \DrawCubes[step=1cm]{0}{3}{0}{3}{0}{2}
\end{tikzpicture}
%
\end{document}