带网格的倾斜正方形

Question

如何在倾斜的正方形上画网格ABCD？

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=1,line join=round,font=\small]
\draw[lightgray] (0,0) grid (7,7);
\coordinate[label=below:$A$] (A) at (4,0);
\coordinate[label=right:$B$] (B) at (7,4);
\coordinate[label=above:$C$] (C) at (3,7);
\coordinate[label=left:$D$] (D) at (0,3);
\draw[thick] (A)--(B)--(C)--(D)--cycle;
\end{tikzpicture}
\end{document}

我的意思就是像这样。

Answer 1

正方形内部的旋转网格可以通过部分修饰符给出的坐标绘制：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[scale=1,line join=round,font=\small]
\coordinate[label=below:$A$] (A) at (4,0);
\coordinate[label=right:$B$] (B) at (7,4);
\coordinate[label=above:$C$] (C) at (3,7);
\coordinate[label=left:$D$] (D) at (0,3);

\draw[lightgray]
  (0, 0) grid (7, 7)
  \foreach \i in {1, ..., 4} {
    ($(A)!\i/5!(B)$) -- ($(D)!\i/5!(C)$)
    ($(B)!\i/5!(C)$) -- ($(A)!\i/5!(D)$)
  }
;

\draw[thick] (A)--(B)--(C)--(D)--cycle;
\end{tikzpicture}
\end{document}

Answer 2

A元帖子替代方案（仅用于比较）。使用 进行编译lualatex。

\RequirePackage{luatex85}
\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);

   path box[];
   box0 = unitsquare shifted -(1/2,1/2);
   box1 = box0 scaled 7cm;
   box2 = box0 scaled 5cm rotated angle (3,4);

   vardef draw_grid(expr Q,N) = 
       for t=1 upto N-1:
           draw point t/N   of Q -- point 3-t/N of Q;
           draw point 1+t/N of Q -- point 4-t/N of Q;
       endfor
   enddef;

   drawoptions(withcolor 2/3 white);
   draw_grid(box1,7);
   draw_grid(box2,5);

   drawoptions();
   draw box1;
   draw box2;

   label.bot("$A$", point 0 of box2);
   label.rt ("$B$", point 1 of box2);
   label.top("$C$", point 2 of box2);
   label.lft("$D$", point 3 of box2);

endfig;
\end{mplibcode}
\end{document}