How to draw grid by given four points in Tikz?

Question

It is easy to draw a grid on a square if the square is not rotated. But for rotated squares it is difficult for me to grid it. I want to grid a square by given four points. for example the following four points:

A(-3,0), B (-2,5), C(-5,3), D(0,2).

Any suggest would be greatly appreciated.

Answer 1

One possibility using the calc library and a loop.

\documentclass[border=10pt,tikz]{standalone}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (3,1);
\coordinate (C) at (2,4);
\coordinate (D) at (-1,3);


\foreach [evaluate=\i as \x using \i/10] \i in {0,...,10} 
{
  \draw ($(A)!\x!(B)$) -- ($(D)!\x!(C)$);
  \draw ($(A)!\x!(D)$) -- ($(B)!\x!(C)$);
}
\end{tikzpicture}
\end{document}

Answer 2

Brute force, without calc

\documentclass{article}

\usepackage{tikz}


\begin{document}



\begin{tikzpicture}
\foreach \t in {0,1,...,10}
  {
   \draw({-3+\t*(-5-(-3))/10},{0+\t*(3-0)/10})--({0+\t*(-5-(-3))/10},{2+\t*(3-0)/10});
   \draw({-3+\t*(0-(-3))/10},{0+\t*(2-0)/10})--({-5+\t*(3-0)/10},{3+\t*(2-0)/10});
  }
\end{tikzpicture}
\end{document}