Prevent tikz to calculate

Question

I just played with an answer to a question I asked here some time ago: Divide a rectangle into n times k equal cells. I wanted to be able to generate the list of points in a separate macro, however if I just put the list into a macro for example

\newcommand{\testlist}{1/2}

And do

\rectDiv{7}{5}{(1,1)}{(4,3)}{\testlist}

I get the following:

So it seems that 1/2 is interpreted as the coordinate (0.5,0.5). If I have something like 2/0 I get an compiler error because of division by zero.

Why is \newcommand{\testlist}{1/2} \rectDiv{7}{5}{(1,1)}{(4,3)}{\testlist}not equivalent to \rectDiv{7}{5}{(1,1)}{(4,3)}{1/2} ?

How do I have to modify the example such that I can put the list of points into a macro which will be the last argument of \rectDiv?

I also tried \def and \edef instead of \newcommand without success.

Answer 1

If you use \foreach \i/\j in {1/2} { .. } then the \foreach macro can see the separator / and then splits 1 and 2. However, if both are hidden inside a macro like \testlist (defined to be 1/2) it does not find the separator and assumes that only a single value is used. Therefore \testlist is takes as \i and \j as empty.
You need to expand \testlist first, or use \foreach \i/\j in \testlist, because \foreach is defined to accept a macro instead of the { } argument.

Expanding would work as follows:

\edef\@tempa{\noexpand\foreach \noexpand\i/\noexpand\j in {\testlist, ..}}
\@tempa { <loop content> }

which works with multiple list macros and assumes \makeatletter and \makeatother around the code.

---

Full example:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
  \def\rectDiv#1#2#3#4#5{%#columns, #rows, rectangle start, rectangle end, list of elements to fill
    \begin{tikzpicture}
      \draw #3 rectangle #4;
      \path #3;
      \pgfgetlastxy{\firstx}{\firsty}
      \path #4;
      \pgfgetlastxy{\secondx}{\secondy}
      \pgfmathsetlengthmacro{\xdiff}{\secondx-\firstx}
      \pgfmathsetlengthmacro{\ydiff}{\secondy-\firsty}
      \pgfmathsetlengthmacro{\myxstep}{\xdiff/#1}
      \pgfmathsetlengthmacro{\myystep}{\ydiff/#2}
      \foreach \x in {1,...,#1}{
        \draw ($#3 +\x*(\myxstep,0)$) -- ($#3 +(0,\ydiff) +\x*(\myxstep,0)$);
      }
      \foreach \y in {1,...,#2}{
        \draw ($#3 +\y*(0,\myystep)$) -- ($#3 +(\xdiff,0) +\y*(0,\myystep)$);
      }
      \edef\temp{\noexpand\foreach \noexpand\i/\noexpand\j in {#5}}
      \temp{
        \path[fill=blue!20,draw] ($#3 + (\i*\myxstep,\j*\myystep)$) rectangle ($#3 + (\i*\myxstep,\j*\myystep) + (\myxstep,\myystep)$);
      }
    \end{tikzpicture}
  }
\begin{document}
  \rectDiv{7}{5}{(1,1)}{(4,3)}{0/0,1/1,2/0,5/3}

  \def\list{1/0}
  \rectDiv{7}{5}{(1,1)}{(4,3)}{\list}

  \rectDiv{7}{5}{(1,1)}{(4,3)}{\list,2/0,5/3}

\end{document}

Or alternatively:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
  \def\rectDiv#1#2#3#4#5{%#columns, #rows, rectangle start, rectangle end, list of elements to fill
    \begin{tikzpicture}
      \draw #3 rectangle #4;
      \path #3;
      \pgfgetlastxy{\firstx}{\firsty}
      \path #4;
      \pgfgetlastxy{\secondx}{\secondy}
      \pgfmathsetlengthmacro{\xdiff}{\secondx-\firstx}
      \pgfmathsetlengthmacro{\ydiff}{\secondy-\firsty}
      \pgfmathsetlengthmacro{\myxstep}{\xdiff/#1}
      \pgfmathsetlengthmacro{\myystep}{\ydiff/#2}
      \foreach \x in {1,...,#1}{
        \draw ($#3 +\x*(\myxstep,0)$) -- ($#3 +(0,\ydiff) +\x*(\myxstep,0)$);
      }
      \foreach \y in {1,...,#2}{
        \draw ($#3 +\y*(0,\myystep)$) -- ($#3 +(\xdiff,0) +\y*(0,\myystep)$);
      }
      \edef\list{#5}
      \foreach \i/\j in \list {
        \path[fill=blue!20,draw] ($#3 + (\i*\myxstep,\j*\myystep)$) rectangle ($#3 + (\i*\myxstep,\j*\myystep) + (\myxstep,\myystep)$);
      }
    \end{tikzpicture}
  }
\begin{document}
  \rectDiv{7}{5}{(1,1)}{(4,3)}{0/0,1/1,2/0,5/3}

  \def\alist{1/0}
  \rectDiv{7}{5}{(1,1)}{(4,3)}{\alist}

  \def\blist{5/3}
  \rectDiv{7}{5}{(1,1)}{(4,3)}{\alist,2/0,\blist}

\end{document}