Paths with PGF/TikZ, in and out of foreach

Question

\documentclass[11pt,a4paper]{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
% CTC : center to center
% Distance is 2*sin(pi/3)
\def\ctc{1.7320508075688772cm}

% Draw an hexagon anywhere.
\def\hexagon#1{
    %\draw #1 +(0:1cm) \foreach \a in {60,120,...,300} { -- +(\a:1cm) } -- cycle;
    \fill[red] #1 circle (0.2cm);
}
% Draw a small hextile anywhere.
\def\hextile#1{
    \foreach \l in {1,2} {
        \foreach \a in {30,90,...,330} {
            \hexagon{#1 ++(\a:\l*\ctc)};
        }
        \foreach \a in {0,60,...,300} {
            \hexagon{#1 ++(\a:\l*3cm-3cm)};
        }
    }
}
\def\hextiles{
    \foreach \a in {0,120,240} {
        \hextile{(\a:6cm)};
    }
}

%\hextiles;
\hextile{(0:6cm)};
\hextile{(120:6cm)};
\hextile{(240:6cm)};

\end{tikzpicture}
\end{document}

I am wondering why, oh why, calling \hextiles and \hextile three times don't give out the same result...

It seems linked with the way paths are handled, but I can't see how...

Answer 1

The problem is that you reuse the macro \a in your \foreach loops. When you do

\def\hextiles{
    \foreach \a in {0,120,240} {
        \hextile{(\a:6cm)};
    }
}

Then \hextile is called with the argument literally (\a:6cm). This gets substituted in to the command wherever there is a #1. Thus the result of \hextile{(\a:6cm)} is to insert the following into the stream:

\foreach \l in {1,2} {
        \foreach \a in {30,90,...,330} {
            \hexagon{(\a:6cm) ++(\a:\l*\ctc)}
        }
        \foreach \a in {0,60,...,300} {
            \hexagon{(\a:6cm) ++(\a:\l*3cm-3cm)}
        }
    }

So the \a which eventually gets used is not the \a of the outer loop, but the \a of the inner loop. One solution is simply to change names:

\documentclass[11pt,a4paper]{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
% CTC : center to center
% Distance is 2*sin(pi/3)
\def\ctc{1.7320508075688772cm}

% Draw an hexagon anywhere.
\def\hexagon#1{
  \draw #1 +(0:1cm) \foreach \a in {60,120,...,300} { -- +(\a:1cm) } -- cycle;
    \fill[red] #1 circle (0.2cm);
}
% Draw a small hextile anywhere.
\def\hextile#1{
    \foreach \l in {1,2} {
        \foreach \a in {30,90,...,330} {
            \hexagon{#1 ++(\a:\l*\ctc)}
        }
        \foreach \a in {0,60,...,300} {
            \hexagon{#1 ++(\a:\l*3cm-3cm)}
        }
    }
}
\def\hextiles{
    \foreach \b in {0,120,240} {
        \hextile{(\b:6cm)}
    }
}

\hextiles
%\hextile{(0:6cm)};
%\hextile{(120:6cm)};
%\hextile{(240:6cm)};

\end{tikzpicture}
\end{document}

A more robust solution would be to ensure that \a is not passed literally but its value is used. The best method of doing this depends a bit on what situations you're going to be using these macros in.