[Tex/LaTex] Computing coordinate numbers in TikZ

tikz-pgf

I am trying to draw three congruent, equilateral triangles unicursally in TikZ (see figure below). Per se, this is rather simple, but I want to write the TikZ code so that I can easily change the shape of the figure by adjusting a few geometrical parameters. More specifically, I want the coordinates in the TikZ figure to vary, depending on the value of the parameters.

three unicursal, congruent, equilateral triangles

The two parameters I want to change are the distances from a to q (later referred to as L) and from q to b (later referred to as Δ) in the figure above. By choosing a to be the origin, the expressions for the coordinates will be as follows

a: ( 0 , 0 )
b: ( cos(60°)*(L + Δ) , sin(60°)*(L + Δ) )
c: ( bx + cos(60°)*L , by - sin(60°)*L )
d: ( L - cx , cy )
e: ( L - bx, by )
f: ( L , 0 )

where bx, by, cx and cy denote the x and y coordinates of points b and c respectively. (The coordinates of q are not necessary in order to draw the figure.)

I tried the following approach, but this gives the output shown below, where only the coordinates of a and f are correct. If this had worked, I would be able to simply change the definitions of \l and \delta and recompile to see how the geometry changes with L and Δ.

\begin{tikzpicture}

\def\cossixty{0.5}
\def\sinsixty{0.866025}

\def\l{6}
\def\delta{2}
\def\ldelta{\l+\delta}
\def\bx{\cossixty*\ldelta}
\def\by{\sinsixty*\ldelta}
\def\cx{\bx+\cossixty*\l}
\def\cy{\by-\sinsixty*\l}
\def\dx{\l-\cx}
\def\ex{\l-\bx}

\coordinate (a) at (0,0);
\coordinate (b) at (\bx,\by);
\coordinate (c) at (\cx,\cy);
\coordinate (d) at (\dx,\cy);
\coordinate (e) at (\ex,\by);
\coordinate (f) at (\l,0);

\begin{scope}[thick]
    \draw (a) -- (b) -- (c) -- (d) -- (e) -- (f) -- (a);
\end{scope}

\end{tikzpicture}

erroneous output

So my question is this: how can I make TikZ compute the coordinate expressions listed above into floating point numbers and get the correct output?

(This is only a small part of a larger image which I am to make in TikZ, so there is, of course, a good reason why I choose to draw the figure unicursally, and with adjustable parameters.)

Best Answer

You code works just fine once you let pgf do the math for you:

enter image description here

Notes:

  • \delta is a greek letter so better to use a different name.
  • I also added a node to label the two parameters.

Code:

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}

\def\l{4}
\def\MyDelta{2}
\pgfmathsetmacro\ldelta{\l+\MyDelta}
\pgfmathsetmacro\bx{cos(60)*\ldelta}
\pgfmathsetmacro\by{sin(60)*\ldelta}
\pgfmathsetmacro\cx{\bx+cos(60)*\l}
\pgfmathsetmacro\cy{\by-sin(60)*\l}
\pgfmathsetmacro\dx{\l-\cx}
\pgfmathsetmacro\ex{\l-\bx}

\coordinate (a) at (0,0);
\coordinate (b) at (\bx,\by);
\coordinate (c) at (\cx,\cy);
\coordinate (d) at (\dx,\cy);
\coordinate (e) at (\ex,\by);
\coordinate (f) at (\l,0);

\begin{scope}[thick]
    \draw (a) -- (b) -- (c) -- (d) -- (e) -- (f) -- (a)
        node [below, midway] {$l = \l, \Delta = \MyDelta$};
\end{scope}
\end{tikzpicture}
\end{document}
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