# Drawing hexagons

I have a case where I need to draw a hexagonal grid in LaTeX. I am considering just reading the grid from an eps file.

Is there an alternative way to do it completely within LaTeX?

-
You can use TikZ and adopt the code from this triangular grid. –  Caramdir Nov 26 '10 at 23:14
as usual tikz or pstricks or metapost among others –  pluton Nov 26 '10 at 23:17
By the way, I was quite amused by your no-so-veiled "threat" to LaTeX: "I am considering just reading the grid from an eps file.".... :-) –  Yossi Farjoun Nov 28 '10 at 9:18
Thanks for mentioning TikZ. I want to typeset some astrology charts and this might be just the thing. –  Larry Coleman Nov 28 '10 at 23:14

Here's a quick option:

\begin{tikzpicture}
\foreach \i in {0,...,3}
\foreach \j in {0,...,3} {
\foreach \a in {0,120,-120} \draw (3*\i,2*sin{60}*\j) -- +(\a:1);
\foreach \a in {0,120,-120} \draw (3*\i+3*cos{60},2*sin{60}*\j+sin{60}) -- +(\a:1);}
\end{tikzpicture}


Which results in

-
I think your approximations are not good enough. The lines of the grid cross each other slightly. –  Caramdir Nov 26 '10 at 23:46
Fixed. I was lazy before, and it was late... –  Yossi Farjoun Nov 27 '10 at 10:40
That is an amazingly good solution! –  Yiannis Lazarides Nov 27 '10 at 12:48
I have to give you the checkmark. You did exactly how I dreamt it. –  John Smith Nov 29 '10 at 0:13
Took a bit of searching for the code to do this (but faster than doing it myself) but thanks. It's helped me too. –  Matthew Orlinski Apr 8 '13 at 23:09

With TikZ, you can define a pattern which allows to fill any shape with a hexagonal grid by adding the option pattern=hexagons:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{patterns}

\def\hexagonsize{0.5cm}
\pgfdeclarepatternformonly
{hexagons}% name
{\pgfpointorigin}% lower left
{\pgfpoint{3*\hexagonsize}{0.866025*2*\hexagonsize}}%  upper right
{\pgfpoint{3*\hexagonsize}{0.866025*2*\hexagonsize}}%  tile size
{% shape description
\pgfsetlinewidth{0.4pt}
\pgftransformshift{\pgfpoint{0mm}{0.866025*\hexagonsize}}
\pgfpathmoveto{\pgfpoint{0mm}{0mm}}
\pgfpathlineto{\pgfpoint{0.5*\hexagonsize}{0mm}}
\pgfpathlineto{\pgfpoint{\hexagonsize}{-0.866025*\hexagonsize}}
\pgfpathlineto{\pgfpoint{2*\hexagonsize}{-0.866025*\hexagonsize}}
\pgfpathlineto{\pgfpoint{2.5*\hexagonsize}{0mm}}
\pgfpathlineto{\pgfpoint{3*\hexagonsize+0.2mm}{0mm}}
\pgfpathmoveto{\pgfpoint{0.5*\hexagonsize}{0mm}}
\pgfpathlineto{\pgfpoint{\hexagonsize}{0.866025*\hexagonsize}}
\pgfpathlineto{\pgfpoint{2*\hexagonsize}{0.866025*\hexagonsize}}
\pgfpathlineto{\pgfpoint{2.5*\hexagonsize}{0mm}}
\pgfusepath{stroke}
}
\begin{document}

\begin{tikzpicture}
\fill[pattern=hexagons] (0,0) rectangle (10,5);
\end{tikzpicture}

\begin{tikzpicture}
\fill[pattern=hexagons] (0,0) circle (3cm);
\end{tikzpicture}

\end{document}


You can change the size of the hexagons by modifying the value of the macro \hexagonsize.

-
I like it! Nice solution. –  Yossi Farjoun Nov 29 '10 at 8:16
Ah finally found it. I was looking for this nice snippet for a while with bad keywords :-) Would you like to write an answer to the open question tex.stackexchange.com/questions/54358/… ? I think this would be the perfect example. –  percusse Jun 17 '12 at 21:32
@percusse: thanks for notifying me. I'll add an answer later on. –  Philippe Goutet Jun 18 '12 at 6:34

Another way could be to draw hexagonal nodes over an adjusted coordinate system. The idea came adapting Paul Gaborit's Pascal triangle for How can I draw Pascal's triangle with some its properties?.

shapes.geometric library helps to draw hexagon where the minimum size is the diameter of the circumcircle. Therefore, selecting adjusted values for x (x=1.5*{minimum size}) and y (y=\sqrt{.75}*{minimum size}/2) the hexagonal grid can be drawn placing an node centered in every pair (x,y).

\documentclass[border=2mm, tikz]{standalone}
\usetikzlibrary{shapes.geometric}
\begin{document}

%
% x=3*(minimum size)/2
% x=\sqrt{3/4}*(minimum size)/2
%
\begin{tikzpicture}[x=7.5mm,y=4.34mm]
% some styles
\tikzset{
box/.style={
regular polygon,
regular polygon sides=6,
minimum size=10mm,
inner sep=0mm,
outer sep=0mm,
rotate=0,
draw
}
}

\foreach \i in {0,...,5}
\foreach \j in {0,...,5} {
\node[box] at (2*\i,2*\j) {};
\node[box] at (2*\i+1,2*\j+1) {};
}

\end{tikzpicture}

\end{document}


-

And a Metapost approach...

prologues := 3;
outputtemplate := "%j%c.eps";

beginfig(1);

% r = side of hexagon, n = repetitions of the grid (- and +)
r = 5mm; n=10;

% make a shape to draw
path tri; tri = for t=0 step 120 until 359: origin -- (r,0) rotated t -- endfor cycle;

% save the pattern as a picture centered on the origin
picture grid; grid = image(
for i=-n upto n:
for j=-n upto n:
draw tri shifted (i*3/2r,j*r*sqrt(3)) if (i mod 2)=1: shifted (0,r/2*sqrt(3)) fi ;
endfor
endfor);

% clip the pattern as required (to get rid of the rough edges...)
clip grid to fullcircle scaled (2*n*r);

% draw as needed
draw grid;
draw grid rotated 30 shifted (2n*r,0) withcolor .67 red;

endfig;
end.

-