Stretching an image

Question

I am trying to create a a grid of deformed hexagons in the y direction. The following solution given by @Ignasi seems okay for the undeformed case

Drawing hexagons

and after trying to modify the code, I am not able to get what I want, so I am thinking of the possibility of deforming the resulting tikz image.

Is there any command that I can use to achieve what I want?

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{patterns}
\def\hexagonsize{0.5cm}
\pgfdeclarepatternformonly
{hexagons}% name
{\pgfpointorigin}% lower left
{\pgfpoint{3\hexagonsize}{0.8660252\hexagonsize}}%  upper right
{\pgfpoint{3\hexagonsize}{0.8660252\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 (5,5);
\end{tikzpicture}
\end{document}

And what I want is to stretch the image in the vertical direction. For example, in terms of images, if this is a 100x100 image, I would like to convert it to a 100x200 image.

In regards to the code, the idea is to extend the length of the sides of the hexagon in the y direction, but I am not able to do it. I have tried to multiply the numbers by 2 or something like that, but I was not successful

Welcome to TeX.SX! So, what did you try exactly? Could you provide some of your code? — Jasper Habicht, Apr 09 '22 at 09:34
I guess that you like to scale image (make it bigger or smaller). Is this a case? If yes, add to tikzpicture option scale=<amount>. However, for better help you please provide a small but complete document with your image, that we see what you try so far. — Zarko, Apr 09 '22 at 09:43
While [yscale=2] doubles the height of the rectangle, the shape of the hexagons doesn't change. You will need to modify the pattern itself. — John Kormylo, Apr 09 '22 at 14:53

John Kormylo · Accepted Answer · 2022-04-09T15:31:46.663

Note that \pgftransformyscale{\hexscale} did not affect the other arguments.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns}
\def\hexagonsize{0.5cm}
\def\hexscale{2}
\pgfdeclarepatternformonly
{hexagons}% name
{\pgfpointorigin}% lower left
{\pgfpoint{3\hexagonsize}{0.8660252\hexagonsize\hexscale}}%  upper right
{\pgfpoint{3\hexagonsize}{0.8660252\hexagonsize\hexscale}}%  tile size
{% shape description
\pgfsetlinewidth{0.4pt}
\pgftransformyscale{\hexscale}
\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}[yscale=2]
\fill[pattern=hexagons] (0,0) rectangle (5,5);
\end{tikzpicture}
\end{document}

Thank you! Also to @kabenyuk – Daniel8 Apr 09 '22 at 15:52 — Daniel8, Apr 09 '22 at 15:52

kabenyuk · Answer 2 · 2022-04-10T07:54:31.200

Here another way of compressing or stretching the hexagonal lattice:

\documentclass{standalone}        
\begin{tikzpicture}
   \def\t{1/2};
   \def\s{1};
  \foreach \i in {0,...,8}
  \foreach \j in {0,...,3} {
  \coordinate (P) at (3*\i*\t,2*sin{60}*\j*\s);
  \coordinate (Q) at ([shift={(3*\t/2,sin{60}*\s)}]P);
  \draw[blue,thick]
        (P) -- ([shift={(\t,0)}]P)
        (P) -- ([shift={(-\t/2,-sin{60}*\s)}]P)
        (P) -- ([shift={(-\t/2,+sin{60}*\s)}]P);
  \draw[blue,thick]
        (Q) -- ([shift={(\t,0)}]Q)
        (Q) -- ([shift={(-\t/2,-sin{60}*\s)}]Q)
        (Q) -- ([shift={(-\t/2,+sin{60}*\s)}]Q);
}
\end{tikzpicture}
\end{document}

or quite simply

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[xscale=1/2, yscale=1]
  \foreach \i in {0,...,8}
  \foreach \j in {0,...,3} {
  \coordinate (P) at (3*\i,2*sin{60}*\j);
  \coordinate (Q) at ([shift={(3/2,sin{60})}]P);
  \draw[blue,thick]
        (P) -- ([shift={(1,0)}]P)
        (P) -- ([shift={(-1/2,-sin{60})}]P)
        (P) -- ([shift={(-1/2,+sin{60})}]P);
  \draw[blue,thick]
        (Q) -- ([shift={(1,0)}]Q)
        (Q) -- ([shift={(-1/2,-sin{60})}]Q)
        (Q) -- ([shift={(-1/2,+sin{60})}]Q);
}
\end{tikzpicture}
\end{document}

Some may not like the "tendrils". They can be removed as follows:

\documentclass{standalone}    
\usepackage{tikz}
\begin{document}    
\begin{tikzpicture}
  \def\t{1/3};
  \def\s{1};
  \def\nrow{3}
  \def\ncol{8}
  \foreach \i in {0,...,\ncol}
  \foreach \j in {0,...,\nrow} {
  \coordinate (P) at (3*\i*\t,2*sin{60}*\j*\s);
  \coordinate (Q) at ([shift={(3*\t/2,sin{60}*\s)}]P);
  \ifnum\j>0 
    \draw[blue,thick] (P) -- ([shift={(-\t/2,-sin{60}*\s)}]P);
  \fi  
  \draw[blue,thick]        
        (P) -- ([shift={(\t,0)}]P)        
        (P) -- ([shift={(-\t/2,+sin{60}*\s)}]P);        
  \ifnum\j<\nrow 
    \draw[blue,thick](Q) -- ([shift={(-\t/2,+sin{60}*\s)}]Q);
  \fi    
  \ifnum\i<\ncol
    \draw[blue,thick](Q) -- ([shift={(\t,0)}]Q);
  \fi 
  \draw[blue,thick](Q) -- ([shift={(-\t/2,-sin{60}*\s)}]Q);                
}
\end{tikzpicture}    
\end{document}

Stretching an image

2 Answers2