How to draw a much more dense grid or lattice?

Question

My inquiries:

1) How to draw a much more dense grid in 2-dim?

2) How to draw a much more dense grid in 3-dim?

Let us say it is still 4 x 4 in 2d or 4 x 4 x 4 in 3D in size, but I want to have each side has 16 or 17 lattice point on unit 4 on the grid? (so 16 x 16 in 2D or 16 x 16 x 16 in 3D.)

Here is what I have:

\begin{figure}[h!]
\centering
\begin{tikzpicture}
\draw [very thin, lightgray] (0,0) grid (4,4);
\end{tikzpicture}
\label{fig:lattice}
\caption{}
\end{figure}

for 3d, take a look on : https://tex.stackexchange.com/questions/435503/drawing-3d-grids-cubes — flav, Dec 11 '18 at 05:23

score 6 · Accepted Answer · 2018-12-11T16:36:41.027

6

Here is a 3D grid.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\tdplotsetmaincoords{70}{110}
\begin{document}
\begin{tikzpicture}[tdplot_main_coords]
 \foreach \X in {0,1,...,16}
 {\foreach \Y in {0,1,...,16}
 {\draw (\X/4,\Y/4,0) -- (\X/4,\Y/4,16/4);
 \draw (\X/4,0,\Y/4) -- (\X/4,16/4,\Y/4);
 \draw (0,\X/4,\Y/4) -- (16/4,\X/4,\Y/4);}}
\end{tikzpicture} 
\end{document}

And here is an illustration that shows what the view does.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\foreach \Rot in {0,10,...,360}
{\tdplotsetmaincoords{70+15*sin(\Rot)}{\Rot}
\begin{tikzpicture}[tdplot_main_coords]
\path[use as bounding box,tdplot_screen_coords] (-6,-2) rectangle (6,7);
 \foreach \X in {0,1,...,16}
 {\foreach \Y in {0,1,...,16}
 {\draw (\X/4,\Y/4,0) -- (\X/4,\Y/4,16/4);
 \draw (\X/4,0,\Y/4) -- (\X/4,16/4,\Y/4);
 \draw (0,\X/4,\Y/4) -- (16/4,\X/4,\Y/4);}}
\end{tikzpicture} }
\end{document}

You can, of course, use very thin gray lines. And yes, you can scale the grid by saying scale=<factor>.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\tdplotsetmaincoords{70}{110}
\begin{document}
\begin{tikzpicture}[tdplot_main_coords]
\begin{scope}[ultra thin,lightgray]
 \foreach \X in {0,1,...,16}
 {\foreach \Y in {0,1,...,16}
 {\draw (\X/4,\Y/4,0) -- (\X/4,\Y/4,16/4);
 \draw (\X/4,0,\Y/4) -- (\X/4,16/4,\Y/4);
 \draw (0,\X/4,\Y/4) -- (16/4,\X/4,\Y/4);}}
\end{scope} 

\begin{scope}[line width=0.01pt,lightgray,xshift=5cm,scale=0.4]
 \foreach \X in {0,1,...,16}
 {\foreach \Y in {0,1,...,16}
 {\draw (\X/4,\Y/4,0) -- (\X/4,\Y/4,16/4);
 \draw (\X/4,0,\Y/4) -- (\X/4,16/4,\Y/4);
 \draw (0,\X/4,\Y/4) -- (16/4,\X/4,\Y/4);}}
\end{scope} 

\end{tikzpicture} 
\end{document}

edited Dec 11 '18 at 16:36

answered Dec 11 '18 at 09:08

Thanks, this is useful +1, but can I make the lines more transparent? – wonderich Dec 11 '18 at 16:25
@wonderich I think so, yes. Do you want to fade the distance lines away? Or just make all lines transparent, regardless of the distance to the front? Here is a proposal for the first option. – Dec 11 '18 at 16:27
I dont need faded away -- this is too advanced for me. Just as transparent, for example, as the original my post OP or other posts! (The lines can be tuned to that gray scale). Thank you! – wonderich Dec 11 '18 at 16:30
I also how can I make the whole figure size tunable? [scale=...]? – wonderich Dec 11 '18 at 16:31
Or [size=4cm] something like this? – wonderich Dec 11 '18 at 16:32
@wonderich I added some proposal. The issue with jfbu's proposal is that it leads to relatively different line widths, but one could also go this way. (What I want to say is that I did not add all the /4 randomly.) – Dec 11 '18 at 16:39
Thanks very nice! Can the gray scale be tuned, like using the opacity? \draw[fill=white!100!black] \draw[fill=gray,opacity=0.5] – wonderich Dec 11 '18 at 16:45
@wonderich You can add any opacity you like or any gray scale, e.g. gray!10 instead of lightgray. Or do you want to use different grays for different planes? – Dec 11 '18 at 16:48

score 3 · Answer 2 · answered Dec 11 '18 at 05:08

3

The step key is used to indicate this.

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
\draw [very thin, lightgray] (0,0) grid (4,4);

\begin{scope}[xshift=5cm]
\draw [very thin, lightgray,step=.1] (0,0) grid (4,4);
\end{scope}
\end{tikzpicture}
\end{document}

answered Dec 11 '18 at 05:08

AndréC

24,137

Thanks +1, very useful! – wonderich Dec 11 '18 at 16:21

score 2 · Answer 3 · answered Dec 11 '18 at 19:46

A PSTricks solution only for comparison purposes.

\documentclass[pstricks,border=12pt,12pt]{standalone}
\newpsstyle{gridstyle}
{
    gridlabels=8pt,
    gridfont=Arial,
    %   
    gridcolor=red,
    subgridcolor=gray,
    %
    subgriddiv=5,
    %
    gridwidth=.8pt,
    subgridwidth=.4pt,
    %
    griddots=10,
    subgriddots=5,
}
\begin{document}
\begin{pspicture}[showgrid](5,5)

\end{pspicture}
\end{document}

How to draw a much more dense grid or lattice?

3 Answers3

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