Qfyilyi

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}

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}

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}