Vtyjkyuk

I would like to draw a path of grey along the tiks nodes of my lattices. I tried with drawing double line and filling them, but it didn't look right. Then I found this:

How do I draw a path of grey background through elements of a matrix?

It seem cleaner than what I did, but the problem of look stay the same. I'll post what I have now.

documentclassarticle
usepackage[T1]fontenc
usepackage[utf8]inputenc
usepackage[french]babel
usepackageamsthm
usepackageamsmath
usepackageamssymb
usepackageurl
usepackageenumitem
usepackagexcolor
usepackagecolor
usepackagehyperref
usepackagefancyhdr
usepackagetitlesec
usepackagetikz
usetikzlibraryshapes
usepackage[margin=1.3in]geometry
setlengthskipfootins1cm

begindocument

begincenter
begintikzpicture[node distance=2cm, strip/.style=draw=gray, rounded corners=1mm, line width=1.5cm, opacity=0.5, line cap=round ]

 tikzset
 every node/.style=
 draw=black, circle, circle,minimum size=1cm, fill=orange, fill opacity=0.8, text opacity=1
 

 % First, locate each of the nodes and name them
 node (void) at (0,0) $varnothing$;

 node [above of=void] (y) $y$;
 node [left of=y] (x) $x$;
 node [right of=y] (z) $z$;

 node [above of=x] (xy) $xy$;
 node [above of=y] (xz) $xz$;
 node [above of=z] (yz) $yz$;

 node [above of=xz] (xyz) $xyz$;

 %Testfield
 draw [double distance = 1.3cm, thin, opacity=0.5, line cap=round] (void) -- (x) -- (xy) -- (xyz);

 % First, locate each of the nodes and name them
 node (void) at (0,0) $varnothing$;

 node [above of=void] (y) $y$;
 node [left of=y] (x) $x$;
 node [right of=y] (z) $z$;

 node [above of=x] (xy) $xy$;
 node [above of=y] (xz) $xz$;
 node [above of=z] (yz) $yz$;

 node [above of=xz] (xyz) $xyz$;

 % Now draw the lines:
 draw [black, thick] (void) -- (x);
 draw [black, thick] (void) -- (y);
 draw [black, thick] (void) -- (z);

 draw [black, thick] (x) -- (xy);
 draw [black, thick] (y) -- (xy);

 draw [black, thick] (x) -- (xz);
 draw [black, thick] (z) -- (xz);

 draw [black, thick] (y) -- (yz);
 draw [black, thick] (z) -- (yz);

 draw [black, thick] (xy) -- (xyz);
 draw [black, thick] (xz) -- (xyz);
 draw [black, thick] (yz) -- (xyz);

endtikzpicture
endcenter

enddocument

I also used some shenanigans so that the grey is in the background, but I was planning on cleaning that up when I had what I wanted.

The correct answer is the one by J. Leon V., who does what Zarko did in his nice answer, namely used the centers. Here are some additional suggestions:

• Put the contour on the background.


• Blur the boundary a bit.


• Simplify the connections.

Here is the result.

documentclass[tikz,border=3.14mm]standalone
usetikzlibrarybackgrounds
usepackageamssymb
begindocument
begintikzpicture[node distance=2cm] 
tikzsetstrip/.style=draw=gray!40, rounded corners=1mm, line width=1.5cm,opacity=0.5, 
line cap=round,on background layer,
postaction=draw=gray!50,opacity=0.5,rounded corners=1mm, line width=1.46cm,line
cap=round,
postaction=draw=gray!60,opacity=0.5,rounded corners=1mm, line width=1.42cm,line
cap=round,
postaction=draw=gray!70,opacity=0.5,rounded corners=1mm, line width=1.38cm,line
cap=round,
postaction=draw=gray!80,opacity=0.5,rounded corners=1mm, line width=1.34cm,line
cap=round

 tikzset
 every node/.style=
 draw=black, circle, circle,minimum size=1cm, fill=orange, fill opacity=0.8, text opacity=1
 


 % First, locate each of the nodes and name them
 node (void) at (0,0) $varnothing$;

 node [above of=void] (y) $y$;
 node [left of=y] (x) $x$;
 node [right of=y] (z) $z$;

 node [above of=x] (xy) $xy$;
 node [above of=y] (xz) $xz$;
 node [above of=z] (yz) $yz$;

 node [above of=xz] (xyz) $xyz$;

 %Testfield

 % I guess in Zarko's nice answer ,transform canvas=xshift=-0.5mm
 % was for the bounding box. It would actually have been easier to use
 % overlay, which just interrupts the bounding box
 draw[strip] (void.center) 
 -- (x.center) -- (xy.center) --
 (xyz.center);

 % First, locate each of the nodes and name them
 node (void) at (0,0) $varnothing$;

 node [above of=void] (y) $y$;
 node [left of=y] (x) $x$;
 node [right of=y] (z) $z$;

 node [above of=x] (xy) $xy$;
 node [above of=y] (xz) $xz$;
 node [above of=z] (yz) $yz$;

 node [above of=xz] (xyz) $xyz$;

 % Now draw the lines:
 beginscope[black, thick]
 draw (void) edge (x) edge (y) edge (z);
 draw (x) -- (xy) -- (y);
 draw (x) -- (xz) -- (z);
 draw (y) -- (yz) -- (z);
 draw (xyz) edge (xy) edge (xz) edge (yz);
 endscope

endtikzpicture
enddocument

The error you make is that you draw lines between nodes instead of coordinates.

RESULT:

MWE:

documentclassstandalone
usepackagetikz
usetikzlibrarybackgrounds
usepackageamssymb
begindocument
 begintikzpicture[
 %Environment config
 node distance=2cm,
 %Environment Styles
 strip/.style=
 draw=gray,
 rounded corners=1mm,
 line width=1.3cm,
 opacity=0.5, line cap=round
 ,
 every node/.style=
 draw=black,
 circle,
 minimum size=1cm,
 fill=orange,
 fill opacity=0.8,
 text opacity=1
 
 ]
 % First, locate each of the nodes and name them
 node (void) at (0,0) $varnothing$;
 node [above of=void] (y) $y$;
 node [left of=y] (x) $x$;
 node [right of=y] (z) $z$;
 node [above of=x] (xy) $xy$;
 node [above of=y] (xz) $xz$;
 node [above of=z] (yz) $yz$;
 node [above of=xz] (xyz) $xyz$;
 % Now draw the lines:
 draw [black, thick] % Here you draw a line between nodes, each line start and end in the shape
 (xz)
 edge (xyz)
 edge (x)
 edge (z)
 (y)
 edge (xy)
 edge (yz)
 edge (void)
 (void)
 -- (x)
 -- (xy)
 -- (xyz)
 -- (yz)
 -- (z)
 -- (void) ;

 draw[strip] % (nodename.center) gives a coordinate from the center of the node, and the line is continuous
 (void.center) 
 -- (x.center)
 -- (xy.center)
 -- (xyz.center);

 endtikzpicture
enddocument

UPDATE

To not shade the nodes the line is drawn in the background layer (as I observed in @marmot's answer, and then in the rest to not stay behind.):

RESULT:

MWE:

documentclassstandalone
usepackagetikz
usetikzlibrarybackgrounds
usepackageamssymb
begindocument
 begintikzpicture[
 %Environment config
 node distance=2cm,
 %Environment Styles
 strip/.style=
 draw=gray,
 rounded corners=1mm,
 line width=1.3cm,
 opacity=0.5, line cap=round
 ,
 every node/.style=
 draw=black,
 circle,
 minimum size=1cm,
 fill=orange,
 fill opacity=0.8,
 text opacity=1
 
 ]
 % First, locate each of the nodes and name them
 node (void) at (0,0) $varnothing$;
 node [above of=void] (y) $y$;
 node [left of=y] (x) $x$;
 node [right of=y] (z) $z$;
 node [above of=x] (xy) $xy$;
 node [above of=y] (xz) $xz$;
 node [above of=z] (yz) $yz$;
 node [above of=xz] (xyz) $xyz$;
 % Now draw the lines:
 draw [black, thick] % Here you draw a line between nodes, each line start and end in the shape
 (xz)
 edge (xyz)
 edge (x)
 edge (z)
 (y)
 edge (xy)
 edge (yz)
 edge (void)
 (void)
 -- (x)
 -- (xy)
 -- (xyz)
 -- (yz)
 -- (z)
 -- (void) ;
 beginscope[on background layer] 
 draw[strip] % (nodename.center) gives a coordinate from the center of the node, and the line is continuous
 (void.center) 
 -- (x.center)
 -- (xy.center)
 -- (xyz.center);
 endscope
 endtikzpicture
enddocument

Just for comparison, here is a Metapost alternative. Compile with lualatex for the luamplib support.

documentclass[border=5mm]standalone
usepackageluatex85
usepackageluamplib
begindocument
mplibtextextlabelenable
beginmplibcode
beginfig(1);

 path s, ss;
 s = unitsquare scaled 70.71 rotated 45;
 ss = s shifted 50 up; 

 draw point 0 of s -- point 3 of s -- point 3 of ss -- point 2 of ss
 withpen pencircle scaled 32 
 withcolor 3/4 white;

 draw s; draw ss; 
 for i=0 upto 3: 
 draw point i of s -- point i of ss; 
 endfor

 vardef node(expr t, p) = 
 fill fullcircle scaled 24 shifted p withcolor red + 1/2 green;
 draw fullcircle scaled 24 shifted p;
 label(t, p);
 enddef;

 node("$emptyset$", point 0 of s);
 node("$x$", point 3 of s);
 node("$z$", point 1 of s);
 node("$xz$", point 2 of s);
 node("$y$", point 0 of ss);
 node("$xy$", point 3 of ss);
 node("$yz$", point 1 of ss);
 node("$xyz$", point 2 of ss);

endfig;
endmplibcode
enddocument

Note that this one is quite hard to adapt to plain old mpost; the mplibtextextlabelenable setting makes it much simpler to create
the node function, as the strings get compiled as TeX automatically.