How to draw dashed lines this figure automatically? - TeX

Anonymous 1123 replying to user 3.14159

This is the code I’m practicing on draw ordered paths.

The plane is outside of the sphere. So the plane has no points in common with the sphere. It is OK for me.   
```  
\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
	\begin{tikzpicture}[3d/install view={phi=110,theta=70},line cap=butt,line join=round,c/.style={circle,fill,inner sep=1pt},declare function={r=3;a=4;}] 
		\path
		(0,0,0) coordinate (O)
		(1,2,-r-2) coordinate (M)
		(0,0,-r-2) coordinate (H);
\path [save named
	path=sph,3d/screen coords] (O) circle[radius=r];
	\path pic{3d/circle on sphere={R=r,C={(O)}, n={(1,3,1)}}};
	%vẽ đường tròn giao tuyến có tâm T với tâm mặt cầu  là  I, bán kính mặt cầu là \myR
	%\draw[3d/hidden] (0,0,r) -- (0,0,-r);
\begin{scope}[canvas is xy plane at z=0]
	\path [shift={(H)}, save named path=bplane] (-a,-a) rectangle (a,a);
\end{scope}
\path [save named path=lineOHM] (O) -- (M) -- (H) -- cycle; 
\path foreach \p/\g in {O/90,H/-90,M/-90}
{(\p)node[c]{}+(\g:2.5mm) node{$\p$}};

\tikzset{3d/draw ordered paths={bplane,lineOHM,sph}}
		\end{tikzpicture}
\end{document}  
```  
![ScreenHunter 216.png](/image?hash=cf45de088d53dda4c3e066f9b8945c54e6e218ceaaa6a9c3850609ef72d3e4a7)

Anonymous 1123 replying to user 3.14159

Thank you very much for all your helps.

user 3.14159 replying to Anonymous 1123

I see. To me this looks great! (And shows a bit how the library evolved, thanks to various suggestions, mainly by you.)

Anonymous 1123 replying to user 3.14159

The result.  
  
![ScreenHunter 215.png](/image?hash=52f6fcf6a96637e1edbdb14ff16ec69e07271f0da01452d5015326c90b820546)

Anonymous 1123 replying to user 3.14159

I am sorry about this. This is the code I'm practicing on `draw ordered paths`.    

There is not wrong in this code. I sent my code to you and hope receive your comment about this code.

user 3.14159 replying to Anonymous 1123

OK, from now on I am going to ignore all requests which I do not understand. This is the first one. If you want others to look at such things, please make an effort in explaining what is wrong, e.g. by putting a screen shot with annotations.

Anonymous 1123

@marmot, re: [your answer](#a1629),  I tried this code. Please comment for me.  
```  
\documentclass[border=2mm,tikz]{standalone} 
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
	\foreach \Angle in {120}
	{\begin{tikzpicture}[line cap=round,line join=round,same bounding box=A,c/.style={circle,fill,inner sep=1pt},
			3d/install view={phi=\Angle,theta=70},declare function={a=4;h=3;}]
			\path (-a/2,a/2,0) coordinate (A)  (-a/2,-a/2,0) coordinate (B)
			(a/2,-a/2,0) coordinate (C)  
			(a/2,a/2,0) coordinate (D)
			(0,0,h) coordinate (S)
		(0,0,0) coordinate (I)	
			;
			\pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(C),(D),(S)")}
			\path (\mybarycenter) coordinate (bary);
			\tikzset{3d/polyhedron/.cd,O={(bary)},fore/.append style={fill=none},
				back/.append style={3d/hidden},
				draw face with corners={{(A)},{(B)},{(S)}},
				draw face with corners={{(B)},{(C)},{(S)}},
				draw face with corners={{(S)},{(C)},{(D)}},
				draw face with corners={{(S)},{(D)},{(A)}}}
			\path[save named path=pyra,convex hull of={A,B,C,S,D}];	
			\pgfmathsetmacro{\myr}{tddistance("(I)","(A)")}	
			\path[save named path=circ] (I) circle[radius=\myr]  ;
			\tikzset{3d/ordered paths/.cd,pyra/.style={draw=none}}
			\tikzset{3d/draw ordered paths={circ,pyra}}
				\path foreach \p/\g in {S/90,A/30,B/-90,C/-120,D/-90,I/0}
			{(\p)node[c]{}+(\g:2.5mm) node{$\p$}};
			\draw[3d/hidden] (A) -- (C) (B) -- (D) (S) -- (I);
	\end{tikzpicture}}
\end{document}
```

Anonymous 1123 replying to user 3.14159

Thank you very much. I will cut `scale=1` in next code, and try to make it simpler.

user 3.14159 replying to Anonymous 1123

I do not think that this is a too serious issue, but there is a reason why users ask for *minimal* examples. There is no reason to write several loops for something that can be done with one. It is harder to maintain, and others using or extending the code will just have to spend more time to understand what's going on, or to add features to the list. Also the resulting code appears than more voluminous than it has to be, and several users equate shortness with elegance, so, as a consequence, these codes appear less elegant than they might really be. Also, if you want to attract others to these methods of drawing diagrams, it can really deter them if they feel that the code has unnecessary repetitions. Therefore it would be great if you tried to minimize codes before presenting them, tried to avoid keys like `scale=1`, which make the code just longer, and unnecessary duplicates. On the long run this will also help you to maintain your own code because after a while one tends to forget which ingredients were important and which ones are there for no real reason.

Anonymous 1123

@marmot, re: [your answer](#a1629), I am sorry about [this question](https://topanswers.xyz/tex?q=1779). In your code, you wrote `% Please please please do not always force me to correct ` . I put question, because I do not understand deeply about it.

Anonymous 1123 replying to user 3.14159

Thank you for your reading.

user 3.14159 replying to Anonymous 1123

If I understand correctly, these are "just" some conical sections.

Anonymous 1123 replying to user 3.14159

The book in old. I  am afraid  it is difficult for you to see . If you can not read, please do not care this problem. Thank you very much. 
![ScreenHunter 131.png](/image?hash=91c88156514af39a4197f7ae641ab0ff0444a35a627e23c29dec261f98bf00fc)  
![ScreenHunter 132.png](/image?hash=00ec3605c598045ab35cdbadca68fce18857889e90a059731cbb6799cc5937f4)  
  
![ScreenHunter 133.png](/image?hash=d770db72c69b4b663bd319bcd143ca70707f652acb216c4631ee9015da237dae)

user 3.14159 replying to Anonymous 1123

I do not have access to the book. But the question is really what these ellipses/circles represent, i.e. if you have the data that determines the planes they are in.

Anonymous 1123 replying to user 3.14159

I see the picture at page 16 of [this book](https://drive.google.com/file/d/1kVaAapotRaU_IErjhZ-Ukbmb58bBLV0-/view)

user 3.14159 replying to Anonymous 1123

I don't know because I do not know what it really depicts.

Anonymous 1123 replying to user 3.14159

Is it difficult to draw this picture?  
![ScreenHunter 130.png](/image?hash=b2793edbb9f0c14be939358940891505cee37107135a0c89e660f53d8f5887be)

Anonymous 1123 replying to user 3.14159

Thanks.

user 3.14159 replying to Anonymous 1123

You can use `draw ordered paths`.  
```  
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,
		c/.style={circle,fill,inner sep=1pt}, 
		declare function={R=5;myphi=60; mytheta =50;},
		3d/install view={phi=10,psi=0,theta=70}]
 \path (0,0,0) coordinate (O)
	({R*cos(myphi)*sin(mytheta)},{R*sin(myphi)*sin(mytheta)},{R*cos(mytheta)}) coordinate (A)
	;	
 \path[3d/screen coords,save named path=circle] (O) circle[radius=R];	
 \path[3d/plane with normal={(A) through (A) named p1},
  3d/plane with normal={(0,0,1) through (A) named p2},
  3d/line with direction = {(0,0,1) through (O) named d}];
 \path[3d/intersection of={d with p1}] coordinate (S);
 \path[3d/intersection of={d with p2}] coordinate (T);
 \pgfmathsetmacro{\h}{sqrt(TD("(T)-(S)o(T)-(S)"))} ;
 \pgfmathsetmacro{\r}{sqrt(TD("(T)-(A)o(T)-(A)"))} ;
 \path[3d/cone/outer/.style={save named path=cone,draw=none}] (T) pic{3d/cone={r=\r,h/.evaluated=\h}};
 \tikzset{3d/draw ordered paths={circle,cone}}
 \path foreach \p/\g in {A/90,O/0,S/90,T/-180}
  {(\p)node[c]{}+(\g:2.5mm) node{$\p$}};	
\end{tikzpicture}	
\end{document}   
```  
![Screen Shot 2021-05-03 at 11.37.36 PM.png](/image?hash=4217f4ec4b8a55c8371ef3dedca0309e8f14338c6341099e4179ca19a4cc8f0a)

Anonymous 1123 replying to user 3.14159

![ScreenHunter 128.png](/image?hash=f236bd4a044392c252e052fb00c0ee5853b27c505b3da6d90c42609c1a88bd06)  
How to correct the line of the sphere inside the cone?

Anonymous 1123 replying to user 3.14159

I am trying to draw a cone and sphre so that `TA` is a tangent of the sphere. I tried  
```  
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{3dtools,calc}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
	\begin{tikzpicture}[line cap=round,line join=round,
		c/.style={circle,fill,inner sep=1pt}, 
		declare function={R=5;myphi=60; mytheta =50;},
		3d/install view={phi=10,psi=0,theta=70}]
	\path (0,0,0) coordinate (O)
	({R*cos(myphi)*sin(mytheta)},{R*sin(myphi)*sin(mytheta)},{R*cos(mytheta)}) coordinate (A)
	;	
\draw[3d/screen coords] (O) circle[radius=R];	
\path[3d/plane with normal={(A) through (A) named p1},
3d/plane with normal={(0,0,1) through (A) named p2},
3d/line with direction = {(0,0,1) through (O) named d}];
\path[3d/intersection of={d with p1}] coordinate (S);
\path[3d/intersection of={d with p2}] coordinate (T);
\pgfmathsetmacro{\h}{sqrt(TD("(T)-(S)o(T)-(S)"))} ;
\pgfmathsetmacro{\r}{sqrt(TD("(T)-(A)o(T)-(A)"))} ;
\path (T) pic{3d/cone={r=\r,h/.evaluated=\h}};
\path foreach \p/\g in {A/90,O/0,S/90,T/-180}
{(\p)node[c]{}+(\g:2.5mm) node{$\p$}};	
	\end{tikzpicture}	
\end{document} 
```

Anonymous 1123 replying to user 3.14159

I have just gone home from my school. Thanks.

user 3.14159 replying to Anonymous 1123

`\pgfmathsetmacro{\myangle}{acos(TD("(A)-(O)o(B)-(O)")/sqrt(TD("(A)-(O)o(A)-(O)")*TD("(B)-(O)o(B)-(O)")))}`?

Anonymous 1123 replying to user 3.14159

Or  
![ScreenHunter 127.png](/image?hash=e4f7baad727800db41c3c046669b7d005508b0acf9e0b653c6337ab7e76b1be8)![ScreenHunter 128.png](/image?hash=9012667eaf886af2ea849dee896b5ad373782491010188029f88e305002ee21e)

Anonymous 1123 replying to user 3.14159

In this code, how can I get measure of the angle `AOB` equal to 120 degrees?

Anonymous 1123 replying to user 3.14159

My new set up  
![ScreenHunter 125.png](/image?hash=bdbab40177e3c6a6dc3c0df0ee6520a927e0c210e9e1a1fae208c7705193beb3)  
![ScreenHunter 126.png](/image?hash=b09fd29ba34daea86b4c78612d2a8c7472f70da7d2d2329f420901c4b8cfde7e)

Anonymous 1123 replying to user 3.14159

Your code works fine. Thank you very much.

user 3.14159 replying to Anonymous 1123

OK, but I really have a problem understanding the setup. As long as it is not defined, I am afraid I cannot help.

Anonymous 1123 replying to user 3.14159

I rotated the picture by hand. Perhalp, I did not make dash line some here. I forgot save it.

user 3.14159 replying to Anonymous 1123

If that's the case, why is the `TY` line not covered by the `OBEC` plane?

Anonymous 1123 replying to user 3.14159

I understand your code. In my picture, I draw the  points `X, Y, T, Z, A, B, O` lies on the same plane `xy`.

user 3.14159 replying to Anonymous 1123

As I said, I do not understand the picture. Above you find a code that produces such pictures, but the interpretation is not clear.

Anonymous 1123 replying to user 3.14159

Yes. In GeoSpace, I use 3d coordinates of the vertices. I think,  we draw ractangles in TikZ.

user 3.14159

This draws something of that sort, but assumes that the horizontal object is not a plane.  
```  
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,
	c/.style={circle,fill,inner sep=1pt}, 
	declare function={a=2;b=3;ap=6;bp=4;h=1;H=5;},
	3d/install view={phi=70,psi=0,theta=70}]
 \draw[->] (0,0,0) -- (1,0,0);	
 \path (0,0,0) coordinate (O)	
  (a,0,0) coordinate (A)	
  (0,b,0) coordinate (B)	
  (0,0,H) coordinate (C)	
  (a,0,H) coordinate (D)	
  (0,b,H) coordinate (E)
  (ap,-bp,h) coordinate (X)	
  (0,-bp,h) coordinate (Y)	
  (ap,bp,h) coordinate (Z)	
  (0,bp,h) coordinate (T);
 \path[save named path=p1] (O) -- (A) -- (D) -- (C) -- cycle;
 \path[save named path=p2] (O) -- (B) -- (E) -- (C) -- cycle;
 \path[save named path=p3] (Y) -- (T) ;
 \tikzset{3d/draw ordered paths={p2,p3,p1}}
 \draw (Y) -- (X) -- (Z) -- (T);
 \path foreach \X in {O,A,B,X,Z}
  {(\X) node[c,label=below:{$\X$}]{}}
  foreach \X in {C,D,E,T,Y}
  {(\X) node[c,label=above:{$\X$}]{}};
\end{tikzpicture}	
\end{document}  
```  
![Screen Shot 2021-05-02 at 9.43.13 PM.png](/image?hash=fbc6f88013b366f5857da06f7b29ec5e8d5ffc6d306b21d91ba008d5c7fdb65d)

user 3.14159 replying to Anonymous 1123

I do not understand the picture. o you have the 3d coordinates of the vertices?

Anonymous 1123 replying to user 3.14159

Thank. How can I draw this pictures?  
![ScreenHunter 122.png](/image?hash=0cec3e80a6bf41fc06005332a23223ce25e1dee2cb5f1630a0438602b0a70ac5)  
![ScreenHunter 123.png](/image?hash=a2f98a3cabda3fc4e23c05e906b98467e8c7533deb1db73f9a2e48235d361a98)

user 3.14159 replying to Anonymous 1123

I really think that it is not very practical to use convex hulls on pgfplots plots, it only works reasonably fast if the number of coordinates is small enough.

Anonymous 1123 replying to user 3.14159

I do not understand all your code. I say to OP ask new question at https://topanswers.xyz/tex

user 3.14159 replying to Anonymous 1123

It is not really practical.  
```  
\documentclass[12pt]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\newcounter{icoord}
\pgfplotsset{% based on https://tex.stackexchange.com/a/75811
	stepcounter/.code=\stepcounter{#1},
    name nodes near coords/.style={nodes near coords={},
        every node near coord/.append style={anchor=center,coordinate,
			/pgfplots/stepcounter=icoord,
            name=#1-\number\value{icoord},
            alias=#1-last,
        },
    },
    name nodes near coords/.default=coordnode
}

\begin{document}
\centering
\begin{tikzpicture}[add coord/.code={\edef\mycoords{\mycoords,c-#1}}]
\begin{axis}[hide axis,
 view={150}{30},
 ticks=none,
  zmin=-5,zmax=5,
  xmin=-3,xmax=3,
  ymin=-3,ymax=3,
name nodes near coords=c 
]

          
\addplot3[surf,shader=interp,domain=-2:2,domain y=-2:2,
	z buffer=sort,opacity=0.5,samples=15]{x^2+y^2};
\path (\pgfkeysvalueof{/pgfplots/xmax},0,0)	coordinate (xmax)
	(\pgfkeysvalueof{/pgfplots/xmin},0,0)	coordinate (xmin)
    (0,\pgfkeysvalueof{/pgfplots/ymax},0)	coordinate (ymax)
	(0,\pgfkeysvalueof{/pgfplots/ymin},0)	coordinate (ymin)
	;
\end{axis}
\edef\mycoords{c-1}	
\tikzset{add coord/.list={2,...,\number\value{icoord}}}
\path[save named path=outline,convex hull of/.expanded={\mycoords}];
\begin{scope}
 \clip[use named path=outline];
 \draw[3d/hidden] (xmin) -- (xmax) (ymin) -- (ymax);
\end{scope}
\begin{scope}
 \clip[even odd clip,use named path=outline][generous outside path];
 \draw[3d/visible,-stealth] (xmin) -- (xmax) node[pos=1.1]{$x$};
 \draw[3d/visible,-stealth] (ymin) -- (ymax) node[pos=1.1]{$y$};
\end{scope}
\end{tikzpicture}
\end{document}  
```  
![Screen Shot 2021-05-01 at 9.52.24 PM.png](/image?hash=528d399f294a32969c5d5332f7756aad1044d5bdee3cfbe9416561da56912439)

Anonymous 1123 replying to user 3.14159

Can you hint me alittle?

user 3.14159 replying to Anonymous 1123

I think you can do that for general surfaces, too, in principle. It is just that the code may become very slow, or even runs out of memory..

Anonymous 1123 replying to user 3.14159

Please see comments at [here](https://tex.stackexchange.com/questions/595219/automatic-dotted-lines/595255#595255).

user 3.14159 replying to Anonymous 1123

I think solutions will be very slow because we need to compute the convex hull of thousands of coordinates.

Anonymous 1123 replying to user 3.14159

I do not know how to start.

Anonymous 1123 replying to user 3.14159

Thanks. Now I post this answer. Many thank to you.

user 3.14159 replying to Anonymous 1123

Also, maybe the OP is looking for longer axes.  
```  
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground} 
\pgfsetlayers{background,main,foreground}
\foreach \Angle in {10,20,...,350}
{\begin{tikzpicture}[line cap=round,line join=round,declare function={a=3;h=5;}, c/.style={circle,fill,inner sep=1pt}, 
	3d/install view={phi=\Angle,psi=0,theta=70},
	same bounding box=A]
	 \path
	 (0,0,0) coordinate (O)
	 (a,0,0) coordinate (A)
	 (a,a,0) coordinate (B)
	 (0,a,0) coordinate (C)
	 (0,0,h) coordinate (O')
	 (a,0,h) coordinate (A')
	 (a,a,h) coordinate (B')
	 (0,a,h) coordinate (C')
	 (a/2,a/2,h/2) coordinate (T);   
	 \tikzset{3d/polyhedron/.cd,O={(T)},
		 fore layer=foreground,back layer=background,
		 fore/.append style={fill=gray!50,opacity=0.5,thick},
		 back/.append style={3d/polyhedron/complete dashes,fill=gray!50,opacity=0.5},
		 %edges have complete dashes,
		 draw face with corners={{(O)},{(A)},{(B)},{(C)}},
		 draw face with corners={{(O')},{(A')},{(B')},{(C')}},
		 draw face with corners={{(A)},{(B)},{(B')},{(A')}},
		 draw face with corners={{(O)},{(C)},{(C')},{(O')}},
		 draw face with corners={{(O)},{(A)},{(A')},{(O')}},
		 draw face with corners={{(B)},{(C)},{(C')},{(B')}}
		 }
	%\path foreach \p/\g in {A/-90,B/-90,C/-90,O/-90}{(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; 
	\path[save named path=hull,convex hull of={O,A,B,C,O',A',B',C'}]; 
	\path[save named path=lx] (A) -- (a+2,0,0) node [pos=1.15] {$x$};
	\path[save named path=lx'] (O) -- (-a-2,0,0);
	\path[save named path=ly] (C) -- (0,a+1,0) node [pos=1.15] {$y$};
	\path[save named path=ly'] (O) -- (0,-a-2,0);
	\path[save named path=lz] (O') -- (0,0,h+1) node [pos=1.15] {$z$};
	\path[save named path=lz'] (O) -- (O);
	\tikzset{3d/ordered paths/.cd,
		hull/.style={draw=none},
		lx/.style={-latex},ly/.style={-latex},lz/.style={-latex}}
	\foreach \Dir/\Line in {{1,0,0}/x,{0,1,0}/y,{0,0,1}/z}	
	{
	\pgfmathtruncatemacro{\itest}{screendepth(\Dir)<0?0:1} 
	\ifnum\itest=0
	 \tikzset{3d/draw ordered paths={l\Line,hull,l\Line'}}
	\else
	 \tikzset{3d/draw ordered paths={l\Line',hull,l\Line}}
	\fi}
\end{tikzpicture}}
\end{document}    
```  
![ani.gif](/image?hash=f51296a353f3d95055c1ca54ab94728daabf091d2ee0eb041486ec638ded30e6)

user 3.14159 replying to Anonymous 1123

P.S. I think that with `convex hull of` one can answer [this question](https://tex.stackexchange.com/q/594560) but the same OP.

user 3.14159 replying to Anonymous 1123

With the new `draw ordered paths` it is actually possible to do this without an overly excessive code.  
```  
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground} 
\pgfsetlayers{background,main,foreground}
\foreach \Angle in {10,20,...,350}
{\begin{tikzpicture}[line cap=round,line join=round,declare function={a=3;h=5;}, c/.style={circle,fill,inner sep=1pt}, 
	3d/install view={phi=\Angle,psi=0,theta=70},
	same bounding box=A]
	 \path
	 (0,0,0) coordinate (O)
	 (a,0,0) coordinate (A)
	 (a,a,0) coordinate (B)
	 (0,a,0) coordinate (C)
	 (0,0,h) coordinate (O')
	 (a,0,h) coordinate (A')
	 (a,a,h) coordinate (B')
	 (0,a,h) coordinate (C')
	 (a/2,a/2,h/2) coordinate (T);   
	 \tikzset{3d/polyhedron/.cd,O={(T)},
		 fore layer=foreground,back layer=background,
		 fore/.append style={fill=gray!50,opacity=0.5,thick},
		 back/.append style={3d/polyhedron/complete dashes,fill=gray!50,opacity=0.5},
		 %edges have complete dashes,
		 draw face with corners={{(O)},{(A)},{(B)},{(C)}},
		 draw face with corners={{(O')},{(A')},{(B')},{(C')}},
		 draw face with corners={{(A)},{(B)},{(B')},{(A')}},
		 draw face with corners={{(O)},{(C)},{(C')},{(O')}},
		 draw face with corners={{(O)},{(A)},{(A')},{(O')}},
		 draw face with corners={{(B)},{(C)},{(C')},{(B')}}
		 }
	%\path foreach \p/\g in {A/-90,B/-90,C/-90,O/-90}{(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; 
	\path[save named path=hull,convex hull of={O,A,B,C,O',A',B',C'}]; 
	\path[save named path=lx] (A) -- (a+2,0,0) node [pos=1.15] {$x$};
	\path[save named path=ly] (C) -- (0,a+1,0) node [pos=1.15] {$y$};
	\path[save named path=lz] (O') -- (0,0,h+1) node [pos=1.15] {$z$};
	\tikzset{3d/ordered paths/.cd,
		hull/.style={draw=none},
		lx/.style={-latex},ly/.style={-latex},lz/.style={-latex}}
	\foreach \Dir/\Line in {{1,0,0}/x,{0,1,0}/y,{0,0,1}/z}	
	{
	\pgfmathtruncatemacro{\itest}{screendepth(\Dir)<0?0:1} 
	\ifnum\itest=0
	 \tikzset{3d/draw ordered paths={l\Line,hull}}
	\else
	 \tikzset{3d/draw ordered paths={hull,l\Line}}
	\fi}
\end{tikzpicture}}
\end{document}    
```  
![ani.gif](/image?hash=bf8b6103711c5a0d947c2a7cfe5ef90446e4ed2d38a2cf01c0e54c95dffd6ae6)

Anonymous 1123 replying to user 3.14159

![thu_may.gif](/image?hash=24d0c6362b1dfb70e12c4e20900ddad690f59e2559b9f674d88b6ae68d2c6ec9)

Anonymous 1123 replying to user 3.14159

I see difficults when I make correct line of `Ox, Oy` of [this question](https://tex.stackexchange.com/questions/595219/automatic-dotted-lines)  
```  
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
	\pgfdeclarelayer{background}
	\pgfdeclarelayer{foreground} 
	\pgfsetlayers{background,main,foreground}
	\foreach \Angle in {10,20,...,350}
	{
		\begin{tikzpicture}[line cap=round,line join=round,declare function={a=3;h=5;}, c/.style={circle,fill,inner sep=1pt}, 3d/install view={phi=\Angle,psi=0,theta=70},same bounding box=A]
			\path
			(0,0,0) coordinate (O)
			(a,0,0) coordinate (A)
			(a,a,0) coordinate (B)
			(0,a,0) coordinate (C)
			(0,0,h) coordinate (O')
			(a,0,h) coordinate (A')
			(a,a,h) coordinate (B')
			(0,a,h) coordinate (C')
			(a/2,a/2,h/2) coordinate (T)
			;   \tikzset{3d/polyhedron/.cd,O={(T)},
				fore layer=foreground,back layer=background,
				fore/.append style={fill=gray!50,opacity=0.5,thick},
				back/.append style={fill=gray!50,opacity=0.5},edges have complete dashes,
				draw face with corners={{(O)},{(A)},{(B)},{(C)}},
				draw face with corners={{(O')},{(A')},{(B')},{(C')}},
				draw face with corners={{(A)},{(B)},{(B')},{(A')}},
				draw face with corners={{(O)},{(C)},{(C')},{(O')}},
				draw face with corners={{(O)},{(A)},{(A')},{(O')}},
				draw face with corners={{(B)},{(C)},{(C')},{(B')}}
				}
			%\path foreach \p/\g in {A/-90,B/-90,C/-90,O/-90}{(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; 
\draw [-latex] (A) -- (a+2,0,0) node [right] {$x$};	
\draw [-latex] (C) -- (0,a+1,0) node [right] {$y$};	
\draw [-latex] (O') -- (0,0,h+1) node [above] {$z$};
	\end{tikzpicture}}
\end{document}  

```

1 Answer