How can I find intersection of two lines with `3dtools`? - TeX

Anonymous 1123 replying to user 3.14159

It works.

Anonymous 1123 replying to user 3.14159

Please see old bug. Now It does not work.  
```  
\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot} 
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\usepackage{tikz-3dplot-circleofsphere}
\begin{document} 
	\tdplotsetmaincoords{70}{120}
	\begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,
		line join=round,declare function={a=3;R=a/2; angC =-20;h=a;},
		tdplotCsBack/.style={cheating dash},
		visible/.style={draw,solid},
		hidden/.style={draw,very thin,cheating dash}]
		\path
		(0,0,0) coordinate (A)
		(5,0,0)  coordinate (B)
		(5, 6,0) coordinate (C)
		(2,0,5) coordinate (S);
		\path[3d/circumcircle center={A={(A)},B={(B)},C={(C)}}] 
		coordinate (G); 
		\path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}] 
		coordinate (I);
		\path [overlay,3d coordinate={(M) = 0.5*(A) + 0.5*(B)}, 
		3d coordinate={(myn1)=(A)-(B)x(A)-(C)},
		3d coordinate={(myn2)=(S)-(A)x(S)-(B)}];
		\path[3d/line with direction={(myn1) through (G) named d1},
		3d/line with direction={(myn2) through (I) named d2}];	
		\path[3d/intersection of={d1 with d2}] coordinate (T);
			\pgfmathsetmacro{\myR}{sqrt(TD("(T)-(A)o(T)-(A)"))}
		\pgfmathsetmacro{\myr}{sqrt(TD("(G)-(A)o(G)-(A)"))}
		\pgfmathsetmacro{\Angle}{acos(\myr/\myR)}
			\begin{scope}[shift={(T)}]
			\draw[tdplot_screen_coords] (T) circle[radius=\myR]; 
			\tdplotCsDrawLatCircle[tdplotCsBack/.style={hidden}]{\myR}{{-\Angle}}	
		\end{scope}
		
		
		\begin{scope}[shift={(T)}]
			\path[overlay] [3d coordinate={(myn)=(A)-(S)x(A)-(B)},
			3d coordinate={(A-T)=(A)-(T)}];
			\pgfmathsetmacro{\myaxisangles}{axisangles("(myn)")}
			\pgfmathsetmacro{\myalpha}{{\myaxisangles}[0]}
			\pgfmathsetmacro{\mybeta}{{\myaxisangles}[1]}
			\pgfmathsetmacro{\myh}{TD("(myn)o(A-T)")/sqrt(TD("(myn)o(myn)"))}
			\pgfmathsetmacro{\mygamma}{asin(\myh/\myR)}
			\tdplotCsDrawCircle[tdplotCsFront/.style={visible},tdplotCsBack/.style={ hidden}]{\myR}{\myalpha}{\mybeta}{\mygamma} 
		\end{scope}
		
			
		\foreach \p in {A,B,C,S,G,I,M,T}
		{\draw[fill=black] (\p) circle (1.2 pt);}
		\foreach \p/\g in {G/-90,A/-90,B/-90,S/90,C/-90,I/90,M/-90,T/90}
		{\path (\p)+(\g:3mm) node{$\p$};}
		\draw[hidden] (I) -- (M) -- (G) -- (T) -- cycle
		(A) -- (B) -- (C) --cycle
		(B) -- (I)
		(S) --(A) (S) --(B) (S)--(C)
		;
	\end{tikzpicture}
\end{document}    
```

Anonymous 1123 replying to user 3.14159

The next few days, I ask you about intersection of a line and a sphere.

Anonymous 1123 replying to user 3.14159

Correct now. Thank you very much.

user 3.14159 replying to Anonymous 1123

Yes, this is because your auxiliary coordinates are large. Use always `overlay` for those.  
```  
\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot} 
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\usepackage{tikz-3dplot-circleofsphere}
\begin{document} 
\tdplotsetmaincoords{70}{120}
	\begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,
		line join=round,declare function={a=3;R=a/2; angC =-20;h=a;},
		tdplotCsBack/.style={cheating dash},
		visible/.style={draw,solid},
		hidden/.style={draw,very thin,cheating dash}]
				\path
			(0,0,0) coordinate (A)
		(5,0,0)  coordinate (B)
		(5, 6,0) coordinate (C)
		(2,0,5) coordinate (S);
		\path[3d/circumcircle center={A={(A)},B={(B)},C={(C)}}] 
		coordinate (G); 
	\path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}] 
	coordinate (I);
   \path [overlay,3d coordinate={(M) = 0.5*(A) + 0.5*(B)}, 
   3d coordinate={(myn1)=(A)-(B)x(A)-(C)},
   3d coordinate={(myn2)=(S)-(A)x(S)-(B)}];
   \path[3d/line with direction={(myn1) through (G) named d1},
   3d/line with direction={(myn2) through (I) named d2}];	
   \path[3d/intersection of={d1 with d2}] coordinate (T);	
   \foreach \p in {A,B,C,S,G,I,M,T}
	{\draw[fill=black] (\p) circle (1.2 pt);}
   \foreach \p/\g in {G/-90,A/-90,B/-90,S/90,C/-90,I/90,M/-90,T/90}
	{\path (\p)+(\g:3mm) node{$\p$};}
   \draw[hidden] (I) -- (M) -- (G) -- (T) -- cycle
   (A) -- (B) -- (C) --cycle
   (B) -- (I)
   (S) --(A) (S) --(B) (S)--(C)
   ;
\end{tikzpicture}
\end{document}  
```  
![Screen Shot 2020-11-28 at 7.19.20 AM.png](/image?hash=d03411a3e183bb6e90549af78da408f2dc2b27a2fa81b1fe04a0a38c0e0a8d08)

Anonymous 1123 replying to user 3.14159

Thanks. It works. But, the picture does not fit standalone.    
```  
\documentclass[tikz,border=2mm]{standalone}
\usepackage{tikz-3dplot} 
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\usepackage{tikz-3dplot-circleofsphere}
\begin{document} 
\tdplotsetmaincoords{70}{120}
	\begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,
		line join=round,declare function={a=3;R=a/2; angC =-20;h=a;},
		tdplotCsBack/.style={cheating dash},
		visible/.style={draw,solid},
		hidden/.style={draw,very thin,cheating dash}]
				\path
			(0,0,0) coordinate (A)
		(5,0,0)  coordinate (B)
		(5, 6,0) coordinate (C)
		(2,0,5) coordinate (S);
		\path[3d/circumcircle center={A={(A)},B={(B)},C={(C)}}] 
		coordinate (G); 
	\path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}] 
	coordinate (I);
		\path [3d coordinate={(M) = 0.5*(A) + 0.5*(B)}, 3d coordinate={(myn1)=(A)-(B)x(A)-(C)},
		3d coordinate={(myn2)=(B)-(A)x(A)-(S)}];
		\path[3d/line with direction={(myn1) through (G) named d1}];
		\path[3d/line with direction={(myn2) through (I) named d2}];
		
		\path[3d/intersection of={d1 with d2}] coordinate (T);	
				\foreach \p in {A,B,C,S,G,I,M,T}
			\draw[fill=black] (\p) circle (1.2 pt);
			\foreach \p/\g in {G/-90,A/-90,B/-90,S/90,C/-90,I/90,M/-90,T/90}
			\path (\p)+(\g:3mm) node{$\p$};
			\draw[hidden] (I) -- (M) -- (G) -- (T) -- cycle
			(A) -- (B) -- (C) --cycle
			(B) -- (I)
			(S) --(A) (S) --(B) (S)--(C)
			;
	\end{tikzpicture}
\end{document}
```    
![ScreenHunter 968.png](/image?hash=c6572fde0c8261d08d065e0e808ea550dd1cc01c32be46253aef669071b3a182)

user 3.14159 replying to Anonymous 1123

I updated the library. Please note that these points were already a bit large, there will be situations in which one cannot compute the intersections because of TeX's built-in limitations.

Anonymous 1123

@marmot, re: [your answer](#a1761),   
![ScreenHunter 966.png](/image?hash=09456bb4bfe64c64adcdc3029936cbf3af7f401501a232ae4d4fad23c75be54d)

Anonymous 1123

@marmot, re: [your answer](#a1761), If I use  
```  
\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot} 
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\usepackage{tikz-3dplot-circleofsphere}
\begin{document} 
\tdplotsetmaincoords{70}{120}
	\begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,
		line join=round,declare function={a=3;R=a/2; angC =-20;h=a;},
		tdplotCsBack/.style={cheating dash},
		visible/.style={draw,solid},
		hidden/.style={draw,very thin,cheating dash}]
				\path
			(0,0,0) coordinate (A)
		(5,0,0)  coordinate (B)
		(5, 6,0) coordinate (C)
		(2,0,5) coordinate (S);
		\path[3d/circumcircle center={A={(A)},B={(B)},C={(C)}}] 
		coordinate (G); 
	\path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}] 
	coordinate (I);
	\path [3d coordinate={(M) = 0.5*(A) + 0.5*(B)}];
		%\path [3d coordinate={(M) = 0.5*(A) + 0.5*(B)}, 3d coordinate={(myn1)=(A)-(B)x(A)-(C)},
		%3d coordinate={(myn2)=(S)-(A)x(S)-(B)}];
		%3d/line with direction={(myn2) through (I) named d2}];
		\path [3d coordinate={(myn1)=(0,0,1)},
		3d coordinate={(myn2)=(0,1,0)}];
		\path[3d/line with direction={(myn1) through (G) named d1},
		3d/line with direction={(myn2) through (I) named d2}];		
		\path[3d/intersection of={d1 with d2}] coordinate (T);	
		
				\foreach \p in {A,B,C,S,G,I,M,T}
			\draw[fill=black] (\p) circle (1.2 pt);
			\foreach \p/\g in {G/-90,A/-90,B/-90,S/90,C/-90,I/90,M/-90,T/90}
			\path (\p)+(\g:3mm) node{$\p$};
			\draw[hidden] (I) -- (M) -- (G) -- (T) -- cycle
			(A) -- (B) -- (C) --cycle
			(B) -- (I)
			(S) --(A) (S) --(B) (S)--(C)
			;
	\end{tikzpicture}
\end{document}
```  
I get correct result.

Anonymous 1123

@marmot, re: [your answer](#a1761), I want to find intersection of two lines `d1` and `d2`. I got massage `dimention too large` and incorrect intersection.  
```  
\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot} 
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\usepackage{tikz-3dplot-circleofsphere}
\begin{document} 
\tdplotsetmaincoords{70}{120}
	\begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,
		line join=round,declare function={a=3;R=a/2; angC =-20;h=a;},
		tdplotCsBack/.style={cheating dash},
		visible/.style={draw,solid},
		hidden/.style={draw,very thin,cheating dash}]
				\path
			(0,0,0) coordinate (A)
		(5,0,0)  coordinate (B)
		(5, 6,0) coordinate (C)
		(2,0,5) coordinate (S);
		\path[3d/circumcircle center={A={(A)},B={(B)},C={(C)}}] 
		coordinate (G); 
	\path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}] 
	coordinate (I);
		\path [3d coordinate={(M) = 0.5*(A) + 0.5*(B)}, 3d coordinate={(myn1)=(A)-(B)x(A)-(C)},
		3d coordinate={(myn2)=(S)-(A)x(S)-(B)}];
		\path[3d/line with direction={(myn1) through (G) named d1},
		3d/line with direction={(myn2) through (I) named d2}];	
		\path[3d/intersection of={d1 with d2}] coordinate (T);	
				\foreach \p in {A,B,C,S,G,I,M,T}
			\draw[fill=black] (\p) circle (1.2 pt);
			\foreach \p/\g in {G/-90,A/-90,B/-90,S/90,C/-90,I/90,M/-90,T/90}
			\path (\p)+(\g:3mm) node{$\p$};
			\draw[hidden] (I) -- (M) -- (G) -- (T) -- cycle
			(A) -- (B) -- (C) --cycle
			(B) -- (I)
			(S) --(A) (S) --(B) (S)--(C)
			;
	\end{tikzpicture}
\end{document}  
```

user 3.14159 replying to Anonymous 1123

OK. I misread your comment. I though you want the intersection between two spheres. Sphere and cylinder is much harder...

Anonymous 1123 replying to user 3.14159

I have just posted a new question.

user 3.14159 replying to Anonymous 1123

Sure. I may be a bit slow answering it. In principle it is not too difficult, it is more or less the same math as the intersection of two circles in 2d.

Anonymous 1123

@marmot, re: [your answer](#a1761),  Can I post a new question about intersection of sphere and a cylinder like [here](http://www.grad.hr/geomteh3d/prodori/prodor_sf_eng.html)?

Anonymous 1123 replying to user 3.14159

I will post some questions about intersection of a plane and a sphere; intersection of  two  spheres;

user 3.14159 replying to Anonymous 1123

It is still highly disturbing that a code that works fine on one system produces these crazy errors on another machine. I have no idea why that could be.

Anonymous 1123 replying to user 3.14159

It works. Thanks.

user 3.14159 replying to Anonymous 1123

I uploaded a new version of the library at https://github.com/marmotghost/tikz-3dtools. Could you try again, maybe with this code:  
```  
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[line cap=butt,line join=round,
	3d/install view={phi=110,psi=0,theta=60}]
 \path[3d/line with direction={(1,1,1) through (1,2,3) named d1},
 	3d/line with direction={(2,-3,1) through (1,2,3) named d2}];
 \draw[red] (1,1,1) -- (1,2,3);
 \draw[blue] (2,-3,1) -- (1,2,3);
 \path[3d/intersection of={d1 with d2}] coordinate (I)
  node[circle,fill,inner sep=0.5pt,
  label=above:{$(I)=(\pgfmathparse{TD("(I)")}%
  \pgfmathprintvector[/pgf/fpu,/pgf/fpu/output format=fixed]\pgfmathresult)$}]{};
\end{tikzpicture}
\end{document}  
```

Anonymous 1123 replying to user 3.14159

Please do not care it.

Anonymous 1123 replying to user 3.14159

I get the same massage  
![ScreenHunter 953.png](/image?hash=73d4ae2c00349252b9002db3973a17774055e3084f0939f7a45cfd44eca0ad75)

user 3.14159 replying to Anonymous 1123

What I wanted to say is that the log file ends before the error message, probably due to size limitations. For some reasons on your machine `\pgfmathprintvector` gets to see a number in plain `fpu` format but I have absolutely no idea why. Can you try this code:  
```  
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[line cap=butt,line join=round,
	3d/install view={phi=110,psi=0,theta=60}]
 \path[3d/line with direction={(1,1,1) through (1,2,3) named d1},
 	3d/line with direction={(2,-3,1) through (1,2,3) named d2}];
 \draw[red] (1,1,1) -- (1,2,3);
 \draw[blue] (2,-3,1) -- (1,2,3);
 \path[3d/intersection of={d1 with d2}] 
  node[circle,fill,inner sep=0.5pt,
  label=above:{$(I)=(\pgfmathparse{TD("(I-1)")}\pgfmathprintvector\pgfmathresult)$}]{};
\end{tikzpicture}
\end{document}
 ```

Anonymous 1123 replying to user 3.14159

I got the picture   
  
![ScreenHunter 952.png](/image?hash=1011bfb65fd04fecced6d83597ffa4d3a6bfd16da03795b3139fd5fc14ef3ff3)

user 3.14159 replying to Anonymous 1123

This one does not seem to contain an error.

Anonymous 1123 replying to user 3.14159

```This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/W32TeX) (preloaded format=pdflatex 2020.11.21)  21 NOV 2020 06:42
entering extended mode
 restricted \write18 enabled.
 %&-line parsing enabled.
**giao_diem_hai_duong_thang.tex
(./giao_diem_hai_duong_thang.tex
LaTeX2e <2020-10-01> patch level 2
L3 programming layer <2020-10-27> xparse <2020-03-03>
(c:/texlive/2020/texmf-dist/tex/latex/standalone/standalone.cls
Document Class: standalone 2018/03/26 v1.3a Class to compile TeX sub-files stan
dalone
(c:/texlive/2020/texmf-dist/tex/latex/tools/shellesc.sty
Package: shellesc 2019/11/08 v1.0c unified shell escape interface for LaTeX
Package shellesc Info: Restricted shell escape enabled on input line 77.
)
(c:/texlive/2020/texmf-dist/tex/generic/iftex/ifluatex.sty
Package: ifluatex 2019/10/25 v1.5 ifluatex legacy package. Use iftex instead.

(c:/texlive/2020/texmf-dist/tex/generic/iftex/iftex.sty
Package: iftex 2020/03/06 v1.0d TeX engine tests
))
(c:/texlive/2020/texmf-dist/tex/latex/xkeyval/xkeyval.sty
Package: xkeyval 2014/12/03 v2.7a package option processing (HA)

(c:/texlive/2020/texmf-dist/tex/generic/xkeyval/xkeyval.tex
(c:/texlive/2020/texmf-dist/tex/generic/xkeyval/xkvutils.tex
\XKV@toks=\toks15
\XKV@tempa@toks=\toks16

(c:/texlive/2020/texmf-dist/tex/generic/xkeyval/keyval.tex))
\XKV@depth=\count175
File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA)
))
\sa@internal=\count176
\c@sapage=\count177

(c:/texlive/2020/texmf-dist/tex/latex/standalone/standalone.cfg
File: standalone.cfg 2018/03/26 v1.3a Default configuration file for 'standalon
e' class
)
(c:/texlive/2020/texmf-dist/tex/latex/base/article.cls
Document Class: article 2020/04/10 v1.4m Standard LaTeX document class
(c:/texlive/2020/texmf-dist/tex/latex/base/size10.clo
File: size10.clo 2020/04/10 v1.4m Standard LaTeX file (size option)
)
\c@part=\count178
\c@section=\count179
\c@subsection=\count180
\c@subsubsection=\count181
\c@paragraph=\count182
\c@subparagraph=\count183
\c@figure=\count184
\c@table=\count185
\abovecaptionskip=\skip47
\belowcaptionskip=\skip48
\bibindent=\dimen138
)
(c:/texlive/2020/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty
(c:/texlive/2020/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty
(c:/texlive/2020/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty
(c:/texlive/2020/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex
\pgfutil@everybye=\toks17
\pgfutil@tempdima=\dimen139
\pgfutil@tempdimb=\dimen140

(c:/texlive/2020/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex)
) (c:/texlive/2020/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def
\pgfutil@abb=\box47
)
(c:/texlive/2020/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex
(c:/texlive/2020/texmf-dist/tex/generic/pgf/pgf.revision.tex)
Package: pgfrcs 2020/10/01 v3.1.6a (3.1.6a)
))
Package: pgf 2020/10/01 v3.1.6a (3.1.6a)

(c:/texlive/2020/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty
(c:/texlive/2020/texmf-dist/tex/latex/graphics/graphicx.sty
Package: graphicx 2020/09/09 v1.2b Enhanced LaTeX Graphics (DPC,SPQR)

(c:/texlive/2020/texmf-dist/tex/latex/graphics/graphics.sty
Package: graphics 2020/08/30 v1.4c Standard LaTeX Graphics (DPC,SPQR)

(c:/texlive/2020/texmf-dist/tex/latex/graphics/trig.sty
Package: trig 2016/01/03 v1.10 sin cos tan (DPC)
)
(c:/texlive/2020/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
)
Package graphics Info: Driver file: pdftex.def on input line 105.

(c:/texlive/2020/texmf-dist/tex/latex/graphics-def/pdftex.def
File: pdftex.def 2020/10/05 v1.2a Graphics/color driver for pdftex
))
\Gin@req@height=\dimen141
\Gin@req@width=\dimen142
)
(c:/texlive/2020/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty
(c:/texlive/2020/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex
Package: pgfsys 2020/10/01 v3.1.6a (3.1.6a)

(c:/texlive/2020/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex
\pgfkeys@pathtoks=\toks18
\pgfkeys@temptoks=\toks19

(c:/texlive/2020/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex
\pgfkeys@tmptoks=\toks20
))
\pgf@x=\dimen143
\pgf@y=\dimen144
\pgf@xa=\dimen145
\pgf@ya=\dimen146
\pgf@xb=\dimen147
\pgf@yb=\dimen148
\pgf@xc=\dimen149
\pgf@yc=\dimen150
\pgf@xd=\dimen151
\pgf@yd=\dimen152
\w@pgf@writea=\write3
\r@pgf@reada=\read2
\c@pgf@counta=\count186
\c@pgf@countb=\count187
\c@pgf@countc=\count188
\c@pgf@countd=\count189
\t@pgf@toka=\toks21
\t@pgf@tokb=\toks22
\t@pgf@tokc=\toks23
\pgf@sys@id@count=\count190
 (c:/texlive/2020/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg
File: pgf.cfg 2020/10/01 v3.1.6a (3.1.6a)
)
Driver file for pgf: pgfsys-pdftex.def

(c:/texlive/2020/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def
File: pgfsys-pdftex.def 2020/10/01 v3.1.6a (3.1.6a)

(c:/texlive/2020/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def
File: pgfsys-common-pdf.def 2020/10/01 v3.1.6a (3.1.6a)
)))
(c:/texlive/2020/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex
File: pgfsyssoftpath.code.te

user 3.14159

Another possibility is that you use a very different/old TeX installation. (I use TeXLive2020, which I updated a few days ago.)

user 3.14159 replying to Anonymous 1123

Can you show the log file of the code that does not work? BTW, every code example that you post in the comments misses `\documentclass`, probably because you put it directly after the three backticks.

Anonymous 1123 replying to user 3.14159

I tried two times.

Anonymous 1123 replying to user 3.14159

With this code, I do not et the error  
```\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools,intersections}

\begin{document}
	\tdplotsetmaincoords{70}{80}
	\begin{tikzpicture}[scale=1,tdplot_main_coords,line join = round, line cap = round, declare function={a = 3;b = 3;}]
		\path
		(0,0,0) coordinate (O)
		(0,5,0) coordinate (A)
		(0,3,-3) coordinate (B) 
		(3/2,3/2,5) coordinate (C)
		[3d coordinate = {(M) = 0.33*(O) + 0.6*(A)}, 
		3d coordinate = {(N) = 0.5*(A) + 0.5 *(C)},
		3d coordinate = {(P) = 0.3*(A) + 0.33*(B) + 0.3*(O)}] ;
		\pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(O)")}
		\typeout{barycenter of (A), (B) and (O) is (\mybarycenter)}
		\path[3d/line through={(O) and (A) named lOA}];
		\path[3d/plane through=(M) and (N) and (P) named pMNP];
		\path[3d/intersection of={lOA with pMNP}] coordinate (Q);
		\path[3d/line with direction={(1,2,3) through (C) named lC}];
		\path[3d/line with direction={(3,0,0) through (8,7/2,8) named lD}];
		\path[3d/intersection of={lC with lD}] coordinate (B');
		\draw[blue] (C) -- ++ (1,2,3);
		\draw[red] (8,7/2,8) -- ++ (7,0,0);
		\path (B') node[circle,fill,inner sep=0.5pt,
		label=above:{$(B')=(\pgfmathparse{TD("(B')")}\pgfmathprintvector\pgfmathresult)$}]{};
		\foreach \p in {O,A,B,C,M,N,P}
		\draw[fill=black] (\p) circle (1pt);
		\foreach \p/\g in {O/90,A/90,B/90,C/90,M/90,N/90,P/90}
		{\path (\p)+(\g:3mm) node{$\p$};}
	\end{tikzpicture}
\end{document}  ```

user 3.14159 replying to Anonymous 1123

I do not get the error and use the latest version of `3dtools`. This is very strange. Maybe you can try to download the library code again, maybe something went wrong in the download.

Anonymous 1123 replying to user 3.14159

I copied your answer  
```\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[line cap=butt,line join=round,
	3d/install view={phi=110,psi=0,theta=60}]
 \path[3d/line with direction={(1,1,1) through (1,2,3) named d1},
 	3d/line with direction={(2,-3,1) through (1,2,3) named d2}];
 \draw[red] (1,1,1) -- (1,2,3);
 \draw[blue] (2,-3,1) -- (1,2,3);
 \path[3d/intersection of={d1 with d2}] coordinate (I)
  node[circle,fill,inner sep=0.5pt,
  label=above:{$(I)=(\pgfmathparse{TD("(I)")}\pgfmathprintvector\pgfmathresult)$}]{};
\end{tikzpicture}
\end{document}```

user 3.14159 replying to Anonymous 1123

Please show the TeX code that leads to the message.

Anonymous 1123

@marmot, re: [your answer](#a1761), I get massage  (I updated 3Dtools)
![ScreenHunter 951.png](/image?hash=0efcb8844ce02099402d803d15710d7cb9c1d315711d9741c8b3efe4a6e439dd)

Anonymous 1123 replying to user 3.14159

Updated.

user 3.14159

@Anonymous, re: [your question](#question), could you perhaps post a complete example in which all points are defined?

1 Answer