How to draw one cylinder and two cones like this by using 3dtools - TeX

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How to draw one cylinder and two cones like this by using 3dtools

tikz add tag

Anonymous 1123

I want to draw this pictures

![ScreenHunter 1067.png](/image?hash=da41f6f2d7c246f047148ff9dc516f6d748de533e802eaf2d88f729b12464b4c)
![ScreenHunter 1068.png](/image?hash=533434280d54a42fea040f100ff3e55ba32919fd793d1e46e392c9080552edf0)

I tried

```
\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
%\usetikzlibrary{intersections,calc}
\begin{document}
\pgfmathsetmacro\th{70}
\pgfmathsetmacro\az{70}
\tdplotsetmaincoords{\th}{\az}
\pgfmathsetmacro\h{3} %height of cylinder
\pgfmathsetmacro\R{3} %radius of base
\pgfmathsetmacro\v{\h + 3} 
\pgfmathsetmacro\t{-\R} 
\begin{tikzpicture} [scale=1, tdplot_main_coords, axis/.style={blue,thick}]
	\path
	(0,0,0) coordinate (O) 
	(0,0,\v) coordinate (B) 
	(0,0,\t) coordinate (A);
	\pgfmathsetmacro\cott{{cot(\th)}}
	\pgfmathsetmacro\fraction{\R*\cott/(\v-\h)}
	\pgfmathsetmacro\fractionTwo{\R*\cott/\t}
	\pgfmathsetmacro\fraction{\fraction<1 ? \fraction : 1}
	\pgfmathsetmacro\angle{{acos(\fraction)}}
	\pgfmathsetmacro\angleTwo{{acos(\fractionTwo)}}
	\pgfmathsetmacro\PhiOne{180+(\az-90)+\angle}
	\pgfmathsetmacro\PhiTwo{180+(\az-90)-\angle}
	\pgfmathsetmacro\PhiOneBis{180+(\az-90)+\angleTwo}
	\pgfmathsetmacro\PhiTwoBis{180+(\az-90)-\angleTwo}
	\pgfmathsetmacro\sinPhiOne{{sin(\PhiOne)}}
	\pgfmathsetmacro\cosPhiOne{{cos(\PhiOne)}}
	\pgfmathsetmacro\sinPhiTwo{{sin(\PhiTwo)}}
	\pgfmathsetmacro\cosPhiTwo{{cos(\PhiTwo)}}
	\pgfmathsetmacro\sinPhiOneBis{{sin(\PhiOneBis)}}
	\pgfmathsetmacro\cosPhiOneBis{{cos(\PhiOneBis)}}
	\pgfmathsetmacro\sinPhiTwoBis{{sin(\PhiTwoBis)}}
	\pgfmathsetmacro\cosPhiTwoBis{{cos(\PhiTwoBis)}}
	\pgfmathsetmacro\sinazp{{sin(\az-90)}}
	\pgfmathsetmacro\cosazp{{cos(\az-90)}}
	\pgfmathsetmacro\sinazm{{sin(90-\az)}}
	\pgfmathsetmacro\cosazm{{cos(90-\az)}}
	\draw[dashed] (\tdplotmainphi:\R) arc(\tdplotmainphi:\tdplotmainphi+180:\R);
	
	\draw[thick] (\tdplotmainphi:\R)  arc(\tdplotmainphi:\tdplotmainphi-180:\R);
	
	\tdplotdrawarc[tdplot_main_coords,thick]{(0,0,\h)}{\R}{\PhiOne}{360+\PhiTwo}{anchor=north}{}
	\tdplotdrawarc[tdplot_main_coords,dashed]{(0,0,\h)}{\R}{\PhiTwo}{\PhiOne}{anchor=north}{}
	\draw[thick]  ({\R*cos(\tdplotmainphi)},{\R*sin(\tdplotmainphi)},0 ) -- ({\R*cos(\tdplotmainphi)},{\R*sin(\tdplotmainphi)},\h );
	\draw[thick]  ({\R*cos(\tdplotmainphi-180)},{\R*sin(\tdplotmainphi-180)},0 ) -- ({\R*cos(\tdplotmainphi-180)},{\R*sin(\tdplotmainphi-180)},\h );
	\draw[thick] (B) -- (\R*\cosPhiOne,\R*\sinPhiOne,\h);
	\draw[thick] (B) -- (\R*\cosPhiTwo,\R*\sinPhiTwo,\h);
	\draw[thick] (A) -- (\R*\cosPhiOneBis,\R*\sinPhiOneBis,0);
	\draw[thick] (A) -- (\R*\cosPhiTwoBis,\R*\sinPhiTwoBis,0);
	\foreach \p in {O,B,A}
	\draw[fill=black] (\p) circle (1pt);
	\foreach \p/\g in {O/-45,B/90,A/-90}
	\path (\p)+(\g:3mm) node{$\p$};
	\draw[dashed]  (A)--(B)    (-\R*\sinazm,-\R*\cosazm,0) -- (-\R*\sinazp,+\R*\cosazp,0) ;
	\end{tikzpicture}
\end{document}
```
![ScreenHunter 1069.png](/image?hash=8cfd72f76356a055d9551474a8561c978c72aab561c445c0346d937270e089ad)
How can I draw them by using `3dtools`?

Top Answer

user 3.14159

This is a very simpleminded code.
```
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}
\tikzset{
	protect/.code={
		\clip[overlay,reset cm,even odd clip,use named path=#1] 
		(-16383.99999pt,-16383.99999pt) rectangle (16383.99999pt,16383.99999pt);
}}
\begin{document}
\begin{tikzpicture}
 \begin{scope}[3d/install view={phi=30,theta=70},
 	declare function={R=3;% radius of the base of the cones and cylinder
	h=2;% height of the cone
	H=4;% height of the cyclinder 
	}]
  \path 
   (0,0,0) coordinate (O) % center of base of the lower cone
   (0,0,H) coordinate (H); % center of base of the upper cone
  \path[3d/screen coords,save named path=tmp] ([xshift=-R*1cm-0.4pt]O) rectangle 
  ([xshift=R*1cm+0.4pt]H);
%  
  % get the correct bounding box
  \path[opacity=0] (O) pic{3d/cone={r=R,h=-h}}; 
  % draw the part of the lower cone blocked by the cylinder
  \begin{scope}[3d/visible/.style={draw,very thin,cheating dash}]
   \clip[use named path=tmp];
   \path (O) pic{3d/cone={r=R,h=-h}};
  \end{scope}
  % draw the part of the lower cone not blocked by the cylinder
  \begin{scope}
   \tikzset{protect=tmp}
   \path (O) pic{3d/cone={r=R,h=-h}};
  \end{scope}
  % cylinder mantle
  \draw[3d/screen coords] ([xshift=-R*1cm]O) -- ([xshift=-R*1cm]H)
   ([xshift=R*1cm]O) -- ([xshift=R*1cm]H);
  % upper cone 
  \path (H) pic{3d/cone={r=R,h=h}};
 \end{scope}
\end{tikzpicture}
\end{document}
```
![Screen Shot 2021-01-09 at 7.55.47 AM.png](/image?hash=784056c9d8c4691af7c55a5c81cc15477b7eed92cc276950d46e19b35e323365)

How about this? ``` \documentclass[border=2mm,tikz]{standalone} \usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools \begin{document} \foreach \Angle in {10} {\begin{tikzpicture}[line cap=round,line join=round, c/.style={circle,fill,inner sep=1pt}, declare function={R=2;H=3;r=1.2;a=3;}, 3d/install view={phi=\Angle,theta=70}] \path (0,0,0) coordinate (O) ({R*cos(230)},{R*sin(230)},-H) coordinate (A) (0,0,-H) coordinate (I) (0,0,H*r/R) coordinate (C) (0,0,H*r/R + 1) coordinate (X) (0,0,-H-2) coordinate (Y); \begin{scope}[canvas is xy plane at z=0] \path[shift={(O)},save named path=tplane] (-a,-a) rectangle (a,a); \path[shift={(I)},save named path=bplane] (-a,-a) rectangle (a,a); \end{scope} \path (0,0,H*r/R) coordinate (C) pic[3d/cone/outer/.append style={draw=none,save named path=uc}]{3d/cone={r=r,h/.evaluated=-H*r/R}} (0,0,-H) pic[3d/cone/outer/.append style={draw=none,save named path=lc}]{3d/cone={r=R,h/.evaluated=H}}; \begin{scope}[3d/screen coords] \path[save named path=lineXY] (X) -- (Y); \path[save named path=lineOA] (O) -- (A); \end{scope} \tikzset{3d/draw ordered paths={lineXY,bplane,lc,lineOA,tplane,uc}} \path foreach \p/\g in {A/-90,I/90,O/0} {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture}} \end{document} ``` ![Screen Shot 2021-06-04 at 10.59.06 AM.png](/image?hash=c60da5a4e82ea69cbedfb2ad1acf9365031dda4bca0c51895e898da0c5c6aaf8)

@marmot, re: [your answer](#a1843), I am trying to draw this picture ![ScreenHunter 213.png](/image?hash=420a488f7045fc85e42d6a63076b57b6b493659f8b3e5726f5e91948fc7aeba2) I tried ``` \documentclass[border=2mm,tikz]{standalone} \usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools \begin{document} \foreach \Angle in {10} {\begin{tikzpicture}[line cap=round,line join=round, c/.style={circle,fill,inner sep=1pt}, declare function={R=2;H=3;r=1.2;a=3;}, 3d/install view={phi=\Angle,theta=70}] \path (0,0,0) coordinate (O) ({R*cos(230)},{R*sin(230)},-H) coordinate (A) (0,0,-H) coordinate (I) (0,0,H*r/R) coordinate (C) (0,0,H*r/R + 1) coordinate (X) (0,0,-H-2) coordinate (Y) ; \begin{scope}[canvas is xy plane at z=0] \path[shift={(O)},save named path=tplane] (-a,-a) rectangle (a,a); \path[shift={(I)},save named path=bplane] (-a,-a) rectangle (a,a); \end{scope} \path (0,0,H*r/R) coordinate (C) pic[3d/cone/outer/.append style={save named path=uc}]{3d/cone={r=r,h/.evaluated=-H*r/R}}; \path pic{3d/circle on sphere={R=R,C={(I)}, P={(I)}}}; \begin{scope}[3d/screen coords] \path[save named path=lineXY] (X) -- (Y); \path[save named path=lineOA] (O) -- (A); \end{scope} \tikzset{3d/draw ordered paths={lineXY,bplane,tplane,uc,lineOA}} \path foreach \p/\g in {A/-90,I/90,O/0} {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture}} \end{document} ```

If you install the latest version of [3dtools](https://github.com/marmotghost/tikz-3dtools) you can do the following: ``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{calc,decorations.pathreplacing,3dtools} % https://github.com/marmotghost/tikz-3dtools \pgfdeclarelayer{background} \pgfdeclarelayer{foreground} \pgfsetlayers{background,main,foreground} \begin{document} \begin{tikzpicture}[3d/install view={phi=0,theta=70}, declare function={R=3;a=2.9;b=1.9;h1=sqrt(R*R-a*a);h2=sqrt(R*R-b*b;}, 3d/hidden/.append style={on layer=background}, 3d/visible/.append style={on layer=foreground},] \path[3d/hidden/.append style={postaction={store path=H1}}, 3d/visible/.append style={postaction={store path=V1}}] pic{3d/circle on sphere={R=R,P={(0,0,h1)}}}; \path[3d/hidden/.append style={postaction={store path=H2}}, 3d/visible/.append style={postaction={store path=V2}}] pic{3d/circle on sphere={R=R,P={(0,0,h2)}}}; \draw[3d/hidden] [stored path/first coordinate of=V2] coordinate (aux2) [stored path/first coordinate of=V1] coordinate (aux1) (b,0,h2) -- node[below] {$b$}(0,0,h2) -- (0,0,h1) --node[below] {$a$}(a,0,h1); \path[3d/screen coords,fill=cyan,opacity=0.6,stored path/restore reversed path=V2] let \p1=(aux1),\p2=(aux2),\n1={atan2(\y1,\x1)},\n2={atan2(\y2,\x2)} in -- (aux2) arc[start angle=\n2,end angle=\n1,radius=R] [stored path/append path=V1] arc[start angle=180-\n1,end angle=180-\n2,radius=R]; \path[fill=blue,opacity=0.6,stored path/restore reversed path=V2, stored path/append path=H2] --cycle; \draw[3d/screen coords,3d/visible] (0,0) circle[radius=R]; \end{tikzpicture} \end{document} ``` ![Screen Shot 2021-01-14 at 9.02.57 AM.png](/image?hash=24affd3e571398b65d9064c0abe41c7c6189e73ec756bebf853acc33276afea9)

``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{calc,3dtools} \begin{document} \begin{tikzpicture} \begin{scope}[3d/install view={phi=30,theta=70}, declare function={R=3;% radius of the base of the cones and cylinder h=2;% height of the cone H=4;% height of the cyclinder }] \path (0,0,0) coordinate (O) % center of base of the lower cone (0,0,H) coordinate (H); % center of base of the upper cone % cylinder \draw[3d/screen coords] ([xshift=-R*1cm]O) -- ([xshift=-R*1cm]H) ([xshift=R*1cm]O) coordinate (BL) -- ([xshift=R*1cm]H); \draw[3d/hidden] (BL) arc[start angle=\pgfkeysvalueof{/tikz/3d/phi}, end angle=\pgfkeysvalueof{/tikz/3d/phi}+180,radius=R]; \draw (BL) arc[start angle=\pgfkeysvalueof{/tikz/3d/phi}, end angle=\pgfkeysvalueof{/tikz/3d/phi}-180,radius=R]; % upper cone \path (H) pic{3d/cone={r=R,h=h}}; \end{scope} \end{tikzpicture} \end{document} ```

@marmot, re: [your answer](#a1843), In this code, how to remove lower cone? ``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{calc,3dtools} \tikzset{ protect/.code={ \clip[overlay,reset cm,even odd clip,use named path=#1] (-16383.99999pt,-16383.99999pt) rectangle (16383.99999pt,16383.99999pt); }} \begin{document} \begin{tikzpicture} \begin{scope}[3d/install view={phi=30,theta=70}, declare function={R=3;% radius of the base of the cones and cylinder h=2;% height of the cone H=4;% height of the cyclinder }] \path (0,0,0) coordinate (O) % center of base of the lower cone (0,0,H) coordinate (H); % center of base of the upper cone \path[3d/screen coords,save named path=tmp] ([xshift=-R*1cm-0.4pt]O) rectangle ([xshift=R*1cm+0.4pt]H); % % get the correct bounding box \path[opacity=0] (O) pic{3d/cone={r=R,h=-h}}; % draw the part of the lower cone blocked by the cylinder \begin{scope}[3d/visible/.style={draw,very thin,cheating dash}] \clip[use named path=tmp]; \path (O) pic{3d/cone={r=R,h=-h}}; \end{scope} % draw the part of the lower cone not blocked by the cylinder \begin{scope} \tikzset{protect=tmp} \path (O) pic{3d/cone={r=R,h=-h}}; \end{scope} % cylinder mantle \draw[3d/screen coords] ([xshift=-R*1cm]O) -- ([xshift=-R*1cm]H) ([xshift=R*1cm]O) -- ([xshift=R*1cm]H); % upper cone \path (H) pic{3d/cone={r=R,h=h}}; \end{scope} \end{tikzpicture} \end{document} ```

Maybe like this? ``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{calc,3dtools} \tikzset{ protect/.code={ \clip[overlay,reset cm,even odd clip,use named path=#1] (-16383.99999pt,-16383.99999pt) rectangle (16383.99999pt,16383.99999pt); }} \begin{document} \begin{tikzpicture} \begin{scope}[3d/install view={phi=0,theta=70}, declare function={R=3;% radius of the base of the cones and cylinder h=2;% height of the cone H=4;% height of the cyclinder }] \path (0,0,0) coordinate (O) % center of base of the lower hemisphere (0,0,H) coordinate (H); % center of base of the upper hemisphere \draw[3d/screen coords] (O) + (R,0) coordinate (BR) (O) + (-R,0) coordinate (BL) (H) + (R,0) coordinate (TR) (H) + (-R,0) coordinate (TL) (BL) -- (TL) (BR) -- (TR); \path[3d/screen coords,save named path=tmp] ([xshift=-R*1cm-0.4pt]O) rectangle ([xshift=R*1cm+0.4pt]H); \draw[3d/hidden] (TR) arc[start angle=0,end angle=180,radius=R]; \draw (TR) arc[start angle=0,end angle=-180,radius=R] [3d/screen coords] arc[start angle=180,end angle=0,radius=R]; \draw[3d/hidden] (BR) arc[start angle=0,end angle=180,radius=R]; \draw (BR) arc[start angle=0,end angle=-180,radius=R] [3d/screen coords] arc[start angle=-180,end angle=0,radius=R]; \end{scope} \end{tikzpicture} \end{document} ``` ![Screen Shot 2021-01-12 at 9.36.01 PM.png](/image?hash=1125696facbdd8b364d932955a9bbc6c2355fd5d6c8c6ff140e1a8f372b05ae0)

1 Answer