How to draw a cone that height does not perpendicular to xy plane? - TeX

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How to draw a cone that height does not perpendicular to xy plane?

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Anonymous 1123

Let be four point 
```0,0,a) coordinate (A')
(a,0,0) coordinate (B)
(0,a,0) coordinate (D)
(a,a,a) coordinate (C')
```

I am trying to draw a cone with vertex at `A'` and circle of base is `BDC`. I tried

```
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
	\begin{tikzpicture}[3d/install view={phi=70,theta=65,psi=20},
		line cap=round,line join=round,
		declare function={a=4;}]
		\path (0,0,a) coordinate (A')
		(a,0,0) coordinate (B)
		(0,a,0) coordinate (D)
		(a,a,a) coordinate (C');
		\path[3d/circumcircle center={A={(D)},B={(B)},C={(C')}}] coordinate (G);
		\pgfmathsetmacro{\R}{sqrt(TD("(G)-(B)o(G)-(B)"))} ;
		\pgfmathsetmacro{\h}{sqrt(TD("(G)-(A')o(G)-(A')"))} ;
		\path[overlay,3d coordinate={(n)=(B)-(C')x(B)-(D)}]; 
		\pic{3d/circle on sphere={R=\R,C={(G)},P={(G)},n={(n)}}};
		%\path (a,2*a/3,a/3) coordinate (T) pic{3d/cone={r=\R,h/.evaluated=\h}};
		\foreach \p in {A',B,C',D,G}
		{\draw[fill=black] (\p) circle (1.2 pt);}
		\foreach \p/\g in {G/-90,A'/-90,B/-90,C'/-90,D/90}
		{\path (\p)+(\g:3mm) node{$\p$};}
	\end{tikzpicture}
\end{document} 
```
![ScreenHunter 81.png](/image?hash=b9f7d28a960e80cd905d6f484f00db700c54bba4f22b2bbd3019627b829717b8)

How can I draw the cone? And can I put the cone inot a cube like this?

![ScreenHunter 80.png](/image?hash=49ec781a70f1943400277c9e9fd3d249844db04b4cb8199ab65e912ba3478f58)

Top Answer

marmot

I can currently only answer the first part of the question. It is as simple as finding an appropriate coordinate system, in which the z-axis points into the direction of axis of the cone.
```
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\foreach \Angle in {5,15,...,355}
{\begin{tikzpicture}[3d/install view={phi=\Angle,theta=65,psi=20},
		line cap=round,line join=round,same bounding box=A,
		declare function={a=4;}]
  \path (0,0,a) coordinate (A')
	(a,0,0) coordinate (B)
	(0,a,0) coordinate (D)
	(a,a,a) coordinate (C');
  \path[3d/circumcircle center={A={(D)},B={(B)},C={(C')}}] coordinate (G);
  \pgfmathsetmacro{\R}{sqrt(TD("(G)-(B)o(G)-(B)"))}
  \pgfmathsetmacro{\h}{sqrt(TD("(G)-(A')o(G)-(A')"))}
  \tikzset{3d/define orthonormal dreibein={A={(D)},B={(B)},C={(C')}}}
  \path[x={(ex)},y={(ey)},z={(ez)}]
    (G) pic{3d/cone={r=\R,h=\h}};
  \foreach \p/\g in {G/-90,A'/-90,B/-90,C'/-90,D/90}
  {\draw[fill=black] (\p) circle[radius=1.2pt]+(\g:3mm) node{$\p$};}
\end{tikzpicture}}
\end{document} 
```
![ani.gif](/image?hash=7860aa64f0b42b8f1f1d3929496b0227264b2f7600bf9d9a5601cab843927b28)

The second part is much harder. One would have to compute a number of intersections. It would be even harder to make this fully rotatable.

1 Answer