How to draw surface x^2 - z^2 =1 and sphere x^2 + y^2 + z^2 = a^2 another way? - TeX

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Top Answer
user 3.14159
There are many ways, here is one. Note that `3dtools` is only used to install a view, so you can use `tikz-3dplot` or the `perspective` library instead.
```
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}%https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[scale=3,>=stealth,semithick]
 \path (1,0) coordinate (ex) (0,1) coordinate (ey);
 \begin{scope}[3d/install view={phi=110,psi=0,theta=70},
 	smooth,variable=\t,fill opacity=0.5]
  \path (0,1,0) coordinate (ey');
  \draw (-1.5,0,0) -- (-1,0,0);
  \path let \p1=(ey'),\n1={atan2(\y1,\x1)} in
   [left color=teal!50,right color=teal,middle color=white,
   	shading angle=\n1] plot[domain=-1:1] ({-cosh(\t)},1,{sinh(\t)})
   -- plot[domain=1:-1] ({-cosh(\t)},-1,{sinh(\t)}) -- cycle;
  \draw (0,-1.5,0) -- (0,-1,0);
  \draw (0,0,-1.5) -- (0,0,-1);
  \path[x={(ex)},y={(ey)},ball color=orange,fill opacity=1] 
  	(0,0,0) circle[radius=1]; 
  \path let \p1=(ey'),\n1={atan2(\y1,\x1)} in
   [left color=teal!50,right color=teal,middle color=white,
   	shading angle=\n1] plot[domain=-1:1] ({cosh(\t)},1,{sinh(\t)})
   -- plot[domain=1:-1] ({cosh(\t)},-1,{sinh(\t)}) -- cycle;
  \draw[->] (1,0,0) -- (1.5,0,0) node[pos=1.2]{$x$}; 
  \draw[->] (0,1,0) -- (0,1.5,0) node[pos=1.2]{$y$}; 
  \draw[->] (0,0,1) -- (0,0,1.5) node[pos=1.2]{$z$};
 \end{scope} 
\end{tikzpicture}
\end{document}
```
![Screen Shot 2021-03-07 at 7.38.36 PM.png](/image?hash=03391fda9c7ee1bdf9296568bdce71b9f1b6e0129e03fa8e917cd6c2ddb5ba79)
1 Answer
