Centering multiple canvas layers in tikz 3D - TeX

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user 3.14159

The depicted diagram does not seem to be an orthographic projection. One can conceivably reproduce it by choosing appropriate basis vectors.
```
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{arrows.meta,3d}
\begin{document}
\begin{tikzpicture}
 \path (-135:0.5) coordinate (ex) (1,0) coordinate (ey) (0,1) coordinate (ez)
  (0,0) coordinate (O);
 \begin{scope}[x={(ex)},y={(ey)},z={(ez)}]
  \begin{scope}[canvas is xy plane at z=0]
   \draw[dashed,thick] circle[radius=2.75cm];
  \end{scope}
  \begin{scope}[canvas is xy plane at z=2,red]
   \draw[dashed,thick] circle[radius=1.75cm];
   \foreach \X in {0,45,...,315}
    {\draw[-Latex]  (O) --(\X:1.75);}
  \end{scope}
  \begin{scope}[canvas is xy plane at z=-2,blue]
   \draw[dashed,thick] circle[radius=1.75cm];
   \foreach \X in {0,45,...,315}
    {\draw[-Latex]  (O) --(\X:1.75);}
  \end{scope}
  \draw[dashed,very thin,draw=gray] (0,0,2) node[left] {$\hbar$} edge ++ (0,1.75,0)
   (0,0,-2) node[left] {$-\hbar$} edge ++ (0,1.75,0);
  \draw[-Latex]  (O) -- (7,0,0) node[pos=1.2] {$x$}; 
  \draw[-Latex] (O) -- (0,4,0) node[pos=1.1] {$y$};
  \draw[-Latex] (0,0,-4) -- (0,0,4) node[pos=1.05] {$z$};
  \draw[-Latex,thick] (O) -- (0,2.75,0) node[midway,above] {$L$};
 \end{scope}
 \path (-3,3) node[draw]{$\ell=1$};
\end{tikzpicture}
\end{document}
```
![Screen Shot 2020-09-07 at 3.31.38 AM.png](/image?hash=e9825b90cb254adb51417b911fc1ee454574a0925c493e33fe879f1816abf3e0)

Notice that I am not claiming that this choice of `(ex)` yields a perfect reproduction, it is just my first guess. So you may want to play with this basis vector to get a more precise match.

The keys you are referring to are 2d rotations but you'd need 3d rotations. They are, with limitations, implemented for orthographic projections (see e.g. [here](https://tex.stackexchange.com/q/438688)) but not really for general coordinate axes. This is not to say that you cannot do such rotations but working out the visibility, i.e. what is in the foreground and what in the background, become even more cumbersome for these projections.

@marmot If I wanted to change the angle of the cone, such that the cone can be rotated around the x-axis. I added the command `rotate around x=30` or `rotate around={30:(O)}` option in the scope, but clearly it was not the best. Do I change the `canvas`option instead?

Ohh I see. Thank you! I will try and toy with it. Eventually I want to be able to change the angle of the cones (i.e. not aligned to the z-axis). But I feel I might need to change a few more things to obtain that sort of edits.

You could use empirical angles. ``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{arrows.meta,3d} \begin{document} \begin{tikzpicture}[declare function={phix=-135;lx=0.5; tcrit1=87; tcrit2=303;}] \path (phix:lx) coordinate (ex) (1,0) coordinate (ey) (0,1) coordinate (ez) (0,0) coordinate (O); \begin{scope}[x={(ex)},y={(ey)},z={(ez)}] \begin{scope}[canvas is xy plane at z=0] \draw[dashed,thick] circle[radius=2.75cm]; \end{scope} \begin{scope}[canvas is xy plane at z=2,red] \draw[left color=red!50,right color=red!60,middle color=red!10] (tcrit1:1.75) arc[start angle=tcrit1,end angle=tcrit2,radius=1.75] -- (O) -- cycle; \end{scope} \draw[dashed,very thin,draw=gray] (0,0,2) node[left] {$\hbar$} edge ++ (0,1.75,0) (0,0,-2) node[left] {$-\hbar$} edge ++ (0,1.75,0); \draw[-Latex] (O) -- (7,0,0) node[pos=1.2] {$x$}; \draw[-Latex] (O) -- (0,4,0) node[pos=1.1] {$y$}; \draw[-Latex] (0,0,-4) -- (0,0,4) node[pos=1.05] {$z$}; \draw[-Latex,thick] (O) -- (0,2.75,0) node[midway,above] {$L$}; \begin{scope}[canvas is xy plane at z=-2,blue,opacity=0.8] \draw[left color=blue!50,right color=blue!60,middle color=blue!10] (tcrit2-180:1.75) arc[start angle=tcrit2-180,end angle=-tcrit1,radius=1.75] -- (O) -- cycle; \end{scope} \begin{scope}[canvas is xy plane at z=2,red,opacity=0.8] \draw[left color=red!50,right color=red!60,middle color=red!10!black] (tcrit1:1.75) arc[start angle=tcrit1,end angle=tcrit2-360,radius=1.75] -- (O) -- cycle; \end{scope} \end{scope} \path (-3,3) node[draw]{$\ell=1$}; \end{tikzpicture} \end{document} ``` ![Screen Shot 2020-09-07 at 8.09.39 PM.png](/image?hash=3002f507527dcb770acf19bd126e172706703441876d0aa1e7af1a92f85861ef)

In this case this is not entirely trivial because a non-orthographic projection is employed, so it is a bit harder to determine the critical angle, but still doable. (BTW, naively I'd guess that Dave2627=Anonymous 1550 and minhthien_2016=Anonymous 1123.)

The `\foreach` is just a loop so that we do not need to draw each arrow with a separate command. The `\path` command is the command that underlies basically all Ti*k*Z commands such as `\draw`, `\fill`, `\node` and so on. It is just my habit to prefer `\path` over others. Instead of `\path (-3,3) node[draw]{$\ell=1$};` I could have written `\node[draw]{$\ell=1$} at (-3,3);`. `scopes` basically mean that all paths inside the scope inherit the pgf keys specified in the options of the scope. They also delimit the object that are subjected to clips, say.

Can you please explain a bit more what you want to achieve? The picture you show does not seem to be an orthographic projection. One can conceivably reproduce it by adjusting the basis vectors by hand, but then `tikz-3dplot` is sort of "in the way". This raises the question why you do not just go with a real orthographic projection. Anyway, here is a non-orthographic projection that seems to come somewhat close. You can presumably find a perfect match by fiddling with the `(ex)` coordinate. ``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{arrows.meta,3d} \begin{document} \begin{tikzpicture} \path (-135:0.5) coordinate (ex) (1,0) coordinate (ey) (0,1) coordinate (ez) (0,0) coordinate (O); \begin{scope}[x={(ex)},y={(ey)},z={(ez)}] \begin{scope}[canvas is xy plane at z=0] \draw[dashed,thick] circle[radius=2.75cm]; \end{scope} \begin{scope}[canvas is xy plane at z=2,red] \draw[dashed,thick] circle[radius=1.75cm]; \foreach \X in {0,45,...,315} {\draw[-Latex] (O) --(\X:1.75);} \end{scope} \begin{scope}[canvas is xy plane at z=-2,blue] \draw[dashed,thick] circle[radius=1.75cm]; \foreach \X in {0,45,...,315} {\draw[-Latex] (O) --(\X:1.75);} \end{scope} \draw[-Latex] (O) -- (7,0,0) node[pos=1.2] {$x$}; \draw[-Latex] (O) -- (0,4,0) node[pos=1.1] {$y$}; \draw[-Latex] (O) -- (0,0,4) node[pos=1.1] {$z$}; \end{scope} \end{tikzpicture} \end{document} ``` ![Screen Shot 2020-09-07 at 3.11.10 AM.png](/image?hash=221c439085433822aa13e1e1628494b82ee6c09b814b5ee68bf1e58cb346fd58)

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