Vertically-centering multiple TikZ pictures, preserving baseline height

Question

I've often need to write out equations between pictures, which are drawn using TikZ. However, to display them properly, I have two requirements: any common features must be on the same horizontal line, and the diagrams as a whole must be vertically centered with respect to any = signs separating them.

Here's a picture of the effect I want: Here's a picture of the effect I don't want, but which is easily achieved:

Of course, for a particular diagram, it's just a couple of lines of code to get the effect I want. But ideally, I'd specify the position of the labels - perhaps by setting the baseline of the diagrams to the label A - and then the rest should happen automatically.

There are many ways I can achieve this manually: for example, increasing the size of the bounding box for the smaller diagram to artificially force it to have the same height as the larger one; or manually setting the baseline of the images to exactly the point which I want aligned with the baseline of the = sign. But both of these are fiddly, and none are robust against future changes of the diagrams.

Here's the code to produce the second image above:

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\[
\begin{aligned}
\begin{tikzpicture}
\draw (0,0)
    node [above] {$A$}
    to [out=down, in=down] (1,0)
    node [above] {$A^*$};
\end{tikzpicture}
\end{aligned}
=
\begin{aligned}
\begin{tikzpicture}
\draw (0,0)
    node [above] {$A$}
    to [out=down, in=up] (1,-1)
    to [out=down, in=down] (0,-1)
    to [out=up, in=down] (1,0)
    node [above] {$A^*$};
\end{tikzpicture}
\end{aligned}
\]
\end{document}

Answer 1

Another try. My basic idea is to have a list of the whole equation, then to map over that list so that the tikz pictures are \vcentered to the tallest of the bunch, while the normal mathematical objects are passed as-is. Please note that I haven't tested this (much):

\catcode`@=11
\input lambda.sty
\input tikz

\def\Unravel#1{#1\Unravel@{}}
\def\Unravel@#1{#1\Foldr\Spaceize{}}
\def\Spaceize#1#2{ #1#2}

\newdimen\tallest
\newcount\index

\def\TypesetThem#1{%
  \advance\index by 1
  \TeXif{\ifodd\index }{\vcenter to\tallest{\hbox{$#1$}\vss}}{#1}}

\def\FindTallest#1{%
  \setbox0\vbox{\hbox{$#1$}}%
  \ifdim\dimexpr\ht0+\dp0>\tallest\tallest=\dimexpr\ht0+\dp0\fi}

\def\SameHeight#1{%
  \index=0
  \tallest=0pt
  \Unravel{\Map\FindTallest{#1}}
  \Unravel{\Map\TypesetThem{#1}}}

\def\MyTikZList{\Listize[
  {\tikz\draw (0,0)
    node[above] {$A$}
    to[out=down,in=down] (1,0)
    node[above] {$A^*$};},
  =,
  {\tikz\draw (0,0)
    node[above] {$A$}
    to[out=down,in=up] (1,-1)
    to[out=down,in=down] (0,-1)
    to[out=up,in=down] (1,0)
    node[above] {$A^*$};},
  +,
  {\tikz\draw (0,0)
    node[above] {$A$}
    to[out=down,in=up] (1,-1)
    to[out=down,in=down] (0,-1)
    to[out=up,in=down] (1,0)
    node[above] {$A^*$};},
  -,
  {\tikz\draw (0,0)
    node[above] {$A$}
    to[out=down,in=down] (1,0)
    node[above] {$A^*$};},
  ]}

$$
  \SameHeight\MyTikZList
$$

\bye

The tikz pictures needed to be grouped.

Answer 2

This is not the optimal solution but required manual adjustment is not so much.

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usetikzlibrary{calc}
\begin{document}

An entangled equation and required meaningless text just to justify this sentence length. 
\begin{equation}
\begin{tikzpicture}[baseline=(current bounding box.center)]
\node (A) at (0,0) {\tikz{\draw (0,0)
    node [above] {$A$}
    to [out=down, in=down] (1,0)
    node [above] {$A^*$};}};
\node[anchor=north west] (B) at ($(A.north east)+(1em,0)$) {
\tikz{\draw (0,0)
    node [above] {$A$}
    to [out=down, in=up] (1,-1)
    to [out=down, in=down] (0,-1)
    to [out=up, in=down] (1,0)
    node [above] {$A^*$};
}
};
\node[left] (equa) at (B.west) {=};
\end{tikzpicture}
\end{equation}
\end{document}

Basically you draw two distinct sides of the equation via nodes and then align them from their top limit and squeeze an equal sign in between.

Answer 3

How about \raisebox{-\height/2}{<tikz code>}?

\begin{equation}
    \raisebox{-\height/2}{\begin{tikzpicture}
    \draw (0,0)
        node [above] {$A$}
        to [out=down, in=down] (1,0)
        node [above] {$A^*$};
    \end{tikzpicture}}
    = \raisebox{-\height/2}{\begin{tikzpicture}
    \draw (0,0)
        node [above] {$A$}
        to [out=down, in=up] (1,-1)
        to [out=down, in=down] (0,-1)
        to [out=up, in=down] (1,0)
        node [above] {$A^*$};
    \end{tikzpicture}}
\end{equation}

It's not exactly versatile, i.e. it doesn't allow alignment w.r.t. common features in different TikZ pictures but it certainly manages the vertical alignment (which might be all others stumbling upon this post are looking for).