labelling with arrows in an automated way

Question

In adding-labels-to-a-formula is a tikz scheme that puts rounded boxes around parts of an equation so that they can be labelled. It looks nicer than plain old \underbrace, and can be automated without too much trouble. Here is an example with latex commands to do this tikz stuff without having to worry about the details:

\documentclass{article}

\usepackage{tikz}
\usepackage{amsmath}

% formula, text, node#
\newcommand{\mathWithDescription}[3]{%
\tikz[baseline]{%
    \node[draw=red,rounded corners,anchor=base] (m#3)%
    {$\displaystyle#1$};%
    \node[above of=m#3] (l#3) {#2};%
    \draw[-,red] (l#3) -- (m#3);%
}%
}

\newcounter{mathLableNode}

\newcommand{\mathLabelBox}[2]{%
   \stepcounter{mathLableNode}%
   \mathWithDescription{#1}{#2}{\themathLableNode}%
}

\begin{document}

\begin{equation}
\boldsymbol{\nabla}^2 = 
\mathLabelBox{
\frac{\partial^2}{\partial r^2} + \frac{1}{r} \frac{\partial}{\partial r}{}
}{$\boldsymbol{\nabla}_{\mathrm{T}}^2$}
+ \frac{1}{r^2} \frac{\partial^2}{\partial \theta^2}
+ \frac{\partial^2}{\partial z^2}
\end{equation}

\begin{equation}
\mathbf{E} = 
\mathLabelBox{
\mathbf{E}_0
}{A vector, with a chosen polarity}
\mathLabelBox{
u(r, \theta, z) 
}{
Slowly varying (complex) envelope
}
e^{i k_0 z}.
\end{equation}

\end{document}

I can use this \mathLabelBox{}{} as a one-for-one replacement for \underbrace{}_{}. Here's what the example latex yields:

I think it looks quite nice for short formulas (equation (1)), but not for short ones that have long text (equation (2)).

What would look a lot better is to stuff the text off to the side and draw arrows to the elements. I see this is possible with tikz too, and copying from the beamer arrows page something like the following can be produced

This was produced with the following MWE

% from http://www.texample.net/tikz/examples/beamer-arrows/ (switching to article class)

\documentclass{article} %
\usepackage{tikz}
\usepackage{amsmath}
\usetikzlibrary{arrows,shapes}

\begin{document}
\tikzstyle{every picture}+=[remember picture]

\begin{itemize}%[<+-| alert@+>]
    \item Coriolis acceleration
        \tikz \node[coordinate] (n1) {};
\end{itemize}

\begin{equation*}
\vec{a}_p = \vec{a}_o+\frac{d^2}{dt^2}\vec{r} +
        \tikz[baseline]{
            \node[fill=blue!20,anchor=base] (t1)
            {$ 2\vec{\omega}_{ib}\times\frac{d}{dt}\vec{r}$};
        } +
        \tikz[baseline]{
            \node[fill=red!20, ellipse,anchor=base] (t2)
            {$\vec{\alpha}_{ib}\times\vec{r}$};
        } +
        \tikz[baseline]{
            \node[fill=green!20,anchor=base] (t3)
            {$\vec{\omega}_{ib}\times(\vec{\omega}_{ib}\times\vec{r})$};
        }
\end{equation*}

\begin{itemize}
    \item Transversal acceleration
        \tikz\node [coordinate] (n2) {};
    \item Centripetal acceleration
        \tikz\node [coordinate] (n3) {};
\end{itemize}

\begin{tikzpicture}[overlay]
        \path[->] (n1) edge [bend left] (t1);
        \path[->] (n2) edge [bend right] (t2);
%        \path[->] (n3) edge [out=0, in=-90] (t3);
        \path[->] (n3) edge [bend right] (t3);
\end{tikzpicture}

\end{document}

but wasn't something that looked easy to automate like the simpler tikz I've used above. (EDIT note: on adding the MWE above, it doesn't look as bad as I originally thought ... a lot of the complexity was actually due to the beamer specific stuff).

I'd like to have an \underbrace like command like my \mathLabelBox that incorporates the spline arrows in the beamer examples? Is there an easier way to do this than the multi-part code in example taken from the beamer arrows page above?

Answer 1

Code

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\newif\ifclipme\clipmetrue
\tikzset{labelstyle/.style={LabelStyle/.append style={#1}},linestyle/.style={LineStyle/.append style={#1}}}
\tikzset{LabelStyle/.initial={},LineStyle/.initial={}}

\newcommand{\mathWithDescription}[4][]{{%
    \tikzset{#1}%
    \tikz[baseline]{
        \node[draw=red,rounded corners,anchor=base] (m#4) {$\displaystyle#2$};
        \ifclipme\begin{pgfinterruptboundingbox}\fi
            \node[above of=m#4,font=\strut, LabelStyle] (l#4) {#3};
            \draw[-,red, LineStyle] (l#4) to (m#4);
        \ifclipme\end{pgfinterruptboundingbox}\fi
    }%
}}
\newcommand{\mathWithDescriptionStarred}[3][]{{%
    \clipmefalse%
    \mathWithDescription[#1]{#2}{#3}{\themathLableNode}%
}}

\newcounter{mathLableNode}
\newcommand{\mathLabelBox}[3][]{%
   \stepcounter{mathLableNode}%
   \mathWithDescription[#1]{#2}{#3}{\themathLableNode}%
   \vphantom{\mathWithDescriptionStarred[#1]{#2}{#3}{\themathLableNode}}%
}

\begin{document}
\begin{equation}
\boldsymbol{\nabla}^2 = \mathLabelBox{\frac{\partial^2}{\partial r^2} + \frac{1}{r} \frac{\partial}{\partial r}}
                                     {$\boldsymbol{\nabla}_{\mathrm{T}}^2$}
                        + \frac{1}{r^2} \frac{\partial^2}{\partial \theta^2} + \frac{\partial^2}{\partial z^2}
\end{equation}

\begin{equation}
\mathbf{E} =
\mathLabelBox[
    labelstyle={yshift=1.2em},
    linestyle={}
    ]{\mathbf{E}_0}{A vector, with a chosen polarity} \cdot
\mathLabelBox[
    labelstyle={xshift=2cm},
    linestyle={out=270,in=90, latex-}
    ]{u(r, \theta, z)}{Slowly varying (complex) envelope} \cdot e^{i k_0 z}.
\end{equation}
\end{document}

Output

A simple example

Code

\begin{equation}
\mathbf{E} = \mathLabelBox{\mathbf{E}_0}{A vector, with a chosen polarity} \cdot
             \mathLabelBox[labelstyle={below of=m\themathLableNode,below of=m\themathLableNode}]{u(r, \theta, z)}{Slowly varying (complex) envelope} \cdot e^{i k_0 z}.
\end{equation}

Output