How to combine equations and tikz to get helpful notes at equations?

Question

Is there any way to combine the helpful syntax of align environments with the graphical options of tikz? I am looking to reproduce equations that look like this picture:

First equation:

\begin{align*}
    a^2=\Big(b\cdot \sin(\alpha)\Big)^2+n^2
\end{align*}

Second equation (the cloud one):

\begin{align*}
    h=b\cdot \sin(\alpha)
\end{align*}

Obviously it is rather hard to produce the exact same result. I would also be happy with an equation in a box with an arrow pointing to the =.

Do you have a good idea how to do it? With nodes it turned out pretty bad.

Answer 1

Here's a TikZ solution without tikzmark that uses amsmath's \overset/\underset/\overunderset.

While this doesn't produce a nice cloud yet it is the base of further customization, for example, like the one by Heiko Oberdiek.

For now, I settled on a rounded rectangle, gray color and smaller text. By default, amsmath sets the over- and undersets in \scriptstyle which we could do, too, but I don't think it looks good.

Code

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\tikzset{
  cloud eq/.cd,
  edge/.style={rounded corners=+2pt, arrows=Latex[round]-},
  c/.style={cloud eq/edge,anchor=north,to path={--++( +0pt,+-2ex)\tikztonodes}},
  l/.style={cloud eq/edge,anchor=east, to path={|-++(+-1ex,+-2ex)\tikztonodes}},
  r/.style={cloud eq/edge,anchor=west, to path={|-++( +1ex,+-2ex)\tikztonodes}},
  node/.style={at end, draw, rounded corners=+1pt}
}
\newcommand*\tikzoverunderInternal[3]{%
  \tikz[trim left=+0pt, trim right=+0pt]
  \draw[cloud eq/#1, #2] (0,0) to node[cloud eq/node] {$#3$}();}
\NewDocumentCommand\tikzUnderset{ O{l} m }{
  \underset{\tikzoverunderInternal{#1}{}{#2}}}
\NewDocumentCommand\tikzOverset { O{l} m }{
  \overset{\tikzoverunderInternal{#1}{yscale=-1.2}{#2}}}
\NewDocumentCommand\tikzOverUnder {O{l} m O{r} m}{
  \overunderset{
    \tikzoverunderInternal{#3}{yscale=-1.2}{#4}}{
    \tikzoverunderInternal{#1}{}{#2}}}
\usepackage{blindtext}

\tikzset{
  cloud eq/node/.append style={scale=.7},
  cloud eq/edge/.append style=gray}
\begin{document}
\blindtext
\begin{align}
    a^2 & \tikzUnderset{h = b \cdot \sin\alpha}{=}
            (b \cdot \sin \alpha)^2 \tikzOverset[r]{a+b}{+} n^2 \\
    c^2 & \tikzUnderset[c]{\vphantom{\int_i} E=mc^2}{=}
            a^2 + b^2 \tikzOverUnder[c]{\int_i e^i}
                           [r, overlay]{a^2 >0, b^2>0}{>} 0
\end{align}
\blindtext
\end{document}

Output

Answer 2

You could use this command I made using some code that someone help mi eith in one question I made Math notes between equations

This is the command I made out of the post:

\NewDocumentCommand{\umathnote}{ mm }
   {
     \overset % ❶
        {% The annotation goes above
          \textcolor{black!20!white}{\hbox to 0pt{\hss % ❷
             $ % return to math mode
               \begin{array}{c} % ❸
                   \displaystyle #2\\ % ❹
                   \Big\downarrow % ❺
               \end{array}
             $
          \hss}
          }
        }
        {#1} % 
   }
   
\NewDocumentCommand{\dmathnote}{ mm }
   {
     \underset % ❶
        {% The annotation goes above
          \textcolor{black!20!white}{\hbox to 0pt{\hss % ❷
             $ % return to math mode
               \begin{array}{c} % ❸
                   \Big\uparrow\\ % ❹
                   \displaystyle #2 % ❺
               \end{array}
             $
          \hss}
          }
        }
        {#1} % 
   }

You can see the results here: math note command