Beamer, TikZ and step by step colored figure ending in PGF Math Error (divide by 0)

Question

I'm new to TikZ, and I'm trying to "animate" successive reading of values on the curve representing a mathematical function. The point is to achieve step by step visual enhancement to focus the care of my pupils.

The joint code compiles successfully, in this precise state. Uncomment lines 57 to 65, this compiles again (but if you start trying to compile directly with the lines 57 to 65 uncommented, it does not). Now uncomment the lines commented out twice, the code does not compile. I'm not enough skilled to understand why. I hope somebody will be able to explain why, and ideally find a workaround or a better way to achieve my goal. Thanks a lot in advance !

[EDIT] The problem seems to be related to the angle options.

\draw [->, >=latex, very thick,color=blue!60] (xO) to[out=80,in=100] (yO) ;
\draw [->, >=latex, very thick,color=blue!60] (fxO) to[out=280,in=260] (fyO) ;

seems to make the thing works. [/EDIT]

Regards,

natsirt

\documentclass{beamer}
\usepackage{mathrsfs,tikz}
\usetikzlibrary{arrows,arrows.meta,bending}

\makeatletter
\renewcommand*{\@textcolor}[3]{%
  \protect\leavevmode
  \begingroup
    \color#1{#2}#3%
  \endgroup
}
\makeatother
\newcommand{\mathcolor}[2][green]{\relax\ifmmode\textcolor{#1}{#2}\else\textcolor{#1}{$#2$}\fi}

\newcommand{\mr}[1]{\mathcolor[red]{#1}}
\newcommand{\mg}[1]{\mathcolor{#1}}


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


\begin{document}

\begin{frame}

Bla \pause Bla \pause

  \begin{center}
    \begin{tikzpicture}
      % Garder une figure stable avec Beamer / empêcher les dessins de sauter :
      % http://tex.stackexchange.com/questions/61260/keep-a-fragmented-tikz-image-at-the-same-place-on-a-beamer-slide
      % http://tex.stackexchange.com/questions/18704/how-can-i-fix-jumping-tikz-pictures-in-beamer
      \path[use as bounding box] (-5,-1) rectangle(6,5);
      % La graduation 1 horizontale
      \alt<4>{\draw [very thick, red] (1,-.75ex) -- node [below=.3ex] {$1$} (1,.75ex) ; }{\draw [very thick] (1,-.75ex) -- node [below=.3ex] {$1$} (1,.75ex) ; }
      \draw [very thick] (-.6ex,1) -- node [left=.3ex] {$1$} (.6ex,1) ;
      % Le grille
      \draw[help lines, color=gray, dashed] (-.2,-.2) grid (4.1,4.1);
      % Les axes
      \draw [-Stealth,ultra thick] (-.2,0)--(4.1,0) node[below] {$x$} ;
      \draw[-Stealth,ultra thick] (0,-.2)--(0,4.1) node[left] {$y$};
      % La courbe
      \draw [very thick, blue] plot [smooth] coordinates {(0,0) (1,4) (2.5,1) (4,2)} ;
      % Le nom de la courbe
      \node [blue] at (3.5,2) {$\mathscr{C}_f$} ;
      % Les points de la courbe
      \foreach \pos/\point in {(0,0)/O, (1,4)/A, (2.5,1)/B, (4,2)/C}{\draw node[green,label={[color=green,xshift=-.8ex,yshift=1ex]280:\point} ]%  below:$\point$]
       at \pos {\Large +}; }
      % Les affichages successifs
      % Le point O
      \uncover<3->{\node [right] at (-3,4) { $O( \tikz[baseline] { \node[anchor=base] (xO) { \alt<3>{\mg{0}}{$0$} } ; } \,; 
                                                 \tikz[baseline] { \node[anchor=base] (yO) { \alt<3>{\mr{0}}{$0$} } ; } 
                                              )$ } ;
                   \node [right] at (-3,3) { $f( \tikz[baseline] { \node[anchor=base] (fxO) { \alt<3>{\mg{0}}{$0$} } ; } ) =
                                                 \tikz[baseline] { \node[anchor=base] (fyO) { \alt<3>{\mr{0}}{$0$} } ; } 
                                             $ } ;
%                    \alt<3>{\draw [->, >=latex, very thick,color=blue!60] (xO) to[out=90,in=90] (yO) ;
%                            \draw [->, >=latex, very thick,color=blue!60] (fxO) to[out=270,in=270] (fyO) ;
%                            \draw [->, >=latex,very thick,dotted,color=green!80] (fxO) to[out=270,in=270] (0,-.3) ;
%                            \draw [->, >=latex,very thick,dotted,color=red!80] (fyO) to[out=0,in=180] (-.3,0) ;
%                            \draw node[green,label={[color=white,xshift=-.8ex,yshift=1ex,opacity=.75]280:O}] at (0,0) {\Large +} ;
%                            \node[green,below right] at (0,0) {$0$} ;
%                            \node[red,above left] at (0,0) {$0$} ; }
%                            {}
       }
% %        \uncover<4->{\draw [->, >=latex, very thick, dashed, color=blue!60] (1,0) -- (1,4) -- (0,4) ;
% %                    \node [right] at (-3,1) { $A( \tikz[baseline] { \node[anchor=base] (xA) { \alt<4>{\mg{1}}{$1$} } ; } \,; 
% %                                                  \tikz[baseline] { \node[anchor=base] (yA) { \alt<4>{\mr{4}}{$4$} } ; } 
% %                                               )$ } ;
% %                    \node [right] at (-3,0) { $f( \tikz[baseline]{ \node[anchor=base] (fxA) { \alt<3>{\mg{1}}{$1$} } ; } ) =
% %                                                  \tikz[baseline]{ \node[anchor=base] (fyA) { \alt<3>{\mr{4}}{$4$} } ; } 
% %                                              $ } ;
% %                    \alt<4>{\draw [->, >=latex, very thick,color=blue!60] (xA) to[out=90,in=90] (yA) ;
% %                            \draw [->, >=latex, very thick,color=blue!60] (fxA) to[out=270,in=270] (fyA) ; }
% %                           {}
% %        }
    \end{tikzpicture}
  \end{center}
\end{frame}

\end{document}

Answer 1

Nesting tikzpictures generally spells trouble. Sometimes it works, but you can't complain they didn't warn you if it breaks. Therefore, it should be considered only as a last resort. In this case, the code is safer and simpler if the tikzmark library is used to support the \subnode{}{} syntax. The first argument is the name. The second the content.

Note that information about the subnodes is always one compilation behind. Therefore, you may get errors on first compilation if, for example, using the distance between subnodes in a calculation because all subnodes will be, by default at one place. So you can easily end up dividing by zero which TikZ cannot (unsurprisingly) do.

Here's your example with subnodes. I've also updated to use the \tikzset syntax rather than the deprecated \tikzstyle.

\documentclass{beamer}
\usepackage{mathrsfs,tikz}
\usetikzlibrary{arrows,arrows.meta,bending,tikzmark}
\makeatletter
\renewcommand*{\@textcolor}[3]{%
  \protect\leavevmode
  \begingroup
    \color#1{#2}#3%
  \endgroup
}
\makeatother
\newcommand{\mathcolor}[2][green]{\relax\ifmmode\textcolor{#1}{#2}\else\textcolor{#1}{$#2$}\fi}
\newcommand{\mr}[1]{\mathcolor[red]{#1}}
\newcommand{\mg}[1]{\mathcolor{#1}}
\tikzset{% update syntax
  every picture/.append style = {remember picture},
}

\begin{document}
\begin{frame}
Bla \pause Bla \pause
\begin{center}
  \begin{tikzpicture}
    % Garder une figure stable avec Beamer / empêcher les dessins de sauter :
    % http://tex.stackexchange.com/questions/61260/keep-a-fragmented-tikz-image-at-the-same-place-on-a-beamer-slide
    % http://tex.stackexchange.com/questions/18704/how-can-i-fix-jumping-tikz-pictures-in-beamer
    \path[use as bounding box] (-5,-1) rectangle(6,5);
    % La graduation 1 horizontale
    \alt<4>{\draw [very thick, red] (1,-.75ex) -- node [below=.3ex] {$1$} (1,.75ex) ; }{\draw [very thick] (1,-.75ex) -- node [below=.3ex] {$1$} (1,.75ex) ; }
    \draw [very thick] (-.6ex,1) -- node [left=.3ex] {$1$} (.6ex,1) ;
    % Le grille
    \draw[help lines, color=gray, dashed] (-.2,-.2) grid (4.1,4.1);
    % Les axes
    \draw [-Stealth,ultra thick] (-.2,0)--(4.1,0) node[below] {$x$} ;
    \draw[-Stealth,ultra thick] (0,-.2)--(0,4.1) node[left] {$y$};
    % La courbe
    \draw [very thick, blue] plot [smooth] coordinates {(0,0) (1,4) (2.5,1) (4,2)} ;
    % Le nom de la courbe
    \node [blue] at (3.5,2) {$\mathscr{C}_f$} ;
    % Les points de la courbe
    \foreach \pos/\point in {(0,0)/O, (1,4)/A, (2.5,1)/B, (4,2)/C}{\draw node[green,label={[color=green,xshift=-.8ex,yshift=1ex]280:\point} ]%  below:$\point$]
      at \pos {\Large +}; }
    % Les affichages successifs
    % Le point O
    \uncover<3->{%
      \node [right] at (-3,4) { $O( \subnode{xO}{ \alt<3>{\mg{0}}{$0$} } \,;  \subnode{yO}{ \alt<3>{\mr{0}}{$0$} }  )$ } ;
    \node [right] at (-3,3) { $f( \subnode{fxO}{ \alt<3>{\mg{0}}{$0$} } ) = \subnode{fyO}{ \alt<3>{\mr{0}}{$0$} }  $ } ;
      \alt<3>{\draw [->, >=latex, very thick,color=blue!60] (xO) to[out=90,in=90] (yO) ;
        \draw [->, >=latex, very thick,color=blue!60] (fxO) to[out=270,in=270] (fyO) ;
        \draw [->, >=latex,very thick,dotted,color=green!80] (fxO) to[out=270,in=270] (0,-.3) ;
        \draw [->, >=latex,very thick,dotted,color=red!80] (fyO) to[out=0,in=180] (-.3,0) ;
        \draw node[green,label={[color=white,xshift=-.8ex,yshift=1ex,opacity=.75]280:O}] at (0,0) {\Large +} ;
        \node[green,below right] at (0,0) {$0$} ;
        \node[red,above left] at (0,0) {$0$} ; }
      {}
    }
    \uncover<4->{%
      \draw [->, >=latex, very thick, dashed, color=blue!60] (1,0) -- (1,4) -- (0,4) ;
      \node [right] at (-3,1) { $A(   \subnode{xA}{ \alt<4>{\mg{1}}{$1$} } \,; \subnode{yA}{ \alt<4>{\mr{4}}{$4$} } )$ } ;
      \node [right] at (-3,0) { $f( \subnode{fxA}{ \alt<3>{\mg{1}}{$1$} } ) = \subnode{fyA}{ \alt<3>{\mr{4}}{$4$} } $ } ;
      \alt<4>{%
        \draw [->, >=latex, very thick,color=blue!60] (xA) to[out=90,in=90] (yA) ;
        \draw [->, >=latex, very thick,color=blue!60] (fxA) to[out=270,in=270] (fyA) ;
      }
      {}
    }
  \end{tikzpicture}
\end{center}
\end{frame}
\end{document}