Stacking plots in animation using fill between library (with dynamic calculation of intersection segments?)

Question

As a followup question to Filling the area under a graph based on intersection with another graph, I'm looking to create the following effect:

• Fill based on the coordinates of the intersection between the two graphs.
• Plots stacked, so area under the normal-curve, but between the two graphs (under normal but above skew) should be cyan!20. The area under the other curve should be green!20.
• None of those graphical anomalies... problem is though, that the first intersection of the graph disappears within the animation and the intersection segments key is completely static (it will always use the n-th intersection of the n-th path, bugger!).

I've fiddled around with the domain key, but I'm getting very underwhelming results. :-(

The intended result I can only reproduce at specific points, not for the entire animation:

Christian Feuersänger suspects a bug, so I've moved the original animation code downward.

\documentclass{article}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{animate}
\pgfmathdeclarefunction{normal}{2}{%
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}
\makeatletter
\pgfmathdeclarefunction{erf}{1}{%
  \begingroup
    \pgfmathparse{#1 > 0 ? 1 : -1}%
    \edef\sign{\pgfmathresult}%
    \pgfmathparse{abs(#1)}%
    \edef\x{\pgfmathresult}%
    \pgfmathparse{1/(1+0.3275911*\x)}%
    \edef\t{\pgfmathresult}%
    \pgfmathparse{%
      1 - (((((1.061405429*\t -1.453152027)*\t) + 1.421413741)*\t 
      -0.284496736)*\t + 0.254829592)*\t*exp(-(\x*\x))}%
    \edef\y{\pgfmathresult}%
    \pgfmathparse{(\sign)*\y}%
    \pgfmath@smuggleone\pgfmathresult%
  \endgroup
}
\makeatother
\pgfmathdeclarefunction{skew}{3}{%
        \pgfmathparse{(exp(-((x-#1)^2)/(2*(#2)^2))*((erf((#3*(x-#1))/(sqrt(2)*#2)))+1))/(sqrt(2*pi)*#2)}%
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
      hide y axis,
      axis lines*=center, 
      axis on top,
      no markers, 
      domain=-1:18, 
      samples=20,
      xlabel=\empty, 
      ylabel=\empty,
      every axis x label/.style={at=(current axis.right of origin),anchor=west},
      every axis y label/.style={at=(current axis.above origin),anchor=south},
      height=5cm, width=12cm,
      xmin = -1, xmax=18,
      xtick=, ytick=\empty,
      enlargelimits=false, 
      clip=false
  ]
  \addplot [name path=normal,very thick,cyan!85!black!50] {normal(10,3.416969)};
  \addplot [name path=skew,very thick,red!85!black!50] {skew(1,4,10)};
  \path [name path=lower, name intersections={of=skew and normal}, intersection segments={of=skew and normal,sequence=B1 -- A2}];
  \path[name path=axis]
(axis cs:\pgfkeysvalueof{/pgfplots/xmin},0) --
(axis cs:\pgfkeysvalueof{/pgfplots/xmax},0);
  \addplot [draw=green!80,fill=green!20] fill between [of=lower and axis, soft clip={(intersection-2) rectangle (axis cs:\pgfkeysvalueof{/pgfplots/xmax},0)}];
\end{axis}
\end{tikzpicture}
\end{document}

---

---

---

\documentclass{article}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
%\usetikzlibrary{calc}
\usepackage{animate}
%\usepackage{fp}
\pgfmathdeclarefunction{normal}{2}{%
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}
\makeatletter
\pgfmathdeclarefunction{erf}{1}{%
  \begingroup
    \pgfmathparse{#1 > 0 ? 1 : -1}%
    \edef\sign{\pgfmathresult}%
    \pgfmathparse{abs(#1)}%
    \edef\x{\pgfmathresult}%
    \pgfmathparse{1/(1+0.3275911*\x)}%
    \edef\t{\pgfmathresult}%
    \pgfmathparse{%
      1 - (((((1.061405429*\t -1.453152027)*\t) + 1.421413741)*\t 
      -0.284496736)*\t + 0.254829592)*\t*exp(-(\x*\x))}%
    \edef\y{\pgfmathresult}%
    \pgfmathparse{(\sign)*\y}%
    \pgfmath@smuggleone\pgfmathresult%
  \endgroup
}
\makeatother
\pgfmathdeclarefunction{skew}{3}{%
        \pgfmathparse{(exp(-((x-#1)^2)/(2*(#2)^2))*((erf((#3*(x-#1))/(sqrt(2)*#2)))+1))/(sqrt(2*pi)*#2)}%
}
\newcommand*{\power}[1]{
\begin{tikzpicture}
\begin{axis}[
      hide y axis,
      axis lines*=center, 
      axis on top,
      no markers, 
      domain=-1:18, 
      samples=20,
      xlabel=\empty, 
      ylabel=\empty,
      every axis x label/.style={at=(current axis.right of origin),anchor=west},
      every axis y label/.style={at=(current axis.above origin),anchor=south},
      height=5cm, width=12cm,
      xmin = -1, xmax=18,
      xtick=, ytick=\empty,
      enlargelimits=false, 
      clip=false
  ]
  \addplot [name path=normal,very thick,cyan!85!black!50] {normal(0.125*#1,3.416969)};
  \addplot [name path=skew,very thick,red!85!black!50] {skew(1,4,10)};
  \path [name path=lower, name intersections={of=skew and normal}, intersection segments={of=skew and normal,sequence=B1 -- A2}];
  \path[name path=axis]
(axis cs:\pgfkeysvalueof{/pgfplots/xmin},0) --
(axis cs:\pgfkeysvalueof{/pgfplots/xmax},0);
  \addplot [draw=cyan!80,fill=cyan!20, stack plots=y] fill between [of=normal and skew,domain=(intersection-2):\pgfkeysvalueof{/pgfplots/xmax}] ;
  \addplot [draw=green!80,fill=green!20, stack plots=y] fill between [of=lower and axis, soft clip={(intersection-2) rectangle (axis cs:\pgfkeysvalueof{/pgfplots/xmax},0)}];
\end{axis}
\end{tikzpicture}
}
\begin{document}
\begin{animateinline}[controls,loop,palindrome]{32}
  \multiframe{94}{ik=32+1}{
    \power{\ik}
    }
    \end{animateinline}
\end{document}

Answer 1

That is a bug in the intersections library of tikz which becomes evident once we show all intersection nodes:

\documentclass{standalone}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\pgfmathdeclarefunction{normal}{2}{%
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}
\makeatletter
\pgfmathdeclarefunction{erf}{1}{%
  \begingroup
    \pgfmathparse{#1 > 0 ? 1 : -1}%
    \edef\sign{\pgfmathresult}%
    \pgfmathparse{abs(#1)}%
    \edef\x{\pgfmathresult}%
    \pgfmathparse{1/(1+0.3275911*\x)}%
    \edef\t{\pgfmathresult}%
    \pgfmathparse{%
      1 - (((((1.061405429*\t -1.453152027)*\t) + 1.421413741)*\t 
      -0.284496736)*\t + 0.254829592)*\t*exp(-(\x*\x))}%
    \edef\y{\pgfmathresult}%
    \pgfmathparse{(\sign)*\y}%
    \pgfmath@smuggleone\pgfmathresult%
  \endgroup
}
\pgfmathdeclarefunction{skew}{3}{%
        \pgfmathparse{(exp(-((x-#1)^2)/(2*(#2)^2))*((erf((#3*(x-#1))/(sqrt(2)*#2)))+1))/(sqrt(2*pi)*#2)}%
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
      hide y axis,
      axis lines*=center, 
      axis on top,
      no markers, 
      domain=-1:18, 
      samples=20,
      xlabel=\empty, 
      ylabel=\empty,
      every axis x label/.style={at=(current axis.right of origin),anchor=west},
      every axis y label/.style={at=(current axis.above origin),anchor=south},
      height=5cm, width=12cm,
      xmin = -1, xmax=18,
      xtick=, ytick=\empty,
      enlargelimits=false, 
      clip=false
  ]
  \addplot [name path=normal,very thick,cyan!85!black!50] {normal(10,3.416969)};
  \addplot [name path=skew,very thick,red!85!black!50] {skew(1,4,10)};
  \path [name intersections={of=skew and normal},font=\tiny] 
    node[draw] at (intersection-1) {1/\pgfintersectionsolutions} 
    node[draw] at (intersection-2) {2/\pgfintersectionsolutions}
    node[draw] at (intersection-3) {3/\pgfintersectionsolutions}
  ;
\end{axis}
\end{tikzpicture}
\end{document}

Apparently, the node 1/3 should not be there at all.

Unfortunately, that makes it hard to find a suitable workaround: if you modify your code such that it uses node 3 instead of 2, your example will fail to compile as soon as you receive a new version of TikZ which contains the fix.