hf-tikz and references edges: draw in background?

Question

I have managed to draw this thing, which I find quite nice (sorry if it's not so minimal, but I tried to reduce it and having the same problem but it was a bit of a mess...):

\documentclass[11pt]{article}
%
\usepackage[textwidth=16cm]{geometry}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{pgfplots}\pgfplotsset{compat=1.9}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}
\usepackage[customcolors]{hf-tikz} 

\begin{document}

\newcommand{\splat}{\phantom{\bigg|}}
\begin{equation}
    H(\omega) = \frac{\vec{v_o}}{\vec{v_i}} = 
    \hfsetfillcolor{green!10}\hfsetbordercolor{green}
    \tikzmarkin{bp-c}(0,0.6)(0,-0.4)\frac{1}{10}\tikzmarkend{bp-c}\;\; 
    \frac
    {\hfsetfillcolor{blue!10}\hfsetbordercolor{blue}
    \tikzmarkin{bp-z}(0,0.6)(0,-0.3) 1+j\splat\dfrac{\omega}{{10^6}}\tikzmarkend{bp-z}} 
    {\hfsetfillcolor{red!10}\hfsetbordercolor{red}
    \tikzmarkin{bp-p}(0,0.5)(0,-0.4) 1+j\splat\dfrac{\omega}{{5\cdot10^6}}\tikzmarkend{bp-p}} 
\end{equation}

\noindent\begin{tikzpicture}[remember picture]
\begin{axis}[
    width=14cm, height=9cm,
    xmode=log, 
    xmin=1e5,  xmax=1e9,
    domain=1e5:1e9, samples=200,
    ymin=-40, ymax=20,
    grid=both,
    major grid style={black!50},
    xlabel = {angular frequency, $\omega$ (rad/s)},
    ylabel = {$||H(\omega)||$ (dB)},
    ytick = {-40,-20, 0, 20},
    legend style = {nodes=right},
]
    \addplot[thick, green] {-20};
    \addplot[thick, blue] {x<1e6 ? 0 : 20*log10(x/1e6)};
    \addplot[thick, red] {x<5e6 ? 0 : -20*log10(x/5e6)};
    \addplot[ultra thick, densely dashed, black] 
        {x<1e6 ? -20 : (x <5e6 ? -20 +  20*log10(x/1e6) : -20 +  20*log10(x/1e6) - 20*log10(x/5e6)};
        \legend{$1/10$, $1+j\omega/{10^6}$, $(1+j\omega/{5\cdot10^6})^{-1}$, total} 
    \coordinate (line-c) at (axis cs: 2e6, -20);
    \coordinate (line-z) at (axis cs: 2e6, 6);
    \coordinate (line-p) at (axis cs: 6e6, -2);
\end{axis}
\end{tikzpicture}%
\begin{tikzpicture}[
    remember picture, overlay, draw opacity=0.5,>=latex, shorten >=4pt]
    \begin{pgfonlayer}{background}
        \path[red] (bp-p) ++(4em, 0) edge[thick, ->, bend left] (line-p);
        \path[green] (bp-c) ++(0.5em, 0) edge[thick, ->, bend left] (line-c);
        %%% this one should go in background
        \path[blue] (bp-z) ++(0,3ex) edge[thick, ->, bend right] (line-z);
    \end{pgfonlayer}
\end{tikzpicture}
\end{document}

with the result here:

As you can see, I tried to use the technique in this answer to have the arrows (especially the blue one) in background, to no avail.

Is there an easy way to have the blue line going below the equation?

PS: I tried with tikzmarks last release, drawing the arrows before the equation, but it seems that hf-tikz uses its own markers definition and they can be used only after definition. So I gave up...

Answer 1

AFAIK the pgflayers are locally to the current tikzpicture. So I think it is not possible to have the blue edge in the background of the equation. But I would change the path of this edge to not cross the equation. For example

\path[blue] (bp-z) ++(0,3ex) edge[thick, ->,out=175,in=150,looseness=2.5] (line-z); 

results in

Code:

\documentclass[11pt]{article}
%
\usepackage[textwidth=16cm]{geometry}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{pgfplots}\pgfplotsset{compat=1.9}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}
\usepackage[customcolors]{hf-tikz} 

\begin{document}

\newcommand{\splat}{\phantom{\bigg|}}
\begin{equation}
    H(\omega) = \frac{\vec{v_o}}{\vec{v_i}} = 
    \hfsetfillcolor{green!10}\hfsetbordercolor{green}
    \tikzmarkin{bp-c}(0,0.6)(0,-0.4)\frac{1}{10}\tikzmarkend{bp-c}\;\; 
    \frac
    {\hfsetfillcolor{blue!10}\hfsetbordercolor{blue}
    \tikzmarkin{bp-z}(0,0.6)(0,-0.3) 1+j\splat\dfrac{\omega}{{10^6}}\tikzmarkend{bp-z}} 
    {\hfsetfillcolor{red!10}\hfsetbordercolor{red}
    \tikzmarkin{bp-p}(0,0.5)(0,-0.4) 1+j\splat\dfrac{\omega}{{5\cdot10^6}}\tikzmarkend{bp-p}} 
\end{equation}

\noindent\begin{tikzpicture}[remember picture]
\begin{axis}[
    width=14cm, height=9cm,
    xmode=log, 
    xmin=1e5,  xmax=1e9,
    domain=1e5:1e9, samples=200,
    ymin=-40, ymax=20,
    grid=both,
    major grid style={black!50},
    xlabel = {angular frequency, $\omega$ (rad/s)},
    ylabel = {$||H(\omega)||$ (dB)},
    ytick = {-40,-20, 0, 20},
    legend style = {nodes=right},
]
    \addplot[thick, green] {-20};
    \addplot[thick, blue] {x<1e6 ? 0 : 20*log10(x/1e6)};
    \addplot[thick, red] {x<5e6 ? 0 : -20*log10(x/5e6)};
    \addplot[ultra thick, densely dashed, black] 
        {x<1e6 ? -20 : (x <5e6 ? -20 +  20*log10(x/1e6) : -20 +  20*log10(x/1e6) - 20*log10(x/5e6)};
        \legend{$1/10$, $1+j\omega/{10^6}$, $(1+j\omega/{5\cdot10^6})^{-1}$, total} 
    \coordinate (line-c) at (axis cs: 2e6, -20);
    \coordinate (line-z) at (axis cs: 2e6, 6);
    \coordinate (line-p) at (axis cs: 6e6, -2);
\end{axis}
\begin{scope}[
    overlay, draw opacity=0.5,>=latex, shorten >=4pt]
    \begin{pgfonlayer}{background}
        \path[red] (bp-p) ++(4em, 0) edge[thick, ->, bend left] (line-p);
        \path[green] (bp-c) ++(0.5em, 0) edge[thick, ->, bend left] (line-c);
        %%% this one should go in background
        \path[blue] (bp-z) ++(0,3ex) edge[thick, ->,out=175,in=150,looseness=2.5] (line-z);
    \end{pgfonlayer}
\end{scope}
\end{tikzpicture}
\end{document}

Note that the code for the background layer is in the same tikzpicture environment as the axis to put the red arrow behind the legend.

---

As you suggested in a comment it is also possible to use a decoration to interrupt the blue edge. Using

\usetikzlibrary{decorations.pathmorphing}
\tikzset{
  continuous/.style 2 args={
    postaction={draw,solid, decorate,
      decoration={moveto,
        pre=curveto, pre length=#1*\pgfdecoratedremainingdistance,
        post=curveto, post length=#2*\pgfdecoratedremainingdistance
}}}}

and

\path[blue] (bp-z) ++(0,3ex)edge[draw=none,thick, ->, bend right,
  continuous={0.08}{0.65}% first 8% and last 65%  are drawn
](line-z);

results in

Code:

\documentclass[11pt]{article}
\usepackage[textwidth=16cm]{geometry}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{pgfplots}\pgfplotsset{compat=1.9}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}
\usepackage[customcolors]{hf-tikz} 

\usetikzlibrary{decorations.pathmorphing}
\tikzset{
  continuous/.style 2 args={%
    postaction={draw,solid, decorate,
      decoration={moveto,
        pre=curveto, pre length=#1*\pgfdecoratedremainingdistance,
        post=curveto, post length=#2*\pgfdecoratedremainingdistance
}}}}

\begin{document}
\newcommand{\splat}{\phantom{\bigg|}}
\begin{equation}
    H(\omega) = \frac{\vec{v_o}}{\vec{v_i}} = 
    \hfsetfillcolor{green!10}\hfsetbordercolor{green}
    \tikzmarkin{bp-c}(0,0.6)(0,-0.4)\frac{1}{10}\tikzmarkend{bp-c}\;\; 
    \frac
    {\hfsetfillcolor{blue!10}\hfsetbordercolor{blue}
    \tikzmarkin{bp-z}(0,0.6)(0,-0.3) 1+j\splat\dfrac{\omega}{{10^6}}\tikzmarkend{bp-z}} 
    {\hfsetfillcolor{red!10}\hfsetbordercolor{red}
    \tikzmarkin{bp-p}(0,0.5)(0,-0.4) 1+j\splat\dfrac{\omega}{{5\cdot10^6}}\tikzmarkend{bp-p}} 
\end{equation}

\noindent\begin{tikzpicture}[remember picture]
\begin{axis}[
    width=14cm, height=9cm,
    xmode=log, 
    xmin=1e5,  xmax=1e9,
    domain=1e5:1e9, samples=200,
    ymin=-40, ymax=20,
    grid=both,
    major grid style={black!50},
    xlabel = {angular frequency, $\omega$ (rad/s)},
    ylabel = {$||H(\omega)||$ (dB)},
    ytick = {-40,-20, 0, 20},
    legend style = {nodes=right},
]
    \addplot[thick, green] {-20};
    \addplot[thick, blue] {x<1e6 ? 0 : 20*log10(x/1e6)};
    \addplot[thick, red] {x<5e6 ? 0 : -20*log10(x/5e6)};
    \addplot[ultra thick, densely dashed, black] 
        {x<1e6 ? -20 : (x <5e6 ? -20 +  20*log10(x/1e6) : -20 +  20*log10(x/1e6) - 20*log10(x/5e6)};
        \legend{$1/10$, $1+j\omega/{10^6}$, $(1+j\omega/{5\cdot10^6})^{-1}$, total} 
    \coordinate (line-c) at (axis cs: 2e6, -20);
    \coordinate (line-z) at (axis cs: 2e6, 6);
    \coordinate (line-p) at (axis cs: 6e6, -2);
\end{axis}
\begin{scope}[
    remember picture, overlay, draw opacity=0.5,>=latex, shorten >=4pt]
    \begin{pgfonlayer}{background}
        \path[red] (bp-p) ++(4em, 0) edge[thick, ->, bend left] (line-p);
        \path[green] (bp-c) ++(0.5em, 0) edge[thick, ->, bend left] (line-c);
        %%% this one should go in background
        \path[blue] (bp-z) ++(0,3ex)edge[draw=none,thick, ->, bend right,
          continuous={0.08}{0.65}% first 8% and last 65%  are drawn
        ](line-z);
    \end{pgfonlayer}
\end{scope}
\end{tikzpicture}
\end{document}