PGFPlots "fill between" causes polar axis to disappear

Question

Having a bit of a tough time figuring out what tikz/pgf want from me here. I've tried a few solutions from previous askers, and still can't seem to get anywhere. When I use \addplot fill between [of=A and B];, my polar axis disappears completely and no shading occurs regardless of other settings like color and opacity. Here's an example:

\begin{tikzpicture}
    \begin{polaraxis}[axis on top,
        xticklabels={,0,$\frac\pi6$,$\frac\pi3$,$\frac\pi2$,$\frac{2\pi}3$,$\frac{5\pi}6$,$\pi$,$\frac{7\pi}6$,$\frac{4\pi}3$,$\frac{3\pi}2$,$\frac{5\pi}3$,$\frac{11\pi}6$}
        ]
    \addplot+[name path = A, mark=none,domain=0:720,samples=600, black] 
        {3*sin(3 * x)};
    \addplot+[name path = B, mark=none,domain=0:720,samples=600, black] 
        {3*cos(3 * x)};]
    % \tikzfillbetween[of=A and B]{gray, opacity=0.5}
    % equivalent to (x,{sin(..)cos(..)}), i.e.
    % the expression is the RADIUS
    \addplot fill between [of=A and B];
    \end{polaraxis}
\end{tikzpicture}

Another asker found a solution with \tikzfillbetween[of=A and B]{gray, opacity=0.5}, but it doesn't seem to do the job of filling the intersection of the two paths, at least in the context of a polar axis (fill between works beautifully in a rectangular axis!). It does great at filling in the union, but I'm looking for the intersection.

For reference, here's a fill between example from elsewhere in the same paper.

I totally understand if it's just not possible given the current version of pgf, but it'd be neat to know for sure. Thanks so much!

Answer 1

Here is a more primitive, yet working way to fill the intersection of both curves.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{polar}
%\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.17}
\makeatletter
\tikzset{reuse path/.code={\pgfsyssoftpath@setcurrentpath{#1}}}
\makeatother
\begin{document}
\begin{tikzpicture}
  \begin{polaraxis}[axis on top,
        xticklabels={,0,$\frac\pi6$,$\frac\pi3$,$\frac\pi2$,$\frac{2\pi}3$,$\frac{5\pi}6$,$\pi$,$\frac{7\pi}6$,$\frac{4\pi}3$,$\frac{3\pi}2$,$\frac{5\pi}3$,$\frac{11\pi}6$}
        ]
    \addplot[save path=\pathA, mark=none,domain=0:720,samples=600, black] 
        {3*sin(3 * x)};
    \addplot[save path=\pathB,  mark=none,domain=0:720,samples=600, black] 
        {3*cos(3 * x)};
    \clip[reuse path=\pathA];
    \fill[gray,opacity=0.5,reuse path=\pathB];
  \end{polaraxis}
\end{tikzpicture}
\end{document}