Shading between curves using polaraxis

Question

I'm using pgfplots and plotting the equations r=1 and r=1-sin(\x/2), but I would like to shade the 3 different regions formed by the curves. I found a link to this bug report asking about using fill between in the polaraxis environment which links to 2 other TeX.SX posts: https://github.com/pgf-tikz/pgfplots/issues/124

This post shades the area containing the origin: Shading between the graphs of two polar equations in pgfplots

This post uses the axis environment instead of the polaraxis environment: Shading a region between two polar curves

Here is the code I'm working with:

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{polar, fillbetween}
\pgfplotsset{compat=newest}
\begin{document}
  \begin{tikzpicture}[scale=1]
    \begin{polaraxis}
      [
      domain=0:360,
      samples=180,
      grid=both,
      grid style={line width=0.1pt, draw=gray!75},
      major grid style={black}, 
      minor x tick num=3,
      minor y tick num=3,
      xmin=0, xmax=360,
      ymin=0, ymax=2.25,
      xtick={0,45,...,360},
      xticklabels={},
      ytick={3},
      yticklabel style={anchor=north},
      ]
      \addplot[draw=red, domain=0:720] {1-sin(\x/2)};
      \addplot[draw=blue, domain=0:360] {1};
    \end{polaraxis}
  \end{tikzpicture}
\end{document}

Answer 1

Here is a method that is not very sophisticated but works.

\documentclass{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{polar, fillbetween}
\pgfplotsset{compat=newest}
\makeatletter
\tikzset{reuse path/.code={\pgfsyssoftpath@setcurrentpath{#1}}}
\makeatother
\begin{document}
  \begin{tikzpicture}[scale=1]
  \pgfplotsset{set layers}
    \begin{polaraxis}
      [axis on top,
      domain=0:360,
      samples=180,
      grid=both,
      grid style={line width=0.1pt, draw=gray!75},
      major grid style={black}, 
      minor x tick num=3,
      minor y tick num=3,
      xmin=0, xmax=360,
      ymin=0, ymax=2.25,
      xtick={0,45,...,360},
      xticklabels={},
      ytick={3},
      yticklabel style={anchor=north},
      ]
      \addplot[draw=red, domain=0:720,save path=\RedPath] {1-sin(\x/2)};
      \addplot[draw=blue, domain=0:360,save path=\BluePath] {1};
      \pgfonlayer{axis background}
       \fill[blue!20,reuse path=\BluePath];
       \fill[red!20,even odd rule,reuse path=\RedPath];
       \clip[reuse path=\BluePath];
       \fill[cyan!20,even odd rule,reuse path=\RedPath];
      \endpgfonlayer
    \end{polaraxis}
  \end{tikzpicture}
\end{document}