[Tex/LaTex] Shading region of circle with Tikz

Question

I am trying to shade in the area of a circle that is cut into three pieces. Here is the code.

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{tkz-euclide}
\usetikzlibrary{arrows,shadows,positioning, calc, decorations.markings, 
hobby, quotes,angles,decorations.pathreplacing,intersections}
\usepgfplotslibrary{polar}
\usepgflibrary{shapes.geometric}
\usepgfplotslibrary{fillbetween}
\begin{document}

\begin{figure}[ht]

\centering

\begin{tikzpicture}[scale=1.25,line width=1pt]
\begin{axis}[
color= white,
xmin=-15, 
xmax=15, 
ymin=-15, 
ymax=15, 
axis equal image, 
axis lines=middle, 
xticklabels={}, 
yticklabels={},
font=\scriptsize,
ticks=none,
xlabel = {},
ylabel = {},
inner axis line style={stealth-stealth}
]

\draw[black, thick, name path=1] (0,0) circle [radius=12];

\addplot[black, domain=-12:12, samples=300, name path = 1] {sqrt(144-x^2)};

\addplot[black, domain=-12:12, samples=300, name path = 2] {-sqrt(144-x^2)};

\draw[white, name path=3] (-12,0) -- (12,0);

\draw[black, dashed] (-3.179,-11.5713) -- (-3.179,11.5713);

\draw[black, dashed] (3.179,-11.5713) -- (3.179,11.5713);

%\addplot[red, fill opacity=0.20] fill between [of=1 and 2,soft clip= 
{domain=-12:-3.179}];


\end{axis}
\end{tikzpicture}

\caption{Slicing the pie into three pieces of equal area.}

\label{pie}

\end{figure}

\end{document}

Here is the image produced when I leave the last part commented out:

Now, when I uncomment out the last line, this is the result.

While I have the desired shading, the image is now slightly off-center and the axis lines have been drawn, even though I do not want them to. What should I do to fix this?

Answer 1

As for the original question: fillbetween is less "innocent" than one may think, it also sets layers in such a way that the fills are behind the plots. (This is something that I learned from a comment by Stefan Pinnow.) However, the simplest way to get rid of the axes is to say hide axis.

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepgfplotslibrary{fillbetween}
\begin{document}

\begin{figure}[ht]

\centering

\begin{tikzpicture}[scale=1.25,line width=1pt]
\begin{axis}[hide axis,
xmin=-15, 
xmax=15, 
ymin=-15, 
ymax=15, 
axis equal image, 
font=\scriptsize,
]

\draw[black, thick, name path=1] (0,0) circle [radius=12];

\addplot[black, domain=-12:12, samples=300, name path = 1] {sqrt(144-x^2)};

\addplot[black, domain=-12:12, samples=300, name path = 2] {-sqrt(144-x^2)};


\draw[black, dashed] (-3.179,-11.5713) -- (-3.179,11.5713);

\draw[black, dashed] (3.179,-11.5713) -- (3.179,11.5713);

\addplot[red, fill opacity=0.20] fill between [of=1 and 2,soft clip= 
{domain=-12:-3.179}];
\end{axis}
\end{tikzpicture}
\caption{Slicing the pie into three pieces of equal area.}
\label{pie}
\end{figure}
\end{document}

Yet, if you do not want the axes, why don't you just draw the thing with tikz? (In any case, I'd recommend using polar coordinates for that.)

\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\begin{tikzpicture}
\draw[clip] (0,0) circle (6);
\fill[red, fill opacity=0.20] (105:6) rectangle (-6,-6);
\draw[dashed] (105:6) -- (-105:6) (75:6) -- (-75:6);
\end{tikzpicture}
\end{document}

Please note also that one can use the pgfplots library fillbetween, see e.g. here. (I'm not claiming that this answer is particularly original, it is just an example that I had at hand.)

As for your last comment: this is what I suggested

\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\begin{tikzpicture}[thick]
\pgfmathsetmacro{\radius}{4}
\draw[clip] (0,0) circle (\radius);
\fill[red, fill opacity=0.20] (105:\radius) rectangle (-\radius,-\radius);
\fill[blue, fill opacity=0.20] ({-\radius*sin(15)},\radius) rectangle ({\radius*sin(15)},-\radius);
\fill[green, fill opacity=0.20] (75:\radius) rectangle (\radius,-\radius);
\draw[dashed] (105:\radius) -- (-105:\radius) (75:\radius) -- (-75:\radius);
\end{tikzpicture}
\end{document}

and this is what I get