Drawing a picture without overlay of the grid

Question

The following TikZ code produces the image below. It's a tiny detail but I do not want the 3pt thick black lines to be overlayed by the grid. However, if I place the grid before, then the interior part of the yellow fill does not have the grid anymore. Ideally I would like to have this order of appearance : the exterior part of the 3pt line (which appears on the image below) > yellow fill > grid. However, this seems to impose to be able to draw directly the appearing 3pt line, which I did not manage to do : I draw to circles and then fill above in the interior part. Thanks for any help !

\begin{tikzpicture}
\draw [line width = 3pt] (0.5,0) circle (1.5cm);
\draw [line width = 3pt] (-0.5,0) circle (1.5cm);
\fill [yellow] (0.5,0) circle (1.5cm);
\fill [yellow] (-0.5,0) circle (1.5cm);
\draw[step=5mm, help lines, color=gray!30] (-2.9,-2.9) grid (2.9,2.9);
\draw[->,thick] (-3,0)--(3,0) node[right]{$x$};
\draw[->,thick] (0,-3)--(0,3) node[above]{$y$};
\end{tikzpicture}

Answer 1

Your yellow fill covers half of your line. I preserve this by doing it like this. To make the grid on top of the yellow fill, simply draw it again, but only inside the same area like this:

\documentclass[tikz, border = 1cm] {standalone}
\begin{document}    
\begin{tikzpicture}
\draw[step=5mm, help lines, color=gray!30] (-2.9,-2.9) grid (2.9,2.9);
\draw [line width = 3pt] (0.5,0) circle (1.5cm);
\draw [line width = 3pt] (-0.5,0) circle (1.5cm);
\fill [yellow] (0.5,0) circle (1.5cm);
\fill [yellow] (-0.5,0) circle (1.5cm);
\begin{scope}
\clip(-0.5,0) circle (1.5cm) (0.5,0) circle (1.5cm);
\draw[step=5mm, help lines, color=gray!30] (-2.9,-2.9) grid (2.9,2.9);
\end{scope}
\draw[->,thick] (-3,0)--(3,0) node[right]{$x$};
\draw[->,thick] (0,-3)--(0,3) node[above]{$y$};
\end{tikzpicture}
\end{document}

Answer 2

I propose to use clipping when drawing the black outline.

\documentclass[tikz, border=0mm]{standalone}
\usetikzlibrary{backgrounds} % for the green background filling

\begin{document}
\begin{tikzpicture}[background rectangle/.style={fill=green!10},
                    show background rectangle]
\fill[yellow] (0.5,0) circle[radius=1.5cm]
              (-0.5,0) circle[radius=1.5cm];
\draw[step=5mm, help lines, color=gray!30] (-2.9,-2.9) grid (2.9,2.9);

\begin{scope}[line width=3pt, radius=1.5cm]
  \begin{scope}
    \clip (0,-2.9) rectangle (2.9,2.9);
    \draw (0.5,0) circle;
  \end{scope}
  \begin{scope}
    \clip (0,-2.9) rectangle (-2.9,2.9);
    \draw (-0.5,0) circle;
  \end{scope}
\end{scope}

\draw[->, thick] (-3,0) -- (3,0) node[right] {$x$};
\draw[->, thick] (0,-3) -- (0,3) node[above] {$y$};
\end{tikzpicture}
\end{document}

Answer 3

Other possibility is drawing the figure using only one \path command. I did it with a \pic but this is not necessary.

Then I offer you two posibities:

1. Setting an fill opacity.
2. Playing with the order of the elements (fill, grid, draw).

Something like this:

\documentclass[tikz,border=2mm]{standalone}

\pgfmathsetmacro\a{atan(3)} % angle
\tikzset
{%
  pics/double circle/.style={
    code={%
      \path[pic actions] (0,{1.5*sin(\a)}) arc (\a:360-\a:1.5cm) arc (180+\a:540-\a:1.5);
    }},
}

\begin{document}
\begin{tikzpicture}
% option 1, opacity
\node at (0,-3) [below] {first};
\draw[step=5mm, help lines, color=gray!30] (-2.9,-2.9) grid (2.9,2.9);
\pic [draw,line width=3pt,fill=yellow,fill opacity=0.5] {double circle};
\draw[->,thick] (-3,0)--(3,0) node[right]{$x$};
\draw[->,thick] (0,-3)--(0,3) node[above]{$y$};
% option 2, playing with the order
\begin{scope}[shift={(7,0)}]
\pic [fill=yellow] {double circle};
\draw[step=5mm, help lines, color=gray!30] (-2.9,-2.9) grid (2.9,2.9);
\draw[->,thick] (-3,0)--(3,0) node[right]{$x$};
\draw[->,thick] (0,-3)--(0,3) node[above]{$y$};
\pic [draw,line width=3pt] {double circle};
\node at (0,-3) [below] {second};
\end{scope}
\end{tikzpicture}
\end{document}

Answer 4

You can calculate start and end angle of arc (cos^{-1}{-0.5/1.5}, cos^{-1}{0.5/1.5}, etc. and draw arcus after grid:

\documentclass[border=3.141592]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
\fill [yellow] (0.5,0) circle (1.5cm);
\fill [yellow] (-0.5,0) circle (1.5cm);
\draw[step=5mm, help lines, color=gray!30] (-2.9,-2.9) grid (2.9,2.9);
%
\draw [line width = 3pt] (+0.5,0) ++ (109.47:1.5) arc (109.47:-109.47:1.5);
\draw [line width = 3pt] (-0.5,0) ++ ( 70.53:1.5) arc ( 70.53:+289.47:1.5);
% axis
\draw[->,thick] (-3,0)--(3,0) node[right]{$x$};
\draw[->,thick] (0,-3)--(0,3) node[above]{$y$};
\end{tikzpicture}
\end{document}