TiKz Path Exclusion - Compound Shapes (pathfinder functionality)

Question

On Adobe Illustrator, it is very easy to use Pathfinder to create compound shapes by (using the path exclude function with the shape to be retained in the back layer and all paths to be removed in above layers):

Clearly, we can use a basic application of clipping in an attempt to recreate this with Tikz, which works fine if we are not concerned with drawing borders:

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}

%   \clip (0,0) circle (1);

    \fill[red!20] (0,0) circle (1);

    \begin{scope}[rotate=-60]
        \fill[white] (0,-0.1) rectangle (1.5,0.1);
    \end{scope}

    \begin{scope}[rotate=-120]
        \fill[white] (0,-0.1) rectangle (1.5,0.1);
    \end{scope}

    \fill[white] (-1.5,-0.1) rectangle (1.5,0.1);
    
    \end{tikzpicture}
\end{document}

However, if we are concerned with draw borders, it then becomes a lot more interesting and cannot achieve the desired solution easily. Best attempt with a heap of issues (accounting for the line width on the clip (currently it cuts into the line) and overlapping lines from the excluded regions).

\documentclass[12pt,tikz, border = 1cm]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}

    \clip (0,0) circle (1);

    \filldraw[fill=red!10,draw=blue] (0,0) circle (1);

    \begin{scope}[rotate=-60]
        \filldraw[anchor=east,fill=white,draw=blue] (0,-0.1) rectangle (1.5,0.1);
    \end{scope}

    \begin{scope}[rotate=-120]
        \filldraw[anchor=east,fill=white,draw=blue] (0,-0.1) rectangle (1.5,0.1);
    \end{scope}

    \filldraw[fill=white,draw=blue] (-1.5,-0.1) rectangle (1.5,0.1);
    
    \end{tikzpicture}
\end{document}

Is there a way for us to achieve the desired result (first image, second circle with excluded regions but draw available) but with TikZ? Can we maybe do this by clipping a path, then filling that path, but also having that path available to draw?

Answer 1

The spath3 library is very powerful and well suited to this question. But in this particular case, we can get a similar result by cheating with a double line like this:

\documentclass[tikz,border=7pt]{standalone}
\begin{document}
  \begin{tikzpicture}
    \clip[postaction={fill=red!20, draw=blue, thick}]
      (0,0) circle (1cm)
    ;
    \path[draw=blue, double, double distance=2mm]
      (-2,0) -- (2,0)
      (0,0) -- (-60:2)
      (0,0) -- (-120:2)
    ;
  \end{tikzpicture}
\end{document}

Answer 2

Here is a possibility using the spath3 TikZ library and following the steps from Andrew Stacey's excellent answer here. The code is not so short but is repetitive and easy to understand (I hope). We need to create the paths (circle and rectangles), split them at the intersections and then use the appropriate components to draw the desired figure

Something like this:

\documentclass[tikz]{standalone}
\usetikzlibrary{intersections,spath3}

\begin{document}
\begin{tikzpicture}[line cap=round,line join=round]
  \useasboundingbox (-1.2,-1.2) rectangle (1.2,1.2);
  % original paths, not drawn
  \path[spath/save=circle]            (0,0)    circle (1);
  \path[rotate=240,spath/save=rect24] (0,-0.1) rectangle (1.5,0.1);
  \path[rotate=300,spath/save=rect30] (0,-0.1) rectangle (1.5,0.1);
  \path[spath/save=rect00]         (-1.5,-0.1) rectangle (1.5,0.1);
  % spath3 operations
  \tikzset
  {% Circles have an "empty" component at the start which
   % moves from the centre to the rim; it can be irritating
   % when trying to count components later so this removes
   % any empty components
     spath/remove empty components={circle},
   % Now split each path where it intersects with the lines
     spath/split at intersections={circle}{rect00},
     spath/split at intersections={circle}{rect24},
     spath/split at intersections={circle}{rect30},
     spath/split at intersections={rect00}{rect24},
     spath/split at intersections={rect00}{rect30},
     spath/split at intersections={rect24}{rect30},
   % Each path is now a collection of components; to work
   % with them individually we split them into a list of
   % separate paths which is stored in a macro
     spath/get components of={circle}\Ccpts,
     spath/get components of={rect00}\Rcpts,
     spath/get components of={rect24}\Scpts,
     spath/get components of={rect30}\Tcpts,
  }
  \draw[fill=red!10,draw=blue,
        spath/use=\getComponentOf\Ccpts{1},
        spath/use={\getComponentOf\Rcpts{2},weld}
       ];
  \draw[fill=red!10,draw=blue,
        spath/use=\getComponentOf\Ccpts{3},
        spath/use={\getComponentOf\Scpts{3},weld},
        spath/use={\getComponentOf\Rcpts{8},weld},
       ];
  \draw[fill=red!10,draw=blue,
        spath/use=\getComponentOf\Ccpts{5},
        spath/use={\getComponentOf\Tcpts{3},weld},
        spath/use={\getComponentOf\Scpts{7},weld}
       ];
  \draw[fill=red!10,draw=blue,
        spath/use=\getComponentOf\Ccpts{7},
        spath/use={\getComponentOf\Rcpts{4},weld},
        spath/use={\getComponentOf\Tcpts{7},weld}
       ];
\end{tikzpicture}
\end{document}

Remark: the last (straight) line of each sector could be drawn with the cycle option, but I did it this way to see the spath3 library working.