Creating node shapes

Question

I am currently learning how to use TikZ/PGF to make some figures for a project report, and so I have a question:

Is there is a practical way of making a particular object into a node?

The object I have in mind is shown in the Figure below. I want the object to consist in the big circle, the two circular arcs, the label and anchors at north, south, east and west. The dotted lines are simply there to indicate that I am going to have paths going out of these points, which is why I need the anchors there.

I include the source, in the case that it is useful to anyone.

\begin{tikzpicture}
\draw[help lines, gray, dotted] (-2,-2) grid (2,2);

\begin{scope}[shift={ (0,0) } ]
    \begin{scope}[rotate=90]
        \draw[thick] (-1,0) arc[start angle=-90, delta angle=90, %
                              x radius=1, y radius=1] -- (0,1) %NW
                     (0,-1) arc[start angle=180, delta angle=-90, %     
                              x radius=1, y radius=1] -- (1,0); %SE
        \draw[gray] (0,0) circle (1);
    \end{scope}
% Anchor replacements
    \node(N1)       at (0,1)    {};
    \node(S1)       at (0,-1)   {};
    \node(E1)       at (1,0)    {};
    \node(W1)       at (-1,0)   {};
% Label
    \node(Crossing number) at (0,0) {1};
\end{scope}

\path[thick, gray, dotted]
[ out=90,   in=270]     (N1.center) edge (0,2)
[ out=180,  in=0]       (W1.center) edge (-2,0)
[ out=270,  in=90]      (S1.center) edge (0,-2)
[ out=360,  in=180]     (E1.center) edge (2,0);
\end{tikzpicture}

PS. I have had a look at the Manual, but I could not find a description of how to do this.

Answer 1

This is described in section Declaring New Shapes under part The Basic Layer in chapter Nodes and Shapes in the manual (Section 75.5 in v2.10, Section 102.5 in v3.0.0, Section 106.5 in v3.1.9). Some familiarity with PGF (rather than TikZ) is required to draw the node shapes, but once you have worked a bit with the low-level commands it is usually quite easy to add some paths to existing nodes. The hard part of creating nodes is usually the calculations involved for the anchors, but here one can simply inherit them from the circle shape.

Additionally the following code defines the key arc style to modify how the two arcs are drawn (some TikZ specific things like preaction and double won't work).

\documentclass{article}

\usepackage{tikz}

\makeatletter
\tikzset{arc style/.initial={}}
\pgfdeclareshape{circle with arcs}{
    \inheritsavedanchors[from=circle]
    \inheritanchorborder[from=circle]

    \inheritanchor[from=circle]{center}
    \inheritanchor[from=circle]{south}
    \inheritanchor[from=circle]{west}
    \inheritanchor[from=circle]{north}
    \inheritanchor[from=circle]{east}
    % etc.

    \inheritbackgroundpath[from=circle]

    \beforebackgroundpath{
        % get and set options
        \pgfkeys{/tikz/arc style/.get=\tmp}
        \expandafter\tikzset\expandafter{\tmp}
        \tikz@options

        % get radius length and center coordinates
        \radius \pgf@xa=\pgf@x
        \centerpoint \pgf@xb=\pgf@x \pgf@yb=\pgf@y
        
        % draw arc starting from north
        \advance\pgf@yb by\pgf@xa
        \pgfpathmoveto{\pgfpoint{\pgf@xb}{\pgf@yb}}
        \pgfpatharc{180}{270}{\pgf@xa}

        % draw arc starting from south
        \advance\pgf@yb by -2\pgf@xa
        \pgfpathmoveto{\pgfpoint{\pgf@xb}{\pgf@yb}}
        \pgfpatharc{0}{90}{\pgf@xa}

        \pgfusepath{draw}
    }
}
\makeatother

\begin{document}
\begin{tikzpicture}
    \draw[help lines, gray, dotted] (-2,-2) grid (2,2);
    \node[
        circle with arcs,
        draw=gray,
        fill=blue!20,
        minimum width=2cm,
        arc style={black,thick}
        ] (c) {1};
    \draw[thick,gray,dotted]
        (c.north) -- +(0,1)
        (c.east)  -- +(1,0)
        (c.south) -- +(0,-1)
        (c.west)  -- +(-1,0);
\end{tikzpicture}
\end{document}