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Given a graph like the one on the right side of the picture below, I want to draw a ribbon graph (that is, a "thickened" version of the graph) like the one on the left.

I already drew the graph using Bézier curves but I don't think the best way to approach the ribbon graph would be using Bézier curves. How could I do it?

Below we have my drawing of the graph:

begin{tikzpicture}

useasboundingbox (-2,-2) rectangle (2,2.5);

begin{scope}[very thick,decoration={

markings,

mark=at position 0.3 with {arrow{>}}}

] 

draw[ultra thick,postaction={decorate}] (0,0) .. controls +(60:3) and +(120:3) .. (0,0);

draw[ultra thick,postaction={decorate}] (0,0) .. controls +(-60:3) and +(-120:3) .. (0,0);

end{scope}

begin{scope}[very thick,decoration={

markings,

mark=at position 0.5 with {arrow{>}}}

] 

draw[ultra thick,postaction={decorate}] (0,0) -- (-1,0) .. controls +(180:1) and +(180:2) .. (0,2.5)

                                                    .. controls +(0:2) and +(0:1) .. (1,0) -- (0,0);

end{scope}

fill[fill=black] (0,0) circle (3pt);

end{tikzpicture}

I do not know if it is time consuming to draw this. For me it would be probably more time-consuming to try to understand the abstract question behind this. If there is a clear, general question, please let me now, otherwise you may want to look at

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{decorations.markings}

begin{document}

begin{tikzpicture}[insert arrow/.style={decoration={

markings,

mark=at position 0.3 with {arrow{>}}}}]

useasboundingbox (-2,-2) rectangle (2,2.5);

draw[fill=gray!20] (0,1) + (-40:2) arc(-40:220:2) to[out=-50,in=45] (200:1)

arc(135:405:1.3) to[out=135,in=-140] cycle;

begin{scope}[very thick,insert arrow=0.3] 

draw[ultra thick,postaction={decorate}] (0,0) .. controls +(60:3) and +(120:3) .. (0,0);

draw[ultra thick,postaction={decorate}] (0,0) .. controls +(-60:3) and +(-120:3) .. (0,0);

end{scope}

begin{scope}[very thick,insert arrow=0.5] 

draw[ultra thick,postaction={decorate}] (0,0) -- (-1,0) .. controls +(180:1) and +(180:2) .. (0,2.5)

                                                    .. controls +(0:2) and +(0:1) .. (1,0) -- (0,0);

end{scope}

fill[fill=black] (0,0) circle (3pt);

draw[fill=white] (0,1.2)+(-30:1.1) arc(-30:210:1.1) to[out=-60,in=-60,looseness=2] ++(0.1,0)

arc(210:-30:0.985) to[out=-120,in=-120,looseness=2] cycle;

end{tikzpicture}

end{document}