What do you call such a figure below and how to parametrize such kind of curve?
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$\begingroup$ en.wikipedia.org/wiki/Cassini_oval $\endgroup$– FredCommented Aug 8, 2018 at 8:59
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This looks like a variant of the dumbbell curve (see e.g. http://mathworld.wolfram.com/DumbbellCurve.html) This one could be parametrized for the upper part by $$x(t)=t,\ y(t)=(t^2 + 0.5)\sqrt{1 - t^2}$$ and the lower part by $$x(t)=t,\ y(t)=-(t^2 + 0.5)\sqrt{1 - t^2}$$ for $t\in[-1,1]$. Of course you can change the $0.5$ to a different positiv value to obtain different shapes.
