I'm experimenting with a (new?) way of drawing curves - see Desmos and whisk - that I have not encountered anywhere else, and I was wondering if these have a name. The closest things I found were the witch of Agnesi, ogives and the line of beauty.
The curves are defined by the vector space of $\vec b$ between $t = 0$ and $t= 1$ for predetermined values of $R_1$ and $R_2$:
$0≤t≤1$
$R = [-1:1, -1:1]$
$r = R_1 + t(R_2 - R_1)$
$\vec a = [t, 0]$
$\vec c = [\frac{1-\cos(\pi t)}{2}, \frac{\sin(\pi t)}{2}]$
$\vec b = \vec a + r(\vec c - \vec a)$
EDIT: I recombined two positive curves to achieve more usable results for negative values, and reintroduced the negative curve as a pinch factor: