I would like to know if somebody knows the name of these objects.
Given a set of $N$ vertices $\{(x_i, y_i)\}_{i=1,\ldots,N}$ (points in $\mathbb{R}^2$) we create a closed curve, defined piece-wise, that goes through all the points, not intersecting itself.
The curve is the union of $N$ polynomial edges
$(x(t),y(t))_i \quad t \in [0,1]$
where $x(t)$ and $y(t)$ are polynomials of arbitrary finite degree and such that:
$(x(0),y(0))_i = (x_i,y_i)$
$(x(1),y(1))_i = (x_{i+1},y_{i+1})$
with $N+1 = 1$