Is it posible to interpolate convex hull in 2d space

Question

I have $n$ points (in this example $11$) and I need to interpolate them in such a way that I have a function $f(t) \rightarrow (R, R)$ where $t \in [0; 2\pi]$. It can be parametric curve, but I need to have a function.

Answer 1

Order the points according to polar coordinates centered at the barycenter. Join consecutive points by a line segment. This gives you a piecewise linear curve using the angle as parameter.