Assume I give you a regular polygon with $n$ sides.
I am trying to find as many ways to parameterize it as possible. So far I know of two:
- Parametrize the boundary polyline as $B(v)$ compute the centroid as $c$ then interpolate from the boundary to the centroid as
$$S(u, v) = (1 - u)B(v) + u c$$
- Split the polygon into upper and lower chains (in case of odd $n$ one chain is longer by one segment). Parametrize each as $U(v), L(v)$ and then interpolate between them as
$$S(u, v) = (1-u)L(v) + u U(v)$$
I am curious what other ways I could use for this.
