Summary: Two-Convex Polygons
We introduce a notion of k-convexity and explore
some properties of polygons that have this property.
In particular, 2-convex polygons can be recognized in
O(n log n) time, and k-convex polygons can be trian-
gulated in O(kn) time.
The notion of convexity is central in geometry. As
such, it has been generalized in many ways and for
different reasons. In this note, we consider a simple
and intuitive generalization, which to the best of our
knowledge has not been worked on. It leads to an ap-
pealing class of polygons in the plane, with interesting
structural and algorithmic properties.