In this paper tight lower and upper bounds for the number of triangulations of a simple polygon are obtained as a function of the number of reflex vertices, thus relating these two shape descriptors. Tight bounds for the size of the visibility graph of a polygon are obtained too, with the same parameter. The former bounds are also studied from an asymptotical point of view.
Hurtado, F., & Noy, M. (1996). Triangulations, visibility graph and reflex vertices of a simple polygon. Computational Geometry: Theory and Applications, 6(6), 355–369. https://doi.org/10.1016/0925-7721(95)00027-5