On sequential triangulations of simple polygons

A triangulation is said to be Hamiltonian if its dual graph contains a Hamiltonian path. A sequential triangulation is a Hamiltonian triangulation having the additional property that the “turns” in the Hamiltonian path alternate left/right. Such triangulations are useful in computer graphics rendering and are related to a new type of two-guard walk. In this paper we present a simple algorithm that determines all sequential triangulations (or equivalently all sequential two-guard walks) of a simple vertex input polygon. The previous best algorithm uses the polygon’s visibility graph and hence runs in worse case time [1].