Before revision:  Lattice triangulations have been studied for their uses in discriminant theory, Hilbert's 16th problem, toric varieties, quantum spin systems, and material science\left(\right)  .
After revision:  Lattice triangulations have been studied for their uses in discriminant theory, Hilbert's 16th problem, toric varieties, quantum spin systems, and material science\left(\right) time, where n is the number of points in the point-set. Eppstein proved this result for lattice point-sets bounded by convex polygons. Caputo et al. extended this result to the cases of non-convex bounding polygons and constrained flip paths that preserve a set of edges. In fact, Eppstein's approach readily extends to both cases .