Computing Triangulations without Small and Large Angles

We propose a heuristic method for computing Steiner triangulations without small and large angles. Given a two-dimensional domain, a minimum angle constraint alpha and a maximum angle constraint gamma, our methodcomputes a triangulation of the domain such that all angles are in the interval [alpha, gamma]. Previously known Steiner triangulation methods generally consider a lower bound alpha only, and claim a trivial upper bound (gamma = 180 - 2*alpha). Available software work for alpha as high as 34 degrees (implying a gamma value of 112 degrees), However, they fail consistently whenever larger alpha and/or smaller gamma values are desired.Experimental study shows that the proposed method works for alpha as high as 41 degrees, and gamma as low as 81 degrees. This is also the first software for computing high quality acute and non-obtuse triangulations of complex geometry.