Impossible Geometry: Advancements in the Field of Counting Triangulations of Planar Point Sets
Summary
Given a set of n points P in the plane, a triangulation of P is a maximal set of non-crossing edges between points in P. Counting the number of triangulations for a point set is a well known problem in the field of computational geometry. In this paper we present an overview of the previous 20 years of publications in the field of counting triangulations. We present four papers in the field that each represent significant advancements or interesting developments in the field. Additionally, we provide an implementation of the most recent and complex algorithm we present.