Triangulations and Flips

Abstract

Let P be a set of points in the plane and assume that P is in general position. A triangulation of P is a maximal non-crossing geometric graph with vertex set P. All bounded faces of a triangulation are triangles (that’s why we call them triangulation), the unbounded face is the outside of the convex hull of P. Triangulations play a prominent role in many applicable and applied disciplines like computational geometry, computer graphics and numerical modeling. In this chapter we discuss combinatorial and geometrical properties of triangulations and of the flip-graph on the set of all triangulations of a point set P.