
Flipping Edges in Triangulations 


INTRODUCTION
Then given two triangulations an important question arises as to can one triangulation be obtained from another in a series of edge flip operations? The question as to if one triangulation can be obtained from a given triangulation of points is of considerable interest in such areas as computational geometry, optimization, geometric combinatorics as well as many others... Edge flipping, being a natural and simple transformation of a triangulation, is applicable to many areas of computational geometry. Mesh generation, Delaunay triangulation and many other areas have used the concept of edge flipping. Our investigation centers around the triangulation and transformation of point sets. The proofs to some natural results of edge flipping in a triangulation are given and a helpful applet is included to give a handson feel for the proofs stated.To begin we will give some definitions... Given a triangulation T of a set P of points on the plane, a edge e of T is flippable if it is adjacent to two triangles whose union is a convex quadrilateral C. By flipping e we mean the operation of removing e from T and replacing it by the other diagonal of C. By this method we obtain a new triangulation T' of P, and we say that T' has been obtained from T by means of a flip. 
Present to: Prof. Godfried T. Toussaint  308507A  Computational Geometry  Web Project 
Present by: Christina Anne Boucher  McGill University 
cbouch35@cs.mcgill.ca  School of Computer Science 
Fall 2003 