Simulating the transformation of plane triangulation using edge flip algorithms

Abstract

In Computational Geometry edge flipping of triangulation is a well-studied topic . Also in computer graphics, triangulations are used to form any kind of shape of an object. Although many algorithms have been introduced for transforming one plane triangulation to any other one, their implementation in the literature could not be found. We have decided to check the behaviour of these algorithms in terms of required flips to transform a triangulation into another triangulation. While worst-case behaviour of these algorithms have been established in terms of number of flips, there is a dearth of average case analysis of these algorithms in the literature. We want to gain some insight as to the average behaviour of these algorithms through performing simulation. We would also like to investigate how to visualize the transformation of these plane triangulations in an intuitive way. While the current best-known algorithm for single edge flip is near-optimal, we believe there is much room for improvement when it comes to transforming plane triangulations using a sequence of simultaneous flips.