Orbiting triangle method for convex polygon triangulation

Abstract

Finding all possible triangulations of convex polygon is a highly time and memory space consuming combinatorial problem. Therefore, it is very important to develop algorithms for generating triangulations as efficiently as possible. This paper presents a new method for generating triangulations of a convex polygon, called Orbiting triangle method (OTM). The method is based on using the set of (n − 1)-gon triangulations during the set of n-gon triangulations creation. The main feature of the OTM algorithm is the use of the Catalan triangle to identify valid triangulations, so that the algorithm spends almost no time to eliminate duplicates. In this way, the method possesses small complexity and saves the computational time required for detecting and eliminating duplicates.

Computing Triangulations of the Convex Polygon in PHP/Mysql Environment

“…For a comparative analysis in presenting the advantages of web technologies, we implement an additional algorithm from the field of computer graphics (Orbiting Triangle method [8]).…”

Convex Polygon Triangulation Based on Symmetry

“…In [12], the authors noticed and exploited symmetry in the proof of lemma 4.2. Some symmetry properties were observed in [13], where the orbiting triangle method was described. The triangle that contained an ear in the n-gon was orbiting the (n − 1)-gon.…”