Convex polygon triangulation based on planted trivalent binary tree and ballot problem

Abstract

This paper presents a new technique of generation of convex polygon triangulation based on planted trivalentbinary tree and ballot notation. The properties of the Catalan numbers were examined and their decomposition andapplication in developing the hierarchy and triangulation trees were analyzed. The method of storage and processing oftriangulation was constructed on the basis of movements through the polygon. This method was derived from verticesand leaves of the planted trivalent binary tree. The research subject of the paper is analysis and comparison of aconstructed method for solving of convex polygon triangulation problem with other methods and generating graphicalrepresentation. The application code of the algorithms was done in the Java programming language.