Accurate, simple and efficient triangulation of a polygon by ear removal with lowest memory consumption

K R Wijeweera,S R Kodituwakku

doi:10.4038/cjs.v45i3.7402

Abstract

Polygons can conveniently represent real world objects. In automatic character recognition, shapes of individual letters are represented by polygons. In robotics, obstacles are represented using polygons. In computer graphics programming, solid objects are represented using polygons on the two dimensional screen. The polygons can be easily manipulated using known mathematical operations. That is the reason for representing real world objects using polygons. However, polygons can be in complicated shapes. Therefore, it is better if there is a way to partition a polygon into smaller pieces. Triangulation is a particular way of doing this from which polygons are partitioned into triangles. The basic triangulation algorithm is widely used in applications where 100% accuracy is necessary. Algorithms with better asymptotic order than the basic triangulation algorithm exist. However they are not 100% accurate and use advanced data structures causing higher memory consumption. This paper proposes a simple, efficient and 100% accurate algorithm which uses lowest amount of memory. The proposed algorithm is more suitable for embedded systems which do not possess large amount of memory. The proposed algorithm was experimentally compared with the basic triangulation algorithm. The experimental results prove that the proposed algorithm is faster than the basic triangulation algorithm.

Highlights

Polygons can be used to represent the real world objects conveniently
Polygon triangulation can be defined as the decomposition of a polygonal area into a set of triangles (Berg et al, 2008; Garey et al, 1975)
Polygon triangulation can be defined as the creation of a set of triangles without non-intersecting interiors whose union is the original polygon

Summary

INTRODUCTION

Polygons can be used to represent the real world objects conveniently. Once the real world objects were represented using polygons, the resultant polygons are too complicated most of the time. The output of the ear clipping methods is a list of triangles in which the union forms the original polygon. The basic triangulation algorithm (O’Rourke, 1998) is a 100% accurate algorithm for polygon triangulation available in literature It is a diagonal insertion method and based on the following theorem called triangulation theorem. The output of the proposed algorithm is a list of disjoint triangles in which the union forms the original polygon. This algorithm is 100% accurate algorithm and it avoids precision error. Theorem 2: Every triangulation of a polygon P of n vertices uses n – 3 diagonals and consists of n – 2 triangles

METHODOLOGY

Findings

CONCLUSION