Ear-clipping Based Algorithms of Generating High-quality Polygon Triangulation

TL;DR

This paper introduces basic and improved ear clipping algorithms for triangulating simple polygons and polygons with holes, effectively reducing sliver triangles and improving triangulation quality.

Contribution

The paper presents novel ear clipping algorithms that minimize sliver triangles and handle polygons with holes by creating bridge edges, outperforming traditional methods.

Findings

Basic algorithm avoids sliver triangles better than traditional methods.

Improved algorithm further reduces sliver triangles.

Both algorithms run in O(n^2) time and O(n) space.

Abstract

A basic and an improved ear clipping based algorithm for triangulating simple polygons and polygons with holes are presented. In the basic version, the ear with smallest interior angle is always selected to be cut in order to create fewer sliver triangles. To reduce sliver triangles in further, a bound of angle is set to determine whether a newly formed triangle has sharp angles, and edge swapping is accepted when the triangle is sharp. To apply the two algorithms on polygons with holes, "Bridge" edges are created to transform a polygon with holes to a degenerate polygon which can be triangulated by the two algorithms. Applications show that the basic algorithm can avoid creating sliver triangles and obtain better triangulations than the traditional ear clipping algorithm, and the improved algorithm can in further reduce sliver triangles effectively. Both of the algorithms run in O(n2) time and O(n) space.