Efficient triangulation of simple polygons

This paper considers the topic of efficiently traingulating a simple polygon with emphasis on practical and easy-to-implement algorithms. It also describes a newadaptive algorithm for triangulating a simplen-sided polygon. The algorithm runs in timeO(n(1+t _o)) witht ₀<n. The quantityt ₀ measures theshape-complexity of thetriangulation delivered by the algorithm. More preciselyt ₀ is the number of obtained triangles contained in the triangulation that share zero edges with the input polygon and is, furthermore, related to the shape-complexity of theinput polygon. Although the worst-case complexity of the algorithm isO(n ²), for several classes of polygons it runs in linear time. The practical advantages of the algorithm are that it is simple and does not require sorting or the use of balanced tree structures. On the theoretical side, it is of interest because it is the first polygon triangulation algorithm where thecomputational complexity is a function of theoutput complexity. As a side benefit, we introduce a new measure of the complexity of a polygon triangulation that should find application in other contexts as well.