# An Output-Complexity-Sensitive Polygon Triangulation Algorithm

• Godfried Toussaint
Conference paper

## Abstract

This paper describes a new algorithm for triangulating a simple n-sided polygon. The algorithm runs in time O(n(1+t0)), with t0< n. The quantity t0measures theshape-complexityof thetriangulationdelivered by the algorithm. More precisely t0is the number of triangles contained in the triangulation obtained that share zero edges with the input polygon and is, furthermore, related to the shape- complexity of theinputpolygon. Although the worst-case complexity of the algorithm is O(n2), 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 thecomputationalcomplexity of which is a function of theoutputcomplexity. 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.

## Keywords

Computational Geometry Simple Polygon Left Turn Polygonal Chain Jordan Curve Theorem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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