Turtlegons: Generating Simple Polygons from Sequences of Angles.

Joseph Culberson and Gregory Rawlins

Proceedings of the First Annual Symposium on Computational Geometry pages 305-310, 1985.


In this paper we present an algorithm to create simple polygons with a particular sequence of exterior angles, given only the sequence of angles. The algorithm has worst time complexity O(Dn), where n is the number of angles, and D is dependent on the angles. As a bonus, the algorithm proves an interesting converse of the ancient theorem that the sum of the exterior angles of a simple polygon is 2 pi radians.