Turtlegons: generating simple polygons for sequences of angles

Authors:
Joseph Culberson;Gregory Rawlins
Affiliations:
Data Structuring Group, Department of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3Gl Canada;Data Structuring Group, Department of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3Gl Canada
Venue:
SCG '85 Proceedings of the first annual symposium on Computational geometry
Year:
1985

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Abstract

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 case time complexity &Ogr;(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&pgr; radians.