ComputingComputer ScienceMathematicsAlgorithmsComputational GeometryGeometryEuclidean GeometryGeometric ConstructionsGeometry ProcessingBest-case ComplexityPolygon Angle SumPolygon GeometryPolygon TheoryStrong Converse TheoremWorst-case Complexity
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 Ο(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 2π radians.