A fast Las Vegas algorithm for triangulating a simple polygon
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
Generating triangulations at random
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Generating random polygons with given vertices
Computational Geometry: Theory and Applications
Heuristics for the Generation of Random Polygons
Proceedings of the 8th Canadian Conference on Computational Geometry
A nearly optimal algorithm for covering the interior of an Art Gallery
Pattern Recognition
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The construction of random polygons has been used in psychological research and for the testing of algorithms. With the increased popularity of client-side vector based graphics in the web browser such as seen in Flash and SVG, as well as the newly introduced tag in HTML5.0, the use of random shapes for creation of scenes for animation and interactive art requires the construction of random polygons. A natural question, then, is how to generate random polygons in a way which is computationally efficient (particularly in a resource limited environment such as the web browser). This paper presents a random polygon algorithm (RPA) that generates polygons that are random and representative of the class of all n-gons in O(n2logn) time. Our algorithm differs from other approaches in that the vertices are generated randomly, the algorithm is inclusive (i.e. each polygon has a non-zero probability to be constructed), and it runs efficiently in polynomial time.