Years and Authors of Summarized Original Work
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1991; Chazelle
Problem Definition
Definition 1
A simple polygon is a polygon whose interior is simply connected, i.e., it consists of a single connected component and does not contain holes.
Definition 2
A triangulation of a simple polygon P with N vertices is a partition of the polygon, considered as a full-dimensional subset of the plane, into N − 2 nonoverlapping triangles such that the set of vertices of these triangles is the set of vertices of P, such that no edge of a triangle lies outside of P, and such that no triangle edges intersect except in their common endpoints.
Key Results
In addition to the regularization-based approach by Garey et al. [7], three other \(\mathcal{O}(N\log N)\)-time algorithms are milestones on the way toward an optimal linear-time algorithm. In the first of these algorithms [2], Chazelle uses a linear-time “polygon-cutting” approach to partition a simple polygon by a suitably chosen diagonal; the resulting...
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Recommended Reading
Amato NM, Goodrich MT, Ramos EA (2001) A randomized algorithm for triangulating a simple polygon in linear time. Discret Comput Geom 26:245–265
Chazelle BM (1982) A theorem on polygon cutting with applications. In: Proceedings of the twenty-third annual symposium on foundations of computer science, Chicago. IEEE, pp 339–349
Chazelle BM (1991) Triangulating a simple polygon in linear time. Discret Comput Geom 6:485–524
Chazelle BM, Incerpi JM (1984) Triangulation and shape-complexity. ACM Trans Graph 3(2):135–152
Clarkson KL, Tarjan RE, Van Wyk CJ (1989) A fast Las Vegas algorithm for triangulating a simple polygon. Discret Comput Geom 4:423–432
Fournier A, Montuno DY (1984) Triangulating simple polygons and equivalent problems. ACM Trans Graph 3(2):153–174
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Vahrenhold J (1996) Triangulierung eines einfachen Polygons in linearer Zeit. Master’s thesis, Department of Computer Science, University of Münster (in German)
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Vahrenhold, J. (2016). Polygon Triangulation. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_506
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