Sorting Jordan sequences in linear time using level-linked search trees
Information and Control
An O (n log log n)-time algorithm for triangulating a simple polygon
SIAM Journal on Computing
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
Polygon triangulation in O(n log log n) time with simple data-structures
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Randomized parallel algorithms for trapezoidal diagrams
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Triangulation and shape-complexity
ACM Transactions on Graphics (TOG)
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
Fast Triangulation of Simple Polygons
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
A theorem on polygon cutting with applications
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Triangulating a simple polygon in linear time
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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This paper presents a very simple incremental randomized algorithm for computing the trapezoidal decomposition induced by a set S of n line segments in the plane. If S is given as a simple polygonal chain the expected running time of the algorithm is O(nlog^*n). This leads to a simple algorithm of the same complexity for triangulating polygons. More generally, if S is presented as a plane graph with k connected components, then the expected running time of the algorithm is O(nlog^*n+klogn). As a by-product our algorithm creates a search structure of expected linear size that allows point location queries in the resulting trapezoidation in logarithmic expected time. The analysis of the expected performance is elementary and straightforward. All expectations are with respect to ''coinflips'' generated by the algorithm and are not based on assumptions about the geometric distribution of the input.