Computational geometry: an introduction
Computational geometry: an introduction
An O (n log log n)-time algorithm for triangulating a simple polygon
SIAM Journal on Computing
Optimal shortest path queries in a simple polygon
Journal of Computer and System Sciences
Generating random combinatorial objects
Journal of Algorithms
Generating binary trees at random
Information Processing Letters
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
An efficient algorithm for enumeration of triangulations
Computational Geometry: Theory and Applications
Generating Outerplanar Graphs Uniformly at Random
Combinatorics, Probability and Computing
SIGITE '08 Proceedings of the 9th ACM SIGITE conference on Information technology education
Randomly generating triangulations of a simple polygon
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Generation of Random Digital Simple Curves with Artistic Emulation
Journal of Mathematical Imaging and Vision
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An O(n3) algorithm is described to count triangulations of a simple polygon with nvertices. This algorithm is used to construct an O(n4) algorithm to generate triangulations of a simple polygon at random with a uniform probability distribution. The problem of counting triangulations of a simple polygon is then related to existing problems in graph theory.