Sorting Jordan sequences in linear time using level-linked search trees
Information and Control
Optimal point location in a monotone subdivision
SIAM Journal on Computing
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
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Minimum partitioning simple rectilinear polygons in O(n log log n) - time
SCG '89 Proceedings of the fifth 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 parallel scan conversion algorithm with anti-aliasing for a general-purpose ultracomputer
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Shading of regions on vector display devises
SIGGRAPH '81 Proceedings of the 8th annual conference on Computer graphics and interactive techniques
Structured visibility profiles with applications to problems in simple polygons (extended abstract)
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Linear-time triangulation of a simple polygon made easier via randomization
Proceedings of the sixteenth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
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We give a new &Ogr;(n log log n)-time deterministic linear-time algorithm for triangulating simple n-vertex polygons, which avoids the use of complicated data-structures. In addition, for polygons whose vertices have integer coordinates of polynomially bounded size, the algorithm can be modified to run in &Ogr;(n log* n) time. The major new techniques employed are the efficient location of horizontal visibility edges which partition the interior of the polygon into regions of approximately equal size, and a linear-time algorithm for obtaining the horizontal visibility partition of a subchain of a polygonal chain, from the horizontal visibility partition of the entire chain. This latter technique has other interesting applications, including a linear-time algorithm to convert a Steiner triangulation of a polygon into a true triangulation.This research was partially supported by DIMACS and the following grants: NSERC 583584, NSERC 580485, NSF-STC88-09648, ONR-N00014-87-0467.