Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Data structures and network algorithms
Data structures and network algorithms
Computational geometry: an introduction
Computational geometry: an introduction
Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Hidden surface removal with respect to a moving view point
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Dynamic trees and dynamic point location
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
An optimal convex hull algorithm and new results on cuttings (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Randomized multidimensional search trees: further results in dynamic sampling (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficient point location in a convex spatial cell-complex
SIAM Journal on Computing
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Range searching with efficient hierarchical cuttings
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
A Singly-Expenential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Motion planning amidst fat obstacles (extended abstract)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
On lazy randomized incremental construction
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications
Proceedings of the eleventh annual symposium on Computational geometry
A new technique for analyzing substructures in arrangements
Proceedings of the eleventh annual symposium on Computational geometry
Efficient randomized algorithms for some geometric optimization problems
Proceedings of the eleventh annual symposium on Computational geometry
Computing faces in segment and simplex arrangements
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
ESA'07 Proceedings of the 15th annual European conference on Algorithms
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We prove that, for any constant &egr;0, the complexity of the vertical decomposition of a set of n triangles in three-dimensional space is O(n2+&egr;+K), where K is the complexity of the arrangement of the triangles. For a single cell the complexity of the vertical decomposition is shown to be O(n2+&egr;). These bounds are almost tight in the worst case.We also give a deterministic output-sensitive algorithm for computing the vertical decomposition that runs in O(n2logn+Vlogn) time, where V is the complexity of the decomposition. The algorithm is reasonably simple (in particular, it tries to perform as much of the computation in two-dimensional spaces as possible) and thus is a good candidate for efficient implementations.