Computational geometry: an introduction
Computational geometry: an introduction
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
ACM SIGACT News
Polling: a new randomized sampling technique for computational geometry
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A deterministic algorithm for partitioning arrangements of lines and its application
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
An efficient algorithm for hidden surface removal
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
How good are convex hull algorithms?
Proceedings of the eleventh annual symposium on Computational geometry
Best-fit bin-packing with random order
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Simple randomized algorithms for closest pair problems
Nordic Journal of Computing
Packing Two Disks into a Polygonal Environment
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Algorithms for optimal outlier removal
Journal of Discrete Algorithms
Dilation-optimal edge deletion in polygonal cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
gHull: A GPU algorithm for 3D convex hull
ACM Transactions on Mathematical Software (TOMS)
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We give a simple algorithmic technique for building geometric structures. The technique is randomized and incremental. As an application, we give an algorithm of this kind for computing the intersection of a set of halfspaces in three dimensions. (This intersection problem is linear-time equivalent to the computation of the convex hull of a point set.) The algorithm requires &Ogr;(n log n) expected time, where the expectation is over the random behavior of the algorithm. A similar algorithm can be used to determine the intersection of a set of unit balls in E3, the problem of spherical intersection. This problem arises in the computation of the diameter of a point set in E3. For a set S of n points, the diameter of S is the greatest distance between two points in S. We give a randomized reduction from the problem of determining the diameter to the problem of computing spherical intersections, resulting in a Las Vegas algorithm for the diameter requiring &Ogr;(n log n) expected time. The best algorithms previously known for this problem have worst-case time bounds no better than &Ogr;(n √n log n) [Agg].