Constructing higher-dimensional convex hulls at logarithmic cost per face
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Euclidean minimum spanning trees and bichromatic closest pairs
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Linear programming and convex hulls made easy
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
In-place techniques for parallel convex hull algorithms (preliminary version)
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Output-sensitive results on convex hulls, extreme points, and related problems
Proceedings of the eleventh annual symposium on Computational geometry
How good are convex hull algorithms?
Proceedings of the eleventh annual symposium on Computational geometry
New lower bounds for convex hull problems in odd dimensions
Proceedings of the twelfth annual symposium on Computational geometry
Fast linear expected-time alogorithms for computing maxima and convex hulls
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Voronoi diagrams and arrangements
SCG '85 Proceedings of the first annual symposium on Computational geometry
Polymake: an approach to modular software design in computational geometry
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Faster geometric algorithms via dynamic determinant computation
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Finding the convex hull of a finite set of points is important not only for practical applications but also for theoretical reasons: a number of geometrical problems, such as constructing Voronoi diagrams or intersecting hyperspheres, can be reduced to the convex hull problem, and a fast convex hull algorithm yields fast algorithms for these other problems. .br This thesis deals with the problem of constructing the convex hull of a finite point set in $R^{d}$. Mathematical properties of convex hulls are developed, in particular, their facial structure, their representation, bounds on the number of faces, and the concept of duality. The main result of this thesis is an $O(n \log n + n^{\lfloor(d+1)/2\rfloor})$ algorithm for the construction of the convex hull of $n$ points in $R^{d}$. It is shown that this algorithm is worst case optimal for even $d \geq 2$.