The ultimate planar convex hull algorithm
SIAM Journal on Computing
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
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
A convex hull algorithm for discs, and applications
Computational Geometry: Theory and Applications
Derandomizing an output-sensitive convex hull algorithm in three dimensions
Computational Geometry: Theory and Applications
An algorithm for constructing the convex hull of a set of spheres in dimension d
Computational Geometry: Theory and Applications
On computing Voronoi diagrams by divide-prune-and-conquer
Proceedings of the twelfth annual symposium on Computational geometry
How good are convex hull algorithms?
Computational Geometry: Theory and Applications
An Algorithm for Convex Polytopes
Journal of the ACM (JACM)
An optimal real-time algorithm for planar convex hulls
Communications of the ACM
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheres
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Determining the Separation of Preprocessed Polyhedra - A Unified Approach
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes
Proceedings of the twenty-seventh annual symposium on Computational geometry
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Given a set @S of spheres in E^d, with d=3 and d odd, having a constant number of m distinct radii @r"1,@r"2,...,@r"m, we show that the worst-case combinatorial complexity of the convex hull of @S is @Q(@?"1"="j"==3 odd, where n"i spheres have radius @r"i, i=1,2, and @r"2@r"1, such that their convex hull has combinatorial complexity @W(n"1n"2^@?^d^2^@?+n"2n"1^@?^d^2^@?). Our construction is then generalized to the case where the spheres have m=3 distinct radii. For the upper bound, we reduce the sphere convex hull problem to the problem of computing the worst-case combinatorial complexity of the convex hull of a set of m disjoint d-dimensional convex polytopes in E^d^+^1, where d=3 odd, a problem which is of independent interest. More precisely, we show that the worst-case combinatorial complexity of the convex hull of a set of m disjoint d-dimensional convex polytopes in E^d^+^1 is O(@?"1"="j"==3. Finally, we discuss how to compute convex hulls of spheres with a constant number of distinct radii, or convex hulls of a constant number of disjoint convex polytopes.