A new technique for analyzing substructures in arrangements
Proceedings of the eleventh annual symposium on Computational geometry
Pipes, cigars, and kreplach: the union of Minkowski sums in three dimensions
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Motion planning of a ball amid segments in three dimensions
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The union of congruent cubes in three dimensions
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Polyhedral Voronoi diagrams of polyhedra in three dimensions
Proceedings of the eighteenth annual symposium on Computational geometry
Recent Developments in the Theory of Arrangements of Surfaces
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Closest point query among the union of convex polytopes using rasterization hardware
Journal of Graphics Tools - Special on hardware-accelerated rendering techniques
Efficient algorithms for bichromatic separability
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On lines avoiding unit balls in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On the union of κ-round objects
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Almost tight bound for a single cell in an arrangement of convex polyhedra in R3
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Efficient algorithms for bichromatic separability
ACM Transactions on Algorithms (TALG)
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Line transversals of convex polyhedra in R3
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Contributing vertices-based Minkowski sum computation of convex polyhedra
Computer-Aided Design
On the union of fat tetrahedra in three dimensions
Journal of the ACM (JACM)
Red-blue separability problems in 3D
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Contributing vertices-based Minkowski sum of a nonconvex--convex pair of polyhedra
ACM Transactions on Graphics (TOG)
Line Transversals of Convex Polyhedra in $\mathbb{R}^3$
SIAM Journal on Computing
Convexity recognition of the union of polyhedra
Computational Geometry: Theory and Applications
A sweep and translate algorithm for computing voxelized 3D Minkowski sums on the GPU
Computer-Aided Design
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We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k3 + kn log k). This bound is almost tight in the worst case, as there exist collections of polyhedra with $\Omega(k^3+kn\alpha(k))$ union complexity. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k3 + kn log k log n) expected time.