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
On the general motion-planning problem with two degrees of freedom
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Arrangements of curves in the plane—topology, combinatorics, and algorithms
Theoretical Computer Science
Computing a face in an arrangement of line segments and related problems
SIAM Journal on Computing
Counting and reporting red/blue segment intersections
CVGIP: Graphical Models and Image Processing
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
The common exterior of convex polygons in the plane
Computational Geometry: Theory and Applications
The Union of Convex Polyhedra in Three Dimensions
SIAM Journal on Computing
On Translational Motion Planning of a Convex Polyhedron in 3-Space
SIAM Journal on Computing
Voronoi diagrams of lines in 3-space under polyhedral convex distance functions
Journal of Algorithms - Special issue on SODA '95 papers
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We consider the problem of bounding the combinatorial complexity of a single cell in an arrangement of k convex polyhedra in 3-space having n facets in total. We use a variant of the technique of Halperin and Sharir [17], and show that this complexity is O(nk1+ε), for any ε 0, thus almost settling a conjecture of Aronov et. el. [5]. We then extend our analysis and show that the overall complexity of the zone of a low-degree algebraic surface, or of the boundary of an arbitrary convex set, in an arrangement of k convex polyhedra in 3-space with n facets in total, is also O(nk1+ε), for any ε 0. Finally, we present a deterministic algorithm that constructs a single cell in an arrangement of this kind, in time O(nk1+ε log2n), for any ε 0.