The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Planar point location using persistent search trees
Communications of the ACM
On the maximal number of edges of many faces in an arrangement
Journal of Combinatorial Theory Series A
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
Separating two simple polygons by a sequence of translations
Discrete & Computational Geometry
The complexity of many faces in arrangements of lines of segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Coordinated motion planning for two independent robots
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Arrangements of Curves in the Plane - Topology, Combinatorics, and Algorithms
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
ACM SIGACT News
On the general motion planning problem with two degrees of freedom
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Coordinated motion planning for two independent robots
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Degree complexity bounds on the intersection of algebraic curves
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Efficient motion planning for an L-shaped object
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Triangulating a non-convex polytype
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Quasi-optimal upper bounds for simplex range searching and new zone theorems
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
ESA'07 Proceedings of the 15th annual European conference on Algorithms
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We show that the combinatorial complexity of all non-convex cells in an arrangement of n (possibly intersecting) triangles in 3-space is &Ogr;(n7/3+&dgr;), for any &dgr;0, and that this bound is almost tight in the worst case. Our bound significantly improves a previous nearly cubic bound of Pach and Sharir. We also present a (nearly) worst-case optimal randomized algorithm for calculating a single cell of the arrangement, analyze some special cases of the problem where improved bounds (and better algorithms) can be obtained, and describe applications of our results to translational motion planning for polyhedra in 3-space.