On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
On arrangements of Jordan arcs with three intersections per pair
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Planning algorithm for a convex polygonal object in two-dimensional polygonal space
Discrete & Computational Geometry
A survey of motion planning and related geometric algorithms
Geometric reasoning
Algorithmic motion planning in robotics
Handbook of theoretical computer science (vol. A)
On the union of fat wedges and separating a collection of segments by a line
Computational Geometry: Theory and Applications
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
The complexity of the free space for a robot moving amidst fat obstacles
Computational Geometry: Theory and Applications
Computing depth orders for fat objects and related problems
Computational Geometry: Theory and Applications
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
On Translational Motion Planning of a Convex Polyhedron in 3-Space
SIAM Journal on Computing
Computational Geometry: Theory and Applications
A technique for adding range restrictions to generalized searching problems
Information Processing Letters
On fat partitioning, fat covering and the union size of polygons
Computational Geometry: Theory and Applications
The complexity of the union of (&agr;, &bgr;)-covered objects
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On the union of k-curved objects
Computational Geometry: Theory and Applications
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
The union of congruent cubes in three dimensions
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
On the Number of Regular Vertices of the Union of Jordan Regions
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
On the boundary complexity of the union of fat triangles
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
On the union of fat tetrahedra in three dimensions
Journal of the ACM (JACM)
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Given a family C of regions bounded by simple closed curves in the plane, the complexity of their union is denned as the number of points along the boundary of 驴C, which belong to more than one curve Similarly, one can define the complexity of the union of 3-dimensional bodies, as the number of points on the boundary of the union, belonging to the surfaces of at least three distinct members of the family. We survey some upper bounds on the complexity of the union of n geometric objects satisfying various natural conditions. These problems play a central role in the design and analysis of many geometric algorithms arising in motion planning and computer graphics.