Computational geometry: an introduction
Computational geometry: an introduction
Voronoi diagrams and arrangements
Discrete & Computational Geometry
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
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
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
Planning algorithm for a convex polygonal object in two-dimensional polygonal space
Discrete & Computational Geometry
Visibility, occlusion, and the aspect graph
International Journal of Computer Vision
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Arrangements of curves in the plane—topology, combinatorics, and algorithms
Theoretical Computer Science
Almost tight bounds for &egr;-nets
Discrete & Computational Geometry
On the zone theorem for hyperplane arrangements
SIAM Journal on Computing
Computing a segment center for a planar point set
Journal of Algorithms
On lines missing polyhedral sets in 3-space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Combinatorial complexity of translating a box in polyhedral 3-space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
On the zone of a surface in a hyperplane arrangement
Discrete & Computational Geometry
Extremal polygon containment problems
Computational Geometry: Theory and Applications
Applications of parametric searching in geometric optimization
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Approximations and optimal geometric divide-and-conquer
Selected papers of the 23rd annual ACM symposium on Theory of computing
Arrangements and their applications in robotics: recent developments
WAFR Proceedings of the workshop on Algorithmic foundations of robotics
Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications
Proceedings of the eleventh annual symposium on Computational geometry
On-line construction of the upper envelope of triangles and surface patches in three dimensions
Computational Geometry: Theory and Applications
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
The Union of Convex Polyhedra in Three Dimensions
SIAM Journal on Computing
Computing Envelopes in Four Dimensions with Applications
SIAM Journal on Computing
On Translational Motion Planning of a Convex Polyhedron in 3-Space
SIAM Journal on Computing
Handbook of discrete and computational geometry
Computational real algebraic geometry
Handbook of discrete and computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Voronoi diagrams of lines in 3-space under polyhedral convex distance functions
Journal of Algorithms - Special issue on SODA '95 papers
Pipes, cigars, and kreplach: the union of Minkowski sums in three dimensions
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Approximation and exact algorithms for minimum-width annuli and shells
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Arrangements in Higher Dimensions: Voronoi Diagrams, Motion Planning, and Other Applications
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
A Singly-Expenential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
On the Combinatorial and Topological Complexity of a Single Cell
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The union of convex polyhedra in three dimensions
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Combinatorial structure of rigid transformations in 2D digital images
Computer Vision and Image Understanding
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We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of efficient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications of the new results to a variety of problems in computational geometry and its applications, including motion planning, Voronoi diagrams, union of geometric objects, visibility, and geometric optimization.