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The power of geometric duality
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1016/0020-0190(78)90062-5openalex-snapshot
Triangulating a simple polygon
inferredcites →https://doi.org/10.1016/0020-0190(82)90090-4openalex-snapshot
Polygonal intersection searching
inferredcites →https://doi.org/10.1016/0020-0190(86)90088-8openalex-snapshot
Halfplanar range search in linear space and O(n0.695) query time
inferredcites →https://doi.org/10.1016/0022-0000(81)90012-xopenalex-snapshot
Maintenance of configurations in the plane
inferredcites →https://doi.org/10.1016/0304-3975(78)90051-8openalex-snapshot
Finding the intersection of two convex polyhedra
inferredcites →https://doi.org/10.1109/sfcs.1983.1openalex-snapshot
A kinetic framework for computational geometry
inferredcites →https://doi.org/10.1109/sfcs.1983.11openalex-snapshot
Constructing arrangements of lines and hyperplanes with applications
inferredcites →https://doi.org/10.1109/sfcs.1983.17openalex-snapshot
Filtering search: A new approach to query-answering
inferredcites →https://doi.org/10.1137/0209046openalex-snapshot
Applications of a Planar Separator Theorem
inferredcites →https://doi.org/10.1137/0212002openalex-snapshot
Optimal Search in Planar Subdivisions
inferredcites →https://doi.org/10.1137/0215024openalex-snapshot
Constructing Arrangements of Lines and Hyperplanes with Applications
inferredcites →https://doi.org/10.1145/282918.282923openalex-snapshot
Primitives for the manipulation of general subdivisions and the computation of Voronoi
inferredcites →https://doi.org/10.1145/800061.808751openalex-snapshot
Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams
inferredcites →https://doi.org/10.1145/800061.808755openalex-snapshot
A 3-space partition and its applications
inferredcites →https://doi.org/10.1145/800141.804662openalex-snapshot
Detection is easier than computation (Extended Abstract)
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Efficient Searching with Linear Constraints
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External Memory Data Structures
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An Optimal Hidden-Surface Algorithm and Its Parallelization
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Unions of Onions: Preprocessing Imprecise Points for Fast Onion Layer Decomposition
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Backwards Analysis of Randomized Geometric Algorithms
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Hyperplane Approximation and Related Topics
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Efficient binary space partitions for hidden-surface removal and solid modeling
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Triangulating a nonconvex polytope
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Partitioning arrangements of lines II: Applications
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Linear space data structures for two types of range search
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New applications of random sampling in computational geometry
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Polygonizations of point sets in the plane
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Constructing arrangements optimally in parallel
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Iterated nearest neighbors and finding minimal polytopes
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Better lower bounds on detecting affine and spherical degeneracies
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Onk-sets in arrangements of curves and surfaces
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On the boundary of a union of Rays
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On Rainbow Quadrilaterals in Colored Point Sets
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Convex Hulls Under Uncertainty
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Robust Shape Fitting via Peeling and Grating Coresets
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On Approximate Range Counting and Depth
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Flip Distance Between Triangulations of a Simple Polygon is NP-Complete
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Relay Node Placement with Assured Coverage and Connectivity: A Jarvis March Approach
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A solution to a problem of Grünbaum and Motzkin and of Erdős and Purdy about bichromatic configurations of points in the plane
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Efficient geometric algorithms for workpiece orientation in 4- and 5-axis NC machining
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The power of geometric duality revisited
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The power of parallel projection
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Topologically sweeping an arrangement
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Bounding the number of k-faces in arrangements of hyperplanes
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Heuristics and bounds for the travelling salesman location problem on the plane
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The K-dense corridor problems
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Finding tailored partitions
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Algorithms for ray-shooting and intersection searching
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Partial visibility for selecting a parting direction in mold and die design
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Some location problems for robot navigation using a single camera
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Reporting points in halfspaces
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Covering grids and orthogonal polygons with periscope guards
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Algorithms for generalized halfspace range searching and other intersection searching problems
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Algorithms for generalized halfspace range searching and other intersection searching problems
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Fast algorithms for collision and proximity problems involving moving geometric objects
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Computational Geometry
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Geometric Algorithms
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Arrangements and Their Applications**Work by PA. was supported by Army Research Office MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by an NYI award, and by a grant from the U.S.–Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR-91-22103 and CCR-93-11127, by…
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Visibility in the Plane
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Space/query-time tradeoff for computing the visibility polygon
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Bottleneck partial-matching Voronoi diagrams and applications
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Half-plane point retrieval queries with independent and dependent geometric uncertainties
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Topological sweep of the complete graph
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On colouring point visibility graphs
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On the zone of a circle in an arrangement of lines
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Reporting intersecting pairs of convex polytopes in two and three dimensions
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Erased arrangements of lines and convex decompositions of polyhedra
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Geometric range searching and its relatives
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Horizon theorems for lines and polygons
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Two-dimensional line space Voronoi Diagram
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Assembling polyhedra with single translations
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Visibility-polygon search and euclidean shortest paths
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Polytope range searching and integral geometry
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Combinatorial complexity bounds for arrangements of curves and surfaces
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Reporting points in halfspaces
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Dynamic half-space reporting, geometric optimization, and minimum spanning trees
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Better lower bounds on detecting affine and spherical degeneracies
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New lower bounds for halfspace emptiness
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Random sampling, halfspace range reporting, and construction of (≤k)-levels in three dimensions
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Low-dimensional linear programming with violations
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An Improved Algorithm for Constructing kth-Order Voronoi Diagrams
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Simplification of 2D Polygonal Partitions via Point‐line Projective Duality, and Application to Urban Reconstruction
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Intersecting Line Segments in Parallel with an Output-Sensitive Number of Processors
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Ray Shooting and Other Applications of Spanning Trees with Low Stabbing Number
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On the Zone Theorem for Hyperplane Arrangements
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Approximate Dynamic Programming using Halfspace Queries and Multiscale Monge Decomposition
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(Near-)Linear-Time Randomized Algorithms for Row Minima in Monge Partial Matrices and Related Problems
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A Simple Algorithm for Computing the Zone of a Line in an Arrangement of Lines
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Elder-Rule-Staircodes for Augmented Metric Spaces
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Binary Space Partitions for Line Segments with a Limited Number of Directions
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Low-Dimensional Linear Programming with Violations
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Space-Time Tradeoffs for Emptiness Queries
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Algorithmic Aspects of VLSI Layout
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ON ENUMERATING AND SELECTING DISTANCES
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TOPOLOGICAL PEELING AND APPLICATIONS
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FINDING SIMPLICES CONTAINING THE ORIGIN IN TWO AND THREE DIMENSIONS
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THREE PROBLEMS ABOUT DYNAMIC CONVEX HULLS
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Point Visibility Graph Recognition is NP-Hard
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An Optimal Algorithm for Reconstructing Point Set Order Types from Radial Orderings
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Partial Enclosure Range Searching
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Solving query-retrieval problems by compacting Voronoi diagrams
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Linear data structures for two types of range search
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Topologically sweeping an arrangement
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Separating and intersecting spherical polygons
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Efficient algorithms for generalized intersection searching on non-iso-oriented objects
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Approximation algorithms for speeding up dynamic programming and denoising aCGH data
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FIFO indexes for decomposable problems
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Three problems about dynamic convex hulls
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Succinct geometric indexes supporting point location queries
inferred← citeshttps://doi.org/10.1145/2213836.2213882openalex-snapshot
Processing a large number of continuous preference top- k queries
inferred← citeshttps://doi.org/10.1145/2261250.2261305openalex-snapshot
Optimal area-sensitive bounds for polytope approximation
inferred← citeshttps://doi.org/10.1145/2344422.2344433openalex-snapshot
Range searching on uncertain data
inferred← citeshttps://doi.org/10.1145/2543581.2543589openalex-snapshot
Unsolved problems in visibility graphs of points, segments, and polygons
inferred← citeshttps://doi.org/10.1145/2582112.2582159openalex-snapshot
Peeling Potatoes Near-Optimally in Near-Linear Time
inferred← citeshttps://doi.org/10.1145/262839.262858openalex-snapshot
Cylindrical static and kinetic binary space partitions
inferred← citeshttps://doi.org/10.1145/262839.262988openalex-snapshot
Space-time tradeoffs for emptiness queries (extended abstract)
inferred← citeshttps://doi.org/10.1145/275487.275506openalex-snapshot
Efficient searching with linear constraints
inferred← citeshttps://doi.org/10.1145/27625.27627openalex-snapshot
Worst-case optimal hidden-surface removal
inferred← citeshttps://doi.org/10.1145/276884.276887openalex-snapshot
Multi-criteria geometric optimization problems in layered manufacturing
inferred← citeshttps://doi.org/10.1145/276884.276916openalex-snapshot
On enumerating and selecting distances
inferred← citeshttps://doi.org/10.1145/2902251.2902290openalex-snapshot
Efficient Top-k Indexing via General Reductions
inferred← citeshttps://doi.org/10.1145/3046673openalex-snapshot
Instance-Optimal Geometric Algorithms
inferred← citeshttps://doi.org/10.1145/3546074openalex-snapshot
Generic Techniques for Building Top- k Structures
inferred← citeshttps://doi.org/10.1145/3656427openalex-snapshot
Maximum Consensus Floating Point Solutions for Infeasible Low-Dimensional Linear Programs with Convex Hull as the Intermediate Representation
inferred← citeshttps://doi.org/10.1145/378583.378709openalex-snapshot
A sum of squares theorem for visibility
inferred← citeshttps://doi.org/10.1145/72935.72950openalex-snapshot
Intersecting line segments in parallel with an output-sensitive number of processors
inferred← citeshttps://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferred← citeshttps://doi.org/10.1145/73393.73416openalex-snapshot
Searching for empty convex polygons
inferred← citeshttps://doi.org/10.1145/73393.73431openalex-snapshot
Arrangements of lines in 3-space: a data structure with applications
inferred← citeshttps://doi.org/10.1145/73393.73432openalex-snapshot
Triangles in space or building (and analyzing) castles in the Air
inferred← citeshttps://doi.org/10.1145/73833.73836openalex-snapshot
Binary partitions with applications to hidden surface removal and solid modelling
inferred← citeshttps://doi.org/10.1145/73833.73876openalex-snapshot
Triangulating a non-convex polytype
inferred← citeshttps://doi.org/10.1145/97444.97697openalex-snapshot
Parallel algorithms for arrangements
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