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On range searching with semialgebraic sets
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1006/jagm.1993.1040openalex-snapshot
Intersection Queries in Curved Objects
inferredcites →https://doi.org/10.1007/978-3-642-61568-9openalex-snapshot
Algorithms in Combinatorial Geometry
inferredcites →https://doi.org/10.1007/bf01187036openalex-snapshot
Ray shooting on triangles in 3-space
inferredcites →https://doi.org/10.1007/bf01758854openalex-snapshot
Quasi-optimal upper bounds for simplex range searching and new zone theorems
inferredcites →https://doi.org/10.1007/bf02122778openalex-snapshot
A deterministic view of random sampling and its use in geometry
inferredcites →https://doi.org/10.1007/bf02187740openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1007/bf02187743openalex-snapshot
Quasi-optimal range searching in spaces of finite VC-dimension
inferredcites →https://doi.org/10.1007/bf02187747openalex-snapshot
Visibility and intersection problems in plane geometry
inferredcites →https://doi.org/10.1007/bf02189304openalex-snapshot
Applications of a new space-partitioning technique
inferredcites →https://doi.org/10.1007/bf02189314openalex-snapshot
Cutting hyperplanes for divide-and-conquer
inferredcites →https://doi.org/10.1007/bf02189317openalex-snapshot
On the zone of a surface in a hyperplane arrangement
inferredcites →https://doi.org/10.1007/bf02573972openalex-snapshot
Range searching with efficient hierarchical cuttings
inferredcites →https://doi.org/10.1007/bf02573973openalex-snapshot
Diameter, width, closest line pair, and parametric searching
inferredcites →https://doi.org/10.1007/bfb0035760openalex-snapshot
A singly-exponential stratification scheme for real semi-algebraic varieties and its applications
inferredcites →https://doi.org/10.1016/0012-365x(81)90274-0openalex-snapshot
Some special vapnik-chervonenkis classes
inferredcites →https://doi.org/10.1016/0196-6774(87)90015-0openalex-snapshot
Space searching for intersecting objects
inferredcites →https://doi.org/10.1016/0304-3975(91)90261-yopenalex-snapshot
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
inferredcites →https://doi.org/10.1016/0925-7721(92)90006-eopenalex-snapshot
Reporting points in halfspaces
inferredcites →https://doi.org/10.1038/133967a0openalex-snapshot
Analytical Geometry of Three Dimensions
inferredcites →https://doi.org/10.1090/s0894-0347-1989-1001852-0openalex-snapshot
Lower Bounds on the Complexity of Polytope Range Searching
inferredcites →https://doi.org/10.1137/0217052openalex-snapshot
A Randomized Algorithm for Closest-Point Queries
inferredcites →https://doi.org/10.1137/0221035openalex-snapshot
Ray Shooting and Other Applications of Spanning Trees with Low Stabbing Number
inferredcites →https://doi.org/10.1145/100216.100260openalex-snapshot
Solving query-retrieval problems by compacting Voronoi diagrams
inferredcites →https://doi.org/10.1145/103418.103470openalex-snapshot
Approximations and optimal geometric divide-and-conquer
inferredcites →https://doi.org/10.1145/109648.109651openalex-snapshot
Efficient ray shooting and hidden surface removal
inferredcites →https://doi.org/10.1145/22145.22163openalex-snapshot
A general approach to d-dimensional geometric queries
inferredcites →https://doi.org/10.1145/41958.41994openalex-snapshot
Partitioning and geometric embedding of range spaces of finite Vapnik-Chervonenkis dimension
inferredcites →https://doi.org/10.1145/73007.73044openalex-snapshot
Lines in space-combinators, algorithms and applications
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.2307/2008200openalex-snapshot
Computational Geometry--An Introduction.
inferredcites →https://doi.org/10.2307/2325168openalex-snapshot
Algorithms in Combinatorial Geometry.
inferredcites →https://doi.org/10.5555/313559.313611openalex-snapshot
A pedestrian approach to ray shooting: shoot a ray, take a walk
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Derandomization in Computational Geometry
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Selection in Monotone Matrices and Computingkth Nearest Neighbors
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Range Searching and Point Location among Fat Objects
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Reporting Intersecting Pairs of Polytopes in Two and Three Dimensions
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Improved Range Searching and Range Emptiness Under FHE Using Copy-and-Recurse
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Simplex Range Searching and Its Variants: A Review
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Ray Shooting and Stone Throwing
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Linear Data Structures for Fast Ray-Shooting Amidst Convex Polyhedra
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Erdős-Hajnal-type Results on Intersection Patterns of Geometric Objects
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All Farthest Neighbors in the Presence of Highways and Obstacles
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A Simple Framework for the Generalized Nearest Neighbor Problem
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Partially Specified Nearest Neighbor Search
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On Subgraphs of Bounded Degeneracy in Hypergraphs
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Vertical decompositions for triangles in 3-space
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Algorithmic techniques for geometric optimization
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Approximating Minimum-Weight Triangulations in Three Dimensions
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Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions
inferred← citeshttps://doi.org/10.1007/s00453-008-9220-0openalex-snapshot
Linear Data Structures for Fast Ray-Shooting amidst Convex Polyhedra
inferred← citeshttps://doi.org/10.1007/s00453-024-01284-7openalex-snapshot
Line Intersection Searching Amid Unit Balls in 3-Space
inferred← citeshttps://doi.org/10.1007/s00454-001-0029-8openalex-snapshot
An Optimal Deterministic Algorithm for Computing the Diameter of a Three-Dimensional Point Set
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Exact and Approximation Algorithms for Minimum-Width Cylindrical Shells
inferred← citeshttps://doi.org/10.1007/s00454-001-0043-xopenalex-snapshot
On the Complexity of Arrangements of Circles in the Plane
inferred← citeshttps://doi.org/10.1007/s00454-001-0084-1openalex-snapshot
Cutting Circles into Pseudo-Segments and Improved Bounds for Incidences% and Complexity of Many Faces
inferred← citeshttps://doi.org/10.1007/s00454-004-1116-4openalex-snapshot
New Constructions of Weak ?-Nets
inferred← citeshttps://doi.org/10.1007/s00454-004-1123-5openalex-snapshot
Cutting Triangular Cycles of Lines in Space
inferred← citeshttps://doi.org/10.1007/s00454-004-2864-xopenalex-snapshot
Computing the Writhing Number of a Polygonal Knot
inferred← citeshttps://doi.org/10.1007/s00454-012-9443-3openalex-snapshot
Simple Proofs of Classical Theorems in Discrete Geometry via the Guth–Katz Polynomial Partitioning Technique
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Dynamic Geometric Data Structures via Shallow Cuttings
inferred← citeshttps://doi.org/10.1007/s00454-023-00621-xopenalex-snapshot
Dynamic Connectivity in Disk Graphs
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Computing Minimum-Volume Enclosing Axis-Aligned Ellipsoids
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Computing depth orders for fat objects and related problems
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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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Derandomization in Computational Geometry
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Ray shooting and stone throwing with near-linear storage
inferred← citeshttps://doi.org/10.1016/j.comgeo.2005.02.003openalex-snapshot
Counting and representing intersections among triangles in three dimensions
inferred← citeshttps://doi.org/10.1016/j.comgeo.2005.03.002openalex-snapshot
Extremal point queries with lines and line segments and related problems
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How to get close to the median shape
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Ray shooting and intersection searching amidst fat convex polyhedra in 3-space
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Separating bichromatic point sets by L-shapes
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On reverse shortest paths in geometric proximity graphs
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Crossing patterns of semi-algebraic sets
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On the Zarankiewicz problem for intersection hypergraphs
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Combinatorial characterizations and algorithms for trajectory planning of an articulated robotic probe in three dimensions
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Efficient randomized algorithms for robust estimation of circular arcs and aligned ellipses☆☆A preliminary version of this report was presented at the Fifth Canadian Conference on Computational Geometry [32].
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Reporting intersecting pairs of convex polytopes in two and three dimensions
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Geometric Approximation via Coresets
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State of the union (of geometric objects)
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The lazy sweep ray casting algorithm for rendering irregular grids
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Dynamic Connectivity: Connecting to Networks and Geometry
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On Range Searching with Semialgebraic Sets II
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Polynomial Data Structure Lower Bounds in the Group Model
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Partial closure grasps: Metrics and computation
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Improved algorithms in geometric optimization via expanders
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Output-Sensitive Computation of All Form-Closure Grasps of a Semi-Algebraic Set
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An improved algorithm for quantifier elimination over real closed fields
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Almost tight upper bounds for vertical decompositions in four dimensions
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Approximate shape fitting via linearization
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Fast rendering of irregular grids
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An exact interactive time visibility ordering algorithm for polyhedral cell complexes
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Output-Sensitive Computation of Force-Closure Grasps of a Semi-Algebraic Object
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Principal Curves for Lumen Center Extraction and Flow Channel Width Estimation in 3-D Arterial Networks: Theory, Algorithm, and Validation
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Vertical Ray Shooting and Computing Depth Orders for Fat Objects
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More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
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Dynamic Connectivity: Connecting to Networks and Geometry
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Semialgebraic Range Reporting and Emptiness Searching with Applications
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On Separating Points by Lines
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Nearly Optimal Planar k Nearest Neighbors Queries under General Distance Functions
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Embeddings of Surfaces, Curves, and Moving Points in Euclidean Space
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On Range Searching with Semialgebraic Sets. II
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Constructive Polynomial Partitioning for Algebraic Curves in $\mathbb{R}^3$ with Applications
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Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications
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Polynomial Data Structure Lower Bounds in the Group Model
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Nearly Optimal Planar $k$ Nearest Neighbors Queries under General Distance Functions
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On Ray Shooting for Triangles in 3-Space and Related Problems
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Semi-Online Maintenance of Geometric Optima and Measures
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Shape Fitting with Outliers
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Pseudo-Line Arrangements: Duality, Algorithms, and Applications
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Output-Sensitive Construction of the Union of Triangles
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Ray Shooting Amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions
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Ray Shooting Amidst Spheres in Three Dimensions and Related Problems
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Computing Envelopes in Four Dimensions with Applications
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An Expander-Based Approach to Geometric Optimization
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Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
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Approximation Algorithms for Curvature-Constrained Shortest Paths
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ON ENUMERATING AND SELECTING DISTANCES
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Approximating extent measures of points
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Almost tight upper bounds for vertical decompositions in four dimensions
inferred← citeshttps://doi.org/10.1145/1064092.1064137openalex-snapshot
Vertical ray shooting for fat objects
inferred← citeshttps://doi.org/10.1145/1137856.1137872openalex-snapshot
Ray shooting and intersection searching amidst fat convex polyhedra in 3-space
inferred← citeshttps://doi.org/10.1145/1137856.1137915openalex-snapshot
How to get close to the median shape
inferred← citeshttps://doi.org/10.1145/1247069.1247135openalex-snapshot
Embeddings of surfaces, curves, and moving points in euclidean space
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More algorithms for all-pairs shortest paths in weighted graphs
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Vertical decompositions for triangles in 3-space
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Computing envelopes in four dimensions with applications
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Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications
inferred← citeshttps://doi.org/10.1145/2344422.2344433openalex-snapshot
Range searching on uncertain data
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Splitting a complex of convex polytopes in any dimension
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Average-case ray shooting and minimum weight triangulations
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Snap rounding line segments efficiently in two and three dimensions
inferred← citeshttps://doi.org/10.1145/262839.262986openalex-snapshot
Realistic input models for geometric algorithms
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Are lower bounds easier over the reals?
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Raising roofs, crashing cycles, and playing pool
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On enumerating and selecting distances
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An exact interactive time visibility ordering algorithm for polyhedral cell complexes
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Efficient algorithms for geometric optimization
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Approximation and exact algorithms for minimum-width annuli and shells
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New results on quantifier elimination over real closed fields and applications to constraint databases
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Deterministic algorithms for 3-D diameter and some 2-D lower envelopes
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Fine-grained Complexity Analysis of Two Classic TSP Variants
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Maintaining the Union of Unit Discs under Insertions with Near-Optimal Overhead
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An Improved Bound for Weak Epsilon-nets in the Plane
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Lower Bounds for Semialgebraic Range Searching and Stabbing Problems
inferred← citeshttps://doi.org/10.1145/3721290openalex-snapshot
Intersection Queries for Flat Semi-Algebraic Objects in Three Dimensions and Related Problems
inferred← citeshttps://doi.org/10.1145/3802821openalex-snapshot
Towards Space Efficient Two-Point Shortest Path Queries in a Polygonal Domain
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Lenses in arrangements of pseudo-circles and their applications
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New constructions of weak epsilon-nets
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Cutting triangular cycles of lines in space
inferred← citeshttps://doi.org/10.1145/972639.972641openalex-snapshot
Lenses in arrangements of pseudo-circles and their applications
inferred← citeshttps://doi.org/10.1145/997817.997851openalex-snapshot
Counting and representing intersections among triangles in three dimensions
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Practical methods for shape fitting and kinetic data structures using core sets
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Dynamic Connectivity in Disk Graphs
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Lower Bounds for Semialgebraic Range Searching and Stabbing Problems
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Dynamic Connectivity: Connecting to Networks and Geometry
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Quantum algorithms for shortest paths problems in structured instances
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Truly Subcubic Min-Plus Product for Less Structured Matrices, with Applications
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Recent Developments on Intersection Searching
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Ray shooting amid balls, farthest point from a line, and range emptiness searching
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Randomized incremental constructions of three-dimensional convex hulls and planar voronoi diagrams, and approximate range counting
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Fast rendering of irregular grids
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Approximation algorithms for curvature-constrained shortest paths
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Exact and approximation algorithms for minimum-width cylindrical shells
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Maintaining approximate extent measures of moving points
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Output-sensitive construction of the union of triangles
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