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On the general motion-planning problem with two degrees of freedom
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/cpa.3160360305openalex-snapshot
On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers
inferredcites →https://doi.org/10.1002/cpa.3160370406openalex-snapshot
On the Piano Movers' problem: IV. Various decomposable two‐dimensional motion‐planning problems
inferredcites →https://doi.org/10.1002/cpa.3160370605openalex-snapshot
On the piano movers' problem: V. The case of a rod moving in three‐dimensional space amidst polyhedral obstacles
inferredcites →https://doi.org/10.1002/cpa.3160390402openalex-snapshot
Generalized voronoi diagrams for moving a ladder. I: Topological analysis
inferredcites →https://doi.org/10.1007/3-540-19488-6_118openalex-snapshot
Arrangements of curves in the plane — topology, combinatorics, and algorithms
inferredcites →https://doi.org/10.1007/bf01840348openalex-snapshot
Generalized Voronoi diagrams for a ladder: II. Efficient construction of the diagram
inferredcites →https://doi.org/10.1007/bf01840360openalex-snapshot
Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons
inferredcites →https://doi.org/10.1007/bf01840368openalex-snapshot
A new efficient motion-planning algorithm for a rod in two-dimensional polygonal space
inferredcites →https://doi.org/10.1007/bf02122559openalex-snapshot
Improved lower bounds on the length of Davenport-Schinzel sequences
inferredcites →https://doi.org/10.1007/bf02187683openalex-snapshot
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
inferredcites →https://doi.org/10.1007/bf02187732openalex-snapshot
The upper envelope of piecewise linear functions and the boundary of a region enclosed by convex plates: Combinatorial analysis
inferredcites →https://doi.org/10.1007/bf02187742openalex-snapshot
Implicitly representing arrangements of lines or segments
inferredcites →https://doi.org/10.1007/bf02187779openalex-snapshot
An efficient motion-planning algorithm for a convex polygonal object in two-dimensional polygonal space
inferredcites →https://doi.org/10.1007/bf02187783openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and spheres
inferredcites →https://doi.org/10.1007/bf02187867openalex-snapshot
Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams
inferredcites →https://doi.org/10.1007/bf02187894openalex-snapshot
Planar realizations of nonlinear davenport-schinzel sequences by segments
inferredcites →https://doi.org/10.1007/bf02187902openalex-snapshot
Separating two simple polygons by a sequence of translations
inferredcites →https://doi.org/10.1007/bf02579170openalex-snapshot
Nonlinearity of davenport—Schinzel sequences and of generalized path compression schemes
inferredcites →https://doi.org/10.1007/bf02579209openalex-snapshot
Almost linear upper bounds on the length of general davenport—schinzel sequences
inferredcites →https://doi.org/10.1016/0097-3165(89)90032-0openalex-snapshot
Sharp upper and lower bounds on the length of general Davenport-Schinzel sequences
inferredcites →https://doi.org/10.1016/0196-6774(85)90021-5openalex-snapshot
A “retraction” method for planning the motion of a disc
inferredcites →https://doi.org/10.1016/0196-6774(87)90038-1openalex-snapshot
An efficient and simple motion planning algorithm for a ladder amidst polygonal barriers
inferredcites →https://doi.org/10.1016/0196-6774(88)90012-0openalex-snapshot
Solving the two-dimensional findpath problem using a line-triangle representation of the robot
inferredcites →https://doi.org/10.1016/0196-8858(83)90014-3openalex-snapshot
On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds
inferredcites →https://doi.org/10.1016/s0747-7171(08)80070-3openalex-snapshot
On the two-dimensional davenport-schinzel problem
inferredcites →https://doi.org/10.1109/robot.1986.1087555openalex-snapshot
Coordinated motion of two robot arms
inferredcites →https://doi.org/10.1109/sfcs.1988.21973openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and surfaces
inferredcites →https://doi.org/10.1109/sfcs.1988.21974openalex-snapshot
A fast planar partition algorithm. I
inferredcites →https://doi.org/10.1109/sfcs.1988.21975openalex-snapshot
An optimal algorithm for intersecting line segments in the plane
inferredcites →https://doi.org/10.1109/tc.1979.1675432openalex-snapshot
Algorithms for Reporting and Counting Geometric Intersections
inferredcites →https://doi.org/10.1145/12130.12142openalex-snapshot
Making data structures persistent
inferredcites →https://doi.org/10.1145/12130.12171openalex-snapshot
Topologically sweeping an arrangement
inferredcites →https://doi.org/10.1145/323233.323244openalex-snapshot
An efficient algorithm for planning collision-free translational motion of a convex polygonal object in 2-dimensional space amidst polygonal obstacles
inferredcites →https://doi.org/10.1145/323233.323252openalex-snapshot
Visibility and intersectin problems in plane geometry
inferredcites →https://doi.org/10.1145/359156.359164openalex-snapshot
An algorithm for planning collision-free paths among polyhedral obstacles
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1145/73393.73399openalex-snapshot
The complexity of many faces in arrangements of lines of segments
inferredcites →https://doi.org/10.1145/73393.73401openalex-snapshot
Red-Blue intersection detection algorithms, with applications to motion planning and collision detection
inferredcites →https://doi.org/10.1145/73393.73420openalex-snapshot
On arrangements of Jordan arcs with three intersections per pair
inferredcites →https://doi.org/10.1145/73393.73426openalex-snapshot
Coordinated motion planning for two independent robots
inferredcites →https://doi.org/10.1145/73393.73432openalex-snapshot
Triangles in space or building (and analyzing) castles in the Air
inferredcites →https://doi.org/10.1145/73833.73837openalex-snapshot
A fast planar partition algorithm, II
inferredcites →https://doi.org/10.1177/027836498300200304openalex-snapshot
On the Piano Movers' Problem: III. Coordinating the Motion of Several Independent Bodies: The Special Case of Circular Bodies Moving Amidst Polygonal Barriers
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/3-540-19487-8_7openalex-snapshot
Intersecting line segments, ray shooting, and other applications of geometric partitioning techniques
inferred← citeshttps://doi.org/10.1007/3-540-19488-6_118openalex-snapshot
Arrangements of curves in the plane — topology, combinatorics, and algorithms
inferred← citeshttps://doi.org/10.1007/3-540-45294-x_16openalex-snapshot
Optimal, Output-Sensitive Algorithms for Constructing Upper Envelope of Line Segments in Parallel
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Recent Developments in the Theory of Arrangements of Surfaces
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An optimal algorithm for the boundary of a cell in a union of rays
inferred← citeshttps://doi.org/10.1007/3-540-56287-7_96openalex-snapshot
Implicit point location in arrangements of line segments, with an application to motion planning
inferred← citeshttps://doi.org/10.1007/3-540-57155-8_281openalex-snapshot
Combinatorial complexity of signed discs
inferred← citeshttps://doi.org/10.1007/3-540-60220-8_55openalex-snapshot
Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications
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Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles
inferred← citeshttps://doi.org/10.1007/978-1-4471-4282-9openalex-snapshot
From Linear Operators to Computational Biology
inferred← citeshttps://doi.org/10.1007/978-1-4471-4282-9_6openalex-snapshot
Jack Schwartz and Robotics: The Roaring Eighties
inferred← citeshttps://doi.org/10.1007/978-3-319-62127-2_40openalex-snapshot
Searching Edges in the Overlap of Two Plane Graphs
inferred← citeshttps://doi.org/10.1007/978-3-540-45058-0_15openalex-snapshot
Hybrid Motion Planning: Coordinating Two Discs Moving among Polygonal Obstacles in the Plane
inferred← citeshttps://doi.org/10.1007/978-3-642-23719-5_42openalex-snapshot
Motion Planning via Manifold Samples
inferred← citeshttps://doi.org/10.1007/978-3-642-55566-4_1openalex-snapshot
On the Complexity of Many Faces in Arrangements of Pseudo-Segments and Circles
inferred← citeshttps://doi.org/10.1007/978-3-642-58043-7_2openalex-snapshot
Combinatorics and Algorithms of Arrangements
inferred← citeshttps://doi.org/10.1007/978-3-642-83539-1_9openalex-snapshot
Davenport-Schinzel Sequences and their Geometric Applications
inferred← citeshttps://doi.org/10.1007/bf01258293openalex-snapshot
Robot motion planning and the single cell problem in arrangements
inferred← citeshttps://doi.org/10.1007/bf01285815openalex-snapshot
The number of edges of many faces in a line segment arrangement
inferred← citeshttps://doi.org/10.1007/bf01530888openalex-snapshot
A new algorithm for shortest paths among obstacles in the plane
inferred← citeshttps://doi.org/10.1007/bf01530889openalex-snapshot
Coordinated motion planning for two independent robots
inferred← citeshttps://doi.org/10.1007/bf01758853openalex-snapshot
Approximate motion planning and the complexity of the boundary of the union of simple geometric figures
inferred← citeshttps://doi.org/10.1007/bf01840405openalex-snapshot
An optimal algorithm for the boundary of a cell in a union of rays
inferred← citeshttps://doi.org/10.1007/bf01931656openalex-snapshot
Storing line segments in partition trees
inferred← citeshttps://doi.org/10.1007/bf02187733openalex-snapshot
The upper envelope of piecewise linear functions: Algorithms and applications
inferred← citeshttps://doi.org/10.1007/bf02187784openalex-snapshot
The complexity and construction of many faces in arrangements of lines and of segments
inferred← citeshttps://doi.org/10.1007/bf02570705openalex-snapshot
On lazy randomized incremental construction
inferred← citeshttps://doi.org/10.1007/bf02570714openalex-snapshot
Almost tight upper bounds for the single cell and zone problems in three dimensions
inferred← citeshttps://doi.org/10.1007/bf02573992openalex-snapshot
On the complexity of a single cell in certain arrangements of surfaces related to motion planning
inferred← citeshttps://doi.org/10.1007/s00453-003-1042-5openalex-snapshot
Comparison of Distance Measures for Planar Curves
inferred← citeshttps://doi.org/10.1007/s00454-006-1272-9openalex-snapshot
A Single Cell in an Arrangement of Convex Polyhedra in ${\Bbb R}^3$
inferred← citeshttps://doi.org/10.1007/s00454-007-9019-9openalex-snapshot
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
inferred← citeshttps://doi.org/10.1007/s00454-009-9178-yopenalex-snapshot
Constrained Minkowski Sums: A Geometric Framework for Solving Interval Problems in Computational Biology Efficiently
inferred← citeshttps://doi.org/10.1016/0020-0190(89)90042-2openalex-snapshot
A note on the papadimitriou-silverberg algorithm for planning optimal piecewise-linear motion of a ladder
inferred← citeshttps://doi.org/10.1016/0020-0190(96)00065-8openalex-snapshot
Excess in arrangements of segments
inferred← citeshttps://doi.org/10.1016/0097-3165(89)90032-0openalex-snapshot
Sharp upper and lower bounds on the length of general Davenport-Schinzel sequences
inferred← citeshttps://doi.org/10.1016/0925-7721(92)90008-gopenalex-snapshot
Improved combinatorial bounds and efficient techniques for certain motion planning problems with three degrees of freedom
inferred← citeshttps://doi.org/10.1016/0925-7721(93)90001-mopenalex-snapshot
A convex polygon among polygonal obstacles: placement and high-clearance motion
inferred← citeshttps://doi.org/10.1016/0925-7721(93)90011-topenalex-snapshot
Tail estimates for the efficiency of randomized incremental algorithms for line segment intersection
inferred← citeshttps://doi.org/10.1016/0925-7721(94)00026-xopenalex-snapshot
Combinatorial complexity of signed discs
inferred← citeshttps://doi.org/10.1016/b978-0-444-88071-0.50013-8openalex-snapshot
Algorithmic Motion Planning in Robotics
inferred← citeshttps://doi.org/10.1016/b978-044482537-7/50002-4openalex-snapshot
Davenport–Schinzel Sequences and Their Geometric Applications**Both authors have been supported by a grant from the U.S.–Israeli Binational Science Foundation. Pankaj Agarwal has also been supported by a National Science Foundation Grant CCR-93–01259, by an Army Research Office MURI grant…
inferred← citeshttps://doi.org/10.1016/b978-044482537-7/50003-6openalex-snapshot
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…
inferred← citeshttps://doi.org/10.1016/j.jpdc.2006.12.006openalex-snapshot
Output-sensitive algorithms for optimally constructing the upper envelope of straight line segments in parallel
inferred← citeshttps://doi.org/10.1016/s0010-4485(97)00030-4openalex-snapshot
Computing planar swept polygons under translation
inferred← citeshttps://doi.org/10.1016/s0020-0190(97)00125-7openalex-snapshot
Computing a single cell in the overlay of two simple polygons
inferred← citeshttps://doi.org/10.1016/s0097-8493(01)00153-4openalex-snapshot
Scalable nonlinear dynamical systems for agent steering and crowd simulation
inferred← citeshttps://doi.org/10.1016/s0747-7171(08)80070-3openalex-snapshot
On the two-dimensional davenport-schinzel problem
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Preprocessing chains for fast dihedral rotations is hard or even impossible
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The common exterior of convex polygons in the plane
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Combinatorial complexity of translating a box in polyhedral 3-space
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Geometric and computational aspects of polymer reconfiguration
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A New Cell-subdivision Approach to Plan Free Translations in Cluttered Environments
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The neural optimal control hierarchy for motor control
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State of the union (of geometric objects)
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Algorithmic motion planning in robotics
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Efficient algorithms for planning purely translational collision-free motion in two and three dimensions
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Scalable dynamical systems for multi-agent steering and simulation
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Fat triangles determine linearly many holes (computational geometry)
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Near-quadratic bounds for the motion planning problem for a polygon in a polygonal environment
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On the combinatorial and topological complexity of a single cell
inferred← citeshttps://doi.org/10.1137/0219020openalex-snapshot
Red-Blue Intersection Detection Algorithms, with Applications to Motion Planning and Collision Detection
inferred← citeshttps://doi.org/10.1137/0221001openalex-snapshot
Efficient Motion Planning for an L -Shaped Object
inferred← citeshttps://doi.org/10.1137/0221035openalex-snapshot
Ray Shooting and Other Applications of Spanning Trees with Low Stabbing Number
inferred← citeshttps://doi.org/10.1137/0222077openalex-snapshot
Computing a Face in an Arrangement of Line Segments and Related Problems
inferred← citeshttps://doi.org/10.1137/s0097539703433900openalex-snapshot
Pseudo-Line Arrangements: Duality, Algorithms, and Applications
inferred← citeshttps://doi.org/10.1137/s009753979018330xopenalex-snapshot
Fat Triangles Determine Linearly Many Holes
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Efficiently Planning Compliant Motion in the Plane
inferred← citeshttps://doi.org/10.1137/s0097539795281840openalex-snapshot
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
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GUARDING A POLYGON FROM TWO NEARLY-OPPOSITE DIRECTIONS
inferred← citeshttps://doi.org/10.1142/s0218195917500017openalex-snapshot
Minimum Cell Connection in Line Segment Arrangements
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Polyhedral Assembly Partitioning Using Maximally Covered Cells in Arrangements of Convex Polytopes
inferred← citeshttps://doi.org/10.1145/1064092.1064099openalex-snapshot
Almost tight bound for a single cell in an arrangement of convex polyhedra in R 3
inferred← citeshttps://doi.org/10.1145/109648.109670openalex-snapshot
The upper envelope of Voronoi surfaces and its applications
inferred← citeshttps://doi.org/10.1145/109648.109683openalex-snapshot
On the complexity of a single cell in certain arrangements of surfaces in 3-space (extended abstract)
inferred← citeshttps://doi.org/10.1145/109648.109684openalex-snapshot
Arrangements of segments that share endpoints
inferred← citeshttps://doi.org/10.1145/1247069.1247125openalex-snapshot
A geometric framework for solving subsequence problems in computational biology efficiently
inferred← citeshttps://doi.org/10.1145/142675.142703openalex-snapshot
Incidence and nearest-neighbor problems for lines in 3-space
inferred← citeshttps://doi.org/10.1145/160985.160992openalex-snapshot
Combinatorial complexity of translating a box in polyhedral 3-space
inferred← citeshttps://doi.org/10.1145/160985.161172openalex-snapshot
Compliant motion in a simple polygon
inferred← citeshttps://doi.org/10.1145/177424.177436openalex-snapshot
Almost tight upper bounds for the single cell and zone problems in three dimensions
inferred← citeshttps://doi.org/10.1145/177424.177521openalex-snapshot
Constructing levels in arrangements and higher order Voronoi diagrams
inferred← citeshttps://doi.org/10.1145/195058.195113openalex-snapshot
On lazy randomized incremental construction
inferred← citeshttps://doi.org/10.1145/225058.225285openalex-snapshot
Computing faces in segment and simplex arrangements
inferred← citeshttps://doi.org/10.1145/73393.73399openalex-snapshot
The complexity of many faces in arrangements of lines of segments
inferred← citeshttps://doi.org/10.1145/73393.73401openalex-snapshot
Red-Blue intersection detection algorithms, with applications to motion planning and collision detection
inferred← citeshttps://doi.org/10.1145/73393.73420openalex-snapshot
On arrangements of Jordan arcs with three intersections per pair
inferred← citeshttps://doi.org/10.1145/73393.73426openalex-snapshot
Coordinated motion planning for two independent robots
inferred← citeshttps://doi.org/10.1145/73833.73852openalex-snapshot
Efficient motion planning for an L-shaped object
inferred← citeshttps://doi.org/10.1145/73833.73854openalex-snapshot
Compliant motion in a simple polygon
inferred← citeshttps://doi.org/10.1145/73833.73868openalex-snapshot
Ray shooting and other applications of spanning trees with low stabbing number
inferred← citeshttps://doi.org/10.1177/027836499301200401openalex-snapshot
The Motion of Planar, Compliantly Connected Rigid Bodies in Contact, With Applications to Automatic Fastening
inferred← citeshttps://doi.org/10.21236/ada228278openalex-snapshot
Implementation and Experimentation with Motion Planning Algorithms
inferred← citeshttps://doi.org/10.22028/d291-25744openalex-snapshot
Interaktive Montageplanung mit Kollisionserkennung
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The Active Bijection between Regions and Simplices in Supersolvable Arrangements of Hyperplanes
inferred← citeshttps://doi.org/10.48550/arxiv.1104.4618openalex-snapshot
Minimum cell connection and separation in line segment arrangements
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Complexity of a Single Face in an Arrangement of s-Intersecting Curves
inferred← citeshttps://doi.org/10.48550/arxiv.1301.4352openalex-snapshot
On complexity of envelopes of piecewise linear functions, unions and intersections of polygons
inferred← citeshttps://doi.org/10.48550/arxiv.1701.02229openalex-snapshot
Searching edges in the overlap of two plane graphs
inferred← citeshttps://doi.org/10.48550/arxiv.1709.06601openalex-snapshot
Parameterization of configuration space obstacles in three-dimensional rotational motion planning
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Pianos are not flat: rigid motion planning in three dimensions
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