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Expected asymptotically optimal planar point location
2004
International Journal of Production Economics
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Given a fixed distribution of point location queries among the triangles in a triangulation of the plane, a data structure is presented that achieves, within constant multiplicative factors, the entropy ...
The data structure is a simple variation of Kirkpatrick's classic planar point location structure [D.G. Kirkpatrick, SIAM J. ...
In a point location problem, a subdivision of space is provided, and a data structure is constructed such that, for each query point, a pointer to the triangle in the subdivision in which the query point ...
doi:10.1016/s0925-7721(04)00047-1
fatcat:gefgbn33tvaaxldoq3arazq4n4
Expected asymptotically optimal planar point location
2004
Computational geometry
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Given a fixed distribution of point location queries among the triangles in a triangulation of the plane, a data structure is presented that achieves, within constant multiplicative factors, the entropy ...
The data structure is a simple variation of Kirkpatrick's classic planar point location structure [D.G. Kirkpatrick, SIAM J. ...
In a point location problem, a subdivision of space is provided, and a data structure is constructed such that, for each query point, a pointer to the triangle in the subdivision in which the query point ...
doi:10.1016/j.comgeo.2004.03.010
fatcat:vnia3qlevvh6pbplsq63uk3fjm
Point-Location in The Arrangement of Curves
[article]
2020
arXiv
pre-print
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We design a data structure for solving the point location problem queries in O(log C(n)+log S(n)) time using O(T(n)+S(n)log(S(n))) preprocessing time, if a polygonal subdivision of total size S(n), with ...
A data-structure for point-location, preprocesses the curves into a data structure of polynomial size in n, such that the queries can be answered in time polylogarithmic in n. ...
Finding a point in a planar subdivision and returning the face that contain that point is called point location. ...
arXiv:2007.11451v2
fatcat:udqcs4ot7rdovjtf2mxqxnfohm
Subdivision Surfaces for Scattered-data Approximation
[chapter]
2001
Eurographics
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The novelty of our scheme is that it applies subdivision only to the ordinates of control points, whereas the triangulated mesh in the plane is fixed. ...
We propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane. ...
We start with a set of planar points Figure 4 . ...
doi:10.1007/978-3-7091-6215-6_7
fatcat:b5rreyfhjfdjnizamchmtdum2e
Subdivision Surfaces for Scattered-data Approximation
[article]
2001
EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization
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The novelty of our scheme is that it applies subdivision only to the ordinates of control points, whereas the triangulated mesh in the plane is fixed. ...
We propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane. ...
We start with a set of planar points ¢ C¤ v § % 4 ¤ ¤ @ (¦ § © ) with associated function values ¢ Q ¤ and a triangulation d of these points. ...
doi:10.2312/vissym/vissym01/055-064
fatcat:soq2wf2uobbrxixf4itvvg7wau
Deterministic Rectangle Enclosure and Offline Dominance Reporting on the RAM
[chapter]
2014
Lecture Notes in Computer Science
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Many additional ideas are then incorporated, including a linear-time algorithm for merging shallow cuttings and an algorithm for an offline tree point location problem. ...
We revisit a classical problem in computational geometry that has been studied since the 1980s: in the rectangle enclosure problem we want to report all k enclosing pairs of n input rectangles in 2D. ...
We thank Christos Makris from the University of Patras, Greece for preliminary work on this problem. ...
doi:10.1007/978-3-662-43948-7_7
fatcat:t2psiqxxnnblpcw5p5yeyo4mjq
2D Fractional Cascading on Axis-aligned Planar Subdivisions
[article]
2020
arXiv
pre-print
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In 2D fractional cascading, the input includes a planar subdivision for every vertex of G and the query is a point q and a subgraph π and the goal is to locate the cell containing q in all the subdivisions ...
In this paper, we show that it is possible to circumvent the lower bound of Chazelle and Liu for axis-aligned planar subdivisions. ...
Given a planar subdivision S of complexity n, in the planar point location problem, we are asked to preprocess S such that given any query point q in the plane, we can find the face f in S containing q ...
arXiv:2009.05541v2
fatcat:4fzeakxnuzebdmyf3npxg3iwfa
Succinct Geometric Indexes Supporting Point Location Queries
[article]
2008
arXiv
pre-print
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Our first and main result is a succinct geometric index that can answer point location queries, a fundamental problem in computational geometry, on planar triangulations in O(lg n) time. ...
We then generalize our succinct geometric index to planar subdivisions, and design indexes for other types of queries. ...
. ⊓ ⊔
Point Location in Planar Subdivisions We now generalize the techniques in Section 3 to design succinct geometric indexes supporting point location queries in general planar subdivisions. ...
arXiv:0805.4147v1
fatcat:o27rcrfifjej5hs7l56mjkq7je
Page 2368 of Mathematical Reviews Vol. , Issue 81F
[page]
1981
Mathematical Reviews
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P. 81f:68056
A note on locating a set of points in a planar subdivision.
SIAM J. Comput. 8 (1979), no. 4, 542-545. ...
Locating a point p in a subdivision means finding the subdivision region which contains p. ...
A CASE STUDY IN ALGORITHM ENGINEERING FOR GEOMETRIC COMPUTING
2001
International journal of computational geometry and applications
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We present the criteria that have inspired the preliminary design of GeomLib and discuss the guidelines that we h a ve followed in the initial implementation. ...
The goal of this paper is to prove the applicability of some advanced software design concepts to geometric computing through a vertical case study. ...
Acknowledgments We w ould like to thank Franco Preparata and Mike Goodrich for their encouragement and support, Jim Baker for his collaboration in writing a preliminary version of this paper, Natasha Gelfand ...
doi:10.1142/s0218195901000390
fatcat:bpb6wyvko5ey7fayv7xbzkoh2m
A higher dimensional formulation for robust and interactive distance queries
2006
Proceedings of the 2006 ACM symposium on Solid and physical modeling - SPM '06
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In this framework, minimum distance between a point and planar curve is solved using a single polynomial equation in three variables (two variables for a position of the point and one for the curve). ...
Given a particular query point, the solution space's remaining degrees-offreedom are fixed and we can numerically compute the minimum distance in a very efficient way. ...
All opinions, findings, conclusions or recommendations expressed in this document are those of the author and do not necessarily reflect the views of the sponsoring agencies. ...
doi:10.1145/1128888.1128916
dblp:conf/sma/SeongJC06
fatcat:edvkta62hvg77b3xue22ssylse
Window Queries On Planar Subdivisions Arising From Overlapping Polygons
2014
Canadian Conference on Computational Geometry
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A dynamic data structure is presented for storing the partitioning that arises from m polygons with at most k sides each in space O(km 2 ) if the polygons are assumed to be convex, and space O(k 2 m 2 ...
We present efficient algorithms for partitioning 2dimensional space into faces arising from the boundaries of overlapping polygons. ...
The problem reduces to planar point location; a query that intersects no segments can be effectively reduced to a single point, as we need only locate the face that contains some point from the query region ...
dblp:conf/cccg/MacgillivrayN14
fatcat:xtwtpkawh5a6vflkdili43woj4
I/O-Efficient Map Overlay and Point Location in Low-Density Subdivisions
[chapter]
2007
Lecture Notes in Computer Science
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in O(scan (n)) i/o's, where n is the total number of edges in the two subdivisions, (ii) answer a single point location query in O(log B n) i/o's and k batched point location queries in O(scan (n) + sort ...
We present improved and simplified i/o-efficient algorithms for two problems on planar low-density subdivisions, namely map overlay and point location. ...
An optimal static structure for point location in general planar subdivisions was already given by Goodrich et al. [18] for the standard i/o-model and by Bender et al. ...
doi:10.1007/978-3-540-77120-3_44
fatcat:kuwc7ktx3vcnzmoxjtcgxpxniu
Comparison of three bounding regions with cubic convergence to planar freeform curves
2015
The Visual Computer
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In other comparison criteria, the BCA approach is more efficient and stable than the other two methods in producing a hierarchy of bounding regions that approximate a family of freeform planar curves within ...
a given error bound. ...
four junction points (each by adding to the center the result of a scalarvector multiplication). ...
doi:10.1007/s00371-015-1093-z
fatcat:maqssb6iobd2xk4oianck476sq
I/O-Efficient Flow Modeling on Fat Terrains
[chapter]
2007
Lecture Notes in Computer Science
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in O(scan (n)) i/o's, where n is the total number of edges in the two subdivisions, (ii) answer a single point location query in O(log B n) i/o's and k batched point location queries in O(scan (n) + sort ...
We present improved and simplified i/o-efficient algorithms for two problems on planar low-density subdivisions, namely map overlay and point location. ...
An optimal static structure for point location in general planar subdivisions was already given by Goodrich et al. [18] for the standard i/o-model and by Bender et al. ...
doi:10.1007/978-3-540-73951-7_22
fatcat:xpz34t53znaa3g4cy3dzd4447u
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