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Expected asymptotically optimal planar point location

J IACONO
2004 International Journal of Production Economics  
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

John Iacono
2004 Computational geometry  
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]

Sepideh Aghamolaei, Mohammad Ghodsi
2020 arXiv   pre-print
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]

Martin Bertram, Hans Hagen
2001 Eurographics  
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]

Martin Bertram, Hans Hagen
2001 EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization  
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]

Peyman Afshani, Timothy M. Chan, Konstantinos Tsakalidis
2014 Lecture Notes in Computer Science  
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]

Peyman Afshani, Pingan Cheng
2020 arXiv   pre-print
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]

Prosenjit Bose, Eric Y. Chen, Meng He, Anil Maheshwari, Pat Morin
2008 arXiv   pre-print
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  
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

ROBERTO TAMASSIA, LUCA VISMARA
2001 International journal of computational geometry and applications  
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

Joon-Kyung Seong, David E Johnson, Elaine Cohen
2006 Proceedings of the 2006 ACM symposium on Solid and physical modeling - SPM '06  
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

Stuart A. Macgillivray, Bradford G. Nickerson
2014 Canadian Conference on Computational Geometry  
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]

Mark de Berg, Herman Haverkort, Shripad Thite, Laura Toma
2007 Lecture Notes in Computer Science  
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

Jaewook Lee, Yong-Joon Kim, Myung-Soo Kim, Gershon Elber
2015 The Visual Computer  
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]

Mark de Berg, Otfried Cheong, Herman Haverkort, Jung Gun Lim, Laura Toma
2007 Lecture Notes in Computer Science  
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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