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Methods for Achieving Fast Query Times in Point Location Data Structures
, 1997
"... Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s) in S intersected by vertical rays emanating out from p. It is well known that linearspace data struc ..."
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Cited by 20 (1 self)
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Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s) in S intersected by vertical rays emanating out from p. It is well known that linearspace data structures can be constructed so as to achieve O(log n) query times. But applications, such as those common in geographic information systems, motivate a reexamination of this problem with the goal of improving query times further while also simplifying the methods needed to achieve such query times. In this paper we perform such a reexamination, focusing on the issues that arise in three different classes of pointlocation query sequences: ffl sequences that are reasonably uniform spatially and temporally (in which case the constant factors in the query times become critical), ffl sequences that are nonuniform spatially or temporally (in which case one desires data structures that adapt to s...
Dynamization of the Trapezoid Method for Planar Point Location in Monotone Subdivisions
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY AND APPLICATIONS
, 1992
"... We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Poi ..."
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Cited by 16 (5 self)
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We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point location queries take O(logn) time, while updates take O(logĀ² n) time (amortized for vertex insertion/deletion and worstcase for the others). The space requirement is O(n log n). This is the first fully dynamic point location data structure for monotone subdivisions that achieves optimal query time.
Calculating the Area of Overlaid Polygons Without Constructing the Overlay
, 1994
"... An algorithm and implementation for calculating the areas of overlaid polygons without calculating the overlay itself, is presented. Overprop is useful when the sole purpose of overlaying two maps is to find some mass property of the resulting polygons, or for an areal interpolation of data f ..."
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Cited by 3 (2 self)
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An algorithm and implementation for calculating the areas of overlaid polygons without calculating the overlay itself, is presented. Overprop is useful when the sole purpose of overlaying two maps is to find some mass property of the resulting polygons, or for an areal interpolation of data from one map to the other. Finding the areas of all the output polygons is both simpler and more robust than finding the polygons themselves. Overprop works from a reduced representation of each map as a set of "halfedges"; with no global topology. It uses the uniform grid to find edge intersections. The method is not statistical, but is exact within the arithmetic precision of the machine. It is well suited to a parallel machine, and could be extended to overlaying more than two maps simultaneously, and to determining other properties of the output polygons, such as perimeter or center of mass. Overprop has been implemented as a C program, and is very fast. The execution time o...
Date _n_Q'd~]t/_l,~_~_\
, 1991
"... We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point ..."
Abstract
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We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point location queries take O(log n) time, while updates take O(log2 n) time. The space requirement is O(nlogn). This is the first fully dynamic point location data structure for monotone subdivisions that achieves optimal query time. 1