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Unformatted text preview: Motivation Segment trees Windowing again Windowing queries Computational Geometry Lecture 15: Windowing queries Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Windowing Zoom in; recenter and zoom in; select by outlining Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Windowing Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Windowing Given a set of n axisparallel line segments, preprocess them into a data structure so that the ones that intersect a query rectangle can be reported efficiently Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Windowing Given a set of n arbitrary, noncrossing line segments, preprocess them into a data structure so that the ones that intersect a query rectangle can be reported efficiently Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Windowing Two cases of intersection: An endpoint lies inside the query window; solve with range trees The segment intersects a side of the query window; solve how? Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Using a bounding box? If the query window intersects the line segment, then it also intersects the bounding box of the line segment (whose sides are axisparallel segments) So we could search in the 4 n bounding box sides Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Using a bounding box? But: if the query window intersects bounding box sides does not imply that it intersects the corresponding segments Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Windowing Current problem of our interest: Given a set of arbitrarily oriented, noncrossing line segments, preprocess them into a data structure so that the ones intersecting a vertical (horizontal) query segment can be reported efficiently Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Windowing queries Using an interval tree? q q Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Definition Querying Storage Interval querying Given a set I of n intervals on the real line, preprocess them into a data structure so that the ones containing a query point (value) can be reported efficiently We have the interval tree, but we will develop an alternative solution Computational Geometry Lecture 15: Windowing queries Motivation Segment trees Windowing again Definition Querying Storage Interval querying Given a set S = { s 1 , s 2 , . . . , s n } of n segments on the real line, preprocess them into a data structure so that the ones containing a query point (value) can be reported efficiently...
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This note was uploaded on 05/27/2011 for the course CIS 4930 taught by Professor Staff during the Fall '08 term at University of Florida.
 Fall '08
 Staff

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