CG_WindowingMoreCh10

CG_WindowingMoreCh10 - Motivation Segment trees Windowing...

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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; re-center 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 axis-parallel 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, non-crossing 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 axis-parallel 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, non-crossing 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.

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CG_WindowingMoreCh10 - Motivation Segment trees Windowing...

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