1,277 research outputs found
Weak Visibility Queries of Line Segments in Simple Polygons
Given a simple polygon P in the plane, we present new algorithms and data
structures for computing the weak visibility polygon from any query line
segment in P. We build a data structure in O(n) time and O(n) space that can
compute the visibility polygon for any query line segment s in O(k log n) time,
where k is the size of the visibility polygon of s and n is the number of
vertices of P. Alternatively, we build a data structure in O(n^3) time and
O(n^3) space that can compute the visibility polygon for any query line segment
in O(k + log n) time.Comment: 16 pages, 9 figures. A preliminary version of this paper appeared in
ISAAC 2012 and we have improved results in this full versio
Segment Visibility Counting Queries in Polygons
Let be a simple polygon with vertices, and let be a set of
points or line segments inside . We develop data structures that can
efficiently count the number of objects from that are visible to a query
point or a query segment. Our main aim is to obtain fast,
), query times, while using as little space as
possible. In case the query is a single point, a simple
visibility-polygon-based solution achieves query time using
space. In case also contains only points, we present a smaller,
-space, data structure based on a
hierarchical decomposition of the polygon. Building on these results, we tackle
the case where the query is a line segment and contains only points. The
main complication here is that the segment may intersect multiple regions of
the polygon decomposition, and that a point may see multiple such pieces.
Despite these issues, we show how to achieve query time
using only space. Finally, we show that we can
even handle the case where the objects in are segments with the same
bounds.Comment: 27 pages, 13 figure
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