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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
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