volume 30, issue 4, P639-648 2003
DOI: 10.1007/s00454-003-2856-2
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Abstract: Abstract. Given a nonconvex simple polygon P with n vertices, is it possible to construct a data structure which after preprocessing can answer halfspace area queries (i.e., given a line, determine the area of the portion of the polygon above the line) in o(n) time? We answer negatively, proving an (n) lower bound on the query time of any data structure performing this task. We then consider the offline version of the same problem: given a polygon P with n vertices, and k query lines, we present an algorithm …

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