Abstract
We consider theorthgonal clipping problem in a set of segments: Given a set ofn segments ind-dimensional space, we preprocess them into a data structure such that given an orthogonal query window, the segments intersecting it can be counted/reported efficiently.
We show that the efficiency of the data structure significantly depends on a geometric discrete parameterK named theProjected-image complexity, which becomes Θ(n 2) in the worst case but practically much smaller. If we useO(m) space, whereK log4d−7 n≥m≥n log4d−7 n, the query time isO((K/m)1/2 logmax{4, 4d−5} n). This is near to an Ω((K/m)1/2) lower bound.
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Tokuyama, T. Orthogonal queries in segments. Algorithmica 18, 229–245 (1997). https://doi.org/10.1007/BF02526035
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DOI: https://doi.org/10.1007/BF02526035