We want to pre-process a set of $ n$ line segments in $ S$ into a data structure, such that we can answer some queries: Given a query line $ l$ , report how many line segment in $ S$ dose it intersect.
It is required that the query should be done in $ O(\log{n})$ time. The data structure itself should take up to $ O(n^{2})$ storage and be built in $ O(n^{2}\log{n})$ time. It is suggested that it should be done in dual plane.
I understand that the question may require me to look for the number of double wedge that the a query point is in, but I can’t think of any efficient data structure to report such information. Any suggestions?
This question is basically a homework question from the textbook Computational Geometry by de Berg et al (Question 8.15). I would like to apologize that this question may not be exciting to you.
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