Segment Intersection Searching Problems in General Settings

@article{Koltun2003SegmentIS,
  title={Segment Intersection Searching Problems in General Settings},
  author={Vladlen Koltun},
  journal={Discrete & Computational Geometry},
  year={2003},
  volume={30},
  pages={25-44}
}
We consider segment intersection searching amidst (possibly intersecting) algebraic arcs in the plane. We show how to preprocess n arcs in time O(n) into a data structure of size O(n), for any ε > 0, such that the k arcs intersecting a query segment can be counted in time O(log n) or reported in time O(log n + k). This problem was extensively studied in restricted settings (e.g., amidst segments, circles or circular arcs), but no solution with comparable performance was previously presented for… CONTINUE READING
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