On Higher Order Voronoi Diagrams of Line Segments

@inproceedings{Papadopoulou2012OnHO,
  title={On Higher Order Voronoi Diagrams of Line Segments},
  author={Evanthia Papadopoulou and Maksym Zavershynskyi},
  booktitle={ISAAC},
  year={2012}
}
We analyze structural properties of the order-k Voronoi diagram of line segments, which surprisingly has not received any attention in the computational geometry literature. We show that order-k Voronoi regions of line segments may be disconnected; in fact a single order-k Voronoi region may consist of Ω(n) disjoint faces. Nevertheless, the structural complexity of the order-k Voronoi diagram of non-intersecting segments remains O(k(n − k)) similarly to points. For intersecting line segments… 
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