Optimal Point Location in a Monotone Subdivision

@article{Edelsbrunner1986OptimalPL,
  title={Optimal Point Location in a Monotone Subdivision},
  author={Herbert Edelsbrunner and Leonidas J. Guibas and Jorge Stolfi},
  journal={SIAM J. Comput.},
  year={1986},
  volume={15},
  pages={317-340}
}
Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let $\mathcal{S}$ denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of m edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for… 
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