Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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A planar subdivision is any partition of the plane into (possibly unbounded) polygonal regions. The subdivision search problem is the following: given a subdivision $S$ with $n$ line segments and a query point $p$, determine which region of $S$ contains $p$. We present a practical algorithm for subdivision search that achieves the same (optimal) worst case complexity bounds as the significantly more complex algorithm of Lipton and Tarjan, namely $O(\log n)$ search time with $O(n)$ storage. Our subdivision search structure can be constructed in linear time from the subdivision representation used in many applications.