We preprocess the input subdivision with $n$ points on the plane in $O(n\sqrt{\log n})$ time to facilitate point location in constant time. Previously the preprocessing time is $O(n\log n)$ and point location takes $O(\log n)$ time.

翻译：我们以$O(n\sqrt{\log n})$时间预处理平面上的$n$个点构成的输入剖分，以实现常数时间的点定位。此前，预处理时间为$O(n\log n)$，点定位需要$O(\log n)$时间。