Repeated point in polygon: preprocessing complexity given logarithmic query time?
Your problem is a special case of planar point location. The algorithm/data structure you found by Snarak and Tarjan can answer point location (and thus point in polygon) queries in $O(\log n)$ time using $O(n \log n)$ preprocessing and $O(n)$ space. That is optimal. There are two other data structures that achieve this: a data structure by Kirkpatrick and a randomized incremental approach. The randomized incremental approach can be improved to $O(n \log^* n)$ expected preprocessing time in case of a simple polygon, and is fairly simple besides.