  In this work, we present a collection of new results on two fundamental
problems in geometric data structures: orthogonal point location and rectangle
stabbing.
  -We give the first linear-space data structure that supports 3-d point
location queries on $n$ disjoint axis-aligned boxes with optimal $O\left( \log
n\right)$ query time in the (arithmetic) pointer machine model. This improves
the previous $O\left( \log^{3/2} n \right)$ bound of Rahul [SODA 2015]. We
similarly obtain the first linear-space data structure in the I/O model with
optimal query cost, and also the first linear-space data structure in the word
RAM model with sub-logarithmic query time.
  -We give the first linear-space data structure that supports 3-d $4$-sided
and $5$-sided rectangle stabbing queries in optimal $O(\log_wn+k)$ time in the
word RAM model. We similarly obtain the first optimal data structure for the
closely related problem of 2-d top-$k$ rectangle stabbing in the word RAM
model, and also improved results for 3-d 6-sided rectangle stabbing.
  For point location, our solution is simpler than previous methods, and is
based on an interesting variant of the van Emde Boas recursion, applied in a
round-robin fashion over the dimensions, combined with bit-packing techniques.
For rectangle stabbing, our solution is a variant of Alstrup, Brodal, and
Rauhe's grid-based recursive technique (FOCS 2000), combined with a number of
new ideas.
