Before revision: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal   n non-crossing segments, e.g. edges from planar subdivisions. It is well known that this point location structure has {\cal O}(n) expected size and {\cal O} (n \ln n) expected construction time.
After revision: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal n \log n) expected time for structures of {\cal O}(n) expected size and {\cal O} (n \ln n) expected construction time.