  Locating apparent horizons is not only important for a complete understanding
of numerically generated spacetimes, but it may also be a crucial component of
the technique for evolving black-hole spacetimes accurately. A scheme proposed
by Libson et al., based on expanding the location of the apparent horizon in
terms of symmetric trace-free tensors, seems very promising for use with
three-dimensional numerical data sets. In this paper, we generalize this scheme
and perform a number of code tests to fully calibrate its behavior in
black-hole spacetimes similar to those we expect to encounter in solving the
binary black-hole coalescence problem. An important aspect of the
generalization is that we can compute the symmetric trace-free tensor expansion
to any order. This enables us to determine how far we must carry the expansion
to achieve results of a desired accuracy. To accomplish this generalization, we
describe a new and very convenient set of recurrence relations which apply to
symmetric trace-free tensors.
