It is *necessary* to *assume* that the least-time
field is the admissible
viscosity
weak solution of the eikonal equation with
respect to the ``time'' variable implicitly defined by
the schedule of expanding
circular or
rectangular fronts -- and
this assumption might or might not be correct! Apparently
the algorithm always computes some piece of a branch of
the traveltime, but it may well stop before filling the
computational domain. This feature is shared with Vidale's code.
Both codes rely on an a-priori prescription of
a version of ``time'', through the family of computational
fronts along which the solution is marched. If the time field
to be computed does not have
an outward-pointing gradient at each front -- i.e. if the
time gradient becomes parallel to the computational front
(a turned ray) -- then the calculation stops. It is easy to
construct examples that cause any a-priori prescribed family
of computational fronts to fail to have this essential
outflow property. Therefore neither this code nor Vidale's
can be relied upon completely -- both succeed only when the user
has general knowledge of the shape of the time field. This
limitation is *essential* -- it comes from the necessary role
of ``thermodynamical'' considerations in picking out the
``correct'' weak (nonclassical) solution.

1/13/1998