*Abstract*
Level set techniques are numerical techniques for tracking the
evolution of interfaces. They rely on two central embeddings;
first the embedding of the interface as the zero level set of a
higher dimensional function, and second, the embedding (or
extension) of the interface's velocity to this
higher dimensional level set function.
This paper applies Sethian's Fast Marching Method, which is a very fast
technique for solving the Eikonal and related equations, to the
problem of building fast and appropriate extension velocities
for the neighboring level sets.
Our choice and construction of extension velocities serves several
purposes. First, it provides a way of building velocities for
neighboring level sets in the cases where the velocity is defined
only on the front itself.
Second, it provides a sub-grid resolution in some cases not present in the
standard level set approach.
Third, it provides a way to update an interface
according to a given velocity
field prescribed on the front in such a way that the signed distance
function is maintained, and the front is never re-initialized; this
is valuable in many complex simulations.
In this paper, we describe the details of such implementations,
together with speed and convergence tests, and applications
to problems in visibility relevant to semi--conductor manufacturing and
thin film physics.

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