We are often interested in the velocity at any point, and different
interpolation methods can be used for that purpose. The patch
programme in CIVx provides interpolation on a regular grid, using
the thin shell spline (ref...). It does not exactly interpolate, but
it also smooths, depending on a parameter 
. Such smoothing
can improve the end result, by removing some noise, but it must be
manipulated with care to avoid cutting off the smaller scales of motion.
The spatial derivatives are also obtained from the spline results
in this patch programme.