andrel <a_l### [at] hotmailcom> wrote:
> I am not sure if I understand your question.

     Entirely my fault.  I feel kind of stoopid for asking such a
poorly-phrased question.  Sorry you had to do all that typing.
     I neglected to state that the points fall on a regular cartesian grid
and I'm interpolating inside a voxel.  Regardless of where the points are
defined (center, face, corner) simiple translation can put all points at a
corner, i.e. <0,0,0>, <1,0,0>, <2,0,0>, <3,0,0>, <0,1,0>,etc... (multiplied
by the grid spacing) for sixty-four points.  It forms a local 4x4x4 point
box as pictured, then it's a matter of figuring out the value of some point
inside.  It's for a fluid simulation as outlined in the Visual Simulation
of Smoke paper, so it is important for stability that the values (of
something like temperature or velocity) interpolated at some point in the
domain do not fall outside of the range of the values actually defined in
that domain.  The paper goes into little detail about how they use tricubic
interpolation other than to define a condition for 1-D cubic interpolation
that does not overshoot the data.
     Now enters my question whether this is what they had in mind for an
extension to 3-D.  My guess (pictured above) is that you can reduce a 3-D
problem to 16 1-D problems which form a 2-D problem.  That 2-D problem is 4
1-D problems which reduce the answer to a 1-D problem.  If they just
clipped the data to the range in the volume, they wouldn't have gone to the
trouble of defining the 1-D criteria, but I'm not sure my guess is exactly
what they had in mind either.  It seems rather anisotropic to favor one
direction over the rest.  It's also requires a whole lot of function calls.
 This isn't a problem until you do it thousands of times; then you post a
question to a newsgroup asking if there's a better way.  I hope that better
defines the question, although I have to wonder if anyone is still reading
this way down here...
Thanks,
Ricky

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