triple_r wrote:
> Also, the small cube is the voxel containing the point to be interpolated,
> the larger cube is the 26 surrounding cubes.

Ok, I didn't get that. Now you mention it is is sort of obvious.
Only, this means that tricubic interpolation is fixed by the
coordinates of the grid points on this center voxel and the
surrounding grid points. You will not be able to get continuity
in any of the edges and faces of the voxels. Take for instance
the upper blue point on the green line. If you approach it from
the underside, from within the grey area, you will find another
point in space after interpolation than if you approach it from
the outside. I am afraid that the only way to get continuity is
to use 64 control points per voxel. That sounds perhaps a bit
worse than it actually is. Most of them depend on other control
points in other voxels. Effectively you have only 8 independent
parameters in this voxel (if you neglect boundaries or assume
a block of voxels that is infinite in all directions).

You may also look into Hermite polynomials as a more compact way
of representing your data.

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