andrel wrote:
> 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. 
NB I implicitly assumed that the idea was to use the 3 by 3 surround
of a voxel to compute the interpolation within that voxel.
If you repartition the entire volume in 3 by 3 voxel 'supervoxels'
then you will have voxels that fit together. However, all derivatives
may be discontinuous at the joining surface.

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