3D scalar field intepolation

I have a scalar field for points in 3d (x,y,z), which i would like to map to another set of points in 3d.
the input data looks somethind as follows
where v is the scalar field value for each point coordinate
[x1,y1,z1] [v1]
[x2,y2,z2] [v2]
[x3,y3,z3] [v3]

which should be mapped to

I have looked through the interpolate functions but could not figure out which can be used in this case
can any one please helpe me here

A similar situation is having measurements of a quantity, say temperature = t, at points defined by three spacial dimensions, x,y,z. You want to compute estimates of temperature at other arbitrary points.

That being the case, I think you are right that none of the functions in Numerics.Interpolation are going to help you. However, I think there are some simple methods, e.g. Shepard’s Method, that can be implemented with only a few lines of code. See https://en.wikipedia.org/wiki/Inverse_distance_weighting.