I think I mean extrapolate in that there are assumptions made. It might actually be interpolation but I am not sure it is as as accurate as that term (under my understanding of the two) imply.
Here is a set of criteria for the setting up and use of a 3D LUT from the abstract for a paper I wrote a long time ago:
"An interpolation algorithm design is divided into three parts: packing (filling the space of the input variable with sample points), extraction (selecting from the constellation of sample points those appropriate to the interpolation of a specific input point), and calculation (using the extracted values and the input point to determine the interpolated approximation to the output point). Seven principles govern the design of linear interpolation algorithms: 1) Each sample point should be used as a vertex of as many polyhedra as possible; 2) the polyhedra should completely fill the space; 3) polyhedra that share any part of a face must share the entire face; 4) the polyhedra used should have the fewest vertices possible; 5) polyhedra should be small; 6) in the absence of information about curvature anisotropy, polyhedra should be close to regular in shape; and 7) polyhedra should be of similar size."
http://spie.org/Publications/Journal/10.1117/12.208656Going from the sampled CIE colors obtained from a grid in printer colorant space needs to be done to construct the LUT. You always want to sample the extremes in printer colorant space. In a CMY printer, you always want 0/0/0, 0/0/1, 0/1/0, 0/1/1, 1/0/0, 1/0/1, 1/1/0, 1/1/1 (assuming 1 is full scale) in your sample set.
If you meant, as I think you're saying, extrapolation in the metaphorical sense, then I won't argue with you.
Jim