The English word interpolate was first seen between 1605 and 1615, and is based on the past participle of the Latin interpolāre, with the meaning to make new, refurbish, touch up.
The Latin Interpolare itself originated in inter- (between) and polare, which is related to polire, with the meaning to buff or smooth. (Our English verb and noun polish has its origin there, as well.)
Extrapolate is the verb form of the noun Extrapolation, which was created by analogy with Interpolation. The prefix inter (between) was replaced with the prefix extra (outside (of) or without.) The first known use of Extrapolation was in 1874, and it was apparently coined specifically as a methematical term with the meaning "an inserting of intermediate terms in a mathematical series." Its more general use with the sense of "drawing of a conclusion about the future based on present tendencies" came later.
It is perhaps logical then to deduce:
If we can interpolate and extrapolate, these two verbs must describe vectors of an action called polation!
Unfortunately, no lexicographer agrees with that deduction. However, it is heartening to remember that extrapolation itself was coined intentionally to satisfy a need for the term. Nothing thus prevents us from coining the verb to polate and its attendant form polation.
We might define to polate (provisionally and with the understanding that more work is needed) as "to alter interstices."
You might get away with coining to polate in English, if you can formulate a useful and precise definition and convince enough readers that the new verb fulfills a need. We should not misunderestimate the capacity of English to adopt new words. In this enterprise, you can be encouraged by the history of such other recent coinages as audiophile, locavore, and even refudiate, which was named as Oxford Dictionary's "Word of the Year" in 2010.