Outside of the context of a convex hull, I don’t know how to make a distinction between interpolation and extrapolation. This is the core of my question.
What precisely is it that you mean when you say that it is interpolating rather than extrapolating? In the only definition that I know, the one based on convex hulls, I believe it would be extrapolating rather than interpolating. But people often say it is interpolating rather than extrapolating, and I don’t know what they mean.
I doubt they're really thinking about it in a mathematical sense when they say that. I'm guessing, for example, that "extrapolate" is meant in the more colloquial sense, which is maybe closer to "deduce" in practice.
What precisely is it that you mean when you say that it is interpolating rather than extrapolating? In the only definition that I know, the one based on convex hulls, I believe it would be extrapolating rather than interpolating. But people often say it is interpolating rather than extrapolating, and I don’t know what they mean.