I’m not sure the article fully justifies the thesis. It shows hyperpolation only for a handful of cases where the given function is a slice of a simpler higher-dimensional function. But interpolation isn’t limited to such cases. Interpolation is general: given any set of (x,y) pairs, there are reasonable ways to interpolate between them. Is there a nontrivial way of doing hyperpolation in general?
The article gives a general but boring example: Extrusion. This is analogous to stepwise interpolation (f(x)=f(xi) such that xi≤x<xi+1), which is also boring. Depending on the constraints put on the function different methods result. For example, analytical functions can plausibly extended in the complex plane by choosing the simplest coefficients.
I’m not sure the article fully justifies the thesis. It shows hyperpolation only for a handful of cases where the given function is a slice of a simpler higher-dimensional function. But interpolation isn’t limited to such cases. Interpolation is general: given any set of (x,y) pairs, there are reasonable ways to interpolate between them. Is there a nontrivial way of doing hyperpolation in general?
The article gives a general but boring example: Extrusion. This is analogous to stepwise interpolation (f(x)=f(xi) such that xi≤x<xi+1), which is also boring. Depending on the constraints put on the function different methods result. For example, analytical functions can plausibly extended in the complex plane by choosing the simplest coefficients.