realazthat / exterpolation

Define the word exterpolation.

Exterpolation

I hereby define the term Exterpolation.

Exterpolation: The generalization of "interpolation" and "extrapolation". Exterpolation unifies both meanings - which share identical equations, but over different domains - to also share identical domains. For example, both linear interpolation and extrapolation can use the "lerp" algorithm, but when $0 \le t \le 1$ it is called "interpolation" and otherwise "extrapolation". Exterpolation lets you refer to both at once, for any $t$.

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From: wiki/Extrapolation#Linear

If the two data points nearest the point $x_*$ to be extrapolated are $(x_{k-1},y_{k-1})$ and $(x_k, y_k)$, linear extrapolation gives the function:

$y(x_*) = y_{k-1} + \frac{x_* - x_{k-1}}{x_{k}-x_{k-1}}(y_{k} - y_{k-1}).$

(which is identical to linear interpolation if $x_{k-1} < x_* < x_k$)