https://github.com/realazthat/exterpolation

Define the word exterpolation.
https://github.com/realazthat/exterpolation

exterpolation extrapolation interpolation lerp prediction

Last synced: about 2 months ago
JSON representation

Define the word exterpolation.

• Host: GitHub
• URL: https://github.com/realazthat/exterpolation
• Owner: realazthat
• License: unlicense
• Created: 2024-02-05T16:26:27.000Z (11 months ago)
• Default Branch: main
• Last Pushed: 2024-02-08T14:35:32.000Z (11 months ago)
• Last Synced: 2024-10-25T22:29:43.580Z (3 months ago)
• Topics: exterpolation, extrapolation, interpolation, lerp, prediction
• Homepage:
• Size: 34.2 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

README

        
# Exterpolation

I hereby define the term **_Exterpolation_**.

_Exterpolation_: The generalization of "[interpolation](https://en.wikipedia.org/wiki/Linear_interpolation)" and "[extrapolation](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Linear_interpolation#Programming_language_support)" 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 $t$.

---

From: [wiki/Extrapolation#Linear](https://en.wikipedia.org/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](https://en.wikipedia.org/wiki/Linear_interpolation) if $x_{k-1} < x_* < x_k$)