Katie Boundary
28th June 2022, 11:49
How polynomial interpolation works in theory:
You have a waveform/signal that passes through an arbitrary number n of sampled values. For any such number, you can create a polynomial function in which X is not raised to any power greater than n-1, that passes through all of those sampled values. This polynomial function should approximate the sampled waveform, at least within the sampled range.
The problem:
Approximating a waveform and intersecting it an arbitrary number of times are EXTREMELY different things... so different, in fact, that a nearest-neighbor algorithm provides a better approximation of the waveform than a polynomial is likely to.
https://i.imgur.com/84DzLwU.png
Multicolored: the sampled signal
Black: the polynomial "approximation"
I can see why this wasn't included in AVIsynth's internal filters.
You have a waveform/signal that passes through an arbitrary number n of sampled values. For any such number, you can create a polynomial function in which X is not raised to any power greater than n-1, that passes through all of those sampled values. This polynomial function should approximate the sampled waveform, at least within the sampled range.
The problem:
Approximating a waveform and intersecting it an arbitrary number of times are EXTREMELY different things... so different, in fact, that a nearest-neighbor algorithm provides a better approximation of the waveform than a polynomial is likely to.
https://i.imgur.com/84DzLwU.png
Multicolored: the sampled signal
Black: the polynomial "approximation"
I can see why this wasn't included in AVIsynth's internal filters.