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A comment on Interpolation Methods.

Re:Interpolation Methods by okaleniuk on Friday December 15, 2023 @07:26AM (#38653462)
Interestingly, I've never heard about cosine interpolation until now. I wonder why? Could it be that in a practical computation, cosine is in fact a polynomial itself and cosine interpolation is a kind of polynomial interpolation with extra steps? Does this also mean that we can "tame" approximating polynomials of high degree by introducing even more degrees?

Fascinating.

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Re:Interpolation Methods by rsp1984 on Friday December 15, 2023 @08:48AM (#38654136)
It's a trick. His example for cosine interpolation is misleading in the sense that the sequence of points' heights is oscillating.

The cosine interpolation simply ensures that the interpolated-function derivative is 0 at the control points. If anywhere in the sequence there was a point that is lower / higher than both its predecessors the downsides of this technique would become obvious.

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Re:Interpolation Methods by blt on Friday December 15, 2023 @10:30PM (#38661466)
Yeah, I was surprised the example input didn't have a sequence of 3 monotonic points to reveal this.
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