[okaleniuk]

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.

[rsp1984]

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.

[blt]

Yeah, I was surprised the example input didn't have a sequence of 3 monotonic points to reveal this.