Hermite interpolator may cause ringing

[ChristopherRabotin]

Hi there,

I'm quite likely to use your library on a current project. However, I noticed that your implementation of the Hermite interpolation uses the typical approach found in literature. This approach causes ringing for orbit data, where the interpolation is visibly poor. A good test is to implement this test: https://github.com/nyx-space/anise/blob/master/anise/src/math/interpolation/hermite.rs#L218.

The solution is to use the exact same algorithm as in SPICE. Here is the re-implementation of that algorithm in Rust, as part of ANISE:

oem/oem/interp.py

Line 23 in fd85a67

def hermite(x, y, dy):

. For the details on the tests, you can look at this huge PR, or specifically this commit.

You could also simplify the Lagrange interpolation by using directly the relatively simple SPICE algorithm: https://github.com/nyx-space/anise/blob/master/anise/src/math/interpolation/lagrange.rs#L15 . I would expect this function to be faster than the numpy implementation, but I'm not sure since numpy is pretty well optimized. From my literature review a couple of years ago, I believe that the Lagrange interpolation commonly found matches the SPICE version, so I don't expect there to be any issue in the Lagrange interpolator. My OEMs use Lagrange so this ticket doesn't preclude me from using your library.

Cheers

[ChristopherRabotin]

Here's a write-up of the algorithm if that's of interest: https://nyxspace.com/anise/reference/mathspec/interpolation/hermite/ .

[bradsease]

Thanks for the feedback! I'll try to get this into the next version