SphericalSplines

Spherical spline interpolation. Quick and dirty implementation, could possibly be optimized a little.

Based on:

• Blick, C. & Freeden, W. (2011). Spherical Spline Application to Radio Occultation Data. Journal of Geodetic Science, 1(4), pp. 379-395. Retrieved 20 Nov. 2018, from doi:10.2478/v10156-011-0017-8.

• Blick, C. (2012). Spherical Spline Approximation and its Application to Radio Occultation Data for Climate Monitoring. 2nd International Radio Occultation Workshop 2012.

Usage

Interpolation spline

Given a number of direction vectors, directions, which is an (N,3) array, and a number of real values associated with those directions, values, return an interpolating spline solution (which passes through all the values in the given directions), and compute the value in new_direction:

using SphericalSplines

S = InterpolationSpline(directions, values)

y = S(new_direction)

The rows of directions need to be normalized to be unit vectors.

Smoothing spline

Given the direction vectors (as an (N,3) array) and values (as a (N,) vector) as above, and additionally a (N,) shaped list of weights for each point and a smoothing coefficient, return a smoothing spline solution and compute its value in new_direction:

using SphericalSplines

S = SmoothingSpline(directions, values, weights, smoothing_coef)

y = S(new_direction)

Caveats

1. This is not (yet) well tested.
2. This is not (yet) optimized for performance.