Multi-Dimensional Interpolation

[jbpezent]

At present, we support interpolating tabular data defined on 1 and 2 dimensional grids. We should add support for N-dimensional grids.
This should probably be done as two new separate classes for 3-d and N-d grids. I'd imagine that there is a cleaner/more efficient algorithm for the 3d case that would merit a standalone implementation, and that we could get out the door quicker. @jdsikes1 , this aligns with your current work so you get this one.

[jbpezent]

@jdsikes1 , while making some improvements to the 1 and 2D interpolators, I went ahead and implemented the 3D interpolator class in #23. Implementation is based on the paper below.

link

May be of use to you in the N-d case.

[wgledbetter]

I'm planning to add Kriging and Radial Basis Functions from my old dissertation branch sometime in the next month-ish.

[wgledbe]

N-dimensional splines complete in C++.

[wgledbe]

Second derivatives implemented and (mostly) verified for Radial Basis Functions and Kriging.

[jbpezent]

@wgledbe I'll go ahead and 4-d splines to hold us over until N-d are ready.

[wgledbe]

Don't hold your breath.
Kriging and RBF are solid, but the current approach to ND splines may not be scalable.
Spline reference: http://www.cds.caltech.edu/~marsden/bib/2005/08-LeMa2005/LeMa2005.pdf

[jbpezent]

4-D Spline tables implemented and merged. Usage is pretty much the same as the 3-D case.