Constraining Rbf Interpolation Of 3d Surface To Keep Curvature

I've been tasked to develop an algorithm that, given a set of sparse points representing measurements of an existing surface, would allow us to compute the z coordinate of any poin

Solution 1:

Just wanted to post my solution in case someone has the same problem. The issue was indeed with scipy implementation of the RBF interpolation. I tried instead to adopt a more flexible library, https://rbf.readthedocs.io/en/latest/index.html#. The results are pretty cool! Using the following options

from rbf.interpolate import RBFInterpolant
spline = RBFInterpolant(X_obs, U_obs, phi='phs5', order=1, sigma=0.0, eps=1.)

I was able to get the right shape even at the edge.

Surface interpolation

I've played around with the different phi functions and here is the boxplot of the spread between the interpolated surface and the points that I'm testing the interpolation against (the red points in the picture).

Boxplot

With phs5 I get the best result with an average spread of about 0.5 mm on the upper surface and 0.8 on the lower surface. Before I was getting a similar average but with many outliers > 15 mm. Definitely a success :)