Note: this question was also posted in StackOverflow and math.stackexchange.
I have a set of 3D points defining a 3D contour, as shown below. The points in this contour lie in their best-fit plane and I want to obtain a 3D triangular mesh representation of the surface inside this contour.
Doing some research I found that this is basically a minimal surface problem and its solution is related with the Biharmonic Equation. I also found that the Thin-plate spline is the fundamental solution to this equation.
So I think the approach would be to try to fit this sparse representation of the surface (given by the 3D contour of points) using thin-plate splines. I found this example in scipy.interpolate where scattered data (x,y,z format) is interpolated using thin-plate splines to obtain the ZI coordinates on a uniform grid (XI,YI).
Two questions arise:
Would thin-plate spline interpolation be the correct approach for the problem of computing the surface from the set of 3D contour points?
If so, how to perform thin-plate interpolation on scipy with a non-uniform grid?