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 my question is: is it correct to try to interpolate the contour points (as shown above) using thin-plate splines so as to obtain the corresponding minimal surface? Is it possible to make such an interpolation on a sparse dataset (given by the 3D contour)?