robust surface approximation

[jbrezmorf]

Problems

• automatic choice of the regularization parameter doesn't work well
• approximation too slow especially for large knot vectors, fine B-spline grid
• we have too small test set

TODO:

1. More test cases with sparse data and extrapolation to a grid out of bounding box of the data.
2. Limit size of the approximation to have the time of the approximation proportional to the input data.
3. Compute various hyper parameter functionals (L-curve curvature, Ubiased risk estimate, Discrepancy principle, GCV, GML) as functions of the lambda and refinement level.
4. Use surface curvature tensor as the regularization.
5. Can we get local measure about overfitting as we get local measure of the misfit ?
6. With such measure we can have adaptive regularization functional and iteratively tune refinement and regularization over the patches.
7. Focus on iterative solvers for the larger approximations, extrapolate solution between the refinement steps.

[jbrezmorf]

GMSH seems to allow remeshing a distrete entities (e.g. surface given by a mesh). Thus the spline approximation is obsolete we should rather create a delunay 2D mesh from given points or other way and then apply remeshing.

Has to be tested: see X2 tutorial of GMSH.