For ease of explanation, suppose that you began with a two-dimensional surface in (x1, x2, x3, x4)-space, and the surface begins as a flat planar region in the (x1, x2)-plane. The boundaries of this flat region is not that important to resolve, but it would have a closed boundary. Pretend it is a square. So this surface might be specified by a triangular mesh, so a listing of points and their neighbours.
Through some operation, the plane now gets deformed into 4D. So for instance, I might assign +(0, 0, 1, 0) for some points and -(0, 0, 0, 1) for other points. At this point, you have a 2-manifold in 4D.
The problem is that I need to remesh this surface. I'd like to capture things like folds in the surface, and I'd like to remesh so that triangles that get stretched out are subdivided, and to avoid things like skinny triangles.
I understand that there is a lot of info on how this is done for two-dimensional planar surfaces in 2D, like Shewchuk's Triangle program. I've read Persson and Strang's article on simple meshing in 2D, but I don't think this is generalizable to 2-manifolds in 4D.
Ultimately, I'm looking for a more-or-less simple algorithm (or program). The need for accuracy is not terribly high, and the boundary regions of my surface are not important to accurately resolve.
Can anybody suggest literature I can refer to? There is a startlingly large amount of work done on meshing and remeshing, so it's difficult to see what is applicable for my problem.