I have a 2D-delaunay-triangulation where each vertex is labeled with an elevation. I now want to remove vertices from the triangulation without making big changes to the form (analogous to douglas-peucker for polylines).
There are a lot of mesh-coarsening algorithms for 3D-meshes. But isn't there something simpler for my task?
Do not remove points from your existing model. Instead construct a second one. Start with a few convex hull points and then refine the new model in a divide and conquer style until comparison with the original model yields that the specified error bound is kept. I have implemented it like that in the Fade library and it works well. You can try my 2.5D Douglas-Peucker implementation if you want, the student license is free.
But best possible output quality requires also that feature lines are detected, simplified and conserved. This is more involved, I work on that topic and hope that I can provide results soon.