Persistence-sensitive simplification of a terrain

We wrote a preliminary implementation using the python language and specialized to the topological simplification of terrains. The terrain is a triangulated 2D grid whose simplices are assigned a height value in [0, 1]. The terrain is made manifold by gluing dummy triangles from the boundary of the terrain to a dummy vertex. The dummy simplices are assigned height greater that one. In practice, this is not ideal, as the many dummy triangles and edges tend to interfere with the pairing of the actual terrain’s simplices; it would be preferable to use a single dummy 2-dimensional face whose boundary spans the whole terrain boundary edges.