At a glance it seems quite similar to Lloyd Relaxation. All these fancy names for iteratively averaging vertex coordinates. I guess the nuance is going over my head.
I don't think the algorithm as presented adds or removes new neighbors, preserving topology (except it won't prevent self-intersections using only neighbor positions). I imagine this is often used with some type of adaptive meshing algorithm for to make something like the clay editing model shown in the Substance demo.
(author here) That's correct. The algorithm preserves topology because no new vertices or indices are created. It can result in self intersecting meshes, but one way that this can be used is what Substance Modeler does, which is continuously remesh.
Funny you should mention that! The surface of a trampoline can actually be modeled as a 2nd-order wave equation PDE, which uses a Laplacian spatial kernel - for the same reasons this is called Laplacian smoothing!
