I have a character made of isolated, flat 2D polys, with no thickness. Previously, I've done tet-based biharmonic capture on 3D meshes which have a defined inside/outside. On flat 2D polys, the biharmonic method has trouble creating a meaningful geo. Is there a simple capture method, where a flat 2D poly is simply captured (as a whole) by the bone closest to it?

Joint capture proximity instead of biharmonic skinning.