Normal Multi-scale Transforms for Surfaces

We prove well-posedness, convergence, and detail decay estimates for the normal triangular mesh multi-scale transform for C surfaces in the simplest case when the subdivision rule S used for base point prediction is given by edge midpoint insertion. A restrictive assumption is that the initial triangular mesh needs to be quasi-regular and of small enough mesh-size. We also provide numerical evidence with other S for dyadic refinement (Butterfly, Loop), and propose a modification of the normal scheme resulting in improved detail decay for smooth surfaces.