Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E.g., B-splines are smooth curves or surfaces that can be constructed by infinite subdivision of a polyline or polygon mesh of control points. New vertices are computed by linear combinations of the initial control points. We present a new non-linear subdivision scheme for the refinement of triangle meshes that generates smooth surfaces with minimum curvature variations. It is based on a combination of edge splitting operations and interpolation by blending circular arcs. In contrast to most conventional methods, the final mesh density may be locally adapted to the structure of the mesh. As an application we demonstrate how this subdivision scheme can be used to reconstruct missing range data of incompletely digitized 3-D objects.