Abstract: A piecewise smooth surface, possibly with boundaries, sharp edges, corners, or other features is defined by a set of samples. The basic idea is to model surface patches, curve segments and points explicitly, and then to glue them together based on explicit connectivity information. The geometry is defined as the set of stationary points of a projection operator, which is generalized to allow modeling curves with samples, and extended to account for the connectivity information. Additional tangent constraints can be used to model shapes with continuous tangents across edges and corners.