Automatic construction of control triangles for subdivided Powell–Sabin splines Original Research Article

In this paper we present an algorithm for calculating the B-spline representation of a Powell–Sabin spline surface on a refinement of the given triangulation. The resulting subdivision scheme is a 3 scheme; a new vertex is added inside every original triangle. Applying the 3 scheme twice yields a triadic scheme, every original edge is split into three new edges, but special care is needed at the boundaries. The scheme is numerically stable and generally applicable, there are no restrictions on the initial triangulation.