On calculating normalized Powell-Sabin B-splines Original Research Article

An algorithm is presented for calculating a suitable normalized B-spline representation for Powell-Sabin splines in which the basis functions are all positive, have local support and form a partition of unity. Computationally, the problem is reduced to the solution of a number of linear or quadratic programming problems of small size. Geometrically, each of these can be interpreted as a problem of determining a triangle of minimal area, containing a specific subset of Bézier points. We further consider a number of CAGD applications such as the determination of a suitable set of tangent control triangles and the efficient and stable calculation of the Bézier net of the PS-spline surface.