Modeling sphere-like manifolds with spherical Powell–Sabin B-splines

Abstract

We present an algorithm for computing a B-spline representation for Powell–Sabin splines on the sphere. The B-splines form a partition of unity and we define control points that constitute control triangles that give us a good insight in the shape of the spline. We further consider a number of CAGD applications such as approximation and compression of a given sphere-like triangular mesh, and editing global shape and local detail of a spline using spline subdivision.