Branching pieces of rational skins from polynomial MOS patches

In this paper we will investigate one certain application of polynomial 2-surfaces possessing the polynomial area element in the Minkowski space $\R^{3,1}$, where they coincide with the so called MOS surfaces (i.e., medial surface transforms with rational domain boundaries). We formulate an efficient algorithm for Hermite interpolation by MOS surfaces and apply the developed method to the construction of branching pieces which occur during the operation of rational skinning. We recall that when branched skins of systems of spheres are constructed then the envelopes of suitable two-parametric systems of spheres must be considered. MOS surfaces are presented as especially suitable candidates for modelling these shapes because they provide not only rational envelopes but also all offsets of these envelopes are rationa