BSplineFunction[...][u] gives the point on a B-spline curve corresponding to parameter u.
BSplineFunction[...][u, v, ...] gives the point on a general B-spline manifold corresponding to the parameters u, v, ....
The embedding dimension for the curve represented by BSplineFunction is given by the length of the lists .
BSplineFunction[array] can handle arrays of any depth, representing manifolds of any dimension.
The dimension of the manifold represented by BSplineFunction[array] is given by TensorRank[array]-1. The lengths of the lists that occur at the lowest level in the array define the embedding dimension.