Abstract
Starting from a tensor product B-spline basis collections of LR B-splines and a corresponding LR-mesh are generated in a sequence of successive local refinements. Such refinements must split the support of at least one B-spline. The approach applies equally well in higher dimensions. To check for linear independence the "peeling algorithm" can be used, or alternatively each refinement must be "hand-in-hand" and generating just the number of B-splines necessary to span the spline space.