Partially Nested Hierarchical Refinement of Bivariate Tensor-Product Splines with Highest Order Smoothness.

The established construction of hierarchical B-splines starts from a given sequence of nested spline spaces. In this paper we generalize this approach to sequences formed by spaces that are only partially nested. This enables us to choose from a greater variety of refinement options while constructing the underlying grid. We identify assumptions that allow to define a hierarchical spline basis, to establish a truncation mechanism, and to derive a completeness result. Finally, we present an application to surface approximation that demonstrates the potential of the proposed generalization.