Abstract
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.
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Acknowledgment
Supported by project NFN S117 “Geometry + Simulation” of the Austrian Science Fund and the EC projects “EXAMPLE”, GA no. 324340 and “MOTOR”, GA no. 678727.
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Engleitner, N., Jüttler, B., Zore, U. (2017). Partially Nested Hierarchical Refinement of Bivariate Tensor-Product Splines with Highest Order Smoothness. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2016. Lecture Notes in Computer Science(), vol 10521. Springer, Cham. https://doi.org/10.1007/978-3-319-67885-6_7
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