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

  • Nora Engleitner
  • Bert JüttlerEmail author
  • Urška Zore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10521)


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.


Tensor-product B-splines Hierarchical B-splines Adaptive refinement 



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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Applied GeometryJohannes Kepler UniversityLinzAustria

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