Quasi-hierarchical Powell--Sabin B-splines

Authors:
Hendrik Speleers;Paul Dierckx;Stefan Vandewalle
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium
Venue:
Computer Aided Geometric Design
Year:
2009

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Abstract

Hierarchical Powell-Sabin splines are C^1-continuous piecewise quadratic polynomials defined on a hierarchical triangulation. The mesh is obtained by partitioning an initial conforming triangulation locally with a triadic split, so that it is no longer conforming. We propose a normalized quasi-hierarchical basis for this spline space. The basis functions have a local support, they form a convex partition of unity, and they admit local subdivision. We show that the basis is strongly stable on uniform hierarchical triangulations. We consider two applications: data fitting and surface modelling.