Hierarchical Powell-Sabin splines are C1-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.
Speleers, H., Dierckx, P., Vandewalle, S. (2009). Quasi-hierarchical Powell-Sabin B-splines. COMPUTER AIDED GEOMETRIC DESIGN, 26(2), 174-191 [10.1016/j.cagd.2008.05.001].
Quasi-hierarchical Powell-Sabin B-splines
Speleers H.;
2009-02-01
Abstract
Hierarchical Powell-Sabin splines are C1-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
