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Locally Refined B-splines and Linear Independence

Locally Refined B-splines and Linear Independence

Category
Conference lecture and academic presentation
Abstract
We will address local refinement of a tensor product grid specified as a sequence of inserted line segments parallel to the knot lines. The line segments are assigned multiplicities to model the continuity across each line segments individually. We obtain a quadrilateral grid with T-junctions in the parameter domain, and a collection of tensor product B-splines on this mesh here named an LR-mesh. The approach applies equally well in dimensions higher than two. By refining according to a hand-in-hand principle between the dimensions of the spline space over the LR-mesh, the spline space spanned by the Locally Refined B-splines and the number of locally refined B-splines the LR B-splines are linear independent and form a basis. Alternatively linear independence is not check during refinement, but the "pealing algorithm" is used to check if the resulting collection of LR B-splines is linear independent.
Client
  • EU / EU Contract 284981
Language
English
Author(s)
Affiliation
  • SINTEF Digital / Mathematics and Cybernetics
  • University of Oslo
Presented at
Algebraic Geometry and Geometric Modeling
Place
Banff
Date
27.01.2013 - 30.01.2013
Organizer
Banff International Research Station for Mathematical Innova
Year
2013