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Locally Refinable B-splines and Linear Independence

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 dimension 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. Specifically we will for the 2-variate case address how this applies to the insertion of a new line segment, to the extension of an existing line segment and to the merging of two separate lines segments.

Category

Academic lecture

Language

English

Author(s)

Affiliation

  • SINTEF Digital / Mathematics and Cybernetics

Presented at

Eighth International Conference on Mathematical Methods for Curves and Surfaces

Place

Oslo

Date

28.06.2012 - 03.07.2012

Organizer

Univsersitet i Oslo

Year

2012

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