Article ID Journal Published Year Pages File Type
441479 Computer Aided Geometric Design 2013 9 Pages PDF
Abstract

•The definition of a B-spline is extended to unordered knot sequences. The resulting smooth piecewise polynomial of minimal support is named U-spline.•U-splines can be negative and locally linearly dependent.•Yet, linear combinations of U-splines share many B-spline properties including smoothness, polynomial reproduction, and evaluation by recurrence.

The definition of a B-spline is extended to unordered knot sequences. The added flexibility implies that the resulting piecewise polynomials, named U-splines, can be negative and locally linearly dependent. It is therefore remarkable that linear combinations of U-splines retain many properties of splines in B-spline form including smoothness, polynomial reproduction, and evaluation by recurrence.

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Physical Sciences and Engineering Computer Science Computer Graphics and Computer-Aided Design
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