| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 441479 | Computer Aided Geometric Design | 2013 | 9 Pages |
•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.
