The paper is concerned with computing the B-spline basis of a multi-degree spline space, namely a space of piecewise functions comprised of polynomial segments of different degrees. To this aim, we provide a general method to work out a matrix representation relating the sought basis with another one easier to compute. This will allow us, for example, to calculate a multi degree B-spline basis starting from local Bernstein bases of different degrees or from the B-spline basis of a spline space where all sections have the same degree. This change of basis can be translated into a conceptually simple and computationally efficient algorithm for the evaluation of multi-degree B-splines.
BECCARI, C.V., CASCIOLA, G. (2021). Matrix representations for multi-degree B-splines. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 381, 1-18 [10.1016/j.cam.2020.113007].
Matrix representations for multi-degree B-splines
BECCARI, CAROLINA VITTORIA
;CASCIOLA, GIULIO
2021
Abstract
The paper is concerned with computing the B-spline basis of a multi-degree spline space, namely a space of piecewise functions comprised of polynomial segments of different degrees. To this aim, we provide a general method to work out a matrix representation relating the sought basis with another one easier to compute. This will allow us, for example, to calculate a multi degree B-spline basis starting from local Bernstein bases of different degrees or from the B-spline basis of a spline space where all sections have the same degree. This change of basis can be translated into a conceptually simple and computationally efficient algorithm for the evaluation of multi-degree B-splines.File | Dimensione | Formato | |
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