Abstract
Products and tensor products of multivariate polynomials in B-patch form are viewed as linear combinations of higher degree B-patches. Univariate B-spline segments and certain regions of simplex splines are examples of B-patches. A recursive scheme for transforming tensor product B-patch representations into B-patch representations of more variables is presented. The scheme can also be applied for transforming ann-fold product of B-patch expansions into a B-patch expansion of higher degree. Degree raising formulas are obtained as special cases. The scheme calculates the blossom of the (tensor) product surface and generalizes the pyramidal recursive scheme for B-patches.
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Communicated by C. Brezinski
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Strøm, K. Products of B-patches. Numer Algor 4, 323–337 (1993). https://doi.org/10.1007/BF02145751
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DOI: https://doi.org/10.1007/BF02145751
Keywords
- Multivariate polynomials
- B-patch
- B-spline
- product
- tensor product
- conversion
- pyramidal algorithm
- de Casteljau algorithm
- blossom
- polar form