Products of B-patches |
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| Authors: | Kyrre Strøm |
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| Affiliation: | (1) Department of Informatics, University of Oslo, Norway;(2) Present address: Center for Industrial Research, Blindern, P.O. Box 124, 0314 Oslo, Norway |
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| 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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| Keywords: | Multivariate polynomials B-patch B-spline product tensor product conversion pyramidal algorithm de Casteljau algorithm blossom polar form |
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