An orthogonal basis for non-uniform algebraic-trigonometric spline space |
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Authors: | WEI Yong-wei WANG Guo-zhao |
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Affiliation: | 1. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China 2. Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
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Abstract: | Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonal. We construct an orthogonal basis for the n-order(n ≥ 3) algebraic-trigonometric spline space in order to resolve the theoretical problem that there is not an explicit orthogonal basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions, which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions. |
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Keywords: | CAGD algebraic-trigonometric spline space NUAT B-spline orthogonal spline |
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