Quadratic spline wavelets with arbitrary simple knots on the sphere

In this paper, we extend the method for fitting functions on the sphere, described in Lyche and Schumaker (SIAM J. Sci. Comput. 22 (2) (2000) 724) to the case of nonuniform knots. We present a multiresolution method leading to C 1 -functions on the sphere, which is based on tensor products of quadra...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2004, Vol.162 (1), p.273-286
Main Authors: Ameur, El Bachir, Sbibih, Driss
Format: Article
Language:English
Subjects:
Approximations and expansions
Compression of data
Exact sciences and technology
Fourier analysis
Mathematical analysis
Mathematics
Multiresolution
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Spline wavelets
Tensor products
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Summary:In this paper, we extend the method for fitting functions on the sphere, described in Lyche and Schumaker (SIAM J. Sci. Comput. 22 (2) (2000) 724) to the case of nonuniform knots. We present a multiresolution method leading to C 1 -functions on the sphere, which is based on tensor products of quadratic polynomial splines and trigonometric splines of order three with arbitrary simple knot sequences. We determine the decomposition and reconstruction matrices corresponding to the polynomial and trigonometric spline spaces. We describe the tensor product decomposition and reconstruction algorithms in matrix forms which are convenient for the compression of surfaces. We give the different steps of computer implementation and finally we present a test example by using two knot sequences: a uniform one and a sequence of Chebyshev points.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2003.08.028