A General Multiresolution Method for Fitting Functions on the Sphere

In [7], Lyche and Schumaker have described a method for fitting functions of class C1 on the sphere which is based on tensor products of quadratic polynomial splines and trigonometric splines of order three associated with uniform knots. In this paper, we present a multiresolution method leading to...

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Bibliographic Details
Published in:Numerical algorithms 2003-12, Vol.34 (2-4), p.159-171
Main Authors: Ameur, El Bachir, Sbibih, Driss, Sablonniere, Paul
Format: Article
Language:English
Subjects:
Algorithms
Decomposition
Knots
Mathematical analysis
Polynomials
Reconstruction
Sequences
Spline functions
Tensors
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Summary:In [7], Lyche and Schumaker have described a method for fitting functions of class C1 on the sphere which is based on tensor products of quadratic polynomial splines and trigonometric splines of order three associated with uniform knots. In this paper, we present a multiresolution method leading to C2-functions on the sphere, using tensor products of polynomial and trigonometric splines of odd order with arbitrary simple knot sequences. We determine the decomposition and reconstruction matrices corresponding to the polynomial and trigonometric spline spaces. We describe the general tensor product decomposition and reconstruction algorithms in matrix form which are convenient for the compression of surfaces. We give the different steps of the computer implementation of these algorithms and, finally, we present a test example.
ISSN:1017-1398
1572-9265
DOI:10.1023/B:NUMA.0000005360.94439.47