Abstract
In [7], Lyche and Schumaker have described a method for fitting functions of class C 1 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 C 2-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.
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Ameur, E.B., Sbibih, D. & Sablonniere, P. A General Multiresolution Method for Fitting Functions on the Sphere. Numerical Algorithms 34, 159–171 (2003). https://doi.org/10.1023/B:NUMA.0000005360.94439.47
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DOI: https://doi.org/10.1023/B:NUMA.0000005360.94439.47