| T. Lyche and L. L. Schumaker, A multiresolution tensor spline method for fitting functions on the sphere, SIAM J. Sci. Comp., 22:724--747, 2000. |
....processing to CAGD and computer animation. That said, there do not seem to exist many methods based on subdivision and or wavelets, specifically designed to deal with the problem of functions on surfaces. Notable exceptions are the various existing constructions of wavelets on the sphere (see [16,32,33,43,51,67]) and the paper [72] where wavelets are constructed on general surfaces. 3.9. Visualization of Surfaces on Surfaces Although visualization is not addressed in this chapter, it is important to stress that a good visualization of the reconstructed modeled surfaces and functions is essential in ....
T. Lyche and L. L. Schumaker, A multiresolution tensor spline method for fitting functions on the sphere, SIAM J. Sci. Comp., 22:724--747, 2000.
....for i = 1, 2, 2d 1. On this (b a) periodic knot sequence we can define periodic B splines which form a basis for a space of periodic splines. The dimension of this space is n. We refer to [31] for further details. Spline wavelets can be constructed for nested periodic spline spaces, see [24] for the quadratic, trigonometric spline case. In general the matrices P and Q will be as in the non periodic case except that we get a few corner elements due to wraparound of some columns. The standard adaptation of any kind of wavelet approach to an interval, as mentioned already in the ....
Lyche, T. and L. L. Schumaker, A multiresolution tensor spline method for fitting functions on the sphere, preprint, 1998.
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