Larry L. Schumaker
(Department of Mathematics,
Center for Constructive Approximation,
Vanderbilt University)
Surface Compression
Using A Multiresolution Spline Method
Abstract
The standard way to create multiresolution methods for surface compression
is to design sequences of nested spline spaces along with corresponding
wavelet spaces. While this is fairly straightforward for tensor-product
splines (where Fourier techniques can be used), this approach is already
very complicated for spaces of C0 linear splines on arbitrary
triangulations. As an alternative to the wavelet approach, we show how
multiresolution methods can be constructed without building wavelets at
all. The approach is based on an old Faber interpolation scheme of 1910.
We illustrate the method using C1 cubic spline spaces
associated with sequences of refined triangulated quadrangulations |
|