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