Fourier analysis of 2-point Hermite interpolatory subdivision schemes

Two subdivision schemes with Hermite data on Z are studied. These schemes use 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives. For a large region in the parameters space, the schemes are C1 or C2 convergent or at least are convergent on the space of Schwartz distributions. The Fourier transform of any interpolating function can be computed through products of matrices of order 2 or 3. The Fourier transform is related to a specific system of functional equations whose analytic solution is unique except for a multiplicative constant. The main arguments for these results come from Paley-Wiener-Schwartz theorem on the characterization of the Fourier transforms of distributions with compact support and a theorem of Artzrouni about convergent products of matrices

Robust Multi-Band Detail Encoding for Triangular Meshes of Arbitrary Connectivity

The flexibility coming along with the simplicity of their base primitive and the support by todays graphics hardware, have made triangular meshes more and more popular for representing complex 3D objects. Due to the complexity of realistic datasets, a considerable amount of work has been spent during the last years to provide means for the modification of a given mesh by intuitive metaphors, i.e.~large scale edits under preservation of the detail features. In this paper we demonstrate how a hierarchical structure of a mesh can be derived for arbitrary meshes to enable intuitive modifications without restrictions on the underlying connectivity, known from existing subdivision approaches. We combine mesh reduction algorithms and constrained energy minimization to decompose the given mesh into several frequency bands. Therefore, a new stabilizing technique to encode the geometric difference between the levels will be presented