Subdivision schemes, network flows and linear optimization

Linear and Non-Linear Subdivision Schemes in Geometric Modeling

Subdivision schemes are efficient computational methods for the design, representation and approximation of 2D and 3D curves, and of surfaces of arbitrary topology in 3D. Subdivision schemes generate curves/surfaces from discrete data by repeated refinements. While these methods are simple to implement, their analysis is rather complicated. The first part of the talk presents the “classical” ca...

Smoothness of non-linear and non-separable subdivision schemes

We study in this paper nonlinear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on the contractivity of the associated scheme for the differences. In particular, we show the regularity of the limit function, in L and Sobolev spaces.

Network Flows and Combinatorial Optimization

Linear Subdivision Schemes for the Refinement of Geometric Objects

Subdivision schemes are efficient computational methods for the design, representation and approximation of surfaces of arbitrary topology in R. Subdivision schemes generate curves/surfaces from discrete data by repeated refinements. This paper reviews some of the theory of linear stationary subdivision schemes and their applications in geometric modelling. The first part is concerned with “cla...

Design of Hermite Subdivision Schemes Aided by Spectral Radius Optimization

We present a method for constructing multivariate refinable Hermite interpolants and their associated subdivision algorithms based on a combination of analytical and numerical approaches. Being the limit of a linear iterative procedure, the critical L Sobolev smoothness of a refinable Hermite interpolant is given by the spectral radius of a matrix dependent upon the refinement mask. The design ...