Joint spectral radius and ternary hermite subdivision

In this paper we construct a family of ternary interpolatory Hermite subdivision schemes of order 1 with small support and ${\mathscr{H}}\mathcal {C}^{2}$ H C 2 -smoothness. Indeed, leaving the binary domain, it is possible to derive interpolatory Hermite subdivision schemes with higher regularity than the existing binary examples. The family of schemes we construct is a two-parameter family whose ${\mathscr{H}}\mathcal {C}^{2}$ H C 2 -smoothness is guaranteed whenever the parameters are chosen from a certain polygonal region. The construction of this new family is inspired by the geometric insight into the ternary interpolatory scalar three-point subdivision scheme by Hassan and Dodgson. The smoothness of our new family of Hermite schemes is proven by means of joint spectral radius techniques.

Construction and Application of Nine-Tic B-Spline Tensor Product SS

In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown.